Talk:Tycho Brahe/Archive 2

Illustrations
The illustrations need sources cited in their captions, especially the pictures from Tycho's Mechanica. They are not watercolors either - they are prints from either copperplate or woodcut, with hand-applied watercolor wash. They look like copperplates to me but can someone go into a rare book library and find out whether they are copperplates or woodcuts? —Preceding unsigned comment added by 69.0.26.33 (talk • contribs) 04:31, 31 January 2006 (UTC)
 * According to Ronald Brashear, the Curator of Science and Technology Rare Books at the Special Collections Department of the Smithsonian Institution Libraries, some were woodcut and some wre engravings:


 * -84user (talk) 17:13, 24 September 2009 (UTC)

Death section
I replaced the unattributed bits: "Tycho may have poisoned himself by imbibing some medicine containing unintentional mercuric chloride impurities. Some have even speculated that..." with an attributed verifiable statement based on the referenced book. Please, if you have other verifiable outlooks on his death, do add them, but not without proper reference and attribution. Dicklyon 01:46, 13 January 2007 (UTC)

The part about him possibly poisoning himself is from the same book, p208. Mossig 13:41, 13 January 2007 (UTC)


 * True, though Kaempe's 1993 conjecture is pretty much superceded by the newer analyses presented in the book. Seems hardly worth mentioning, but if we do we should put in the actual source and date, since this book just mentions it in passing as a previous interpretation of finding extremely high mercury levels in his hair. Dicklyon 05:58, 15 January 2007 (UTC)


 * But the conjecture presented in "Heavenly Intrigue" is not accepted as the final word either. One of the latest books published about Tycho Brahe, by the Dansih National Museum toghether with the ongoing (very good!) exhibition about his life and work, does not even mention it! Mossig 10:15, 15 January 2007 (UTC)


 * And it's not presented as final word, but as "Recent investigations have suggested." We should also present other suggestions, but we need to find them first. Dicklyon 00:08, 17 January 2007 (UTC)


 * This recent event would seem to make the "not urinating" death more plausible: . I don't think his bladder would have to "explode" for him to die. &mdash; Chowbok  ☠  03:46, 15 January 2007 (UTC)


 * The book explains that the mercuric cloride causes kidney failure, stopping the production of urine, and explaining his inability to urinate in the painful week before he died. It's a great read. Dicklyon 05:53, 15 January 2007 (UTC)


 * Water poisining does not give the drawn-out illness of 10 days which Tycho was experiencing. (The book is a great read, and makes a compelling case. But it is hard to say that it is conclusive. There are other possible culprits if he where poisoned, and he may still have died from another ilness.) Mossig 10:15, 15 January 2007 (UTC)


 * Conclusive or not, if we want to represent other theories, we need other sources, don't we? Personally, I thought it was enough for a conviction. Dicklyon 17:19, 15 January 2007 (UTC)

I took out the sentence that starts "Critics of the mercury theory point to the fact that Isaac Newton's hair had many times the mercury level of Brahe's" because the reference did not support any part of the statement. It had nothing about critics, or Brahe, or comparative mercury levels. If someone has info on these critics, or how they compared mercury levels, please do add it back with a ref. Dicklyon 18:51, 16 January 2007 (UTC)

Mossig has removed most of the meat of the Gilder conclusion. Why the reluctance to include material from this recent book, which appears to be the most thorough and detailed study of Tycho's death that is available? What are we trying to balance against it? Dicklyon 22:49, 23 January 2007 (UTC)


 * In the Kepler article the notion that Tycho was murdered is thought as 'fanciful'. I believe we must have some agreement between the two entries as both pertain to the same encyclopedia.  This is the first time I hear about Kepler being a murderer and I confess I'm a bit shocked.  I suddenly remembered two other men:  Salieri and Mozart. —The preceding unsigned comment was added by 201.19.179.192 (talk) 23:40, 29 April 2007 (UTC).

Dear all: I would like to note that I added today Kepler's account of Tycho's death. I hope it looks okay. It is drawn from Kitty Ferguson's 'Tycho & Kepler' (included in the suggested reading list) who in turn sourced it from volume 10 of Tycho's collected work 'Tychonis Brahe Dani Opera Omni'. I was unsure of how to add the reference notations. Perhaps someone could add it or indicate to me where Wikipedia has such instructions outlined. (BB) —Preceding unsigned comment added by Benjaminbudde (talk • contribs) 04:43, 8 May 2009 (UTC)

Leaps wildly to conclusions
The current version is:
 * Recent investigations have suggested that Tycho did not die from urinary problems but instead from mercury poisoning: extremely toxic levels of it have been found in his hair and hair-roots.

and then uses source Tychos life, which contain nothing of that sort. The source instead says that died 24th October 1601 of a urinary bladder infection that he
 * may have died 24th October 1601 of a urinary bladder infection that he may have tried to cure himself, with a medicine containing mercury

saying nothing about "extremely toxic levels", and nothing about "mercury poisoning". From the above discussion one can conclude that there are theories, very contested theories of mercury poisoning, but if this is not one authors wild pseudoscientific speculation, then more sources are needed. ... said: Rursus ( m bork³ ) 08:11, 30 October 2009 (UTC)

Wikipedia books
I just noticed the "Create a book" that appears on the left navigation bar allows logged in users to assemble books from a set of articles. Help:Books states that the function is being tested, so just for fun I created Books/Tycho_Brahe titled Tycho Brahe's life and work.

It's only ten articles, and it is not possible to add images or articles from other wikis. However, I'm thinking of creating some User-space gallery pages to include some nice Commons images of Tycho's instruments. The book is available for editing by anyone (even logged out users). 84user (talk) 08:16, 2 March 2009 (UTC)


 * File:Tycho Brahe Wikipedia book.pdf is the latest output from Books/Tycho Brahe : it has 35 pages with 4 page appendix of images from Commons. 84user (talk) 16:31, 2 March 2009 (UTC)

Tycho
Tycho seems to have been the first to cast doubt on the honesty of Ptolemy. This could be mentioned in the article. —Preceding unsigned comment added by 86.137.170.8 (talk) 09:56, 25 April 2009 (UTC)

results from readability and other tools
Out of curiosity I ran article Tycho Brahe through a few Toolserver tools. I noticed the webchecklinks was reporting as dead but it seemed fine to me. However, WebCite was unable to archive the timesonline link, so I added a note to look for a longer lived cite, as it will likely succumb to linkrot. 84user (talk) 06:53, 29 May 2009 (UTC)
 * readability: 5021 prose words and reader age of 17+ (Fry index 15).
 * find dead links - I fixed a few
 * find ambiguous wikilinks - I fixed them
 * Traffic reported "Tycho_Brahe has been viewed 27453 times in 200905."
 * edit history shows about 500 edits per year, so 1 edit per 50 readers?

The accuracy of Tycho's observational astronomy and its significance
The first paragraph of the article’s section ‘Tycho’s observational astronomy’ appears to have numerous problems.

The current claim that Tycho's planetary observations were "consistently accurate to within about 1' " is surely false if this means Tycho's estimations of temporal planetary positions. For his most cosmologically crucial estimation of all, that of Martian parallax in its 1582 conjunction, was out probably by as much as 4', inasmuch as he eventually estimated it as greater than solar parallax that he mistakenly put at 3', reportedly simply following Hipparchus rather than doing any observations for himself. Surely the relative consistent accuracy/reliability of a set of astronomical estimates/predictions should not be identified with the greatest accuracy achieved, but rather with the least accuracy consistently achieved. I propose this claim should be replaced by something like the more modest neutral claim that although SOME of Tycho's planetary position estimates were accurate to within about 1', other crucial estimates such as that of Martian parallax at opposition in 1582 were out by 4' or more, and so the overall consistent reliability of his planetary position estimates may be no more than 4'+. --Logicus (talk) 16:40, 25 August 2009 (UTC)
 * This entire discussion suffers from logical incoherence, as it appears to confuse observations (i.e., pure observational data) with estimates and predictions, which are based on the interaction of observational data with theoretical models and are an entirely different thing. Please read the secondary literature more carefully before removing comments based upon it.  --SteveMcCluskey (talk) 19:46, 25 August 2009 (UTC)

Logicus to McCluskey: No, as I understand it, surely it is the article's paragraph itself that suffers the logical incoherence of confusing estimates and predictions of celestial positions with observations, rather than my discussion, which rather seeks to eliminate that apparent confusion.

This confusion seems evident in the following passage, in which a claim about 'observations of positions', which can surely only mean statements or estimations of positions based upon observations, is immediately followed by a claim about planetary observations, which for logical continuity must surely mean observations of positions, as follows:

"his observations of stellar and planetary positions achieved unparalleled accuracy for their time. His planetary observations [of stellar and planetary positions ?] were "consistently accurate to within about 1'," "

For it is difficult to make any sense of 'observations of positions' unless it means 'statements of positions'. Otherwise what would pure data of planetary positions consist of in your view ?

And the same confusion also seems evident in the following passage

"...the stellar observations as recorded in his observational logs were even more accurate, varying from 32.3" to 48.8" for different instruments,[24] although an error of as much as 3' was introduced into some of the stellar positions Tycho published in his star catalog..." [My itals]

What sense is to be made of this passage unless the phrase 'stellar observations' means 'stellar positions' ? For otherwise is seems chalk is invalidly compared with cheese here. Why compare a 3' error in stellar positions with a 32.3" error in stellar observations, unless these two magnitudes are for the same thing and so whereby the former is being said to be much bigger than the latter, rather than being incomparable, and hence whereby the latter phrase must also really mean stellar positions ?

Or are the limits of the precision of instruments being confusingly malcompared with errors in estimated stellar positions in this passage? (i.e. is Wesley's article The Accuracy of Tycho Brahe's Instruments about instrumental error, whilst Rawlins' is about errors in stellar locations ?) On your interpretation surely what we need to know here is what the error was in the stellar observations on which the 3' erroneous stellar positions were based. Were they within 32.3" to 48.8" ?

Is this passage saying Tycho's observational log was much more accurate than his star catalogue ? If so, what is the yardstick against which the accuracy of the stellar observations (i.e. pure stellar data in your view?) in the observational log are being measured ? And what is the yardstick against which the accuracy of the stellar positions in the star catalogue are being measured ? Is the latter maybe nowadays contemporary accepted values of their positions ?

I also point out that the analyses of the accuracy of Tycho's star catalogue by Thoren 1989 and also Hoskin 1999 tend to support my hypothesis that 'stellar observations' in the above passage means 'stellar locations'.

What does it mean for pure data to be accurate or inaccurate in themselves ? Surely data are just data, which cannot be said to be accurate or not unless they are interpreted as representing something else.

'To perhaps help sort this disagreement out, in the first instance, in observance of Wikipedia Verifiability etiquette would you please kindly provide the quotation from the Journal for the History of Astronomy'' article cited that you think verifies the claim that "[Tycho's] planetary observations were "consistently accurate to within about 1',[23]" ", when 'observations' means 'pure planetary data' as you claim ? This may at least clarify whether this apparent confusion is actually in the 'verifying' article, or has been introduced by Wikipedia.'''

Re your editorial comment, "Undid revision 309999203 by Logicus (talk) per the source you removed which was accurately quoted (consider reading WP:NOR)) (undo)", please note that the quotation did not itself include any reference to "planetary observations", thus not in itself verifying the Wikipedia claim made.

For the record, the replacement text I edited which you reverted was:

"Tycho was the preeminent observational astronomer of the pre-telescopic period, and his estimates of stellar and planetary positions achieved unparalleled accuracy for their time. Some of Tycho's planetary position estimates were accurate to within about 1', but other crucial estimates such as that of Martian parallax in 1582 were out by 4' or more, and so the overall consistent reliability of his planetary position estimates cannot be more than some 4'+. The stellar observations as recorded in his observational logs were even more accurate, varying from 32.3" to 48.8" for different instruments,..."

Further to this I have drafted the following provisional replacement for the current passages on the star catalogue accuracy.

'The maximum accuracy of Tycho's estimates of the positions of stars published in his star catalogue was even greater than that of his planetary estimates, to half a minute or so for some of its reference stars.[p101 Hoskin 1999]. But the maximum inaccuracy of many of the stellar positions he published in his star catalogue was as much as 3' or more, due to his use of an erroneous ancient value of solar parallax due to Hipparchus that he used as a reference for stellar positions, and also due to his neglect of atmosphetic refraction.[25]. So overall Tycho achieved little better accuracy in his stellar astronomy than in his planetary astronomy, and for a similar reason.'

However, I am currently reviewing whether his max inaccuracies in celestial positions were not in fact far greater.

I do hope you will agree that at the end of the day it is the overall consistent standard of accuracy of Tycho's estimates of celestial locations that is of primary importance in evaluating the accuracy achievement of his observational astronomy. The degree of instrumental precision/error of his instruments is irrelevant to the accuracy of observations in locating a body if, for example, in his absence Tycho's observers were all drunk, the drunken moose ran amok and damaged all the instruments, and they were pointing at the Moon rather than Jupiter whose position they were supposed to be locating.

I do hope that together we can perhaps constructively sort out what the accuracy of Tycho's estimates was from what seems to me the highly confused and apparently conflicting dog's breakfast the literature makes of it. In this context I note Swerdlo commented in Walker 1996 p209 "Various statistical evaluations of his observations have been made, with different results..." --Logicus (talk) 17:20, 26 August 2009 (UTC)


 * Two points:


 * First, and least importantly, you objected to my edit to this article, which reverted your text, and to the associated comment. I did not make that edit, which was made by User:77.215.191.91 who can be shown by a Whois check to be from Denmark.  It's not me.


 * Secondly, your proposed text does not make clear the distinction between the accuracy of Tycho's observations (of planetary and stellar positions) and that of the final estimates (both the estimate of Martian parallax at opposition and the estimates of the positions in the star catalog).
 * It will be helpful if (1) you made clear to the reader the basis and nature of Tycho's estimate of Martian parallax at opposition (I suspect it's a theoretical value, not an observational one) and (2) found an authoritative source on the representative accuracy of Tycho's star catalog and cited it, rather than selected outliers from the data. --SteveMcCluskey (talk) 18:21, 26 August 2009 (UTC)


 * Steve, apologies for identifying you with User:77.215.191.91 and for your advice on its geographical origin. Now I suppose the Vikings have it in for me (-:


 * Thanks for your comments, but I don’t understand the distinction you make between the accuracy of observations and of position estimates. You seem not to have read nor understood my criticism of this distinction. For example, the observation that a star is seen at an elevation of 45 degrees above the horizon at some time is neither accurate nor inaccurate, but just an observed fact or not. It is the conclusion that the star is itself located at an elevation of 45 degrees that can possibly be inaccurate, by virtue of atmospheric refraction e.g. So could you possibly please give me an example of what you mean here ?


 * And I do cite a source on the accuracy of Tycho’s star catalogue, namely Hoskin 1999.


 * And your removal of my request for the verifying quotation overlooks the point that the quote marks exclude the term "observations" within them, and therefore it does not verify Gingerich and Co were making this claim about observations, rather than positions. OK. SO I restore the flag.--Logicus (talk) 18:19, 27 August 2009 (UTC)

What Hoskin says "[In compiling his star catalogue] First he [Tycho] and his teams determined the positions of selected 'reference' stars as carefully as possible, and then they measured the positions of other stars relative to appropriate reference stars. The accuracy of the catalogue therefore depended in the first place on the positions of the network of reference stars, and by the late 1580s Tycho had determined their positions to within half a minute or so of the true values. Yet although the places of the brightest of the non-reference stars are accurate to around the minute of arc that was his standard, the fainter ones are less accurately located, and there are many errors."--Logicus (talk) 16:27, 28 August 2009 (UTC)


 * Steve, thanks for providing a verifying quotation from Gingerich & Voelkel 1998 ? I suppose the next question is whether it actually means observations rather than positions, given the literature tends to confuse the two. But if it is about the accuracy of observations in your view, does that article also make any evaluation of the accuracy of Tycho's planetary positions as well as that of his planetary observations ? It is after all the calculated positions that are more important.


 * And would you care to give your evaluation of the relative accuracy of Tycho's planetary positions and stellar positions ?--Logicus (talk) 14:42, 29 August 2009 (UTC)


 * Logicus to McCluskey, or anybody: What does 'Tycho consistently achieved an accuracy of observations to within 1 arcminute' mean ? That at some specified time a celestial object could be seen on a line of sight defined by some longitude and latitude angles for some terrestrial location defined by its longitude and latitude such that any difference between that line of sight and the corresponding line of sight specified by Tycho was never more than 1 arcminute ? Or were the observations only of the latitudinal and longitudinal angles between the object and some reference star(s) at some location at some time ? --Logicus (talk) 14:30, 30 August 2009 (UTC)


 * Hi Logicus,


 * In your earlier note, you suggested that it is the accuracy of the calculated positions that are more important. I'd have to disagree for several reasons:
 * First, the section is titled "Tycho's observational astronomy."  Clearly for that section it is his observed, rather than calculated positions that are more important.
 * Second, from a historical perspective, Tycho's observed positions were used by Kepler in the work that led to his Astronomia Nova, and the accuracy of those observations sheds light on the validity of Kepler's concern over the famous 8 minutes of arc discrepancy that led him to an elliptical orbit.
 * Finally, the section does go beyond the raw observations to discuss the reduced observations (I prefer that term to the ambiguous calculated positions) that appear in his star catalog.


