at the

American Astronomical Society

Leading Scientific Society Announces Discovery of

World's 1st Dorsally Breasted Woman

Journal for the History of Astronomy Referees Snore Thru Gaffe-Honeypot

Amer Astronomical Soc Convention Struggles with Missing-Ass Problem

The Paper Nobody Read: Amer Astron Soc's FarOut Farnese Farce

Hitman&Run      Scared Hitless      A 7th Magnitude Star-is-Born



Unlike the case of the 2005 Jan 11 AAS-promoted BS-paper under scrutiny below,
the technical parts of what follows here have been and are still being
carefully checked for accuracy by the most skilled experts in the field.
So far, no problems have turned up.

Nonetheless, DIO readers' factual criticisms are encouraged, as ever.
[All comments welcome — phone: 410-889-1414; email:]

Dave Barry, Historians of Ancient Astronomy, & Light Bulbs

A prefatory interlude is inserted here, to create an atmosphere of a sobriety appropriate to entering the realm of recent history-of-ancient-astronomy scholarship. Though knowledgeable astronomers have known for centuries (since Tycho: 1598) that C.Ptolemy stole the Ancient Star Catalog from Hipparchos, a cult of 20th century historians (called the “Muffia” by DR) made it a holy mission to resuscitate Ptolemy's alleged authorship. (And, purely incidentally, convert him into a classic grantmoney-cow.) Then, tragically for our saviour-wannabees, their position received (starting in 1976) one lethal evidential blow after another. But, for decades, none of these effected any lit light-bulbs in believers' skeptic-slandering cementalities. (Though the controversy has now privately ended in the Hipparchans' favor, not one of the losers has shown the decency to publicly acknowledge who won. Including the Amer Astron Soc-Hysterical Astronomy Division's rulership — despite explicit private 2005/4/28 assent.) So, when laying out the devastating spectrum of pro-Hipparchos arguments (DIO 2.3 [1992] ‡8 §C22 [p.110]), plus a history of Muffiosi's vaudevillian back&forth unfalsifiability-gyrations (ibid §C31 [p.113]), and even funnier pretenses to brow-furrowed seriousness & neutrality [about the alleged “enigma” of the Catalog: see N.Swerdlow at ibid n.24], DR brought in the right kind of commentator, introducing him thusly (ibid §C25 [p.111]):

The overwhelming array of evidence against Ptolemy ensures that skepticism on the Catalog will continue, so the loyal Muffia will stand ever vigilant to defend its weirdo hero, and — as part of that effort — Muffiosi will keep right on pretending to impartial scientific curiosity on the Catalog issue. The spectacle of the Ptolemy lobby struggling with the Ancient Star Catalog pseudo-enigma reminds me of another farce, Dave Barry on the tobacco lobby [Orange County Register 1988/6/5 p.G2, sent to DIO by Steve Wooldridge]:

It's time somebody spoke up for the troubled US cigarette industry …. [and] the fine research being done at the famous Tobacco Institute, which is staffed by leading tobacco-industry scientists using sophisticated equipment and wearing state-of-the-art leashes. These scientists have been researching for years, but they are darned if they can find any solid evidence that smoking is bad for you. Although naturally they are continuing to look just as hard as they can:

FIRST SCIENTIST: Well, Ted, for the 13,758th consecutive experiment, all of the cigarette-smoking rats developed cancer! What do you make of it?


FIRST SCIENTIST: It's a puzzle, all right. Hey, look at this: These rats have arranged their food pellets to form the words “CIGARETTES CAUSE CANCER, YOU ZITBRAINS.” What could this possibly mean?

SECOND SCIENTIST: I'm totally stumped, Bob! Back to square one!

THIRD SCIENTIST (entering the room): Hey, can you two guys lend me a hand? I need to screw in a light bulb.


The astronomer “BS” [Bradley Schaefer] has lately unleashed plenty of typically-uncritical “science press” Hipparchos-Hype, by claiming he has discovered the allegedly-Lost star catalog of ancient Greek astronomer Hipparchos, hidden-in-plain-sight in the constellation-figures upon the famous Farnese Atlas celestial globe in Naples, and has mathematically (BS p.194) dated it to 125BC ± 55 years — obviously suggesting Hipparchos, whose famous star catalog is known to have been from the 120s BC.
[The globe is generally believed to be a Roman copy of a Greek original. Only color photos can do full justice to the Farnese Atlas and its celestial globe. Beautiful photos by the able Naples mathematician Vladimiro Valerio (generously sent to DIO's researchers to assist in testing our surprisingly productive investigation into the globe's possible origins) engender affectionate admiration of the artist's genius. If these become available on the internet, a link will be inserted here.]

[Note added 2007/2/23:
DR has now added his own photos to these documents. All color photos of the Farnese globe on this website were taken by DR at the Naples Archaeological Museum 2005/7/27&29.]

  • Below, this “discovery” is revealed to be an epochally magnificent farce, a kind of desecration of that precious and beautiful marble heritage from deep antiquity.
    [See also D.Duke's thorough and (inevitably!) more sedate dismantling of BS' thesis. (Duke's paper was finally allowed to be re-posted in 2006 late Summer).

    [Notice that New York Times's 2005/1/20 email defense is heavily based upon the claim that Schaefer was, after all, the 1st to promote Hipparchos as Farnese-globe source. When DR soon after sent the New York Times the information that this was untrue and that Schaefer had submerged that important fact, the New York Times refused to face such a discomfitting contradiction, diverting instead to complaining that it would not deal with anything throwing doubt upon the veracity of “Dr.Schaefer” — as it invariably referenced bumbling BS. Question: is the New York Times protecting BS? Or its own original credulous 2005 Jan article? Or its own earlier email's false position? Or all of the above? Or did it just lose interest during the confusion (created by BS' failure to admit any among his DOZENS of errors), which leaves the public just as confused.]

    What follows here contains much that desecrates the BS-desecration, hopefully an ultimately consecrational effort — not merely by the math of multiplied-negatives, but through contribution of original findings of value, arising out of DIO's fresh investigation of the Farnese globe.
    [Uninitiated readers should take note of the extremely high quality and internationally recognized expertise of DIO's several boards, in order not be misled by the (quite deservedly) satirical nature of parts of the present posting.]

    The following analyses will demonstrate in detail:
    [A] The Hipparchos star-catalog (formal epoch 128BC Sept 24) wasn't lost in the 1st place (in BS' sense of lost, at any rate), since, e.g., Ptolemy's long-recognized plagiarism of it (tiny-cultishly denied until recently by the BS-JHA-Gingerich-&-clonies mob) has been continuously available since antiquity — and is about 10 times more accurate and 15 times more voluminous (over 1000 stars) than the 70 mostly-way-out-of-place “stars” which BS tries to elicit from the starless pictures upon the marble Farnese globe.
    Moreover, except for Ptolemy's 5' fudge for stars which Hipparchos recorded with celestial longitudes ending in 1 or 3 quarters of a degree, a −2°2/3 longitude-shift (to remove Ptolemy's plagiarist-addition of 2°2/3 of precession) will recover Hipparchos' data with perfectly precise fidelity (i.e., zero rms deviation), which not even BS will claim is possible from a starless picture-book globe.
    [B] The Farnese globe's constellations differ in so many ways from Hipparchos' constellation-descriptions, that BS is dizzyingly far out of line in deeming the globe a near-perfect-match to Hipparchos.
    [C] If mathematical analysis can lead to a verifiable solution for the epoch of the ancient astronomer whose star-mapping inspired the Farnese globe (a point much more debatable in itself than suggested by recent p.r.), the best indications are for roughly 200BC or 200AD.
    [The astronomy of both periods may well have influenced the Farnese globe's sculptor(s).]
    [D] Krates, the ancient best-remembered for a globe (unmentioned by BS), flourished near the former date. (Carrying such admittedly speculative theorizing further: a still-controversial feature of the Farnese globe may hint at a possible circle-remnant in a coordinate-system known to have been of special fascination to Krates.)
    [Dennis Duke has found indications consistent with yet another plausible candidate: Germanicus Caesar.]
    [E] Tracing the globe to Hipparchos isn't a “Discovery”. Even BS (2005 p.170) ambiguously remarks in passing that Georg Thiele did so in 1898, but says that Thiele's analysis was “based on stylistic considerations” — nowhere mentioning that Thiele cites star-positional evidence, and that Thiele's key Hipparchos-argument “stars” are the very ones which BS adduces as his strongest convincers for Hipparchos, e.g., γAri, ηCMa, & τBoo.
    [Thiele's learned if largely non-mathematical discussion (which bears many of the merits & demerits of BS') has been translated into English for the 1st time by DIO's Hugh Thurston and posted by Dennis Duke at]
    [F] Considering the BS paper's number of obvious and elementary (JHA-referee-undetected) problems, the mystery of how an article so frivolously executed has attained such wide uncritical acceptance ought now to be examined as thoroughly as the immortal marble globe that triggered the fuss. But we will here start with a compact summary of said difficulties (featuring a dense set of links for those seeking background details):

  • Brief Compendium of Fallacies in BS' Farnese Analysis:
    After extensive intra-DIO discussions, we can summarize the main historical problems with BS' Farnese paper under several largely independent headings.
    1. Arriving at Hipparchan epoch 125BC essentially by averaging two obviously incompatible samples, which signalled not-especially-Hipparchan epochs: 283BC and 21AD.
    2. Once having concluded for Hipparchos as Farnese-source — not even an original theory (unlike DIO's two proposed possible source-astronomers): failure to carry out careful re-check comparisons of the Farnese globe to Hipparchos' constellation bounds, etc, tests which (we have found) reveal manifold inconsistencies.
    3. Data-unreliability, intrinsic and extrinsic.
    4. Exaggerated precision in epoch-estimation, due to:
    [a] assuming random data-independence;
    [b] falling into the classic delusional trap of supposing that massive data-gathering ensures an accurate solution;
    [c] setting aside a huge non-random 400 year ambiguity.
    5. Forgetting the plenitude of ancient star maps, thereby assuming that eliminating merely 3 candidates (as Farnese-source star-cataloger) is strong evidence that a 4th candidate must be the answer.
    6. Fixating upon artificially unfuzzing a fuzzy solution for epoch, while equally-artificially fuzzing and setting aside a distinctly unfuzzy (and distinctly un-Hipparchan) latitude-clue.

  • The OverConfident Initial Announcement:
    BS' fantasy-discovery of the non-lost catalog has spread abroad by the prime-snookeree New York Times 2005/1/18 (dateline 1/12, including Owen Gingerich's fateful promo-send-off: “quite astonishing”), also L.A.Times 2005/3/30, Discover April, even Physics Today (!) April. And the American Astronomical Society's own current AAS Newsletter (#124 [2005 March] p.18) endorses the “discovery” — with a totality of unqualifiedness that even most newspaper accounts have not quite attained — along with a photo of two showbiz-partners and fellow smear-bunglers: BS standing beside Owen Fair&Balanced Gingerich, longtime fundamentalist regarding ancient astronomy. And the rest of the universe.

  • [Note to readers who prefer drilling right down to bedrock essentials:
    The BS-OG connexion will be reverted-to here and there throughout, since it is the real story behind BS' otherwise-inexplicable Farnese-sensation.
    So it's appropriate to provide an upfront-intro right here to the pol primarily responsible for this and other recent fallacious pop-sci sensations.
    An allegedly pious Mennonite and a paragon of evidence-immunity, Gingerich has been an incorrigible pump-prime denigrator, suppressor, and libeller of DR for decades — as well as the glorifier, ghostwriter, & promoter of any purported scholar willing to lend himself to the same degrading ends. (The AAS through its [hitherto] unsupervised HAD have permitted this boil to fester for years without the slightest action, aside from repeatedly honoring the degraders.) As early as 1968, Gingerich attempted to run now-overwhelmingly-vindicated Robert R. Newton (Supervisor of the Space Sciences Division at Johns Hopkins University APL) out of the field of ancient astronomy (DIO 4.3 [1994] ‡15 §B [pp.121f]) for the sin of doubting the legitimacy of the long-notorious 2nd century AD astrologer-mathematician-plagiarist C.Ptolemy. As ever more scholars — DR among the earliest — realized that Newton was right (by now, Ptolemy's fraudulence is no longer even particularly controversial), OG simply widened his shunnings! — all this in a crusade to defend astronomy's most notorious hoaxer.
    Question: what kind of dedicated kook hound (DIO 11.3 [2002] ‡6 §G10 [p.85]) would spend a half-century intently working his way up into a position of academic-political power — and then squander such precious capital on a quixotic crusade against earnest scholars who happen to oppose academic fraud and intimidation?!
    More important question (which perhaps eliminates the apparent contradiction): what kind of scientific institutions repeatedly go out of their way to unquestioningly exalt such an obsessive Van Helsing?
    By 2000 (in a referee report!), Owen VH Gingerich was typically (DIO 18 [2014] §F3 [p.14]) broad-brush slandering Ptolemy-skeptics (a class including many of the greatest astronomers of the ages) as just a tiny bunch of paranoids! (See DIO 11.3 [2002] ‡6 n.23 [p.75].) These attacks' obvious aim and consistent theme (typical of the religiously censorial mind-behind) has been to discourage anyone from reading heresy at all. The accelerating reality-departure one discerns in Gingerich's latest destructive anti-DIO wish-fantasies, presumably stems from sheer frustration at the success of the DIO enterprise in spite of his worst efforts to kill it off. (In the eyes of relevant specialists, we've been proved right in each of our controversies.)
    [Note added 2011.
    By 2003 — merely 3y after OG's mass-libel mdash; no serious scholar remained who would deny Ptolemy's scholarly deceptions. And so the Ptolemy Controversy just quietly faded away.]

    What does it say of OG's intelligence that it took 1/3 of a century of anticipating that he's just-about-finally-stamped-out that smoldering little Ptolemy-skeptic heresy, for him to begin seeing that principled scholars — truly dedicated to high scholarship, equity, and integrity — are not a trifling brush-fire but an unsubmergeable blaze of decency, and will not be jack-booted into silence by the ultimate Little Big Man, and indeed will oppose dictatorship all the harder when it plays dirty.
    And what does it say of the state of the field, when both of BS' 2002 Feb Sky&Telescope demented national smears of DIO and DR are pathetically easy to trace textually to “Mr. History of Astronomy”, AAS-HAD co-founder, S&T-historical-gooroo, and AAS-awardee Owen Gingerich?]

  • Note: the promotion of BS' 2005 Farnese joke was by the American Astronomical Society's own organ, not that of the AAS' Historical Astronomy Division [HAD], which did not officially include the BS paper in its sessions. (Though, the AAS-p.r. for it was reportedly handled by an individual HAD official — not the Chairman, who [after an initial 2005/4/28 genuine out-loud belly-laugh at our title] resorted to cultishness in this connexion only subsequently [9/16].) The AAS-copy (photo-caption) reads exactly as follows (emph added):

    [BS] identified the lost star catalog of Hipparchus on a statue called the Farnese Atlas (he holds [in the photo] a replica). Expert commentator Owen Gingerich, holding his The Book Nobody Read [DR: an admirably deft title], praised [BS]' work and [justly] was awarded the Education Prize at the AAS banquet.

    JHA Attains Its Apt Perfection:
    The academic paper allegedly justifying this unchecked and “almost insane orgy of hasty approval” (to quote Ann Arbor Prof.W.Hobbs' just comment on fake-explorer Frederick Cook's 1909 laurels: see DR's Peary … Fiction? Wash 1973 p.85) is extensively appearing (2005 May pp.167-196), wrapped up as sober science, in the ideal venue: the all-too-often effectively-unrefereed Journal for the History of Astronomy (JHA), which is (yet again) willingly being made a perfect fool of.

  • After decades of similar pure-formality JHA refereeing-episodes (see, e.g. DIO 1.2 [1991] n.8 [p.97]), no-one can complain that the JHA has not thoroughly earned serial-duncecap notoriety.

  • The paper's author, BS, is possessed of astronomy's most impish giggle. And he has scored big this time. He is presumably kidding at least himself — either about the Hipparchos catalog's perfect-fit recovery or about being an appropriately-expert investigator. [Readers must decide which.] Whether from playful Mencken-esque audacity, establishmentaryan arrogance, refined careerism, or an evidently-well-justified sense of political impunity, his research exhibits a charmingly if carelessly blithe unconcern with factual accuracy and truth (evidently caring more about the sheer number of published papers rather than their validity), both in research [details below] and in cultist-parroting of slanders against pet-hate-objects of emotionally-vulnerable ossified archons — archons who so appreciate the practice that they actually [rote-]DEFEND plagiarism.
    As non-cultist astronomers have known for centuries (since Tycho's 1598/1/2 announcement): virtually the whole “lost” Hipparchos 1025-star catalog has been in-plain-sight right along: merely subtracting 2°2/3 from the longitudes in Ptolemy's catalog undoes Ptolemy's (now almost universally acknowledged) plagiarism of it, and recovers nearly all the 1000-plus Hipparchan star-positions of the great Catalog for which proper credit was killed for the kiloyear 'til Tycho's exposure of Ptolemy's kilotheft. All Hipparchos' stars' longitudes are exactly recovered except for those that had ended in 1/4 or 3/4 of a degree: see DIO 4.1 [1994] ‡3 §C1 [pp.37-38], discussing Ptolemy's deliberate killing of precious data, in an [ultimately] unsuccessful effort to hide a massive scientific crime.

  • But by far the most important implication of what follows here is what it reveals of the astonishingly backward — not to say corrupt — state of refereeing in the allegedly “Reputable” wing of the persistently-SICK history-of-astronomy community: the JHA's BS-paper palpably pulsates with so many elementary, often hilarious — even self-contradictoryscrew-ups and inadequacies, that merely cataloging them below has proved such a dauntingly Augean task that one cannot pretend it has been done here with perfect efficiency.
    So: reader's patience required, occasionally.
    But: reader's funnybone rewarded, unoccasionally.
    Also, at a nobler level of pleasure: a flock of new DIO additions to our serious scholarly knowledge are provided.
    (And more highly expert Farnese-related researches by other scholars [primarily by Dennis Duke (his scholarly analysis is now posted at & V.Valerio] are proceeding simultaneously. A few of these valuable results are incorporated here, invariably identified as non-DR.)

    Though specialists will certainly be intrigued by most of the findings below, one of course understands that not every reader will wish to swim through all details of the huge number of BS-JHA-foulups which are about to be examined & corrected. (This number's enormity is not DR's fault: one doesn't blame the doctor for the illness.) And there will be no interest in institutional pathology in some quarters (esp. institutional hinds), which DR discusses frequently within because it is THE main hopefully-short-term significance of what is otherwise a largely (though not entirely) forgettable paper. [Those who wonder at occasional bluntness within should be apprised: the present DR paper emerges out of a context of submerged decades of certain AAS-affiliated scholars' systematic attempts — by suppression, slander, pseudo-science, and claim-jumping — to stamp out certain mathematically superior but socially-leprous dissenting historians.] So: those who wish to skip past most of the April-Foolesque AAS-self-victimization and ghastly JHA-BS science (and even ghastlier DR “humor”) can right-now click on any of the several highlighted “New Findings” links just below, or — quicker-escape yet — can go right to a very brief concluding section (five-minutes-to-over&out) providing: [a] DR's own famous speculated candidate as Farnese-globe source (not Hipparchos, who is ruled out by numerous and varied hard criteria, including BS' own), and [b] DR's novel proposed solution for the globe's most contended physical feature.

    To whisk there immediately, just click on the following:


  • New Findings Arising from DIO's Farnese-Globe Independent Researches:
    [1] Hitherto-unnoted extra evidence for thinness of ancient atmospheric extinction.
    [2] Simple new possible solution to Hipparchos' long-perplexing mis-location of Athens at 37°N.
    [3] Possible indication from the Farnese globe (gratefully building upon the potentially valuable and original part of BS' work on it) that non-Hipparchan astronomers knew Athens' real 38° latitude.
    [4] Hopefully-future-researcher-enticing examples of the Hipparchos Commentary constellation-bounds' huge disagreements with Ptolemy (and with the Farnese globe).
    [5] Inviting use of such analysis to gather a sample of Ptolemy-listed stars which were surely not in Hipparchos' Commentary, so as to learn if they were H's own post-Commentary addition or not.
    [6] The Hipparchos Hour-Star list's indicated pollution by obsolete hour-stars, suggesting use of right ascension (RA) and integral-hour-star sidereal-time sky-markers by astronomers somewhat earlier than Hipparchos.
    [7] Perhaps much earlier than Hipparchos.
    [8] A more likely (if quite uncertain) potential Farnese-source than Hipparchos, namely the famous early-2nd-century-BC globist Krates of Mallos.
    [9] Original & potentially-revealing (if admittedly speculative) solution to the mysterious and controversial Farnese-globe line-segment in Cygnus' wing, to which V.Valerio has drawn attention.
    [10. Note added 2007/2/24:
    It seems hitherto unrecognized that the Farnese globe's 38°N basis provides not only spatial but temporal information. Professional astronomers at that latitude seem to have become sparse by the time of Hipparchos, so that the FACG latitude alone argues against Hipparchan authorship.]

    DR thanks BS for incidentally helping trigger such inductions, which represent DR's highest enjoyment.
    (Further gratitude: in a 2004 Winter Solstice flyer accompanying DIO's latest mailout, DR announced his effective retirement from further research in ancient astronomy. So again our thanks go to BS, for so swiftly and irresistibly effecting DR's temporary un-retirement.)

    [And DR wishes to emphasize by reiteration: what follows is much less importantly a critique of still-climbing BS than of the American Astronomical Society's degree of supervision of its long-out-of-control politician-historian-higher-ups.
    The very number of this BS-paper's problems — none detected by any responsible AAS or JHA official, before publication, or even after (during months of slatheringly unqualified media-hype) — makes this affair a neatly stark upcoming experimental test of the AAS and of the inevitable institutional tendency to prefer proud damage-control to honest humility.
    DIO asks that readers — especially historians and sociologists of scientific institutions — keep a sharp eye on the truth-facing or truth-ducking process, which is only now beginning — a process during which we will learn just how the AAS will react to the disgrace of launching a (weirdly disproportionate) national publicity-blitz based upon an effectively unreviewed paper concocted by the politically-leashed gofer of a few cemental leading academic archons. No historical paper in the AAS' history has ever been so lustily promoted.]

    A rich nest of links should assist perusers who wish fully to appreciate the unprecedented astronomical-April-Firstness of JHA's BS-achievement.
    (If the links are confusing, then: just ignore them. [Many are even-handedly bi-directional, which some will dislike. But the intent is that a busy reader be enabled to connect two related items, whichever he happens to encounter 1st.] Like our extra-scrupulous BS-page-citations here throughout [in stark contrast to BS' own (referee-inhibiting) slackness on that point], these links are intended as a helpful feature [for fast in&out sampling of the muff-muck section — to get on past, into DR's constructive finds], in knowledgeable anticipation of the familiar chapter-one-verse-one from the Institutional Damage-Control Handbook, which urges in-deep-bleep archons to buy breathing-room-time [while concocting a plausible cover] by pretending they can't read the indictment. Of course, in the present JHA&referees-didn't-even-read-the-JHA-BS-paper context, such protests would merely constitute pleading illiteracy to cover for innumeracy.)]

    Comments to those who will object to the manner of the present posting:
    [1] History-of-astronomy archons' several limitations have made such a joke of the field's quality-controls, that caricature and life have become ever harder to separate.
    [2] Despite over 3 years of private & public urging, BS has failed to correct his JHA-echoing, gratuitous, deliberately-delivered national smear of DIO and DR, which turned out to be more-than-Dan-Ratherly unsupportable. (In gratitude, the ever-so-subtle JHA instantly appointed BS a JHA Advisory Editor! Just as the JHA had elevated James Evans to Advisory Editor, right after his 1998 book's lengthy attack on DR.) So, though DIO's critical analyses do not fail to highlight the one or two contributing results of BS' otherwise desecratory Farnese farce, it can hardly be said that his behavior has merited dignified respect.
    [3] To a scientist, correct numbers count more than correct style.
    [4] DR's style is demonstrably irrelevant to the self-correction paralysis of BS & AAS, anyway, since Keith Pickering & Dennis Duke got the same unbudging BS to their elementary rock-solid, staid, polite demonstrations (DIO 12 [2002] — entirely uncited in BS 2005's discussions of atmospheric extinction) that BS' 2001 JHA Hipparchos-vs-Ptolemy paper had undeniably reached a fallacious conclusion. Recalling a DR pseudold-proverb:

    Archons who won't tolerate mild criticism always get their way.


    The Lost Catalog of AAS-JHA Refereeing Standards

  • Astronomer-historian BS is a vibrant & engaging teacher of Astronomy 101 at Louisiana Aggie. He loves a good laugh, and so has appropriately become one of the world's great experts in delicately negotiating his way upward (with the foresight of a dedicated chess-player) into automatic-credence in the perpetually-laughable political-animal world of the historians most durably connected to the American Astronomical Society (AAS). (Career-profitably catering to their foggy-brain prejudices is just too easy & tempting. Rolling drunks would be more challenging.) He is also a suddenly-elevated “Advisory Editor” of no less than the self-flattered “premierJournal for the History of Astronomy (Editor-for-Life: Michael Hoskin; on Whom, see DIO 6 [1996] ‡3 §§H&I [pp.42-43]; DIO 9.1 [1999] ‡3 §F [pp.39-42] DIO 11.1 [2002] p.2.).

  • BS recently created a mysteriously out-sized press-stir, at the 2005/1/11 San Diego meeting of the American Astronomical Society, by there bellowing his purported recovery of the “lost” star catalog of 2nd century BC astronomer Hipparchos.

  • This grand joke of a paper is now billed as a Big-Discovery in the April (aptly enough) issues of Discover (p.16) and Physics Today (p.27), and has evidently fooled a wide spectrum of press-folk who share the same naïve delusion: they assume, from the BS-thesis' kick-off promotion by the p.r. wing of the Amer Astr Soc, plus its upcoming publication in the extremely-handsome if pseudo-scientific Journal for the History of Astronomy, that relevant experts have actually read the paper (published at JHA 36.2:167-196, 2005 May) and checked its procedures.
    Does Discover also believe in the tooth fairy?
    [Journal for the History of Astronomy's Number Two — Owen Gingerich — whose touching&touched faith in BS' work triggered the whole Farnese farce, has now owned that he had checked no numbers at all in BS 2005, before rewarding. his current-fave heresy-defamer by hyper-promoting the paper to the whole world as the production of extraordinary expertise.
    (Question: even if [hypothetical] expert JHA referees weren't checking numbers, how could every one fail to have noticed that the BS paper mis-spells the constellation “Ophiuchus” five times out of five? — a preciously preserved idiosyncratic BS-tradition of transforming Ophiuchus' Greek-letter “χ” into “c” instead of “ch” — a tradition which BS maintains and even manages to exceed in his 2005/9/18 email — eight times out of eight.)]

  • Genuine non-historian scientists, who run the largely admirable Amer Astr Soc, have for years at least winked-at the scholarly & emotional shortcomings of the clique that dominates ancient-science studies associated with the AAS: astonishing source-unfamiliarity (almost incredible example to come), mathematical-naïveté (below), cemental tenet-obsessions, shunnings, amusingly inappropriate arrogance and unappreciativeness in treatment of able (often superior) scholars not in one's cult (mathematician Vladimiro Valerio, among others in this case), etc. Thus, a classic inmates-running-asylum pathology has gripped AAS discussion of ancient astronomy for decades — and such trifles as truth, accuracy, & ability have become of little account.
    In such a milieu, intellectually limited, don't-bother-me-with-inconvenient-facts, brook-no-contradiction archons publicize their like; and, if ever there were an archonal going-showbiz work-in-progress, it's BS.
    [It reflects less credit on DIO's IQ than discredit on the those promoting the JHA-BS-paper to point out (a fact which their cult- swell-headedness forces us occasionally to remind observers of): pretty much any scientist on DIO's refereeing or judging boards (e.g., Duke [FSU], immortal Chiron-discoverer Kowal [Johns Hopkins Univ APL], Pickering [Assoc. Editor DIO], Standish [CalTech JPL], etc) has more math talent than — with one or two happy exceptions — virtually the whole long-dominant old-guard AAS-historian-clique. And adding in the Journal for the History of Astronomy's everyday rulership [Premier Hoskin, F&B Gingerich, Evans, Swerdlow, et ilk] wouldn't alter that inequality half a whit.
    [This is not meant to imply that DIO's results should be accepted without scrutiny. (To the contrary: investigation of both parties' math is encouraged.) Nor is it meant to imply that the DIO side is always right. See our tolerant and (sorta) humble attitude in “Black Affidavit” towards our shooting-fish-stories-in-a-barrel-of-monkeys hashing of the Muffia's self-important fantasies; DIO 1.3 [1991] ‡10 [p.177]: the Neugebauer-JHA [“Muffia”] gang's “essential attitude is that [hate-objects R.Newton] and DR are not ever right…. By contrast [DIO] will merely show that [Muffiosi] are not always right. I recommend careful attention to this distinction. (Though, admittedly, [DIO is] not denying the tenuous possibility that the inverse of these propositions is nearer the truth.)”
    The point is: world-acceptance of the JHA-BS-paper's “discovery” has been entirely due to the supposed Authority-glow of the AAS having been conferred upon it — without anyone checking a digit. Thus, the present examination is forced to confront and expose the worthlessness of that tacitly presumed Authority. (Obvious lesson: if theories were promoted on their scientific merits rather than the theorists' purported Expertise & Authority, academic debates of issues would be much less ugly than has become all too common under rulership-cults whose petrification has led to defensive preference for opponent-smearing-exiling and pal-favor-trading, vs simple weighing of evidence & logic.)]

    The sheer incongruity of the AMERICAN ASTRONOMICAL SOCIETY's attachment to such prejudice, carelessness, & scientific mediocrity — which has persisted for years and appears likely to continue indefinitely — is as puzzling to us as it (and what follows here) presumably is to the reader. (The foregoing information-that-unfortunately-needs-to-be-kept-in-mind appraisal does not mean that DIO fails to realize that there is a wide spectrum of abilities other than math, which go into doing high-level history of science — and that many scholars are our superiors in at least some of these areas. We try to point this out wherever appropriate. See, e.g., DIO 9.1 [1999] p.2 and ‡1 n.11 [p.6].] Unfortunately, very little similar generosity has occurred in the reverse direction.)]

  • BS possesses an impressive verve (which merited better refereeing than he got). But BS&co are blithely innocent of the numerous booby-traps lying in wait for an enthusiastic but partially-limited author who plunges (without knowledgeable guidance and refereeing) into the practice of scientific history in the refined field of ancient astronomy.

  • In his paper, BS 2005 [], BS claims that he has discerned the legendary “lost” Hippachos catalog's stars — barely-hidden in the antique marble Farnese Atlas' starless celestial globe (henceforth “FACG”). The initial 2005/1/11 announcement acted as if this were the 1st serious scientific analysis of the globe (a slip since somewhat remedied). The claim is that the “lost” Hipparchos catalog had been in-plain-sight on the Farnese globe all along. (See any of numerous news articles based upon the press-releases of the Amer Astr Soc, etc.) Well, we will see what has been in-plain-sight all-along in this paper, since the 2005 Jan AAS announcement of it.

