[Lancelot Hogben] Astronomer Priest and Ancient Ma(Bookos.org)

8/13/2019 [Lancelot Hogben] Astronomer Priest and Ancient Ma(Bookos.org)

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ont nts

Acknow ledgements Illustrations viiForeword Xl

Chapter IThe Coming of the Calendar

Chapter 8Pyramids and Temples

Chapter 3 43The Legacy of the Temple

Chapter 4 The Greek Contribution

Chapter 5 7The Ancient Mariner

Chapter 6 9Maritime Geography and Maritime Astronomy


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knowledgement

The author is indebted to the following for permissionr ep ro du ce p ic tu re s on the pages indicated: Aerofilms32; George Allen Unwin Ltd, 34 50 51,54,56,57,771 04 ; B ri ti sh Tourist Authority, 33; The Trustees of thBritish Museum, 19 20 47 , 61 62 65 67; CBS Television Network, 35; Les Chefs-d Oeuvre de la Peintur.Egyptienne, Andre Lhote [Librairie Hachette, Paris 54Cia Mexicana A erofoto, 20; Encyclopaedia Britannica, 27Her M aj es ty s S ta ti on er y Office 10 MacdonaldCo. Ltd, 24 26 44 45 52; Mansell Collection 109N. G. Matthew Esq. 2 4 5 ; M ex ic an N at io na l T ou ri sCouncil 21; Paul Popper Popperfoto), 22 104; PeabodMuseum of Archaeology an d Enthnology, Harvard Univcrsitv, 2 1; P re hi st or ic Society .36; The Trustees of thScience Museum, London, 49 60 71 105 Crown pyrigh t 49 71 ; Staatlichc Museen Preu ssischer Kul turbesitz Berlin 73.


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ustr t ons

Chapter I. Night sky at latitude of L on do n a t m id -M ar ch2. Night sky at latitude of London a t m id -J un e3. N ig ht s ky at latitude of London at mid-September4. Night sky at latitude of London at mid-December5. a Apparent diurnal motion of the starsb The changing heavens6. a Night Dial

b Night Dial in use7 The sun s a pp ar en t) a nn ua l retreat through the

zodiacal constellations8. The monthly cycle of t he m oo n s phases9. a T he E gy pt ian y ea rb Heliacal rising and setting of a star

Chapter10. a Ziggurat at Ur as it l oo ke d a ft er e xc av at io ns of

Woolleyb Reconstruction of ziggurat

II . a Tectihuacan, M exico, from the airb Mayan stele at Quirigua, Guatemala12. a M ay an T em pl e of Warriorsb The Caracol, an ob ser vat or y a t Chicken Itza,

Yucatan13. Pyramid of Khehren14. Karnak Mathematics in the Making15 . T he t hr ee pyramids of Gizeh16. Centre section of the Great Pyramid of Khufu, Gizeh,

3000 B.C.17. a Aerial view of Stonehenge

b G ro un d v ie w of Stonehenge18. Heel Stone, Stonehenge19 . S un ri se o n m id su mm er day, Stonehenge20. Plan of the stones a nd e xc av at ed areas, Stonehenge


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21. Aubrey holes an ecl ipse clock as interpreted byProfessor Hawkins

Chapter 322. Egyptian hieroglyphic writing showing numerals.23. a Cuneiform Tablet

b Old Babylonian cuneiform script24. Rhind papyrus25 A Reconstruction of ancient Egyptian merkhet 6 Merkhet and b y one use of the plumbline in

ancient Egypt27 Bisecting a line28. Speculative reconstruction of the Set Square of the

Temple Architects29. a Diagram showing means of measuring noon

shadowb Temple Architects recording of equinoctialpositions

30. Fifteenth century B.C. Egyptian surveying from awall painting

31. Diagram showing measurement of the noon shadowcast by the Great Pyramid at Gizeh

12. The Abacusa Romanb Chinesec Japanese

Chapter 33. Egyptian sea going ship c 2600 B C34. Phoenician warship35. Phoenician bracelet36. Phoenician script37. a Greek sea going vessel, vase paintingb Greek Galley


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38 Early Greek drama39 Cast of water clock from Karnak40 Masters an d pupils at an Athenian schoolChapter 41 Th e visible limits of the horizon42 Map of th e Mediterranean43 Southern Cross44 Map of Europe45 Ma p of Africa

Chapter46 Eclipses47 Moon eclipse seen in East Germany48 Solar eclipse49 Inclination of th e m oon s track to the Ecliptic50 Romantic n in ete en th c en tu ry engraving of how

Greeks imagined the Pi llars of Hercules


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orewor

I am sure that most younger people are much morefamiliar with the contemporary term Iraq than with theancient names of Chaldea, Babylonia, Mesopotamia andAssyria. I therefore refer to Iraq when writing of thetemple sites in these regions.

Some scientists are most reluctant to recognise thegreat antiquity of star lore and the important part it playsin the struggle for existence of people who, even at thestart of this century, lived in a way scarcely moresophisticated than tha t of men and women on the thres-hold of the New Stone Age, Dr Nilsson a Swedishscientist, has collected available material from manysources in a treatise on Primitive Time Reckoning, fromwhich these quotes are taken (words in parenthesisinserted) :Observation of the morning rising and evening setting[ixed stars is extraordinarily widespread, but otherpositions of the stars are also sometimes observed.The Krivai Papuans New Guinea also compute the timeof invisibility of a star. When a star has sunk below thewestern horizon, they wait for some nights during whichthe star is inside then it has made a leap and showsitself in the east before sunrise The Hottentots con-nect the Pleiades with winter. These stars at their lati-tude become visible in the middle of June, that is in thefirst half of the cold season The appearance of thePleiades also gives the Bushman of the Anob dis tr ic t thesignal for departure to the tsama field The Melane-sians of Banks Island and the Northern Hebrides are alsoacquainted with the Pleiades as a sign of the approach ofthe yam harvest. The inhabitants of New Britain Bis-marck Archipelago are guided in ascertaining the time ofplanting the position of certain stars.

Elsewhere, Dr Nilsson says of the star lore of the


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Australian aborigines: The winter stars are Arcturus,who is held in great respect since he has taught thenatives to find the pupae of the wood-ants which are animportant article of food in August and September ustralian wintermonths and Vega, who has taughtthem to find the eggs of the rnallee-hen WhenCanopus at dawn is only a very little way above theeastern horizon, it is time to collect these eggs andupae.

Writing of the natives of the Admiralty Islands, hestates: When the Bird Canis major is in such a positionthat one wing points north but the other is invisible, thetime has come in which the turt les lay eggs, and manynatives then go to the Los-Reys group in order to collectthem. Of the natives in the Bougainvil le Strai ts offQueensland) Nilsson mentions that the rising of thePleiades is sign that the Kai-nut is ripe

The first volume in this series, Beginnings and Blunderstraced the story of the skills our ancestors acquired, andthe skulls they left in their wake, before science began.This bool starts with the need for a calendar to regulatethe seasonal order of seed-sowing and flock-tending. Forthe construction of such a calendar men of the NewStone g doubtless drew on the knowledge gainedthroughout many millennia from the scanning of the nightskies ymen who were still nomads and from the observation. of the sun s seasonal changes when village lifebegan. The art of keeping a written record of the lapse oftime took shape about 5000 years ago and was theachievement of the priestly guardians of the calendar inthe temple sites of Egypt and Iraq. An incidental, butnot itself useful, by-product of this phase of infantscience was the art of forecasting correctly the occurrenceof eclipses.


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y B.C. ships from the trading centres of theMediterranean had travelled beyond the Pillars ofHercules Straits of Gibraltar and literate MasterMariners who relied on star lore to navigate, couldrecord y a new and more economical way of writ ing-alphabetjc how the aspect of the heavens changes withlatitude. A compelling consequence of such observationsmaterialised y about 500 B.C. in the recognition that theearth is a spherical body. stronomer riest nd ncient riner brings the reader to this stage in the history ofscience.

Lancelot Hogben


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he oming o the alendarAs most of us nowadays us e the word s ien e and as weshall us e it in this book one may say that it began whenmen were first able to record in w ri ti ng t he ir observations on t he ir s ur ro un di ng s and to convey in writing apicture of the world as they saw it and with some pay-offin t he w or ld s work.

This happened at least 5000 years ago in the citytemples beside the Nile in Egypt and in Iraq y the riversTigris and Euphrates. During at least 4000 years wherelife was cheap and slave labour abundant there was noscience of medicine and very little scientific mechanics.What science existed was what we now call astronomyand closely allied studies. T he pay -off in the world swork was how to find our w ay abou t in time and spacei n s ho rt to devise a reliable calendar and to draw a mapof the p la ne t w e inhabit.

Most of us realise at least vaguely th at ou r calendard ep en ds o n ob se rva tion of a regular recurrence of th echanging appearance of the night sky and the sun shighest elevation above the horizon. o many of ushowever it may seem paradoxical that man had to learnhow to make a map o f th e heavens before he was able tomake a map of the earth.