 * In your more recent note, you seem to be confusing terrestial latitude and longitude, which measure positions on the earth from the equator and the prime meridian, with celestial latitude and longitude, which measure positions on the celestial sphere from the ecliptic and the first point of Aries. Position on the Earth can be ignored for most of Tycho's observations. The only role of position on the Earth in Tycho's observations would be to convert observations related to the local vertical to observations related to celestial coordinates; those observations measuring distances between celestial bodies would not require position on the earth at all. (the diurnal parallax for the sun and planets are measured in seconds of arc, and are too small to be detected by Tycho's instruments).  --SteveMcCluskey (talk) 16:21, 30 August 2009 (UTC)  edited 17:38, 30 August 2009 (UTC)
 * Thanks. Will comment on this later. But immediately could you possibly please answer the question I posed of what a Tychonic 'observation statement' consists of, whether innhis star catalogue or planetary observations log, and with respect to what yardstick it may be said to be relatively accurate/inaccurate. Surely such things need to be made clear to the reader trying to learn something about this subject ?--Logicus (talk) 17:59, 1 September 2009 (UTC)

Hello Logicus,

I'm wondering based on some of your comments how much do you understand about observational astronomy and what difficulties would you experience in making an astrometric catalog using late 16th-century technology. You seem capable of writing a lot, but I ask this to determine what you actually understand. That would help me to answer any confusion. --Dgroseth (talk) 05:31, 2 September 2009 (UTC)


 * Dgroseth,


 * I share your puzzlement with Logicus's latest comments. The sentence presented in the main article speaks for itself, assuming one is familiar with the difference between the concepts of accuracy and precision. --SteveMcCluskey (talk) 14:38, 2 September 2009 (UTC)

Logicus to McCluskey:Your reference here says

“In the fields of science, engineering, industry and statistics, accuracy is the degree of closeness of a measured or calculated quantity to its actual (true) value. “

So in that case that sentence would be saying Tycho’s measurements of planetary positions were consistently accurate to within 1’ of their actual value = actual positions ?

This is what I originally suggested it meant, but you denied that..--Logicus (talk) 18:23, 3 September 2009 (UTC)

What is the relevance of Tycho's measurement of Earth's axial tilt ?

The article currently claims

"For example, Tycho measured Earth's axial tilt as 23 degrees and 31.5 minutes, which he claimed to be more accurate than Copernicus by 3.5 minutes."

But what on earth (pun intended!) is this measurement an example of ? The immediate context of the preceding sentence makes it read as though it is an example of errors in stellar positions in the star catalogue discussed immediately beforehand, but yet which it is obviously not. So is it an example of the accuracy of Tycho's planetary observations to consistently within 1 minute proclaimed in the second sentence of this paragraph? But it clearly does not provide any such example because (1) the Earth is not a planet in Tycho's astonomy, and (2) telling the reader Tycho claimed his measurement was more accurate than Copernicus's measurement(?) by 3.5 arcminutes does not tell us whether or not it was accurate to within 1'. So is it an example of how his observations of stellar and planetary positions achieved unparalleled accuracy for their time, proclaimed in the first sentence of this paragraph ? Again obviously not, since this measurement is not about the Earth's position, which Tycho placed at the centre of the universe, also making the Earth completely immobile with no axial rotation. In conclusion, this whole sentence seems to be entirely irrelevant as an example of any claim preceding it. I request clarification of its relevance, or else its deletion.

Moreover, insofar as Copernicus made no observations as many claim and never published any observational astronomy, then it seems Copernicus’s value here may well not be an observation, but rather the actual value of the tilt he gave in De Rev. Thus this sentence may confuse observational measurements with real values. And if Tycho measures the tilt as 23 degrees and 31.5 minutes, then his measurement was some 5 arcminutes in error compared with what I understand to be the modern real value of 23 degrees 26.3 minutes.--Logicus (talk) 17:57, 3 September 2009 (UTC)


 * The sentence about axial tilt has been around since (at least) 2005 without any documentation to support it; I've changed your "clarification needed" tag to "citation needed". I've removed your other "clarification needed" tag about precision as it was explained above.  --SteveMcCluskey (talk) 20:49, 4 September 2009 (UTC)


 * Tycho's value of 23°31.5' is given in Albert Van Helden, Measuring the Universe, pp. 91-2. Your comparison of it to the modern value of 23° 26.3' assumes obliquity is constant; it isn't.  Modern formulas give a value of about 23°29.5' for the obliquity in 1600.  Van Helden attributes the remaining discrepancy in Tycho's derived value to Tycho's difficulties incorporating solar parallax and refraction into the analysis of his solar measurements.  --SteveMcCluskey (talk) 00:19, 5 September 2009 (UTC)

Logicus to Steve McCluskey: Thanks for this and the info on history of this sentence. I am of course aware of the variable obliquity. So on the analysis you present here, it seems Tycho’s error would have been some 2.5’ if he measured it in 1600. So on that basis I reckon he was probably even more inaccurate than Copernicus by some 1.5’ rather than just by 1’ on the basis of my following analysis, drafted before I read yours. But then my estimate of 1600 obliquity is 36” less than yours. And Copernicus (1525?) at 23d 28.5m is only about 0.5' out and De Rev value of 23d 29m is virtually spot on your 1600 value of 23d 29m 5s.

I propose to go ahead with deleting the sentence for same reasons stated below. I hope you agree, unless of course you can provide some better analysis that extracts some relevant point out of this dog’s breakfast.

- Predraft

Logicus to Mc Cluskey: I propose to delete this bizarre sentence for the following reasons. It seems the only sense to be made of it is that it is a botched attempt to at least illustrate, if not demonstrate, an implicit thesis unstated here, namely that Tycho achieved unparalled accuracy in his ascribed celestial positions for his time. And it apparently seeks to illustrate such superior accuracy by comparison of Tycho's value for the Earth's axial tilt - the angular orientation of the Earth's polar axis to the polar axis of the plane of the ecliptic - with that of Copernicus. But it appears to be botched even as a non-probative illustration of the superior accuracy of Tycho's values for celestial positions for the following reasons.

First note that the sentence only reports that Tycho claimed to be more accurate than Copernicus by 3.5', but not that he actually was more accurate. But it is the truth of Tycho's relative accuracy that is important here, not what Tycho claimed it was. So what is the truth ?

In De Revolutionibus [p559 Britannica Great Books 16], Copernicus gave the value of the obliquity of the ecliptic as 23 degrees 29 minutes. According to Pannekoek 1961 (p212), Tycho's value of 23d 31.5m was 2' too big. Thus apparently Pannekoek took the true value to be 23d29.5m whenever it was that Tycho measured it. Now if this were also the true value for whenever Copernicus put it at 23d 29m, then Copernicus's value would have been more accurate than Tycho's, with an error of only 0.5' compared with 2' for Tycho.

However, I do not know when Copernicus and Tycho made their measurements, and thus what the true values of the secular variable axial tilt were at those times. We may speculate that Copernicus's value of 23d 29m in De Rev was intended to be that at the time of its publication. But Pannekoek (p197) tells us Copernicus measured it to be 23d 28.5m in 1525, and gave it as 23d 28m in De Rev (whereas, admittedly in haste, I read him as giving it as 23d29m in De Rev). Pannekoek also claims Walther measured it, like Copernicus, to be 23d 28m, but fails to say when Walther measured it. Presumably not 1525. As for Tycho, my calculations of the axial tilt in 1600 based on a value of 23d 26m 21s in 2000 and an annual decrease of 0.5" arcsecs per annum put it at 23d 29m 41s that year, only some 11" difference with what Pannekoek took its true value to be when Tycho measured it, which was presumably sometime between 1580 and 1600. Thus it seems fair to conclude Tycho's value was in the order of 2' in error as Pannekoek reports. But it also seems fair to conclude Copernicus's value was at most not much more than 1' in error, and hence probably more accurate than Tycho's by some 1’.

But as a mere layperson, I hand over to experts in medieval astronomy such as McCluskey and Dgroseth for further comment, and hopefully to learn what the truth of this matter might be.

However, I delete the claim because of its apparent confused irrelevance within the current text, and because it seems so dubious that Tycho's estimate of the axial tilt was more accurate than Copernicus's. But I offer the following constructive suggestion.

There are two separate issues raised here. Was Tycho's astronomy more accurate than Copernicus's ? and Was Tycho's astronomy the most accurate for his time, say for the 16th century ? On the first question, we read that Tycho set about the renovation of astronomical accuracy because the Ptolemaic Alfonsine Tables and the Copernican Prutenic Tables were in error by 1 month and 2 days respectively in their predictions of the 1563 Jupiter-Saturn conjunction. Thus one centrally much more appropriate measure of whether Tycho's astronomy achieved greater accuracy than Copernican astronomy, or indeed than Alfonsine, would be the accuracy of his predictions of Jupiter-Saturn conjunction, if any. But hereby hang tales of their highly anomalous conjunctions from Kepler to Newton and beyond....

On the wider question of whether Tycho's astronomy was the most accurate in the 16th century, Regiomontanus and Walther seem to be likely fellow contenders. However the highly confused and conflicting literature on Tycho's accuracy reveals that the key problem here is determining a scientifically valid overall citerion of accuracy, rather than indulging in the bad habit of citing the odd value here and there that was more accurate than another astronomer's  corresponding value. The two main contenders are surely that of the maximum deviation of the whole set of values from their actual values at the time according to modern reckoning, and that of their least mean deviation. Both are useful, but the former arguably more important. Such evaluations may reveal some interesting historical surprises.--Logicus (talk) 14:54, 5 September 2009 (UTC)

It's not just accuracy

Although accuracy is a major part of Tycho's contribution, equally important is his extensive and systematic program of astronomical observations and the way that they contributed to Kepler's theoretical work. The game of seeking the most accurate astronomer of his time is not very enlightening; what we really want is the astronomer who had the most significant influence on the astronomy of his time. In looking for historically significant astronomers, we need to consider the accuracy and extent of an astronomer's observations and their influence on his contemporaries and successors. --SteveMcCluskey (talk) 22:48, 5 September 2009 (UTC)


 * Logicus to McCluskey: I don't understand what your point is here, or what proposition your are talking to, albeit I largely agree with it, except for the view that Tycho's most important historical contribution was that of his data to Kepler's theoretical work. Rather I regard the contribution of his cometary data to the dissolution of the celestial spheres along with his mistaken value for Martian opposition parallax and the influence of his planetary model as the prevailing 17th century model as far more important. The dissolution of the solid spheres, involving all the planets, was by far the most important development in 17th century astronomy, making the heliocentrism v geocentrism issue relatively trifling. And on Rheticus's analysis in the first Copernican publication it was of course their presumption combined with the belief that Martian opposition parallax was greater than solar parallax that necessitated a heliocentric planetary model as the only physically possible model. This of course belies the silly nonsense that Kepler introduced physics into astronomy and initiated celestial physics.


 * However, I did not introduce the issue of Tycho's relative accuracy into the article anyway. Was that not you ? Are you now implying it should be removed ?


 * On the issue of looking for historically significant astronomers, with respect to the 16th & 15th centuries it was arguably Regiomontanus because of his introduction of Arabic trigonometry into Latin astronomy, if it is true as I have seen claimed that this is what enabled accurate measurements of parallax that became so cosmologically crucial in Tycho's hands.


 * On the issue of the identifying the historically most significant pre-telescopic astronomers for the extent of their influence and relative accuracy, I reckon Hipparchus is the main contender, possibly along with the Babylonian astronomers whose secular data so impressed Eudoxus and Aristotle, and also Ptolemy, pace Robert Newton. Hence I strongly disagree with this paragraph's opening claim that "Tycho was the preeminent observational astronomer of the pre-telescopic period". Since the claim is unsourced and anyway contentious, I propose it should be deleted as adding nothing positive to the article and simply raising a probably undecideable contentious issue.--Logicus (talk) 18:21, 7 September 2009 (UTC)


 * OK, I see you're still trying to advance your reinterpretation of the astronomical revolution against the consensus of mainstream history of science. You may think that the view that Kepler introduced physics into astronomy and initiated celestial physics is "silly nonsense", but it can be documented by innumerable secondary sources.  If you can provide sources that explicitly reject that consensus, please cite them.  Do not, however, expect other editors to give much credence to extensive quotations of primary sources accompanied by your own unique syntheses.


 * I'll grant you the small point that Hipparchus, the Babylonians and Ptolemy have a claim to the "most significant," but an assertion of the historical significance of Tycho's observations belongs in the article, and I will rephrase it citing an appropriate reference.  --SteveMcCluskey (talk) 20:03, 7 September 2009 (UTC)


 * But could you please expain what the following claim means: Tycho's observations of stellar and planetary positions were noteworthy both for their accuracy and quantity.[23] His "planetary observations [were] consistently accurate to within about 1'," " for the layperson ?--Logicus (talk) 18:19, 8 September 2009 (UTC)


 * No, I do not intend to continue participating in your filibuster. Perhaps others may wish to engage in your perpetual debate, but I do not.  I will continue to edit the articles on my watch list.  My edits will reflect valid criticism, but I will not engage in further debate.  --SteveMcCluskey (talk) 22:48, 8 September 2009 (UTC)


 * Sorry you lost your rag (-: ! No filibuster intended. There is a serious confusion in the literature here that needs sorting out for the layreader. --Logicus (talk) 18:27, 9 September 2009 (UTC)

Did Tycho neglect atmospheric refraction or not ?

The article currently claims

"an error of as much as 3' was introduced into some of the stellar positions Tycho published in his star catalog due to his application of an erroneous ancient value of parallax and his neglect of refraction." [My italics]

but also claims

"He was aware that a star observed near the horizon appears with a greater altitude than the real one, due to atmospheric refraction, and he worked out tables for the correction of this source of error." [My italics]

These two claims about Tycho's treatment of atmospheric refraction appear to be inconsistent. What is the truth ? Did he neglect it or not ? Is Rawlins possibly wrong, and the errors only due to error in solar parallax ? --Logicus (talk) 18:22, 9 September 2009 (UTC)

Rawlins does not verify star catalogue max error claim

The article currently claims

“an error of as much as 3' was introduced into some of the stellar positions Tycho published in his star catalog due to his application of an erroneous ancient value of parallax and his neglect of refraction.[25]”

But the source referenced in p20 n70 of Rawlins 1993 make no such claim. Rather it only claims:

"However, since TB's error[70] in obliquity is +2’, we find that, while many primarily refraction ­caused errors in delta stand uncorrected,....

70 The error introduced, by TB's false oversized (ancient) adopted parallax plus his ignoring of polestar refraction, is about 2'.8, which approximately accounts for the +2' error in his obliquity."

Hence it makes no claim about the maximum error of the 1000+ stellar positions in the star catalogue. On Rawlins testimony it is much greater, at least 6 degrees. I am currently trying to identify the max error he identifies, in pursuance of the apparent aim of this paragraph to identify the consistent accuracy of Tycho’s celestial positions, that is, their maximum inaccuracy. A consistent level of accuracy is defined by the maximum outliers, contrary to McCluskeys advice to exclude outliers.

In the first instance I therefore flag this claim as a failed verification.--Logicus (talk) 16:25, 18 September 2009 (UTC)


 * So your latest claim is that any stars with total errors bigger that 3' prove that this statement is false:


 * An error of as much as 3' was introduced into some of the stellar positions Tycho published. - fascinating --Dgroseth (talk) 05:32, 19 September 2009 (UTC)


 * Logicus to Dgroseth:


 * No ! But quite funny, smartypants !


 * However, you completely miss the main issue here, namely that this footnote has nothing whatever to do with stating any error in Tycho's stellar positions, be it a maximum error or mean error or any other stellar position error. Rather it is explaining the error in a terrestrial position, namely explaining Tycho's 2' error in the Earth's obliquity as the product of the error in a 2'.8 'correcting' factor introduced by his adopting the oversized ancient Hipparchan solar parallax value and also discounting polar refraction. So the quoted footnote 70 is not about any error in any stellar positions whatever. Sorry if my comment did not make this sufficiently clear for you, and created the impression that my complaint about this footnote was just that this 3' is a stellar error that is not the maximum stellar error in Rawlins' analysis, rather than not a stellar error at all.


 * In fact as you may not have noticed, contrary to the claim of this sentence, it seems Tycho never published any star catalogue whatever. So far as I can tell from the literature I have reviewed, the only 'Tychonic' star catalogue ever published was the posthumous publication of Tycho's 777 star Catalogue C, published by Longomontanus, who claimed to have been the supervisor of star cataloguing at Hven. It seems the 1004 star Catalogue D analysed by Rawlins was never published. Why he elected to pour his admirably Herculean efforts into analysing  this "error plagued" catalogue rather than the only published one, I can only wonder ?
 * Correction: If Swerdlow is to be believed, Catalogue C was not the only Tycho star catalogue published. For according to Swerdlow 1996 p210, Tycho himself had circulated Catalogue D in manuscript form, which arguably counts as publication, and Kepler published it in his Rudolphine Tables. This casts a negative light both on the alleged great accuracy of Tycho's publications, and also on Kepler's on Rawlins' report of that "error plagued" catalogue. For if Tycho and Kepler both published it verbatim as now published in Tycho's collected works. including all the errors in that publication reported by Rawlins, even replete with its entirely bogus stars, then they published a catalogue with a max error in excess of 20 degrees and a likely mean error of several degrees. For example, one need only consider the gross total effect on its mean error of the latitude error of some 23 degrees incorporated in each of its 188 southern star latitudes by virtue of its 'typo' (i.e. 'scriberr'?) that misrepresented their latitudes south of the Ecliptic as south of the Equator.--Logicus (talk) 11:27, 24 September 2009 (UTC)


 * Seriously though, the statement in question is clearly intended to be a statement of the max error of the star catalogue. For if not, then why arbitrarily pick out a 3' error or any lesser error than the max error ?


 * I therefore propose to delete this entire clause as an unsalvageable and misleading dog's breakfast, pending some reliable objective evaluation of the level of accuracy of the 777 stellar positions published in Tycho's star catalogue C to be gleaned from the literature, if such be possible. I suggest we need to know the max error, mean error and in comparison with the max and mean errors of previous or contemporary star catalogues such as those of Hipparchus and Hevelius. I am currently reviewing the literature to see whether these have been determined. Can you help, or is your intended contribution to this constructive project just that of sniping at Logicus from the sidelines ?


 * So I propose the following provisional holding clause pro tem:


 * 'But the stellar positions posthumously published in his 777 star catalogue C were far less accurate.'


 * I do hope you concur.


 * --Logicus (talk) 21:03, 22 September 2009 (UTC)

"Stellar positions more accurate than 1' " unsourced and mistaken

The article currently claims

"the stellar observations as recorded in his observational logs were even more accurate, varying from 32.3" to 48.8" for different instruments."

and this claim is sourced in a JHA article by a Walter Wesley.

