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Alchemy & Mathematics

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Alchemy & Mathematics
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  ROSKILDE UNIVERSITETSCENTER ROSKILDE UNIVERSITY Faggruppen for filosofi og Section for philosophy videnskabsteori and science studies  ALCHEMY AND MATHEMATICS  Technical knowledge subservient to ancient   γνωσις   J ENS  H ØYRUP FILOSOFI OG VIDENSKABSTEORI PÅROSKILDE UNIVERSITETSCENTER 3. Række: Preprints og reprints  2000 Nr. 2  ISSN 0902-901X  A parallel – a model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Is this really a parallel and a model? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Summation of series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Side-and-diagonal numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Geometrical riddles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Concluding remarks  A parallel –a model  In [1966], Leo Oppenheim analyzed two cuneiform texts containing chemicalrecipes, one written for the library of Nebuchadnezzar I (1124–1103  BCE ) but copiedfrom an older text, the other from Ašurbanipal’s library and thus copied in theseventh century  BCE . Correlating them with “the sudden appearance of technicallyverysophisticatedglasscontainersallovertheAncientNearEast –Egyptincluded”and a number of other technical texts he concluded that “sometimes in the secondhalf of the second millennium B.C. the traditional, unwritten technology of Mesopotamia must have clashed on a rather broad front with a new technology of alien srcin” (p. 35).We need not go into details with this part of the argument. What is importantfor the present purpose is a passage on pp. 41  f  : Two well known and early Greek manuscripts with chemical instructions, the PapyrusX of Leiden, and the very closely related [1] Papyrus Graecus Holmiensis, dating fromabouttheendofthethirdcenturyA.D.,containanumberofprescriptionswhichparallelto an astonishing degree both typesof chemical instructions in cuneiform discussedabove.These two papyri, both srcinating in Egypt – most likely in Thebes – seem to havesurvivedthesystematicdestructionofallmanuscriptsdealingwithalchemy,themakingof gold and silver, allegedly ordered in 290 A.D. by the Emperor Diocletian. It is mainlyonthesetwopapyrithattheclaimofEgypt,Hellenisticandpre-Hellenistic,asthemothercountry of chemistry and alchemy is based. In fact, the technological traditions whichfind expression in these Greek papyri from Egypt are attested already in Mesopotamiain the 13th and 7th centuries B.C. as shown by the fragments of clay tablets discussedin the first part of this article. This I will try to demonstrate by comparing the topicalranges of both sources and certain characteristic phrases which recur in them.The respectively 101 and 150 recipes of the Leiden and Stockholm papyri deal withthree main topics: methods of imitating precious metals, i.e. gold, silver, and electron, bymaking alloyswhose colorand polishis toresemble thesemetals; methodsof coloring(or otherwise changing) stones to give them the appearance of precious stones; and, lastly,producingpurple dyesofmanyshades.[...]thelasttwosectionsoftheNinevehfragment(7th century B.C.) and the Babylon fragment (12th century B.C.) correspond respectivelyto the first two topics of the papyri. Both the tablets and the papyri point out that the fake precious metals cannot bedetected, and both emphasize that the recipes should not be revealed but kept as 1 According to Robert Multhauf [1966: 97], the two papyri are not only closely related buttwo parts of the same jeweller’s recipe book that accidentally have landed in two differentlibraries. 1
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