Observations o n the changes of the ni ght s ky a nd of thesun day did not begin as th e result of the introductionof writing. On the contrary the imperative need forrecording them was a p ow er fu l i mp et us t o devising themost primitive scripts. Villagers of the N ew Stone Agewhose dwellings and allotments coalesced to form thecities where the priestly caste had leisure to record thevagaries of sun moon and stars had received from theirancestors a rich legacy of information transmitted fromone generation t o a no th er w ord o f mouth.

Even in our o wn c en tu ry t he re h av e s ur vi ve d outside


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2 Astronomer Priest and Ancient Mariner

LOOKING NORTH E

r : :. _ ~ \ SBOOTES . . ~ \

CORONA BOREALISJ J4 a ./~ HERCULES

. LYRA . / \

OVERHEAD

IAURIGA eCapellaPERSEUS e / C ~ S S I O P E 1 A

eA/90/ I Var: e \I .--T . e \ E ~ H E U S\

/eANDROMEDA e .\ Nebula\

RIES.w

w

OVERHEAD

LOOKING SOUTH

CastorPol lux ~ M I N II.... -, . .:. . \ .Praesepe

/ \ . .0 < /? e eD l\ e9u/us TAURUS CANIS - \ MINOR __ Procyon Aldebaran .....

etelaeusee \ 1 ~ r JORION I~ c ir ius fCORVUS ' ' ... . ~ /CA NIS Rigel < .\ \ MAJOR IERlDANUS. . ~

\ . / /

VIRG1l/-./S . Ip ca

E

Night sky 81 latitude ofLondon at mid March


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The Coming of the Calendar 3

w

Praesepe Castorr o l l l J x ~ \

G\EMINI- \\ e\

-\ .eneh __ ~ N U S

e Capella AURIGA IPERSEUS 0 Nehula _ / .A lgo . /e\_. PEGASUS

Vor ANQROMEDA .LOOKING NORTH E

w

\ V I ~ 0 . Spica

e ~ CORVUSIf y e______ /o

OVERHEAD

LOOl lNG SOUTH

/ . \e,. j BOOTES . . CORONA \BOREALIS e e Arcturus\ SERPENS

et\HIU HUj_\ /.Antares s 0 R P JUS

ieHERCULES_ 1 \\ .-

/_1 tairAQ)U1 boA..........

E

2 N I9 t Skv J t Ia II t lJde 0 fLondon at rrud Ju


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4 stronomerPriest and ncientMariner

LOOKING NORTH

ERSEUS 1\ AI I sVa,.Capella

\ A ~ I ~ Pleiadz: iTAURUSI

CASSIOPEIA/, CEPIjIEUS-\.

ANESVENATICI

. CORONA.., BOREALIS ---1

/ : BOOTES. lcturus\ I

w

\ .< I\\H E R ~ l E S \I / ~ .i ~ eP OPHIUCHUS 1 \\ I/ .t,P

OVERHEAD

DELPHINUS . ~l tairI ~ U I L A

LOOKING SOUTH Fomalhaut

.I .--QUARIUS - ,.-.--. C PR CORMUS

--_/ . I ~Square

: of PEG SUSI p e ~ a s U S ~ ~ /.CE TfJJS ~ I I

E

3 Night sk y at latitude ofLondon at September


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The oming of the alendar 5

OVERHE D

. /\ __e

DELPHINUSHERCULES

LOOKING NORTH

G ~ m \ \ \ G ~{ ~ \ Q . n \ 8Cast-Ore:Po/lux

M I N ~

PraesepeI

l EO / .

LOOKING SOUTH w

OVE.RHEAD1 \PERS EUS -A/sol/ Var.

NISSirius e M JORI \

l Pleiades ~e---e . - . . . . Aldebaran ..G E M ~ N I r

. _ - - ~ .-/. . M i ~ .Betelgeuse 1 ORiON Var: - C E T U S\ -- . __ e . _. / . \ \ R ~ ; E R I D A N U S ~ - - - - . \ - / / gel //0 .\

E

4 Night sky at latitude ot~ o n d o n at rrud])eC8tli ber


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stronomer riest and ncient ariner

the pale of civilisation people who wander in search offood as did nomadic tribes of the Old Stone Age beforevillage life began and such folk know vastly more aboutthe changing aspect of the night sky throughout theseasons than do the vast majority of people who grow upto-day in cities. It is not hard to understand why theyhave such knowledge and hence to reconstruct thetraditional store of know ledge which the priestly astronomers of the earliest cities inherited from millennia ofobservation by their ancestors.Without roads and without maps nomads of the OldStone Age from at least 25 000 years ago had to learnwhere and when to locate camping sites where game,eggs, berries and edible grasses were available as theironly source of food. Without clocks, without calendarsand without maps they had to learn both how to date thetrek to new hunting grounds in the season at which foodwas abundant and to locate their sites.

To do either, they had to rely on the aspect of the sky.Sitting beside the camp fire in the hours of darkness ourOld Stone Age ancestors would learn to memorise landmarks on the horizon by the rising and setting positionof bright stars such as Sirius or bright star clusters suchas Orion or the Pleiades. They would learn to keep trackof the seasons by the day on which one such star orconstellation was first visible rising or setting just beforesunrise or just after sunset.

Such events were thei r signals of when to strike campand whither to trek. At a time when each tribe enjoyedthe patronage of it s own sacred animal fancifully identifled with a particular star cluster-such as ri s theRam , Taurus the Bull , ancer the Crab , eo the Lion ,Scorpio the Scorpion in the zodiacal belt- the firstappearance of a constellation was also the time signal for


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The Coming of the Calendar

the sacrificial feast of a victim otherwise immune fromattack throughout the year Such is a practice amongletterless people still living Then as now tribal ritualalso dictated elaborate ceremonies associated with sexualmaturity The elders of the tribe had to enumerate howmany moons elapsed between birth and the initiation

Many readers of this book will have grown up in sur-roundings where tall buildings obscure the horizon inevery direction They will have had no opportunities towatch what positions the stars occupy at different timeson the same night or at the same time on different nightsIt is therefore fitting to start the story of how sciencebegan by scanning the night sky through the eyes ofStone Age men and women for whom trees and hillockson the horizon of the camping site labelled the rising orsetting positions of the heavenly bodies

The first city dwellers who were able to record inwriting the fruit of many millennia of nightly vigilsthemselves lived in the northern hemisphere So we needconcern ourselves only with the night sky of northernlatitudes First let us be clear about the distinctionbetween two sorts of heavenly bodies respectively calledfixed stars and planets In terms of what the nightwatchman can see for himself or herself one calls thestars fixed because the rising and setting positions of eachone correspond at any camp site to the same two landmarks

The planets of which only Venus Jupiter and Marsare conspicuous to the naked eye are not fixed in thissense However we shall need to bear in mind that theterm fix is relative to the lifetime of a few generations

the naked eye the rising and setting positions of starsat one and the same latitude do not detectably shift in acentury In a millennium they do so conspicuously


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stronomer riestand ncient ariner

Though they do not vary perceptibly within the limits ofa single trek of tribes with no means of transport otherthan their own limbs, they vary greatly in widelyseparated latitudes a fact on which the mariner has torely for his bearings when he ventures into the unknown.

We now know that the shifting position of the stars atrising or setting and their elevation when highest in theheavens happens in cycles which occupy between 25,000and 26 000 years, and the first Cave Painters-people ofour own species-appear on the scene about 25,000 yearsago. So we may speak of the aspect of our own night skyas essentially like that of the first artists.

one and the same latitude the fixed stars areseparable into two groups. Those of one class, such asSirius or the stars in Orion at the latitudes of London andNew York in our life-time, are seen at some seasons risingor setting or both during the hours of darkness but atanother season invisible throughout the night. At thesame latitudes today the other class, called circumpolarstars such as those Figs. 1-4 of the cluster rs Majorthe Great Bear also called The Plough or The Dipper arevisible at all hours of a clear night and at all seasons.

At the present time, as in the time of the first CavePainters, one star in the northern half of the sky is ofspecial interest. It is at the tail end Figs. 1-4 of the constellation Ursa nor the Little Bear . To the nal


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The Coming of the Ca\endar 9

seem to the naked eye to remain fixed at all hours andthroughout the year.Round this star, called by astronomers ol ris and byothers the Mariner s Pole Star, or more precisely roundthe Celestial Pole as centre th e visible circumpolar starsseem to revolve a nd othe r stars when visible above thehorizon appear to sweep out circular arcs tilted towardst he s ou th er n margin of the sky Figs Sa and 5b . Facing

north i.e. towards the circumpolar constellations, the OldStone Age n ig ht w at ch er would see other stars risingtowards his right hand and setting towards his left.Facing south i.e. towards t he o pp os it e boundary of thehorizon, he would see stars rising towards his left handand setting towards his right. He would thus learn todistinguish an e sterly and a westerly boundary to thehorizon at whatever site the tribe bivouacked.

U nw it ti ng ly S to ne A ge Man has thus learned toorientate himself in the plane of the horizon by reference

5 a Apparent diurnalmotion of the stars

b The changing heavens


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to a North South axis we now call it the terrestrialmeridi n nd an East West axis at right angles to it. Hehas also gained a new awareness of the passage of time.The position of the clock hands of a circumpolar con-stellation such as the Great Bear Dipper in our epochtells him how far or near is the hour of dawn Figs 6aand 6b .