But that article only considers the accuracy of the positions of 20 stars altogether, and is therefore useless for determining the overall accuracy of the 777 star Catalogue C or of the 1004 star Catalogue D, being less than 2% of the latter stars for example.

I therefore delete this claim, as having a failed verification and which anyway seems preposterous.--Logicus (talk) 23:53, 23 September 2009 (UTC)

The myth of Tycho's 1' accuracy ?
The article currently claims

His [Tycho's] "planetary observations [were] consistently accurate to within about 1'."[24]

and its footnote 24 source in Gingerich & Voelkel 1998 JHA says

"[24] We have found Tycho's mature planetary observations to be consistently accurate to within about 1', in agreement with Dreyer's and Thoren's assessments. See Victor E. Thoren, "New light on Tycho's instruments", Journal for the history of astronomy, iv (1973) 25-45, pp41-42."

However, this reference and its footnote has numerous possibly fatal problems that suggest the Gingerich & Voelkel ( and Wikipedia) claim is unreliable and indeed false, as follows:

(1) G & V give no published reference for their alleged finding of the level of accuracy of Tycho's planetary observations, and of their methodology and data source. This is peculiar. So did they really undertake any such independent exhaustive research akin to that of Rawlins? And where is it published, if anywhere ?

(2) The G & V footnote fails to identify what Tycho's mature planetary observations are, as distinct from his immature planetary observations. For example, were his 'crucial' observations of Mars at opposition in 1582-3 mature or immature ?

(3) The G & V footnote notably also give no reference for Dreyer's alleged assessment of the accuracy of Tycho's planetary observations. Is this possibly because Dreyer never made any, but only assessed the accuracy of a limited number of Tycho's stellar positions compared with Bradley's ?

(4) Unlike G & V, Thoren's article does not credit Dreyer with making any proper assessment of Tycho's accuracy, rather than just making an unfounded assumption about it. He simply says "[Dreyer] was willing to assume that [by 1585] the accuracy of roughly +- 1' was typical of Tycho's mature observations."[My itals] But 'typically accurate' can be a far cry from 'consistently accurate', the far stronger claim made by G & V.

(5) Pages 41-2 of the Thoren article referred to do not make any assessment whatever of the accuracy of Tycho's specifically planetary observations. Rather the article is only concerned, at most, with the accuracy of all his celestial positions in general, stellar, planetary and cometary.

(6) Thoren's article is really only concerned with assessing the max possible reliable precision in measuring celestial astronomical angles that could possibly be achieved by Tycho's instruments, but not with assessing the minimum or mean accuracy of all his actual observations and celestial positions in relation to some yardstick of their 'true' observations or positions. Thus G & V go way beyond Thoren's findings in claiming agreement with any Thoren finding of a consistent accuracy within 1' in Tycho's planetary observations. What Thoren says at most on Tycho's accuracy is this: "[Dreyer] was willing to assume that [by 1585] the accuracy of roughly +- 1' was typical of Tycho's mature observations. For stellar and planetary positions this was probably true, although for some reason in secondary reports of Tycho's work the 4' figure has been cited more frequently than the 1' value."

(7) The fact that Thoren apparently interpreted accuracy of 'observations' to mean accuracy of actual 'positions', and so judged Tycho's 'observational' accuracy to be within 1' of actual celestial positions, and G & V's citation of being in agreement with Thoren about Tycho's accuracy, suggests G & V made the same semantic equation, and so also really meant 'calculated positions' when they confusingly spoke of 'observations'. If so, then their evaluation of Tycho's consistent accuracy in celestial positions was most likely grossly wrong in the light of such as Rawlins' findings of Tycho's stellar position errors,

In conclusion, G & V's claim seems multiply confused, and at the end of the day seems little more than a case of simply uncritically parrotting Tycho's own (now known to be grossly mistaken) claim that he had plotted celestial positions to consistently within 1' accuracy, rather than the result of any serious scientific research into evaluating the relative accuracy of Tycho's estimated celestial positions of stars and planets.

I propose this claim of the accuracy of Tycho's planetary observations be deleted as false, and this whole paragraph be replaced by a scientifically serious analysis of the comparative accuracy of Tycho's celestial positions, if at all possible. But if the academic history of science literature cannot provide such, then maybe this paragraph should be replaced by a report on the gross failings of that literature on this issue. --Logicus (talk) 20:35, 26 September 2009 (UTC)


 * Gingerich and Voelkel clearly state that their research finds "Tycho's mature planetary observations to be consistently accurate to within about 1'." If you can find explicit sources that state that Tycho's observations did not reach this accuracy, fine; cite them.  Please cease your continued practice of placing your own interpretations against the findings of published sources.  I am reverting your recent edits.  --SteveMcCluskey (talk) 02:12, 28 September 2009 (UTC)


 * Logicus to McCluskey: Given it is plainly evident from the G & V article and its references, as pointed out in my points 5 & 7 above, that what it means by "planetary observations" is in fact neither 'observations', nor just specifically of planets, but rather 'calculated celestial positions' in general, including both stellar and planetary positions, then many sources that state Tycho's consistent accuracy (i.e. max level of error never exceeded) in celestial positions was very significantly less than achieving +-1' error can be cited. But why bother with what would be a long and tedious resume of the confused and conflicting literature on this issue, recounting all the confusions and conflicting opinions of such as Dreyer, Thoren, Wesley, Gingerich, Voelkel, Swerdlow, Hoskins, Rawlins etc. ? Why not just state the best scientific summary of Tycho's accuracy that can be gleaned from the highly confused and inconsistent literature by the application of common sense and elementary logic to its analysis in order to try and determine the truth of the matter ? This is only what the best Wikipedia editors can do at best anyway in giving their summary interpretations of all the literature, albeit many history of science editors seem to have read very little of it, and elementary logic and common sense seems well beyond them., as may even be English language literacy, as in the case of Dgroseth by his own most admirably candid admission below, for example.


 * What you are doing in restoring the G & V claim is imposing your own idiosyncratic interpretation of the literature as accurately represented by this G & V claim, but which it is most certainly not.


 * Contrary to your claim, I do not place my own interpretations against the findings of published sources. Rather I point out the contrary findings of other published sources in what is typically the context of there being no broad consensus, but rather only confused and conflicting opinions, just as I have variously pointed out above. I then attempt a fair NPOV summary of what logical common sense suggests is the likely scientific truth of the matter from the literature. In this particular case, given the G & V finding of the max error in celestial positions conflicts with that of many others and is pretty obviously grossly mistaken (for example, the Rawlins publication on the star catalogue D reveals many errors of many degrees, as much as well over 20 or 30 degrees, if not over 200 degrees), I offered a provisional holding summary in its stead, provisional upon determining an agreeable more specific fair summary of the levels of accuracy of planetary and stellar positions achieved in Tycho's planetary and stellar catalogues /'observations'.


 * I therefore restore my previous edit, hopefully this time with your agreement that it is a fair holding position in view of all the circumstances I have depicted. For the record it is:


 * “He aspired to a level of accuracy of within 1', but many of the stellar positions in his star catalogues were far less accurate than that.”
 * --Logicus (talk) 18:01, 30 September 2009 (UTC)


 * Hi, Prof. McCluskey, I see your back from the Wikibreak you took from this article. I'm a bit green to Wikipedia and might want help with policy and such. Btw, is asking someone a crude question or making a vulgar remark possibly considered a personal attack?


 * Regarding this same person and some of his comments on errors and precision:


 * I'm not quite sure how to parse everything correctly regarding his/her earlier opinion of how Rawlins' and other people's analysis of Catalog D was "the highly confused and apparently conflicting dog's breakfast" and again a few blunders such as misidentification, reading the instruments or poorly written values, or whatever in the data set that resulted in a few stars with errors up to 6 degrees would render it, "an unsalvageable and misleading dog's breakfast".


 * Wow, I guess I'll tear up my list of Messier objects, and all of those Near-Earth object surveys that are supposed to save us, even the latest have questionable data. It would NOT be logical to save the world without knowing every NEO to some minimum precision. What about the data set consisting of every statement by Logicus, does it have any blunders, and if so, should his/her standard apply to him/her, assuming he/she calls it a blunder?


 * On further analysis of the Edit history of Logicus, I see this comment to 84user revision as of 11:00, 2009 September 24. It seems like some deleted items were worth keeping after all.


 * Anyway, lets let bygones be bygones, I'd be happy to start over and discuss the 7 points of Logicus and a few more mentioned earlier, only I won't write as much. I write with a splint quite slowly, and I see Logicus often likes to add 2K text every time, often making several erroneous statements in a single post. If he/she is patient, we can reach some agreements.


 * I'm a klutz with remembering policy, grammar, spelling and such, although I do understand astrometry quite well in different circumstances, optical and radio, differencing errors and combining different kinds of reference frames.


 * My first question for Logicus as an authority in astronomy, if I take a photograph of a region of the sky say 30 degrees above the horizon with a few objects with known positions and an object with an unknown position, how big could the photo be before the calculated position error ignoring refraction is 1 arc minute? --Dgroseth (talk) 05:31, 28 September 2009 (UTC)


 * Hi Dgroseth,


 * Nice point about the problems with evaluating a survey on the basis of its maximum errors. The studies I've read tend to employ the average error, sometimes after discarding "obvious outliers."  Some discussions of robust statistics have proposed using the median of the absolute value of the deviation, which includes outliers but in such a way that they do not have a great influence on the measure or variability.
 * Given Wikipedia's restrictions on original research, we'll have to go with the statistical analyses found in the published literature on the history of astronomy. --SteveMcCluskey (talk) 15:10, 28 September 2009 (UTC)
 * Logicus to McCluskey: But Dgroseth’s comments here make no such point, nice or otherwise. And your other general comments about the appropriate stats for evaluating surveys are logically irrelevant to the issue of logically evaluating whether Tycho achieved his declared aim of having a max error no greater than 1', which is the issue raised by the article. It is not a survey that is being evaluated here, but rather the claim that all Tycho's celestial positions were accurate to within 1', that is, that his max error was no greater than 1’. OK ? --Logicus (talk) 19:11, 28 October 2009 (UTC)

Observational logs

I have just restored the passage "the stellar observations as recorded in his observational logs were even more accurate, varying from 32.3" to 48.8" for different instruments." That is exactly what the article cited is about -- see Wesley's discussion of his method (and his critique of those of his predecessors) at pages 42-3, JHA 9(1978). --SteveMcCluskey (talk) 12:30, 29 September 2009 (UTC)


 * You have apparently overlooked the fact that this article is useless for the purpose at hand because Wesley only considers 20 stars. I therefore re-delete it. Logicus.


 * Wesley focused only on what could be best reconstructed.


 * We should be using Thoren 1973 instead of a footnote in Owen Gingerich and James R. Voelkel for footnote 24 along with Wesley for the next one.


 * Victor E. Thoren, New Light on Tycho's Instruments, 4 (1973) 25-45 1973JHA.....4...25T


 * Logicus also removed the following half-truth that needs to be fixed before reinsertion into the lead or wherever:


 *  He did what others before him were unable or unwilling to do – catalogued the planets and stars with enough accuracy to determine whether the Ptolemaic or the Copernican system described the heavens more accurately. 


 * In fact, The claims that Tycho makes in his personal correspondence can only make sense if at times believed in a model where the orbit of Mars and the orbit of the Sun do not intersect and Tycho believed the diurnal parallax of the Sun was a measurable nearly 3 minutes of arc as this value was never challenged by Tyhco. That is the heart of the article by Gingerich and Voelkel, so don't toss it.


 * Owen Gingerich and James R. Voelkel, "Tycho Brahe's Copernican Campaign," Journal for the History of Astronomy, 29(1998): 2-34,


 * Also note the graphs on page 22 has Tycho's different adopted refraction values. Note that they are different for stars and sunlight. It is reasonable to not think they are the same, when refraction was poorly understood. Unfortunately he was wrong. --Dgroseth (talk) 05:47, 30 September 2009 (UTC)


 * Logicus to Dgroseth: No doubt due to your admirably self-professed poor literacy, you seem to misunderstand why the Wesley reference given was invalid and so deleted. May I therefore explain its invalidity for you, as follows. The issue at hand as raised by the G & V 1998 quotation was the level of accuracy consistently achieved by Tycho's celestial positions, which is of course measured by their maximum error. But the immediately following clause on the error of Tycho's stellar observations in his observation logs that apparently reports a max error of 48.8" is taken from Wesley's Table 4. But Table 4 does not state the max error, but rather the average error for 7 instruments for only 8 'fundamental' stars. But obviously the max error will be greater than the mean error. And it is apparently to be found in Table 3, as reported by my new footnote 24 as 2' 3". However, even this finding is irrelevant since it is Tycho's general level of accuracy that is at issue here, but Wesley only reports the max error of just 8 stars, which is obviously a wholly statistically wholly invalid of the 1004 stars catalogued. The only valid use that can be found for Wesley in this context is that which I have cited in my footnote because it scuppers the silly claim that the max error of Tycho's celestial positions was +-1'.--Logicus (talk) 14:33, 3 October 2009 (UTC)
 * Logicus to Dgroseth and McCluskey: BTW, you may be interested to note that Wesley's 1978 finding of a max error of 2' 3" in a declination in 8 of the 9 'fundamental' stars when compared with computer retrodictions based on the Smithsonian Astrophysical Observatory Star Catalogue's positions seems in virtually identical agreement with Dreyer's 1890 finding of a max error of 2' 2" in the declination of Alpha Virginis out of the 9 fundamental stars compared with Bradley's positions. But Rawlins' 1993 found the maximum error in the 9 'fundamental stars' to be a 2' 30" error, namely in Alpha Virginis's latitude, and with a 2' 12" error in its declination in contrast with the Dreyer/Wesley 2' 2/3" error finding. But McCluskey seems blithely unaware of this in his restoration of the improperly sourced Wesley reference --Logicus (talk) 08:28, 8 October 2009 (UTC)
 * Logicus to Dgroseth: Your Edit commentary for deleting my article revision 317492700 -“The WP:SYN removes an important reference while not containing another discussed) (undo)”- is clearly threefold mistaken.(i)This was not WP:SYN and I challenge you to demonstrate otherwise given your own admission that you do not understand WikiPolicy, (ii) it did not remove an important reference, but rather removed a clearly mistaken and patently fringe view and (iii) it discussed no less than 11 references. May I respectfully suggest you consider whether you are as yet sufficiently literate to be editing an encyclopedia. Please stop your highly confused reversions of my revisions concerned to improve the scientific accuracy of this article. --Logicus (talk) 14:50, 3 October 2009 (UTC)


 * Yes my eyes glaze over when trying to learn WikiPolicy, and yes I am responsible, even for rules that I don't understand. This is why I am going slow. I can find ways to use references that make Tycho look bad, and I can find ways to use references that make him look better than he was. See Fundamentals of Astrometry, Jean Kovalevsky and P. Kenneth Seidelmann, Cambridge University Press, 2004, p 2,3. Either way compromises the integrity of the article in a way considered synthesis. I do know Tycho discovered the next four previously unknown terms in the motion of the moon, in agreement with what Brown published less than a hundred years ago. Did he consult a mystic or determine them by careful observation? --Dgroseth (talk) 05:26, 4 October 2009 (UTC)
 * This is irrelevant confused nonsense ! You clearly fail to cite any WP:SYN policy rule that my contribution demonstrably breaches. The issue here is not to make Tycho appear more or less accurate than he was, but just to establish precisely how accurate he was, which is what my efforts are directed towards and towards eliminating the ludicrous mythologizing of his accuracy by some fringe elements. My contribution does not compromise the integrity of the article in any way. Nobody is denying Tycho made careful observations. But what he discovered or not, however worthy, is irrelevant to determining his general level of accuracy.  Please stop your invalid reversions. I have restored your last deletion.--Logicus (talk) 14:40, 4 October 2009 (UTC)


 * I don't actually enjoy reverting an hour or more of work. I think think it would be best to thrash it out calmly on the talk page, one detail at a time. It seems like the axial tilt had its own section once, buried in the middle only to disappear. Wouldn't it be best if it and other issues had their own section? I find some sections to meander quite a bit.


 * Does a point of view have to be original to qualify for WP:SYNTHESIS? For example, would a series of edits that were pro Flat Earth and the elimination of references against a Flat Earth viewpoint count? I thought the degree of NPOV qualified for synthesis, but I might be wrong. Anyway, I see SteveMcCluskey has done some hard work, with the the result a bit less biased in my opinion. --Dgroseth (talk) 05:00, 5 October 2009 (UTC)

Remedying the current muddle over Tycho's level of accuracy ?

The article currently claims

"He [Tycho] aspired to a level of accuracy of within 1 arcminute of real celestial positions, and his "mature planetary observations [were] consistently accurate to within about 1',"[24] The average error of Tycho's instruments, derived from his logs of stellar observations, varied from 32.3" to 48.8" for different instruments,[25] but many of the stellar positions in his published star catalogues were far less accurate than that.[26]

But this has just restored the thoroughgoing confusion and unrepresentative minority fringe views Logicus sought to eliminate with the following provisional text, pending further quantitative information on the levels of accuracy of Tycho's stellar, planetary and cometary positions.

"He [Tycho] aspired to a level of accuracy of within 1 arcminute of real celestial positions, but many of the stellar positions in his star catalogues were far less accurate than that.[26]."

(1) Judging from the literature the claim that Tycho's "mature planetary observations [were] consistently accurate to within about 1'," is a fringe minority view whose source may be in a minority of one. It is clear from the contexts of the sources quoted that "planetary observations" here means 'planetary positions'. But it is obvious from the literature that some of Tycho's planetary positions were out by well over 1', with his terrestrial obliquity out by some 2', some solar positions out by some 3', and some Martian positions at opposition out by maybe some 4'+. Hence either one just deletes this minority fringe view, or else includes it but then detail that it is a mistaken minority fringe view. I suggest the former option may be less embarrassing for the author and also less potentially confusing.