  • The Farnese globe is borne upon the shoulders of the statue of Atlas at the Naples Archaeological Museum. (See illustration [Piranesi?] at right.) The globe is covered with constellation-pictures (again: not their stars) such as equine Pegasus, Queen Cassiopeia, hunter Orion, feline Leo, etc. A fundamental point to keep in mind — the consequences of which have evidently eluded BS&co — is that: the bodies of all the mythological persons depicted on the globe are facing away from the observer (see illustration), since the Earth (from which we normally view the heavens) is taken as being within the globe, at its center. (Which obviously should have given BS pause — regarding precision if nothing else — when he began trying to pin “chest” stars and even a “breast” upon constellation-legends' backs.) This has always been the overwhelmingly normal convention for celestial-globes: the constellations are shown backwards, and the implicit star-arrangements are seen as mirror-images of those familiar to sky-gazers on Earth.
    [The other two surviving ancient celestial globes (Kugel & Mainz) both follow the same convention. However, one notes that the precession-film shown to BS' 2005/1/11 press-conference provides the rare experience of an inside-out (cartoon) celestial globe, i.e., with the constellations not mirror-images.]

  • The Farnese globe is also adorned by traditional circles: Zodiac, Equinoctial Colure (eqnColure), Solstitial Colure (solColure), Equator. And the tropics: Tropic of Cancer (TropCnc) & Tropic of Capricorn (TropCap). Also the polar circles: Arctic Circle (ArcCirc) of stars that never set & Antarctic Circle (AntCirc) of stars that never rise. [Note: for terrestrial globes, the polar circles' radii both equal the Earth's obliquity [which in reality was about 23°.7 during the classical period]. But, for ancient celestial globes, the polar circles' radii both equal the geographical latitude of a specific locale, presumably (though not certainly) relating to the globist's latitude. As we will see below, the Farnese globe's originating locale is indicated to have been at a latitude of 38° which is close to that of Athens and Pergamon. Though this is far from sure, it is a firmer result for the Farnese globe than BS' induced epoch of 125BC.]

  • Muffia-Reborn:
    BS' ultra-disastrous analysis was published in the 2005 May Journal for the History of Astronomy.
    It was alleged (2005/1/14) by BS [] that six referees saw it before publication: “When my paper was in draft form, I had it reviewed by six of the leading scholars in the field in America, Italy, and England” — predominantly selected by JHA “Advisory Editor” BS himself. (DR knows who the Italy reviewer is — and can only assume that he never really read through the paper.) It is typical that the BS-JHA combine pre-publication-showed-it-around to politically-trustworthy people, rather than to specialists one could trust on the relevant science and history. Whether they specifically passed on it is almost irrelevant. JHA Editor-for-Life Michael Hoskin would nix nixers anyway.
    [As has happened before: in the JHA's 1982 Oct disaster (retraction and fundamental re-computation credited to DR by the admirably honest and generally able author in the 1984 June JHA), both of two referee reports were superficial (DIO 1.2 [1991] nn.7&8 [p.97]) but nonetheless told MH the paper was incredible — yet MH published it anyway!]
    No matter what general doubts referees might have of BS' Farnese paper, MH would publish it regardless, in carte-blanche gratitude for BS' brainkissingly hitmanning-the-barricades with false abuse & slander, to punish those offenders charged from-on-high with commission of impious contra-JHA heresy in the sight of the Hoskin Godhead.

  • The Servile Problem:
    Loyally, unquestioningly attacking archons' obsessive hate-objects is becoming a standard stepping-stone to the top, in certain academic-mobster arenas. Paying such favors to dons is part of standard Chicago-style pay-to-play. Indeed, Al Capone began his rise to Chicago 1920s-lordship just this way: the dues for becoming a “made man” consisted of destroying an uppity Troublemaker. Likewise what Sydney Falco had to stoop to, in the 1957 classic film Sweet Smell of Success. But certain archons have a legit gripe: target-DR keeps rubber-duck-surviving&thriving — and each of J.J.Gingerich's potential-hero made-men turns out to be just a bumbling maid-boy.
    Like they say, you just can't find good help anymore….

  • Scared Hitless:
    In reaction to the present posting and to DIO's previous exposure of the falsity of slanderous attacks, the JHA clique's selectively-bold hitmen-wannabees have continued (as always) to hide from encountering DR in face-to-face debate.
    [Note that BS' 2002 Feb S&T article claimed that, after the Notre Dame debate on the Ancient Star Catalog's authorship (from which DR was barred) no one on either side was converted. Translation: debates are a waste of time; what we need to find truth is an Authoritative slick-mag decree&smear, to which the smearee will not be allowed to respond.]
    Note: if Hoskin (not to mention Gingerich & BS) cared about the validity, scrupulousness, and competence of what He disseminates, He would have already expressed ready eagerness to publish not just all the counter-Hipparchan indications BS missed (D.Duke's JHA contra-BS paper restricts itself just to these), but DR's findings on the JHA Farnese disaster's various problems of math, accuracy, source-familiarity, etc. (And to set the record straight on Sky&Telescope's 2002 JHA-based slanderous fantasies.) When in the same position, DIO hasn't hesitated for a moment. (DIO 11.2 [2003] ‡4 §G1 [p.41].) But, then, it is unrealistic to expect concern for integrity from a journal that has so long and persistently promoted plagiarists. And so even-handedly: from any era.

  • Immediately upon the BS Farnese paper's launch, #2 JHA Editor Owen Gingerich gave the press unqualified public raviews for it — though neither Number Two nor anyone else at JHA (none of whom had checked anything, before JHA put this paper over on the national press as a Great Discovery) realized that it positively bristles with astonishingly goofy and elementary problems.
    Highlighted links connect to details. These include: flat-out errors (see long [though merely partial] list of Muffs below), fantasies (including strange), trying to use an obviously invisible 7th magnitude star (35Cnc) to help place FACG's Equator, inconsistent and-or selective criteria, contradictions of Hipparchos and (remarkably often) of self, amnesia (e.g., BS [pp.170, 174, 175, & 176] keeps mis-dating Ptolemy's Almajest  to 128AD) or unfamiliarlity with central sources (e.g., Hipparchos' highly relevant Hour-Star list), innocence of well-known and utterly BS-contradicting key numbers (e.g., Hipparchos' crucial rising&setting data), embarrassingly primitive math techniques, etc.

  • Apparently, press-folk are not aware that such difficulties are nothing new, for theories recommended by the pseudo-authoritative, publicly ubiquitous pop-sci historians who have become politically embedded at (and socially swirl about) the AAS-JHA-Sky&Telescope circle.

  • BullyFlop:
    Indeed, AAS-mascot Gingerich's promotional discrimination is so spectacularly inverted that an alternate brand of kooks — the parapsychologist cult — might begin to beam-dream that there's evidence for “psi-missing” at the (political) heights of the science establishment it hates:
    [A] When J.Evans' 1987 dumb 64pp attack on R.Newton & DR arrived at JHA, OG was struck dumber by delusions of vindication. (With suicidal evidence-impenetrability and Hegelian timing, the paper's reasoning started its 1987-1998 academic swim a year AFTER G.Graßhoff's 1986 thesis [which Evans was pre-warned of: JHA 18.3:155f [1987] n.9] had independently confirmed the Ptolemy-skeptics and thus utterly ended any legitimate case for Ptolemy as star-cataloger.) Thus, truecome-dream-OG's Journal for the History of Astronomy ran it not just as a lead-paper but two Pb-papers — and its follies were even repeated in a peculiarly long section of Evans' 1998 Oxford Univ Press book (published with Gingerich's blessing). As even the JHA now knows, the paper's conclusion was false.
    [What kind of field is increasingly dominated by the type of scholar who is willing to plunge ahead with a scientifically semi-competent paper which he knows is invalid, so long as he very-competently senses that the paper's conclusion will trigger political advancement?]
    [B] Gingerich wrote a special boost-preface for telegenic K.Spence's 2000 pyramids-paper, thus ensuring it would become Nature's 2000/11/16 cover story. DIO quickly informed Nature that the paper's astronomy was miscomputed (as finally acknowledged: Nature at 2001/8/16 p.699).
    [C] When BS' Ancient-Star-Catalog paper debuted on 2000/1/15, Gingerich instantly (from the floor) deemed it “truly stunning”, ran it as a lead-paper in the JHA (2001) and almost got it into Discover (as DR learned from Aaron Spender, 2000/1/13). Since the polite but crushing revelations by Pickering & Duke in DIO 12 [2002], it's gone the-way-of-all-flush.
    [Excerpt from DR's 1st warning (2000/1/27 HASTRO) to HAD: “Are no other historians besides Keith Pickering and DR seeing anything (internally and externally) obviously amiss in [BS]'s test? (I.e., if this paper turns out to be baseless, what does it say about the HAD that no one else noticed?)”
    BS' resulting bizarre 2001 Journal for the History of Astronomy paper (which momentarily gave Gingerich his last delusion of Ptolemist victory and thus forged the BS-OG science-historical-genius-alliance) was from the outset a jaw-dropper larf among the top scholars of the field, since it was wilfully oblivious to a huge array of solid counter-evidences (Tycho, Delambre, R.Newton, DR, Graßhoff, Thurston, Pickering) — AND [seemingly incredibly] ignored the sole extant (STAR-data-stuffed) opus of the party (Hipparchos) he was attacking — ON A STAR CATALOG CONTROVERSY, mind you….
    Its ill-timed 42pp mega-defense of Ptolemy reminds one of Sen.Yarborough's remark on John Connally's defection to the Nixonites [for current update: see Joe Lieberman] (even as the Watergate scandal was growing): he'd never before seen a rat swim towards a sinking ship. (But, then, as the Ptolemy-as-star-cataloger ship now slips beneath history's waves, we find that 2005's version of the Vicar of Bray has jumped it — and doesn't even remember his former naval post! Not even Connally had that kind of brass.) No citation of the most recent and temperate findings: Pickering-Duke. I.e., you will search in vain throughout JHA-BS 2005 for any kind of retraction of JHA-BS 2001 — or the slightest word of credit to the many leading contemporary scholars who established the very pro-Hipparchos Ancient-Star-Catalog position he and OG are now finally flirting with. This because the BS-OG twosome is boldly trying to take this credit for their own gang. Can daylight robbery really succeed this easily? Well, in certain particularly degenerate academic fields, yes. Especially those whose denizens are so (oft-justly) insecure that, even when a fresh open forum beckons, they opt instead for the standard archon-kissing careerist-climb: spurning freedom for life-time slavery.
    (Don't miss the forest for the trees, when reading here. Throughout, keep noticing: Which party is obviously a free spirit? Which is obviously a chained one?)]

    Irony: with misunderstood good intent, DR repeatedly and vainly warned deaf-as-cement BS&co that his 2000 JHA paper was certain to fall. Back on 2000/1/27, soon after The-Brad publicly Verdicted (2000/1/15) for Ptolemy at HAD (ecstasizing O.Gingerich&clo), DR faxed the following prediction of disaster to K.Pickering (who immediately posted it on HASTRO, slightly edited):

    As soon as this latest white-hope implodes, everybody who's now acting so excited will just quietly crawl back into their rabbit holes, and re-adopt the previous mantra of calling the whole issue “inconclusive” for another decade or so — until comes the next Hero's hallucination that HE can at last slay the [black-hat] DIO dragon, in loyal service to archons. (And this orthodoxy will hold sway for another decade or so — until comes the next Hero's [draconicidal] hallucination ….. Is this the way falsifiability is supposed to work in academe?)

    Also (2000/2/2 [caps in orig]) on HASTRO: “Brad's complex result is CERTAINLY wrong.” (DR's judgement here is now completely vindicated. But this fact will never be permitted to appear in His Lordship's captive JHA.)
    Note: both OG & BS have made private acknowledgements of the value of R.Newton and DR researches. But they act as if saying so publicly would constitute a kind of treason. Happily, such transparent behavior is not a total waste, for: it is by such obvious (except to “science reporters”) indicia that we are most easily able to distinguish politician-glitterati from genuine scholars.]
    [D] In 2000-2002, in concern at DIO's growing influence and readership, Gingerich spread two defamatory deceptions regarding DIO (neither ever retracted by him to this day), using BS as vehicle, in initially-bold-bully (later evading & finally just hiding) Sky&Telescope: 2002 Feb p.40. The charges:
    [1] That DIO publisher DR had started abusive correspondence with the JHA's Editor-for-Life. (See OG→BS ghostwriting.)
    [2] That DIO was just a tiny vanity publication (omitting, with typical Gingerich integrity, the fact that DIO's boards are more eminent and FAR more independent and scientifically capable than his own semi-competent circle of sycophantic parrots, bumblers, and DR-debate-dodgers) — a deliberate deception which BS (loc cit) agreeably spread nationally for OG. (Countered in a 2002 June S&T letter by the US' greatest living celestial mechanics figure [CalTech-JPL], a letter which BS privately approved of; but BS has never publicly withdrawn any of the article's falsehoods.) Given false-content-similarity, Harvard-reference, and neat-chronology, the source of this particular BS 2002 slander is clear from some peculiarly out-of-place (and weirdly inaccurate) remarks in the 2001/7/28 Amazon review by John Rummel (Madison, WI) of T.Standage's mis-titled book (The Neptune File):
    “My own [Rummel's] brief research revealed that an historian of science named Dennis Rawlins has written several articles about” the Neptune affair.
    Rummel then (badly) summarized these articles (which he obviously never bothered to read), charging DR with being anti-Cambridge, though the University of Cambridge is (as also Oxford University) a DIO subscriber, and DIO 10 (which Univ Wisconsin & OG had just received a few weeks earlier) stated right on its cover “Copublished with the University of Cambridge”. Rummel continues [DR will add comments in brackets]:

    I contacted two historians of science [but of course didn't contact DR], one [unnamed but obviously Mike Shank, who denies it] at the University of Wisconsin-Madison, and one [no need to name] at Harvard. Neither knows of any evidence as to the truth of [DR's] allegations, and both attest that Rawlins tends to gravitate toward farfetched notions that mainstream science regards with suspicion. [An outright lie. An especially odd one, coming from a religious nut — who is here, yet again, bravely spreading his slander anonymously, while for decades ducking face-to-face debate with the slanderee! (Such transparent cowardice seeks new depths for hiders' familiar lodge&dodge tactic: DIO 9.1 [1999] ‡1 n.82 [p.21].) It seems that Conscientious-Objecting to combat can get to be a habit.]
    In fact, Rawlins doesn't publish his papers in mainstream journals [false (recent non-DIO publications by DR: Isis, University of Cambridge, Nature) — and irrelevant to research-validity, anyway], but in his own self-published journal ‘Dio.’

    [Curious that founding one of the two leading journals in the field can be so perversely described by the seething other journal's Number Two. (Might we say that JHA Number-One-Hoskin's papers in His JHA are Himself-published? Does it matter? Hoskin's JHA papers on the Herschels alone [not to mention MAH's seemingly-unself-conscious account of the J.South-R.Sheepshanks shun-cycle] vindicate said self-publication, as well as the oft-ignored truth that even scientific non-genii [e.g., F.Baily] can through dedication and industry contribute solid & valid scholarship to the history of science.)]
    Of those (Gingerich and BS) who spread such scurrilously deceptive and diversionary slander, one need only say that no honest scholar could do so, since even if he were too scientifically dim to discern DIO's academic quality directly, he could get some idea merely from the stature of the DIO boards and the leading institutional libraries worldwide that subscribe. (Detailed information on both points is provided on the inside & outside back-cover pages of each DIO.)
    [E] Gingerich has now launched yet another publicity-blitz for a baseless paper, the Farnese analysis of BS 2005, allegedly checked by six referees, none of whom actually studied it. In this case, the key snookeree was the (New York Times), whose coverage triggered the others.
    Each of the above-cited five OG-hyped botches ([A]-[E]) were primarily designed to convince well-meaning public forums that those involved were producing genuine discoveries, expert-certified as such — yet all were instead (at best) sloppily rendered, because the prime criteria (in selection for OG-hype) involved cult-political or pop-media considerations, not genuine scientific expertise; and the prime aim was not accuracy but enemy-denigration and-or the creation of a pop-science-world splash.
    Well, there's no bigger splash than a belly-flop.

  • The AAS has been requested to at least supervise the politicians who dominate ancient astronomy discussions at the AAS; but the incident here under review indicates that at the Amer Astr Soc, when it comes to astronomical historians: deft publicity and-or publication-package generators utterly out-rank solid-scholarship creators — meriting AAS-HAD cash-award honors and-or national publicity-promotion, regardless of conversancy with the math & science essential to establishing their sacred positions. (See, e.g., DIO 11.1 [2002] p.2; DIO 11.2 [2003] p.30 n.3 & p.33 n.7.)
    Naturally, the backward upshot has been: devolution of the impact of scientific skills and (much more crucially) scientific attitudes [a] upon the practice of astronomical history associated with the AAS — and [b] upon the reliability of widely-promulgated astronomical history.
    [Of the incestuous popular-publishing wing of the science community, it could be said that most of the writers may not know much math — but they do know how to group-cover for each other.]

  • [How will future historians of the history of astronomy community explain how it happened that DIO, the most technically-competent journal in the field and the only history of astronomy journal in the Americas, was effectively shunned for years by the American Astr Soc's Historical Astronomy Division? (See, e.g., the latest [2005 Feb p.5] HAD NEWS' naturally-DIO-frei coverage of present hist-astr journaldom. (Coverage attributed to Owen Gingerich, a religious fundamentalist whose well-earned reputation for generosity towards scholars evaporates when it comes to heretics R.Newton&DR.)
    Question: Is it the rôle of a central forum to take sides in a controversy?]
    Nor does HAD acknowledge even the bare existence of DIO's several new prizes, all governed by extremely eminent judging boards.) This, while the HAD fawns upon and glorifies the semi-numerate Publisher of the incurably-fake-refereeing Journal for the History of Astronomy — Who has (without the slightest AAS comment, other than awarding Him the HAD Doggett Prize) unilaterally severed communication for [thirty-three] years with the publisher (DR) of the [US] journal in His own field.

    Note: heresy-banishments [stains upon what could yet become a noble field] long predated DR's entrance into ancient astronomy — far earlier such shunning was applied to gentle Robert Newton: see, e.g., JHA 21:364-365. And, when Keith Pickering & Dennis Duke (in DIO 12) utterly atomized the 2001 JHA's 42 Pb pages of pure-BS atmospheric-extinction alibis for Ptolemy, it was all done sedately — nonetheless, BS has admitted nothing on the record (and has never cited the DIO 12 articles — nor did any JHA referee or official ask him to, for the extinction-related portions of the Farnese paper). I.e., DR's style is not the problem. (Read carefully DIO 1.1 [1991] ‡1 n.19 & n.20 [p.8] on the same point.) The community's dictatorial, fear-ridden state is the problem. A community that is not deeply disturbed by such a situation, a community that would let large fractions of scholars' lives go by (and in the cases of pioneering Aubrey Diller and Robert Newton: come to an end), without effecting remedial action, can hardly wonder why DIO occasionally disrespects its pretensions.]

  • It is doubtful whether what follows will enlighten anyone, since genuine scientists (and classicists) are already eye-rollingly aware of JHA refereeing's limitations in competence, ethics, and reality, while most press-folk really won't want to learn anything sad about their fave archonal-contacts, society-dinner inviter-companions, opinion-cynosure-gooroos, and coffeetable-book-author pals.
    [Few outside high academe seem to have noticed that DIO's boards are composed of the very opposite types: genuine scholars (not pop writers), including several world leaders in their respective fields: e.g., Standish (CalTech-JPL), Kowal (Johns Hopkins University APL), Walker (British Museum).]
    Nonetheless, details of the JHA-S&T kwasi-scholarship cult's distortions of truth ought to be recorded somewhere — as should their klannishness, careerism, political priorities, & long history of opting for private or safe-forum smear-techniques instead of uncontrollable face-to-face debate with DR. (See, e.g., at foregoing links and-or DIO 1.1 [1991] ‡1 §§C5-C10 [pp.7-9], especially n.20; ‡3 §§D2-D3 [p.20]; DIO 4.3 [1994] ‡15 [pp.120-138].)

  • Goooood Doggie.   Oldest-Professionals and Unprofessionals:
    A potential research-project for sociologists of media & science.
    In Sky&Telescope (2002 Feb p.40), BS openly admits that the Ptolemy Controversy has been the hottest in the field for the last thirty years, and even provided the common knowledge that it has been rife with “unprofessional” acts on all sides, including shunning. (Of course, the shunners aren't identified, while the shunned are named and falsely slandered and [well, pop-sci-lit likes a Happy Ending] ultimately blamed for all ills via the biggest whopper of all: the charge that the Ptolemy-skeptic side started the ugliness. Classic problem-of-evil sleight, hitherto found primarily in religious-apologetics tracts.) Given the fact that the scholars composing DIO's boards are far more able (several are THE world-#1 in their respective areas) than the field's more-politician-than-scientist Farces of Dorkness, whose bungles & slanders have persistently for 30 years screwed-up both science and generous cooperativeness in history-of-astronomy, one asks (in awe at the dedicated, ever-alert political manipulation): HOW have the coldly-careerist pol-perpetrators of a scandal — as durably dumb&dirty as this — remained TOTALLY vacuum-seal-protected (like the modern Ptolemist-smear-machine scandal — and case after similar case) from investigation by the marvelously-domesticated police-dog “science press” for decades on end — akin to a baseball league where every game is a Perfect Game, throughout an entire generation — while one Defender-of-the-Faith after another is nakedly blessed with advancement after volunteer Sweet-Smell heresy-hound duty and-or emission of lawyeresque pseudo-science in defense of Ossified-Oldboyperson-OrthoDoxy?
    But, then, it's common knowledge that the Oldest-Profession's legendary durability has always been based upon police protection.
    (See detailed discussion of one example at DIO 2.2 [1992] n.110.)

    Even more revealing than the above-cited 30 year PerfectGameness (a durability which applies to numerous other popsci-coverup cases):
    How did the perpetrators know ahead of time that they could depend on such perfection? After all, given the stakes involved (in risking the pop-science mestablishment's integrity-credibility against documentary proof to the contrary), there seems to be no rationality at all in adhering to a cover-up unless there is general awareness of absolute certainty that the lapdog “science press” will — with perfect-reliability-roboticity — cooperate in protecting the public from knowing of it.
    I.e., a philosophically fascinating (perhaps even trail-blazing) perversion of Pascal's Wager (DIO 8.2 [1998] ‡5 §L [pp.58f]), in which the gamble's seeming surethinghood derives from the supposed awesomeness of the probability P rather than of the value V of what is (purely technically) at-risk.

  • HippHype:
    BS' baseless Hipparchos-hypothesis will probably be as unstopperable as Mencken's equally fantastic 1917/12/28 Bathtub Hoax. Mencken prominently owned up on 1926/5/23 that his purported history-of-the-bathtub was “of spoofing all compact” — but his wholly-invented canard that Millard Fillmore took the 1st White House bath in the 1850s yet lives.
    [See the entire pathological Newspaperworld-Truth extravaganza — and its serious yet delightfully expressed lessons — in Mencken's “Hymn to the Truth” (H.L.Mencken: Prejudices, a Selection ed. J.Farrell, Vintage 1958 pp.242-247; e.g. [p.244]): “something in the human mind … turns instinctively to fiction … even the most gifted journalists succumb to it …. That this truth about the so-called truth is true needs no argument.”]

  • Before getting swiftly to simple and obvious contra-Hipparchan evidence regarding the Farnese globe, we will start by concisely itemizing the BS paper's manifold problems. In the précis below, one need only click on the linked word to go to the gruesome back-up details farther down.

  • Cornucopic Confusion: A Flood of Flagrant Fluffs:
    The star-positions provided by BS' JHA paper are riddled with screamingly patent screwups of direction, of orientation, of sign, and of the very constellation-features which are being matched with star-positions — none of these problems detected by SIX referees for the Journal for the History of Astronomy, before the paper's 2005/1/11 release to the world under (what the press [somewhat rightly] took to be) the august auspices of the American Astronomical Society. (Comments: [a] The JHA-Six have evidently also slept well in the months since: compare the BS 2005 paper's Jan pdf-posting to its present only-superficially-revised pdf-posting. [b] This paper probably couldn't have gotten by a SINGLE referee at DIO or any other journal run by scientists, mathematicians, or classicists.
    A noteworthy oddity: BS 2005's numerous references to Hipparchos' Commentary only very rarely provide citations to a page or section of that central work — a serial-omission which doubtless impeded referees' ability to check his uses of it. However, this service would have been immediately requested by any serious referee (who had the time to plow through 30pp of prolixity).
    [Upon reading this DR remark, Leroy Ellenberger rightly chuckled at the irony that the present frolixity is longer than the BS-paper it so characterizes! — though, at least scholars have read, checked, and materially improved the present rather less dry-pedantic posting.]

  • Several depictions of the FACG [Farnese Atlas Celestial Globe] will be cited in the following analyses. Of DR's own photos (taken in Naples, dates already noted), eight appear here (plus one elsewhere of the entire Farnese heaven-lifting Atlas sculpture). The eight: photo θ, photo σ, photo α, photo μ, photo ω, photo κ, photo υ, photo λ.
    In addition to those eight DR photos:
    We refer to BS' widely-circulated pictures (good images by Gerry Picus, Griffith Observatory) as photo 1 [p.168] and photo 2 [p.169] (Figs.1&2 on BS 2005 pp.168&169, resp). Photo 3 will be that at Enciclopedia dell'Arte Antica vol.7 [1966] p.1277 (not quite clear enough to merit reproduction here). We will also consult five photos from Encyclopedia of World Art vol.2 [1960] plate 23 (cited in BS 2005 n.1), which are usefully sharp. On this plate, we will designate the upper left photo as photo A, that below it as photo B; the three photos on the right, we will reference in top-to-bottom order as: photo C, photo D, photo E.)
    [More helpful photos (from Thiele's paper) are now on-line, thanks to Duke. And the 1739 M.Folkes projection of FACG, though occasionally slightly imperfect, is surprisingly useful — as confirmed by the recent cooperative investigations of V.Valerio (a highly competent specialist in the math of spherical projection) and D.Duke. The Folkes projection (plus a helpful imposed grid) can now easily be viewed by consulting Duke's 2005 paper — along with the appropriate associated equations, as well as a tabular comparison of some FACG points: Folkes-Duke vs BS' photogrammetry.]

  • In-Plain-Sight Confusions, Un-noted by JHA Referees:

  • Self-contradiction Type 1. Using the same star for two quite different positions in a constellation. And then doing it again.

  • Self-contradiction Type 2. Using two different stars for the same place. Orion's mid-waist: in Table 3 (p.187), star#15 is δOri, called “Middle of Orion's waist”; but in Table 5 (p.192), star#51, εOri, is called “Middle of Orion's belt”. Now εOri is the actual center of Orion's Belt, so: why did BS' Table 3 choose — seemingly-arbitrarily — δOri as mid-waist?! (Well, δOri is helpfully closer than εOri to the Hipparchos-era Equator….) The (at-best) ambiguity here raises another obvious question in passing: rather than vainly & contradictorily trying to estimate the position of something as vague as a person's middle (especially a person partly hidden! — see photo 2 [p.169], or photo B at right, Orion being the figure whose head is next to Atlas' huge thumb — much of his right side being under said thumb) — why not instead use famous Rigel (βOri), the nearby, far brighter & much-more-definable and wholly unobscured Orion left foot?

  • The Latitude-Switcheroo Two-Step:
    We next present two key synergistic confusions, which together constitute the main basis for BS' fumbling (and thus dropping) the sole potentially-firm mathematical clue (if such can be said to exist at all) to the Farnese-globe's origin:

  • Self-contradiction Type 3. Citing a sentence that explicitly contradicts the very information claimed from it!
    Hipparchos' value for Athens' latitude is confused with his value for his own Rhodes latitude (BS p.173 item [K]): 37°N latitude substituted for 36° latitude. This amazing trick is accomplished by the simple expedient of chopping off the Rhodes=36° half of the very Hipparchos sentence which said Athens=37° — and then chopping off the “Athens” part of what was left!
    (A single degree is crucial to the discussion. Keep in mind that the entire titular conclusion of the BS 2005 paper hinges upon a precession-based estimate [±55y] purported to be accurate to less than a half-degree.)

  • [A neat (if appalling) explanation of this truly dazzling gem: BS' failure (now replicated in a BS 2005/9/18 email!) to realize that HC1.11.3's reference to the ever-visible circle's 37° radius is not for Hipparchos' [Rhodes] sky but (as stated atop HC1.11.1) is for the [Athens] sky of the very Eudoxos whom both Hipparchos & BS are trying to put down! — and Hipparchos (presumably associating Eudoxos with his legendary career in Athens) then soon after explains (HC1.11.8) that 37° is NOT for Rhodes (36°N) but for Athens.
    Some remarkable information & ironies in this connexion:
    [a] HC1.11.5 says that εCas represents the feet of Cassiopeia (contradicting BS Table 3 star#44), 38° from the Pole. (NPD exactly 38° in c.150BC.) Since her feet are right on the Farnese globe's ArcCirc (see bottom photo C) this is visual support for our eventual tentative conclusion below that FACG was created for the non-Hipparchan latitude 38°.
    [b] Had BS read HC1.11.3&8 carefully, he would have realized that the Commentary's Athenian equation (by Eudoxos and-or Hipparchos) of both the ArcCirc (ever-visible stars) and AntCirc (ever-invisible stars) as 37° in radius, utterly obliterates BS' shall-we-say “naïve” (language inspired by JHAAssocEd-Evans: L.A.Times 2005/3/30) and excruciatingly contorted attempt to impose 4° of near-horizon invisibility upon both northern & southern horizons — while switching signs in mid-stream! It would be hard to improve upon the Commentary's clarity in indicating that for bright stars, the “extinction angle” was effectively zero, though Ptolemy has said the same thing to equally deaf Muffiosi: DIO 3 [1993] §L8 [p.25].
    [In the midst of a BS-vs-DR discussion of atmospheric extinction, it might be appropriate to note that DR is inventor of the 1st altered-argument compact expression that easily and simply provides accurate values for atmospheric extinction from zenith to horizon: Publ Astr Soc Pacific 94:359-373 [1982] p.363 eq.6.]
    [c] Finally, this same Hipparchan discussion of Eudoxos' latitude generates a potential speculative answer to an old question, the source of ancients' persistent mis-rendering of Athens' 38°N latitude as 37°, in centuries of handed-down ancient astronomical tables: Hipparchos' Commentary 1.11.3&8 took Eudoxos' location to be Athens, since Eudoxos became famous there; however, Eudoxos' astronomical observations were made (Strabo 2.5.14) at a sea-level observatory at Knidos, 36°40'N latitude or about 37°. So this hitherto-mysterious error — as durable in ancient tables as that for Carthage (and from the same scientifically-isolated ultimate source, Hipparchos) — could have been caused by a simple Hipparchan confusion of Knidos with Athens.
    [Another possible explanation might be Hipparchos' use of 37° as the klima for Athens: 14h5/8 (Vistas in Astronomy vol.28 pp.255-268 [1985] p.262 or [for latitude atn(3/4)] 14h3/5 (ibid p.263).
    Further, Hipparchos' HC1.11.8 states that Canopus was north of the Antarctic (ever-invisible) circle for said klima (which he now calls Greece's klima) and thus was visible there. His inter-changeable references to Athens and Greece are a strong suggestion that 37° or arctan(3/4) was a klima. But this leads us to an alternate version of an earlier speculation: was Hipparchos' belief that Canopus could be seen at Athens related to the ancient account that Eudoxos saw it?]
    Note, too, the implication: if the Farnese globe was for Athens, then this suggests most scientists knew that the actual latitude of Athens was 38°N, not Hipparchos' erroneous 37°N. (Regarding whether Hipparchos was out of touch with most of the science world: some have commented that, after all, Rhodes is geographically isolated.) DR earlier traced much of a millennium of random latitude-misgeography (ordmag 1°) to Hipparchos. (And systematic longitude-misgeography, to equally-isolated Ptolemy — though he may not have been its originator. [Poseidonious?].)
    [So: how did the works of two astrologers outside ancient science's mainstream survive so long and so exclusively? [a] The growth of astrology and the fame of a variously-instrumented Rhodes team's remarkable star catalog (Hipparchos). [b] The attachment of astrology to the growing Serapic cult (Ptolemy).]