6 3 Night Dldl fur usesee 6 b

The first dwellers in villages, the men of the NewStone Age had opportunities of leisure to make otherdiscoveries more especially about the apparent motionof the sun and the moon. They would notice that the


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The Coming of the Calendar

b The stars rnarkedX and Y are theclock stars of theGreat Gear P isthe Pole Star

length of the sun s s ha do w a ft er dawn first decreasesthen increases being shortest when pointing due northin the northern hemisphere where village life began.They would thus divide the d ay li gh t in te rva l i nt o twoparts on e from sunrise to noon the other from noon tosundown.

The y w ould also notice tha t the sun s position relativeto the fixed stars changes in two ways. One is that a starwhich rises on the eastern boundary just before sunriseon a particular day will be seen well above the horizon afew days later. In short the sun seems to be slippingbelow the eastern horizon da y by day As it does soFig 7 its rising and setting positions correspond tothose of different constellations those we call the zodi c


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They would thus begin to recognise another thing aboutth e sun s seemingly annual track ig. 8). When its risingand setting positions are furthest north the sun s noonshadow is sho rter than at any other time. Th e h ou rs ofdaylight are then longest and t he e ar th is w ar me r. W h enthe sun s rising and setting positions are furthest southit s noon shadow is longest, the h ou rs of daylight shortestand the weather cooler. Midway between the longestday called midsummer or the summ r solstice and theshortest day called m id winter o r the w nt r solstice arethe spring and autumn equinoxes when the sun s risingand setting positions are almost exactly due e as t a nd du ewest. On these two days the hours of light and darknessare almost exactly equal. In our calendar the solsticesare June 2 and December 21, the equinoxes March 21and September 23.

7 T he s un s a p pa r en t )annual retreat throuqhth e zodiacal constella-tions Th e South Poleof th e 8 1 rth rs nea restto yo u in th e figure.)

u n R ~ 2 1 ~ 1 : - ~ S u . n . m u ~ r Cencer I is :;sets witl . tlw Slut t is i n . v j ~ 1 . b l ~ -th1 oog1w lllt night Ge mini rising in ast b ~ . f l . J l > .

5Ul t.t. isQ;. I.e a setti ng in. west a H a SH.llset


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Th e am ing of the alendar 3

The word most u se d t wi ce in the last paragraph iswarning signal. Because we learn in childhood that thesun rises in the east and sets in the west many tow n-bred p eo pl e t ak e the catchphrase to mean that it rises dueeast and sets due west daily t hr ou gh ou t t he year. Thestatement s stands is approximately true only of twodays in the year i e the equinoxes. Even if th e sun on theequinox of particular year rises exactly due east itcould not set exactly due west on the same day. Like-wise should it set exactly due west it could not haverisen exactly due east on the same day. The re son is thatthe sun s position relative to th e e ar th is changing albeitslightly between sunrise a nd s un se t.

Just s th e s un s r is in g a nd s et ti ng p os it io ns change inits a nn ua l cycle the moon s rising and setting positionsalso change in the cycle Fig 8 between one full moon

8 The rnonthly cycle ofth e moon s phases


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Astronomer Priest and Ancient Mariner

and another. It seems to be slipping daily a little furtherbelow the eastern horizon, as does the sun, but morerapidly than the sun does. We can defer the details ofthe track follows till we learn a little ab out th e preoccupation of the priests with l un ar a nd solar eclipses int he d aw n of city life.

Before village life began, we may be certain that thecIders of the tribe had learned to reckon time in terms ofthe interval between one full or one new) moon and thenext, i.e. a month.At what stage men recognised th emonth as approximately 30 d ays an d the complete cycleof the season as approximately 12 such months, we donot certainly know. What is certain is that an annualc al en da r w as an i m pe ra ti ve n ee d of a seasonal economyof agriculture, and that any measure of the year moresophisticated than the 36 day cycle of the priestlyastronomers of Iraq made prohibitive demands on thememory of those responsible for keeping track of theseasons.

Long before the b ui ld in g 3 00 0- 25 00 B C of thePyramids the Egyptian year Figs. 9a and 9b of 12 thirtyday months and 5 extra days, i.e. 365 days in all, hadbeen fixed as t he i nt er va l b et we en successive occasionswhen Sirius, brightest of all the stars, was visible justa bo ve t he horizon immediately before sunrise. That suchprecision was possible depends partly on two facts. Thed og st ar Sirius, being the brightest star in the firmament,is visible in tw ilight before any other fixed star, andtwilight is much shorter, nearer the tropical Belt than in theprosperous centres of modern civilisation. The EgyptianBy a study of bones, pieces of r oc k a nd wood with regularly indentednotches in groups separated by intervals, Alexander Marshack 1970ha s recently made a strong case fo r th e conclusion that people from th eearliest appearance of man as a p ic tu re m ak er some 10,000 years agokept tallies of t he m oo n s phases as a means of counting th e months.


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he om ing of the alendar 5

estimate of the year proba bly made as early as 4 4 B.C.is equivalent to our own estimate except in so far as weinsert a leap year to accommodate the fact that theinterval between noon on successive solstices is almost

exactly 6S } days.The possibility of such precision at so early a date docs

not depend merely on the brightness of Sirius and shortduration of twilight. It presupposes the means of makinga record. Counting 365 successive days is not like count-ing 365 sheep in the same field at the same time Withoutsome material i d to the memory it would overtax themental powers of the wisest elder of the village com-munity. We can indeed make a good guess about how heor she tackled the task. e re all familiar with the Roman numerals still

sometimes used for chapter headings and on sundials. Intheir earliest form as is true of the Egyptian and Baby


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~ Q r tJ t onnu l Retreat l

Star andSun bothrisingJan 1

HEUACAL RI SING A ND S ETTI NGOF A STAR

E

Star whenSun setsFeb 1

Stor risingat SunsetJan 1

b) Hehacal ri ing andsetting of a star Ionian numerals of the temple sites they followed a

consistently repetitive plan e.g. Roman VIllI for later IX.This fact strongly suggests that the pioneers of the earliestannual calendar counted off the days by chippingnotches on a pillar or slab of stone or wood as schoolboyonlookers now make strokes on paper to score runs at acricket match.

As village communities became larger and coalescedon the banks of great rivers-Nile Tigris EuphratesIndus and the Yellow River Hwang Ho of China therewas increasing specialisation of tasks other than tillingthe soil and herdmanship. Thus craftsmen with differentskills undertook the building and surveying. A casteconcerned with the custody of the calendar and theperformance of the ritual of sacrifice and prayer asso-ciated with different celestial events gained increasingprestige and power to exact tribute from those whocultivated their allotments.


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he oming of the alendar 7

As they sacrificed and offered up prayers to their skvborn deities they preyed more and more on the credulityof the farmers and artisans. Meanwhile they had leisureto elaborate the art of recording and were thus the firstclass of l iterate persons. They supervised the construction of gigantic buildings in honour of supposedly sl


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8

yramids nd emplesIn the clumsy scripts of documents and tablets whichhave come down to us intact from the ruins of templelibraries of Egypt and Iraq we get some insight into thelevel of mathematical knowledge current among thetemple architects surveyors and astronomer priests inthe first few thousand years of civilisation. If we ask ourselves how they built such vast tombs and even vastertemples, we can also gain much insight by studying theirmaterial achievements in massive masonry. Let us therefore think back to a time when architecture calendarmaking and the technique of keeping a permanent recordof events were still facets of the same preoccupation.

A feature common to samples of such massive masonrycharacteristic of the two earliest civilisations of the OldWorld and the two best-known indigenous ones of theNew i.e. the Maya of Central America and the Toltec ofMexico is the step-wise construction of terraces on amore or less quadrilateral lay-out the whole being thuso diminishing horizontal dimensions in the upwarddirection. Such, for example were the ziggurat Figs lOaand lOb) temples of ancient Iraq. Such also were theearliest Egyptian Pyramids and the Mexican st yr -m s which have been intensively studied only duringthe last fifty years Figs l Ia and 11b).

o say the least, it is highly probable that conveniencefor observation of astronomical phenomena relevant tocalendar keeping dictated the terraced structure. That thetemples of the Maya were essentially observatories isbeyond dispute. As one expert remarks: every piece ofMayan construction was part of a great calendar ofstone Huge stone pillars in the forecourts recorded incarved symbols a succession of dates since the time ofconstruction. Even the number of steps in a stairwayleading to the temple door might s tand for days inter-


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Pyramids and Temples

10. 0 Ziggurat at Ur asit looked afterexcavations ofWoolley

b Reconstruction ofziggurat


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11 a Tectihuacan.Mexico, from theair Foreground,Pyramid of theMoon, furtheraway Pyramid ofthe Sun

b Mayan stele atOutriqua.G aterna la

calated for calendar adjustment Figs. 12a and 12b .From this point of view the yramid of the Serpent

excavated in 1925 on the North West Boundary ofMexico City is of special interest As Ceram says, it is anan onion in stone. It consists of 8 shells, the smallest in thecentre; and it appears that each shell records the Mexicanalendar Round of 52 years. The whole structure musthave therefore taken over 400 years to complete. Somethirty miles away is another step pyramid 128 feet high.This is of height comparable to that of a ten-storeybuilding The area of the base of the largest of all theMexican step pyramids is greater than that of the socalled Great Pyramid of Cheops at Gizeh Fig 13 a fewmiles outside Cairo.

