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- The Diagrams as Floating Bodies by Reviel Netz of Stanford University

funds that is he guarantees you that however much the opponents are offering you are allowed to beat their offers According to one rumor such was the authorization given by the current owner of the Archimedes Palimpsest going into the Christie s auction They offer one million and you offer two They offer a billion and you a trillion However much they put up you may put up more You are the representative then of potential infinity Why is this infinity merely potential Because you are always making a finite commitment In other words you know that if the auction is ever to end then it will end with a finite commitment however large that finite commitment may be It may be a million a trillion or it may be the number 1 followed by a trillion zeroes but it will always be some finite number Potential infinity then may be viewed as an endlessly extendible and yet forever finite magnitude Not so actual infinity By actual infinity we mean something such as say the number of points on a line If your buyer would have authorized you to offer as your price in that auction a dollar for each point there is on a line then he would have authorized you to make an actually infinite bid This is a very high bid indeed After all even the number 1 followed by a trillion zeroes is still dwarfed by actual infinity It is a curious bid too If it takes you say a minute to pass a suitcase with a million dollars than it will take you all of eternity to pay your bid actually infinite bid Actual infinity actually never ends And for this reason many philosophers throughout the ages have doubted its very existence The established historical wisdom on infinity and the history of mathematics then used to go something like this At first came the Greeks who preferred above all to have precise rigorous proofs For this reason they have completely avoided the concept of actual infinity concentrating instead on potential infinity whose rigorous treatment was perfected by Archimedes in his measurement of curves Next came the early modern mathematicians who wanted to get results come what may To obtain general result concerning curves they have brought in the notion of actual infinity paying the price that their mathematics was less rigorous and precise compared to that of the Greeks Along came the mathematicians of the 19th and 20th centuries slowly and laboriously building up a new kind of mathematics where the concept of actual infinity is meticulously built up so as to have the same kind of rigorous foundations that the Greeks have provided for potential infinity The most important discovery made through the Palimpsest over the last few years involved some 12 lines of Greek in an otherwise neglected proposition of Archimedes Method They have changed no less than our understanding of how western mathematicians came to handle infinity To be sure the Method

Original URL path: http://www.archimedespalimpsest.org/about/scholarship/method-infinity.php (2016-02-18)

Open archived version from archive - How many ways can you have a stomach ache? by Reviel Netz of Stanford University

Archimedes foray into the game We always knew he has something to do with this game because some ancient authorities refer to the game simply as Archimedes Box In 1899 an Arabic text was published based on a manuscript in Berlin containing a brief passage claiming to derive from a work by Archimedes on the Stomachion And then in 1906 the Palimpsest was discovered Here is where the Stomachion is in really bad luck Archimedes treatise on the subject was apparently the last treatise in the original Archimedes manuscript from which the Palimpsest was made Most of its pages were in bad shape already in the 13th century and so were discarded by the makers of the Palimpsest Only a single page survived the first one Thus we have the introduction to the Stomachion together with a brief introductory theorem This is in principle very useful the introduction after all should state what the treatise is about and so should furnish us with crucial information but worse is to come the maker of the Palimpsest inserted this page right towards the end of the book At around the 16th century apparently a few pages were lost from the end of the book perhaps to a fire and the page containing the introduction to the Stomachion now became the very last page of the book The result is that this is now among the most difficult pages in the book indeed was very difficult to read already when Heiberg came to look at it Since the Arabic fragment is also very tantalizing and is anyway no more than a very late compilation the end result is that up until recently we could not put together this particular jigsaw puzzle No one knew what Archimedes treatise was about The standard view was we shall never know The interpretation put forward in 2004 based on the new readings made possible thanks to digital technologies is still tentative Nothing better is possible seeing that our evidence is so fragmentary But this interpretation is widely considered to be very likely This is quite a result too it makes Archimedes into the first author of an entire field of mathematics one that until recently we thought no ancient author has ever worked in This is the field of combinatorics Combinatorics as its name suggests is the study of the number of possible combinations Suppose you have three blue socks how many pairs can you form Answer three Each choice of pair leaves exactly one sock unmatched so that the number of pairs is the same as the number of individual socks Suppose you have three green socks too and you wish to form bicolored pairs a green and a blue in each How many combinations Answer nine Each choice of blue is allowed and so is each choice of green allowing the entire multiplication table of three by three i e nine This kind of study we can immediately see is a far cry from the

Original URL path: http://www.archimedespalimpsest.org/about/scholarship/combinatorics.php (2016-02-18)

