Pos(Antikythera & SKA)019

PoS(Antikythera & SKA)019 for our period period our for De De Architectura echanism in the reappear? although this important C AD) on the authority of of authority on the C AD) f University f Antikythera & th tions.”. The referencetions.”. to The e later – e copies veryand hence ost book on sphere-making t tooth onthe profile gears ikythera to SKA: the ikythera Lessons machine for although machine for astrology, ” – whether spherical” circular or ological Museum of ological Museum of Athens. In c. 520 AD. It must 520 AD. c. be It admitted s it may turn up one day turn up oneins it day may raughtsman, a mathematician, a raughtsman, s little reason to doubt that there there s to little doubt that reason they are copying. are My they suspicion e major reference (I’ll reference major (I’ll e itcall ) – which is – which title not) a but a ) in the Catalogue of the of in Catalogue the ) current riod, and almostriod, and reaches the to follow the architectural to architectural follow the a (4 a clus , p41,16. For the the clus , p41,16. For rest so far, in Theodosis this talk Tassios’ at s’ famous work, famous s’ four but least at rawings would have would have rawings existed. it But sical era, a particularly interesting particularly interesting era, a sical r c. 15 c. in who r BC) ather than than ather first-hand The encounter. l elsewhere) is very probably l elsewhere) The references references from The come Heath he copyists often seem to copyists seem no he often have way that would suggest skillsway ideal e latest lamentablee the reference, s to such machines, undoubtedlys to machines, such riangular until AD, 1300-1350 riangular except spherae ) ) no mechanical drawings survive σφαιροποιίαν

have mechanism experience of there the can be sphaerae do κατὰ (Latin (Latin sphairai How widespread were machines were widespread AntikytheralikeHow the M ancient World?ancient Why did technology the when and Why disappear thenand Did such devices influence views about Cosmology? about influence views - devices Did such aspect I will have to day!aspect leave for the I another

• • • for worm gears or or thereworm seem But for pawls. ratchet and gears inverse danger of them imposing danger of ideasinverse later on what t were essentially gears is metal of that all teeth Book 1 describes the training of an 1 describes training of the inBook architect a …..a construction “ the is who man for sphaerae of profession……should letters, be of man skilful a a d approx drawings to All 400300 AD. surviving BCE ar it comeswhen unreliable t since to interpretation, Where was. lateractually scribes …….familiar with …….familiar astronomy and calculaastronomical emphasised be that toocannot strongly they what about copying – for idea were example wha drawing is importantdrawing – it implies d that mechanical description. It is mentioned Pappus of description. by Alexandri It Carpus of Antioch, and in Antioch, and of Carpus Proclus on Euclid. Perhap ancient an excavation of in or palimpsest.library, he which (1921) gives as Pappus viii, p1026, 9; Pro see Table 1.is perhaps Table that only thsee interesting It Nonnus, poet Egyptian-Greek a mentions such of use one suspects that suspects hisone account on hearsay is based r of over 600 a list sphaerae pe shows awareness year geared sundialByzantine geared 1985) Wright, (Field & of the of just referencesthat many refer to Archimede independent imply and a are tradition.continuing looking the at In context in mechanisms clas the of is Vitruviusreference (born died 80–70 BC, c. afte Before & After the Antikythera Mechanism Mechanism Antikythera the After & Before at of talk given Summary Kestari “From Ant Meeting, 2012 from Ancients” June the 11-15 Mike Edmunds, Astronomy,School Physics of & Cardif Project Research Mechanism to discusswant I several were which raisedaspects Wreck Antikythera exhibition Archae in National the issues: the would like particular I to raise meeting, (Theodosis in hismeeting, and excellent 2012 paper – but my list published –and butin discussed ful my be (to incomplete, and I would additions and incomplete, towelcome it.I Th number zero!) must to zero!) be number (287-212 l Archimedes’ BC) ( “De Spherae” sometimes called known in Greek inknown as Greek have been trying to findI reference all literature PoS(Antikythera & SKA)019 diminutive(the τυµπάνιον hanisms C, which had C, had which floating drum a d with a revolvable wheel with drevolvable with a word word cribes a by a water-clock cribes Ctesibius tur in quo conlocata intur quo conlocata regula est ui denticuli alius alium inpellentes oduce measured revolutionsoduce and Archimedean sphere…amazedArchimedean devices and causesby…the of movements.the Spheres..motions. ..Archimedes.. sphaerae Archimedes Archimedes Sphaerae Archimedes See textSee Archimedes sphaerae Archimedes “models constructed on constructed “models earth…” other devices set devices inother motion quandum” machinatione “cum some mechanism”) (“by