There are also very good reasons for regarding thetemples of the first city sites as observatories In histreatise on the awn oJ stronomy Sir Norman Lockyer,


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Pyramids n Temples 2

2 a Mayan Temple ofvvarriors

b The Caracol. anobservatory atChicken ltzaYucatan


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Astronomer riest and Ancient Mariner

Pyrarnid of Khehren

a former Astronomer Royal puts the case thus: therewere sacrifices at daybreak stars were watched beforesunrise and heralded the dawn these observationswere among the chief duties of the sacrificial priests andit is obvious that a knowledge of star-names must havebeen imperative to those morning watchers who eventually compiled lists These are the exact equivalentsof the moon-stations which the Indians and Arabians andother peoples invented for the purpose ndeed repre-sentations in ancient temples disclose the constellationsof marker stars whose rising and setting positions tally


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yramids and emples

with those of the sun in it s annual track through the lipti belt within the zodiacal constellations p. 7As mentioned earlier, the fixed stars very slowlychange their rlsin.g and setting positions on the horizon.So it is not certain what orientation corresponds to aparticular star un.less we know the date, or to a particulardate unless we know the star. However, the inclinationof the sun s apparent annual retreat, or as we now say,that of the earth s orbit, to the celestial equator haschanged only very slightly in the whole of recordedhistory As Sir Norman Lockyer puts it, once a solartemple, a solar temple for thousands of years; once astar temple, only a star temple for something like 300years Indeed, there is reason to believe that someEgyptian star-set temples changed their allegiance afterthe lapse of centuries to greet the coming of new heavenlyvisitants.

When we speak of a solar temple of ancient Egypt, wemust f igure to ourselves an open door leading to a longcorridor with the holiest place at the end of it Fig. 14).We then envisage the placing of the portal and corr idorso that only once a year a thin beam of l ight exactly atdawn, noon, or sundown could pass without interruptionthrough the whole length of the corridor to the sanctuaryin most resplendent fashion , as Lockyer says, strikingthe sanctuary wall Egyptian solar temples might havethe portal and corridor point ing direct east or west tosunrise or to sunset on the Equinoxes March 21 andSeptember 23). If so, their orientation raised a geometricalproblem which we shall touch on later.

They might also face the rising or setting sun of theSummer Solstice (June 21 in our calendar). Such was theEgyptian New Year s Day Alternatively, they might facedawn or sundown on, the winter solstice December 21).


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Astronomer Priest and Ancient Manner

4 Karnak Mathematiin the Making


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yramids and emples

L oc kye r m en ti ons si x solstice temples including anavenue of Sphinxes. Three of them were at Karnak. Ofthese three two faced sunset on midsummer day onegreeted midwinter sunrise. The great temple of the sun inPeking, China, greets the rising sun o f the winter solstice.On a plain near T he be s i n S ou th Egypt with faces turnedtowards sunrise on that day were two colossal images oft he P ha ra oh A m en -h et ep III. Each was 60 feet high andcut from a single rock.

T he s te p p yr am id s of Mexico like the ziggurats wereobservatory temples. The step pyramids of Egypt an dtheir smooth-faced successors at Gizeh were essentiallyburial mounds fo r di vine Kings: bu t each was in closepropinquity to a temple devoted to his worship in theeast-west axis of the latter. Seemingly the worshippersentered the temple from the East, facing w es t t ow ar ds theSarcophagus. Typically the north face of the pyramidhad a passage leading down to a burial chamber.

The Great Pyramid of Cheops Khufu at Gizeh is ofabout the height of a 40-storey building w el l a bo ve thatof St. Paul s Cathedral in L on do n. O ne observer cites themean error of the base angles in comparison with those ofa perfect square to be about one three hundredth of adegree and the mean error of the lengths to be little morethan half an inch. As regards placing of the sides withreference to the so-called compass points the angularerror according to the same source is little more than athousandth of a degree.

Of the three larger pyramids of Gizeh still standingFig. 15 , t wo h ad a tt en da nt groups of three smaller onespossibly for royal ladies. The mean inclination of thefaces of the former was about 50 to the base. For th at o fCheops it was 51.85 A peculiar feature of two largepyramids Sneferu at Medum and Cheops at Gizeh, is


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6 stronomerPriest and ncient ariner

5 he three pyramids ofGizeh

that the ratio of the base to the height is 11:7 That oftwice the base to the height is thus 22 :7 i e the numeri-cal approximation we now first learn to usc at school fort So the ratio of the perimeter of the base to the heightis a very close approximation to the ratio of the circum-ference to the radius of a circle This has no knownastronomical significance and has prompted fruitlessspeculation some of it silly

The internal structure Fig 16 of the Great Pyramid ofCheops is more complex than that of the others Thecentrally placed entrance faced north as was commonlyso; and the passage therefrom descended to a subterra-nean chamber From this descending passage another ledup to a gallery connected below with a supposedly


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Pyramids and Temples 27

Queen s ch am be r and above with a I


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stronomer Priest and ncient ariner

judiciously we should shun the temptation to draw ahard and fast line between science and magic. Nor shouldwe insist on a clear-cut distinction b etween the practicaland the ritual. After all, future generations may wonderwhy people sufficiently intelligent to measure the speedof l ig ht c ou ld regard the so-called luminiferous ether asan intelligible entity.

While it is easy for hindsight to r ea d i nt o the structureof the Pyramids intentions which had little or nothing todo with the preoccupations of their priestly architects, itis also unwise to assert that the precision of their construction had no intelligible end in view other thansuperstitions which are alien to our own habits orattention from this viewpoint. The ventilating shafts ofthe Great Pyramid at Gizeh claim special attentionfrom this viewpoint. The on e facing north like thetunnel leading to t he u nd er gr ou nd chamber is about3 below the Polar Axis as if se t to greet a circumpolarstar then at lower culmination i.e. when lowest belowthe Celestial Pole. The shaft facing South is at right anglesto the face itself and thus sloped at an angle of 78 to thePolar axis, i.e. 22 to the Celestial Equator.

According to an ancient tradition it greeted at itstransit Sirius, the brightest of all the fixed stars; andSirius, as we know p. 14 , had a special significance inconnection with the Eg ypti an year. I t is not certain thatits aperture remained open when the facing was complete; but the light of Sirius would shine directly intothe king s burial chamber during the later stages ofconstruction if the tradition is true. On this assumption,we can estimate w he n th e building was complete by a notvery elaborate computation which makes use of thephenomenon usually called the Precession the quin-oxes


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Pyramids and emples 29

This is the name given to a roughly 25,000 moreprecisely 25,800 year cycle p 8 , known to the astronomers of Alexandria nearly two centuries before thebeginning of the Christian era. Because of it , the positionof the fixed stars very slowly changes in a calculable way.According to a calculation of the writer, the declinationof Sirius*, i.e. i ts inclination at transit to the CelestialEquator p 103 was 22 South about the year 2400 B.C.This is remarkably close to 2575 B.C. the latest figurecited for the age of the Great Pyramid on the basis ofhistorical chronology, i.e. the dates of the reigningPharaohs and their successors. It is all the more sobecause there are gaps in the historical record and anysuch fIgure therefore relies to some extent, albeit small,on intelligent guessworl .

Be that as it may, it will not be profitless to take a lookat the Great Pyramid, and at others built in accordancewith the same underlying principles, from the standpointof what the secular advisers of the dynasty of Greekspeaking conquerors with their capital in Alexandriaknew two centuries before Julius Caesar landed there andinitiated the Julian Calendar on the advice of theAlexandrian astronomer Sosigenes.

In 238 B.C. the ruler Ptolemy II I issued the so-callede ree nopus to replace the traditional 365-dayEgyptian year y what we have come to call the Julianyear of 365.25 days. Seemingly, his officials and successors did not enforce it . Whether the Alexandrianastronomers took over this figure from their priestlypredecessors we do not certainly know; but we do knowthat the construction of the Great Pyramid could havematerially aided their own observations in the search forgreater precision of time reckoning. Today, it is about 16-t South.


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The vast size of t he p yr am id s is very relevant to whatus e the astron.omer priests could have made of them.Before the time of Newton, when the vernier came intouse, the only way of achieving greater accuracy was tomake one s measuring instrument larger. A generationbefore the introduction of telescopes or microscopes of acrude sort, Tycho Brahe A D 1546-1601) used for hisobservations of planetary motion a quadrant whosediameter was 19 feet. On this scale a degree was aninterval of 4 inches; and a difference o f one h un dr ed th o fa degree would be detectable by the naked eye. Itshould not g re at ly t ax our c re du li ty t o su ppo se that theCalendar Custodians of remote antiquity had stumbledon the fact that bu ild in g in a bi g way has therefore apay-off.