Open archived version from archive - Scholarship on Hyperides

these folios just like the Archimedes ones and so we imaged them anyway Slowly other texts started to be revealed In 2002 Natalie Tchernetska discovered speeches by the Athenian Orator Hyperides Five bifolia have now been discovered Deciphering these pages has been a collaborative endeavor involving very many classicists It was an extraordinarily difficult enterprise as you can see from these three Fly on The Wall videos of meetings held in London However good the images are the text remained extremely difficult to read An important part of the process was interaction and feedback between the scholars the imagers and the conservators Laszlo Horvath from Budapest came to study the manuscript in person and he and Abigail Quandt discussed the arrangement of the leaves in the original Hyperides manuscript Judson Herrman came also during the imaging of the manuscript and advised the imagers on capturing raking the Hyperides text with raking light Now in 2008 the Hyperides texts in the Archimedes Palimpsest have all been transcribed and published in three articles published in the Zeitschrift fur Papyrologie und Epigraphik listed in the Bibliography The authors of these articles are in sum and in alphabetical order Colin Austin Chris Carey Mike

Original URL path: http://www.archimedespalimpsest.org/about/scholarship/hyperides-intro.php (2016-02-18)

Open archived version from archive - The New Hyperides in the Archimedes Palimpsest

and overwhelmed the jurors with her beauty Longinus wasn t the only reader of Hyperides during the first centuries of the Roman Empire A second century AD biography of Hyperides reports that seventy seven extant speeches circulated under his name ps Plutarch Lives of the Ten Orators 849D These copies of Hyperides speeches circulated as papyrus rolls By the fourth century AD a newer format had become common These codices made out of papyrus or parchment and more or less equivalent in design to modern books supplanted the older format of rolls These new books were easier to use and rolls soon fell out of general use Moreover the papyrus rolls were less durable than codices and authors who were not recopied in the new format were at risk of disappearing forever Such was the fate of Hyperides it was assumed until the discovery of the five Byzantine leaves in the Archimedes Palimpsest We have a tantalizing report of a Byzantine edition of Hyperides the sixteenth century humanist Johann Alexander Brassicanus claimed that he saw a complete Hyperides with rich scholia in the library of king Matthias Corvinus of Hungary but Nigel Wilson has persuasively argued that no complete edition of Hyperides existed in the Byzantine period Greek Roman and Byzantine Studies 16 1975 99 100 and his pronouncement has created a new orthodoxy of scepticism D Whitehead Hypereides p 2 Until these new leaves turned up in the Archimedes Palimpsest it appeared that only short excerpts of Hyperides survived beyond the classical period Byzantine reference works such as the Suda and Photius Bibliotheca and Lexicon made frequent reference to Hyperides They preserved dozens of short quotations by the orator but it was assumed that their source for this material was not a complete Byzantine edition but rather earlier compilations and dictionaries such as Athenaeus and Harpocration s second century AD Lexicon of the Ten Orators Now we have little reason to doubt Photius claim to have read several speeches of Hyperides Photius Bibliotheca codex 266 cf Wilson Scholars of Byzantium p 95 Before the discovery of more extensive material on papyri and now in the Archimedes Palimpsest the surviving corpus of Hyperides consisted of a few hundred short quotations many consisting of only a single word and none longer than a few lines In the nineteenth and twentieth centuries numerous important classical works were discovered on papyrus manuscripts including four sizeable manuscripts of Hyperides discovered between 1847 and 1891 These papyri were written in Egypt and the date of composition ranges from the second century BC to the second century AD They confirm Hyperides popularity in the ancient world and they have reconstituted a corpus for the orator that now fills more than fifty pages in a modern printed edition We now have extensive sections from five court room speeches one survives complete and also Hyperides famous Funeral Oration These speeches evince the lively style described by Longinus and contribute much to our understanding of fourth century literature and

Original URL path: http://www.archimedespalimpsest.org/about/scholarship/hyperides-texts.php (2016-02-18)

Open archived version from archive - Scholarship on Other Texts in the Archimedes Palimpsest

the wall video Robert Sharples Richard Sorabji and Nigel Wilson tackle a very difficult problem Progress is being made but this is was difficult text to read and progress was slow A report was written by Robert Sharples in 2007 that makes clear just how challenging this task was This manuscript was the hardest to image and the hardest to transcribe But by the end of 2010 Roger Easton and

Original URL path: http://www.archimedespalimpsest.org/about/scholarship/other-texts.php (2016-02-18)