(2) “The average error of Tycho's instruments, derived from his logs of stellar observations, varied from 32.3" to 48.8" for different instruments,[25]”

is misleading gobbledegook and a reading of Wesley reveals it should rather be

‘The average error of Tycho's positions of 8 of his 9 most fundamental reference stars, derived from his logs of stellar observations, varied from 32.3" to 48.8" for different instruments’

But this is anyway logically confusing and irrelevant to the subject at issue here, which is rather the level of accuracy consistently achieved in all his celestial positions, and not the mean error in just his 9 fundamental stars. The whole Wesley reference should therefore be deleted as logically irrelevant.

I therefore propose this passage be replaced by the following, based on further research of the literature to determine Tycho’s stellar, planetary and cometary levels of accuracy.

'He aspired to a level of accuracy in his positioning of celestial bodies of being consistently within 1 arcminute of their real celestial locations, and also claimed to have achieved this level. But in fact many of the stellar positions in his star catalogues were far less accurate than that by very many degrees out <ref]In fact Tycho even invented some entirely fictitious stars to make up an apparent 1000+ stars in his star catalogue D But in fact it seems it has never been determined just how more or less accurate Tycho's celestial positions were overall with respect to their maximum, minimum and mean errors than those of the Babylonians, Hipparchus, Ptolemy, Copernicus and Walther, for example, or of any other predecessor or contemporary.'


 * Logicus, I now know you're not a teenager, so I'll have to point out a bit less gently that you have made some mistakes. I already pointed out that the fictitious stars in Tycho's catalog are as fictitious as objects in other important catalogs that are also unidentifiable today with absolute certainty. As for errors, we'll need to get to the basics of what is meant by errors, and what is in error. btw, I left something unrelated on my talk page, hope it helps.

--Dgroseth (talk) 05:57, 23 October 2009 (UTC)

What was the historical significance, if any, of Tycho’s alleged superior accuracy ?
One of the historical fairy tales about Tycho to be found in some of the literature, and which underlies this article's concern with Tycho's accuracy, is that planetary orbits were thought to be circular before Kepler proposed they were elliptical as a result of Tycho's more accurate planetary positions that revealed they were more elliptical rather than circular.

But of course this tale is nonsense from the very outset in its presumption that before Kepler planetary orbits were circular. For as is evident from more intelligent and scholarly aspects of the literature and such as Dennis Duke's animations of geocentric planetary orbits, the historical facts of the matter are that planetary orbits were thought to be non-circular millenia before Kepler, being epitrochoidal around the Earth in such as the Ptolemaic model, for example. They were also non-circular around the Sun in Copernicus's heliocentric model.

The upshot of the influence of this nonsensical tale by virtue of its erroneous presumption that Copernican heliocentrism posited circular planetary orbits is that maybe nobody has ever yet bothered to determine the crucial issue of whether Kepler's planetary orbits were more accurate than Copernicus's or Reinhold's

In the case of pure heliocentric astronomy post Copernicus, key questions that arise with respect to the issue of what contribution, if any, Tycho's planetary positions made to determining Kepler's ellipse hypothesis are as follows. In the first instance we solely consider the paradigmatic case of Mars and Tycho's plots of its orbital positions.

NB Answering these questions may require reference to the Prutenic tables as well as or even rather than De Revolutionibus.

1) What was the path/shape of the Martian orbit in Copernicus's heliocentric planetary model ? Just how non-circular or elliptical/ovoidal or not was it ?

2) What were the max, min and mean deviations of Copernicus's predicted Martian orbit from all of Tycho's plots/predictions for whatever period ?

3) What were the max, min and mean deviations of Kepler's predicted Martian orbit from all of Tycho's plots/predictions for whatever relevant period ?

4) Was Kepler's Martian orbit more accurate or not than Copernicus's or Reinhold's Prutenic Martian orbit according to Tycho's orbital position plots/predictions for some same orbital period, and on what measure ?

5) Was Kepler's Martian orbit more accurate or not than Copernicus's or Rheinhold's Martian orbit for some orbital period according to modern orbital position plots/predictions for that same period, and on what measure ?

6) Was Kepler's Martian orbit more accurate or not than Longomontanus's Astronomia Danica Martian orbit according to Tycho's orbital position plots/predictions for some same orbital period, and on what measure ?

7) Was Kepler's Martian orbit more accurate or not than Longomontanus's Astronomia Danica Martian orbit for some orbital period according to modern orbital position plots/predictions for that same period, and on what measure ?

It should be noted that Copernicus's astronomy was apparently more accurate than Tycho's at least in respect of the Earth's obliquity, an important referential constant in which Tycho was some 2' in error whereas it seems Copernicus was possibly virtually spot on. Hence this does raise the issue of whether Tycho's astronomy was generally more accuarte than Copernicus's.

The overall key issue here is whether Kepler's planetary orbits were any more accurate than Copernicus's or Reinhold's, and if so whether their greater accuracy was in any way crucially enabled by Tycho's observations. There is also the issue of whether Kepler's orbits were more accurate than those of Longomontanus, who also used Tycho's 'observations'.

Contributing editors may wish to help improve the article by detemining such questions. --Logicus (talk) 18:27, 30 September 2009 (UTC)


 * Try and get your novel ideas about Tycho Brahe published in a peer reviewed magazine before trying to change the Wikipedia article. This is not the place for OR. --Saddhiyama (talk) 20:07, 30 September 2009 (UTC)


 * Logicus to Saddhiyama:But Logicus has no peers (-: And anyway only in the weird and whacky feudal ivory tower of academia does anybody regard peer review as anything other than a recipe for reactionary corruption by the usual suspects, a paradigm of 'the police investigating the police'(-:


 * Thanks for this unsolicited advice, but you should consider trying to improve your literacy, for no novel ideas about Tycho Brahe are presented here, and this is not Wiki OR. So may I invite you to provide a demonstration that it is OR, and identify what idea(s) about Tycho presented here you imagine to be novel ?


 * Perhaps you should read my above apposite comments of 30 September to Steve McCluskey, especially re your deletion of my 30 September article edit, which was not OR as you alleged:


 * "Contrary to your claim, I do not place my own interpretations against the findings of published sources. Rather I point out the contrary findings of other published sources in what is typically the context of there being no broad consensus, but rather only confused and conflicting opinions, just as I have variously pointed out above. I then attempt a fair NPOV summary of what logical common sense suggests is the likely scientific truth of the matter from the literature. In this particular case, given the G & V finding of the max error in celestial positions conflicts with that of many others and is pretty obviously grossly mistaken (for example, the Rawlins publication on the star catalogue D reveals many errors of many degrees, as much as well over 20 or 30 degrees, if not over 200 degrees), I offered a provisional holding summary in its stead, provisional upon determining an agreeable more specific fair summary of the levels of accuracy of planetary and stellar positions achieved in Tycho's planetary and stellar catalogues /'observations'."


 * I do not know what ideas about Tycho you imagine to be novel, but it is certainly not the idea that Tycho's observations did not determine Kepler's elliptical orbits. For example, as Curtis Wilson's 1989 article Predictive astronomy in the century after Kepler. wisely says


 * "Because of the level of unavoidable error in observations of position, and the near circularity of the orbits, the departure from circularity could be detected observationally only in the orbits of Mars and Mercury, where the eccentricity was exceptionally large; and even in these cases the choice between ellipse and other oval shapes was, as far as the observations could show, a matter for conjecture. Kepler, of course, had reasons for his choice: a causal account of which led both to the elliptical orbit and to the planet's motion on that ellipse, with close agreement between the theoretical prediction and observation in the particular case of Mars."


 * Stop making bogus allegations of OR and stop reverting my edits without demonstrated valid reason ! --Logicus (talk) 16:06, 2 October 2009 (UTC)


 * I will be answering some of your questions soon. See my comment in the previous section for now. --Dgroseth (talk) 05:21, 4 October 2009 (UTC)
 * Logicus to Dgroseth: Are you Saddhiyama or replying for them ? --Logicus (talk) 14:25, 4 October 2009 (UTC)


 * Dgroseth here, not Saddhiyama. I didn't mean to but in on a private exchange, I was interested in the topic. While we are discussing epitrochoids, deferents, equants and epicycles, I wanted to join if I may. I used to have a spirograph and it was fun. Almagest rules? --Dgroseth (talk) 05:17, 5 October 2009 (UTC)
 * If you want to do some useful work here, could you possibly determine the shape of Mars' orbit according to Copernicus's De Rev, or find some reference in the literature that states what it is ? And also determine its deviations from Brahe's plots. --Logicus (talk) 17:42, 5 October 2009 (UTC)


 * Shapes, shapes, shapes. It seems like philosophers only care about shapes. How true Copernicus did not have orbits with a quantum leap improvement in orbit shape. He tried to simplify something but failed. By the way, wasn't he before Tycho? Anyway if only Logicus will permit the simple Dgroseth to pick just the right pair of spirograph wheels he wishes, Dgroseth can make any ellipse that Logicus chooses, as well as some interesting ovals Logicus might like better. Dgroseth does get to choose the wheels as well as offsets such as deferents, equants and epicycles, right? And if Logicus allowes Dgroseth 3 or 4, who knows what shapes can be made! This kind of science is fun! But Dgroseth is not quite the peer of Logicus. Dgroseth needs to know more of the theory of Logicus or what Logicus wants exactly. --Dgroseth (talk) 05:39, 6 October 2009 (UTC)
 * Dgroseth apologies if his writing was unclear. Copernicus had a model that was complicated and did not work that much better than the model that Ptolemy had (or Hipparchus or whoever was the real genius that Ptolemy might have stolen from). I would never want to say bad things about the ancient Greeks. Check out the Antikythera mechanism. Amazing! Copernicus only put the Sun in the middle, and had a better value for the obliquity. (Was I allowed to discuss more than you invited me to? Sorry if I went out of bounds.) Now Dgroseth waits patiently for the next queston, idea, problem or whatever I'm allowed in this section. --Dgroseth (talk) 17:44, 6 October 2009 (UTC)

Wot planetary parallax observations ?
The article currently claims

"Tycho's naked eye measurements of planetary parallax were unprecedented in their precision - accurate to the arcminute, or 1/30 the width of the full moon."

But to what planetary parallaxes does this refer ? He got the Sun’s parallax wrong by some 3’ and that of Mars at opposition by some 4’. Did he give any values for the Moon, Mercury and Venus ?

This unsourced claim is surely simply grossly false and must be deleted ? Meanwhile I flag it for a source and for clarification. --Logicus (talk) 14:48, 4 October 2009 (UTC)


 * Again, Dgroseth is not quite the peer of Logicus. Dgroseth doesn't understand the fancy words Logicus uses. Dgroseth looked at Wot and wot, tried to take Logicus seriously and got confused. Dgroseth types with one splint. (It looks odd too.) Did Logicus use a secret shorthand?
 * Also, is the next section related. It doesn't help Dgroseth understand the first part. --Dgroseth (talk) 05:50, 6 October 2009 (UTC)

The article also currently claims "These jealously guarded measurements [of planetary parallax] were "usurped" by Kepler following Tycho's death."

But this is surely nonsense, even apart from the misuse of the word 'usurped' for the word 'stolen'. For the literature suggests, rightly or wrongly, that what Kepler stole from Tycho's legally legitimate heir(s) was not just whatever records of measurements of planetary parallax he had made, as claimed here, but rather at least all of Tycho's observational data of the Martian orbit, or possibly his data of all planetary orbits, or at most his data of all celestial motions. But which of these he stole is utterly unclear from the literature, even from Dreyer's admirably detailed and fascinating account of the posthumous career of Tycho's records. For example, what Tychonic data did Longomontanus have access to or not in compiling his geo-heliocentric Tychonic Astronomia Danica model of the planetary system that was regarded as the completion of Tycho's astronomical programme of improving the accuracy of planetary motion prediction. And what Tychonic data was he deprived of by Kepler, if any ? Longomontanus had been the supervisor of stellar obsevations at Hven, and posthumously published Tycho's star catalogue, so it seems Kepler did not steal all of Tycho's records. And why did Newton negotiate with Roemer to try and get Tycho's data for publication in Halley's astronomical catalogue in the early 18th century ? It seems incredible that Newton was trying to get data from the pre-telescopic era published with those of the telescopic era.

This unsourced sentence must surely be deleted, and replaced or covered elsewhere by an account of what Kepler actually did steal, and what became of Tycho's records. --Logicus (talk) 17:36, 5 October 2009 (UTC)

What support for heliocentrism did Kepler’s laws provide ?
The article currently claims Kepler's laws of planetary motion "provided powerful support for the heliocentric model of the planetary system".

But this claim is both false and unsourced. On its falsity, Kepler's laws simply presumed circumsolar elliptical orbits with the sun at one focus for all planets, including the Earth, but without any prior supporting evidence for their heliocentrism. And nor did they make any predictions that specifically supported heliocentrism against all forms of geocentrism. Certainly their heliocentrism did not entail any superior accuracy of Kepler's heliocentric model of planetary orbits For example, reportedly Longomontanus achieved a level of accuracy for his Martian orbit to within 2' with his semi-Tychonic geo-heliocentric (non-elliptical ?) planetary model, [whereas Wilson’s 1989 in Taton & Wilson reports the max and mean deviations of Kepler's Martian orbit from the 28 Tychonic Martian observations Kepler presented in Astronomia Nova were greater than the 5' 33" and 2' 4" max and mean deviations respectively achieved by Boulliau's elliptical orbit (p179 T & W), and even had an error of some 20' in its Martian aphelion (p168 T & W) --Logicus (talk) 18:15, 7 October 2009 (UTC) ].

Hence this claim at least needs clarification that identifies what  exactly this alleged powerful support for heliocentrism was, and also a source for this apparently mistaken claim. So I flag it for both. --Logicus (talk) 18:18, 6 October 2009 (UTC)


 * Logicus Hey, no fair. I needed a clarification to the previous question. I still don't understand wot. --Dgroseth (talk) 18:32, 6 October 2009 (UTC)


 * According to the theory of relativity, heliocentrism and heliostaticism are meaningless or untrue.
 * Thus, anything by way of support is merely a matter of the psychology of science. A late 15th. century A.D.
 * writer mentioned ellipses as orbits for the planets, but put the Sun at the center, not a focus.
 * See Arthur Berry, in 1898, A Short History of Astronomy. —Preceding unsigned comment added by 81.148.88.25 (talk) 10:36, 7 October 2009 (UTC)


 * Logicus to User 81.148.88.25: You would seem to be rather confused. Wot is "heliostaticism" ? Surely geostatism is ruled out by the theory of relativity, since it entails the fixed stars must be travelling faster than the speed of light ? For example, if the fixed stars rotate daily rather than the Earth, then even Alpha Centauri must travel almost 10,000 times faster than light. But thanks for the elliptical planetary orbits reference.--Logicus (talk) 16:18, 16 October 2009 (UTC)


 * All this, except Logici original point, is anachronistic reasoning. Heliocentrism here is a model opposed to geocentrism. Not Kepler nor Tycho could have the slightest idea of relativity. Their universe had a center as clearly as a box have a center. The question posed is about whether Kepler's laws provided powerful enough support for heliocentrism versus geocentrism. It is very clearly defined: are the planets revolving around Sun or around Earth? ... said: Rursus ( m bork³ ) 08:54, 30 October 2009 (UTC)


 * The date 1899 is also used. There was a reprint in 1961.
 * Kepler seems to have been unaware of any previous reference to ellipses. —Preceding unsigned comment added by 81.148.88.25 (talk) 10:56, 7 October 2009 (UTC)
 * See http://wlym.com/drupal/ —Preceding unsigned comment added by 81.148.88.25 (talk) 11:04, 7 October 2009 (UTC)


 * "Ultimately his [i.e. Kepler's] version of Copernicus' proposal would almost certainly have converted almost all astronomers ro Copernicanism, particulary after 1627 when Kepler issued the Rudolphine Tables, derived from his new theory, and clearly superior to all the astronomical tables in use before." Thomas Kuhn, The Copernican Revolution, p.219;
 * "Astronomers came to see that these tables [i.e.the Rudolphine Tables] were the most accurate tables of planetary motion devised up to that time." Michael Crowe, Theories of the world from antiquity to the Copernican Revolution, p.156‎;


 * &mdash;David Wilson (talk · cont) 15:29, 8 October 2009 (UTC)


 * Wow Logicus, you're saying or trying to imply that because of Tycho's incompetence Kepler ended up with an ellipse that was twisted by a third of a degree? Given the orbit is still fairly circular with an eccentricity less than 0.1, I would have trouble noticing an error several times larger. Now if Tycho had a number of observations of a comet, and the calculated orientation was nearly a degree off, I'd like to know if it was the observations or the math.
 * Also, are you saying or trying to imply that Boulliau was at odds with Kepler or Tycho or what? And reportedly Longomontanus achieved a level of accuracy ... but you don't even know the shape? ... Wasn't Longomontanus the brilliant mathematician that could prove a way to geometrically square the circle? Comparing apples and oranges? I suppose your critical eye never gets blinded by your favorites? --Dgroseth (talk) 05:42, 9 October 2009 (UTC)


 * Logicus to Wilson: Thanks for your above lengthy and detailed critical contribution, albeit now deleted, and especially for its attempted corrections of my alleged ‘astronomy errors’ that I shall study asap to let you know if any of them are valid.


 * However, unfortunately your main criticism of Logicus's claim here is logically irrelevant to the question at issue, which is whether Kepler's three laws provided any logical empirical support specifically for heliocentrism  against all forms of geocentrism. For just as you quote me, I said


 * "Certainly their heliocentrism did not entail  any superior accuracy of Kepler's heliocentric model of planetary orbits." [My italics added.]


 * But you comment:


 * "It is very easy to find numerous reliable sources which say otherwise. ... Here are quotations from a few such sources:"


 * But in fact none of the 4 sources you then quote say otherwise. For none of them claim any superior accuracy of Kepler's model of planetary orbits in conformity with his three laws was a logical consequence of their heliocentrism. And nor did Wilson so far as I recall. But do you wish to claim Wilson 1989 did ?


 * It would certainly seem foolish to do so since inasmuch as the heliocentric and Tychonic geo-heliocentric models were held to be observationally equivalent, the Tychonic data Kepler used could not decide between them. And inasmuch as the accuracy of Kepler's model was due to his devising it to try and fit Tycho's plots, then arguably any superior accuracy was rather a consequence of Tycho's geo-heliocentric positions than of Kepler's heliocentrism, and whereby Kepler's heliocentric model was arguably an ad hoc manoeuvre to try and match the accuracy of the geo-heliocentric model that could thereby not possibly provide any empirical support for heliocentrism.