Since the setting of the Great Pyramid is such that itfaces so precisely North, South, East, and West, itnecessarily provides the observer with sight lines fo r thepositions of the noon shadow when visible s belowand of the risin.g and setting su n at the equinoxes. Thisequips us with four different ways of measuring the 5 0 called tropical year with great precision, if recordedsufficiently often to yield a reliable mean. The tropicalyear is the interval between successive vernal equ noxes March 21) or between successive autumnal equinoxes

*In contradistinction to th e tropical year we now speak of th e Siriusy ea r o f t he earliest Egyptian calendar as th e sidereal y ea r, t hi s being th einterval between w hich the su n retreats as th e a nc ie nt s w ou ld say)back to th e same position with reference to th e fixed stars. Owing toPrecession, as we n ow k no w, this takes about 20 minutes longer than th ein ter val b etw een tw o successive spring or autumn equinoxes an d be-t we en t wo successive summer or winter solstices, i.e. th e tropical yearwil l have become about a day less than th e same number of siderealyears after a lapse of 75 years.


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September 23 , and it is also the interval between twowinter solstices December 21 when the noon shadow islongest. It does not however confer the means of makinga measurement based on the summer solstice June 21 .For a reason we shall now see, this occurs during a periodwhen the pyramid casts no noon shadow.

That it does not, is itself advantageous. In fact, itprovides an opportunity for two sensitive measure-ments, namely intervals between consecutive dates onwhich the noon shadow first disappears and intervalsbetween consecut ive dates when the noon shadowreappears. The reason for this vanishing trick depends-on the slope of the faces These make an angle of 52 at thebase, whence 38 to the plumb line.By a simple formula, which we shall learn about laterPart 3 , we can calculate when the noon sunbeam willmake an angle of 38 to the plumb line, if we have at ourdisposal a star map and know our latitude. This happensat the latitude of Cairo, that of the Great Pyramid ofCheeps. about February 28 and about October 4Between these dates the shadow of the noon sun cast the Great Pyramid will disappear. Including the wintersolstice and the two equinoxes we thus have at our dis-posal five different annually recurring events as a basisfor an estimate of the length of the tropical year. Whetherthe Pyramid architects took all these facts into considera-tion we do not certainly know. It is extremely likely thattheir priestly successors knew how to make use of them.Indeed it is on record that the earliest Greek traveller togain knowledge of elementary geometry in Egypt spentsome of his time in conference with the temple astrono-mers boastfully devising or more probably learningways of measuring the height of the Great Pyramid fromthe length of its shadow.


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32 stronomer Priest and ncient ariner

17 a Aerial view ofStonehenge The cult of sun worship and the priestly art of impres

sing the laity by the forecast of eclipses spread intocloudier northern regions. There the lay out of templeand tombs had to do the task of regulating the calendarwithout recourse to a written record. One example ofsuch an architectural feat in the colder north has latelydisclosed its secrets. On the lonely landscape of SalisburyPlain in southern England, stands visibly nea.r a mainmotorway what is perhaps the most impressive relic ofthe Bronze genorth of the Alps Figs. 17a and 17b .

Such is Stonehenge. Even in ancient times, whenimposing temples were a familiar feature of the Mediterranean scene, it excited the admiration of Diodorus, aGreek-speaking Sicilian who wrote extensively on


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yramids and Temples

b GroundviewofStonehengehistory and geography. Writing of Britain about 40 B.C. ,

he could have referred to none other when he states thatthere is also on the island both a magnificent sacredprecinct of Apollo and notable temple Apollo heremeans the Sun, and it has long been known, as is stillconspicuous, that the main axis of the huge standingstones greets sunrise at the summer solstice. As the mid-summer sun first becomes visible above the skyline, onestill-standing stone, called the h l ston half conceals itsdisc as seen from the centre of i ts circle of pillars. Thatthe edifice was, in effect, an observatory with a specialsignificance for the maintenance of a calendar based onthe tropical year is therefore beyond dispute . There arealso good reasons to believe that its role as a repositoryof astronomical lore was much more comprehensive.First, let us look at what remains today. As seen from


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Heel StoneStonehenge

the nearest roadway across the Plain, what is most conspicuous is an outer and an inner group of standingpillars of quadrilateral section capped above by massivehorizontal stones lintels , themselves also of quadrilateralsection Fig. 18 . The outer group stand in a circle nearly100 feet wide. The upright stones which carry the lintelsare of equal size, 18 feet long with 4 feet below theground. Originally, there were thirty pillars; but somehave fallen, as have lintels between adjacent pillars of theinner group. When the outer group was complete thelintels formed a continuous ring.

The inner group consisted originally of 5 trilithons ,i.e. pairs of pillars supporting a single horizontal stone;of these only two are now complete. Their dispositionrecalls the shape of a horseshoe whose open end faces theheel stone, i.e. the rising sun of midsummer day Fig. 19 .The middle t ri li thon at the opposite end was higher 22feet than the two at the free end about 16 feet .

Where the inner surface of the uprights and the undersurface of the lintels have not suffered exposure to the*J-irom the Greek for three as in tri nylc and for stone as in eolithic andlithograph, i.e. three stones.


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Pyramids and Temp\es 35

Sunrise of rrud-summ r dayStonehenge

weather it is still evident that the edges and surfaces hadbeen fashioned with great care and skill. The latter donot lie loosely on the former but have peg and holejunctures Adjacent lintels of the outer ring of pillarsfitted together by tongue and groove There is no evidencethat either group of pillars and lintels ever supported aroof. It is improbable that they could have done so. Thereis therefore a pr m f ie reason for the supposition thatthey had another function

t eye level there are remains of other circles ofsmaller stones and from above as we can now see soclearly by recourse to aerial photography Fig 20 thepicture includes three rings of pits which do not seem tohave been sockets for standing stones Three of theser ings are concentr ic with what is recognisable from the


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36 stronomerPriest and ncientMariner

-;\ \H: If J i. \

~ ~ ~ j.. .. Holesl J ExistingStones.: G fat len -Stoneso Absentton se Post-holes

20. Plan of the stones andexcavated areasStonehenge

N

so 20ICourtesy; Prehistoric Soclety]

Plan of the stones and excavated areasair as once a vast circular ditch. The ditch itself is concentric with the outer ring of pillars. The outermost of therings of pits are the Aubrey stones, so called after aneighteenth-century antiquarian who drew attention tothem. Inside and nearer the outer ring of massive pillars,are those known as the Y and Z holes Fig. 21 .

Of the Y and Z holes more anon. Their gaps are notspaced at even crudely measured equal intervals. On theother hand the Aubrey holes are as near as may beequally spaced. Oddly enough there are 56 of them. Tolayout 32 or 64 equally spaced pits by the peg and ropemethod pp. 48-54 of the temple architects of antiquitywould be simple to accomplish by successive bisectionof 4 right angles with a common apex; but to layout 56pits as equally spaced as the Aubrey holes is a far moresophisticated performance. The difficulty of the under-


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taking tempts us to ask what end the architects had inVIew

Before we examine one answer to this question le t ustake stock of recent discoveries which throw some lighton who were the architects of the final structure.Geological evidence has shown that some of the stonesare not of local origin. Indeed they can have come onlyfrom the South West of Wales If so they must havetravelled by sea most of the way to their destination. Amore recent discovery adds to the interest of this fact Inthe construction of the great standing pillars somearchaeologists have long since discerned indications ofskills peculiar to those of the Greek conquerors of Creteat a date about 1600 B.C. In 1953 a hitherto unnoticedcarving of a hil ted dagger came to light. Experts haveidentified it as Grecian and date it at about 1600 B.C. Itnow seems that trade between the Mediterranean andthe South West of Britain where tin is most abundant

21 Aubrey holes, aneclipse clock, as inter-preted by ProfessorHawkins. The sunmarker would need tobe moved tw o holesanti-clockwise every13 d ays to completeon e circuit a year Themoon markerwouldbe moved two holesanti- clockwise eachday one circuit eachlunar month.T he m oo n o rb itrnarkers o r n od emarkers , represent-i ng t he points wheret he m oo n s o rb it asseen from the earthintersects th e sun spath through thezodiac, would bemoved clockwisethr ee h oles a y e a r on e circuit every 18.6years.An eclipse would takeplace when sun andmoon markers coincided at one of thesepoints or nodes


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existed long before 1000 BAC. i.e. at a date very muchearlier than when one used to believe that Phoenicianships and those of their Greek speaking trade rivals firstventured north of the Straits of Gibraltar in search of tinfor the manufacture of Bronze. If so we have an answerto one enigma of Stonehenge. The changeable weather ofBritain is most unpropitious to astronomical observation.Indeed it is inconceivable that folk confined by its shoresin such a climate could have constructed under their ownsteam a calendar based on the tropical year.On the o ther hand it is easy to believe that migrantsfrom or one might say missionaries of a culture whichflourished in a sunnier climate would be welcome to theAborigines if they brought with them the magic of acalendar to serve the purposes of a seasonal economy. Inmuch the same way Africans in our own century havewelcomed Christian intruders whose arsenicals and anti-biotics are so much more efficacious than the ministra-tions of the native medicine man.