  • Self-contradiction Type 4. Addition backwardly confused with subtraction (following the “premier” lead of the Journal for the History of Astronomy's Editor-for-Life Michael Hoskin), a botch that originated in confusion of a key astronomical angle with that angle's complement, which utterly sinks BS' manipulatively elastic mathematical discussion of the Farnese-globe-source's indicated latitude.

  • Self-contradiction Type 5.
    Elaborate computation (Table 1→Table 2→Table 5) putting the head of Ari [Aries] at 5°.6 west (Table 5 p.192) of the equinoctial colure, while displaying a photo (p.169) showing it east of that colure. (This will require earnest exorcism later on here.)

  • Further Equally Remarkable Items:

  • Besides such above-cited confusions as Athens confused for Rhodes, there are a bunch of equally goofy foulups, which we'll just briefly list here. Since we just noted where east (αAri) is confused with west, fairness requires:

  • North confused with south: βCMa (Canis Major).

  • Top confused with bottom (φGem), an internal contradiction.

  • Positive confused with negative.

  • Second confused with 1st: θPer [Perseus] vs χPer.

  • Observed-minus-Calculated confused with Calculated-minus-Observed.

  • Left confused with right: νTau (Taurus).

  • Non-Hipparchan constellation-bounds (Tau, etc) confused with Hipparchan.

  • Confusion of criteria: wings of Peg (Pegasus), and all of CrA (Corona Australis).

  • Neck confused with chest: ξCep (Cepheus).

  • Neck confused with breast: αCas (Cassiopeia).

  • Neck confused with shoulder (Tau): an ordmag 10° discrepancy.

  • Shoulder confused with (invisible) chest: Cen (Centaurus).

  • Unavoidable but BS-unmentioned confusion among BS' only three Antarctic Circle (AntCirc) stars. Star α confused with star β.

  • Muzzle confused with pate: αAri.

  • High-Precision Photomammetry:
    Summing up a general problem (brought on by BS' indiscriminate use of vague and virtually-unplaceable “stars”):
    BS repeatedly confuses front with rear, culminating in Table 5's nonpareil feat of precisely locating (Table 5 star#66 [p.192]) Queen Cassiopeia's breast


    [Classic high-precision-low-accuracy. For whatever reason (globe-distortion or photogrammetric-implant), BS' longitude for Cassiopeia's “breast”-star αCas is so far in error that it would be right for about 1035BC. Didn't it occur to anyone around JHA to wonder whether “stars” this wackily non-Hipparchan might be sending a message about the value of the entire Table 5 trash-collection…?]

  • Likewise in same Table 3 her husband King Cepheus' “chest” is placed on his back (photo κ or photo 3): star#43 = ξCep. And the Centaur's spine (see photo E at right; or near globe's rt.edge in photo 1 [BS p.168]) is labelled “chest front”: same Table 3's star#7 = θCen, later becoming “shoulder” in same Table 3 star#34.

  • So What?
    It is completely predictable that BS will claim that this mountain of muffs doesn't alter a single BS conclusion. In the slightest.
    Nothing ever has. See, e.g., BS p.173. More indicative: despite the far superior scientist K.Pickering's scholarly devastation (DIO 12 [2002] ‡1) of BS' 2001 JHA megapaper on the Ancient Star Catalog (definitively overturning BS' conclusion through an avalanche of independent tests — including atmospheric data unknown to BS, gutting the very atm opacity BS' case rested upon), BS has retracted zero. (His whole JHA-HAD mob behaves this way. Why should he be uncultishly different?)

  • Records — Broken and Unbroken:
    For concise, perceptive summaries of both science & free-speech in this affair, see Pickering's wholly-suppressed 2002/2/5 letter to S&T (items 1-17). And see Florida State Univ Physics Dep't statistician and super-computer specialist (and genuine BS friend & sometime helpful advisor) D.Duke's simple astonishing clincher. (DIO 12 [2002] ‡2 pp.32-33, summarized in Table 2. Equally simple: Pickering op cit Fig.1 p.5; see further at DIO 10 [2000] n.177 [p.79].)
    [Competing cultists will just as dependably claim that tropical astrology still “works”, even though 2000yrs of precession has swept most of their precious constellations into adjacent signs. Hey, there are people who just are never wrong.]
    It ought to be noted for contrast that DR promptly corrects, severely criticizes, and hopefully learns from, ALL his very occasional errors.
    [But let us not pretend that BS is not also learning from his mistakes. He is. From every encounter with his own tendency to spectacular error, he is learning the same lesson the grand hoaxer Frederick Cook learned: never confess. And, by its UNBROKEN RECORD OF FAILING TO REQUIRE HONEST OWNING-UP after each JHA-gang blunder — many inspired by decades of broken-record cult-parrot-alibis for formerly-sacred C.Ptolemy — the history-of-astronomy community (with the apparent blessing, of the American Astronomical Society) is educating BS&co (with that perfect consistency which is the hallmark of all great educators), teaching the same drumbeat lesson: retract nothing — take no responsibity for misleading readers, since the image of Authoritative Infallibility is more important than trivia such as truth, good science, and good character.
    One can only wonder at the pressures (of politics and talent-limitations) that are constraining someone who has evidently calculated that his future is better served by winning the trust of academic pols and the admiration of the even-less-numerate masses, while losing the respect of the finest scholars of his field.]
    By contrast, detection of errors in the present DIO analysis will be gratefully acknowledged and corrected as soon as received.
    (Also, notices even of trivial typos in this posting have already been and will continue to be appreciated.) Further, see DR's own openly acknowledged past foul-ups and strong self-criticisms at, e.g., DIO 1.1 [1991] ‡1 §C3 [p.7]; DIO 2.1 [1992] ‡3 n.26 [p.29]; DIO 11.2 [2003] 30-point-type cover-headline; p.31 n.2. And ‡4 n.21 [p.42] removes a Gongggggggggggg from a less-deserving scholar and transfers it to DR.]
    You will look in vain for any such list from Schaefer or his circle; because, again: they are never wrong.

  • Ducking the Clear & Hugging the Ambiguous:
    BS 2005 makes pretzellian attempts (see p.177, p.179 item 3, & n.10 [p.195]) to evade the simple implications of the FACG's lethal symmetry in the size of its polar circles, an equality first metrically established (though accompanied by wise warnings regarding the circles' non-trivial random-wander) by Vladimiro Valerio years earlier (1987): equalling a mean value (56°.1) to within ±2°/3. According to BS Table 4, & p.190, both these marble circles coherently place the FACG source's at 38°N latitude, distinctly north of Hipparchos' Rhodes (36°N). But BS then perversely diverts attention instead to far fuzzier indicia which (despite the math errors cited above) get him pseudo-unerringly right into allowance of his Hipparchan conclusion after all.

  • The JHA's Mathematical Innocence:
    Some of the paper's key math steps are attempted (not always successfully) by trial&error when well-known analytic methods would obviously be insisted-upon by a capable mathematical scientist — a creature as mythical as Pegasus among those who've consistently for decades dominated the JHA (whose Editor-for-Life is a self-confessed mathematical nin).
    [Understand DIO's position: scholars with limited technical-grasp can make and have made important contributions to astronomical history. DIO has always delighted in pointing out such wonderful events, e.g., DIO 11.2 [2003] cover & p.30 n.1. The objection here is narrowly just to those journals & archons who project (to, e.g., gullible newsmen) expertise as judicious establishment-archonal-wisdom-arbiters-for-whom-all-others-must-stand-aside, while lacking essential tools appropriate to the pose.
    (Again: this refers not just to the skills of the genuine scientist but to the scientific attitude that has produced the very knowledge that makes us glad to be part of the scientific tradition: receptivity to ideas on the basis of evidence [whatever the prejudice that may've inspired initial-investigation] — rather than on the basis of which side of a controversy is best-connected financially and [redundance-alert!] politically.)
    Further, when a contributor obviously needs help, it is the rôle of the refereeing-process of a truly scientific journal — especially one which claims field-premiership — to advise & assist regarding accuracy, math, logic, citations, etc.]

  • BS says (p.189) that the on-circle data for the five parallels can't tell anything about epoch. (Which would be news to Hipparchos or Ptolemy: see Almajest 7.3.) This false statement itself hints yet again that BS is inwardly aware:
    [a] The FACG “data” are too imprecise for the task at hand, for indeed epoch tests even upon all 35 of the parallel-circle “stars” find quite lax limits on epoch.
    [b] Strangely, BS isn't doing 2-unknown simultaneous-stats (p.196 n.23). As in his JHA 2001 disaster, he finds unknowns 1-at-a-time.
    [A specialist has made an observant comment in this connexion (2005/4/5): BS is claiming to use 70 stars to find the FACG epoch. But he is using stars#13-47 (the stars on the five parallels) by feeding (into his big 70-star chi-square finale) these 35 stars' Decl-deviations from the parallels — whose own Decls were derived by assuming (as 125BC: p.189) the very unknown he is searching for: the epoch. (Less of a problem in the present case, since sought variables are less inter-dependent than in BS 2001.)]

  • Full Analytic Solution:
    DR has devised a program which performs the entire BS experiment in one simultaneous swoop. (The method is direct — not BS' trial&error-poking-about testing for the effect of inclusion or exclusion [of individual data or sub-samples] is conveniently immediate.) It combines all seven of BS' variously disparate sub-samples (Tables 3&5 [pp.187&192]): [A] 12 on-colure stars (#1-#12), [B] 9 Equator stars (#13-21), [C] 9 TropCnc stars (#22-30), [D] 7 TropCap stars (#31-37), [E] 7 ArcCirc stars (#38-44), [F] 3 ArcCirc stars (#45-47), [G] 23 trash stars (#48-70). (Though these are indeed just sub-samples of the entire 70-data sample, we will feel free below to occasionally refer to each as a “sample” — depending upon context. Or whim.)
    An unusual added feature of the program: the stars of the TropCap sample [D] and those of the AntCirc sample [F] are neatly merged with those of the TropCap sample [C] and ArcCirc sample [E], resp — such that the four samples ([C]-[F]) become just two, thus setting up a quick hunt for each joined-samples' common unknowns (obliquity & colatitude, resp). [We will be glad to receive reader's guesses as to the three elementary steps which effect such delicious alchemy. (Hint: the 3-step alchemic program-line is under 20 characters.)] On this data-basis, the DR program seeks all three Farnese-globe unknowns simultaneously: epoch, obliquity, and colatitude. (It is obvious that the globe's creator took it for granted that: the polar circles' Decls were [typically for antiquity] identical to each other [both = colatitude, i.e., latitude's complement]; the tropical circles' Decls, identical to each other [both = obliquity]; and the Equator's Decl equals zero by definition. (Note that BS understandably treats the five parallel circles' Decls as unknowns in Table 4 [p.188], but he correctly regards discrepancies as not significant and there shows them to be thus.) It should be noted first-off that our initial results below are not seriously discordant with BS' announced solutions. (And this shows that — whatever the theoretical crudeness of the procedure — BS was justified in thinking he would not go very far wrong in, e.g., solving for epoch with 1-variable-analysis-based obliquity & latitude. [This works out OK for the full sample; less well for the AntCirc stars, or for BS JHA 2001.]

  • The full simultaneous solution (on the basis of the data BS used):
    epoch 132BC ± 58y   colatitude 51°.7 ± 1°.1   obliquity 23°.8 ± 0°.9    (χ2 = 65.2).
    The χ2 does not agree with BS' value: 66.3 (pp.193&196).

  • But let's assume BS silently weighted the trash-“stars” precisely 1/2 as much as the on-circle “stars”. And of course BS could solve for just one unknown at a time, so we set obliquity and colatitude to the BS values (23°.95 & 51°.7, resp: BS pp.189-190) and the Equator's Decl to zero and solve analytically only for epoch:
    epoch 130BC ± 57y      (χ2 = 66.3).

  • Now, though we noted just above that this result is not very different from BS', there remains the obvious question: since the chi-square is identical, why does the solution differ at all? But both the mean and its σ (standard-deviation) do differ. (The effect of roundings?)

  • Further, it is slightly provocative that we can recover BS' exact χ2 by assuming that he rounded the 0.49 weight-ratio (on-circles data vs trash) to precisely 0.5. BS states in detail (p.193) that he used one-datum σ = 3°.5 for “stars”#1-47, one-datum σ = 5° for trash-“stars”#48-70. But instead of 0.49 (i.e., the square of 3°.5/5°), he has evidently used 0.5. If the experiment were being done entirely by computer, it's easy to write a line demanding 0.49. But — if the final chi-square total was being added up by hand, just halving the total chi-squares for the trash would be reasonable.

  • Massaging the Titular Epoch:
    If this addition was done by hand (at least at an intermediary point), then BS did not just do the whole experiment in one run with pre-determined weights. (BS' confusion of O−C with C−O for some samples is obviously consistent with this speculation.) Rather, he had instead developed seven stacks of chi-square totals (one for each of the sub-samples [A]-[G]), and only subsequently decided how (e.g., were all sub-sample sizes pre-determined?) to assign their relative weights. (Samples [A]&[G] being the main contributors to dating the globe, we elsewhere give reasons for the sample [G] trash's weight — vs on-colure sample [A] — being made no greater than the square of 3°/5° — which is more than 25% less than 0.49. In truth, the ratio should be virtually zero.) Picking & choosing weights allows opportunity for (consciously or no) massaging the epoch-solution, which is the prime desideratum & very title of the BS-paper.
    N.B.: As we argue later, to have given any weight at all to the trash-data is THE essential massage — a central point which should not be lost sight of, amidst relatively minor and speculative questions here regarding choice of precise non-zero weight-ratio.

  • BS held obliquity & latitude fixed, finding by-trial where χ2 is 67.3, 1 unit higher than best-fit χ2 (66.3). BS p.193 states this occurs at 180BC & 70BC. By the same process, DR instead finds 188BC and 70BC, with a mean of 129BC, not 125BC. If one tests for those dates when S (sum of squares of great-circle angular deviations) exceeds minimum sum S0 (for 129BC) by the square of single-datum σ, DR instead finds 186BC and 72BC. Which is consistent with solution:
    epoch 129BC ± 57y      (χ2 = 66.3).

  • This result (from 1-variable trial&error-testing of deviations' rms) is virtually identical to the above analytically arrived-at solution. (The trivial 1y discrepancy occurs because the problem is not perfectly Gaussian.)

  • But, of course, all the solutions just cited are illegitimate, thanks to a glaring, undeniable sign-error for star#60 (αAri), which changes that datum's longitude by more than 10° (from BS Table 5's 2°.6 to a more accurate value of 12°.7). Correcting for this, we can provide for the 1st time the mathematically-legitimate solution for the “stars” BS has chosen & photogrammetrically placed (i.e., the correct solution for his own data-base):

    epoch 112BC ± 58y
    colatitude 51°3/4 ± 1°.1
    obliquity 23°.8 ± 0°.9

    This is clearly a non-trivially different result from 132BC or 129BC or BS' 125BC — though [a] it comes nowhere near ruling Hipparchos out, and [b] it is based on so much horribly-selected data that it can convincingly rule out (or in) almost no ancient astronomer.

  • Given BS' national self-aggrandizement by adducement of hilariously irrelevant “stars” as well as non-existent and-or mis-identified body-parts, we may pluck out (from the foregoing sample) THE most “ludicrously” illegitimate “star” of an already bad lot — Cassiopeia's by-now-notorious “breast” (αCas — actually her neck) which BS' Table 5 star#66 placed upon her back! — and see how its merciful elimination will alter the deduced epoch; result:

    epoch 101BC ± 57y
    colatitude 51°3/4 ± 1°.1
    obliquity 23°.8 ± 0°.8

    We're now 1/4 century away from BS' 125BC solution. So BS' two most “absurd” screw-ups (αAri & αCas) were so misleading that correcting them has moved the epoch-solution nearly half-way from his mean to his upper-bound.

  • We could go further. Since BS' Table 3 star#2 claims to put the westernmost Per star on the equColure, and since Table 3's star#38 is a far-further-west Per “star ”, χPer, one may justifiably substitute χPer into the on-colure sample [A] and re-do the whole BS computation. If we retain our other two corrections (above: correcting αAri & dumping αCas), we find:

    epoch 85BC ± 56y
    colatitude 51°8 ± 1°.0
    obliquity 23°.8 ± 0°.8

    This now puts us 40y later than the widely-disseminated false Farnese date 125BC.
    But, to repeat: none of these solutions actually tell us anything. (Beyond illustrating how unreliable the BS paper's date really is.) They are all invalidated by a different unreliability: the incorporated trash-data of sample [G] (Table 5).

  • The DR program may easily be adjusted for checking among the seven sub-samples, which is where we will find several difficulties, regarding, e.g., data-reliability and sample-compatibility.

  • Arctic Circle:
    Analysing the on-parallel-circle data via 2-unknown least-squares. Arctic Circle (ArcCirc) results:
    For BS Table 3's seven ArcCirc stars:
    Decl +51°.7 ± 1°.5 and epoch 208BC ± 330y.
    Since outlier χPer is not a star but a diffuse cluster — and a double-cluster at that — and not surely on FACG's ArcCirc, it should be dropped. The 2-variable solution for the remaining six BS stars:
    Decl +52°.6 ± 0°.8 and epoch 493BC ± 190y.
    DR tried to clean up the ArcCirc sample further: replacing ιCas by εCas and dropping Cep entirely. (The ArcCirc goes through Cep's neck [see bottom of (inverted) photo C], but the only serious star there [νCep] isn't in any ancient catalog. [Note: its Decl (52°.2) would be no problem for our conclusions, anyway.]) This leaves five stars, from which DR finds:
    Decl +51°.5 ± 0°.5 and epoch 195BC ± 121y.
    Note: Both the epoch results are expressed much too precisely, given their σ. (BS' restraint in this regard sets a good example [better than DR's, rather too often]: he rounds to the nearest 5 years throughout.) For results with σ around 100 years or more, we will henceforth round to the nearest decade. Restating the foregoing solutions thusly, we have:
    7 BS stars: Decl +51°.7 ± 1°.5 and epoch 210BC ± 330y.
    6 BS stars: Decl +52°.6 ± 0°.8 and epoch 490BC ± 190y.
    5 DR stars: Decl +51°.5 ± 0°.5 and epoch 200BC ± 120y.
    [Comparable AntCirc results are provided below, where we now additionally find non-trivial impact of BS-ignored p.m..]
    These tests tell us little about epoch (though not nothing), but confirm BS' new & potentially useful estimation of the (distortion-adjusted) sizes of the polar circles at about 38°.

  • Hipparchos as Source?:
    The Farnese globe (FACG) is plainly not son-of-Hipparchos, as claimed. (The two allegedly-connected sources may perhaps be the equivalent of cousins. But that could be said of pretty much any two roughly contemporaneous constellation-depictions throughout the history of celestial cartography.)
    Valerio makes (2005/3/28) the trenchant point that it is trivial to trace some Hipparchan influence if Ptolemy's catalog was used, since the at-last-esteemed R.Newton showed years ago that the Ptolemy catalog was stolen from Hipparchos and then updated for the 2nd century AD — and this agrees roughly with Valerio's estimated date, which he based in part upon the FACG Ecliptic-Equator intersections.

  • The BS study's publisher, the Journal for the History of Astronomy, regards Reliability as a political not a scientific word, a mentality which may perhaps be related to its long and consistent history of inadequate refereeing. As noted above, there were six JHA referees for the FACG paper, yet evidently none succeeded in repairing any of the wide range of problems just précised above.
    [Mega-Irony: the hottest rage (1983/3/3) of JHA Editor-for-Life Michael Hoskin's esteamed papal career occurred when the JHA's refereeing inadequacies were helpfully pointed out by DR. (And BS was invited onto the JHA board in 2002 right after his national-popsci-mag attack upon the very same critic.) For partial catalogs of history-of-astronomy-journal refereeing lapses, see DIO 4.1 [1994] ‡4 §A [p.48]; DIO 10 [2000] n.177 [p.79]; and DIO 11.1 [2002] p.2 n.2.]

  • JHA-Evaded Proof of non-Hipparchan Origin
    The Farnese globe bears two prominent polar circles: the Arctic (ArcCirc) & Antarctic (AntCirc). (Before going off into alibi-land, BS starts well by rightly realizing that the polar circles' size [p.176] “must be related in some sense to the latitude of the observer.”) Each circle represents the boundary of stars that are ever (ArcCirc) or never (AntCirc) visible at the FACG cataloger's latitude. (Thus, to put it simply: the polar circles' size [radius] is the latitude; and their Decl is the co-latitude [the complement: 90° − latitude].) Now, two undeniable key facets of these circles syllogistically kill the Hipparchan theory. (BS tries evading both by:
    [1] using a hilariously out-of-context quote. [2] confusing plus with minus.) The remarkable details follow:

  • Latitude Investigations and the Elimination of Hipparchos:
    The three famous bright stars on FACG's AntCirc (BS 2005 Table 3 stars#45-47) argue persuasively that this circle's Declination (Decl) is about 52° South. (BS acknowledges this at Table 4 and p.191.)

  • North-horizon atmospheric extinction affects the size of the Arctic Circle in a sense opposite to the way in which south-horizon atm-extinction affects the Antarctic Circle: for a northern hemisphere observer, extinction obviously expands the AntCirc (as BS rightly realizes), but extinction just-as-obviously shrinks the ArcCirc. (Yet another BS sign-confusion.) BS' discussions appear inversely mixed-up regarding this elementary point, which is crucial to the issue of the Farnese-source observer's latitude because ancients realized that the size of one's Arctic and Antarctic circles (both) equalled one's latitude. The FACG has visibly-obvious symmetry for these circle's distances from their respective poles. (The experienced prior FACG-investigator, mathematician Vladimiro Valerio, had already shown this equality [and BS agrees to it], years ago: analysis published in the Der Globusfreund [Vienna 1987], pp.97-114 [English] with illustrations on p.124 plus Figs.18&19 [Report of the 6th International Symposium of the Coronelli Society, Amsterdam]), “Historiographic and Numerical Notes on the Atlante Farnese and Its Celestial Sphere” — which includes a generous introduction and a generously full bibliography: see Valerio 1987 p.105.) The circles' equality alone proves beyond question that whoever was responsible for the Farnese globe's creation ignored extinction and simply placed both polar circles the same distance from their respective poles in accord with a chosen geographical latitude. (This was just standard ancient practice [see, e.g., Geminos 5.2&9]: the ancients described the horizon in purely mathematical terms: DIO 12 [2002] ‡1 §§F3 & especially F11 [pp.17&19].
    [Strabo 2.5.14 says Eudoxos could see αCar [Canopus] (less than 1° above the horizon) from Knidos, which presumably influenced Hipparchos' rendering of both his polar circles as identically large (HC1.11.3&8): i.e., null extinction-angle-correction.] Note, too, the following well-known items, all of which confirm the consistency of ancient practice in this connexion:

    1. All of the hundreds of phenomena in Hipparchos' Commentary are computed vis-à-vis a simple, ideal great-circle horizon, precisely 90° from the zenith. (An example of the math is provided at DIO 7.1 [1997] ‡‡2&3 [pp.14-17].)

    2. At GD 1.7.4, Marinos is quoted as equating the southern limit of the ever-visible circle for UMi with αUMi's NPD, an equation probably due to Hipparchos, who is there cited for the NPD's value (12°2/5, correct for H's not M's epoch).

    3. In the extremely important and meticulous K.Pickering study just cited above (which should be known to all students of ancient astronomy), it has been thoroughly proven (DIO 12 [2002]) that the ancients' data for planets' arcus visionis and (inevitably! — see ibid §F11, Fig.4, & Table 3 [p.19]) acronychal risings are also figured — as anciently stated & diagrammed — for such ideal horizons.
      (For individual planets, there is, in fact, no meaningful way to define acronychal risings based upon extinction — a crucial point evidently 1st announced by DIO (idem). When Pickering informed BS of this inconvenient but inevadable truth, BS' response was that of one utterly trapped between the force of factual truth and the force of Authority-pretense: he fled — no reply.)

    There will always be disagreement over the FACG-circles-Decl's value & meaning; but there is none whatever about the fact that the N&S circles (tropical or polar) were designed to have the same size: [a] on the marble; [b] in ancient tradition; [c] and (BS correctly contends) in the associated stellar Decls. BS realizes these two circles' symmetry (equal size) — indeed, he even laboriously proves and explicitly concludes for it (p.191). But then, inexplicably, BS chooses (p.177) to fast-shuffle-evade the fact that if extinction actually affected these circles (an assumption which in itself evidences scant familiarity with ancient thought), the effect would be asymmetric. He is thus cementally in-denial regarding the plain implication (of the polar circles' size-symmetry) that extinction is being ignored on FACG. (This finding tells us something of physical interest: ancient air was a great deal clearer than now. [If this point seems self-evident, DIO can only note that: [a] it has been controversial until very recently (NYT2004); [b] BS spent 42pp of the 2001 JHA arguing otherwise.]) Despite this unalterable fact, BS plunges ahead (with his characteristic trainwreck-determination) in demanding (p.177) that extinction bail him out of his own concluded latitude's obvious disagreement with Hipparchos'….

  • How does BS make symmetric his inherently asymmetric extinction-fudge? By screwing-up, that's how. (But, be reasonable! — there's no other way….) Though BS is arithmetically correct in arguing that his 4° of southern-horizon extinction might induce an extremely atypical FACG-source astronomer (observing) at 34°N into putting his AntCirc 38° from his globe's S.Pole, BS' titanic paper then sails smack into yet another of his megapapers' icebergs (DIO 12 [2002] ‡1 §A4 [p.4]) when he tries the same argument for the ArcCirc, where obviously raised-horizon-extinction would shrinknot expand — the effective polar circle. Watch carefully the misarithmetical illusionism in BS' spectacular blunder for the ArcCirc (p.177):

    the depicted [FACG polar] circles might be intended to match actual observations of the lowest declination where the stars never set …. For the Arctic Circle, the observer … might have adopted a visibility definition such that a star is circumpolar [within the ArcCirc] only if it is actually visible [over the northern horizon] at its lower meridian passage. In [that] case, the adopted declination would be closer to the pole and lead to our deriving a latitude that is too far north, and hence the latitude of the observer might be closer to 34°.

  • BS has simply confused a star's Decl with its complement, the NPD (North Polar Distance). If we follow BS in assuming that the visible-stars' effective northern horizon is raised 4° by atmospheric extinction, that indeed increases (by 4°) the lowest stars' Decl — however, the indicated latitude is not equal to but is the complement of that Decl. Viewing this in another way: if the northern horizon's lowest stars' extinction-enhanced Decl is 52° (as on FACG: Table 4 [p.188]), then the Decl of the on-horizon stars (4° below them) must be 48° so the observer's latitude is 42°N, not BS' 34°N. Thus, the same BS p.177 extinction-argument which showed that a 38° FACG AntCirc came from a 34°N astronomer, actually shows (when applied to the ArcCirc) that a 38° FACG ArcCirc would come from an astronomer at 42°N.
    [It is rather ironic that the over-gross size of the 8° discrepancy (2 times 4°), which BS has laboriously & unwittingly created for himself, originated in BS' own abusive personal denigration of DR — extending to 42 upfront JHA pages — for DR's and Keith Pickering's ancient-source-based contention that planets & bright stars could be seen on the horizon in antiquity (DIO 3 [1993] §L8 [p.25]; DIO 12 [2002] ‡1 §F11 [p.19]).]

  • It is by such fallacious reasoning that BS evades his own work's obvious implication (hardly proof, of course) that the FACG-source observer was at 38°N.

  • Returning to reality: Given the claimed ordmag 1° accuracy of the BS analysis of the polar circles, FACG's circles may be able to help identify the FACG-source observer more reliably via his latitude (38°N) than is possible (since precession is so slow) by his epoch. (The epoch is obviously the classical period — Valerio 1987 & BS 2005 are both quite correct on that point. But the FACG-data's softness regarding epoch leaves the door pretty wide-open, given the number of astronomers who lived then.) After all, if we cannot (according to BS) fix the FACG-source-cataloger's latitude to better than 2°, then how can we get the FACG's epoch to a half-century which implies about 4 times better accuracy (about a half-degree)? [Answer: more wishful selectivity.] Nonetheless, BS becomes so determined to downplay his own latitude solution's significance that one soon senses imminent kitchen-sink-invocation. He suggests (p.177) extinction, extinction-related constellation-stretching (forgetting that tropical circles' Decls are [pp.190-191] distorted by almost exactly the same near-linear ordmag 10%-factor [as polar circles'], though they are unrelated to extinction), ending his entire latitude-discussion with 2 sentences that deserve special preservation (p.177 emph added): “In all, the declinations [sic] of the Ant/Arctic Circles (±51.7°±0.9°) has an unknown relation to the latitude of the observer who provided the constellation positions. Any observer in the Greco-Roman world is consistent with this constraint.”
    (BS' dealing with the implications of his own 38° latitude result is a rare-gem instance of a prime DR germ: “There is no agnostic so indiscrimately-doubting as a believer when inconvenient facts intrude.”)

  • So the 38°N latitude of BS' own concluding numbers (colatitude 51°.7±0°.9 [p.191]) are contra Hipparchos, who was from Nicaea (41°N) and did his lasting astronomy on Rhodes Island (36°N).

  • Extra speculation: it is possible that the sculptor paid more attention than usual to his hypothetical source-star-catalog when he was near the polar circles (and the colures, as well). Once BS' identification-errors are cleared out of Table 3, errors of position appear to be less anomalous than for, say, the Equator. This would favor the supposition that the 38° size of the circles was of local importance. (Possibly to a king?) But one mustn't lose sight of the fact that all this supports Thiele's & BS' general theory that a star catalog was involved — a contention which can be mercifully regarded as more important than the detail of identifying the cataloger: this theory appears moderately if nonetheless uncertainly confirmed by very fact that the on-colure and on-polar-circle data have so much less scatter than the off-circle data.

  • However, even had recovery of FACG's source been accomplished as claimed, it would hardly merit the attention JHAvolk drummed up. It was particularly curious to see the JHA's BS and Owen Gingerich imply in the press that the FACG bears strongly upon the needlessly JHA-cult-contended question of whether Ptolemy stole Hipparchos' catalog (a matter which hasn't been controversial among capable astronomers for centuries). If we were to rank the dozen or so evidences of Ptolemy's multi-proven theft, the BS-Farnese contribution would be very near (perhaps at) the bottom of the list.