 * But the basic logical point here is that since heliocentrism does not entail Kepler's laws, then their corroboration could not logically support heliocentrism.


 * However, whilst the Wikipedia’s philosophy of science claim that


 * “Kepler's laws provided powerful support for the heliocentric model of the planetary system.[28] “


 * is logically false, it may be that some astronomers mistakenly thought it did provide support for heliocentrism. And of course there is no philosophy of science claim too silly for it to be impossible for some academic historian of science to have made it (-:


 * I note you have subsequently added references from Stephenson and Swerdlow to justify this logically mistaken claim. I have not had the opportunity to check whether they do indeed claim such. So would you please be kind enough to provide their actual quotes that you claim make this claim, in compliance with Wiki Verifiability etiquette? --Logicus (talk) 14:32, 11 October 2009 (UTC)
 * Logicus to Wilson: Please ignore my last request. My apologies, I note you have kindly put in direct links to your Swerdlow and Stephenson sources. However at a glance the Stephenson ref is a failed verification inasmuch as I can see no such claim made there. So I flag it. I have not yet digested the Swerdlow ref. Logicus (talk) 14:51, 11 October 2009 (UTC)


 * The Stephenson reference was not added by me but by Steve McCLuskey. I had aleady removed one of the pages cited from that reference on the grounds outlined below. How did you determine that the material on page 49 doesn't support the disputed assertion?  That page is not included in the on-line copy available at Google books.
 * &mdash;David Wilson (talk · cont) 15:20, 11 October 2009 (UTC)
 * I may have made an error, but since you have not provided the quote as requested, can we take it that it is indeed a failed verification ? As for Swerdlow, clearly a fringe view, as he admits, but I will take a look at it when time --Logicus (talk) 18:19, 12 October 2009 (UTC)


 * Logicus wrote:
 * " ... since you have not provided the quote as requested, can we take it that it is indeed a failed verification ?"
 * Other than in some exceptional circumstances, I believe it's quite unreasonable to claim that a citation has failed verification merely because one editor has been unable or unwilling to provide a quotation from the cited source. Claiming that a citation has failed verification is completely unjustified unless either you or some other trustworthy editor has determined that this is so by personally checking the cited source.  As it happens, I have now checked pages 48-50 of Stephenson's book in a local library and found nothing relevant on them. So, yes, we can now take it as a failed verification.
 * —This is part of a comment by David J Wilson   which was interrupted by the following:
 * Logicus to Wilson: No, the reason I decided it must be a failed verification was because you told me McCluskey had provided it (-: Thanks for checking out I was right (-: --Logicus (talk) 18:27, 13 October 2009 (UTC)


 * Next:
 * "As for Swerdlow, clearly a fringe view, as he admits, ... "
 * Really? Where does he do that?  The only statement of his which I have found where he indicates a difference of opinion with anyone else is the following:
 * "It has been said that Kepler's laws do not necessitate the Copernican theory, but anyone who believes this has not thought the matter through."
 * Surely you're not taking that as an admission of holding a "fringe view" ?
 * &mdash;David Wilson (talk · cont) 12:49, 13 October 2009 (UTC)


 * Logicus to Wilson: On Swerdlow, I did take that comment to mean he realises it is the general opinion that Kepler’s laws do not entail a heliocentric kinematical astronomy, and that he is arguing against that general opinion. And indeed nor does Swerdlow demonstrate any such logical relationship of necessitation as he claims, but rather presents an interesting hypothetico-deductive ‘elimination of all articulated alternatives to heliocentrism’ argument. However, it clearly logically depends upon the lemma of some additional physical principles in addition to Kepler’s 3 purely kinematical laws, which is why he concept-shifts to the term ‘(modified) Copernicanism “, apparently meaning ‘dynamical heliocentrism’. But this then raises the whole issue of the plausibility and corroboration or not of Kepler’s celestial physics. However, it is most interesting and in sympathy with my view that it was Kepler’s physics that was most important. I shall attempt a detailed logical reconstruction of his argument and its ultimate invalidity when time. Thanks for bringing it to my attention. --Logicus (talk) 18:27, 13 October 2009 (UTC)

Convenience break to separate off live discussion immediately above
Since writing the comments now struck out above, I noticed that SteveMcCluskey had already provided a citation as requested by Logicus. So my comments are now moot, which is my reason for having struck them, even though I'm not aware of anything else wrong with them.

Since I couldn't see how the first cited page of Steve's reference supports the disputed assertion, I have flagged it as a failed verification, pending an explanation to clear up any possible misunderstanding on my part. Since the second cited page is not included in the Google books copy of the reference, I haven't been able to check it yet. Nevertheless, I have found and added another reference which very obviously does support the disputed assertion. So unless there are equally credible sources which contradict those provided, there doesn't seem to me to be any reasonable grounds for continuing this discussion. &mdash;David Wilson (talk · cont) 16:31, 10 October 2009 (UTC)
 * Thanks for the edits; I've reread the section on Stephenson that I've cited, pp. 44-9) and found that this is the passage on p. 44 where I saw evidence for how Kepler's laws provided support for the Copernican system: "he had actually constructed a longitude model [the area law] as good as even that of Tycho, but with the further advantage that the planet's variation in speed was tied to its distance from the sun [as indicated by the ellipse law].  If that seems a stretch, feel free to delete it (your Swerdlow ref handles it nicely).  It seems that if the ellipse and area laws are true physical laws -- as Kepler insisted they were -- then they directly imply heliocentrism.  The third law isn't mentioned in Stephenson here, but it is entirely heliocentric, since it relates speed to distance from the sun, again on the basis of physical causes.  A source for the third law's historical impact on heliocentrism could be found in discussions of its use by Newton and its application to later heliocentric tables.  --SteveMcCluskey (talk) 17:20, 10 October 2009 (UTC)
 * I don't think "longitude model" on p.44 refers to the area law. The preceding and subsequent context seems to me to indicate that it refers to the model Kepler used in his so-called "vicarious hypothesis", which was a variation of the Ptolemaic equant rule.  The variation was that the centre of the orbit divided the line joining the Sun to the equant in the ratio of about 5:3, instead of bisecting it as in Ptolemy's theory.  While this model gave good predictions for longitude, it didn't do so for latitudes (see p.45).  To get the latter right he had to return to the Ptolemaic ratio, and this introduced the 8' error in longitudes which he was famously unwilling to accept (see p.46).   I'll delete page 44 from the citation.
 * &mdash;David Wilson (talk · cont) 07:43, 11 October 2009 (UTC)
 * PS: On p.162 of Logicus's own reference, Curtis Wilson cites Thomas Steele as the first (in 1661) to publish tables in which the third law was used to get better estimates of mean solar distances. According to Wilson "The resulting improvement in accuracy was particularly noticeable in the cases of Mercury and Venus."
 * &mdash;David Wilson (talk · cont) 07:59, 11 October 2009 (UTC)
 * PPS: On further reading of the Stephenson book, I found a passage on pp.67-68 which further supports the disputed assertion. I have now added a citation to those pages.
 * &mdash;David Wilson (talk · cont) 16:58, 11 October 2009 (UTC)

The accuracy of Longmontanus's Tables

One key question for the issue of whether any greater accuracy of the Rudolphine Tables provided support for heliocentrism contra geo-heliocentrism is whether they were any more accurate than Longomontanus's 1622 Astronomia Danica Tables on scientifically acceptable measures such as their max, min and mean errors. Does any body know ? --Logicus (talk) 16:27, 16 October 2009 (UTC)

Misuse of the Clarify template.
The documentation for the Clarify template (AKA the Huh template) states that it is to be used in the following circumstances:


 * Use this template in the body of an article as a request for other editors to clarify text that is difficult to understand. When the problem is not with the wording, but the sourcing, one may use instead. For dealing with dubious information, please use one of the following:, ,  or.

Logicus repeatedly uses the template when he disagrees with the reasoning of the source being cited or when he considers an argument illogical, even though the source or argument is perfectly clear. Please use appropriate templates in tagging disputed points in the article. --SteveMcCluskey (talk) 19:32, 6 October 2009 (UTC)


 * Also, I'd like to know how many hours the clarify has to stay up before unilateral deletion is acceptable? Today it looks like about 50 hours is sufficient according to Logicus, even though there are also active discussions that need to be handled point by point. I think it was only a day once, but I notice that SmackBot only tags it with a month and year. No hour or day.
 * Until now, I've chosen to discuss some topics I think related before I start making big changes. I resent the rapid removals. Sometimes I'm offline a few days. Some other people even have lives. --Dgroseth (talk) 20:23, 6 October 2009 (UTC)


 * Dgroseth:
 * Logicus has been playing this game for years now, and tends to focus his disruption on specific articles where he has developed strongly held opinions, at odds with the general scholarly consensus. His method is to flag passages he disagrees with as unclear, often accompanied by a long theoretical discussion of his opinion on the talk page, and then delete them from the article, even when they are properly sourced because he finds the sources unclear (i.e., they don't agree with his particular interpretation).
 * Like you, I have a life to live, but his pushing the limits of civility is getting increasingly exasperating. I try to avoid discussion with him -- it's proven to be nonproductive.  --SteveMcCluskey (talk) 21:57, 6 October 2009 (UTC)

Ignoring an active discussion before editing
I see that Logicus can start a discussion at Talk:Tycho Brahe regarding his future edit. Less than 24 hours later Logicus proceeded without looking at the discussion regarding his edit. Any ideas besides reverting everything? The section needs work, but not like that. --Dgroseth (talk) 05:34, 24 October 2009 (UTC)

Logicus to Dgroseth: You are mistaken, as per usual. (i) There is no rule against when an edit can be made, and prior discussion is not even required. (ii) I did look at your remarks in the discussion, and found them logically irrelevant and mistaken as per usual. If you can provide a better more accurate summary of the literature on Tycho's level of accuracy, please offer one. But do not revert mine without valid grounds ! --Logicus (talk) 15:54, 25 October 2009 (UTC)

Definitions for Errors and Precision
Before I can discuss the subject of Tycho's errors, I need to ask what standard do you want to hold Tycho to? Some kind of modern standard? That would seem acceptable for a modern reader. I don't know what kind of physics was offered at LSE, or what other schools everyone went to. When you took a physic lab, How did you describe errors in measurements? Did you only use maximum errors? A probability or degree of confidence of being in an interval? A standard deviation? Some other parameter? --Dgroseth (talk) 05:56, 23 October 2009 (UTC)

Wot wos the comparative accuracy of Kepler’s Rudolphine Tables ?
The purpose of this section is to try and arrive at some fair and accurate executive summary of what reliable judgments, if any, the history of science literature has to say about the overall comparative accuracy of Kepler’s 1627 Rudolphine Tables, to go into the article. The intended context and motivation of this project is that some historians claim the superior accuracy of Kepler's heliocentric tables somehow provided empirical support for heliocentrism itself or even entailed heliocentrism, and others claim their superior accuracy converted almost all astronomers to heliocentrism, but without also claiming they entailed or provided empirical support for heliocentrism.

But temporarily setting aside whatever possibly intractable problems of the logic of empirical support and of the historical facts of community conversion these views raise, or indeed of any historical evidence that scientists so regarded them, and also discounting the question of how widespread such views may be amongst historians, the first thing that needs to be established for this claim to be sustained is whether Kepler's tables were indeed everywhere more accurate than all geocentric tables. Were all their predicted planetary positions more accurate than those of all competing tables, or were they sometimes less accurate or even largely less accurate than some competing tables ? A historical situation where no tables were uniformly more accurate than all others would presumably result in astronomers judiciously using a range of alternative tables. And this may well have been the case in the 17th century.

It seems the Rudolphines' main contemporary competitors were Longomontanus’s 1622 'semi-Tychonic' geocentric Danish Astronomy tables and Lansberge’s 1632 epicylical heliocentric tables Tabulae motuum coelestium perpetuae.

And it seems the Rudolphines' ' leading geocentric competitor may well have been Longomontanus's Danish Astronomy  tables. They were highly popular and went into two reprints, in 1640 and 1664, which may even be more reprints than the Rudolphine Tables had. It seems they were also somehow based on Tycho's planetary observations and intended to be the completion and successful fulfilment of Tycho's uncompleted programme for the renovation of the accuracy planetary astronomy.

Wot were Kepler's max and mean errors in planetary positions ?


 * Curtis Wilson's 1989 pp179-180 in Taton & Wilson 1989 reports a maximum error in Kepler's planetary aphelia of some 4 degrees 41' for Venus's aphelion compared with Newcomb's values for 1600 (See Wilson's Table 10.1). (An aphelion is the furthest planetary position from the Sun achieved in a planet's orbit.)


 * Wilson’s 1989 also reports the max and mean deviations of Kepler's Martian orbit from the 28 Tychonic Martian observations Kepler presented in Astronomia Nova were greater than the 5' 33" and 2' 4" max and mean deviations respectively from those same observations achieved by Boulliau's post 1957 revised elliptical orbit (p179 T & W). But he does not say what they were. We presume Wilson means 'Tychonic positions' here rather than 'Tychonic observations'.

In provisional conclusion it seems nobody has done an evaluation of the Rudolphines'  max, min and mean errors against Tycho's planetary positions, nor against Newcomb's or any other acceptable contemporary data set of planetary positions. So it seems that all that can be said on this reportage is that their max error was at least almost 5 degrees compared with Newcomb's positions.

Comparisons of the accuracy of the Rudolphine Tables with that of other tables


 * In what must surely be the most extremely unreliable and outlandish comparison of the accuracy of the Rudolphines, in the first paragraph of her 1999 St Andrews University MacTutor article on Kepler, London University Kepler 'expert' Judith Field says "Moreover, he calculated the most exact astronomical tables hitherto known, whose continued accuracy did much to establish the truth of heliocentric astronomy (Rudolphine Tables, Ulm, 1627)." (My italics)

But it surely cannot be the case that even by 1999 more accurate astronomical tables had not superseded Kepler's, and in fact Curtis Wilson's 1989 p180 Table 10.1 comparative analysis reveals the Rudolphines were not the uniformly most accurate tables by 1651 at the very latest, when Vincent Wing's Harmonicon coeleste planetary orbital elements were already more accurate than Kepler's in various respects when compared against the yardstick of Newcomb's orbital elements for 1600.

Field also comments:

"All astronomical tables that made use of new observations were accurate for the first few years after publication. What was remarkable about the Rudolphine Tables was that they proved to be accurate over decades."

But contrary to Field's claim that they were the most accurate for at least the 37 decades to 1999, on Wilson's above 1989 analysis they had already ceased to be the uniformly most accurate tables available after only two decades. But of course this was as little as after even only 5 years on Dreyer's analysis in comparison with Lansberge's 1632 tables, albeit perhaps not apparent until the 1639 transit of Venus. And of course there is the distinct possibility that they never were the most accurate tables if Longomontanus's 1622 tables were more accurate in any respect. Rather it may be that at best the Rudolphines were more accurate than other tables in some respects but less accurate in others, and hence strictly incommensurable in a situation where astronomers therefore used a variety of alternative tables, cherry-picking and maybe synthesising the best from each. --Logicus (talk) 18:24, 28 October 2009 (UTC)

But it seems that what Gingerich has done here is to most invalidly conclude from the fact that Kepler's prediction for the 1631 Mercury transit was 30 times less inaccurate than other tables, i.e. had only a 10' error compared with a 300' error, that all the Rudolphines' predicted planetary positions were 30 times less inaccurate than those of all other previous or contemporary tables. Certainly Gingerich did not cite any other statistical research on the comparative accuracy of the tables, neither his nor anybody else's.
 * Gingerich's 1989 claimed that "the predicted positions [of the Rudolphines] were generally [my italics] about 30 times better than those of the prior or competing tables, but this was not immediately obvious when the tables were published. However, Kepler had used the tables to predict a transit of Mercury, and in 1631 (the year following his death) Pierre Gassendi in Paris dramatically verified the prediction with a successful observation: for the first time the planet Mercury was seen to cross the face of the Sun. Kepler's prediction erred by only 10', compared to 5 degrees for tables based on Ptolemy, Copernicus, and others. This graphic demonstration was a forceful testimony to the efficacy of the heliocentric system, and in particular to Kepler's version of it."

Hence it seems this is a grossly invalid generalisation from just one cherry-picked example, and unlikely that the Rudolphines were generally 30 times better than all other tables just because one prediction was, if so.

It especially seems most unlikely that all the Rudolphines' predicted planetary positions were 30 times less inaccurate than those of Longomontanus's or Lansberge's tables, for example. And in fact Dreyer's 1906 p420 fn1 reported that the Rudolphines' prediction of the 1639 Venus transit was way off disc whilst Lansberge's was on disc, whereby it seems quite possible that Lansberge's prediction could have been at least some 30 times or more less inaccurate than Kepler's, and from which, by the same absurdly invalid logic as Gingerich's, it must be concluded that Lansberge's predicted planetary positions were generally 30 times better than the Rudolphines'. But Dreyer does not say how successfully or not Longomontanus's geocentric Danish Astronomy tables predicted the 1639 Venus transit, and nor does Gingerich.

Nor does Gingerich say just how mistaken Kepler’s predicted Mercury transit in 1607 was, and how inaccurate it was compared with other tables. It is also of interest whether the Rudolphines retrodicted a transit of Mercury in 1607.

Gingerich's evaluation of a 30fold superior accuracy of the Rudolphines must surely be discounted as unreliable, and an extreme example of hagiographical pseudo-history of science displacing reliable scientific history of science ?


 * Linton's 2004 claim that the Rudolphines were 30 times more accurate than all previous tables would seem to be a mere parroting of Gingerich's 1989 invalid claim rather than an independent finding, and thus equally to be discounted as a reliable summary of the comparative accuracy of the Rudolphines. He said “We know that the errors in Kepler’s tables were about 30 times smaller than those in previous astronomical tables, though this would not have been apparent when they were first published, and not all astronomers were convinced immediately.”