From the remains of charred bones by recourse to theRadio-Carbon Test it is now possible to date withconfidence both who were the earliest builders of theStonehenge remains and when they built it in Britain.The Bronze Age there began about 2000 with arrivalfrom the Continent of the Beaker FolI so called becauseof the characteristic vessels found with their remains. Inabout 1600 B.C. it reached its highest level in the part ofEngland called Wessex. This includes Salisbury Plainwhere Stonehenge stands. Between these limits we cannow date the construction of the great Sun Temple inthree stages. The first stage occurred about 1900 B.C. Itconsisted of a great circular banked ditch already men-tioned with an aperature facing a boulder of local stone.See eginnings n lun ers p. 15.


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yramids and Temples

So placed, an observer at the centre of the circular ditchlooking towards the gap to its north-eastern extremitywould see the sun rising above it on midsummer day.Such was the eel Stone still standing. The other conspicuous standing stones belong to the thi rd stage, whenthe Wessex culture was at its peak, i.e. about 1600 B.C.On the other hand, the ring of 56 Aubrey holes was partof the original plan to which the Heel Stone belongs.

Lately, researches by ProfessorHawkins of the HarvardSmithsonian Observatory have thrown new light onthese 56 pits, which were never sockets for a ring ofstanding pillars. His quest began by showing that thebuilders placed the gaps in the trilithons of the horseshoeand corresponding visible gaps in the outer continuouscircle of pillars so that an observer looking outwardsfrom the former would see sunrise and sunset at midwinter and midsummer, midwinter moonrise and moonset, likewise midsummer moonrise and moonset. Otheralignments made visible the positions of moonrise andmoonset on successive equinoxes at extreme limitssomewhat beyond those of midsummer and midwintersunrise or sunset.

Such extreme limits of the alignments for moonrise ormoonset to the north-south axis of the ou ter circle andhorseshoe correspond with a trivial error to theirpositions calculated in accordance with what we nowknow to be inclination of the moon s orbit to the CelestialEquator p. 103 , that is to say, roughly 5 greater thanthat of the sun in the Ecliptic p. 99 . Seemingly therefore, we have here a sequence of observation posts to*Some archaeologists have rid ICU led th e conclusions of ProfessorHawkins; bu t he has received strong support from the British Astronomer Professor Hoyle. For other work on the calendrical significance ofBritish Bronze ge stone circles and stone avenues, see egalithicun r bservations by A. Thorn 1971 .


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Astronomer Priest and Ancient Mariner

keep track of the relative positions of the rising sun andmoon and of their setting Since we know that eclipsesdepend on the relative positions of the sun and moonand since we also know that eclipses were events investedwith dread or exultation in ancient times the wholepicture suggests that the end in view of the architects wasto forecast them

That eclipses of the moon occur only when it is fulland of the sun only when it is new must have been afamiliar fact to the priestly astronomers in remote anti-quity when the number of days between successive fullor new moons was a basic datum for keeping track of theseasons solar eclipse on midsummer day when the sunrises over the Heel Stone and a lunar eclipse whenmoonrise tallies with sunrise or midwinter sunset musthave seemed very auspicious events to the architects ofStonehenge If so the number of Aubrey holes is highlysuggestive of their intentions Calculations no longerprohibitively laborious where electronic computers areavailable have made it possible to date all eclipses in theperiod ~ l O O O B C The outcome is that they occurredonly when the midwinter moon would like the mid-summer sun rise behind the Heel Stone

We now know that the mean number of years betweeneclipses of either sort is a little over 18 6 that is almostexactly a sequence of 19 18 and 19 years making a totalof 56 years This makes intelligible a reference by Dio-dorus to the visit of the god at intervals of 9 years; andit is difficult to regard as mere coincidence the fact thatthe num ber of Aubrey holes is 56 Thus by moving asingle stone or post from one hole to the next once a yearit would complete an eclipse cycle of 56 years Withthree stones or posts used in the same way and spacedaccordingly it could keep track of sequences of 19 18


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yramids and Temples

and 19 years.Such a procedure would be of no consequence unlessthe priestly watchers of the sky had a means of keeping

track of the approach of midwinter day. We have a clueto this as well. The interval between two full moons ortwo new moons, being almost exactly 29.5 days is themean of 29 and 30 days. It happens that the number of Yholes outside the main edifice is 30 and the number of Zholes is 29. Also, though less certainly the number ofsmall stones in the circle between the outer pillars andinner trilithons would appear to be59 30 29. I f thelatter figure is correct moving a marker stone or wedgemorning and even.ing from one stone to the next wouldcomplete a 29- -day cycle. In any event moving a stonefrom one to the next Y hole in the morning and one to thenext Z hole in the evening or vi vers would accomplish the same result.

The architects and the Druids have left no traces of awritten record as we usually speak of such. Even if theyhad left no relic other than a crumbling circle whosecentre is in line with the Heel Stone at midsummer sunrisethey would have bequeathed us a clue to the most com-pelling circumstance that made the written recordnecessary. Because time flies, and because keeping trackof the seasons was a necessity for stocking the larderwhen settled life began folk had to learn in some way orother to keep a tally of time.

What strokes if any the Druid priests inscribed onmaterials of which we have no remains we may neverknow. What is certain is that the architects of Stonehengebrought to a land more barbarous than their own theknow how for keeping track of the seasons deviceswhich other peoples with t.he art of writing a record ofthe passage of time had already mastered. That they did


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so gives us one of m ny clues to how writing must h veegun two thous nd ye rs earlier


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which became more or less conventionalised at an earlydate i.e. before 2500 B.C. Such pictorial signs representedindividual words having at first no relation to the soundswe utter.

l ~ ~ I C :o1YdC dO .==

In the course of time Egyptian scribes Fig. 22 en-larged their battery of signs by what one may callpictorial puns which did in fact have sound values. Whatthis means may be illustrated in English by setting thepicture of a bee in front of a picture of a leaf to representthe sound of the word elief However Egyptian scriptnever consistently became phonetic in the sense thatJapanese syllable script and European alphabetic scriptis phonetic and as such call for the memorisation of acomparatively small number of signs. In short the pupilwho aspired to become a scribe in ancient Egypt had tomemorise an enormous num ber of signs, as is still true ofChinese students. Learning to read was thus a very pro-tracted and laborious process; and this was a formida bleobstacle to the spread of literacy beyond the templeprecincts.

An obstacle of a different sort obstructed the spread ofliteracy in the Middle East during the same period of time,i.e. before the contribution of the maritime Greeks, Thiswas the nature of their wri ting materials. At an earlydate i.e. before 2500 B.C. the Egyptians had learned tomake by glueing strips of a locally abundant grass, a thin

VUti In 9 D C 1 II unnnnon 64

t i l l I Af i l l II I l f t

22 EgypLian hieroglyphicwriting showrnqnumerals


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The Legacy of the Temp e 45

23. C] Cun if rrnTablet

b) Cuneiform scriptshowing rnathe-matical problems.EIghteenthcentury K, c O l dBabylonian


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membrane papyrus on which the scribe could write withink of a sort. Such a membrane was very flexible and likeour toilet paper easy to roll into a compact cyl inderscroll which was light to hold and made no excessivedemand on space. Contrariwise our documentary recordsfrom Iraq are baked clay tablets or metal cylinders vastlymore bulky than scrolls.

As the pictorial origin of the signs became less and lessrecognizable there emerged in Iraq a new style ofrepresentation by wedge like strokes made initially bya wooden punch in the moist clay before baking. Onespeaks of this script as cuneiform Figs. 23a and 23b . Itgoes without saying that any record of this sort couldaccommodate a sizable store of information only invery large buildings. This rather than the difficultiesof learning the arts of reading or writing was the mainobstacle to a high level of literacy.

Actually cuneiform writing had become phonetic at acomparatively early date. It began in the region of thetwo great r ivers Tigris and Euphrates among a priest-hood which spoke a tongue Sumerian, possibly allied toTurkish but certainly not Semitic. Before 2000 B.C. animmigrant Semitic population had gained ascendancy inthe same region and had continued writing in the cunei-form style but the symbols though visibly like those ofthe Sumerian period were now comparable to theJapanese syllabaries based on borrowed Chinese signsbut used as symbols of sound. Possibly the reason for thetransition was the same. Pointing to a sign, the illiteratealien who spoke a foreign language would associate itwith its sound though ignorant of its meaning

From the site of one of the ziggurats p. 19 , steptemples of the ancient city of Nippur in Iraq excavationhas brought to light some 50,000 clay tablets in cuneiform


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The egacy of the emple 7

script composed at latest about 2000 B.C. Such is thesource of what we shall later learn about the knowledgeof computation in the temple libraries of Iraq. It is likelythat some progress in astronomy and in mathematicscontinued long beyond that date and even after the greatleap forward of science among Greek speaking inno-vators in Alexandria about 300 B.C.