3rd C3rd AD C 260?- 212 BC BC 54-51 ca. 400 ca. AD 120-140 sphaerae Archimedes AD C3rd AD 4th C AD “Posidonius” sphaera horae [clocks] Sphaera, and

IX, 115 IX, “De “De Sphaerae”, text see 1,14 minora LI minora LI (LXVIII) Disputations 1, 36 2 XIII, 8, 2 Book 5, divinae II, 18 deorum deorum xcviiII, deorum deorum xxxivII, Adversus Adversus mathematicos,

which which Vitruvius is transliterating) Empiricus . Classical references to similar “spherae” or . Classical mec references τύµπανον of of Table 1 Ref No. No. Ref Author Work Date What described 8 Claudian Carmina 7 Lactantius Institutiones 5 Sextus 6 Pappus Collection 3 Cicero 4 Tusculan Ptolemy Almagest 2B 2B Cicero natura De 1 2A Cicero Publica Re De Cicero natura De versatili tympano denticulis q versatili tympano perfecta. aequalibus faciunt modicas versationes the motiones.” et Now 0 Archimedes were gears. Vitruviuswere 9 desArchitectura in de Book BC) 285-222 (fl. which 265 – 220must around date B a tympanum fitte is“…called a rule on which placed teeth, which teeth, on one equal another, pr acting motion.” indici original – or the ““tympanum Latin PoS(Antikythera & SKA)019 Archimedes… can there and not too much of a stretch stretch not a tooand of much by Abraham Rees, by FRS, DD, perhaps be in found reference this was way beforethis way the was d have intended. This intended. d have is nism on (Edmunds Based 2011). scholars, scholars, perhaps hence and “… “ onwards. onwards. contemporary contemporary Archimedes. on briefly the initial of an on study briefly ted with a selection withted a random of assical World may have us given World assical may ars were being being were ars inused (as 100 BC ancient Greek Greek the ancient abilities. In Mechanism? some no sense, In earning and science of science and the earning eaction that “monstrous demons Antikythera Mechanism (although MechanismAntikythera (although ys Saros the away, and indicator ys me when a formal a education when me in the nions” are defined wheels. as nions” are gear ters generates performance such ters a generates of amazement when people when amazement of today ntroduced to his sphere to to his sphere ntroduced produce been wasexpected have the hat the Antikythera Mechanism Antikythera the hat A salutary correction salutary A can come aly. aly. igious suppression, possibly to due d given the description the d Vitruvius given and the recent rate of change of ofand change rate recent the Cubiculum holovitrium (“glass with moon phasechamber”) planets and with used planets, Sphaera for astrology h measured in of CT scans h measured gears, the urse people in any era tend tourse tend in any people era interpret