 * Thoren's 1989 in Taton & Wilson 1989 p19 reported Longomontanus achieved a level of accuracy for the longitude of his Martian orbit to within 2' with his 'semi-Tychonic' geocentric (non-elliptical ?) planetary model even before Kepler started modelling it. However, he did not say whether Kepler's Martian orbit in the Rudolphines ever exceeded the 2' accuracy of Longomontanus's in longitude, nor whether it exceeded Longomontanus's latitudinal accuracy. Nor did he say whether Kepler's max and mean errors for the Martian orbit reported by Wilson (p179 T & W 1989) to be respectively in excess of 5' 33" and 2' 4" were less than those of Longomontanus's Danish Astronomy tables.

* >> See immediately below for Logicus's later discussion of Curtis Wilson's analyses of the Rudolphines'  comparative accuracy, which properly belongs here.


 * In provisional conclusion, at least from these examples from the literature, it seems there are no reliable comparative analyses of whether the Rudolphine Tables were more or less accurate than any preceding or contemporary tables. For it seems nobody has done any kind of scientific systematic evaluation of their accuracy nor of that of any competing tables such as required for such comparative judgments. In fact more generally Rawlins seems to be alone in his magnificent effort to provide a systematic analysis of the accuracy of a historical set of astronomical tables.

The most appropriate provisional summary of the sometimes alleged superior accuracy of the Rudolphine Tables would therefore seem to be of the following ilk:

'Some historians of science have claimed that Kepler's 1627 Rudolphine Tables were more accurate than all previous and contemporary astronomical tables, but none have ever provided any reliable scientific evidence for this claim.'

There would also seem to be a reasonable suspicion that the Rudolphines were not generally more accurate than all other previous and contemporary tables, and at least not generally more accurate than Longomontanus's 1622 Danish Astronomy  tables, and on Dreyer's testimony, certainly not generally more accurate than Lansberge's 1632 tables.

--Logicus (talk) 19:17, 27 October 2009 (UTC)


 * Logicus adds the following analysis of Curtis Wilson's discussions of the Rudolphines'  comparative accuracy to that above and its provisional conclusion:
 * On the issue of the comparative accuracy of the Rudolphines, Curtis Wilson's 1989 summarily concludes:
 * "Gassendi's observation of the transit of Mercury of 1631 showed Kepler's tables to be the best available at the time, but van Lansberge's and Longomontanus's tables went on being used into the 1660s, recognition of their inaccuracy increasing the while." (p205)


 * But in the first instance the first clause here apparently just repeats Gingerich's apparent folly of concluding they were the best available at the time just because of one superior prediction, if not committing Gingerich's more extreme apparent folly of also claiming they were 30fold better than all alternatives based on that one superior prediction.


 * However, secondly, more significantly Wilson then testifies that Lansberge's and Longomontanus's tables were still being used into the 1660s. But this surely suggests astronomers did not regard the Rudolphines as clearly the best available tables superseding all others in their accuracy, but rather at least that they regarded these other tables to be better in at least some respects, if not all respects, than the Rudolphines. Or else if the Rudolphines really were the best available, and this was also manifest to astronomers at the time, then Wilson effectively condemns astronomers as being irrational for some 40 years following the publication of the Rudolphines because they still used inferior tables into the 1660s.


 * But this latter possibility seems most unlikely, and it seems that rather the real historical situation was most likely that the Rudolphines were not wholly superior to all other tables in that period and nor were they perceived to be, but were rather seen as at best ‘’incommensurable’’, that is, better in some respects but worse in others, and that as a matter of fact, they were so.


 * In fact Wilson's own Table 10.1 reveals that Kepler's tables were only more accurate than all those of Boulliau, Streete and Wing in just 3 out of the 18 orbital elements for 6 planets. On this basis it can be concluded that the judgment of the Paris Academy of Sciences that they had not been improved upon by 1666 (p176) was certainly grossly mistaken, and that even its exclusion of Boulliau for inaccuracy and Wilson’s own claim that he was an inexact and unreliable observer is apparently belied by the revelation of Wilson’s own Table 10.1 that his tables were more accurate than Kepler’s in no less than 7 out of 18 planetary orbital elements !


 * Thirdly, not only does Wilson testify that the tables of Longomontanus and Lansberge were still being used in the 1660s, but his Table 10.1 also shows that Wing’s 1651 Harmonicon coeleste tables were already better than Kepler's in 6 out of 18 orbital elements of the 6 planets against the yardstick of Newcomb's values for 1600.


 * Thus it seems Kepler's tables can only have been the most accurate for no more than 2 decades at the very most, if ever. But most notably Wilson never provides any similar accuracy comparisons with the tables of Longomontanus and Lansberge, nor indeed with the Alphonsine or Prutenic tables. Thus Wilson provides no evidence that the Rudolphines ever were the most accurate to justify his unevidenced bald assertion that they were the best tables available at the time.


 * Wilson p176 reports that in 1666 when it was founded, the Paris Academy of Sciences adopted the Rudolphines as not yet having been improved upon and the starting point for further improvements. However, p179 he also reports that in 1669 Flamsteed contradicted this opinion, declaring Streete's 1661 Astronomia Carolina to be the most accurate of all tables, saying


 * "I esteem Mr Streete's numbers the exactest of any extant."


 * However, Wilson himself only claims that 'Streete's planetary tables are rather better than... any other tables published earlier, in some respects', rather than in all respects, and only claimed their three orbital elements of eccentricities, aphelia and mean solar distances for Mercury, Earth and Mars presented in Table 10.1 are clearly superior to those of Kepler, Boulliau and Wing against the yardstick of Newcomb's 1600 values for them, that is, for just half of all the planets. But even contrary to Wilson's claim, his own Table 10.1 itself shows that this was only true for Mercury, but not for Mars nor Earth, in terms of being superior to the others in all three orbital elements. And it shows Streete’s tables were only superior to those of Kepler, Boulliau and Wing in just 6 of all the other 15 various planetary orbital elements of the other 5 planets known at that time.


 * On the issue of when the Rudolphines were superseded in accuracy, whether or not they ever were the most accurate, it is evident from Wilson's Tables 10.1 and 10.2 that neither Cassini's 1740 Tables Astronomique nor Halley's 1749 Tabulae Astronomicae superseded them in accuracy by being at least as or more accurate in all respects, and thus nowhere less accurate. For Kepler’s were more accurate than both Cassini’s and Halley’s in 3 out of 18 orbital elements in each case. But Wilson provides no evidence of when they were completely superseded in accuracy.


 * Wilson’s analysis of the case of Flamsteed and the comparative accuracy of Streete’s 1661 tables highlights the importance of distinguishing between what the comparative accuracy of any tables were, measured against the yardstick of some more modern values, and what they were thought to be at the time against some yardstick of the day, such as Flamsteed’s own estimated positions, for example. Using ahistorical yardsticks may be all well and good for deciding just how accurate tables really were, but the more important criterion for explaining the history of science, such as trying to explain the success of heliocentrism as somehow due to some superior accuracy of Kepler’s tables, may be how accurate they were thought to be against some accepted common yardstick of the day.


 * In conclusion, the continuing use of Longomontanus’s 1622 geocentric tables well into the 1660s on Wilson’s testimony, with no less than a third printing in 1664, surely suggests astronomers did not regard them as having been superseded in accuracy by Kepler’s heliocentric tables on some contemporary yardstick(s), contrary to the conclusions of some historians of science that they superseded all previous tables in accuracy, and then that of all other tables published for many decade, if not to the present day as in Field’s opinion?
 * --Logicus (talk) 18:55, 31 October 2009 (UTC)


 * Logicus wrote:


 * "The most appropriate provisional summary of the sometimes alleged superior accuracy of the Rudolphine Tables would therefore seem to be of the following ilk:


 * 'Some historians of science have claimed that Kepler's 1627 Rudolphine Tables were more accurate than all previous and contemporary astronomical tables, but none have ever provided any reliable scientific evidence for this claim.'"


 * Absolutely not. The article's current text on this issue:
 * "After his death, his records of the motion of the planet Mars provided evidence to support Kepler's discovery of the ellipse and area laws of planetary motion.[25] Kepler's application of these two laws to obtain astronomical tables of unprecedented accuracy (the Rudolphine Tables)[26] provided powerful support for his heliocentric model of the solar system.[27]"


 * is a verifiably accurate account what the cited reliable sources say, and Logicus has yet to provide a single source (beyond his own opinion) that contradicts it. In fact, it is easy to find a plethora of other reliable sources which all agree on the unprecedented accuracy of the Rudolphine tables.  I have already cited Thomas Kuhn's The Copernican Revolution and Michael Crowe's Theories of the World from Antiquity to the Copernican Revolution above.  Here are three more:
 * Curtis Wilson, in The Cambridge companion to Newton p.204;
 * Nicholas Kollerstrom, William Crabtreee's Venus Transit Observation, in Transits of Venus: new views of the solar system, IAU Colloquium no. 196 (2004), p.36;
 * Albert van Helden, Measuring the universe: cosmic dimensions from Aristarchus to Halley, p.105.


 * On the other hand, Logicus's proposed replacement tendentiously suggests that there are some historians of science who would disagree with the claim that the Rudolphine tables were much more accurate than their preceding and contemporay competitors, but he has not provided a single example of anyone who has done so. Nor has he provided any credible evidence for the second phrase (" ... but none have ever provided any reliable scientific evidence for this claim ... ") of his proposed replacement.  Even if the long-winded argument with which he has tried to support this claim were thoroughly convincing, and its logic impeccable, it would still constitute a synthesis of published material that advances a new position (i.e. a position not advocated in any of the sources cited). As such, according to Wikipedia's policy on no original research, its conclusion is prohibited from being added to the article (unless, of course, someone can provide a reliable source which does explicitly and unequivocally support it).


 * I have now transferred material which editor Rursus has correctly pointed out is off-topic for this talk page to here.


 * &mdash;David Wilson (talk · cont) 00:12, 29 October 2009 (UTC)
 * Logicus to Wilson: Do you want to cross this all out now, as you did with your previous contribution, before I demolish it, thus saving me the trouble (-:? —Preceding unsigned comment added by Logicus (talk • contribs) 18:00, October 30, 2009


 * Instead of all this long argumentation for and against the accuracy, which does actually not befit a wikipedia talk page, collect all relevant outside sources in one short list here, so that all editors can give their say about what the sources say in general about the quality of the Rudolphine tables.


 * Actually: this talk page is not a discussion forum about the facts behind the article, it is a discussion forum about the article itself. What the article should tell us, is just a matter of shallow evaluation of sources — not about their underlying "truth", but instead just what they tell — we do actually not care about what precision Keplers calculations actually have, we only care about sources telling this or that precision. ... said: Rursus ( m bork³ ) 09:20, 30 October 2009 (UTC)


 * I agree[with qualification&mdash;see below], and apologise for my indiscipline. I have now transferred the off-topic arguments in my comments above to a subpage of my user page.  I believe the remaining parts of my comments are firmly on-topic, since they are limited to a defence of some of the article's current content as properly sourced according to policy, and an objection to a proposed edit to the article as completely unsourced and, in fact, inconsistent with numerous reliable sources.


 * Here is a consolidated list of the sources I have so far cited, all of which say that the Rudolphine tables were of unprecedented accuracy:
 * C. M. Linton, |From Eudoxus to Einstein, p.224;
 * Owen Gingerich, Johannes Kepler, p.77, in Wilson and Taton's Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Vol 2A;
 * Thomas Kuhn, The Copernican Revolution, p.219;
 * Michael Crowe, Theories of the world from antiquity to the Copernican Revolution, p.156‎;
 * Curtis Wilson, in The Cambridge companion to Newton p.204;
 * Nicholas Kollerstrom, William Crabtreee's Venus Transit Observation, in Transits of Venus: new views of the solar system, IAU Colloquium no. 196 (2004), p.36;
 * Albert van Helden, Measuring the universe: cosmic dimensions from Aristarchus to Halley, p.105.


 * Here is a consolidated list of the sources Logicus has so far provided which say otherwise:


 * &mdash;David Wilson (talk · cont) 19:57, 30 October 2009 (UTC)


 * Logicus on Wilson's bizarre logic: Here is a consolidated list of the sources Wilson has so far provided that provide some reliable scientific evidence that Kepler's 1627 Rudolphine Tables were more accurate than all previous and contemporary astronomical tables:
 * --Logicus (talk) 23:38, 31 October 2009 (UTC)
 * On second thoughts, I need to qualify my above agreement with editor Rursus's comment. I don't agree with the statement "...  we do actually not care about what precision Kepler's calculations actually have, ..."  I most certainly do care about such things, but I recognise that it is not a suitable subject for Wikipedia talk page discussion, except insofar as that discussion is limited to what can be verifiably said about the issue in the article, as documented explicitly in reliable sources.
 * &mdash;David Wilson (talk · cont) 22:36, 30 October 2009 (UTC)

Death
The death section needs some shrink. The grand citations aren't needed. The poisoning theory is not supported by the current sources. We need at least two independent sources to have such wild theories, save giving WP:undue_weight to fringe. The section needs sources. It should tell uss that the cause of the disease and death is not known, and not sufficiently researched. ... said: Rursus ( m bork³ ) 09:01, 30 October 2009 (UTC)


 * I have now rewritten this section from information contained in Dreyer's and Thoren's biographies. Fortunately all the pages containing the relevant material are availabe online at Google books, so other editors can easily check them and make further amendments if they seem warranted. I don't think the citation I have added for the poisoning theory is sufficiently authoritative, but it should do for the moment, pending the location of better ones.
 * &mdash;David Wilson (talk · cont) 03:44, 31 October 2009 (UTC)

I have added some clarification and a new independent reference to the section. Please review my changes, and slap my hand if I erred somewhere. My only intention was to be able to get rid of the 'citation needed' tag. Jules112 (talk) 08:37, 7 December 2009 (UTC)

Polemic section: Tycho's observational astronomy
The section "Tycho's observational astronomy" takes a firmly polemic point of view. It sets out to prove that the typical claims of average accuracy to around 1 arcminute are exaggerated. Here are specific instances where novel conclusions appear to have been drawn by the author:


 * The analysis criticizes Wesley as "unjustifiably" eliminating incorrect entries in the logs. According to whom is this unjustifiable?
 * The following "refutation" of Swerdlow's claim cannot be in Wikipedia's voice:
 * "But this summary conclusion of the literature is apparently blatantly contradicted as unsafe and unreliable by Dreyer's 1890 evaluation, Wesley's 1978 evaluation and Rawlins' 1993 evaluation of the errors in Tycho's 9 'fundamental' reference star positions, which all found errors exceeding 1' in at least a third of them, and a maximum error exceeding 2'."


 * The entire second paragraph (including almost the entire text of the footnote) is utterly unsourced opinion, and should be removed:
 * "Nevertheless historians of science typically assert his celestial positions were much more accurate than those of any predecessor or contemporary. But they do so either as a mere assertion without any evidence, or at best by invalidly cherry-picking just one favourable example of a more accurate position in comparison with some predecessor(s)'position. But in fact it seems it has never been determined just how much more or less accurate Tycho's celestial positions were overall with respect to their maxima, minima and mean errors than those of the Babylonians, Hipparchus, Ptolemy, Copernicus and Walther, for example, or of any other predecessor or contemporary.

Perhaps this section should simply be reverted to an earlier version that does not have the WP:NPOV and WP:OR problems that this one has. 173.75.158.49 (talk) 21:47, 3 November 2009 (UTC)


 * [From Terry0051] Hmm, I agree it does look polemical and POV. Are there any RS to show whether this is a subject of significant scholarly controversy with some weight on both sides? Or is the view that's currently put in this polemical way also unsupported by any weight of RS? Terry0051 (talk) 22:21, 3 November 2009 (UTC)


 * The first paragraph isn't so bad. It does need to be brought more into accord with the predominant view among sources, though.  They tend to focus on the mean error (with outliers excluded) rather than the max errors.  Ideally, we should include both points of view.  For brighter stars, the mean error is within the 1' accuracy.  Even for dimmer stars, a mean of 3' is achieved.  (I refer to the Rawlins source, which appears to contain the most detailed analysis to date.)  The second paragraph comes to a rather preposterous conclusion, that is refuted by just about every source we have.  Even on the most tendentious reading of the sources, there is no way the conclusion of the paragraph can possibly be the case.  A perfunctory googling turns up this, placing Brahe at several orders of magnitude greater accuracy than Hipparchus and Ptolemy.  Although the methodology with which this particular comparison is made is open to some debate, there is no serious controversy over the essential conclusion.  Unless sources are brought forth immediately, I suggest that this entire paragraph be excised as WP:OR and non-WP:NPOV.  173.75.158.194 (talk) 14:10, 4 November 2009 (UTC)

Logicus to 173.75.158.49 & Terry0051: As the author of the passages you two criticise here, first of all, thanks for your criticisms that I shall consider and respond to asap. But immediately overall may I say that these passages were not intended to be nor appear polemical, nor are they in my view. Rather they were intended to replace the previous hagiographical and highly muddled polemic that sought to exaggerate Brahe’s level of accuracy with a historically correct evaluation of the level of accuracy he achieved, to be gleaned from the literature. I would be most grateful for your assistance in achieving a fair and accurate evaluation based on the literature, which I had not yet fully completed. But my provisional evaluation was the following :

“But in fact many of the stellar positions in his star catalogues were far less accurate than that by very many degrees out [23], his planetary positions had a maximum error at least in excess of 3', and even the mean error of his 1577 comet orbital positions was as much as 4', suggesting a possibly much greater maximum error.[24]”

The idea is to state the level of accuracy variously achieved for stars, planets and comets. Max and mean errors would seem most appropriate.