The same can scarcely be said ofwhat Egypt bequeathedposterity. Two scrolls which have survived the ravagesof time and climate, each dated about 1500 B.C. supplyus with all the documentary evidence we have aboutEgyptian mathematics and there is little, if any, evidenceto record considerable later progress on the banks of theNile. One such scroll, the beautifully preserved RhindPapyrus, composed by a temple scribe known as Ahmes,is in the British Museum in London Fig. 24 . The othercalled the Moscow Papyrus is where we should guess it

Rhind papyrus

~ r : ~


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8 Astronomer riest and Ancient ari ner

to be. Neither scroll gives us any insight into whetherEgyptian astronomy ever advanced greatly in theory orpractice beyond it s contribution to the calendar.

From the tomb of Rameses VII, at a date a l it tle beforethe one last mentioned excavation has produced a textwhich depicts grid-wise a lay-out to determine thehighest altitude of particular stars at different times of thenight. In short it anticipates what we now call a graph.Possibly the hours of this chart were of equal lengthbased on. the position of the stars in a circumpolar con-stellation, as some shepherds can still keep t rack of timeat night and as some people in the west used night dialsFig. Sa two or three centuries back.

Before we < at what the scrolls and ta blets tell us ofour debt to the temple cultures of remote antiquity le tus ask what know-how made it possible to bui ld theirenduring monuments. Direct information concerning theinstruments the temple architects used is scarce, but wehear from the Greek writer Democritus [about B.C. ,father of the atomic view of matter and pre-eminent as amathematician in his own generation that he learnedmuch from the Egyptian rope stretchers That what helearned was not trivial is clear from his own declarationthat:there is no one who has surpassed me in geometric construct ions and demons trat ions no not even the geometers of Egyptamong whom 1 passed five full years of my life.

If we ask ourselves how the temple and pyramidarchitects got results so impressive with the means attheir disposal, we here have a clue. For large scale geo-metrical constructions a rope stretched vertically by aweight a p um lin Figs. 25 and 26 is the only way thearchitects of antiquity had of building a right angle inthe vertical plane. If s tre tched between two pegs a rope


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The Leg acy of t Temple 9

USE OF THE MERKHET IN AN CIENT EGYPT

5 Reconstruction ofancient Egyptianmerkhet The plumbline was an essentialpart of the merkhetused the Egyptianastronomer priest as asort of sundialSeorninqlv in con-junction with anmstrurnent called modern scholars thebay t y used It whensiqhunq rising andsetting positions ofstars

26 erkhet and b yone use of the plumbline in ancient Egypt


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can also serve as a ruler to draw a straight line on a flatsurface of sand or soil. If one peg is free to rotate leavinga dent on the latter it will also trace out a circle. Inshort it can do the work of rule and compass sacrocanctto later geometers of Plato s school.

Alike for a temple wall and the base of a pyramid howto make a right angle on the horizontal plane was essentialto the construction. We may infer that the templearchitects first used the familiar Euclidian recipe rule andcompass which serves also as a means of dissecting a lineFig. 27). A second method known seemingly to theEgyptians and certainly to the temple architects of Iraq

, , , -rp . . . . . . . . . . . . .B , ,,,,

\:

27

depends on a recipe fo r making a set square on sand orsoil.

T his m eth od Fig. 28) takes advantage of th e fact thatone angle of a triangle is a right angle, if the lengths of itssides ar e in the ratio 3:4 :5, the right angle itself being the


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The egacy of the Temple

angle opposite the longest side The rope stretcher couldtake advantage of this rule as follows Make 4 knots in acord with their centres respectively 3 4 and 5 lengthsof a straight bar or rod apart. Peg down on the sand orsoil the two middle knots after stretching taut the ropebetween them. Then with a peg through the two endknots stretch each remaining segment and fix themdown.

Needless to say the ratio 3:4:5 is an example of whatwe learn at school as Pythagoras Theorem i e a 2 bZ c 2 if c is the longest side The temple computers of Iraqknew many other sets of whole numbers which illustrate

28 Specu latrve recon-struction of the SetSquare of the Templerchitects


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the same rule, e g . :12 :13. They also knew another ropeand peg recipe for making a right angle on the flat. Thisdepends on the very important geometrical truth that atriangle is right angled if one of its sides is the diameterof a circle and the remaining apex is a point on itsboundary

Given a means of identifying the shortest and longestday the orientation of a temple entrance to greet therising sun of either solstice was a purely empirical prob-lem; but the identification itself is a more sophisticatedmatter One simple method is to make daily observationsaround the time when the noon shadow of a pole orpillar is longest or shortest to ascertain the date of itsseasonally minimum or maximum values. Here again arope trick Fig. 29a suffices to determine the direction ofthe noon shadow on a given day

With cord and peg one may trace a half circle pointingnorthwards around the pole or pillar at a distancedetermined by previous observation somewhat beyondthe reach of the shortest shadow of the day The watchermust then wait unt il the tip of the shadow touches thecircular arc successively before and after mid-day,marking each point Bisection of the angle between the

29 a)//

/,

-----0- -,

\ \ \

\


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The legacy of th TerT r le 53

pole or pillar and these two points precisely fixes theposition of the noon shadow. The rope-trick rule forbisection of an angle is, of course, our first rope and pegrule for making a right angle.

In achieving this we have settled the North-South axisof our local horizon and the rope stretcher has also provided himself with two ways of making a temple site togreet the rising or setting sun of the equinoxes i.e. thetwo days when the sun actually rises and sets as nearlyas possible due East and due West. The East-West is atright angles to the North-South axis which we havedisposed of. Hence the rope and peg 3:4: 5 set squaresuffices to fix it

This may seem to be the simplest, but not necessarilythe earliest, way of solving the problem. Alternativelywith less geometrical know-how those of an earliervintage than the pyramid architects may have adoptedwhat was intuitively though not obviously at first sighta more direct approach. Having sited empirically by asuitable monument the rising sun of the longest andshortest days, the temple architect or surveyor could fixthat of the equinoxes to a high level of precision bybisecting the angle between them Fig. 9b w

Architecture was not the only pace-maker for geo-metrical rule of thumb in. the dawn of science; the worditself based on Greek literally means e rth me surementA Greek-speaking Iraq emigre from whom we get ournot wholly reliable first glimpses of contemporarycivilisation in the Mediterranean world of antiquityasserts that geometry had its origin in the task of theEgyptian income tax collectors who levied temple tributeon the basis of allotment acreage. At a time when theannual flooding of the Nile might wash away landmarkswhich bounded allotments of the tillers of the soil,


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29 b

w

-//

NII

IIS

< -, \ \ \l E

30 Fif leenth century c.Eqvptian surveyingtrorn a wa II pa inti ng

frequent measurements of this sor t were necessary Fig30 .

What we certainly know from scrolls of papyrus whichhave withstood the hazards of the weather is that thetemple computers of the Nile could calculate correctlyareas of rectangles and right angled triangles. Curiously,the rule given for the latter is to divide by two the pro-duct of the lengths of the two shortest sides. For instancefor the 3:4:5 triangle t 3 x 4 6. From the same scroll


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he egacy of the emple

the Rhind p apyr us), we learn that the value of theratio of the area to the square of the radius of a circle is,in our way of writing down numbers, 3.16. This isremarkably close to the true value 3.142 to three decimalplaces, an error of approximately 2 in 300, i.c. less thanone per cent .

A good value for had a p ay -o ff i n terms of templetribute, because a c yl in de r op en at one end is a convenient shape for a container in which to measure grain,oil, or wine. An achievement in measurement of volumerecorded in the p ap yr us n ow in Moscow is more remarkable and less obvi ousl y-i f at all-usefuL Before thecompletion of Stonehenge, the E gy pti an te mp le computers could correctly calculate the volume of a w ho le o rtruncated pyramid.

When measuring h ei ght levels in sunny climates,where skies are mostly cloudless, information fromo ri en ta l s ou rc es suggests that the architects of ancientt im es m ad e much us e of the s u n s s ha do w. T ra di ti on tellsus that Thales, the earliest of the Greek geometers onrecord, determined the height of the Great Pyramid ofGizeh Fig. 31 fo r the instruction of hi s priestly hosts. Todo so, we need to know only the basic principle of trigonometry, i.e. t ha t t he ratios of the corresponding sides ofsimilar right-angled triangles ar e equivalent. One measuresthe length of the noon shadow of a pole of known height,an d that of the Pyramid added to half the width of it sbase. It is at least as likely that h is p rie stl y instructorstaught Thales the trick as that he made the discovery

In the domain of practical mensuration, the Egyptiantemple teachers were in some ways in advance of theiropposite numbers in Iraq. The latter clung, like theHebrews in the Old Testament I Kings VII, 23 , to thevalue .3.0 fo r Contrariwise, the art of computation, as


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56 stronomer Priest and ncient Mariner

we learn from the Nippur tablets, reached a much higherlevel in the Middle East than in Egypt.In Iraq, there was a more powerful impetus to calculation that in the Egypt of the Moscow papyrus about 1600B C In Egypt, the priestly hierarchy with its associatedscribes architects, engineers, and surveyors preyed on avast population of slave labour in the fields and themines. The cities of Iraq were more lively centres ofoverland trade routes and a large class of freemen in-

31 One way In whichThales may havemeasured the heightof the reat Pyramidat izeh by measuringthe length of the noonshadowH - b + S) tan A = p -:- s

H P S) 7 S

eluded bankers as well as merchants and pedlars. Therewas an elaborate code of weights and measures andcustoms concerning wages. Commercial arithmetic flourished accordingly. For instance, one cuneiform recordgives a recipe for computing compound interest at 20over a specified period of time.