Open archived version from archive - The New Commentary on Aristotle's Categories in the Archimedes Palimpsest

the author of the commentary is reporting what represents his objections to a particular view and what is an expression of his own view is not always easy and this is an area where work is on going The text is part of a formal commentary on Aristotle s Categories covering 1a20 1b24 This work was a focus of philosophical debate from the first century BC onwards the arguments which it prompted are most accessible to us now in the massive commentary by Simplicius but even that is necessarily selective and Simplicius does not always name the participants in the debates he echoes Not surprisingly there are numerous parallels between the new text and the debates in Simplicius it contains named references not all in Simplicius to Andronicus and Boethus the leading Peripatetics of the first century BC and to Herminus the second century AD teacher of Alexander of Aphrodisias It also includes a reference to Strato the third head of Aristotle s school parallel to others in the doxographical tradition Reviel Netz has suggested that the structure of the commentary indicates that the author took 1b10 15 with what preceded it rather than with what follows i e that he did not regard the start of the modern chapter 3 as a significant division in the argument A terminus post quem is given by the reference to Herminus Marwan Rashed has argued and I am convinced that the way in which Plato s view on the origin of the world is referred to shows that the author of the commentary is not himself a Platonist as he does not himself take sides on the question of Plato s view as a Platonist surely would That the text is later than Herminus and not by a Platonist suggests strongly that

Original URL path: http://www.archimedespalimpsest.org/about/scholarship/commentary-aristotle.php (2016-02-18)

Open archived version from archive - Sample Images from the Archimedes Palimpsest

The Archimedes Palimpsest Palimpsest Exhibition Digital Community Links Digital Images from the Archimedes Palimpsest Project Palimpsest History Archimedes Conservation Imaging Scholarship Project Management

Original URL path: http://www.archimedespalimpsest.org/slideshow/ (2016-02-18)

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CORE YES TYPE SINGLE DOMAIN pixel centimeters millimeters micrometer 2 2 X Resolution number of resolution elements per coordinate unit in the x direction CORE YES TYPE SINGLE DOMAIN REAL NUMBER 2 3 Y Resolution number of resolution elements per coordinate unit in the y direction CORE YES TYPE SINGLE DOMAIN REAL NUMBER 2 4 Upper Left XY Coordinates upper left coordinate of the limit of imaging expressed in resolution units CORE YES TYPE COMPOUND DOMAIN x n and y n 2 5 Lower Right XY Coordinates lower right coordinate of the limit of imaging expressed in resolution units CORE YES TYPE SINGLE DOMAIN x n and y n 2 6 Bounding Coordinates the limits of coverage of the complete data set for the entire sample expressed by Cartesian coordinate values assigned by the x y table software in the order upper left lower right CORE YES TYPE COMPOUND DOMAIN REAL NUMBER 2 7 Grid Coordinate System Orientation of and definition of Cartesian coordinate so that spatial positions can be readily transformed to and from plane coordinates CORE YES TYPE COMPOUND DOMAIN TEXT 2 8 Vertical Coordinate System Definition the reference frame or system from which vertical distances altitudes or depths are measured CORE NO TYPE COMPOUND DOMAIN TEXT 2 9 X Positional Accuracy an estimate of accuracy of the horizontal positions of the spatial objects CORE YES TYPE SINGLE DOMAIN REAL NUMBER 2 10 Y Positional Accuracy an estimate of accuracy of the horizontal positions of the spatial objects CORE YES TYPE SINGLE DOMAIN REAL NUMBER 2 11 Vertical Positional Accuracy an estimate of accuracy of the vertical positions in the data set CORE NO TYPE SINGLE DOMAIN REAL NUMBER 3 Imaging and Spectral Data Reference Information information describing the conditions used to acquire image or scanned data objects 3 1 Spectral Range Spectral range of imaging expressed giving lowest and highest captured wavelengths CORE YES TYPE COMPOUND DOMAIN TEXT 3 2 Illumination Type of lighting or energy used to produce image or scanned data CORE YES TYPE SINGLE DOMAIN Tungsten Quartz LWUV X Ray 3 3 Illumination filters filters placed between light or energy source and object during image or scanned data acquisition CORE NO TYPE COMPOUND DOMAIN TEXT 3 4 Acquisition filters filters placed between object and camera or detectors during image or scanned data acquisition CORE NO TYPE COMPOUND DOMAIN TEXT 3 5 Imaging System pertinent imaging variables and parameters CORE NO TYPE COMPOUND DOMAIN TEXT 4 Data Type Information 4 1 Data File TYPE File type of the data file CORE YES TYPE SINGLE DOMAIN PSD Photoshop format TIFF Tagged Image File Format JPEG Joint Photographic Experts Group format GIF Graphic Interchange Format ASCII American Standard Code for Information Interchange 4 2 Format Version Number Version number of the data file format CORE NO TYPE SINGLE DOMAIN TEXT 4 3 Format Version Date date of the version of the data file format CORE NO TYPE SINGLE DOMAIN TEXT 4 4 File Compression Technique description of

Original URL path: http://www.archimedespalimpsest.org/pdf/Metadata%20Standard%201.02.txt (2016-02-18)

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