    The Emperor-of-China Paradox: The entrapping allure of fantasy-statistics cannot be more efficiently warned of, than in a delightful illustration-by-extreme-example (relayed to DIO by Peter Huber and printed by us at DIO 2.1 [1992] ‡2 n.18 [p.19]): “You are supposed to estimate the height of the [Chinese] emperor. Unfortunately, he lives in the Forbidden City, and the few people who see him won't talk to you. But there are [a billion] Chinese. So you simply go and ask every one of them what he or she thinks the height is. Then you average [the data and, after of course dividing the mean deviation by the square root of a billion: normal statistics, after all, you] get a fantastically accurate estimate (with a standard error of the order of [a few microns]!).”

  • Mahler called Strauss's opera Salome a work of genius founded upon a slag-heap. BS may not be a genius (though he plays one on television), but he is far more scientific than the FACG “data” he is analysing.

  • Few scientists fall for garbage-in-garbage-out quackmires. Fewer yet delude themselves into garbage-in-granite-out. Yet BS has made such statistical alchemy his guiding principle in consecutive JHA megapapers now (2001-2005), each based squarely & laboriously upon it.

  • Confidently asserting they are “virtually identical” (p.174), BS says all constellation-features fit Hipparchos And he's absolutely right. Except for the features that don't.

  • Key Fallacy: Absence of Evidence:
    Since BS knows of only a handful of ancient star catalogs, he has unthinkingly presumed that FACG positively MUST be based upon one of them. (Oddly, in a more rational moment, he recognizes [p.179]: “The concept of globes was common in Greek times”, from the 4th century BC onwards.) So he is persuaded by his analyses' “exclusion of all other KNOWN candidate sources” (BS p.178, caps added). (Yet another case of presuming that absence of evidence is evidence of absence [this in a context where all but a jillionth of the documents have long since been lost forever]: DIO 11.1 [2002] ‡2 n.7 [p.12].)

  • Therefore, only faintly in the tradition of Shakespearatorialists (hopefully more in the rational Twain-strain of these: see “Is Shakespeare Dead ” [1909], Complete Essays of Mark Twain ed. C.Neider pp.407f; also Calvin Hoffman's 1955 book demonstrating C.Marlowe's authorship), we will pose the Lost Small Catalog Hypothesis: “LSCH”. Because it will quickly be apparent that no known ancient star catalog fails to be repeatedly contradicted by features of the Farnese globe.
    [The fact that a few key stars seem well-placed, while many do not, is consistent with the theory that the hypothesized catalog underlying FACG was quite modest in size. Such a theory would obviously rule out Hipparchos' catalog as source.]

  • Later, we will offer an alternate candidate — with evidence that the precessional date for him is rather better than for H. But it will be just a speculation. I.e., no AAS press-conference.
    OK, now let's return to the heady JHA world of speculation-dressed-up-as-proof.

  • Even while announcing the recovery of a non-lost “lost” ancient star catalog, BS also implicitly overlooks the possibility that there might have been other star catalogs than the four he has considered.
    [One of DR's most important ancient-astronomy discoveries:
    At least as early as 300BC, Greek astronomers (as they recorded surprisingly accurate star positions in the equatorial frame) knew their observatories' geographical latitudes to ordmag 1': e.g., Timocharis (300BC) and Aristyllos (260BC). (See Almajest 7.3; Isis 73:259-265 [1982] n.17; DIO 1.2 [1991] nn.126-127 [p.125].)]

  • BS pleads (p.194) that he is using standard statistical procedures. (Of course, every toothpaste-ad can make the same claim.) But these procedures and their formulae all depend upon the biaslessness of the analyst — and so are mere window-dressing if said premises are violated.

  • If someone wanted to “push” the FACG “data”, there are easily enough holes in BS' procedure to push them through.

  • If a precise Hipparchos star catalog truly were FACG's source, the most obvious question here is: was the sculptor BLIND? (Back to the Chinese Emperor?) Or was BS? — not to see manifold differences between Hipparchos and FACG: huge “errors” of position, orientation, and-or features. (Note: it was proper of BS to begin the investigation without circularly building-in Hipparchan features into identifications. But once BS began zeroing in on Hipparchos as FACG-source, it would have been wise to re-check Hipparchos' Commentary to see whether a sculptor with eyes, using H's correlations between stars & constellation-features, would make some of the placements we see on FACG.)

  • Which is why we have proposed our modest alternate LSCH theory here: if FACG is based upon a star-catalog, it is a truly lost one — and its original will almost certainly remain lost forever.

  • BS (pp.184, 190-191) acknowledges serious “distortion” of about 10% (!) in the FACG's N-S coordinates, adjusted by a piece-wise linear function. (DR investigations used a very similar automatic quadratic, of quite small 2nd-order coefficient.)

  • There is also the problem that the E-W position of each equinox (where the Ecliptic crosses the Equator) is over 5° of RA west of the appropriate colure. (These important measurements were 1st performed by Vladimiro Valerio; see data at Valerio loc cit: their mean = 5°.2. See also BS p.172 item 8.) Such scientific nonsense leaves an epoch-ambiguity of about 4 centuries. BS opts for assuming that the colures are FACG's true framework, but it is hard to be certain of the truth. Thus, even if we accept all BS' math leading to Hipparchos' century, the true date (based on using the Equ-Ecl intersection as RA-zero-point) might really be c.200AD (not far from the date commonly accepted for the globe's construction: see BS p.170 on Valerio).

  • How to resolve the discrepancy? Well, what if both parties' superficially incompatible solutions have merit? I.e., perhaps the sculptor got amateur advice on updating a globe several centuries old, and precessed matters along the Equator instead of the Ecliptic.
    [The details of precession's mechanics were still unsure at least as late as Hipparchos' era and presumably much later. (E.g., the huge Aristarchan error in precession's very size persisted until the Arabic period.) So if the globe was precessed along the equator, this does not prove that the sculptor wasn't familiar with astronomy current in his day.]
    (Another [outside] possibility: the sculptor was copying from two globes [each covered with pictorial constellations], one from his own time [bearing the zodiac-circle he went with], the other from a few centuries earlier (bearing equatorial-frame circles that might have been lacking from his own era's globe). Either way, if the globe is from the 2nd century AD, then the equatorial-frame circles could have been for roughly 200BC. (Even further back if the precession was computed using the Aristarchos-Hipparchos-Ptolemy precession of 1°/cy.)

  • sMiles & Miles of Gloriosus:
    Given the obvious weaknesses of his case, BS' dense & mantric repetitions of claims that it's copper-fastened are waaaay over the protesteth-too-much line:
    BS' analysis “uniquely points” to Hipparchos (p.167);
    previous researchers' results “cannot be taken seriously” (p.170);
    [Miles Gloriosus (Imperial General, & basso-pro-fun), in the Plautus-based film-musical, Funny Thing Happened on the Way to the Forum: “Stand aside. I take LARGE steps.” (Nothing new here. Consulting a BS 1994/1/17 self-intro to his evaluation of some questions relating to Columbus' landfall [emph added]: “First, I should establish my authority for being able [to do so]. I received both my S.B. and Ph.D. degrees from M.I.T. and [was then] an astrophysicist at NASA's Goddard Space Flight Center. I have published 71 papers in refereed astronomical and historical journals….”)];
    “I will derive a very confident date” for the FACG (idem);
    FACG is “virtually identical” to Hipparchos' constellations (p.174);
    “my result is very strong and solid ” (p.176);
    “with a very high confidence in the [BS] derived epoch” (idem);
    “we have confidently ruled out all [previously] published proposals” (idem);
    “we can confidently eliminate all … except Hipparchus” (idem);
    perfect match with Hipparchus ” (idem);
    our analyses “all compel us to the [Hipparchan] conclusion …. [which is] consistent with everything else we know about ancient Greek astronomy” (p.179) [hifi-Muffialogic (DIO 1.2 [1991] n.66 [p.111])];
    BS' date (125BC ± 55y) is “a very strong conclusion, with no real likelihood” that it's accidental (p.181);
    all previously published proposals for the origin of the [FACG] observations [!] are easily ruled out with high confidence as a result of [BS'] results” (idem [et idem MilesG]);
    virtually perfect match” (p.182);
    constellation points “can be unambiguously identified” (p.191);
    and, just in case you hadn't noticed: “It is appropriate here to note that this derived date [125BC] is a very confident result” (p.194);
    BS' methods are “definitive” (idem);
    “the derived date of 125 B.C. is of high confidence” (idem).

    Words like “strong” gush out so readily that in BS' late-addition to n.2 (p.195), the description “wrong iconography” is mis-rendered as “strong iconography”.
    [This typo is not the fault of most referees since it's in a late note. Less forgivable is the reference on p.193 to the 13th star in Table 1 (which has only 12 entries), when Table 3 is meant. Had referees checked the paper's statistics (which BS is explaining at this very point), wouldn't said typo have been easily apprehended?] Obvious question: WHO is supposed to have edited this paper? DIO 1.2 [1991] n.6 [p.97]: quotes a 1980 Hoskin-DR exchange. The Editor-for-Life proudly described JHA's lofty standards for how it evaluates first submissions: “Anything considered for publication must, prima facie, be in a state ready for the typesetter”. DR response: “editors who ask for ready-for-the-printer copy upon first submission may give the impression that they are more publishers than editors.”

  • Leroy Ellenberger (the world's top anti-Velikovsky expert) has discovered a potentially-more-revealing item at BS p.174: in BS' list of 9 differences between Eratosthenes and the Farnese globe, difference #8 is simply missing. If something was eliminated here, then: why?

  • DIO's Publisher, DR (Dennis Rawlins) would not referee a paper for JHA if asked (though by publishing criticism ere publication, he's effectively quasi-volunteering anyway), since those running said journal have proven over decades to be semi-competent, bigoted, censorial (DIO 9.1 [1999] ‡3 §F [pp.39f] especially §F8 [p.42]), & not excessively encumbered by integrity. (When DR attempted to provide good advice on refereeing to Hoskin in 1983, the reaction was non-communication plus ex-communication.) And this cult is possessed of such rare bravery that it has religiously attacked physicists R.Newton & DR for decades exclusively in captive forums (where no reply will be allowed), while just as religiously fleeing open debate with them.
    (Man has the wonderful ability to dream, which permits us to imagine seemingly impossible combinations: centaurs, competent-neutral referees at JHA, talking horses, etc. And DIO is already on record as wondering whether one of the more credible of said dreams mightn't someday come true: DIO 8.2 [1998] ‡5 §N [p.60].)

  • So, what follows (starting a few paragraphs hence) is merely what an attentive JHA referee MIGHT have noticed. (If the imaginary centaur can merit a constellation, then possibly the following exercise in alternate mythology can grab a starry piece of sky bye&bye.)

  • Intro to Mythic Ref-Report:
    With p.r.-hype-assistance from the seething popsci-archon clique he has so faithfully served, BS announced at the 2005/1/11 AAS conference his sensational recovery of Hipparchos' long-“lost” star catalog. (Outside the JHA asylum, it's long been known that the catalog was far more completely recovered [all but a few percent] over 400 years ago by Tycho's public perception that subtracting 2°2/3 from the longitudes of Ptolemy's extant ecliptical star catalog would restore the one he stole from Hipparchos. Details elsewhere.)

    BS adamantly declared that the FACG's source was Hipparchos' star-catalog, which had thus been right out in the open for 2 millennia, in pictorial form. In the lengthy analysis in support of the contention, BS connects stars to the limbs etc of various legends & critters depicted on the Naples Archaeological Museum's 2000-yr-old Farnese-Atlas globe. BS elaborately adorned his obviously non-math-based conclusion with pages of impressive-looking math analysis — producing BS' usual Chinese-imperially-STRONG result for the catalog's date: −124(125 BC)±55yrs.
    Thus, from his photos and high-school-trig photogrammetry, BS estimated the positions of 70 stars of Hipparchos' “lost” star catalog.
    [Half of the data have almost no input for determination of the epoch, where only samples [A]&[G] are seriously involved. So one can crudely (ignoring non-gt-circ weighting, etc) confirm BS' 55y epoch-uncertainty thusly: sample[G] is twice as big but half as weighty as sample[A] (12 data); so, effectively we have 24 (twice 12) data, with σ = 3°1/2. Dividing σ by 24's square-root and then by 1°.38/century, we find that the epoch solution will be uncertain by about ±1/2 century.]

    Politics in Standard-Eternal Mode:
    Now, −124 is barely 2 yrs from the Besselian date for Hipparchos' formal epoch (−126.278) induced by DR in DIO 1.1 [1991] ‡6 §D7 eq.28 [p.58]). And BS' induced FACG obliquity is 23°57', which (as for the epoch) is nearer to a DR result than to any other ever published. (DR found 23°56' in the very PASP analysis upon which BS wasted 42pp of bungled Pb-paper denigration in the 2001 Feb JHA. See Publ Astr Soc Pacific 94:359-373 [1982] pp.367-371.)
    [Note that BS' 2001 paper abusively (see DIO 12 [2002] ‡1 §E1 [p.14]) attacked DR for contending that Hipparchos was the Ancient Star Catalog's author. But now that BS finds cause to believe that DR was right after all (and starts promoting Hipparchos instead of Ptolemy as chief ancient star-cataloger and “the greatest ancient astronomer” [BS p.180]), he nowhere cites DR…. But, then, that's about what we have come to expect of the JHA's semi-skilled politician-salesmen, elaborately posing as expert scholars.]
    So, BS' pro-Hipparchos result would of course be extremely gratifying to us. (Especially as DIO 11.1 [2002] ‡3 eq.3 & §D1 [pp.21-22] has produced startlingly unexpected evidence consistent with Hipparchos' authorship [long Muffia-denigrated, despite Almajest 4.2-certification: Toomer 1984 ed. p.176] of the famous and magnificently accurate period-relation: 5458 synodic months = 5923 eclipse months.)
    If valid.
    But is it? Several DR analyses of this question follow.

    The number of blunders in the proffered “data” are a record — even for the pathetic JHA. Some have a sizable effect on the results — rendering BS' “luck” (in getting a solution smack upon H's epoch) all the more amaaaazing: how did BS hit within 2y of the true epoch of Hipp's star catalog by using botched data? Especially since several of these errors correspond to ordmag 1000 years of precession, though BS claims to compute (from such bungle-filled “star”-positions) the precession-based Farnese source-date to within about a 1/2 century.
    Of course, when 70 “stars” are involved, each screwup's effect is proportionally diluted. (The mushiness of the data has a far greater effect on the trustworthiness of the end-product [epoch 125BC] than do the miscues.)
    [To DR, the prime significance of the number of glaring problems with BS 2005 is what it reveals of the JHA refereeing process. Which reminds one: the JHA Editor-for-Life's infantile 1983/3/3 fury and unilateral breach with DR — STILL unilaterally continuing (STILL without the slightest protest from cowering establishmentaryans) — began precisely because DR committed the sin of criticizing His Lordship's refereeing “process”! And, far, far worse — the most unforgivable DR offense of them all: being vindicated. (To cover His shame, Hoskin then spread the [now-at-last-out-in-the-open — and-found-to-be-unsupportable] falsehood that DR had initiated hostilities. Does 24 years of seething and deception constitute some sort of Guiness record?)
    DR hereby thanks the esteamed Editor-for-Life for his magnificent BS 2005 demonstration of just how wrong DR was about ever-alert JHA refereeing….]

  • Is a butterfly-net in order? — to inhibit scholars from falling into statistical homeopathy: polluting their own samples with masses of junk, which can weaken or distort the outcome — or just numerically overwhelm the valid&high-signal data, thereby introducing uncontrollable errors.
    [Statisticians realize that such folly ends in trying to discern relatively-microscopic sag in a probability-function lying atop a towering castle of noise.]
    See, e.g., D.Duke on the ordmag 10 stars that almost entirely determine the outcome of an earlier BS analysis (JHA 2001), though BS pointlessly brought in 8000 more (mostly trivial-relevancy) stars. (For two brilliant analyses of the BS 2001 noise-tower disaster, see Pickering at DIO 12 [2002] ‡1 §§G-H [pp.24-26]; and Duke at DIO 12 [2002] ‡2 [starting at bottom of p.32] & Table 2 [p.33]).

  • Statistical Leg-Pulling:
    Some commentators, esp. Dennis Duke ( have already noted the riskiness of BS' simplistic division of his chi-square by 69 (BS' apparent number of dfs: 70 stars minus 1 unknown [n.23 (p.196) from p.193]), since it assumes data-independence. (By the way, 69 is certainly at least a little too high: the Decl of αHer is involved in both Table 3 star#29 and Table 5 star#65. Likewise for αCar: Table 3 star#45 and Table 5 star#48.) This central point is crucial to the entire paper. Are we, e.g., really to suppose that when the sculptor was accidentally (presaging the JHA by) overstretching someone's leg, the distortion of this constellation's limb had no effect when the sculptor next started in to create contiguous constellations?
    Such considerations typify why DR's own statistical analyses of FACG are so brief and simple — e.g., we will immediately throw out all the stars-not-on-circles (BS' entire Table 5 [p.192]) as effectively valueless, compared to the on-circle stars — which are troublesome enough (for BS, anyway) in themselves.

  • In his present 2005 dreckdata-jammed analysis, BS knows that his chosen dozen on-colure stars (the non-trash stars that are most precessionally-sensitive to epoch, his titular grail) give a result in the early 3rd cy BC! (BS p.189 estimates 280BC.) BS then offers an alibi that is impressively “ludicrous” and “absurd”.
    [To borrow BS' own JHA 32 p.21 [2001] ultimately ironic language, when he publicly sneered at the expertise of DR, who (much more typically than is realized by those who do not know [and do not wish to know] the true JHA-vs-DIO history) had gone to much trouble and expense to try heading off a fight with BS.]
    So much so, that one can't help but sympathize with BS' puzzled disappointment, which alone can explain his explanation: BS falsely complains that a weighting-problem renders “crude” this result from his own best epoch-finding data. (BS&co don't know how to deal with RA precession? This, in a paper whose titular key result is primarily RA-founded….) DR has included such weighting and still gets a similar result from these data (as do other investigators, e.g., K.Pickering).
    DR's weighted solution:
    283BC ± 80yrs [single-datum σ: ]. (Which would [if valid] put Hipparchos' epoch rather too near the 2σ edge of the sample's Gauss curve.) BS either knew that fact (and omitted it) or he doesn't know what he's doing.

  • We have elsewhere remarked the oddity of BS inserting insignificant (magn 5) φGem into his colure-star list. The 1st thing statisticians notice about the BS paper is that, of the 12 on-colure stars, this is the sole star which is to the west of its 125BC colure: check out the dozen C−O residuals atop Table 3 (p.187) — it's the lone negative value. Moreover, it is (slightly) furthest from the mean — φGem didn't cross the solColure until about 185AD! Since no part of either Gem or Cnc touches the FACG solColure, there is no reason to include a star from that region in the sample, so we will throw it out.

  • More Mathematical Innocence:
    DR has yet to see a recent astronomical-history BS-JHA paper which could pass DIO refereeing. The reader is about to understand why.

  • Uses trial&error for task which freshman sph trig can solve immediately, directly, analytically.

  • Seeks mean-square deviation-minima by trial&error or crude averaging.

  • Approaches two-variable case via fixing-one-variable trial, instead of simultaneously. This practice has the potential of seriously misleading a researcher regarding the true uncertainty of a given variable, or (as in BS' JHA 2001 paper) regarding the probability of a specific two-dimensional deviation.

  • Shy (n.20 [p.195]) of computing proper motions (p.m.) miscalling them “negligible”.

  • Hooked on way-oversampling: JHA 2001-2005.

  • Dick&Jane and Hipparchos Get Lost&Found:
    Regarding the Hipparchos star-catalog's supposed “lostness”! The Hipparchos catalog was actually recovered by Tycho Brahe over 400 years ago, when he announced (in the preface to his own 1598/1/2 catalog of 1004 stars: see the standard Tychonis Brahe Dani Opera Omnia [J.Dreyer, Ed.] 15 vols Copenhagen 1913-1929; vol.3 p.337) that Ptolemy had “usurped” Hipparchos' catalog by simply adding 2°2/3 to all its longitudes. [Detection of this theft was crucial to Tycho's discovery of the near-constancy of (and a correct value for) precession.] Simple subtraction of that amount (2°2/3) recovers far more than 70 stars. It resurrects virtually the entire 1000-plus-star Hipparchos catalog — and to an accuracy about 10 times better than BS' claimed reconstruction from FACG.
    So the Hipparchos catalog is only lost to those who have difficulty at the addition-&-subtraction level.
    [AmerAstronSoc-HAD-Doggett-prizewinning but astronomically innumerate Journal for the History of Astronomy Editor-for-Life Michael Hoskin is unquestionably so disabled: see Hoskin's believe-it-or-not (multiply-published) confusion of the addition with the subtraction in this specific 2°2/3 case.
    [In 1997, Hoskin published His magnificent discovery that precession actually goes in the reverse of the direction every previous astronomer thought it did: M.Hoskin Cambridge Illustrated History of Astronomy [Cambridge Univ 1997] p.42. He proudly published it again two years later: see His Cambridge Concise History of Astronomy [Cambridge Univ 1999] p.40. Which may hint at part of the reason why the JHA took decades to finally perceive the obvious regarding Ptolemy's precessional theft of the Ancient Star Catalog.]
    Soon after Hoskin discovered this gem, the Editor-for-Life realized that Great Minds are less likely to be remembered for merely one epochal discovery — so He went for yet another Nobel by rendering positive the retrograde motion of the lunar node (Hoskin 1997 p.35; Hoskin 1999 p.31).

    Meritocracy at the Historical Astronomy Division of the American Astronomical Society:
    Reflect here upon the state of competence and integrity in history-of-astronomy today, as Hoskin and Gingerich select referees and who to publish and not publish in the field's “premier” journal.
    We recall the Hoskin-Gingerich official-guidelines for doing JHA-acceptable history (DIO 1.2 [1991] n.36 [p.104] or JHA 11.2:145 [1980] p.146): “It is, needless to say, a mortal sin to judge the past solely in the light of the present and to hand out medals to those who ‘got it right’.” (Here, this translates into: moderns can't condemn an ancient's plagiarism. Often parroted in the OG circle; see, e.g., Sky&Tel 2002 June p.12 headline, and JHAAssocEd-Evans: L.A.Times 2005/3/30.)
    It seems that Muffia ancient-historical-hero-ranking, JHA-board-promotion criteria, and the AAS-HAD's Doggett-Prize committee have for years cohesively been taking such precious reasoning to the next just-as-logical step:

    systematically handing out medals to those who got it wrong.

    [The 2002 Feb Sky&Tel noted that at that time the hottest controversy in history of astronomy had been over the Ptolemy star catalog. The modern debate was ended by analyses conceived by (the late) R.Newton (1977-1983), D.Rawlins (1982-1994), G.Graßhoff (1986-1990), K.Pickering (2002), D.Duke (2002). Not one of the dozen papers here referred-to was published in the Hoskin-Gingerich-Evans “premier” journal for the History of Astronomy. (Which instead obsessively opposed the truth to the extent of over 100 [usually Pb] pages of pseudo-astronomy.) Many were published in Rawlins' scientifically superior DIO — which the HAD tries to pretend does not exist, while showering the dim losers with honors.
    All with the evident approval of the American Astronomical Society.]

  • Vultures & Voltaires:
    Press reports have indicated that the BS-Gingerich combine is now — on the basis of BS' “new” result — allegedly “re-thinking” (Gingerich) their cult's former adamant 30yr denial that Ptolemy took the Ancient Star Catalog from Hipparchos.
    [OG's “re-” is debatable, but one must note that it is more admirably humble than anything BS has ever said.]
    Comment: of the dozen now-standing proofs showing Ptolemy's plagiarism, this is the weakest — for the excellent reason that, since its titular contention is baseless, it is irrelevant to the Hipparchos-vs-Ptolemy Catalog controversy. But since the JHA gang thought of it, said clique will now take (not to use a stronger word) credit for proving what has been perfectly plain to virtually all competent astronomers for centuries. JHAvolk's position appears to be: OK, OK, so R.Newton-DR published firm evidences of Ptolemy's theft decades earlier than ours, but those were not Convincing-to-Us, so — they don't count. (Neither's name is even mentioned when BS p.180 [or BS & Gingerich's various recent public semi-conversions] discuss the Farnese globe's alleged relevance to the ex-controversy regarding authorship of the Ancient Star Catalog. But, then, one can see how suppressing recognition of others' genuine foresight by come-lately-grabbing credit for those scholars' hard-earned pioneering-induction conclusion is conveniently allowed [not to say encouraged] by the JHA's pompous “principles”, quoted at DIO 1.2 [1991] n.127 [p.125], with the DIO comment: “Academe's vultures know their business.” By the way, see also ibid n.128. Isn't the delusional We-are-the-arbiters-even-when-We're-wrong-30y-straight arrogance just precious?)
    Questions: Does the non-convincing reflect on the prior proofs' validity? Or on archons' perceptiveness? Is the BS' Farnese announcement's lesson that: archons need pretty pictures to finally comprehend the long-obvious truth of the Ancient Star Catalog controversy?! Was BS' idea here to render a case for Hipparchos' authorship at the old Dick&Jane kindergarten coloring-book level, to assist history of astronomy's mentally-lost-child archons?

  • [A few days after composing the foregoing guess (and months after posting [2004/9/26] an earlier one) that JHA will try to usurp credit for proving the very proposition (Ptolemy's plagiarism of Hipparchos' Ancient Star Catalog) which it had religiously denied, during decades of suppression, exile, and slander (of those whose competent and definitive researches multi-proved the point years ago), DR came upon the following quote from the JHA's O.Gingerich
    ( — emph added): “There has long been a debate whether Hipparchus actually had a star catalog or at least what its nature was. [BS]' work shows that evidence was there all the time, but it required the proper expertise to decipher it.”]

  • With a nod to Voltaire's famous cryptic remark, DR cannot help but suspect that if a sudden JHA Hipparchos-was-the-cataloger-after-all-and-WE-proved-it pseudo-discovery hadn't conveniently come-along, it would have had to be purposefully invented. (Classic archonal behavior, satirically delineated-predicted long ago at DIO 2.1 [1992] ‡1 §K2 [pp.10-11]. Prior analogous grab-try: DIO 1.2 [1991] §§I7-I8 [pp.131-132].) By the time of DIO 11.3 (publicly circulated in 2003 June), the Gingerich&co Ptolemy-was-The-Greatest gang had been driven from denying Ptolemy's frauds and were now instead defending Ptolemy's he-had-to-do-it resort to these (formerly non-existent) frauds. Thus DIO 11.3's sardonic cover (Are Ptolemy's Apologists Right …. Are Admittedly Fabricated Data THE GREATEST ASTRONOMY?) and prefatory comments to DR's article on Ptolemy within (“Nobody's Perfect”: pp.70-90) all of which finally impelled even the most cemental cultists to abandon the sinking Ptolemist ship:

    Can [R.Newton]-DR be accused of cruelty to dumb animals, given the tightness of the evidential vise they've closed on the poor [Ptolemy defense-corps]? To watch prominent scholars thrashing about in such pathetic credibility-death agonies is akin to viewing Animal-Rights films of stoats caught in spring traps — trying to weasel out.
    Scholars who wish never to find themselves in the excruciating & logicbending position of Believers who've spent decades cornering themselves into having to keep forever alibiing Ptolemy's Venus, stellar, & etc pretensions, are urged to ponder DIO 10 [2000] … pp.83-84 [on data-sensitive foresight, vs where ignoring discomfitting evidence leads]. Watching Muffiosi forgive sin after Ptolemy sin, [Barbara] Rawlins recalls [the classic 1959 film] Some Like It Hot's finale: in-love Osgood hitch-pitches in-drag “Daphne”, who reluctantly protests that “she” smokes, dyes, is barren, etc, etc. But Osgood forgives all. Desperate, Daphne finally [rips off “her” wig and] bellows the ultimate impedimentum-crucis-bomb: “I'M A MAN!!!” Osgood: “Well, nobody's perfect.”

  • Decades ago, an extremely well-known paper by H.Vogt (Astronomische Nachrichten 224:17-54 [1925] — extensively discussed in, e.g., O.Neugebauer's famous History of Ancient Mathematical Astronomy [Springer 1975] and Graßhoff's History of Ptolemy's Star Catalogue [Springer 1990]) analysed data in Hipparchos' Commentary (his sole extant work, which we are commonly abbreviating “HC”), to carefully reconstruct the positions of 122 stars from Hipparchos' famous catalog of stars. Again, both the number of stars and their accuracy far exceeded anything BS is even claiming.
    [The 1894 translation of the Commentary (into German) by Karl Manitius has long been the standard one, and it ably pioneered the identification of the hundreds of stars Hipparchos cites. (BS fatefully appears completely unfamiliar with this central source. [Commendably explicit confirmation of this DR suspicion appears at Schaefer JHA 35.2:161-223 [2004] p.217.]) But the work may soon be superseded in some respects by the upcoming highly useful edition in English being prepared by Brigham Young Univ's Roger Macfarlane, with able technical assistance from Paul Mills. DR is extremely grateful for Roger Macfarlane's 2002/9/10 transmission to DIO of a pre-publication typescript copy of this important and welcome contribution to the field — which was of repeated utility during development of the present analysis.]

  • Slightly obvious question: since BS is (p.173) justifying his conclusion by comparing the (positionally crude) Farnese globe of non-stars to Hipparchos' un-new (and positionally precise) Commentary, how can he be aggressively advertising his result as a New&Improved discovery of Hipparchos' stars?!

  • Which brings us to the strangest source-omission in the BS analysis. Most FACG circles are equatorial: right ascension (RA: east-west) and declination (Decl: north-south). Since the BS conclusion is based entirely upon stellar precession, and since on average his stars precess much faster in Right Ascension (RA) than in Declination (Decl), the FACG's most epoch-information-bearing on-circle points are those falling upon the four colures. Yet (unlike Thiele 1898) BS seems oblivious to the “Hour-Star” list provided at the Hipparchos Commentary's very end (did busy-BS just not read that far?), specifying stars on those very colures: Commentary 3.5. [See also HC1.11.9ff.] Indeed, given that BS 2005 is a bulky study of a globe marked primarily in equatorial coordinates (RA & Decl) it is striking that the very word “hour” (the same unit which Hipparchos' Hour-Star list used for quantifying RA) appears nowhere in BS 2005's 30pp.

  • BS hasn't posted photos of half the globe, and the photos he has posted do not include the one he computes with as a (p.182) “worked example”. (This despite saying [p.171]: “I will here present a detailed example, with all intermediate values presented. This will allow researchers to test my procedures and to see typical values, and will provide a known example to check later applications.”)
    Such practice is consistent with his already-cited omission of place-citations for almost all of his references to Hipparchos' Commentary.
    [Suggestion: the Macfarlan-Mills translation provides only a smattering of such info. Manitius gives full sectioning, but BS never consulted it.]