Without goin.g into further details two features of theart of computation as i t flourished in Iraq. are of special


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h Legacy of the Temple

3 The Abacus0 orn

b Chinese

c Japanese


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computation revealed by the Nippur tablets, let us lookat the way in which a t emple scr ibe in Egypt wouldperform addition and multiplication. To do this he wouldrely on a device of great antiquity At a later date, itbecame a flat board Roman type on which beads werefree to move in parallel grooves, or a frame Japanese andRussian types in which perforated beads moved freelyon parallel rods Fig . .32 .

t a more primitive level in Egypt, such a device calledan abacus was probably a tray sprinkled with a thicklayer of sand in which parallel grooves accommodatedten pebbles. Actually, the Latin word for a pebble iscalculus whence calculation. To count out 527 pebbles,the computer would s tart with all grooves empty, placing9 in the first groove for units . He would then empty it,placing one of the remaining pebbles on the next groovefor tens . When he had placed 9 on the second groove,he would empty it and place one of the remaining pebbleson the third groove for hundreds Proceeding in thisway, he would end by having 7 on the first, in thesecond, and on the third groove. In his own script hewould record the result in reverse order to RomanDXXVII as:

To add 716 to 527, the computer would s tart with thefinal set of 7, 2, and 5 pebbles on the first three grooves,and count out 7 6 in the same way. Multiplication beingrepeated addition and division being repeated sub-traction need not trouble us. What we have seen sufficesto show that the Egyptian temple scribe did not usenumber signs in the way we use them as counters forcalculation. He used them only as a device for recordingan operation performed with a mechanical device. As for


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he egacy of the emple 9

most of the world before the Hindu-Ara bic script cameinto general us e and made possible c rrying over on paperwithout mechanical aids, they were merely labels for anoperation performed on the abacus. The latter becameredu n dan t w h en the Hindus h it upo n a symbol zero forthe empty column.

Unlike their successors for several millenia thereafterthe computers of Iraq relied on tables which t he y us ed aswe now use tables of trigonomctrical ratios or oflogarithms and as a ship s captain uses tables o f theposition of stars. A temple library could accommodatethousands of clay tablets on which columns of numbershad b ee n i ns cr ib ed ; but t he e qu ip me nt for performinga wide range of calculation would be vastly to o bulkyfor a ship s cargo to accommodate. The literacy or mightwe say the numer cy of Iraq was still largely circumscribed by the temple walls.

Tables constructed in Iraq before 2000 B.C. includereciprocals fo r dealing with division multiplicationsquares and cubes as well as square roots and cuberoots. According to Dr . Neugebauer a value assigned toJ is equivalent in our notation to 1.414213 instead of1.414214 i.e. correct to six significant figures, anerror of in a million. Tablets show that computers usedsuch tables for solving by numerical approximationsimple quadratic and even some types of cubic,equations.


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60

The ree ontributionFrom even earlier than the beginning of the secondmillennium before the Christian era, i.e. 2000 B.C. Fig. 33the Mediterranean had already become a centre of mari-time trade and colonisation by two wide different speechcommunities which founded trading posts along itsshores. One eventually founded colonies along theAfrican coast as far as Spain. Its homeland was what wenow call Lebanon the Phoenicia of the Christo Judaicscriptures. Its language was one of the Semitic dialectsakin to Hebrew and to the dominant speech of the peopleof Iraq during the same period.

33 Eqyptlan sea goingship c 26 H.C From waves of invaders north of modern Greece, and

speakin.g different Greek dialects, the other spread outfirst to Asia Minor in the neighbourhood of the Dar-danelles, i.e., the region where the Trojan wars tookplace. Thence they founded trading colonies along thecoast of what is now Turkey in Asia, and annexed Cretewhich was then the seat of a flourishing temple culturecomparable with that of contemporary Egypt and Iraq.They also occupied Cyprus Sicily and the toe of Italy.Later they founded a mercantile colony at what we nowcall Marseilles.


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The Greek Contribution 6

34 Phoenician warship

t tPhoenician trade between Lebanon and Egypt had

begun before their ships set up trading stations furtherafield Figs. 34 and 35 . The main export from the latterwas then the much prized cedar wood of the former. Thetraders themselves are relevant to how science began fortwo reasons. One is that they were probably the first tosail beyond the Pillars of Hercules i.e. the Straits ofGibraltar coasting north to Britain in search of tin andalong the African coast in search of spices, ivory andblacl< slaves. From what we now know about the 50-called Wessex culture of which the Stonehenge SunTemple is a relic, it now seems certain that Greek-speaking pilots from Crete also penetrated the Atlanticbefore 1500 C By doing so they and their rivals brought 35 Phoenician braceletwithin the range of human experience an en tirely newpicture of the firmament.

The date las t mentioned puts the spotlight on a secondfact of relevance to our story. Somewhere later than2000 B.C. but not later than 1500 B.C. Semitic slaves in


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6 stronomer Priest and Ancient ariner

6 Phoenician script

the mines of the Sinai peninsula began to adapt a smallbattery of Egyptian hieroglyphics to represent thesounds of a tongue alien to that of their masters andoverseers. Such was the first alphabet as some expertsmaintain and the parent of all truly alphabetic writing.Be that as it may the Semitic Phoenicians were using analphabet Fig 36 of consonant signs for inscription onstone or clay tablets at a date not much later than theirfirst foray beyond the Mediterranean and it is certainthat their trading stations were the route by whichalphabetic writing first spread throughout the Mediterranean region

The Phoenicians did not like their Greek pupilsperfect it as an instrument of scientific communication oras a gateway to wider literacy. To why they failed onecannot give a complete answer; but two reasons arerelevant. One is tha t they continued for the greater partof their history if not till the end to use tablets of thesort used by their neighbours throughout the MiddleEast. Another is that they were the most priest riddenpeople of the ancient world. Wherever the Phoeniciansset up colonies they established the cult of Baal-Ammon


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The Greek ontribution

the Moloch of the Old Testament. They propitiated himwith human sacrifice that of young children on a scalewhich no other civilisation has ever practised.

Both in Crete and in Cyprus their Greek speakingtrade rivals had learned to use alternative forms ofsyllabic writing comparable to the k n syllabaries of theJapanese. Such writing meets the need of people whosewords are strings of simple syllables made up of a vowelor a vowel preceded by a simple consonant e.g. TO-KI-OO-SA-I A KO-BE YO KO HA MA. Sylla bie writing ishowever a Very clumsy and unreliable method of con-veying the sounds of words in an Indo European languagesuch as Greek or our own which embraces thousands ofdifferent syllables some closed by a consonant orconsonant cluster as in our words strips and pl nts atboth ends.

In languages other than those of the Semitic group wemay make many words with no common thread ofmeaning with the same framework of consonants in afixed order e.g. m n moon mine mo n me n inEnglish. This is not true of languages of the group usedby the Phoenicians. An alpha bet of consonant signssuffices for identification of a Semitic word because everyroot with a particular meaning is a unique permutationof conson.ants. o make the consonant alphabet suitableto their own needs Greek speaking traders and mastermariners had to incorporate vowel signs borrowed fromone or other of syllabaries they had previously used.This happened at some date a l it tle before 600 B.C.; andit is significant that the colonising Greek speaking traderivals of the Phoenicians had by then or earlieracquired the use of papyrus scrolls from their Egyptiancustomers. This date therefore pinpoints what proved tobe a momentous expansion of literacy and the beginnings


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Astronomer riestand Ancient Mariner

of what we may rightly call the Greek contribution toSCIenceWhen some writers on the dawn of science write aboutthe Greek contribution, it is doubly misleading to our-selves So we must be clear what we shall henceforthmean by it When we speak of Greeks nowadays, weusual ly mean people who live on the mainland ofGreecetogether, it may be with the inhabitants of Crete andsome of the inhabitants of Cyprus. In fact the Greek-speaking world of the first millennium and especially ofthe last two centuries before the Christian era covered amuch larger territory. Before 400 B.C. it extended fromAsia Minor to Spain. For several centuries after 300 B Cit also included parts of Egypt and the Middle East

The different city states and colonies in the earlierperiod were often at war and never under a singlegovernment except during a period of less than half acentury when Philip of Macedon and his son Alexanderthe Great brought them to heel and spread the use of theGreek language as a medium of cultural communicationinto Africa, Palestine, and Iraq. To speak of the Greekcontribution to science when one means the contributionto science of people who spoke Greek is therefore on allfours with talking about the English contribution toscience embracing all the work of learned professions ofEngland Scotland the United States Canada AustraliaNew Zealand and India where English is still the chiefmedium of higher education from the reign of Elizabeth to our own time There is however, another reasonwhy it is misleading to speak of the Greek contributionin connection with the progress of science over the wholeper

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[Lancelot Hogben] Astronomer Priest and Ancient Ma(Bookos.org)