Talk:Archimedes Palimpsest

Suidas wrote the original document ?

According to the Wikipedia entry for Archimedes , the original mathematical treatise, later erased by 13th century religious writers, had been previously penned, in the 10th century AD, i.e. the very era when the scholar Suidas lived. Perhaps Suidas wrote the original mathematical treatise ? 24.143.92.97 (talk) 04:27, 25 February 2012 (UTC)

discovered vs. not generally known

To say that it was "discovered" in 1906 makes it sound as if no one knew of its existence before then. It is true that it was not generally known among either mathematicians or historians, but, if I understand correctly, neither was it something that had not been mentioned in print. Heiberg's translation was what made its contents well known, but its existence was hardly a secret. Michael Hardy 18:46 Apr 25, 2003 (UTC)

Yep, the second external link (my isisletter "Did Isaac Barrow read it?") contains an accurate chronology of the discovery compiled from various sources Arivero 15:28, 14 June 2006 (UTC).

I have read that the gold illumination was forged in the 10th century, not the twentieth. Can someone confirm this? —Muckapædia 5h38, 7e Août 2006 (EST)

Where was this read? --Wetman 11:13, 7 August 2006 (UTC)

http://www.abc.net.au/science/news/stories/s1707926.htm - erroneously says "Then 10th century forgers painted gold foil imagery onto the recycled pages in an effort to increase the manuscript's value." This is a typo, all other articles say 20th century, and it is also impossible, as the palimpsest was not created until the 13th century. MakeRocketGoNow 00:13, 8 August 2006 (UTC)

It is worded extremely unclearly at the beginning of the article. Was it in Istanbul leading up to 1906 or was it taken there to be examined? When was it first known that it was not just a liturgical document? Is it known where in the world it was recycled into that in the first place? Salopian (talk) 06:48, 13 July 2008 (UTC)

There is a good history of the Palimpsest here. Perhaps some of this could be incorporated into the article. --♦IanMacM♦ ^{(talk to me)} 07:10, 13 July 2008 (UTC)

Unclear pagagraph

This is amusing because the collaboration on indivisibles between Galileo and Cavalieri—ranging between years 1626 to around 1635—has as a main argument the hull and pyramid of the n = ∞ dome. So in some sense it is true that the Method is only a theorem behind the modern infinitesimal theory.

I removed this because I don't understand the amusement, and the "a theorem behind" phrase. AxelBoldt 22:37, 29 March 2007 (UTC)

The Method

The article states: "Essentially then, the method consists in dividing the two areas or volumes in infinitely many stripes of infinitesimal width, and "weighing" the stripes of the first figure against those of the second". Really? So you think Archimedes actually succeeded in dividing the areas/volumes into infinitely many stripes of infinitesimal width? Wow. I am amazed at how stupid you are. Archimedes' method was one of approximation. It is very similar to natural integration by approximation (no trial and error involved). However, that Archimedes used infinitesimals is highly unlikely. Infinitesimal is an ill-defined concept that Archimedes knew nothing about. The term infinitesimal was only coined in the 16 or 17th century. Yet another factually incorrect article by Wikipedia Sysops/Administrators. 70.120.182.243 16:58, 4 July 2007 (UTC)

Archimedes himself said it's an ill-defined concept and therefore that the arguments he wrote that used them were not complete proofs. That didn't stop him from using them. See Archimedes' use of infinitesimals. Michael Hardy 22:01, 10 July 2007 (UTC)

How could he have used a concept he knew nothing about? Where did Archimedes make a reference to an 'infinitesimal' in the palimpsest? The Greek text nowhere mentions 'infinitesimal' or anything remotely similar. On what grounds do you arrive at your conclusion that equates the terminology Archimedes used with your interpretation of 'infinitesimal'? Do you read and understand ancient Greek? How could Archimedes have anticipated a concept he knew nothing about? 70.120.182.243 02:22, 11 July 2007 (UTC)

I don't think he used that word in this text. Nonetheless he used infinitesimals in this text. As for how he did it, just read this page; that tells you how. And he said in this text that these are not complete proofs. I think it was elsewhere that he in effect rejected any attempt to take infinitesimals literally, by stating a sort of Archimedean axiom, as we would now call it. Michael Hardy 02:32, 11 July 2007 (UTC)

I have read all the text you refer to. This page tells me how he used approximations but nothing about how Archimedes may have used infinitesimals (whatever these are). The link to how Archimedes found areas such as between the parabola and a secant also says nothing about how he might have used infinitesimals. All the articles claim he, Newton and certain others used infinitesimals, but there are no examples. What is an infinitesimal? Please don't refer me to your article on infinitesimal as it does not provide a satisfactory definition or anything that can be used in a calculation. Again, how do you perform calculations using a non-existent concept (infinitesimal)? 70.120.182.243 15:03, 11 July 2007 (UTC)

Archimedes did not have what we would call modern integral calculus. He did use summation to provide approximate answers to certain problems, and this is why he is sometimes credited with being the founder of integral calculus. However, the method of exhaustion was known to Eudoxus of Cnidus and approximation was known to the Babylonian mathematicians, so Archimedes built on this tradition.--Ianmacm 07:17, 11 July 2007 (UTC)