  • Antarctic Circle and Proper Motion:
    BS 2005, like BS 2001 (another massive JHA mis-fire), again refuses to compute stellar proper-motion! — and p.m. is, after all, slightly relevant to a study based upon stellar positions. In extenuation, BS 2005 says (n.20) that the effect is too small to matter. Comments:
    [a] This is not true regarding the AntCirc, due to the unusually large p.m. of αCen, which affects the AntCirc result by ordmag a century: DR's 2-variable least-squares test (upon the 3 AntCirc stars) finds
    Decl −52°.5(+) ± 0°.5(+) and epoch 170AD ± 120y;.
    (Compare to parallel ArcCirc result, above.)
    But without p.m. (as BS strangely appears to prefer), it's
    Decl −52°.5 ± 0°.9 and epoch 210AD ± 200y — a 4 decade difference in epoch, not to mention affecting the Decl σ by nearly a factor of two.
    [b] BS omitted p.m. previously (in his big 2001 JHA paper), which suggests that he's simply had trouble figuring how to compute p.m.
    [By contrast, Evans' vain 1987 JHA attacks on RN&DR were at least quite solid on p.m., doing it (better than DR 1982) in 3-D — as well as (compared to BS) computing extinction both more scrupulously and using less indefensible opacity-extremes.]
    [c] As Hoskin should know as well as anyone, p.m. is not random noise: a scientific pioneer Hoskin & DR share an affection for, Wm.Herschel, profitably showed otherwise 2 centuries ago — when he announced the direction of motion of the Solar System among the stars.
    How did six JHA “referees” let all this pass?
    [Among those most eagerly asked by BS-JHA to referee the paper were probably the usual unusuals (assuming JHA itself was involved at all — beyond just turning over referee-choice to BS himself): primarily Gingerich, who publicly, paternally, and proudly plugged BS' upcoming 2005/5 JHA Farnese paper in the NY Times [2005/1/12], as well as L.A.Times [2005/3/30; see this article on-line, a familiar S.Cal press-agent-style-bigwetkiss-buildup for BS: “behind that mop of blond hair and the twitchy mannerisms …. a twinkle in his eye” — all of it charmingly accurate, it should certainly (and warningly) be noted]. L.A.Times relayed a JHA official's old-ritual Ptolemist defense of plagiarism — suggesting plagiarism was OK in antiquity — in the typical JHA-cultist fashion of rote-plagiarizing each other's plagiarism-alibis, rather than: [a] just common-sense-musing upon how well a let's-all-steal-from-each-other society would function; [b] consulting what extant ancient documents actually say about plagiarism (DIO 1.2 [1991] n.156 [pp.131-132]); or [c] asking oneself where in the 1st place one ever got unqualifiedly-locked-certain onto such a whacko alibi for establishmentaryans' insanely-Ptolemy-worshipping 3-decades.]
    Some of the effects of p.m. are non-trivial in size; though minor for the full 70-star experiment, p.m. is certainly non-ignorable for αCen, where BS' Decl error (from omitting p.m.) is worth decades of motion and nearly a factor of two in Decl's σ. As for αCen's RA (actual, not FACG): BS' Table 5 Hipparchos-era computation is correct for the time of Eudoxos!

  • Though BS rightly concludes (p.191) for symmetric distances for tropic & polar circles (obliquity & latitude), he does not merge these data for a combined 2-unknown least-squares. [Merging is helpful, because solving for the AntCirc's epoch and Decl simultaneously — using just 3 stars — leaves but one df!] So we will next do so, pooling all the ArcCirc and AntCirc stars into one sample, solving simultaneously for the mean polar-circle-size (FACG's implied latitude) and epoch that best satisfies the entire polar-circle sample. Merging the three agreed-upon AntCirc stars with our cleaned-up ArcCirc sample of 5 stars provides an 8-star sample, yielding:
    colatitude 51°.5(−) ± 0°.4(−) and epoch 130BC ± 90y.
    (Note: this implies a latitude very slightly nearer 39°N than 38°N. In any case, it's obvious that neither value is eliminated from consideration.)

    If instead we look for the same variables from BS' north and south polar-circle data (minus non-star χPer), the results from this 9-star sample are:
    Decl 52°.1 ± 0°.7 and epoch 300BC ± 170y.
    Ignoring proper motion alters things to: Decl 52°.1 ± 0°.8 and epoch 290BC ± 180y. (Rounding has obscured an 18y difference in epoch: p.m. vs no p.m.)

  • [Note: One might argue that the southern sample of 3 is too small to allow enough choice for their mean −52° Decl to be significant. If we take this view, then the ArcCirc becomes the prime indicator in latitude. But, if it was constructed so that its size would match that of an AntCirc built on 3  bright stars, then its position too could be meaningless. Whether or not this line of reasoning is convincing, it needs to be mentioned here.]

  • Groping-in-Boundary-Space for Obscure Stars:
    BS' sample includes too many dim stars that are not in Hipparchos' Commentary (some that ought to be if he used them) — some not even in Ptolemy. One among several examples we find in Table 3 star#21 (“Between Pegasus and [western] Fish”): 55Peg is supposed to help fix FACG's Equator. The star's magnitude is slightly dimmer than 4 1/2, and it's unmentioned in any extant ancient catalog. So why use it as part of an argument that FACG must be based upon an ancient star catalog?

  • The choice of 35Cnc as p.187's Table 3 star#25 (“Middle of Crab”) reaches past even this paper's usual weirdness-bound. The star is magn 6.57 — so, even when overhead it would appear (through one of BS' JHA 2001 atmospheres, at 0.23 mags/atm), to be nearly 7th magnitude (6.8).
    (Shades of the still-BS-unmet problem of how Hipparchos saw γAra through that same old thick atmosphere BS used to insist upon.) Astronomers might at 1st glance assume that this must be just a way of locating the mass of dim stars in Praesepe the Beehive; but it's not. This star is well outside Praesepe (to the west) and is simply invisible in practice. There was no brighter star nearer the middle of Cnc's central quadrilateral which was nearer the TropCnc — but the star is supposed to be chosen not from that criterion but from the FACG, where we instead find that since Cnc is symmetrically placed on the FACG Ecliptic, Cnc's middle is roughly 1° south of the TropCnc; so the apt-choice star would be in Praesepe: 41εCnc. It's dim (magn 6.29), but part of the visible Beehive. (The Decl difference here is tiny, but procedure is what matters.)

  • This is one of so many aspects to this paper that suggest the zany hypothesis that it could be just a BS prank (among BS' several virtues is a jolly sense of humor) — perhaps to pull some folks' legs, or to prove what DIO's been saying for years about JHA refereeing. (If BS just dodges meeting the mass of serious screwups in BS 2005, then the prank-hypothesis will be strengthened, and — as with his unretracted 2002 Feb Sky&Telescope false-rumor slander-relay — the matter will turn into another deliberate deception. After nearly 80pp of 2001-2005 BS kwasi-science and just-pwain-kwasi false personal slander on the Ptolemy-Hipparchos flap in JHA and Sky&Tel, we learn [L.A.Times 2005/3/30]: “The [H-vs-P] feud holds little interest for [BS], who has moved on.” — which appears to presage a classically slippery hit&run archonal-gofer routine.)
    But give due credit: the JHA reffing in this case is a bigger hoax than the paper can ever be.

  • As usual, BS goes for a tight standard-deviation (σ) by bombing his sample into submission via lots of junk-stars (with acknowledged 5° scatter [pp.192&193]), when only on-circle stars are needed and could possibly be reliable enough to use in an analysis which is trying to get a precessional result accurate to about a half-degree.
    [BS p.193 says that the Table 3 on-circle data get mixed-in with the Table 5 slop, according to an assumption of mean-single-datum σ = 3°1/2 (p.189) and 5° (p.192), resp. Yet for the on-colure stars, the former σ matches only if the stars are computed for BS' 125BC. If the date is left as an unknown to be solved for (which comes out at 283BC), we find that σ becomes just . Further, if one eliminates such outliers as the (at best) worthless φGem, then the sample's σ drops much more — adding yet another suggestion that each of the on-colure stars' weight should be so much higher than that of the Table 5 trash-stars, as to make the latter ignorable.] A few solid stars will give a better result than lots of trash ones. All analyses of on-colure stars lead to a date (for FACG) ordmag a century earlier than 125 BC. (See BS' own rough 280BC result at his p.189.) BS knows this. Nonetheless, he says (p.194): “The selection of various sub-samples of the data still yields the same [125BC] date” — only partially & parenthetically tossing-in the fine-print: “(to within the quoted error bars)”, fine-print which we here complete: to barely within the quoted error bars), error-bars of a partially-worthless on-circles sample (error-riddled Table 3) plus an obviously incompatible and totally-worthless off-circles 23-star trash-sample (Table 5: non-independent and error-riddled data).

  • How Homeopathy Happened-upon Hipparchos'-Heyday:
    Before analysing BS's slag-heap, we must not forget to exorcise Aries the Ram, as promised, by restoring the correct sign for αAri's Table 5 RA (5°.6, not p.192's −5°.6). (This shifts the Table 5 sample's indicated date forward by several decades, vs where BS' figures would have put it.) DR's weighted least-squares test upon the corrected Table 5 yields:
    21AD ± 88yrs (single-datum σ: 5°).
    This way-out result, based upon the 23 “stars” of Table 5 [p.192], appears right-off to be statistically incompatible with the result from BS' on-colure dozen (top of Table 3 [p.187]), 283BC ± 80yrs from 12 data: a 303y discrepancy in the means. The incompatibility is especially odd in the context of repeated references (e.g., p.192 & n.22 [p.196]) to good-Gaussian-distributions.
    [In fact, if one graphs the dates when the on-colure “stars” were at BS' positions for them, the distribution hardly looks Gaussian. Nine of the dates bunch close together between −389 (pPup) and −138 (31ηCMa) — a range of ±c.75y— while three outliers all are at least 430y from the mean — i.e., all three are more than 5 times further from the 9-star-mean than the outermost of the nine. (For the errors in RA degrees, the ratio is about four, as one can easily see by checking out the top 12 “stars” in Table 3 [p.187].) Any experienced statistician would immediately jettison all three data. The solution for the remaining 9 stars: 253BC ± 31y.]
    Regardless, both samples get pooled together (p.176 & n.23 [p.196]): at about (p.193) a 2-to-1 weight-ratio per star — which (as just noted) should be much higher.
    Since the parallel-circles stars (Table 3 stars#13-47: Equator, tropics, & polar) precess so relatively slowly in Decl, the on-colure (Table 3 stars#1-12) and trash stars (Table 5 stars #48-70) dominate the arrival at an epoch solution; thus we see that BS has found his Hipparchan epoch by smothering sample [A]'s 12 possibly useful data (indicating c.280BC) with sample [G]'s 23  worthless junk-data (indicating several centuries later), where by an odd coincidence each sample happens to have virtually the same net weight. (About twice as many trash-stars, each with nearly [BS' math quietly makes it exactly] half the on-colure stars' weight.) So, crudely averaging both dates, we find roughly Hipparchos' era, which tells us that homeopathically watering-down (with junk-pollution) the indication of the only potentially worthwhile sample has dragged the non-Hipparchan on-colure 283BC (−282) result most of the way (forward in time) towards the eventual happy-Hipparchos-hit at 125BC.
    [If (temporarily reverting to overprecision) we combine just samples [A]&[G] (the only data with much influence on the epoch-solution: BS p.189) with BS' weighting, we find:
    epoch 149BC ± 66y.
    (After Aries-flip-exorcism:
    epoch 126BC ± 66y.)
    If on the other hand, we use exclusively the 35 “stars”-on-parallels (i.e., every “star” except those in samples [A]&[G]), and solve simultaneously for all 3 unknowns, we naturally find slack limits on epoch:
    epoch 30BC ± 150y      colatitude 51°.9 ± 1°.1      obliquity 23°.8 ± 0°.8.
    (Solving for epoch alone, holding the other two unknowns at BS' values still yields: 30BC ± 150y.]

  • Merging such differently signalling samples is obviously weird (or transparent) procedure. Including p.m. and αAri sign-correction (to reflect accurately the exact implications of BS' chosen data-points), let's test for compatibility of the two samples ([A] on-colure stars#1-12 vs [G] trash stars#48-70) which are the dominant determiners of epoch; applying the t-test, with 33 degrees-of-freedom (12 + 23 − 2):
    t = |−28221|/{(1/12 + 1/23)×[12×11×802 + 23×22×882]/33}1/2 = 2.24

    Thus (for 33 dfs), the two samples' incompatibility is significant at approximately the 3% level.
    [An ingenious colleague (D.Duke) prefers simply investigating dates: find the date when each star of each sample is at the FACG position. This is a neat and usefully illustrative approach. Only slightly imperfect because the best solution attempts to minimize the sum of visible great-circle errors; but for the on-colure stars, a best-mean time is not linearly related to a best-mean-angle.) If weighted for the square of cosβ, this procedure yields pretty accurate dates, but with rougher σ.]
    I.e., just jamming-together-and-averaging two differently-signalling samples to get a Hipparchan-epoch result somewhere in the middle appears to have been unjustifiable: the odds are roughly 30-to-1 against Tables 3&5 having both been drawn by chance from the same hypothetical astronomer's data.
    And, forgetting statistical fine-points: the barest glance at such disparate samples (whose means are over 300y apart!) would give most researchers paws — to tear up this strangely-conjoined sample and think afresh.

  • Statistical Rad-Mastectomy:
    Just how misleadingly trashy the trash-data of Table 5 can get is illustrated by effecting breast-removal.
    Dropping BS' hilariously-misplaced (and mis-identified) backward-boob→nape-“star” αCas, we find via least-squares:
    51AD ± 83yrs (single-datum σ = 4°1/2).
    Repeating the above t-test, using these values for Table 5, we find t = 2.58 — which, for 32 dfs is significant at nearly the 1% level.

  • DR's prime statistical maxim:
    A small clean sample is always preferable to a big dirty one. (DIO 4.1 [1994] ‡3 n.49 [p.46].)
    [And over-sampling's dirtiness-problem is not always due to bad data: see above.]

  • The Emperor-of-China NoiseTrap:
    The foregoing bears on a BS pattern. As in his 2001 JHA 42pp mega-folly: BS throws in lots of noisy data (esp. Table 5) to artificially shrink the inverse-square-root of N (N being the total number of data used), thus pseudo-lowering the formal error-of-the-mean.

  • Statistical Morals:
    [a] Doing statistics requires clean samples and clean conscience.
    [b] Prefer sample-cleanliness to sample-size.
    [c] A common stat-sleight is betrayal of the random-basis of one's formula. I.e., no statistical study is better than the integrity of its perpetrator. (So: can academic pols' stats ever be trusted?)

  • This leads to a bit of an aside (as if that's unusual here…), the relevance of which the (rare) non-skimming reader can judge.
    One notes that BS fails to cite DIO 12 and its meticulously complete K.Pickering and D.Duke refutations of BS' huge 2001 JHA anti-Hipparchos paper, which BS' present 2005 Farnese paper continues (by citing his 2002 Sky&Telescope promotion of it) to pretend is serious science. Nor has he corrected his utterly gratuitous archon-kissing 2002 false smear of DR, which any scholar (who so quickly discovered that his alleged evidence did not exist) would immediately retract. Instead, he unqualifiedly cites (n.17 [p.195]) — as an accurate history of the modern Ptolemy controversy — the very article containing the smear. (BS' ugly — and immediately JHA-rewardedSky&Telescope 2002 Feb p.40 attempt to puff the JHA as a Bigger journal than DIO naturally avoided discussing whose board obviously contains the better scientists. BS' alluding to journal-size tells us little more than that inferior scholars will always outnumber superior ones.)

    The Brainkisser's Brainkisser:
    Realizing all too well what will become of his scholarly reputation when his power is gone, perhaps aging ultra-notorious archon-kisser-extraordinaire Gingerich believes he has found in BS his post-retirement eternal-Flamekeeper. (As earlier did O.Neugebauer, when he replaced in his affections scholarly sometime-dissenter G.Toomer with careerist Noel Swerdlow.) Launching BS into national prominence could ensure said Flamekeeper's lasting influence. Self-answering question: what quality of scholar signs up for such duty?
    [DIO 10 [2000] end-note 21 [p.105]: sacred-tenet-obsessed careerist academic archons hide “behind the squid-ink ‘research’ of the kind of scholar who figures that (DIO 4.3 [1994]) ‡15 §A3 [p.120]) the side with the most money is the one that's right. And each paymaster-archon is so limited that he can't even tell who'll be a non-embarrassing hired gun and who won't — not realizing that in science it's hard to find&entice capable ‘consultants’ or dupes, because the very best scientists are so self-confident and established that they aren't for sale. Those who dwell in perpetual intellectual and moral twilight cannot of course even begin to understand this. But when one is so detached from the real world — even while perversely supposing that distorting reality is practical-realistic — a tragedy of eternal frustration is predetermined. (Analogously, see DIO 7.1 [1997] News Notes n.3 [p.2].) Truth can be rented but not bought.”]
    Similar question: is this academe, or American-Idol-hype-agentry? Whence cometh the determination in certain quarters to laud and protect the Ptolemy Controversy's longtime Prince of Dorkness from the reckoning he thoroughly deserves — for the scholarly blood he has caused to be pointlessly spilled for over a third of a century of slander, banishment, and censorship aimed at competent, productive contributors, while politico-selectively promoting rigid & one-track-blindered crankish folly (DIO 11.3 [2002] ‡6 n.23 [p.75]), masquerading as judicious scholarship?
    A community which wastes and drains legitimate scholars' labor and enthusiasm FOR DECADES by insulating itself from the impact of evidence (when many of the issues could be cleared up IN MINUTES by non-cowards) — all to protect archons from mere admission of error (a passing & trifling embarrassment to genuinely able and honest scholars) — inevitably discourages, kills-off, or exiles creative people and will not only result in an ultimately profitless community (see John Stuart Mill at DIO 4.3 [1994] ‡15 §J4 [p.138]) but, additionally, one which becomes as insane and hostile as any other party or entity that systematically rejects unwelcome data. (Is protecting-stroking the vanity and pettiness of a few pretend-editors really more important than such deeply and durably poisonous factors?) Archons' current retreat-strategy is aiming, with typical self-centeredness, only to maintain the hegemony of the very same parties that knowingly and persistently-for-years committed such offenses against academic ideals. Will it succeed?
    (As to those responsible: one of course wishes to recognize their positive contributions to the field [even though they are themselves constitutionally incapable of returning such fairness]; but that should not prevent an open, remedial, & cleansing recognition of the immense damage caused by careerism's near-exclusive primacy.)

  • Bigness at S&T:
    The article's predictable but fantastically-inverted general-extrapolation-conclusion (grievously-abused-Establishment-reluctantly-reacting-to-intolerable-rebels) is the explicit and cohesive Big Lie that is the article's Message — which of course earned instant boardship at JHA — dwarfing in import the BS attack's personal particulars on DR & DIO, and proving that BS is more expert at modern mythology than ancient. For the truth on the broader subject of Neugebauer-Muffia vitriol (much of it greatly pre-dating DR's Ptolemy-Controversy debut), see DIO 1.1 [1991] ‡1 §§C4-C7 [pp.7-8] (of which fake-balanced BS [S&T 2002 Feb p.40] naturally quoted only §C4); DIO 4.3 [1994] ‡15 §C2 [p.123]; DIO 11.2 [2003] p.30 n.3.
    In neither case can BS acknowledge that he produced false results. Nobody at the scientifically-insecure JHA can. See catalog of over 40 unacknowledged Muffia muffs at DIO 4.1 ‡4 §A [p.48]. [Forty-plus often incredible scholarly foulups in the Journal for the History of Astronomy alone are listed in a partial catalog of such elsewhere here; indeed, there are a comparable number of botches just in a single JHA paper, namely, the BS Farnese paper examined in the present satire.]
    [While JHADists and Muffiosi keep pratfalling all over the place, they are (while dishonestly admitting virtually none of their own mountain of muffs) simultaneously good-defense-diversionally charging that Ptolemy-skeptics are incompetent bunglers. But when asked to back the charge, they just flee:
    DIO 6 [1996] ‡1 n.26 [p.7]: “Princetitute-supported slander-scholarship continues (e.g., [Britton 1992] p.xvi) to bluff-suggest that dissenters' work is massively error-riddled — but, when challenged … to reveal the purportedly enormous List-Here-in-My-Hand of actual heretics' errors, Muffiosi have for years stayed as secretive as Joe McCarthy.”
    Cited at this point was DIO 1.3 [1991] n.252 [p.161]:

    [Britton 1992 p.xvi's] unsubstantiated claim of “errors scattered throughout Newton's work” …. offers the usual Muffia capo gotta-go-now excuses for not providing “extensive references” to RN's allegedly copious … errors. The same Muffia pretense to apprehension of scores of serious RN mistakes has been going on for over 20y: [Swerdlow American Scholar 48:523 (1979)] p.530 says the very few RN errors he alleges “could be multiplied twentyfold”. DR's 1979/10/26 letter forcefully challenged NCS to prove it. NCS instead just repeated himself unquantitatively at [JHA 12:59 (1981)] p.61, still refusing to substantiate the big lie. (Instead of multiplying exposures of RRN errors, Swerdlow multiplied big lies: in 1989, he told a local reporter that DR's work was “crazy and full of mistakes”. NCS hasn't been able to substantiate a jot of that slander, either — and why should he, when its purpose was not knowledge-advancement but Swerdlow-advancement. And it works.) See DIO 1.1 [1991] ‡5 n.6 [p.38]; also DIO 2.3 [1992] ‡8 n.61 [p.113], which directly replies to repeated unbacked BigLie-charges of RRN&DIO massive errors: “the Muffia klan has simply been bluffing in this regard”, especially with respect to its capos' (unwritten) slanders against DR's accuracy. But Hist.astron's brave & just leadership still hasn't required that  decades of Muffia libels be made good. (Or noticed which parties' outputs actually are full-of-mistakes.)] (Compare Newton's frankness to Toomer's … behavior when upset by the very same problem: altered number-basis.) Thank heavens for NCS' alertness. Without the Muffia on guard, why, academe might become corrupt.

    When the same brave warriors charge DIO misbehavior, the same perverse truth emerges (DIO 11.1 [2002] [p.2]):

    Never in its 60y history had S&T run such an ad-hominem attack upon a capable astronomer. Worse, its dirt was based on documents it hadn't even consulted, merely echoing Gingerich's gossip instead. S&T pretends to possess an abusive, war-starting DR letter to J.Hist Astron's M.Hoskin, but MH is loathe to release it publicly (despite DIO challenges to MH-S&T), since DR's letter triggering MH's abusive 1983/3/3 rage (charging a “damned lie” by DR & intimating libel-suit & ostracism: trifles omitted from [S&T's sly&]telescoped story!) was just sympathetic but pointed constructive criticism. (DR's “lie” was that refereeing of a misbegotten 1982 Oct JHA paper was poor; but, to JHA's chagrin, after unhinged MH's 83/3/3 tantrum, the paper's memorably honest author agreed with DR [on math & reffing], and re-computed his main results: 1984 June JHA.) S&T went on: DR's “abuse” was revenge (classic projection-fantasy) for JHA rejecting a 1982 DR paper, a paper in fact recommended by both JHA refs & JHA-accepted (see JHA ad: 1982/3 Isis and Isis 73:262 n.14). But again: S&T silently lies low, after DIO requested the date of JHA's “rejection”.
    Familiar act: bully-attacking heresy with here-in-my-hand hidden documents. After 4y of 1950s terror, the Senate censured witchhunter Sen.McCarthy. But, faced with S&T's inverted (DIO 11.2 [2003] n.7 [p.30]) fable-smear: the understandably ethics-committeeless AmerAstrSoc & its HAD (HistAstronDiv) simply hid.]

  • Further on Referee Nullity:
    BS repeatedly confuses Observed−Calculated with C−O (p.193), specifically: confuses O−C with C−O for Table 3 then reverts to normalcy for Table 5. Says at p.193 that the data-“points” from FACG “constitute the observations” (to be compared to modern calculated places) — yet further up on the same page he says the calculated values are the observations. (How did six referees miss an item this elementary? — assuming that any one of them checked anything….)

  • Out-of-Context Becomes Refined to Out-of-Sentence:
    Why is BS promoting his vaguely-based epoch-solution over his solidly-based latitude solution? BS ends up hawking the former result as more accurate than the latter. (Note the BS-paper's very title.) And then tries to throw the latter away. As part of his bizarre attempt to muddy the context and thereby stomp out his own latitude solution, he claims (p.173) that Hipparchos used an Arctic circle of radius 37°. This astonishing error is even repeated at p.177: colatitude 53°. But in both citations, BS leaves out the key OBVIOUS condition: in Hipparchos' Commentary (1.11.8) Hipparchos openly states (should he even have had to? — for anyone smarter than the JHA volkflock) that the 37° figure applies not to himself at Rhodes but to Athens which H (wrongly) believed was at 37°. (Note: so even if the Farnese globe's hypothetical source-globe was created for Athens's latitude [actually 38°N], the 37°-vs-38° discrepancy argues against H being the creator.) Hipparchos of course adds (also at Commentary 1.11.8) that at his own Rhodes, the figure is 36°. Understand: Rhodes' latitude is specified as 36° not just on the same page as the Athens statement which BS has taken out of context, not just in the same paragraph, but IN THE SAME SENTENCE.
    The Macfarlane translation of this sentence (HC1.11.8): “But in Athens the ever-invisible circle is about 37° from the Pole, while in Rhodes it is 36°.” See the same thing in German at Manitius 1894 p.115, or in Greek at idem p.114 lines 24-26.

  • Accuracy Sentenced Again:
    Regarding his latitude-dilemma, detecting BS' pro-Hipparchan selectivity doesn't even require source-checking when he says (p.177) in consecutive sentences that his latitude-solution would “likely rule out” Mesopotamians as far north as 36° latitude, but “is not greatly inconsistent with Hipparchos in Rhodes (36.4°).” At this rather delicate point, one can readily understand why BS 2005 never cites DIO 4.1 [1994] ‡3, which provided coherent statistical evidence that Hipparchos' star catalog was observed at two sites, latitudes 35°.9 and 36°.1. In any case, in accepting Hipparchos while rejecting Mesopotamia at 36°, BS-alibiing is cutting it pretty fine here.

  • Wriggle as he mightily tries, BS can't rationally explain-away the equality of radii of ArcCirc & AntCirc, which (if one accepts BS' globe-distortion factor [and DR is sympathetic to the idea, if not necessarily BS' precise coefficients]) positively proves that [a] the globe was created for the non-Hipparchan latitude 38° — (a conclusion also consistent with HC1.11.5's Decl for Cas' feet), and [b] atmospheric extinction was disregarded by FACG's source & creator. (Item [b] is obvious from the marble, regardless of the distortion's acceptability.)

  • Several features of this paper make checking it difficult:
    Tables 1&2 analyse a photo taken at 6ft or about 183cm, yet that photo is not among those which BS reproduces (photos 1&2 [pp.168&169]).
    Nor does he provide the distance D for either of these two, which impedes the reader's ability to check anything.
    Also, BS only rarely cites the section of Hipparchos' Commentary he is quoting or drawing data from. It is remarkable that any academic journal (outside of the FACook Society's) would publish a paper whose material was so poorly referenced.

  • Are we taking the FACG circles too seriously? — (see Valerio op cit p.104's understandable salt-grain comment) — and over-assuming that figures correlate with stars?

  • BS p.192 Table 5's star#70 guess-uses αLyr (Vega) as Lyr-shell center (which Vega's nowhere near in HC), getting an 0°.4 fit to Hipparchos' era!
    [Note H's error at HC2.5.6 in supposing that εLyr rose before αLyr; at H's epoch & latitude, the latter rose nearly 1/10 of an hour before εLyr. (This error may just be from sloppily mis-supposing that the northernmost Lyr star [εLyr: HC1.11.2] would have to rise first.) To see εLyr rise 1st in the northern hemisphere in H's era, an observer's north latitude would have to be roughly between 47°— & 51°. If this is not a Hipparchan error or appropriation, then was one of the two stars' recorded places altered between HC and the catalog Ptolemy took over?]

  • Similarly, BS Table 5 star#67 makes αCrB into “South edge of CrB [Northern Crown]”, though αCrB was not medially-placed vis-à-vis the N-S axis of CrB. (In fact, αCrB was clearly nearer CrB's westernmost star [βCrB] than its southernmost star [δCrB].) Another (at-best) over-vague placement, which should not have been included in the sample. (CrB is partly visible in the upper left of photo λ.)

  • Twice BS uses the same star two times quite contradictorily in the same list, Table 3 (p.187):
    [i] In Table 3, θCen appears as star#7 “Centaur's chest front” — (though his thorax is seen entirely from the back on FACG), but then lower down on the same list it re-appears as star#34 — with exactly the same coordinates — as it then transforms into the “Centaur's shoulder”.
    [ii] Also in Table 3: star#6 = φGem is identified as “Just east of Pollux” (emph added), yet the same table's star#24 calls the same star — with, again, identical coordinates — “Bottom of Pollux' head”. Given FACG's orientation of Pollux (see photo A at right), that puts it at the west end of Pollux' head. (If BS means “Bottom” = south, then this would simply represent a different sort of non-eastness. In truth, φGem was [at c.ESE] much nearer east than south of the 1st magnitude star Pollux = βGem.)
    All of which gives one some idea of the ambiguity (and thus manipulability) of the junk-data-base underlying too much of the material used by BS. (When cases of contradictory uses [of the same material] are repeatedly encountered, a suspicion of some level of manipulation is naturally encouraged.)

  • In Antiquity, Was the Crab Devouring the Twins?
    So BS is using φGem as the east edge of Gem — but, for Hipparchos, Pollux's hand (μCancer [Cnc]) was right on the solColure, while FACG has this colure near Pollux' head instead (and FACG's Pollux-right-hand hangs, far [and aiming away] from the colure, next to his right thigh — see bottom of photo A, at immediate right) — which resembles Ptolemy much more than Hipparchos. (See Toomer pp.364-365, where Pollux head & shoulder are eastmost.) BS must know this since he has resorted to using the non-cataloged 5th-magnitude starlet φGem — mentioned by neither HC nor Ptolemy.
    A DR speculation (contra BS p.180): the boundaries of (especially zodiacal) constellations were adjusted over centuries, as precession affected them; note that as the solColure moved across μCnc (during Hipparchos' lifetime), it becomes removed (by him?) from the stars of Gem (where H filed it) and becomes part of Cnc: “the star on the [crab's] northern back-leg”. (See Ptolemy's Almajest  [Toomer 1984 p.366].) The process perhaps ceased as astronomy ossified sometime during the H→P period, thus (see ibid p.365) ζCnc — wrongly mapped slightly east of the colure in H's time — is still in Gem for Ptolemy, though given by him as by now 40' east of the colure dividing Gem from Cnc. (Since Ptolemy stole Hipparchos' star catalog by adding 2°2/3 onto the longitudes, we know that Hipparchos' cataloged ζCnc at longtd 88°. Note how Toomer's scrupulousness in consulting Arabic mss resulted in seriously correcting Manitius and Peters-Knobel here.)
    Keith Pickering realized Hipparchos made a sign-error (DIO 12 [2002] ‡5 §C12 [p.61]) with ζCnc, when doing spherical trig, since ζCnc was at longtd 92° not 88° for his epoch.
    [Which proves that this datum [i] was stolen by Ptolemy (since Keith's neat sign-error solution won't work for Ptolemy's era), [ii] was from sph trig not globe (since such a screwup comes only from sph trig), and [iii] was not directly read off of an armillary astrolabe. Note that its polar longitude is also 88°, an integral value. So, both by its ending and its constellation, ζCnc belongs to the part of the Ancient Star Catalog where the observed E-W coord tended to be a polar longitude (probably for reasons connected to astrology, where the Midheaven is almost as revered as the Ascendant), which was unrandomly likely to have an integral ending.
    (On the rate of polar-longitude integral endings, see DIO 10 [2000] n.177 [p.79]. This note also recounts a weird early DR experience with BS. Further on that theme: BS is the sort of person who actually had the nerve [1999/10/1] to phone-up DR privately, [a] Asking DR what could go wrong with BS' upcoming 2001 JHA attack on DR! [b] Contemptuously passing off the atmospheric expertise of Bemporad, Laulainen, Evans [and DR] as worthless. [c] Feigning neutrality, without realizing that DR knew that BS had [in 1994, behind DR's back] advised Keith Pickering not to publish with us.)
    Both phenomena are heavily cataloged and meticulously correlated for stars in Hipparchos' Commentary.]
    For ζCnc, Hipparchos' is exactly the same sort of sph-trig-calculation sign-slip which BS makes with αAri, during his Farnese investigations. Note: Pickering's paper is the most thorough inductive study and explanation of individual errors in the Ancient Star Catalog, ever. Anyone working in the area is urged to read it as carefully as it was created.