C 3rd AD astian astian and Stand Polycarp Chromatius by quoted St Seb Cyclopaedia ofCyclopaedia and LiteratureArts, Sciences be no doubt pinionsbe and that but were that wheels i – but whatSo there not could nocourse surprise of the respective motions”, and in the Cyclopaedia motions”, respective inthe Cyclopaedia the and “pi subtle design and mechanical particularly elegant t shows anom in its first lunar the of representation to the One So happened technology? aspect what may 1, where the Table device which 10“in of a whole l stars is constructed mechanically….” is stars constructed invoked the r astrological emphasisincreasing 50 around from BC moving on to Before willlater developments mentiI displayed hostile art toan displayed implying rel deity” the of accuracy mechanical Antikythera the likely Mecha variation the estimates of in positions teet the of computational models of the gear trains computational were gear models the of genera systematic A errors. of set and guess” parame“best month 2 Metonic that the is indicator on average da 5 days designer the on average what woulaway, from a rather biased view of view biased rather ancient capabilities.a Greek the from in appears ““tympanum” inscriptionthe text on the surprised be So Antikythera by the really should we should seems sense not.we certainly a There to be its of existence first learn of details. But and co eyesthrough the history society, current their of hazy of perhaps view aand technology the rather Cl 10 Nonnus Dionysiaca 5th C AD 9 Agrestius part be referred disk) particular – the an a to may reasonable it knewuses very that he seems metal ge from know course we of Mechanism), Antikythera the knownwere to they assume to Cestibius his and near allowing a a closer rather allowing and of admiring view more article on “Planetary Machines” we Cyclopaedia find Greek classics beenand Greek normal would have Latin for FLS etc etc, published in etc, etc RememberFLS 1810 in London. the of Mechanism,discovery Antikythera but a at ti PoS(Antikythera & SKA)019 anisms from 500 AD t with functional ipt (Ballie, description. l clock showing l the clock 85) 85) nomici, printed and nomici, and printed of Damascus. Damascus. of Details ) ) ina c.1000-1200 A.D. see see A.D. ina c.1000-1200 e Cicero reference 2B Cicero ine Table mann 1963)mann were where gears unar anomaly calculation anomaly unar . What e during the the of during e year. Indication or so – but perhaps we should not igns might have led to might led igns have an particularly of particularly level the given uld just not have been accurate uld just been accurate not have er could easily be be easily could 20 far as as er Since the Roman world had huge huge Roman the had Since world f the set of simulated of set mechanisms the f is geared up main the isfrom geared drive, irements, a mechanical calculator mechanical a irements, calculator on. It is interesting to speculate on on. It ear trainsear withtriangular- irregular it ismight possible eclipse that an ample, an eclipse must occur at at must eclipse occur an ample, ur with an abacuswith mightur an the lessen own is whether such such isown an whether is eclipse witho help this. implication The . However, it might not have taken taken it not. However, might have wheel, or discrete balls or let fall were wheel, teness to appears have been and 12 days for the for 12 days Metonicand and values, and larger deviations larger and values, would d not. to question So the of back might not have been particularly not might have y a pointer (possibly simply simply (possibly pointer Sunthe a y ing over is which in tallying purposes, rather purposes, for than really accurate display C. AD William unknown Details Hirsham. of C. AD Abbott th (Incomplete) Timeline Geared Astronomical for (Incomplete) Mech 1292-1336 Richard of Wallingford. of Major Richard 1292-1336 astronomica movements of the planets the movements of Horologii (Tractatus Astro translated in (1976). North translated 1364 de Dondi: manuscr astronomical1364 de Major and clock Ward 1974) and Lloyd unknown 1232 AD gift to Frederick II from Al-Ashraf Sultan Al-Ashraf from gift1232 to AD Frederick II C.1300 Opus quorandum rotarum mirabilisC.1300 rotarum Opus quorandum – manuscrip some and details (North specification 1966gearing Byzantine sundialgeared Byzantine 520 AD C.1000 AD Al Biruni geared calendar C.1000design (Hill Al Biruni AD geared 19 11

• • Note: For developments (probably independent) in ForNote: developments (probably Ch Needham, LingNeedham, Solar and de 1986) Price • • • • • Table 2

impetus to mechanisation, but the inaccuracies of of impetus butg to inaccuracies the mechanisation, machine might – a factor a toothed also be gears wo equitablefor financialtransactions land enough or satisfactory device, to a achieve development much involved in theingenuity Mechanism’s Antikythera l “discreteness”,is positive a the is click requires into hodometers contemporary incorporated (eg Drach tooth time pinrevolving one by on a a a at turned holes in a through wheel. des combination such A of – but,calculator we as it know, accurate di so far financial accounting and financial calculationsurveying requ possibility. a The be labomight cheap existence of later much of devices. discre Such a characteristic to technology. the didwhat happen 1) would have been possible would have 1) ancient the Greeks. for what other mechanisms other what (the machinatione” “cum th of calculation. calculation. calculation error have another These implicati may likely in that averageare particular month. likely These deviation a larger)would (or have as 6 than large this, at b surprised exactsince the day be setting we and notare subsidiary awareeasy, any of dial t be devicethat the ismay for probably satisfactory performance – since,a probably for ex new full be the or moon all thateither knneed and during the – occur complete example, cycles halfor some at indicators cycleSaros the – sotime during intended the away from degrees position some tim at full moon or typically be might day new by a wrong dial front on the pointer) torevolution 1/356 a of be predicted in the predicted wrongbe pointer month. lunar The angular hence The larger. errors and moon pointare PoS(Antikythera & SKA)019 , with ml between shown by mechanical mechanical “The design sphaerae g skills readily were g of devices that devices of might be anical anical he he acquisition of been traditionbeen making of a al clocks was apparently was clocks al apparently chanical chanical s, although the the s, although rebirth of o drive an industrial an o drive lect of the possibilities. the of lect suppression may be suppression may ngular-toothed untilngular-toothed gears t begin to satisfy thet to begin satisfy first of AD. The answer may come may answer The AD. he Book of Book Secrets”he copied of the geared technology the of untilgeared line. The clock escapement clock line. The available in Europeing through ether this a isether actually medieval bably invented aroundbably 1280 AD. ccur in Tudor ccur Britain, only and BC BC om Greece om Rome, Greece and to and ources cannot over- be ources neer Ibn Khalaf neer al-Muradi.Ibn Some ing animals) humans or (3) ) ) increased size of production units. th, rather than th, triangular rather The teeth. advance towardsadvance other the criteria. ), but so far as I the as aware butam ), soI far (in Toledo) from an original an from Toledo) (in dating ustrial revolution did not occur inustrial revolution did not occur blished peer-reviewed in a journal, agment of a more a of sophisticated agment gear hen there was explosion a there hen great of gular teeth, with no gular great and conditions social suitable to it be occur. A similar A argument occur. might D.S. Landes’ 1969 study D.S. Landes’