How is 'modern integral calculus' different from what Archimedes knew? As far as I know, there is no difference in any respect except in the few cases where one can apply the mean value theorem to evaluate integrals without approximation/exhaustion. Whether Eudoxus knew of exhaustion before or after Archimedes is actually irrelevant to the discussion since we are talking about the ill-defined 'infinitesimal' notion. 70.120.182.243 17:43, 15 July 2007 (UTC)

Modern integral calculus relies on the fundamental theorem of calculus, which says you can find an integral if you can find an antiderivative. Michael Hardy 17:49, 15 July 2007 (UTC)

The mean value theorem (mvt) is the fundamental theorem of calculus (ftoc). The ftoc follows in one step from the mvt. Just multiply both sides of the mvt by one average and you have the ftoc. In the case of single variable calculus, this average is the width. The following link illustrates this clearly: [[1]]. As for the Archimedean property (or Euxodian, it doesn't matter what it is called for this discussion), it is a result of the least upper bound property. It's 'complement' does not define an infinitesimal. 76.31.201.0 12:19, 16 July 2007 (UTC)

It's complement defines zero? 65.28.94.67 14:49, 7 September 2007 (UTC)

This discussion is becoming rather ill-tempered. The term "infinitesimal" has always been vague and hard to pin down, which is why it is rarely used nowadays. Integral calculus is used to provide approximate answers to certain types of problem involving area etc, and is not the same as a formal geometric proof. Archimedes knew how to do this although he did not have all the techniques of calculus that are available today.--Ianmacm 07:02, 16 July 2007 (UTC)

There are some specific contexts where it's not vague at all. See non-standard analysis. It's hardly true that it's rarely used in the present day. And as one with much experience teaching calculus, I think it ought to be used a lot more than it is in such freshman-level courses. Michael Hardy 11:45, 16 July 2007 (UTC)

When calculus was new in the 18th century, Bishop George Berkeley (after whom University of California, Berkeley is named) wrote The Analyst, in which he attacked the whole concept of infinitesimals or fluxions. Sir Isaac Newton seems to have realised that some people would not like calculus and argue that it lacked formal rigour. This may have been one of the reasons why he delayed publication of his work in this area. In today's mathematics textbooks calculus is regarded as mainstream, but at the time it was as controversial an non-Euclidean geometry during the early 19th century. Calculus is intended to provide approximations rather than exact proofs, and this is what may displease some of the purists. However, the success of the Apollo moon missions shows that approximations are all that is needed in most engineering situations. At one point during the Apollo 13 mission, the commander Jim Lovell remarked that Newton was in the driving seat. This is an impressive vindication of the uses of integral calculus, and tends to make arguments about the existence or non-existence of infinitesimals into a philosophical side issue. (see also:Oliver Heaviside)--Ianmacm 15:03, 16 July 2007 (UTC)

Criticism?

This beautiful article is still lacking of any mention to the strong criticism raised by many historicians on the Palimpsest's operation (to quote one issue, some people think that the analysis on the poor remains of the Stomachion is a series of uncontrolled guesses, where the logic implication has been replaced by "then why not" or "so it could also be that" &c.)--pma 11:43, 5 December 2010 (UTC)

Broken Link

The link on Palimpsest seems to be broken.

Style of greek writing of photo.

Greek writing of the photo appears in the Middle Byzantine style, maybe not so much prior to the religious text that has replaced it. Am I wrong? — Preceding unsigned comment added by 84.222.77.231 (talk) 15:45, 26 June 2011 (UTC) Perhaps Komnenos or Angelus period ?

The article says "the copy of his work was made in the 10th century AD by an anonymous scribe". Presumably this scribe would use Middle Byzantine. He was a few centuries before the work was overwritten... which I guess is a short time in comparison to the delay between Archimedes and him. Yaris678 (talk) 18:59, 29 May 2012 (UTC)

Wrong date

1229 is the thirteenth century, not the twelfth68.49.247.221 (talk) 20:27, 6 July 2012 (UTC)

According to the sourcing at [2], "the prayer book, technically called a euchologion, was completed by April 1229, and was probably made in Jerusalem." According to [3], "The Archimedes Palimpsest was originally written in AD 950 before the text was erased and the paper reused by a monk in 1229 to produce a Christian prayer book." The article has been adjusted accordingly.--♦IanMacM♦ ^{(talk to me)} 06:32, 7 July 2012 (UTC)

Incorrect sentence

The following sentence:

In Heiberg's time, much attention was paid to Archimedes' brilliant use of infinitesimals to solve problems about areas, volumes, and centers of gravity.

Has been changed to:

In Heiberg's time, much attention was paid to Archimedes' brilliant use of the method of exhaustion to solve problems about areas, volumes, and centers of gravity.