  • The foregoing discusses the possibility of constellation-adjustment for precession in RA. But, what of adjustment for (slower) Decl precession?

    PHOTO θ:

    How did Spica (αVir) transform from plain Stachun [ear of grain] for Hipparchos (HC2.5.12&13, 3.3.5) into “the star on the left hand called Stachun [ear of grain]” for Ptolemy (Toomer p.369)?
    Possible Clues:
    [a] As can be seen near the top of photo E (just at the tip of the Crow's tail), and is crystal clear from examination of the above photo θ [or an excellent close-up image of Virgo's grain-ear: photo taken by V.Valerio and generously lent to DIO], the ear's center is slightly above the Equator, while the left hand holding it (from the bottom) is slightly below the Equator.
    [b] A point that came up in a 2005/4/9 collegial DIO discussion: between the epochs of Hipparchos and Ptolemy (in 32BC), the Equator crossed Spica — as Ptolemy was aware (Almajest 7.3).
    Hypothesis That Satisfies This Evidence:
    The existence in antiquity of traditional-image constellations such as the Farnese globe, thus faced astronomers with a problem (since precession wore away traditional placings vis-à-vis celestial circles): unless they wished to wince through serious re-drawing of their various celestial globes and re-chiseling the marble ones, they had to do some re-defining. All that was needed to set Spica straight was to switch the star's definition from grain-ear to hand-holding-the-ear and — tell the re-chiseler: he won't be needed….
    The theory is consistent with what we find, though that is in itself not proof that it's true.

  • How Stringily Co-operative Could the Star-God Be?
    FACG has Lup's front paw (Ptolemy's 2fLup) on the TropCap; but its 125BC Decl was −20°.4. Note that all Lup's paws are on TropCap, like Cas' feet & throne-feet. Does anyone really believe that a legitimate astronomer's star-catalog would coincidentally misplace so many stars in order to make them be strung-along these convenient circles? (Even BS [in full alibi-mode (regarding latitude) at p.177] wonders about this possibility, which would have a degenerative effect upon what one can derive from even the on-circle stars.) Obvious implicit question here: were the FACG figures which are separated by circles arranged thusly from then-current natural stellar groupings — or were they simply reflecting old rough constellation-boundary-traditions? E.g., CMa-vs-Arg & Sco-vs-Sgr? All of which reminds us of our previous suggestion that the Gem-Cnc border might've perhaps been shifted for a few centuries in order to maintain a tradition that the solColure divided the two constellations.

  • Further on constellation-features artificially-dotting FACG circles:
    FACG's Aql (upside-down eagle) has feet, which rest smack on the TropCnc (as if it were a telephone line). But neither Hipp nor Ptol give Aql any feet at all.
    [If Ptolemy even imagined Aql feet, they'd be shown chicken-hawking the constellation that Ptolemy (in the academic-pol sycing-up tradition preserved so devoutly by JHAdum) evidently invented in 130AD to glorify Emperor Hadrian's lamented boytoy, Antinoüs. (The absence of the 6-star asterism Antinoüs [Toomer p.357] from FACG counts [more than missing asses, a mere star-pair] against post-130AD Ptolemy as FACG-source, as BS has rightly noted [L.A.Times 2005/3/30], though not definitively.)]
    [H&P's Aql instead is in-flight, so feet needn't be visible. Aql's shoulders are described, and he is seen (from Earth) from the back.]
    Our LSCH strikes.

  • Points Where the Farnese Globe Resembles Ptolemy More Than Hipparchos:
    BS treats with typically BSian arrogance the researches of Vladimiro Valerio, whose groundbreaking work presents reasons (at least as persuasive as those BS gives for his Hipparchan-origin theory) that the Farnese globe is from the era of Ptolemy (2nd century AD).
    [Discursion (as if such is unexpected by this time…):
    Hasn't the US' (official) politicians' oil-addict pre-emptive foreign adventurism given the nation enough of a rep for insufferability — without assistance from yet more politicians, from the academic world?]

  • Fair&Balance — Scorpio as Lady Justice:
    Since the Balance (Libra) is shown on FACG, BS pp.171&173 discusses ancient usage of “Balance” vs the then-more-common alternative of Scorpio's “Claws” for the same region. FACG shows both Claws & Balance overlapping: Scorpio's left claw actually grips the Balance near mid-bar (very near the left foot of the Fair Virgin) as clearly shown by one of the several crystal-clear photos Vladimiro Valerio helpfully has sent to DIO) — somewhat like modern statues of Fair Lady Justice's upheld balance. BS balances the evidence and of-course finds for Hipparchos; p.173: “Hipparchus usually calls the constellation ‘The Claws’; however, in one place Hipparchus does recognize the constellation as ‘The Balance’ (Commentary 3.1.5), so this cannot be regarded as being a true difference.” On the other hand, BS p.174 says that the Almajest always refers to Claws, not Balance. So, score one against Ptolemy as FACG-source? Not so fast. There are two problems with BS' assertions here.
    [a] Toomer (p.371 n.1) remarks a Ptolemy-exception at Almajest 9.7 (Heiberg 2:267), where Ptolemy refers to an earlier [237BC] Chaldaean observation, and specifically says it's in the southern pan of the Balance (“notiou Zygou”). That's not a reference to Claws. (Not presented as a quotation [which appears to be Toomer's implication]; though admittedly Ptolemy was a sloppy serial-plagiarist.)
    [b] Neither party notes that at least twice in the Tetrabiblos (1.19 & 4.4) Ptolemy refers to the Balance (though this work uses Claws more frequently, as does the Almajest  — and Hipparchos' Commentary).
    Which adds up to three Ptolemy Balance-references vs one for Hipparchos. I.e., what BS presents as a feature eliminating Ptolemy in Hipparchos' favor instead ends up either as a tie or somewhat favoring Ptolemy.

  • Having excused Hipparchos' general reference to Claws instead of Balance, BS p.174 feels free to claim that the ONLY definite difference he found between Hipparchos and FACG was: “the head of Pollux [βGem] is close to the [FACG] Tropic of Cancer …, whereas [H] says that the heads of both Twins are north of the Tropic and he even says that Pollux is north of the Tropic by 6° [which it is]. But that is all. I can find only [that sole] difference between the globe and the Commentary.”

  • Yet there is another difference (of dozens) right at-hand, if you will. FACG doesn't show Pollux' arm extending out to μCnc right on the solColure. Yet for Hipparchos, μCnc was Gem's easternmost extremity: Pollux' right hand, the last Gem star to rise&set (HC3.3.12 & 3.4.12). But FACG doesn't have either Twin's hand at the colure or stretching eastward at all: see upper right of photo B (just above Atlas' enormous index finger). By contrast, for Ptolemy's depiction of Gem, there is no conflict with FACG on this point, since (during the H-to-P interim), μCnc got converted from a Twin-hand into a Crab-leg!

  • FACG's Taurus the Bull clearly incorporates the Pleiades (the mythological 7 daughters of the globe's bearer) into Tau's huge shoulders, as does Ptolemy (Toomer p.363). But Hipparchos' Commentary treats the Pleiades as a separate group outside Tau. (See HC1.6.14 & 2.5.15, 6.6&11&14.) [All discussed with far greater erudition than DR's at Kidd 1997 p.274.] This is undeniable when we find that HC3.3.11 says that the Tau “cut-off” (5f, 4s, 2ξ, & 1οTau) is the 1st part of Tau to rise (see Manitius 1894 p.304 n.44), though for Rhodes in Hipparchos' time, the Pleiades rose about a 1/2 hour before the cut-off. (Note that the sph trig math of Graßhoff 1990 pp.383-384 finds close matches to 1οTau for all five HC phenomena cited to the Tau “cut-off”. [Both Peg and Tau have the disadvantage of possessing no rear-halves in their HC celestial demi-incarnations.] So, while FACG & Ptolemy extended Tau to 42ψTau (PK406) & the Pleiades, there is no doubt whatever that, by contrast, the Hipparchos Commentary's Tau constellation did not come close to any of these stars.)

  • FACG's Pegasus has a prominent right wing (see photo C [where south is at top] or photo 2 [north at top], BS p.169), a point which BS reasonably adduces to eliminate “Psuedo[sic at BS p.170]-Eratosthenes” as FACG-source, given E's “explicit denial” (BS p.174 item 6) of Peg having wings. But Hipparchos never mentions Peg's wings, either. [Again, DR finds that this is all discussed at Kidd 1997 pp.258-259.] (HC assigns wings only to Cyg, Aql, Vir. [Note that Aratos, Hipparchos, & Ptolemy put no wings on Per's ankles, yet FACG does: see photo A.]) If BS is aware of said discomfitting fact, perhaps this is why he refers to “explicit” for Eratosthenes.

    PHOTO σ:

    But that will not save the situation, since it is obvious (from, e.g., photo σ [above], photo C [south at top], photo 2 [p.169], or photo 3) that the last part of FACG's Peg to rise&set was the right wing-tip.
    (Note that for Mediterranean observers, the diurnal rotation of a typical celestial globe [including the Farnese] is right-to-left [mirror-image of the sky], i.e., east-to-west.)
    Further, the last part of Hipparchos' Peg to rise&set is γPeg (HC2.5.11 & 2.6.11); but it is Ptolemy, not Hipparchos, who refers to γPeg as the wing-tip and hip. Indeed, Ptol cites Peg's right wing in connexion with α, γ, & τPeg — while wings are wholly unmentioned for Peg by HC, though HC explicitly cites γPeg (“hip” HC1.10.23, 2.5.11, 2.6.11, 3.1.11) & τPeg; (“body”HC2.6.3).

  • [Other investigators (esp. Dennis Duke) have lately been pointing out that the Southern Crown (CrA) is also missing from Hipparchos' Commentary, though CrA is prominently visible (see, e.g., lower right of photo α) on FACG. (In this connexion, see the note to Geminos 3.13 in the Germaine Aujac 1975 translation pp.131-132, pointed out to DR by Duke.)
    DR notes the parallel with Peg's wings: since BS p.174 discards Eratosthenes for not recognizing CrA, wouldn't consistency require that BS dispense also with Hipparchos?
    [The rising&setting data at HC3.1-2 have all other Ptolemy southern constellations (except CrA), and in exactly the same order (not quite true in the north), except that H starts at the solColure instead of the eqnColure: Hya instead of Cet.]

  • Following the FACG, Table 3 star#30 puts βCyg on the TropCnc. But HC1.10.8 explicitly denies this, attacking it as an Aratos error (Macfarlane transl): “the Bird's nose [βCyg] is 25°1/3 [Manitius] north of the equator …. neither the Bird's head nor its neck can lie upon the [24° Decl] circle of the summer tropic.”
    [Note (see lower right section of photo C) that the FACG depiction of Cyg is non-cygnal: it's a bird, not a swan. This is consistent with the Greek interpretation of these stars. Conversion to the Swan (Cygnus) is thought to be from Roman mythology. Same explanation might relate to the conversion of the Greek constellation Beast into Wolf (Lupus). In any case, as is clear from Valerio's photos, FACG's Beast is definitely not a Wolf.]

  • BS uses υBoo as on the TropCnc, but HC2.2.25 says its Decl = 27°1/3, which is well north of the Tropic.
    On FACG, Boo's feet (both on TropCnc) are more like Ptolemy than like Hipparchos, who has only one heel (ζBoo) on TropCnc.
    BS uses τBoo as on the eqnColure, and Hipp says (HC3.5.6) that's where it is — though Hipp calls it the middle of Boo's left foot, while the Farnese globe's colure touches this foot's toes (υBoo?). Still, the toes are westmost in FACG's Boo, and τBoo is indeed the westernmost serious star in Boo.

  • At Table 3 star#16, BS calls θCrt “Top of Cup” — not committing himself to what Crt's top actually is: lip or handles. This matters because the two stars (θ&ηCrt) at the top of Crt are regarded at HC3.2.2 as the mouth of the “bowl”, while Ptolemy (Toomer p.393) calls each of those two top Crt stars Crt a handle (otiou) and specifies ζ&εCrt for lip-duty. This is not merely a matter of star-identification, it additionally shows that Hipparchos' Commentary did not put handles atop the Cup, though FACG depicts the Cup that way (see here at photo θ or photo E; or photo 1 [BS p.168] to right of top of Argo's mast, just beyond serpentine Hydra) — much as Ptolemy described it.
    Moreover, it is the lip not the handle that is on FACG's Equator (photo θ); so, our best guess for the associated star must be εCrt (Toomer p.394: “star on the northern rim”), which should therefore have been Table 3's star#16 instead of BS' θCrt. With respect to coordinates (as against pictorial features): εCrt (P's lip) was on the Equator in H's era, while θCrt (H's lip & P's handle) was on the Equator in P's era; so neither H nor P quite fits FACG positionally, since Crt's lip not handle is on the FACG Equator. (LSCH again?)
    [Note that Graßhoff p.333 (lines 5&6) accidentally uses γCrt for checking phenomena #3&#4 (and gets anomalous results), instead of using θCrt (as correctly specified at Manitius 1894 p.233), which fits both the HC3.2.2 phenomena very neatly.]

  • Note: In the absence of detailed extant pre-Hipparchan star catalogs, our findings of post-HC extensions of constellations (e.g., Cas, Lyr, Tau) favor Valerio's opinion that the Farnese globe was created about the 2nd century AD. Even if there were many prior catalogs (containing more extended versions of the constellations than in HC), and even if Hipparchos changed the bounds of an occasional constellation, would he have wished to make drastic alterations in lots of constellations? We do not know — but these points are worth keeping in mind as research continues.

  • Further Disagreements with Hipparchos:
    From double-confirmation computational phenomena-checking (Graßhoff p.334 star#995), we can be certain that Ptolemy took from Hipparchos the somewhat erroneous position of γAra, which HC3.2.6 cites as the 1st Ara star to set. (So it's not βAra — a point unambiguously clear from the neat γAra matches [vs βAra's obviously inferior matches] at Graßhoff loc cit.) Incidentally, we have yet to see indication that BS has ever performed such sph-trig phenomena-checks [or even consulted Graßhoff's checks], which are necessary for verification of Manitius' identifications in dubious HC cases. Such math was the key to Graßhoff's ingenious & pioneering 1986-1990 discoveries, which added to our arsenal a spectacular new independent proof (convincing even former true-believer-Ptolemist G.Toomer) that Ptolemy indeed plagiarized most of the Ancient Star Catalog from Hipparchos. (For the seven leading pre-GG proofs, see DIO 2.3 [1992] ‡8 §C22 [p.110]. And don't miss §§C23-33 [pp.110-113].)

  • Converting the Almajest position for γAra (PK995) to equatorial coordinates for BS' epoch of −124 (125BC), we find that H's Decl for γAra was −51°.2. (Very close to H's −51°.8 for αCru & −51°.4 for αCen [both precessed & transformed from Almajest  data] & −51°.5 Decl for αCar [HC1.11.7].) This is almost exactly equal to BS' −51°.3 Decl for the FACG AntCirc. (BS averages real Decl values for αCar [−52°.7], αCru [−51°.4], & αCen [−50°.0], finding [Table 4p.188] −51.3 — and when BS' erroneous place for αCen [too far north by ordmag a degree] is corrected for p.m., his AntCirc average becomes −51°.5. For our two-variable solution of the AntCirc's size, see elsewhere here.) Yet, on the Farnese globe, one sees that the altar's base is placed about 4° north of FACG's AntCirc.
    More striking, yet: at p.326 of his edition of Aratos [Cambridge Univ 1997], Douglas Kidd rightly emphasizes that even Ara's orientation, on FACG is different from Hipparchos-Ptolemy.

    PHOTO α:

    Indeed, FACG's Ara is almost exactly opposite the rather upside-down Hipparchos-Ptolemy orientation. On the Farnese globe (see photo α here), Ara is tilted to the right: i.e., the flame aims roughly NE and the base SW. But Hipparchos (HC2.1.6, 2.2.6) & Ptolemy (Toomer p.397) instead reverse this orientation. LSCH strikes yet again.
    And there may be an extra significance to the FACG rendition of Ara. In earlier times and-or more southern climes than Rhodes, the whole constellation was visible, as shown on FACG, where it appears symmetric and whole. But Hipparchos could not see the whole constellation. (Ara is a constellation which [unlike Cen] is small enough that star-identifications do not present a problem for us.) One of the most obvious evidences of H's authorship of the Ancient Star Catalog is the clarity with which we can detect the southern horizon (at Rhodes in H's era) cutting through Ara: the seven northern Ara stars are all there (σ, θ*, α*, ε, γ*, β*, ζ* [asterisks for those in HC]), but for H's Rhodes ηAra was too low, and δAra was even below the horizon — so neither star is in the Catalog. BS' 2001 JHA paper was oblivious to the implications; indeed, the southernmost Ara star recorded (HC3.2.6) by Hipparchos (at BS' latitude for him: 36°.4 N), γAra, would have been effectively invisible (μ = 6.7) according to BS' extinction model (0.23 mags/atm) — thus invalidating the model upon which the entire BS 2001 paper is founded — as Keith Pickering repeatedly pointed out to BS in person (2000/1/15 at the Atlanta AAS-HAD meeting where BS launched the paper later published in JHA as BS 2001) and via email long before publication — i.e., that one star (γAra) alone gutted BS' whole 42pp JHA disaster. BS initially replied (2000/1/22 email) by computing as 1.5% the associated probability that H would record it. When Pickering pointed out that even this elementary computation was grossly bungled (DIO 12 [2002] ‡1 §B2 & n.6 [p.4]), BS did not reply — and let BS 2001 go ahead to press A YEAR LATER without changing a digit.
    [This behavior is worth some serious pondering: what kind of scholar thinks that being accurate is less important than not upsetting chance-of-publication by insisting upon proof-corrections, fearing such might scare-off the journal by implicit admission that he's bungled some numbers? And: what kind of journal is known to be governed by such superficial-evaluation that such creditable honesty could endanger publication?
    (Note: BS' failure to admit that BS 2001 was utterly razed by DIO 12 presumably contributed to a confident if baseless projected image of reliable expertise that conned Hoskin, Gingerich, etc into publishing and nationally promoting BS 2005 without checking any numbers at all. Well, when a bigoted journal angrily cuts itself off from a helpful, competent critic for 24 years [31 years, as of 2014], this is the kind of cascading insanity that will happen.)]
    These matters bear on both the ability and the integrity of what appears in the obsessively political JHA. (Which throughout the Ptolemy flap has never had the ability, concern, or honesty to correct anything unless its errant author agrees to the correction. [Note: JHA publication of D.Duke's gentle but thorough refutation of the BS 2005 mess, has made this criticism at least partly obsolete. Some progress, though Duke could not cite DIO explicitly since the shunning continues unabated.] See, e.g., DIO 6 [1996] ‡3 §§B1-B3&C3 [pp.36-38].)
    And in equally-neutral Sky&Telescope, where BS in 2002 Feb kept pretending that the 2001 JHA paper was solid science — as he continues to do in the present 2005 paper, without so much as citing the DIO 12 papers by Pickering and Duke which exhibit the prior [2001 JHA] paper's manifold fallacies.
    But neither JHA nor S&T appear to have the slightest interest in looking into these matters.

  • The Whim of the Dim:
    Note: BS did not merely hide from admitting he'd miscomputed γAra — as Pickering has noted, BS also took the extra precaution of nationally slandering DIO as a tiny crackpot journal (S&T 2002 Feb p.40), evidently hoping to encourage onlookers never even to read the highly competent and polite Pickering-Duke dismantling of BS 2001. Given BS' resumé in ethics & courage, little wonder the JHA could hardly wait to add him to its cringing rooster-roster. Such political selectivity has only exacerbated the JHA rulership's naked fear of skilled, well-intentioned non-pol scholars, while exhibiting a level of scholarly competence which is aptly matched by JHA competence in hiding the tragic consequences — leaving the JHA ethically disemboweled, at the mercy of agile and evasive sycophants' servility to the whim of the dim.
    [Do the HAD&JHA cults ever wonder whether DR has all along been engaging in a deliberate scheme of moral evisceration of them? While granting that the results are strikingly consistent with the theory, DR can happily take pious refuge in OG's alternate-explanation mantra.]

    [Passing note: the Hipparchos-computed phenomena for a star called εAra by Manitius at HC3.1.6 is probably for ζAra, as revealed by DR's checks of the two phenomena provided there. (Note that D.Duke published this point several years ago at DIO 12 [2002] ‡2 n.12. Note also that Graßhoff 1990 p.334 proved that HC3.2.6 Ara star “x” at Manitius p.222 was σAra.) Curiously, HC3.1.6 cites this star as the 1st Ara star to rise, even though, of the Ara stars cited in the Ancient Star Catalog, the actual order of Rhodes rising was: εAra 1st, αAra 2nd, and ζAra 3rd. Evidently just a mixup of records and-or computation within the ancient Hipparchos-school. (For a similar [also two-different-hands-at-work] H-school confusion, see DIO 1.3 [1991] on the scribal slip that converted eq.23 into eq.24 [pp.160-161] — thereby fortunately revealing the origin of central Hipparchan lunar numbers. Also discussed by H.Thurston in Isis 2002 Mar.)]

  • Astonishing Specific-Constellation Items
    (All evidently missed by the JHA's Snore-Adora-Sextette of mythological referees):
    [BS p.191's comment upon the firmness of Table 5's off-circle stars (emph added): “I have determined 23 specific points within constellation figures that can be unambiguously identified with single stars in the sky.”
    DR must add that the following items are the fruits of a quite non-systematic search. These are merely problems DR stumbled upon in reading here and there in the BS paper. (I.e., there could be more. [Not surprisingly, it turns that there certainly are a GREAT many more. See Duke's scholarly analysis, now posted at])

  • Dumb Sheep-Tricks — Aries' Head Exorcist-Spins, Somersaults, & Explodes :
    As a jolly triple-feature illustration of the BS paper's numerous unadvertised problems, let us examine BS' work with the head of Aries (the Ram).

  • BS produces a photo (photo 2 [p.169]) of Farnese's Aries, stating (emph added) “The edge of the [western] horn of Aries [γAri] is exactly on the eqnColure, and this immediately tells us that the constellations [DR: all the other 40 on the globe?] were placed for around the time of Hipparchus.” (So why a 30pp paper?) But, despite this up-front VISUAL flagging of Aries' head as a Dick&Jane-level picture-book proof of the BS paper's thesis, none of JHA's six alleged referees noticed that in both of two tables, Table 2 (top line) & Table 5 (star#60), the Farnese globe's RA for αAri is signed wrong. Which at a stroke deletes BS' hyped ultra-Hipparchan 125BC formal result. Head flipped-backward from positive to negative. (Exorcist's Linda Blair without the upchuckle. Though — alert referees might've obliged.) And the consistent succession of calculations developed for αAri through Tables 1, 2, & 5 prove that this is no typo.
    [Note that this slip had to be made repeatedly by BS, since the −5°.6 position in Table 5 is obviously an average of several photogrammetric results for αAri. This remarkable point is quite undeniable, due to the fact that Table 2's RA for αAri is −4°.2 [p.186], which disagrees with the final-concluded RA of −5°.6 in Table 5 [p.192] — disagreeing because the Table 2 result was averaged-in (p.184) with yet more RA values for αAri, obtained from similar (and thus identically screwed-up) photogrammetry-math analysis for αAri on other photographs.]
    The 11° αAri error is a slip in choice between two possible solutions to the same sph trig problem. (In this special case, the two solutions have the same absolute magnitude, but are of opposite sign.) Given the error's size, this mistake alone must noticeably (though not massively, since there are 70 data) alter BS' world-announced epoch-solution of 125BC.
    [Since αAri's longitude must be corrected by over 10°, the effect upon the date induced from Table 5 is a forward shift of several decades, so the effect upon BS' final 125BC will be ordmag a decade in the same direction. (Later testing showed the effect to be about 20y.)]
    And the error contains an astonishing revelation regarding JHA refereeing: the mistake here is due to a sph-trig ambiguity which BS explicitly warns the referees of, correctly explaining just how to avoid going wrong (p.184, emph added): “In principle, there will always be two points in the sky that have the same angular distances from the two reference points on the globe, but this ambiguity is always easy to resolve with certainty on the basis of the visible position on the globe.” BS not only says this but actually provides the visible position of Aries' head in p.169's detailed photo#2. If [BS] were actually, deliberately aiming a sheep-count sleep-experiment (using an actual celestial sheep, no less) at JHA [pseudo]refereeing, he could not have designed a more perfect test.
    The αAri slip would constitute an error of more than 11° (twice 5°.6) if BS' 5°.6 absolute value were correct.
    From viewing the very Fig.2 photo which BS prominently advertises as proof of FACG's Hipparchan source, this 11° error could not be more obvious, since NO PART OF ARIES' HEAD is to the left (west = negative RA) of the colure, though its RA is listed as negative in both Tables 2&5. (See Aries the Ram in photo 2 [p.169], the most immediately & up-front-visible constellation in the photo. Or see photo B here.) So Table 5's mis-placement of αAri 5°.6 west of that colure could not possibly have been missed by a JHA referee who checked out the paper's procedure with the slightest care.
    [Notice that αAri is star-number-one (again: was BS testing the referees?) in Tables 1&2 (pp.185&186): top of the list. So our six JHA referees never even started verifying any of these calculations.
    (An experienced historian of astronomy might in-joke that each of the six refs' checking-labor remains exactly 39 stars behind that of the “immortal” James Challis. See DIO 9.1 [1999] ‡1 n.14 [p.6].)]

    Further, for Aries, BS follows Hipparchos in calling αAri the “muzzle”, but actually (flipping again) BS gives RA&Decl coordinates instead (Tables 2&5 [pp.186&192]) for the top of Ari's head: just another datum which BS thinks leads us to Hipparchos, though (Toomer p.361: “over the head”) it's really Ptolemaic. (The reverse of BS JHA 2001, where he falsely deemed Ptolemaic a set of stars [vital to his then anti-Hipparchan assault] which Duke via Graßhoff then showed were provably from Hipparchos. See D.Duke in DIO 12 [2002] ‡2 Table 2 & discussion [pp.32-34].)
    [Implicit question here: why even use the star αAri when Hipparchos (“muzzle”) & Ptolemy (“over the head”) disagree so about its location?]

  • The MathFlub Hoax:
    And there's a better Aries trick, which one suspects BS knowingly slipped by those alert JHA referees:
    The idea here is to find the photogrammetrically-based angles Γ between any “star” and two selected reference points and then locate an equatorial-frame position (RA & Decl) that is in fact the correct angular distances from the two ref-points. As reference points for his photogrammetry-worked-example's concluding sph trig, BS chooses the two tropics' intersections with the eqnColure, that is, points 2&3 atop Table 1 (p.185) “as they give a long baseline which does not get near to the edge” (p.186). Suppose we instead risk moderate edge-proximity to get an even longer base-line, adopting Table 1's points 2&4 as reference points. Using the last equation on p.183 (sph trig law of cosines), we find the two Γ for αAri, the head of Aries the Ram (top star in Tables 1&2), i.e., the angular distance of the star from each of the two reference points. (In Table 2, each stars' two Γ are listed in cols.2&3.) Computing just as BS did (to produce Table 2) we find Γ2 = 45°.636 and Γ4 = 37°.826. Now comes the dynamic surprise: as we see from lines 2&4 of Table 1, the angular distance between reference points 2&4 is 57°.5 − (−26°.2) = 83°.7 which exceeds the sum of the two Γ. To point up the problem with a simpler example: satisfying both Γ here would be like finding a ram's head that's 2 meters from each of two points separated by 5 meters. Nice to finally justify modern moronic-grue-cinema's hitherto-inexplicable staple: now at last we know what exploding heads are for.
    [Note: when the meticulously determined data of projective-geometry specialist Vladimiro Valerio (1987 p.105) are inserted (instead of BS') into BS' own math scheme, there is no explosion. The implications are obvious. So that readers may check this point for themselves, we provide Valerio's important mean measurements in their entirety (note his conservative cautions at, e.g., op cit pp.102 & 104). TropCnc 25°30', TropCap 25°06', obliq 25°18', ArcCirc 56°43', AntCirc 55°26'; offset of Ecliptic-Equator intersections' RA-distance from eqnColure (fig. at Valerio op cit p.124): Vernal 5°09', Autumnal 5°19'; zodiac-width 13°29'. (Geminos 5.53 [1st cy BC] has it 12°.)]

  • It is astonishing that BS' final sph trig steps to find the position of each “star” are done by trial&error. But this problem can quickly be done purely analytically (as we are about to see), and one can only marvel that any journal could have found six referees without hitting upon a single one who didn't realize (or notice) this.
    [Readers may wish to skip over the following Tycho diversion, to arrive immediately at the elegant way of doing this sph trig.] The math here is but a trivial special case (both ref-pts on same colure) of the far more serious sph trig done by Tycho during the construction of his 1598/1/2 (Julian Calendar) 1004-star catalog — and by DIO during the preparation of DIO vol.3: see its §B2 [p.8]. (DIO 3 [1993] still remains the sole critical edition ever accomplished of that catalog.)

    [Groucho Marx: I Feel a Perfect Archon:
    Despite the eminence and expertise of DIO's board, and despite the 7 years of scrupulous care that went into the creation of our pioneer critical edition of the Tycho Star Catalog (DIO vol.3), the JHA crowd has almost uniformly pretended it doesn't even exist.
    [One is glad to see BS himself break this pattern in the 2013 Feb JHA, though he counters this positive with a couple of his usual technical screwups (magnitude and extinction), and by sucking-up to the field's archons by the toadily-awesome fantasy that the Star Catalog controversy isn't over simply because a few cultists (who can't even understand the massive evidence's asymmetry) cling to repeating their longtime mantric position. (So the Flat Earth Society's persistence proves the Earth's roundness is still controversial?) One doubts that BS actually takes his own statement seriously or expects academe to: it's just mischief from a hit&run joker with a record of departing whenever he's shown to be flatout wrong.
    [Which, of course, he never is. (One of his few commonalities with James Evans.)]
    Cause of chauvinism here: the JHA believes that it can ameliorate the academic crime it has committed for decades (suppressing and amateurishly attacking the side that ultimately proved right on the Ancient Star Catalog) if it can keep some dim portion of academe believing that perhaps Ptolemy didn't steal it. No. The crimes here are JHA's censorship, shuns, & smears, not the cultish, unperceptive scholarship and insubstantial refereeing that supports its decades-long blindness to the Catalog's true observer.]