Do you disagree with my provisional evaluation ? --Logicus (talk) 19:17, 4 November 2009 (UTC)


 * As I have asserted above, for his stellar catalog D, the rms errors on the order of <1' for brighter stars and <3' for dimmer stars (with an average somewhere in between) are compiled by the Rawlins source, which seems to be the most comprehensive to date. Since most of the other authors cited quote similar numbers, I think WP:WEIGHT should be placed on the mean errors rather than max errors.  Although I have no objection to mentioning some anomalies in the data, as the article presently does, I disagree with the way they are presented as part of an argument that Brahe's data was not the most accurate to date.  (There is no serious scholarly debate on this, as far as I know&mdash;please correct me, with sources, if I am mistaken.)  The means should be given upfront, and these can be followed by a thorough discussion of outliers, transcription errors, etc., perhaps in a footnote.  173.75.158.194 (talk) 20:57, 4 November 2009 (UTC)


 * I should add that, while the attempt to clear out the hagiographical elements of the article is admirable, it is important not to go too far. Again, there is substantial agreement among all of the reliable sources that the stellar catalog measurements were orders of magnitude more accurate than those of Brahe's predecessors.  Any version of the article that understates this (or attempts to undercut it) is not appropriately balanced.  173.75.158.194 (talk) 21:06, 4 November 2009 (UTC)

[From Terry0051] Thank you Logicus for stepping up to the discussion as the editor who introduced the material discussed. But I'm afraid I can't yet express agreement with your provisional evaluation, in part because it seems to embody a specific agenda. I am also baffled by your expressed view that the current text is not polemical.

On the agenda point, I suggest there shouldn't be any specific agenda, because the purpose of editing any WP article is to summarise fairly and explain whatever is out there in reliable sources on the topic at hand, using editorial skills to give due weight to mainstream and consensus views, and fairly present in a factual way the subject matter of any notable diversity of view or even dispute out there. (I suggest that it fosters the spirit of the project to refer to our efforts as 'editors' rather than as 'authors' -- this is no place for WP:OR.) The present text does seem to show positive signs of unfair and biased presentation. For example, the words "in fact" are used to introduce favored statements that relate to matters that certainly include at least an element of scholarly judgment, disagreed or not, correct or not. They are clearly not pure fact, and the text appears to that extent as polemical and tendentious. And to say of author X that he "doesn't have a clue", as the current text does, is not only polemical, it also appears as uncivil and aggressive, besides being irrelevant to the subject matter, since it doesn't contribute to the work of informing the reader in a fairly explanatory way what facts and views are out there in reliable sources. Another example: the general accusation of "invalidly cherry-picking" favorable examples clearly appears as part of a polemical campaign, and again it begs questions without giving the reader any facts. There is no reason in principle why all of Tycho's results have to be lumped together, he might have done well on category A and badly on category B -- if the RS's give facts and reasonably-supported conclusions about such a matter. I also had a look at the article-section before its revision. A couple of unsupported and unnecessary intensive adjectives in the opening sentence doesn't add up to 'hagiography', I suggest. They could quite well have been dealt with by recasting the opening of the section in moderated style without the intensives, and then the diversity of views introduced in a fact-based way. What would be wrong with putting it that a widely held view has been X, on the other hand recent authors have shown for example (some fact Z very specific and supported) that stands in contrast with that.... perhaps adding, if it's clear, that judgment X can't apply to the area that includes fact Z; and so on. Why the campaign? I hope at least to have pointed out a couple of ways of putting a diversity of view fairly into the article without mounting a polemical campaign about it. With good wishes Terry0051 (talk) 00:27, 5 November 2009 (UTC)

Logicus to User 173.75.158.194 & Terry0051: Again, thanks to you both for all these many critical points and constructive suggestions, but again which I have not yet had time to properly read and digest. I do hope to respond criticism by criticism eventually. But immediately, can I propose perhaps we should first focus on establishing what the facts of Tycho's accuracy and also his comparative accuracy seem to be from the literature ? This is surely the most important issue. Having sorted that out hopefully, then I shall try and deal with your other various criticisms. Here may I just make four points.

1) User 173.75.158.194 challenges the conclusion of the second paragraph, which was

"But in fact it seems it has never been determined just how much more or less accurate Tycho's celestial positions were overall with respect to their maxima, minima and mean errors than those of the Babylonians, Hipparchus, Ptolemy, Copernicus and Walther, for example, or of any other predecessor or contemporary."

and of which they say

"The second paragraph comes to a rather preposterous conclusion, that is refuted by just about every source we have. Even on the most tendentious reading of the sources, there is no way the conclusion of the paragraph can possibly be the case. A perfunctory googling turns up this, placing Brahe at several orders of magnitude greater accuracy than Hipparchus and Ptolemy. Although the methodology with which this particular comparison is made is open to some debate, there is no serious controversy over the essential conclusion."

But if you first care to read what my conclusion says carefully, I hope you will realise that to falsify it by counterexample and show it is preposterous, you must find at least just one source that has determined the maximum, minimum and mean errors of all the celestial positions of each of the Babylonians, Hipparchus, Ptolemy, Copernicus, Walther and Tycho, and has then calculated the differences between Tycho's max, min and mean errors and those of each of these other 5 astronomers. To the best of my knowledge nobody has ever done such. I would be delighted if you could find somebody who has done so reliably once you have understood the logic of the proposition. But an admittedly very quick scan of the Erik Hog article Astrometry accuracy in the last 2000 years that you so very kindly provided a web link to reveals he has not done so, and not least because he never even deals with the Babylonians, Copernicus and Walther, hence suggesting you have not understood the elementary logic of the proposition in at least one key respect.

You may well find that conclusion I make quite shocking, as I certainly did when I investigated the matter. But I think you will eventually find, and must accept, it is true.

2) With respect to the issue raised of the most appropriate measures of accuracy, the discussions of Tycho's accuracy found in the literature typically concern a claim that his celestial positions were the most accurate historically thereto, and also typically mostly concern his reported declared aim to locate all celestial positions to within 1 arcminute accuracy and his reported claim to have actually achieved this goal. (Exactly where he made these two claims I have not yet determined.) The discussions are typically then concerned with evaluating whether Tycho's claim is true or not. And of course the logic of the claim is such that it is false if his errors were ever greater than 1 arcminute, and more or less false according to just how many were. You might ask yourselves how many of his 1004 stellar positions, for example, were out by more than 1 arcminute ?

Hence various authors point out various examples of where this aspired standard was breached by errors greater than 1 arcminute. Hence the leading question they are concerned with is what was Tycho's maximum error and whether it exceeded 1 arcminute. This is the standard discourse in the literature, and was reflected as such in this article before my intervention. It is not my invention or some idiosyncratic standard I am imposing. I just accepted it, but tried to correct the misleading and muddled claims made about Tycho's maximum error in the article. And the literature reveals maximum errors of many degrees, even over 200 degrees in the extreme. This is the measure that is the most and only relevant measure for evaluating Tycho's claim, which is what the literature is principally concerned with. But of course on the other different issue of determining whether he was the most accurate astronomer thereto, then I agree an evaluation based solely on the max error measure would be inappropriate and possibly misleading, and that at least comparisons of mean errors should also be made. For example, it may well be that some predecessor such as Ptolemy had a max error much less than 238 degrees because of better scribes, but a much greater mean error than Tycho because of less precise instrumentation. But then this all becomes academic if nobody has established the mean errors of any of Tycho's predecessors. Much more to be said on this issue, but all I have time for now

3) User 173.75.158.194 says “Although I have no objection to mentioning some anomalies in the data, as the article presently does, I disagree with the way they are presented as part of an argument that Brahe's data was not the most accurate to date.” But nowhere in my text is there any argument nor claim that “Brahe's data was not the most accurate to date.” I have no idea whether it was or wasn’t.

4) Neither of you answer my leading question of whether you disagree with my provisional evaluation:

“But in fact many of the stellar positions in his star catalogues were far less accurate than that by very many degrees out [23], his planetary positions had a maximum error at least in excess of 3', and even the mean error of his 1577 comet orbital positions was as much as 4', suggesting a possibly much greater maximum error.[24]”

I meant by this,

Do you disagree that many of his stellar positions were far less accurate than 1 arcminute error by very many degrees out ? Do you disagree that his planetary positions had a maximum error at least in excess of 3'?

Do you disagree that the mean error of his 1577 comet orbital positions was as much as 4', suggesting a possibly much greater maximum error.[24]” ?

So the questions I am asking are

Do you claim that not many or even none of his stellar positions were very many degrees out ?

Do you claim that the max error of his planetary positions was 3’ or less ?

Do you claim that the mean error of his 1577 comet orbital positions was less than 4’ ?

I just ask the question to establish some kind of base point of possible agreement for further analysis, formulations and development, whatever redraft or not we may agree on.

More later...

--Logicus (talk) 19:22, 5 November 2009 (UTC)


 * The question isn't what other editors "believe" or "claim". The question is what the reliable sources say and how we can best summarize them, fairly and proportionately where they differ. You still owe me an answer to the question I asked on your talk page. —Finell (Talk) 07:26, 6 November 2009 (UTC)


 * Regarding your point (1) above, I should not need to provide a citation to override material that, as it stands, is totally uncited. Every source I have seen says that the increase in accuracy is impressive.  This may not be quantitative enough to satisfy your own personal requirements, but your own argument from personal ignorance is not a valid justification for including material that apparently contradicts many published sources (refer to above post by David Wilson for a list).  Regarding point (2), discounting obvious errors in transcription, we can just state up front that Brahe did not achieve the 1' accuracy to which he aspired on many of his observations.  However, (and we can cite several sources for this) the average accuracy of his observations were a substantial improvement over the other star catalogs that existed at the time.  For the brightest stars, his mean error was under the 1' that he sought, but for the dimmest stars the mean error was under 3'.  This seems to give a more balanced picture of things.


 * While point (3) may be true to the letter, the POV of the section attempts most inappropriately to explode the "hagiographical dogma" that Brahe was the most accurate to date. I would also be very surprised if, as you seem to believe, "nobody has established the mean errors of any of Tycho's predecessors," not that it is necessarily relevant for the article. (We can still quote the majority opinion among published sources even if we ourselves cannot track down the data that they base their assessment on.)  Finally, I think that the sentence you quote in point (4) has been discussed implicitly: "many degrees out" gives a false impression, max errors are entirely emphasized over mean errors, which are mentioned only at the very end and for one of the less accurate datasets. 71.182.236.206 (talk) 12:31, 6 November 2009 (UTC)

Logicus to User 173.75.158.194 & Terry0051, and new User:71.182,236.206: I thought we should discuss the issues of Tycho's accuracy here first to try and reach some consensus about it, and to negotiate an agreeable possibly improved neutral text before posting it in the article. But User:71.182,236.206 has suddenly intervened and now revised it without prior mutual consent or discussion.

However, although I don't fully agree with the revised text, and it unfortunately reintroduces the original muddle between max error and mean error my previous text eliminated, I am happy to collaborate on improving it further. In the first instance I raise 3 issues.

1) Where does Rawlins make the following two claims for brighter stars and for dimmer stars ? On what page(s) of his 1993 article quoted do they appear?:

"Only for the brighter stars in his final catalog did Tycho achieve a mean error of less than 1'. For dimmer stars, the mean error was closer to 3'.[23]"

I was unable to find any such claims with a quick search, but I may well have overlooked them somewhere. However, they seem questionable given Rawlins' own following key finding:

"J4 We find (contra previous commentators) that accuracy was not much degraded by stellar dimness, so long as the star's u was brighter than about 5th magnitude. Indeed, what our tables show is that from 3rd to 5th magnitude, there is no statistically significant decline in accuracy, a startling finding for orthodox scholars, but one which is in fact quite consistent with what one ought to expect after examining Tycho's raw stellar data." (p20)

Also see fn 37, p9 where Rawlins seems to claim that stars of 4th magnitude are not less accurate than those of 1st magnitude.

So is Rawlins' claim that only stars of the 6th magnitude are statistically significantly less accurate than brighter stars ?

Or have I possibly misunderstood something here ?

(Note Rawlins' old sparring partner Hoskins' 1999 p101 makes the claim Rawlins had already challenged here in 1993.)

2) But anyway, the reportage of mean errors does not belong in the discussion of what level of accuracy Tycho achieved consistently, that is, without exception, and which discussion should therefore only be about max errors, and whether they were at most only 1'. Reporting mean errors in this context just introduces conceptual muddle and confusion with an irrelevancy. However it might be useful to report what number/proportion of the 1004 stars listed in catalogue were accurately positioned to within 1'.

Rather the reportage of mean errors belongs, if anywhere, to the subsequent discussion of how accurate Tycho's positions were, starting "Nevertheless....". So I have made this a new paragraph in order to separate out the discussion of whether Tycho achieved the standard of accuracy he claimed to have achieved, which must thus be a discussion of his max error, from the discussion of what level of accuracy and of historically comparative accuracy he really achieved, in terms of whatever appropriate statistical measures, such as mean error or median error, for example.

However, insofar as this latter discussion is about whether or not he achieved the most accurate celestial positions thereto, then what is the point of stating his mean errors for brighter and for dimmer stars if that of any of his predecessors is unknown?

3) What does "ordermag 1' " mean in the Rawlins quotation provided? Do you interpret it as claiming Tycho located most of the stars in cat D, that is, more than 502 stars, to within 1' of their FK4 positions  ?  Note that this measure of comparative accuracy, namely the proportion of stars located to within 1' of their FK4 positions, raises the question of what proportion of stars were located to within 1' of those positions by previous star cataloguers, and whereby Rawlins' judgment that Tycho's catalogue D achieved a level of accuracy far beyond  that of earlier catalogues may be justified or not. Was it only a small minority, for example ? This is a particularly interesting question given Rawlins' own important observation that Tycho's level of accuracy could have been achieved at least since the second century BC given the invention of armillaries by then (fn37, p9).

BTW, does anybody know if Michael Hoskins has done a critical review of Dennis's paper anywhere ? —Preceding unsigned comment added by Logicus (talk • contribs)

1. See the tables of mean errors in the cited Rawlins source. I have spared the reader a detailed analysis, but rms<1' for brighter stars and rms<3' for dimmer stars is fully supported. As for the quotation you cite, allow me to shift the emphasis somewhat:
 * "J4 We find (contra previous commentators) that accuracy was not much degraded by stellar dimness, so long as the star's u was brighter than about 5th magnitude."

Most stars of the catalog did not even fall into this range. At any rate, I'm willing to accept the change "brighter" for "brightest" in the text, if that will satisfy you. 2. No muddle has been introduced. The article now clearly states "mean error" and "max error" where such comparisons are made. Also I disagree with your opinion that only max errors are relevant to the article. I have stated this several times already, and indeed most sources do seem to emphasize the mean errors. So we must be observant here of WP:WEIGHT. 3. Ordermag = Order of magnitude. --72.95.232.90 (talk) 16:48, 8 November 2009 (UTC)


 * Logicus to User 72.95.232.90: Thanks, but No, 'brighter' does not satisfy me. See my comments below. On your second point, I have never said and positively deny that only max errors are relevant to the article. I only point out that it is only max errors that are relevant to evaluating the specific claim made that all his errors were within 1’ and to the evaluation of which mean errors are irrelevant. Geddit ? Thus the sudden disconnecting jump to discussing mean errors when the topic is rather evaluating whether he made any errors greater than 1’ is logically irrelevant, confused and confusing. The logically more relevant point to be made there is rather as follows:


 * ‘He aspired to a level of accuracy in his estimated positions of celestial bodies of being consistently within 1 arcminute of their real celestial locations, and also claimed to have achieved this level. But in fact many of the stellar positions in his star catalogues were less accurate than that, and only some 40% of the 1004 stars recorded achieved that level of accuracy, albeit nevertheless a substantial minority.’


 * But mean errors are potentially very relevant to discussing whether Tych was more accurate than predecessors, if only we knew what their mean error was. Geddit ?--Logicus (talk) 19:28, 10 November 2009 (UTC)

Logicus to User 72.95.232.243: Thanks for your supplying a Rawlins page number, if not a verifying quotation for the article’s claim that

"Only for the brighter stars in his final catalog did Tycho achieve a mean error of less than 1' for the right ascension, and even then mean errors of just over 1' for the declination. ...[23][24]."

In fact as I pointed out in effect, Rawlins draws no such conclusion and the claim contradicts his own that dimmer star positions are no less accurate than brighter ones..

So are you actually claiming that this proposition is verified by the fact that Rawlins' 1993 Table 5 on p13 shows a mean error of 0.84' in the right ascensions of just the 12 very brightest stars of all, namely those with magnitude < 1.5, out of some three quarters of the 1004 stars listed in Cat D ?

If so, this is surely a failed verification. On Rawlins' evidence the non-hagiographical truth of the matter expressed in a counterpart true proposition is surely of the following ilk:

'Only for the 12 very brightest stars of all out of a select 761 in his final catalogue of 1004 stars did Tycho achieve a mean error of less than 1' for their right ascensions, and even then the mean error of their declinations was 1.23', whereby possibly even none of even these very few very brightest of 761 select stars were within 1' of their FK4 positions.' (But I am not proposing this text go in the article.) Note the logically relevant context here is what the max error was, not the mean error, which is off-topic here.

I shall therefore flag the Rawlins source as having a failed verification. (Brighter stars surely can only mean those of magnitude 3 or less.)

May I urge editors here yet again that it would surely be best to try and establish and agree the facts of Tycho's (in)accuracy here first as revealed in the literature, and then secondly try and agree a fair and balanced text reporting them, before posting edits in the article. I fear the recent edits have restored these paragraphs yet again to a dog's breakfast of appalling conceptual muddle and hagiography that will surely have to be re-edited.