Archimedes knew nothing about infinitesimals. — Preceding unsigned comment added by 197.64.207.71 (talk) 07:47, 25 June 2013 (UTC)

John Gabriel and/or his IP will be blocked again if he persists in making disruptive edits. Tkuvho (talk) 08:53, 25 June 2013 (UTC)

Good 84.216.157.87 (talk) 09:20, 10 September 2023 (UTC)

See http://en.wiki.x.io/w/index.php?title=Special:Log/block&page=User%3A12.176.152.194 Tkuvho (talk) 09:04, 25 June 2013 (UTC)

Oh, of course. If any facts are different to those of the dimwits in the core editing group, they are blocked? Where is your source that Archimedes used "infinitesimals"? There is not a shred of evidence this is true. "In Heiberg's time, much attention was paid to Archimedes' brilliant use of infinitesimals to solve problems about areas, volumes, and centers of gravity." is just your opinion. It's not fact that you can substantiate. 197.79.11.22 (talk) 11:55, 27 July 2013 (UTC)

External links modified

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Stomachion size?

It seems wrong to me that this section should be much larger that the \\{{main\\}} that it points to. It also reads very oddly. Snori (talk) 07:55, 10 February 2017 (UTC)

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Speculation

I've removed the following speculation "This almost certainly refers to Rick Adams because of a blogpost by Michael Shermer where he describes seeing it at a birthday party for James Randi in the collector's home in Falls Church, Virginia, where Adams (a benefactor and treasurer of the James Randi Educational Foundation) is known to live."
The source given does not name the person owning the palimpsest, even supposing it is reliable, so any assumption as to their identity is speculative (and, for WP, original research). Also, as Rick Adams is still alive, it contravenes our guidelines on information about living persons. Moonraker12 (talk) 22:55, 18 December 2018 (UTC)

Dubious

I've tagged the following assertion "Archimedes often used what are now called Riemann sums" as dubious; there's no source given to back this up (in fact, the whole section is unsourced); so, did Archimedes really work out a method that wasn't re-discovered until the 19th century, and if he did, shouldn't we be calling them Archimedean sums? Moonraker12 (talk) 23:00, 18 December 2018 (UTC)

The section certainly needs reworking in terms of citations and possibly for tone as well. This claim needs to be cited, as you say, and reworded as well in my opinion. However, it does contain some truth: Archimedes did use Riemann-sum-like methods in certain area calculations: for example in The Method of Mechanical Theorems he divides a triangle and a parabola balanced on a lever into small (Reiman-sum-like) slices. The similarity is great enough that the current page for the work uses an integral to describe the calculation. Also note that an important integrability criterion is named for Archimedes: the Archimedes Riemann Theorem. Winthrop23 (talk) 11:09, 25 October 2021 (UTC)

Claim of Bezos ownership insufficiently sourced

The article currently asserts that:

Unable to sell the book privately, in 1998 the businessman's daughter risked a public auction in New York contested by the Greek church; the U.S. court ruled for the auction, and the manuscript was purchased by Jeff Bezos.

However, the given source for this claim asserts merely that:

The identity of the purchases remains secret, although Finch allowed that he is a private American involved in the high-tech industry—specifically not Bill Gates. (The German magazine Der Spiegel reports that the palimpsest’s owner is most likely Jeff Bezos, founder and CEO of the online retailer Amazon.com.)

https://archive.org/details/eurekamanlifeleg0000hirs_c0p0/page/186/mode/2up

This appears to be referring to https://www.spiegel.de/international/world/revolutionary-authentic-stolen-the-story-of-the-archimedes-manuscript-a-490219.html

Typometer (talk) 21:58, 8 March 2023 (UTC)

References

Truthfulness of a claim in this article

I find this paragraph in this article:

Archimedes used exhaustion to prove his theorems. This involved approximating the figure whose area he wanted to compute into sections of known area, which provide upper and lower bounds for the area of the figure. He then proved that the two bounds become equal when the subdivision becomes arbitrarily fine. These proofs, still considered to be rigorous and correct, used geometry with rare brilliance. Later writers often criticized Archimedes for not explaining how he arrived at his results in the first place. This explanation is contained in The Method.

Is there some reason to think this is true? A line parallel to the axis of a parabola, drawn through the midpoint of a chord of the parabola, intersects the parabola, so that that point of intersection is one vertex of a triangle whose other vertices are the endpoints of the chord. Archimedes said the area bounded by that chord and the curve has 4/3 the area of that triangle. To show that he looked at the two other chords that are the other two sides of the triangle. With each of those two chords, he constructed a triangle in the same way. He showed that each of those two triangle has 1/8 the area of the first triangle, so that the sum of those two areas is 1/4 the first area. Then he iterated the process, getting $$1+{\tfrac {1}{4}}+{\tfrac {1}{4^{2}}}+{\tfrac {1}{4^{3}}}+\cdots ={\tfrac {4}{3}}.$$ The argument in the Palimpsest for the area bounded by the curve and the chord is radically different from that. It does not appear to explain in any way how he found that argument.

Moreover, is there some reason to think somebody criticized him for not explaining how he arrived at that result? That should be cited. And I doubt it can be. Michael Hardy (talk) 18:39, 3 August 2023 (UTC)

The entire section on The Method of Mechanical Theorems is unsourced. The part that you mentioned looks like unsourced commentary which isn't ideal.--♦IanMacM♦ ^{(talk to me)} 18:50, 3 August 2023 (UTC)