    As part of a much larger, uglier, vindictive, unabashedly naked, and almost beyond-belief sycophantic pattern of unbalanced citation-practice (detailed at DIO 8 [1998] p.2; see also DIO 8 [1998] pp.38-41), JHA's present Editor James Evans, in his 1998 book's discussion of Tycho's Star Catalog, deliberately (citing instead the old non-critical, not-even-numbered Dreyer list of TB's stars) ignored the existence of this monumental work. (Fortunately, Annals of Science [1996 July] had not been so narrow, having commissioned an expert and appreciative review. In fairness to BS, we should remark that he was the first [only?] scholar ever to cite DIO's Tycho catalog in the JHA [2001] — however unbenign his ultimate purposes at the time.)
    The Evans 1998 book's faking that DIO (not just the TB catalog) did not exist was deliberate, since DR informed OxfordUP's Kirk Jensen of it by phone & 1997/7/17 letter (while the text was still in flux). It gets even weirder: Evans not only refused to cite any DIOs in his book (even when they provided extensions and confirmations [expertly refereed] of the nonDIO DR paper he was extensively attacking) — moreover, he even refused to read the DIO 8 [1998] p.2 [inside front cover] note mentioning his refusal! Evans 1999/4/2: “I have been told that Rawlins printed a diatribe on the inside cover of DIO, with the usual sarcasm and ridicule. Life is too short (alibi echoing verbatim JHA's Swerdlow: DIO 2.3 [1992] ‡8 §C29 [p.112]) to waste one's time on that sort of thing, so I've just thrown away that issue without opening it or looking at it.” [Evans' pretense of not reading DIO is as honest as would be the non-reading he's pretending to.] (Readers should check DR's inside-cover “diatribe” for themselves, to see that it is not language [yet another copied Muffia alibi for hiding] but the detailed demonstration of dishonest citation-practice that embarrassed Evans: our listing of ten post-1982 scientific demonstrations of Ptolemy's fraudulence in leading academic forums, mostly not by DR and almost all staid [four by neither DR nor DIO], ALL of which Evans refused to cite, while extensively fixating on re-attacking DR's old 1982 paper, without citing its ironclad later vindications DIO 4.1 [1994] ‡3 §C & fn 5 [pp.37f & 34].) One can see why Evans is the ideal choice to succeed the equally open Hoskin & Gingerich minds now running JHA. Similarly, the extensive Tycho entry in the 2001 Encyclopedia of Astronomy & Astrophysics (written by a loyal protégé of JHA's Number Two, DIO-hater O.Gingerich) evades citing the DIO Tycho star catalog by simply omitting all mention that Tycho ever did a star catalog. (Meeting the obligation [to note that Tycho did a star catalog at all] is left instead to a turgid no-citation sentence in the nonhistorical article following. Cute. If contrived.) Until 2007/9/27, the popsci-crowd was following suit in Wikipedia's Tycho entry (flouting Wikipedia's ideals of neutrality and integrity, thereby attempting to corrupt its essential good idea and intent), preferring to detail stuff about Tycho's pseudo-psychic dwarf and how Kepler-of-course-secretly-poisoned-TB-anyway. But — nary a word on a massive, career-long astronomical Tycho achievement, which boasted a First of which Tycho was particularly proud (DIO 3 [1993] §I1 [p.15]): the Tycho Star Catalog's ability to (non-pseudo-correctly) predict the places of 100 stars a century hence. (For the largely admirable accuracy of all 100 predictions, see ibid Table 23 [pp.102-105]. For summary and revelations regarding Tycho's sph trig computing procedures, see ibid §I5 [pp.17-18].) The 1993-2007 shun-history of near-total noncitation (on which no institutional forum has uttered the slightest word of criticism) regarding DIO's carefully-wrought Tycho 1004-Star Catalog is one of the starkest proofs of a lamentable but undeniable sociological truth: history-of-astronomy has for decades not been conspicuous for integrity, originality (plagiarism prominently defended & practiced), courage, or astronomical expertise. Its cultish obsessions are indeed so patently dominant that the history of astronomy field is even prepared to systematically fake (for well over a decade now) the non-existence of the only critical edition of history of astronomy's greatest pre-telescopic star catalog (an intent which became obvious almost immediately [well before Evans' 1998 dodge]: DIO 6 [1996] ‡3 §H4 [p.43]), a deliberate fraud, perpetrated merely to syc-up to the very littlest bigmen's political hates, part of a campaign of attempted murder of a contributing scholar's career. Largely by exile, since attempts at direct assaults at R.Newton and DR on scholarly grounds have kept redounding (DIO 4.1 [1994] ‡3 §B [p.36-37]) to the detriment of biggies' holy tenets. And poses of expertise. As we've just seen, the field is ever-more stoutly retaining and glorifying the Perfect-Archons for upholding such traditions.
    Parallel weirdness resulted in another temporary betrayal of Wikipedia: avoidance of all mention of DIO or DR in its Neptune-discovery article! (As of 2007 Autumn. Since expertly corrected by Keith Pickering, with the gracious approval of the Wiki article's author. In the interim, Wikipedia's talk-page reviewers were not misled and stood by the revolutionary new case for Leverrier's priority.)
    Note: DIO's board — alone among disputant journals here — contains scientists who have [like DR] published papers on the math relevant to Neptune's discovery, in professional astronomical journals, and is obviously superior in this respect to ScAm's refreshingly bold but too often inadequate & technically uncomprehending article. (It is common knowledge among historians of this period of astronomy that DR's 1966-1984 groundwork questioning of Adams' claim and DIO's 1992-1999 summation-analyses & math pioneered the revolution underlying the ScAm article.]

    We will compute out (ridiculously over-exactly, so rounding won't interfere) the missing non-trial&error αAri calculation, to check the top line of Table 2 — using BS' p.186-chosen reference points2&3:
    arccos[(cos8° − cos52°.4 cos 45°.6)/(sin52.4° sin45°.6)] = ±5°.59566
    Decl = arcsin[−sin26°.2 cos45°.6 + cos26°.2 sin45°.6 cos(±5°.59566) = 19°.21454
    RA = arcsin[sin45°.6 sin(±5°.59566) sec 19°.21454] = ±4°.2309
    These data (Decl and RA's absolute magnitude) agree perfectly (to BS' precision) with the result listed for αAri in BS p.186's Table 2 (as do the calculations for all the other Table 2 stars, when done in the simple analytic fashion just demonstrated). But clearly there is sign-ambiguity; and, as already noted, BS unfortunately chose the wrong sign here (αAri), ultimately (Table 5 star#60 [p.192]) introducing into his data-pool an αAri error exceeding 10° — thereby putting αAri into the wrong hemisphere, west of the eqnColure instead of east, where his own photo 2 [p.169] clearly shows Ari's head to be.

  • NoiseCastle:
    To provide some idea of the shakiness of what comes out of BS-photogrammetry, we provide the epoch that results from testing (by exact BS math procedures) his p.185 Table 1 data (8 stars) for each of the six possible pairings of his listed reference points (Table 1 top 4 lines). Results:
    Ref pts. 2&3:    100±180y
    Ref pts. 2&1:    150±220y
    Ref pts. 2&4:    150±180y [7 stars (exploding αAri omitted)]
    Ref pts. 1&3:    140±180y
    Ref pts. 1&4:    170±170y
    Ref pts. 3&4:    120±170y
    Now, understand that, if the globe and method are OK, the epochs ought to agree (since the eight stars' data-points are exactly the same for each of these six tests). But, instead of agreement, we find disparities of ± 1/3 of a century.
    (Given that the entire structure of the BS experiment has far too many and too large random errors [virtually an edifice of scatter] this latest finding is simply carrying-noise-to-NoiseCastle.)

  • An extra note along the same lines.
    To find the real Decl of the AntCirc, BS uses an average of the 3 bright AntCirc stars of Table 3: αCar, αCru, αCen. From these, he says (Table 4) he finds AntCirc's Decl = −51°.3 ± 0°.8. However, in Table 5, we find one of them (star#48 = αCar) at Decl −49°.4. Yet, it is mathematically impossible to average two other Decls with −49°.4 to get a mean of −51°.3 — and end up with that mean's σ as small as 0°.8.

  • Perseus-Time:
    While usefully noting (p.6) FACG-vs-Aratos discrepancies for Perseus, BS fails to learn anything on FACG origins from the glaring fact that neither Hipparchos nor Ptolemy have Per near the ArcCirc (obvious from Table 3 star#38 “Top of Perseus”, whose Decl is 46° — about 6° short of BS' ArcCirc), though FACG's Per virtually touches the globe's ArcCirc.
    [Perhaps the below theory (regarding star HR1035) will ease the problem — not to mention the outside possibility that the discrepancy is a glimmer of a long-submerged tradition (revived by Tycho): LSCH again.]

  • FACG has the Medusa-head hanging much more eastward than southward from Per's left shoulder; but for Hipparchos (& Ptolemy: Toomer p.353) that shoulder is θPer (HC1.10.5, 3.4.7), and the Medusa-head is βPer (HC1.2.27, 3.5.19), a star named Algol, which is much more southward than eastward. [Duke has noted that the whole body of Perseus is similarly much-mis-oriented vs Hipparchos' description.] A detailed examination of this discrepancy reveals how essential it is: according to BS himself, the Farnese globe has βPer at about 2hrs of RA. (BS Table 5 star#59: RA=29°.3.) This is hugely east of Hipparchos's Algol RA, which was 15° or 1hr of RA. Indeed Algol itself is (pretty accurately) Hipparchos' 1h (15°) hour-star marker! See Hipparchos' Commentary 3.5.19. (Atop BS p.178 [see post-press-conference fine print]: “The constellations are placed onto the Farnese Atlas with remarkable accuracy”…!) This discrepancy is more than twice as large as the 6° error which BS p.173 flags as the sole difference between Hipparchos & FACG. And it is comparable to the positional discrepancy which BS n.2 (p.195) uses to cast aside the theory that FACG has Sagitta with Cygnus. Note that Commentary 3.5 is a concluding chapter devoted entirely to listing Hipparchos' “Hour-Stars” — including Algol. In an era before reliable clocks, Hour-Stars were used to tell sidereal time. These data are purely RA. (H's Hour-Star list gives stars lying on or very near integral values for each of the 24  sidereal hours.) Yet BS (in a paper analysing a globe prominently marked with four key lines of constant RA [the colures]) appears oblivious to the data contained therein. Indeed, several of BS' own chosen colure stars are right on Hipparchos' special-finale list of precise Hour-Stars — yet BS (unlike Thiele, in his 1898 Hipparchan analysis of the Farnese globe) never even mentions the list….
    These stars are (using the star-numbers of BS' Table 3 p.187):
    star#1 = γAri, (HC3.5.18),
    star#4 = ηCMa (HC3.5.1b),
    star#9 = τBoo (HC3.5.6).
    Further, Table 3 star#7 (“Centaur's chest front”) is θCen, which Hipparchos (also Ptolemy [Toomer p.394] and BS [Table 3 star#34]) instead calls a shoulder (HC3.2.13); and, according to Hipparchos' Hour-Star list (HC3.5.6) the Centaur's chest star is instead φCen (PK948) — which is there stated (extremely accurately for his era) to be right on the colure.

  • Some Beef About the Bull:
    Table 3 lists (star#14) on FACG's Equator the star νTau, labelled “Taurus' right” hoof, but FACG has the left hoof there: see photo 2 [p.169]. (Right hock would have matched Ptol's description of νTau and it's about on the Equator, but typically too inexact for reliable use.) Also (see elsewhere) wrong hoof of Cen on AntCirc. And perhaps wrong back hoof of Cen on same. (Though see Pickering at DIO 12 [2002] ‡5 §C36 [p.64].)

  • Bull's-eye αTau is at Decl 15° on the FACG. (Easily shown by interpolation between FACG Equator & TropCnc in photo B.) BS' repeated finding (of this sharply-defined point) instead at 12° suggests a photogrammetric slip of several degrees — similar in magnitude to his mis-rendering of the relation of the Scorpion's sting to the Archer's arrow-tip.

  • BS equates the Bull's “shoulder ” (p.187: Table 3 star#23) with 42ψTau, though this dim (magn 5.22) starlet — unmentioned in HC — is way, way further north than the boundary of Tau in Hipparchos' Commentary — roughly a 10° Decl discrepancy.
    Moreover, Ptolemy says (Toomer p.363 PK406) 42ψTau is in Tau's neck, not shoulder (which is well to the Ptolemy neck's east). This neck-shoulder confusion (typifying the mush BS is trying to get a half-degree-accurate bottom-line result out of) can only be resolved if Tau was on NoNeck-Steroids or designed by Picasso.
    (HC2.6.6 and Ptolemy put 30e Tau in the rt. shoulder; Ptolemy puts 37A Tau [which rises ahead of 1οTau] in the neck but HC2.6.6&11 puts it outside the constellation Tau, as he does the Pleiades.)

  • Extras:
    HC1.10.18 puts Ari entirely north of the Equator except hind feet upon it. FACG's Ari indeed has hind-feet on the Equator but has both Ari fore-feet crossing the Equator (photo 2 [p.169]) — indeed, extending further south than the hind-feet, in clear contradiction of Hipparchos.

  • Wrong front paw of CMa: Table 3 star#32 calls βCMa “big dog's front forefoot” and says it is on FACG's TropCap. But the CMa forepaw we find upon FACG's TropCap is the south forepaw, while HC3.1.12 says βCMa = north forepaw. (See photo μ, below.)

    PHOTO μ:
  • BS p.187: Table 3 (star#10) has ξCap on the solst colure, “Just west of Capricorn's head”. But HC never mentions that star, and Ptolemy puts it on the tip of the western horn — yet, (as we see from photo ω) FACG has Cap's horns east of the colure.

    PHOTO ω:
  • BS 2005 p.173 rightly (see photo C or photo CC) states that the FACG ArcCirc goes through Cep's neck. Yet in Table 3's ArcCirc stars, the Cep star listed, ξCep, is said by BS (from Ptolemy [Toomer p.346]) to be in Cep's chest. (Note: ξCep [magn 4.4] isn't even mentioned in HC.)

  • Table 3 (p.187) star#2 calls θPer “Westernmost star in Perseus” though star#38 of the very same BS Table 3 rightly puts χPer much further west: 26m — nearly a half-hour!

  • Taking χPer as Per's north limit fails. But — a speculation (on rather thin ice, considering the huge inexplicable distortion of the Medusa's place — though at least that is not on a Farnese circle): was HR1035 (Tycho star D647) meant? Did a more northern tradition for Per survive and re-emerge with Tycho? (Did the ancients consult more than H&P? LSCH glimmers again — “strikes” would be overdoing it.) For, in the 1598 star catalog of Tycho, D647 was indeed the northernmost star in Per. (Though D644 was further north, it was hugely removed from other Per stars — and was shared with UMi as star D348. See tables of DIO 3 [1993].)

  • An Apparent Hipparchan Inconsistency:
    By contrast, we note that HR1035 is nearer αPer than βPer is. Without HR1035, Hipparchos' Commentary has left Per with no right elbow. (But: Strabo puts H's Per right elbow = ηPer just north of 45°.) Yet Hipparchos' Commentary calls ηPer the rt hand. So it seems H's body-part for ηPer may have changed during his career. Since Ptol copied Hipp's star catalog and calls εPer the rt.elbow (in agreement with Strabo on H), we can assume that the Comm was earlier and thus may have reflected the actual (possibly pre-H) prime source of the Farnese globe.

  • If ηPer was Per's right hand in some ancient maps, then HR1035 may have been his right elbow — which would put Per nearly up against the Farnese-latitude ArcCirc. And behold: Per's FACG-elbow IS virtually on the FACG ArcCirc. This could favor a Hipparchan connexion; it surely disfavors Ptolemy. Ptolemy unknown anyway publicly until c.300AD (e.g., Porphyry, Pappos).

  • Cassiopeian-Confusion-Cornucopia:
    Table 3 (star#44) identifies ιCas as “Cassiopeia's foot”, which agrees with Ptolemy; however, Hipparchos' Commentary says her feet are εCas instead (HC1.11.4, 2.6.9, 3.1.12). Correcting this point fortunately tightens the spread of the Table 3 Decl data connected to FACG's ArcCirc, firming BS' perhaps-more-valuable-than-he-wanted-to-know conclusion that the FACG ArcCirc was nearly at Decl = 52°N.

  • 0fer Gofer:
    There are numerous points included by BS in his Table 5 trash collection which are way too positionally-vague (though weighted same as others) to be called points in any meaningful sense. And this particularly indefensible part of the paper's sample-padding leads directly to BS' grand Cassiopeia-Breast-Sighting beaut — which gives new impact to the phrase in-a-class-by-itself.
    The AAS paper's place for αCas (Tables 1&2 and Table 5 star#66) is doubly odd. This star happens to be completely uncited in Hipparchos' HC. Undeterred, our American Astronomical Society-hosannahed expert feels free to grab the description “breast” from Ptolemy's αCas listing (Toomer 1984 p.351).
    Hmmmmmm. In accord with celestial-globe practice which has been pretty standard for thousands of years, ALL of FACG's human figures are obviously facing inward (away from us) — towards the globe's center (Earth). [Which is why the globe is butt-city: seven full-backal-nudity cases of unadorned rumps, as well as several more clothed ones. See, e.g., antique illustration of one side of FACG. Yet not a single butt appears among BS' stellar entries in Tables 3&5 &mdash: 0fer 70.]
    Again: while backward constellations have long been the almost-universal convention for celestial globes — including FACG — BS assigns only chests and fronts to FACG's “star” positions.
    including assigning CASSIOPEIA'S BREAST TO HER BACK — thus, the American Astronomical Society has loudly elevated Cassiopeia to the honor of being: the world's first backwardly-breasted woman.
    [Photo CC at right (detail from photo C) is of the Farnese globe's Cassiopeia, with south-at-top. (Andromeda's right-foot sole is visible at lower left, since her body too is facing-away. King Cepheus' face (remarkably detailed) is seen in profile at lower right; his body also faces-away: the soles of his feet appear at the top of photo 3, and in profile at the upper part of photo 2 [p.169], just to the left of the eqnColure.) As one can see by comparison to the from-Earth view (see [at below-right] simple illustration from W.Barton Starcraft 1946 p.24: Cassiopeia's body is facing Earth, her familiar stellar chair naturally reversed vis-à-vis the Farnese Cassiopeia depiction, where her smooth back & rounded shoulders are facing us) or the virtually identical Ptolemaic description (Toomer 1984 p.351), Cassiopeia's outstretched arms are: left arm (rightward in Barton illustration below) = the stars θCas & φCas (reaching out towards Andromeda: leftward in FACG-photo CC above) and right arm (leftward in Barton illustration, rightward in FACG-photo) = σCas. [Another view (looking west on FACG): Cas' “breast” looms like a pancake on the far horizon of photo A.] And, not only did this AAS-world-press-release-promoted paper let its imagination get so udderly out of control as to declare in print that the Farnese globe exhibited breastness on Cassiopeia's back, the JHA even provides equatorial and ecliptical positions each coordinate thoughtfully expressed to the impressively-scientific-looking formal precision of a tenth of a degree — for the non-existent αCassiopeia-breast which (through world-promoting the BS 2005 paper) the AAS has effectively announced it has located upon the globe, with such elaborate photogrammetric pomp. (Table 1 [p.185] → Table 2 [p.186] → Table 5 star#66 [p.192]): RA = 333°.9 & Decl = 40°.2; Longtd = 356°.0 & Latd = 46°.5.)
    [Note that, so as not to neglect the other gender, BS places the chests of the Centaur and of Cepheus upon their backs, too. See Table 3 star#7 & star#43, resp. (Leo's chest [star#26] is of course not out-of-place, since the Lion is seen in profile.)]

  • The Mysterious Missing-Ass Problem:
    Astronomers have for centuries called two Cnc [Cancer] stars (γCnc & δCnc) the Northern & Southern Asses, respectively and (hitherto) respectfully. (Some saith they truly represent the donkeys present in the manger at the supposed Bethlehem birth of Jesus-of-Nazareth.) Arguing against pseudo-Eratosthenes or Ptolemy as Farnese-sources, BS p.174 darkly notes (Erat item 2 & Ptol item 6, resp) that the requisite “Asses are not shown … [in] Cancer” upon the Farnese globe.
    [Sober comment: Would the Asses be rigorously expected on a celestial sphere? After all, they're stars, not constellations.]

  • Rumper-Room Romp (2005 April First):
    Even if we assume that the Asses should be at Cnc, mightn't they be just as invisible as the chests (etc) of Cen, Cep, & Cas? — since they'd be on the other (Earthward — possibly SanDiegoward) side of Cnc.
    But Hark! There are obviously asses all over the FACG. Yea, verily, but a dozen asses sufficeth not to close the JHA universe. Understand, our knows-no-peace-relentless BS-Discoverer agitatedly seeketh only after the MISSING asses, and fain would giveth them succour that he may kisseth them.

  • So just fahgetabout astronomers' trivial Missing-Mass Problem. This is a mystery that really matters, understandably meriting high-press-priority scientific-society investigation — one which bids fair to herald the dawn of universal closure & peace, and one that just cries out for solution at April's start….

  • Scientific Breakthrough: Cervical BoobJob:
    As for the alleged Hipparchan Cassiopeia-“breast”-star, αCas (not mentioned anywhere in Hipparchos' Commentary, which skips stars that aren't necessary to Hipparchos' intent to evaluate the astronomy of Aratos & Eudoxos): in a passage evidently unknown to the Journal for the History of Astronomy archons directly responsible for skyrocketing this paper into media-land, our sole extant detailed ancient account of Hipparchos' klimata tells us (Strabo 2.5.41) that αCas is Hipparchos' Cassiopeian “neck”, not breast.
    Which is reasonable, since αCas is between two stars which HC calls the “body” (γCas: HC2.6.2 etc) and the head [ζCas: HC2.5.9, 2.6.4&9; Graßhoff 1990 pp.321-322 star PK178] — and is much nearer the head.
    [Strabo-Hipparchos loc cit correctly places αCas at Decl = 45°, “equidistant from the pole and from the equator” — a helpfully unambiguous identification, since no other serious Cas star's position fits that description. See the pioneering discovery (in connexion with this Decl) by A.Diller Klio 27.3:258-269 [1934] p.265 Table & p.267, also Neugebauer op cit p.1313; DIO 11.1 [2002] p.26 n.1 item [iv].]
    Note that such mixups were launched by the Journal for the History of Astronomy, despite the helpful rôle αCas openly played at DIO 4.1 [1994] ‡3 §F2 & n.26 [p.42], in pinning-down the location of Hipparchos' long-lost legendary observatory to Lindos (Rhodes Island) — a revelation which some might find almost as important to Hipparchan studies as a starless non-Hipparchan ancient globe….

  • Discoveries from Constellations' Hipparchan 1st&Last Rising&Setting Stars:
    The Farnese Globe's Non-Hipparchan Constellation-Bounds:
    Another provocative Cassiopeian revelation suggests an idea that may ultimately prove far more fruitful than projecting curious fantasies upon a starless globe — and will lead to numerous contradictions (of Hipparchan connexions to FACG) of which JHA was astonishingly innocent. FACG's Cassiopeia has far outstretched arms (also existing in pre-Hipparchan versions of Cas), very clearly displayed in photos 3& C), rather as in Ptolemy (all arm-stars identified above) [FACG's left arm reaches rather more southward even than Ptolemy has it] while HC's data for Cas' rising&setting unambiguously eliminate these arms from HC's Cassiopeia. (See HC2.5.9 & 2.6.9, esp. the 1894 edition [pp.192-195 & 208-209] of Karl Manitius, who devoted years of his scholarly life to patiently performing mathematical checks [of which JHA appears quite unaware] of all the HC phenomena, to verify star-identifications. [Note that nearby ιCas (Ptolemy's “star on the end of the leg”) never rises or sets for H's place & time, which is one reason H doesn't mention the star.])
    Hipparchos says (HC2.5.9 & 2.6.9) that Cassiopeia's head (ζCas for Hipp loc cit & ibid 2.6.4; also Ptolemy [Toomer p.351]) is last to rise and 1st to set — obviously impossible if circumpolar Cassiopeia has the Farnese globe's extended arms. (See above photo, remembering that south is at top. Or see globe's upper left on photo 2 [p.169].) So these arms are yet further proof that, far from indicating inspiration by a Hipparchan-globe, FACG instead again contradicts Hipparchos. The rising-setting situations for Cas are easy to check visually via, e.g., the handy SkyMap Pro visual program, set for ancient times. At epoch 125BC & north latitude 36° (using the descriptions of Toomer loc cit): σCas (“star on the right fore-arm”) will set before ζCas, and θCas (“star on the left upper arm”) will rise after ζCas.
    These considerations are much more than a debating point regarding a particular strange paper. They present us with a potential research-project which could be of genuine value to our understanding of ancient astronomers' techniques: use the numerous HC rising&setting data for dozens of constellations, to collect a sample of stars that cannot have been in HC but do appear in the Almajest  star catalog.
    [There is no doubt at all that there are at least dozens of Hipparchan stars which did not appear in the Commentary. See Pickering's comments at DIO 12 [2002] ‡1 n.2 [p.3].]
    Then investigate:
    [a] What are the statistics of their longitudes' fractional endings?
    [b] Were they added by Hipparchos after completion of HC?
    [A preliminary look at θCas, φCas, σCas, ψTau, χTau, φTau, and the Pleiades suggests Yes: half of those 10  stars have 40' endings. If the trend turns out to be representative, this might ultimately lead to some genuine re-thinking.]

  • Note: FACG's Lyr extends into dim regions (southward virtually to the TropCnc), far beyond anything in ancient star catalogs. Which suggests again that one is on shaky ground when assigning stars to features on an art-object. Hipparchos' rising&setting stars for Lyr (HC2.5.6&6.6) show that, for H, Lyr consisted of no more than the little parallelogram-with-equilateral triangle that we're all familiar with. (See also HC1.11.2 on εLyr being the north limit of Lyr.) LSCH strikes again.

  • HC's rising&setting data for Crv [Corvus the Raven or Crow] limit him to the sail-quadrilateral (α, β, γ, δ, & perhaps ηCrv), all at least 4° from the Equator. But FACG shows the Crow's tail just about touching the Equator (definitely crossing [exceptionally under] the very-nearby Ecliptic-southern-bound, as shown in a beautiful V.Valerio close-up image).
    LSCH strikes again.
    [Note that where a constellation's feature intersects a Farnese-globe circle, the circle almost unfailingly goes beneath the feature. Two exceptions: the Crow's tail and the Virgin's right hand. The observation that they have very proximate Right Ascensions suggests the hypothesis of more than one globe-sculptor. (However, distant Argo's lower rudder-oar disappears under the AntCirc. There may be other examples — DR has not carried out an exhaustive study on this point.)]

  • BS' Table 3 star#23 lists 42ψTau as “Taurus's shoulder” — but 42ψTau is not part of Taurus in Hipparchos' Commentary. HC3.3.11 specifies 1οTau as the 1st Tau star to rise, and it is eight degrees below Hipparchos' horizon when 42ψTau, HR1188, & the lead-Pleiad (19Tau) are all rising. (Again: check this out via SkyMap Pro or similar program.) This case is similar to that of θCas & σCas.

  • Other Notes:
    Table 3 star#36 (λSgr) is “Top of Sagittarius's bow” on the TropCap, yet the very top of his bow touches the Ecliptic (not TropCap) — which makes it even more misplaced vs the real H-era sky.

    PHOTO κ:
  • The Farnese-Centaurus Hoof-Confusion:
    BS has confusedly guessed vague spots where Cen touches the eqnColure, while ignoring Cen's definite left front hoof smack on the colure. (See above photo κ) Why?

  • The Cen left fore-hoof which is on the FACG's AntCirc and which BS (Table 3 star#47 [p.187]) has understandably taken to be αCen is well west (left) of the other fore-hoof — and is thus actually on the (left) leg that contains βCen, not αCen. (Check any star-map: αCen was and is to the SOUTH-EAST of βCen.) Indeed, βCen's Hipparchan RA is slightly less than 181° (see polar longitude at Graßhoff p.333), thus implying it was on the colure c.200 BC. This RA is a far better match to FACG's colure than αCen's. FACG's Cen has no part of his forelegs west (left) of the hoof that's on the AntCirc, which (since βCen is over 10° of RA west of αCen) means that if the hoof on the AntCirc is αCen (whose Decl is about correct) then the sculptor has confused βCen & αCen: giving the lower fore-hoof βCen's RA & αCen's Decl, and vice-versa for the upper fore-hoof. (HC3.1.4&6 just calls α&βCen the fore-feet, without distinguishing. Ptolemy [Toomer pp.395-396] puts αCen at the end of the right fore-leg, βCen on the left front knee. If we take βCen as left knee, αCen as rt hoof, FACG complies; BUT: FACG's AntCir (through alpha;Car) would then be c.3° further south than FACG's αCen.

  • We can check where such reasoning leads by assuming that the raised right hoof (not on AntCirc) is αCen, which would require dropping αCen from the above 8-star merged-polar-circle sample; least-squares analysis on the remaining 7 stars then yields:
    colatitude 51°.6 ± 0°.4 and epoch 160BC ± 100y.
    If we wish to test what happens on the broader assumption that no Cen on-circle hooves equal αCen or αCru, then we repeat the foregoing but including from the south only αCar in the merged sample; this yields:
    colatitude 51°2/3 ± 0°.5 and epoch 190BC ± 120y.

  • Followup on the foregoing hoof-confusion.
    Thanks to an excellent photo sent DR by Vladimiro Valerio, DR was able to resolve a previous ambiguity and misimpression: it appears that the Cen hind hoof on the AntCirc is the left one. This would suggest that the RA of FACG's on-AntCirc-hind-hoof probably corresponds to αCru: — and this appears a little greater than 160° on FACG, which would correspond to roughly 200BC.

  • HC1.8.22 places the southerly star in Cen's rear legs at RA = 163°; but Manitius calls this βCru, not αCru, and Ptolemy's coordinates for star PK966 support him. The Cru-star identity-question is worth close examination in-passing; αCru's pre-extinction magnitude is about 1/2 again brighter than βCru's, but its culmination-altitude is lower for Rhodes; so, for Hipparchos the post-extinction brightness ratio would be inverted. (Assuming clear air c.130BC from Hipparchos' southern Rhodes observatory-spot: 214m-high-cliff above Cape Prassonesi, 35°53'N 27°3/4 W; DIO 4.1 [1994] ‡3 §E4 [p.41].)
    The main evidence for determination: [a] The real Hipparchos-era RA for αCru was rather nearer HC1.8.22's 163° than was the RA for βCru. (Though, the difference is not large enough to provide a crucial-test by itself.)
    [b] Hipparchos refers to the “southerly” star, and αCru is southernmost for the legs (or Crux).
    [c] Transitting αCru was brighter than 3rd magnitude on a clear night, as seen from Cape Prassonesi's cliff.
    So DR concludes that the RA recorded in Hipparchos' Commentary (1.8.22) reflected his observation of αCru. This implies that the southern horizon agreements of the stars in the Commentary and the Almajest  rise from nearly-perfect to perfect in the key region south of Decl −50°. (See DIO 12 [2002] ‡1 Fig.1 [p.5].)