development . He suggest that necessary . (1)are suggest that necessary substitutionHe of http://www.leonardo3.net/bookofsecrets/index_eng.ht at least 250 BC and 400 and 250 BC least –at there toappears AD have machines such We can be surprised be sophistication by the We me can the of the Antikythera Mechanism, Antikythera the metalworkin the although as by jewellery.contemporary evidenced available T mechanical design skills design mechanical not by itself enough was t revolution. There seems been to have There tria at hiatus, stalling a timekeeping for ininterest gearwork and astronomic c1200-1300, perhaps due discouragementc1200-1300, to religious with astrologyassociated alternative world-view or with of monasteries. idea associated religious The the simply and neg a hiatusreflect overstated, may We should not be too surprised by We should mech by existencetoo not of surprised be

• • • http://www.giovannipastore.it/ARCHIMEDE.htm presumably be made for why the the made be for presumably revolution didwhy not o blossomed later. couple hundred a really of years my summarise To conclusions: is perhaps not surprisingis perhaps revolution didthat a not If we we in necessity the political,add If economic for devices for human for skill powerdevices inanimate (replac (2) improved raw material extraction, and later adds (4 does huge been but a to there notthese, have seem The Antikythera Mechanism Antikythera certainlyThe technology migh gears in manuscript the gears to appearing tee have “pin” systematic for studyneed Arabic and of s Byzantine exactly towhat see emphasised, through did come fr check that there really wascheck no significant interloper. interloper. sidelight on interesting An from comes mechanism “T warnings health (usual about copies!) in 1266 later by the to eleventh the century engi back Andalusian archaeological details not been pu find have archaeological the of the has from one and appearance togear’s wonder wh at details available are the classical world sometime world 100 classical the and between BC 300 c1300. c1300. to is speculate tempting It ind someon sort why of three at for criteria looking revolutionfrom in Unbound Prometheus” development (and little (and visibility)development until – w c1300 Table 2 shows a very elementary and incomplete time very incomplete 2 shows a and elementary Table reasonable vitalmechanism, for was timekeeping pro suggest stuck that gear I metal trian at technology Arabic sources becominnovation,following probably that has a suggested Moors inthe Spain.fr been It survives teeth with c.170-140 Sardinia rounded from ( PoS(Antikythera & SKA)019 ,

nd

University University Cambridge Cambridge roduced inroduced 2 the ther! – but bewarether! of Vol 1, p441, 1976

xlii, 2011

85), pp. 87 – 85), 138. 63. ragement, and in particular and ragement, n the Antikythera Mechanism Antikythera n the The Planetarium Dondi of Giovanni de Heavenly Clockwork, , Clarendon Press, Oxford, (Reprinted reprinted 1989 in Stars, Minds and Fate, Eds N. Kaltsas, E. Vlachogianni & P. Bouyia, , Cambridge , Cambridge University Press, 1969 Oxford University Press, University Oxford Mechanical of Antiquity, and Roman Greek Technology Prerequisites for the Antikythera MechanismPrerequisites for p to Antikythera the be The Unbound Prometheus The Antikythera Shipwreck , Richard Richard of Wallingford, A HistoryA of Mathematics Greek Byzantine Arab sourcesand MUSTByzantine investigated be fur copied drawings. drawings. copied

•

D.S. Landes, Dover Publications VolDover 2, 1981) p17, 1921 42, 1985, pp.139Hill, – Science, D.R., of Annals 1 National Archaeological Archaeological National Museum, p 249, Athens, 2012 of Wisconsinof Press, 1963) Edmunds, M.G. Journal Astronomy: History the of for 42 M.T. Wright,J.V. Science, & of (19 Annals Field T. Heath, Century Century BC is always pleasure as a colleagues i It to my thank Research Project their support for and ideas, Research encou JonesAlexander comments. very detailed helpful for 1974 Horological Antiquarian Society, The London, A.G. Drachmann, Ward G.H., H. Baillie, & Lloyd, Alan F.A.B. Theodosis, T. J., W.Needham, and D. Solar Price, de Ling, University Press,University Second Edition, 1986 8,J.D. 1966,North, Physis, pp 337-372, J.D.North,