Meanwhile I propose that if the current first para of this section is to stand, as follows:

“Tycho's observations of stellar and planetary positions were noteworthy both for their accuracy and quantity.[22] His celestial positions were much more accurate than those of any predecessor or contemporary. Rawlins (1993, §B2) asserts of Tycho's Star Catalog D, "In it, Tycho achieved, on a mass scale, a precision far beyond that of earlier catalogers. Cat D represents an unprecedented confluence of skills: instrumental, observational, & computational—all of which combined to enable Tycho to place most of his hundreds of recorded stars to an accuracy of ordermag 1'!" “

Then this shamelss hagiography should be balanced by the following additional counterbalancing two sentences:

‘But if this means ‘he placed most with an error of 1' or less’, then to the contrary, Rawlins' 1993 Table 21 critical analysis of Cat D shows that only some 40% or so of its 1004 recorded stars had, for example, latitudinal errors of 1' or less.. And Rawlins notably failed to say what proportion this was for any earlier cataloguers.’ --Logicus (talk) 19:02, 10 November 2009 (UTC)


 * I have changed the text to "brightest" stars, per my offer above. I disagree with your assessment of "shameless hagiography", unless by hagiography you mean verifiable presentation of the statements made by reliable sources.  The purpose of the article should not be to give a complete literature review, examining every conceivable aspect of what accuracy Tycho achieved.  That is rightly the task of historical scholars, who publish in academic, refereed journals, not online encyclopedias.  I would also like to solicit the input of other editors.  Your position is known and understood and already amply disagreed with.  Is there some other voice that can help to balance this embattled section? 74.98.45.40 (talk) 21:35, 10 November 2009 (UTC)


 * I agree. Too much detail is a disservice to Wikipedia's typical readers. —Finell (talk) 02:10, 11 November 2009 (UTC)


 * The current state of the discussion of Tycho's accuracy, with the discussion of both median and mean errors in the body of the article and the change from "brighter" to "brightest" and the discussion of both the instrumental errors and the maximum errors in the extended footnote shows the right balance and level of detail for an encyclopedia article. This is clearly not "hagiography," but good reporting of what's in the secondary historical literature.  --SteveMcCluskey (talk) 14:17, 11 November 2009 (UTC)

Newton
I deleted unsourced attributions to several scholars, digression about whether Newton based his theories on Kepler, and other analyses of Newton which aren't sufficiently relevant to this article. I question the suggestion, which I did not delete (yet), that Newton believed in Tycho's model (the paragraph that begins "Even the 1726 third edition of Newton's Principia was no more than Tychonic geo-heliocentric ..."). That Newton doesn't mention Earth as a primary planet is otherwise explainable. Is there direct support in reliable secondary sources for the proposition that Newton accepted the Tychonic model? Is it the prevailing view of scholars? —Finell (Talk) 19:39, 6 November 2009 (UTC)


 * [From Terry0051] I believe your question is very well taken, as was the comment last year by 92.237.108.47. In the first place, the suggestion in the article section discussed here, that the Principia [in certain respects] is "studiously no more than Tychonic ....", is a synthesis not itself present in the Principia nor in any cited RS. (That is irrespective of whether the italicized words in the post above are taken into account.)  Accordingly this characterization of the Principia appears to be inappropriate here at least under the heading of WP:OR.  I also read through today the paper by Imre Lakatos cited in the present text; in the present text footnote this is said "apparently" to contain support for the suggestion discussed; but I find that it does not contain anything about any allegation of Newtonian geoheliocentrism, nor about the verbal point about Earth and Planets raised in the text; the suggested support is lacking even if the cited article is potentially RS in relation to Newton (and Lakatos was known as an epistemologist and philosopher of science, not as a historian of Newton or a physicist).

It can also be seen in another way that the suggestion in the article text also substantially distorts Newton, because Newton preserves his verbal stylistic distinction between "Earth" and "Planets" (the point on which an extraordinarily heavy weight is currently being placed), even in the very same sentence as that in which he declares his heliocentric/barycentric position (clearly against any geocentric position) thus, that "the common centre of gravity of the Earth, the Sun and all the Planets is to be esteem'd the Centre of the World".(Newton, "Principia", Book 3 Proposition XII (Corollary), in the 1729 translation, at page 233. Newton made it also clear on the same page or the preceding page that the barycenter and the Sun's center are not the same but are never far apart, no more than than scarcely a diameter of the Sun even when Jupiter and Saturn, whose mass ratios he has estimated (surprisingly close, for the 1680s, to modern estimates), are ranged together on the same side of the Sun -- a thoroughly modern position, cf. Center of mass, with a diagram that vividly illustrates just what Newton wrote. So the verbal formulation about Earth and Planets clearly can not, in its Newtonian context, bear the weight of geo(helio)centric interpretation that the current WP:OR and article text attempts to place upon it.

The same section of the discussed article text also contains criticism of Newton's alleged reasoning in support of his heliocentric/barycentric position.

(a) The whole question of the goodness or otherwise of Newton's reasoning in support of his heliocentric/barycentric position appears to be irrelevant to this article on Tycho Brahe and his geo-heliocentric model and its acceptance or otherwise. (The irrelevance of the Lakatos article is also underlined by the consideration that the discussed article section is about Tycho's physics and its acceptance, not about epistemology.)

(b) The whole passage about Newton in the present article text, even if relevant here, is also a very substantial distortion of Newton's arguments for the heliocentric/barycentric position: these are specifically misrepresented by putting forward one of the background matters (the observed fact that the orbit of Mars as well as that of Jupiter and Saturn goes around the Sun: beyond the Sun when in conjunction) incorrectly, as if it was the whole basis of the argument. The effect of the present text seems indistinguishable from a straw-man tactic. Newton's arguments can be specifically seen not to rely wholly, or even mainly, on the point on which here they are incorrectly said to rest. (Specifically, the Principia at Book 3, Prop.II, shows Sun-directed inverse-square forces in the case of the Planetary orbits (a) by referring firstly back to Phenomenon 5, which brings in the observations about the planets' equal area-rates of motion with respect to the Sun but not even approximately with respect to the Earth; and then back to Book 1 Prop.2 for the centripetal force significance of those observations; and (b) by reference to the 3/2 power relation between the orbital sizes and periods and to the quiescence of the planetary aphelia, of which the inverse-square law significance is shown by Book 1 Prop.4 (cor.6) and Prop.45 (cor.1). But this discussed text, wrong though it is and not in accord with RS about Newton, is also not about Tycho Brahe at all.)

I'd offer the following text in substitution for the current paragraph about Newton, which includes clearing up a possible misconception in the preceding paragraph and providing online sources: Terry0051 (talk) 21:47, 6 November 2009 (UTC)

(Amending as from the sentence starting: --)

The Tychonic model lasted into the late 17th century and even the early 18th century; in particular, after the 1633 Church decree over the Copernican controversy, to the end of the century, the Jesuits produced "a flood of pro-Tycho literature". Among pro-Tycho Jesuits, Ignace Pardies declared in 1691 that it was still the commonly accepted system, and Francesco Blanchinus reiterated that in 1728.

Isaac Newton made clear he was not a Tychonist when he stated in Book 3 of the Principia (all editions) that "the common centre of gravity of the Earth, the Sun and all the Planets is to be esteem'd the Centre of the World", and "that centre either is at rest, or moves uniformly forward in a right line". (Newton rejected the second alternative, because he adopted as starting point the position that "the centre of the system of the world is immoveable", which "is acknowledg'd by all, while some contend that the Earth, others, that the Sun is fix'd in that centre.") Newton, who earlier assessed the mass ratios Sun:Jupiter and Sun:Saturn, also pointed out that these put the centre of the Sun usually a little way off the common center of gravity, but only a little, the distance at most "would scarcely amount to one diameter of the Sun". Newton's position is clearly seen to go also beyond literal Copernican heliocentrism nearly to the modern position in regard to the solar system barycenter.

Terry0051 (talk) 21:47, 6 November 2009 (UTC)


 * Support for the Tychonic cosmology, who and when, is certainly relevant to this article, including any additional material you have. Since you make clear that Newton was not a supporter, I see no reason that this article needs to discuss him at all. We should simply take out the suggestion that Newton was a supporter, and not replace it with a showing that he wasn't. (There may be a place for Newton's position, preferably supported by secondary sources, in Heliocentrism or Copernican heliocentrism, if it isn't already there.) Since Lakatos doesn't support this idea and no other source is cited, Newton should just be eliminated from this article. Frankly, the claim that he supported Tycho (or even was agnostic between Tycho and Kepler) struck me as bizarre, but I don't know everything about history. —Finell (Talk) 01:29, 7 November 2009 (UTC)

Logicus: I fear you have misunderstood and misrepresented the paragraph on Newton’s ‘’Principia’’, which was, along with its footnote, as follows:

"Even the 1726 third edition of Newton's Principia was no more than Tychonic geo-heliocentric in its declared six established astronomical phenomena in the preliminary 'Phenomena' section of Book 3, from which it sought to demonstrate its theory of universal mutual gravitational attraction. For example, Phenomenon 3 stated, "The orbits of the five primary planets—Mercury, Venus, Mars, Jupiter and Saturn—encircle the sun."[citation needed], which appears to exclude the Earth from primary planethood, in agreement with Tycho's model.[38

1.	^ This interesting fact was apparently first pointed out in the 20th century by the philosopher of science Imre Lakatos in his Newton's effect on scientific standards posthumously published in his 1978 Philosophical Papers Volume 1. In addition to the many logical reasons that have been adduced by such as Duhem, Popper, Feyerabend, Lakatos and others, such as Leibniz and Roger Cotes, to show that Newton did not validly deduce his law of gravity from Kepler's three laws of planetary orbits, this fact also further scuppers the inductivist-positivist claim that he did, since Kepler's laws were heliocentric. Of course in the General Scholium added to its 1713 second edition Newton did endorse heliocentrism in stating "The six primary planets revolve about the sun in circles concentric with the sun..." (p940 Cohen & Whitman Principia) But the Principia never gave any proof that the Earth orbited the sun, not even an invalid one such as were his Phenomenon 3 proofs that Mars, Jupiter and Saturn did."

Contrary to your misreading that it claims Newton was a Tychonic geoheliocentrist, if you now read it carefully I hope you will see that not only does it make no such claim, but even points out Newton explicitly endorsed heliocentrism in the second edition of Principia.

The relevance of this paragraph to the article is that of providing possible evidence of the longevity of geoheliocentrism into the early 18th century. The relevant point is that it would seem Newton wanted to be neutral between Tychonic geoheliocentrism and heliocentrism when it came to stating what he regarded as established hard facts from which his inductive proof of universal mutual gravitation was to proceed.

Would you therefore be so kind as to constructively suggest some revision of it that you think would avoid such a gross misreading amongst those functionally literate in English ?

Do you think the following revision might be better ?

In the six established astronomical phenomena declared in the preliminary 'Phenomena' section of Book 3 of Newton’s Principia, from which it sought to prove its theory of universal mutual gravitational attraction, even the 1726 third edition of it was no more than Tychonic geo-heliocentric. For example, Phenomenon 3 stated, "The orbits of the five primary planets—Mercury, Venus, Mars, Jupiter and Saturn—encircle the sun."[citation needed], which appears to exclude the Earth from primary planethood, in agreement with Tycho's planetary model, or else just be neutral between Tychonic geoheliocentrism and pure heliocentrism.[38


 * And by the way, did Tychonic geoheliocentrism claim where the universal centre of gravity was or where the centre of the world was, rather than just claim the Earth was static and the Sun orbited it along with the planets ? --Logicus (talk) 15:59, 7 November 2009 (UTC)


 * No. It doesn't belong in this article at all unless that interpretation of Newton is supported by reliable sources. Based on Terry0051's analysis, it is unlikely that you will find it in reliable sources, because it appears to be a misinterpretation. It certainly is not a mainstream view among scholars. But Terry0051's interpretation of Principia on this point wouldn't belong in Wikipedia's article space, because it isn't published in a reliable source. Logicus, you still owe me an answer to the question I asked on your Talk page. —Finell (Talk) 16:33, 7 November 2009 (UTC)

Logicus: Terry is quite wrong in my view, but perhaps due to my careless edit above, now corrected, not made sufficiently clear that there is no suggestion in my text Newton was a geoheliocentrist. Apologies ! Principia's 'Phenomena' section makes it clear heliocentrism still unproven in 1726, geo-heliocentrism still a goer. Hence of central relevance to this section on longevity of Tychonic geoheliocentrism. --Logicus (talk) 19:28, 9 November 2009 (UTC)


 * I agree with Terry0051 and Finell that Newton does not belong in this article, but let me briefly discuss Newton's phenomena section at the beginning of Book III of the Principia.
 * For all of the six phenomena discussed in that section, Newton presents the direct astronomical evidence that supports these observable phenomena. For the case in point: "Phenomenon III: That the five primary planets, Mercury, Venus, Mars, Jupiter, and Saturn, with their several orbits, encompass the sun", he advances the alternation between the full and crescent phases of Mercury and Venus as evidence that those two planets revolve about the Sun, and for Mars, Jupiter and Saturn, he advances their alternation between full and gibbous phases as observational evidence that they revolve around the Sun.  He does not discuss the Earth here because he cannot produce analogous astronomical observations of the Earth to provide simple observational evidence for the idea that the Earth goes around the Sun.  This passage does nothing to support the notion that Newton saw geo-heliocentrism as "still a goer."  That the Earth revolves around the Sun just wasn't an observable phenomenon.  --SteveMcCluskey (talk) 20:36, 9 November 2009 (UTC)

[From Terry0051] I agree with Steve McCluskey, and I'd offer a couple of further points. It's not clear why the 'Phenomena' section in Principia Book 3 considered in isolation is thought to have any bearing on whether heliocentrism was then proved. The 'phenomena' present a consensus set of astronomical data, but Newton's arguments for heliocentrism (first published 1687 not 1726) were not based just on the data alone, they involved the combination of the astronomical data with his mathematical demonstrations. Also, in Newton's precursor of Principia Book 3, posthumously translated and published as 'System of the World', he gave a specific refutation of geoheliocentrism by reductio ad absurdum: "If the Sun was revolved about the Earth, and carried the other planets round about itself, the Earth ought to attract the Sun with a great force, but the circum-solar planets with no force producing any sensible effect", adding that this would be contrary to [the precursor of] Book 1 Prop.65 corollary 3. He also wrote in reference to the attractive force of the Sun, which "does more than a thousand-fold exceed all the rest", that all bodies within and "beyond the bounds of the planetary system must descend directly to the Sun, unless by other motions they are impelled towards other parts: nor is our earth to be excluded from the number of such bodies". Terry0051 (talk) 02:57, 10 November 2009 (UTC)


 * Under Wikipedia's content policies and guidelines, the only interpretations of Newton that matter are interpretations by reliable sources. —Finell (Talk) 03:09, 10 November 2009 (UTC)


 * How does this connect with what has just been posted? Is a direct quotation an interpretation?  Is a standard edition of Newton other than a reliable source? Terry0051 (talk) 03:17, 10 November 2009 (UTC)


 * To expand on Finell's criticism, the discussion on this talk page has seduced us (myself included) into proposing rival interpretations of primary sources—in this case of Newton's Principia. It is a temptation to respond to other's interpretations but I should have known better; I had crossed the line into those "analytic, synthetic, interpretive, explanatory, or evaluative claims about information found in a primary source" that don't belong in Wikipedia. Mea culpa  --SteveMcCluskey (talk) 03:51, 10 November 2009 (UTC)

A comment in response: WP:NOR allows "descriptive claims" about primary sources:
 * "Our policy: Primary sources that have been reliably published .... may be used in Wikipedia, but only with care, because it is easy to misuse them. Any interpretation of primary source material requires a reliable secondary source for that interpretation. Without a secondary source, a primary source may be used only to make descriptive claims, the accuracy of which is verifiable by a reasonable, educated person without specialist knowledge."

"Descriptive claim" clearly appears to include factual statements about what the sources do or do not contain.

Terry0051 (talk) 13:10, 10 November 2009 (UTC)


 * I don't think that is the issue. The issue is using statements from Principia to lead to a conclusion that Newton was a Copernican (or Keplerian) or a Tychoist, or was indifferent between them. That is what was being argued above. For Wikipedia, saying that Newton was a Copernican or a Tychoist can only be based on the conclusions that reliable secondary sources have published. Policy prevents Wikipedia from saying, for example, that Newton's failure to mention Earth as a planet shows Newton opinion was no closer to Copernicus than to Brahe. It would be different if Newton said what his position on this matter was, in such unequivocal terms that no interpretation is required. —Finell (talk) 02:33, 11 November 2009 (UTC)

Thanks for the additional reply. I'd suggest that the issue depends on the content being considered. I agree with you about the issue that arose on the point in the former article text -- suggesting that Newton studiously left room for the Tychonic model: clearly an interpretation. (It also contradicted the source content.) But the reminder post (of 03:09, 10 November 2009, above), about interpretations, was stated with complete generality in respect of the content to which it seemed to apply: and it also did not appear to leave room for the policy provision that allows giving direct facts from primary sources. That was what prompted my question about how it was thought to apply, and brings in the relevance of the quote from NOR (after I found the policy wording). It's welcome that you agree the position is different for the case that Newton stated his position unequivocally. The quotes further up this page quote him actually doing so. I sympathize with where it seems you might be coming from, not wanting to 'give an inch' on policy in case somebody 'takes an ell' -- there clearly have been excesses. But there's also the concern I had, that the reminder post could be understood in an over-generalized sense, as taking away an important 'inch' about fact-giving that the policy, so it turns out (after searching through quite a lot of words), actually allows. Terry0051 (talk) 21:08, 11 November 2009 (UTC)


 * I agree with you completely that the propriety of using primary sources in an article depends specifically on what is used and how it is used. Based on experience elsewhere on Wikipedia, I try to be vigilant in promoting compliance with WP:NOR. I didn't mean to offend anyone, and I apologize if my comments lent themselves to that interpretation. —Finell (talk) 23:13, 11 November 2009 (UTC)

Signatures plus
Throughout Wikipedia generally, signature of a talk page comment at the end (the original meaning of subscribe) by user name or IP address (at least) is considered sufficient. The instructions above and below the edit box on talk pages say "to sign your posts by typing four tildes (~) " (above) and, "Sign your posts on talk pages: ~ " (below). See Signatures. On this talk page and Talk:Celestial spheres, some editors also preface their comments with a self-identification. I'm curious how this practice evolved in this corner of Wikipedia; I haven't seen it elsewhere (although I haven't been everywhere). —Finell (Talk) 03:33, 10 November 2009 (UTC)


 * This convention is also used on Talk:Johannes Kepler. Curious. Is this a guideline of WikiProject History of Astronomy? —Finell (Talk) 03:46, 10 November 2009 (UTC)

Maybe it's a function of how complicated the thread of comments has become. The tilde-signature form does not always leave it visually very clear where one contributor's paragraphed comment ends, and a contribution by another begins, and misattributions of who said what have sometimes resulted. Terry0051 (talk) 13:16, 10 November 2009 (UTC)