  • The Sale Begins When the Evidence Says No: JHA as Bureau of Double-Standards:
    (DIO 1.2 [1991] §J7 [p.140].)
    BS previously (2001) spent 42pp of valuable Pb-article space in the Journal for the History of Astronomy, lawyerly attempting to distract-from numerous close resemblances of Ptolemy's star-positions to Hipparchos', in order to defend JHA-love-object C.Ptolemy against charges that P copied the Ancient Star Catalog from Hipparchos. But in his current effort, BS busies himself alibiing the huge non-resemblances of the Farnese non-stars to Hipparchos' stars (disjuncts ordmag ten times larger than Hipparchos-Ptolemy agreements) — in order to cobble together a “confident”, “strong”, even “virtually perfect” case that the Farnese sculptor MUST have copied Hipparchos, regardless of all manner of blatant discrepancies.
    Well, as we once summed up the religiously rigid, fear-ridden history-of-ancient-astronomy assylum (DIO 1.2 [1991] §J7 [p.140]):

    For the archon-angels above: double norms are the single norm.
  • So ends our main detailed discussion of BS' folly. It is thus a good time to note BS' potentially positive contributions to FACG-investigations:
    First to correct for the sculptor's distortion of the globe, and thus to close-in-on FACG-source's inherent values of obliquity.
    First to get a (possibly) useful estimate of the true (celestial) size of the polar circles.
    First to concentrate on the 2nd century BC, which is about right if one measures RA from the colures instead of from the Ecliptic-Equator intersections — though Valerio's unfairly-BS-scorned argument (op cit p.103) in favor of a few centuries later has equal validity if one uses the Ecl-Eq intersections. Note our above theory that roughly justifies both researchers' dates.

  • Independent Indications of Non-Hipparchanness:
    The only group of “stars” that have a hope of being accurate and are likewise usefully sensitive to precession are the on-colure stars. BS lists twelve in his Table 3, and we have already given elsewhere here the result of a weighted least-squares solution:
    But most of these stars are invalid:
    Star#2 θPer is just a self-contradictory screw-up.
    Star#5 pPup is a shot in the dark for something resembling the west limit of Argo's prow — which doesn't touch the colure, anyway (photo 2 [p.169]).
    Star#6 φGem contradicts star#24's description of the same star — a dim star unmentioned in either HC or Ptolemy, where additionally the description of this whole region contradicts FACG.
    Star#7 θCen attempts to exploit Cen's on-FACG-colure spine by picking θCen as “Centaur's chest front”; — but the same star is elsewhere identified as “shoulder”.
    Star#8 λVir is mere rough guesswork at locating the “West edge of Libra”.
    Star#10 ξCap: more guesswork — and for a constellation not touching the FACG colure, and adducing an HC-unmentioned star.
    Star#11 ηLyr “Just east of Lyra's edge” (actually brighter θLyr was right next to ηLyr and about 1/3 of a century's worth of precession east of it) — guesswork again by the kindest interpretation, use of a minor star (magn 4.41), and not in Hipparchos' Commentary, and just-so-happening to be right on the Hipparchos-era colure.
    Star#12 2Cyg — again guessing — by just-so-happening to pick another dim (magn 4.99) non-HC star that just-so-happens to be right-on the Hipparchos-era solColure.

  • To estimate the epoch of the FACG source-astronomer(s), DR has cautiously (very possibly over-cautiously, given the mushiness of so much of the “data” from the FACG “stars”) formed a sample, largely from BS' on-colure stars. While throwing out the obvious junk-stars that BS includes in his on-colure dozen (which artificially inflated BS' resultant standard deviation, thus quite improperly lowering this key sample's weight (vs sample [G]'s trash-data) in BS' final solution — the key trick that gets BS near-to H's date), DR is perhaps being way too optimistic in the other direction about what can be elicited even from on-colure material. The four stars DR ultimately used were: γAri*, γAnd, ηCMa*, & τBoo* — most of which (asterisked) are colure stars in Hipparchos' own Hour-Star chapter of his Commentary (HC3.5). Weighted least-squares analysis formally yields a reasonable date:

    192 BC ± 21yrs

    — suggesting an earlier epoch than Hipparchos'.
    [One might have included φCen, βCen, and-or βCyg, but their qualifications were slightly uncertain. (The double-cluster χPer [Table 3 star#38] may or may not touch a FACG-colure; but it's much too vague an object, and Per is too grossly distorted to trust.) In any case, their inclusion only alters the result by a few years, to: 182BC ± 21y. Adding in just the Cen stars: 172 ± 21y. Or, including just βCyg instead: 202BC ± 21y.]
    The standard deviation is either gratifyingly or curiously small (depending on one's bent), with single-datum σ at barely 0°.4.
    [Note that with so few data, probability estimates regarding deviations from this date can't be simply induced from the Gauss curve; instead, the t-test is appropriate — which, with just dfs, suggests [formal] odds of ordmag 100-to-1 against 125BC data producing by-chance any of the above several on-colure samples.]
    But this 4-star sample was obtained simply by choosing stars that were identifiable and seemed [from FACG and-or Hipparchos' records] to be genuine colure stars. All were based on features that unquestionably touched the FACG colures. (Underlying point: if the sculptor wasn't adhering to the colures with 1° precision, then BS & DR have been wasting our statistical analyses, anyway. Some have pointed out that the very thickness of the FACG relief-marble circles is comparable to the net precision we have sought.) The use of some Hipparchan hour-stars looks superficially circular in favor of his epoch, but: [a] the result is distinctly pre-Hipparchan, perhaps partly because [b] his Hour-Star list includes obsolete entries, though no effort whatever was made to include just those.

  • Note that if Valerio is correct in measuring RA from the Ecliptic-Equinox intersections, then the foregoing result must be altered to roughly 200AD. Note also our proposal that both dates could have validity.

  • The Hipparchos Commentary's Hour-Star list (HC3.5) is a compilation of stars chosen for their sidereal-time-keeping utility of being virtually right-on integral hour-values of RA. (E.g., βPer at RA = 1h, ηCMa at RA = 6h, εPeg at 20h. At least one star is provided for each hour.) But a sizable fraction are given by Hipparchos as a little bit E or W of integral RA-hours. It has evidently not been previously remarked that most of these 14 not-quite-integral-RA stars are off in the eastward direction: 11 out of 14. Moreover, the eleven's mean eastwardness is greater than the mean westwardness of the other three: the former group's (stated) deviations are 2-6 timemin eastward (actually, all timemin are expressed as fractions of hours), while the westward stars' deviations are given as no more than 2 timemin. Since (except near the poles) precession causes stars' RAs to increase (become more eastward), we have indication that some of Hipparchos' hour-stars may have come from a prior hour-star list, and so needed to be updated for several decades of precession. (There is no discussion of precession in the Commentary; however, accounting for the crude precession estimate of 1°/cy was probably common practice at least as early as the mid-3rd-century BC: DIO 9.1 [1999] ‡3 §D5 [p.37].)

  • Hipparchos left a few solar equinoxes from c.160BC (Almajest 3.1), and there has been disagreement over whether they were his. But his authorship is consistent with the date indicated (albeit with a large σ: 19y) by least-squares analysis of the sample of 10 precise Decl data in Hipparchos' Commentary (DIO 4.1 [1994] ‡3 n.49 [p.46]):
    latitude +36°02' ± 04' and epoch 160BC ± 19y. (If the latitude is not treated as an unknown but is set at 36°08'N, then one finds: 158BC ± 19y.)
    [Note that the fractional endings of these data were consistent (ibid §F4 [p.43]) with the latitude (36°08'N) of the Lindos main observatory DIO has induced for him at idem, suggesting that his move from his native Bithynia to Rhodes may have occurred earlier than some had believed (incl. DR: DIO 1.3 [1991] §K3 [p.142]). For the HC hour-stars he gives as exact, the epoch appears to be in the −130s, so precession (during the approximately 1/4 century gap indicated) might account for some of the eastward bias in our 14-star sample of un-exact HC hour-stars; but it doesn't look like enough, certainly not for the Vir stars cited. So we here have a hint that some of Hipparchos' hour-stars might have been inherited from slightly earlier astronomer(s) — an independent suggestion that a substantial equatorial-frame catalog pre-existed Hipparchos'.

  • Since (from tests upon the on-colure stars) we were already looking backwards in time (for pre-Hipparchan star-mapping), we may perhaps be permitted to use one-tailed stats to gauge the odds on a 11-or-more eastward-instead-of-westward split in our above-cited sample of 14 Hipparchos hour-stars which are not quite on an integral RA. Probability of chance occurrence: 1 in about 34. (By convention, this is only moderately significant. Regardless, such odds are not negligible.)

  • H used some dim stars as hour-stars, e.g., ιTau, mag 4.62. So brightness is no explanation of some of his odd hour-star selections, a few of which hint (in the context of the eastward bias in those stars Hipparchos says are not exactly on the integral hour) at list-pollution by obsolescence.
    (At the same time, let us note that most of his hour-stars were well-measured and appear to be original choices for his epoch. Particularly excellent selections include, e.g., αTri at 0h, ηCMa at 6h, εPeg at 20h.)
    Our examination will use BS' 125BC epoch for convenience.
    HC3.5.5 says that RA of the star Vindemiatrix (εVir) as well as nearby δVir are more than 6m east of 11h. (Twice elsewhere Hipparchos treats these two stars as if their RA were identical: HC2.5.5 & 3.4.12, though they differed by 7m.) Well, “more than” is quite an understatement: Vindemiatrix' RA was in fact 15m more than 11h, a huge discrepancy; δVir was 8m past 11h. So why didn't Hipparchos choose γVir, the star that's right together with them in a familiar line — which was brighter than either and a better hour-star: only 6m west of 11h. (Note also: from c.235BC onward, εUMa was a better 11h hour-star than any of the three Vir stars — and brighter than all three put together.)

  • Vindemiatrix:
    The obvious obsolescence of Vindemiatrix hints that it had been a traditional hour-star for many years — which implies that observatories, equatorial-frame observations, and cataloging go back long before Hipparchos — as well as use of hours not degrees to measure the sky, which smells like early Greek (not Babylonian) science (though the star was recognized by both cultures).
    We note that the 11h RA-line crossed Vindemiatrix during 409BC(!), approximately in the time of the astronomer Euktemon, near the dawn of Greek fundamental astronomy.

  • Further on peculiarities of Hipparchos' hour-stars: ρPer was a much better 1h Hour-Star (virtually right-on) than βPer (Algol), which was 2min east of 1h though not stated to be.

  • Also, why — when 6αVul was less than a time-min east of being right on 18h — would Hipparchos instead use γAql for 18h when he knew it was well east of that important solstitial colure? HC3.5.12 puts the γAql discrepancy at 3 time-min, but it was really nearer 5 time-min by the time he listed it. The 2 time-min Hipparchan errors for βPer & γAql (and perhaps δVir) represent several decades of real precession, again hinting (far more precisely than the FACG) at the existence of an earlier star-catalog (from which Hipparchos perhaps gained a few of his HC data).

  • Gru on the Floor:
    BS continues to insist on too-thick an atmosphere for ancient nights (largely supported [at great length] in the JHA by modern daytime data….) BS cannot face the obvious γAra vs αPhe-&-αGru contradiction pointed out below. (Details: DIO 12 [2002] ‡1.) In BS' Hipparchos-related JHA Gigapaper#1 (2001), BS had to make his atmosphere's opacity rise up to wipe out the bottom six degrees of Ptolemy's sky (the highest starless-horizon in the history of 1000-star naked-eye catalogs) and thus alibi the 6° gap between Alexandria's 31° latitude and the Ancient Star Catalog's 37° AntCirc, in order to get the result he wanted at the time. But if he applied that bit of BS-science to the Farnese globe's 38°-39° AntCirc, he'd over-shoot Rhodes and end up way down south at 32°-33°N latitude without a candidate — and, mainly, not backing his typically-unalterable strong-&-confident Hipparchan-origin FACG-conclusion from his analyses' infallible and “perfect” Hipparchan-fit to FACG's constellation. Sooooo, in BS' Hipparchos-related JHA Gigapaper#2 (2005), we find that the blockage at the horizon is now somewhat less — but we still have the curious irony that BS 2001's tendency to way-overly-thick extinction hugely exaggerates BS' own 2005 FACG extinction-affected solution for the polar circles, creating a vast & BS-undercutting gulf between the implications of these two circles.

  • Moreover, let's recall the BS 2001 JHA paper's thick atmosphere (extinction: 0.23 mags/atm). Unfortunately for BS, once he assumed such Ptoley-saving-folly, he unexpectedly had then to explain (which he won't) how γAra — unquestionably recorded by Hipparchos — could have been seen at the post-extinction magnitude μ = 6.7 which BS-extinction demands (a μ-value which BS has yet to show he can compute correctly — DIO will be glad to agree to independent refereeing by specialists, on this glaring key refutation of BS's entire 42pp 2001 JHA paper), while according to the very same BS atmospheric model Ptolemy missed αGru at μ = 4.3 (though “his” catalog lists at least one [higher] Gru star: γGru) also αPhe, quite accessible at μ = 4.2. (Note: both cutting-room-floor stars' μ were for Ptolemy about ten times brighter than γAra for Hipparchos.) And this despite BS 2001's conclusion that Ptolemy recorded lots more stars than Hipparchos (whom BS 2001 credited with only one quadrant of the Ancient Star Catalog).
    [If BS is now abandoning his 2001 paper's super-opacity, why can't he do so explicitly, out in the open? Is BS instead simply going to pretend indefinitely — by silence — that both his 2001 anti-Hipparchos JHA paper and his 2005 pro-Hipparchos JHA paper were correct, even while he and Gingerich are admitting to the papers' mutually-contradictory conclusions regarding the authorship of the Ancient Star Catalog? (Was a partial spur to BS' interpretation of the Farnese globe his realization that his JHA 2001 paper was wrong — but it was less humiliating to outsized pride [than a frank admission] to [a] in BS 2002 cite Duke's statistical argument while pseudo-perplexedly pretending that the BS 2001 paper it totally destroyed had equal validity, and [b] then just publish a different paper [BS 2005] suggesting the opposite conclusion from BS 2001? Is it so painful to admit explicitly that an opposite party (Pickering) was right? DIO keeps doing it with ease.
    [DIO not only possesses an essential humility — which some (understandably!) don't immediately discern — but attempts to promulgate that virtue, because humility is one of the most vital and least appreciated keys to high scholarly creativity. (See, e.g., DIO 10 [2000] end-notes 2 [p.84] & 21 [p.105].)]
    Shouldn't archons, who vie for social primacy in AAS' historical wing, be able to adhere to integrity-primacy, as well? — especially by comparison to those they ever-entertainingly affect to regard as inferiors?]


  • Possible Sources for the Farnese-Atlas-Globe Celestial Vision:
    Now, were there ancient astronomers operating at a latitude of about 38°N?
    Any working in Athens (38°N) could have been the source of the FACG. (Remember that, simply because an ascription to “anonymous” doesn't interest the average newsman, doesn't make it wrong.)

  • As DIO has frequently noted, Aristarchos of Samos was genuinely one of the great astronomers of the ancient (or any) era: probable discoverer of precession (generally and wrongly credited to Hipparchos), undisputed 1st public announcer of the truth of heliocentricity and the vastness of the universe. (BS-Gingerich's candidates as Greatests [Hipparchos & Ptolemy] were small-universe geocentrist astrologers.) And we recall that Samos is at 38°N, though it is generally presumed that Aristarchos worked in Alexandria. (Note that a pre-Eratosthenes map of Egypt in spherical coordinates was probably from around the era of the school of Aristarchos and its Dionysios Calendar.)

  • Krates:
    Another candidate is Krates of Mallos, who flourished a few decades before Hipparchos and worked at Pergamon (latitude 39°N), a cultural center whose library (with which Krates was associated) rivalled Alexandria's.
    [Speculation-in-passing. Was the supposed astronomer Attalos (who did a commentary on Aratos before Hipparchos') from the royal Pergamon family that sponsored Krates? (Attalos the 1st through the 3rd ruled intermittently from 269BC to 133BC.)]
    Though a linguist and self-styled critic, Krates was also the earliest ancient who remains famous today as a globist. (See Strabo 2.5.10.) Oddly, it is little known that the same source mentions that Krates thought like an astronomer (Strabo 1.2.24 ). Krates is said (Neugebauer op cit p.611) to have had contact with Seleukos, the best-remembered of those few ancient astronomers who openly sided with Aristarchos of Samos on geomobility, heliocentricity, and the universe's enormity.

  • The proposal of Krates as FACG-source resolves a problem: how could a globist at Pergamon (39°N latitude) see the 3 stars on the AntCirc of the globe? Well, even aside from the obvious possibility of 2nd hand knowledge: Krates' native city of Mallos was at 36°.6 N latitude (35°1/3 E longitude) — so all the three stars (αCar, αCru, αCen) would have been nearly as visible to the young Krates as they later were to Hipparchos, who evidently recorded them on Rhodes (Prassonesi 35°.9N or Lindos: 36°.1 N).

  • On the celestial sphere, Krates stressed (as later did, e.g., Geminos) the import of all the circles we see on the Farnese globe: the zodiac, the two pole-piercing great-circle colures (cutting the [twelve-part] zodiac into four equal sections, at its equinoctial and tropical points), the five circles perpendicular to the polar axis: the Equator, the Tropic of Cnc, the Tropic of Cap, the Arctic Circle bounding always-visible stars north of it, and the Antarctic Circle of always-invisible stars south of it. (Hans Joachim Mette Sphairopoiia München 1936 pp.34-35.) So it is not unreasonable to suppose that Krates was among the many scientists who presumably made celestial globes before Hipparchos.

  • However, a direct record of Krates' sky is lost. So the theory suffers from un-contradictability.
    [Note analogy to BS' comparisons [pp.172f] of FACG to various astronomers' constellations, where Hipparchos has an inherent advantage over Ptolemy: Hipparchos' Commentary contains so much less constellation-detail (than the Almajest ) that can be contradicted. (Though, not as little as BS thought.)]
    Which renders the otherwise-enticing Krates-hypothesis impossible to test in any solid fashion. (However, an upcoming novel speculation will turn out to add a surprising extra argument in favor of Krates.)

  • In a final-proofs late addition to n.2 (p.195), BS highlights the odd line-segment — here dubbed the “CygSeg” — extending from Cyg's wing to the TropCnc. Some of the CygSeg's SW portion can be seen in photo D, at right here (the small diagonal, just to the right of Cyg's beak, in the lower-right corner of the photo). And all of the CygSeg can be seen near the right edge of photo C. (Far clearer photo by DR elsewhere here.) On 1st glance, DR wondered if it were simply Cyg's other drumstick. (Thiele concluded for this theory, which BS n.2 [p.195] soundly avoided.) It may be, though it seems virtually thighless — and way too thin, plain, & clawless to be compared to the single meaty, befeathered, & beclawed Cyg leg that is visible. Also, unless birds' legs grow out of their wings (see Cyg at extreme right in photo C) instead of their bodies, the line-segment is not where a leg can be. But note: the segment's width and linearity are strikingly similar to the FACG's various circles. (The segment's very slight variations in width are typical of the FACG circles: see detailed discussion at Valerio op cit p.102.)
    Valerio is perhaps the first scholar to draw serious attention to the segment as being worth investigation. He has undogmatically proposed that it could be the little constellation-asterism Sagitta (Sge) the Arrow. In favor of his view is: Sge, in (very) roughly the same area of sky, is missing; and the segment is very roughly the right size, though it evidences no features such as feathers. (Note that the west end [α, β, & δSge] of real outdoor Sge does have a slim-triangular shape, which the ancients understandably saw as the Arrow's feathering.) Some celestial globes depict Sge piercing a wing — though it is of course the wing of more-proximate Aql — and is shown exiting (unlike FACG) through the wing, where the arrow-head is thus visible. The FACG segment is tilted at the wrong angle for the real Sge (which aims at Peg's head, not Cas — as on the FACG) and is roughly 10° from Sge's place. But if Sge is supposed to be entering (not exiting from) Cyg's wing, then the FACG segment is aimed into the correct quadrant (though nonetheless still c.1/4 of a quadrant different from the FACG segment's orientation).

  • So, we now present a novel — albeit knowingly speculative — hypothesis.

  • Cygnal Success?
    The hitherto-uncertainly-identified Cyg-segment is on and along the Milky Way
    Extending the segment towards the northeast takes it right through Cas (as one can readily discern from, e.g., photo C, at right [and inverted: south at top]), much like the direction of the Milky Way.

  • Checking the Galactic Equator as modernly defined (visible on, e.g., SkyMap Pro), one will see that it goes through almost exactly the same part of Cyg and at pretty close to the same angle as the Cygnal segment on the Farnese globe. So:

    Is the Cyg-Segment a Surviving Fragment of the Parent Globe's Galactic Circle?

    Both position and orientation of the CygSeg are in good agreement (with the actual Galactic Circle — or, as we now call it, Galactic Equator) to within just a few degrees. However, it must be said [though see 2007 comment below] that extension in the other direction goes rather further north over Sgr (clipping Oph's ankle and bisecting Sco) than one would expect in a great-circle tracking the [full] Milky Way. Other than the too-easy suggestion of artist-error, this discrepancy could mean: [a] the DR theory is pure fantasy (perfectly possible); [b] the ancient Galactic Equator was defined by northern constellations more than is done today (when we have ready access to the deep southern sky); [c] the segment represented not a perfect great-circle but a local branch or boundary of the Milky Way in the Cyg region. [Or Cas-Cyg-Aql region.] (DR prefers option [b].)

  • Though Sagitta (almost 6°1/2 long) is an imperfect match to the 10°-long Cygment, the shortness itself obviously fits the FACG [Farnese Atlas Celestial Globe] segment's length better than the Galactic Circle (which extends 360°). Thus, DR's theory has the serious disability that it must seek a plausible explanation of why most of the circle is missing. And why fairly-nearby Sge is missing. (BS p.171 notes that several small constellations are missing from FACG, most mysteriously Tri & Sge.) But otherwise: the segment's utterly featureless appearance, its position, and its orientation are all in better agreement (than Sagitta's) regarding what FACG would show if the segment were part of a line meant to track the Milky Way. (That, of course, does NOT prove the truth of the DR proposal. Among all the possibilities here, keep in mind that the one that ever lurks: we may all be wrong.)
    Concluding, it must be said that the Sagitta explanation has much in its favor.
    [Note added 2005/4/12. There is one final DR observation that seems to favor the Galactic Hypothesis: we can see that the neck of Cygnus is round: part of a circular cross-section. One would expect the same of Sagitta the Arrow — yet we find otherwise with the Cyg-segment. As shown in a V.Valerio ultra-close-up image, kindly sent to DIO by Valerio. (Who is admirably open to airing all sides on the interpretation-question here.)
    See DR's own photo υ of the Farnese globe's Cygnus (reproduced just below.)

    PHOTO υ:

    The CygSeg's cross-section appears to be an only-slightly rounded narrow near-rectangle (barely-trapezoidal) — much like the (other?) FACG celestial circles.]

    [Note added 2007/2/23:
    The effect of invisibility of the deep southern part of the Milky Way would have magnified (for ancients estimating a best Galactic Equator) the effect of the northern Milky Way's deviation (nearly 10° southward) in the Cas region from the full (modernly-defined) Galactic Equator. (See, e.g., Norton's Star Atlas.) Thus, an ancient-Greek-estimated Galactic Equator great-circle would
    and should very naturally go further north through Sgr and Sco than the modernly defined GalEq. As it does.

    See DR's color photos: photo υ (above) and photo λ (just below), noting from both that the great-circle along the Cyg-Segment (upper right) goes through the thigh of Oph.
    [Oph = large man on left, bearing Ser (serpent) and enjoying an upside-down staring-contest with inverted Her (hero & kneeler) — their opposition hinting that these Greek constellations were invented when both heads' declinations equalled Greece's latitude.]
    From photo λ, we see the gt-circ containing the Cyg-segment then going north of Sgr's bow & arrow (lower right), piercing the middle of Sco (bottom, with stinger visible, but otherwise much hidden by Atlas' wrist), and finally going nearly through a brown dot-stain (lower left corner, beyond Atlas' wrist) — which (see photo κ) is where Cen's right arm holds the hind leg of Lup (beast).

    PHOTO λ:

    Moreover, the proximity of Cas to Cygnus would have had a strong effect upon an ancient Galactic Circle's orientation, and photo C shows that the Cyg-Segment indeed lines up appropriately for the mean Milky Way position at Cas. (A Galactic Equator passing through the MW-thickest parts of Cyg and of Cas would have passed roughly 5° further from the equatorial poles than a GalEq based upon the entire Milky Way — as it is now defined. [Keep in mind that the brightest parts of Cen&Crux were invisible from ancient Athens at 39°N.])

  • Attempt at Reconstruction of Farnese-Global Evolution:
    Speculative Hypothesis (to explain [explain-away might be franker] the segment's shortness): the full Galactic Circle adorned the original astronomer's globe, but the later sculptor or his masters didn't share our source-astronomer's fascination with the Milky Way (or just thought it over-cluttered-up the Globe), and so he intended to completely eliminate it. But, regarding the little fragment (of the original Galactic Equator) between Cyg's left wing and the TropCnc, he made DR's initial mistake and assumed that this tiny portion was the missing leg of Cygnus (which was in truth simply hidden under the body, like other limbs on FACG: e.g., Peg's left wing, Cas' right leg, Perseus' left arm). [Note that Cen's left front leg is nearly coincident with a circle, though the distinction is fairly obvious in that case.] (We recall that BS also found the FACG Cyg's one-leggedness peculiar: p.174 item 11 & p.195 n.2.)
    Given that nearby Aql (among other FACG figures) clearly has its legs ON the FACG's TropCnc, note that the Galactic-Circle hypothesis' leg-confusion implication (that the sculptor mistook the segment for Cyg's leg) explains — better than the Sge theory — the striking circumstance that the segment ends precisely upon FACG's TropCnc.

  • [Playing Joker With Every Star Wild:
    Possible extra implication: the sculptor is indicated as having been meticulously faithful (at least in this instance) to the original globe. Which might stir our caution about excusing discrepancies by pleading that the sculptor was an unreliable copyist. (Valerio op cit p.105 proposes that the globe is not a copy at all.) See, e.g., the catch-all escape-hatch which BS has quietly slipped into his otherwise hardly-altered original AAS-distributed 2005/1/11 text (in which not a datum has been changed since!) — once most newspapers' 15min attention-span had been tickled to exhaustion (p.179): “Farnese Atlas is not a perfect rendition of the Hipparchus star catalogue, as there are small random errors in position introduced by the scupltors as well as a variety of universal differences that must have been made after the figures left Hipparchus. There may be substantial uncertainties in taking a figure's position on the globe to be identical to that in Hipparchus's catalogue for purposes of comparison with the Almagest.” (Compare this to prior [and still-retained] confident assurance: “The constellations are placed onto the Farnese Atlas with remarkable accuracy.”) See DIO 9.3 [1999] ‡6 §G2 [p.128] on the Cook Society's religious interpretations of squishy materials: “Reminds one of [Andrew] Salter on Freudian dream-analysis: like playing poker with every card wild.”
    See elsewhere here on BS' evidently un-selfconscious p.177 paragraph on the “constraint”-that-isn't.]

  • So, what ancient globist do we know of, who specially emphasized that the Galactic Equator was as important as the other eight primary circles (not counting the auxiliary zodiacal bounds) that appear on the Farnese globe? It's not Hipparchos, who showed (HC1.9.15) little interest in the Galactic Equator. Nor Ptolemy, who (Almajest 8.2) discourages the idea of seeing the Milky Way as a circle, understandably preferring (like Geminos, who however does deem the Galactic Circle important) to describe the varying-width, occasionally-forked reality.
    But there is an ancient scholar who worshipped the Galactic Circle, and he is the same versatile early 2nd century BC scholar whose productive era (see other temporal hints at DIO 11.2 [2003] ‡4 §L [pp.49-50]) was suggested by DIO least-squares analysis of on-colure FACG stars and whose globist fame and astronomical bent were attested by Strabo (setting DR wondering early-on [2005/2/12] if this well-known ancient figure might have some connexion to the putative true FACG-source):

    Krates of Mallos

    Mette loc cit emphasizes the special cosmic importance which Krates placed upon the sky's “slanted” circles: the Zodiacal Ecliptic and the Galactic Circle.

  • I hope that those with access to the Farnese globe will now perform close examination and measurement of the suspected galactic fragment, which is the only lone line on the globe not heretofore explained to general satisfaction. The odds against this “short, simple line segment” (BS n.2 p.195) having by random chance such close positional and orientational agreement with the Galactic Equator are 1 in ordmag 100.
    (Again: that does not prove the galactic theory's truth.)

  • CygSeg's Possible Significances:
    There are further potential implications here that should not be left unsaid, despite the galactic theory's highly speculative nature:
    [a] The Cyg-segment's straightness and near agreement with the true Galactic Equator suggest an ancient mathematician-astronomer's use of an averaging technique, to find the great-circle that would be a best-fit line following the Milky Way.
    [A worthwhile modern statistical project: discover what was the best-fit Galactic Equator for stars easily and often visible from Greece — after all, the modern Galactic Equator is partly based on heavy parts of the Milky Way that were not visible in the ancient Mediterranean.]
    [b] And this thought takes us right on to another: one would probably not get good averaging from a small set of stars — so (if this very speculative hypothesis is valid) whoever did the math presumably worked with a serious star catalog's data. If this was not Hipparchos' catalog, then we have (very) tenuous evidence that before Hipparchos there existed a major star catalog (not necessarily the small one which we have elsewhere speculated could have underlain the Farnese globe), perhaps not so large as Hipparchos' later one, though possibly representing a world-record-achievement at the time.

  • The theory that Krates was behind the FACG is bound to remain very debatable. Likewise the speculation that a Galactic Circle origin might explain the still-controversial CygSegment.

  • In case we have added anything to scholarship on these matters, it is built upon what has been left to us by ancient astronomers, the sculptor, and recent fruitful decades of expert researches thereon by such scholars as, e.g., Vladimiro Valerio, and the equally dedicated predecessors (such as M.Fiorini [1827-1901]) whom Valerio graciously credits from the very 1st sentence of his summation of his own findings (op cit), as crucial in laying the groundwork for them.

  • This concludes DR's [a] firm analyses and [b] openly-identified speculations (also flagrant speculations) — on the Farnese Atlas globe.
    Despite some (well-merited) ribbings of BS here&there in the foregoing, it would be ungrateful not to thank him for leading DR into this area — whatever may be of worth in the above would probably not have occurred without the initial stimulus provided by the BS paper, as well as, e.g., his (hopefully) useful and partly original revelation of the true celestial sizes of FACG's tropical & polar circles. (Though Matteo Fiorini anticipated this pretty well in the 19th century, as BS p.191 creditably notes.) Also, someone as energetic as BS is bound to add to our knowledge in the future, so the nest of foulups in the present instance should not cause automatic discounting of anything yet to come. But genuine refereeing is always in order, as a kindness both to BS and to his readers.

    The assistance of Keith Pickering, Vladimiro Valerio, Dennis Duke, Leroy Ellenberger, Hugh Thurston, Bob Bryce, & Polly Connor is gratefully acknowledged.

    [Occasionally revised 2005/4/2-2011/11/10.]