1996{r}10 clagettvol i&ii

7/30/2019 1996{R}10 ClagettVol I&II

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A HISTORIANS HISTORY OF

ANCIENT EGYPTIAN SCIENCE

Jens Hyrup

Essay review of:

Marshall Clagett, Ancient Egyptian Science. A Source Book. Volume One:

Knowledge and Order. Two tomes. (Memoirs of the American Philosophical

Society, 184). Philadelphia: Am erican Ph ilosophical Society, 1989. Chron o-

logy, Bibliograph y, Index of Egyp tian Words, Index of Proper N am es an d

Subjects. Pp. xv+736+127 pp. illustrations.

Marshall Clagett, Ancient Egyptian Science. A Source Book. Volume Two:Calendars, Clocks, and Astronomy. (Memoirs of the Am erican Philosophical

Society, 214). Philadelphia: American Philosophical Society, 1995. Biblio-

graphy, Index of Egyptian Words and Phrases, Index of Proper Names

and Subjects. Pp. xiv+575+146 pp. illustrations.

Written for Physis


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The volumes under review represent the scholarly facet of that vita nuova

in wh ich the author engaged after finishing his monum ental Archimedes

in the Middle Ages in five volumes and many more tomes (the dedication

For Sue Once Again tells us that the impressive work they must have

asked for has fortun ately left space for oth er facets). Let it be said at on cethat they constitute the beginnings of a worthy successor the planned

third volume will deal with mathematics, medicine and biology, and

contain a detailed presentation of Egyptian techniques for representing

nature [I:x].1

The original idea w as to p rod uce a Source Book in An cient Egyptian

Science consisting of enough extracts to illustrate some of the aspects of

that science [I.ix]. However, on the premise that the interesting questions

are the nature of Egyptian scientific knowledge and the p rocedu res to

acquire th at know led ge [II:307] as w ell as the intent of the Egyptian

scholars [II:424], the au thor realized that a few d ocum entary extracts w ere

insufficient to give a historian of science without any special knowledge

of the Egyptian langu age and culture a w ell-roun d ed v iew of the growth

and development of that science [I:ix].

Each section of the w ork thu s starts with an extensive chapter w hich

discusses its theme broadly and in depth. A number of documents intranslation follow, each provided w ith a sp ecific introduction. All tran sla-

tions are prep ared by the au thor, often follow ing existing translations into

modern languages closely but deviating from these when required, e.g.,

in the interest of consistency between docum ents, and always w ith a critical

eye; at tim es, the translation bu ilds on a more comp lete Egyp tian text than

previous translations. Chapters, introductions and d ocum ents are provided

1 I shall use this simp lified reference system for all qu otations from the two volumes.Everywhere in the following, Egyptian means ancient Egyptian. Datings

follow the chronology of [I:629635], and thus in the main J. Baines & J. Mlek,A tlas of A ncient Egypt, 3637 (Oxford, 1980), and O. Neugebauer & R. A. Parker,Egyptian A stronomical Texts, vol. I, 129 (Providence & Lond on, 1960); D. stan d sfor Dynasty, which remains the most adequate frame of reference for Egyptianrelative chronology. In the chronology adopted, the Old Kingdom (D.3D.8) is26642155 BC, the Midd le Kingd om (D.11D.13) covers 20401640 BC, and the New

Kingdom (D.18D.20) 15501070 BC.

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w ith copious notes, m eant to illustrate the historical steps taken by ear lier

scholars to ad vance our kn ow ledge [...] not on ly to give the read er a good

sense of the development of scholarship over the last two centuries but

also to give honor and cred it [and , w hen ap propriate, criticism/ JH] w here

they are due [II:ix]; by way of this presentation of earlier views anddebates, the notes provide amp le opp ortunity for philological comm entary

and critical discussion (also in cases wh ere Clagett suggests new read ings

or interp retations). Some of the docum ents represent comp lete texts, others

such excerpts as are deemed relevant for the theme to be illustrated. No

doubt these annotated translations will allow readers without detailed

knowledge of the original language, i.e., most students of the history of

science, a good sense of what the documents intend, while the reader

who controls the Egyptian language will find most texts from Volume

Two and some from Volume One in original or in hieroglyphic transcrip-

tion in the illustr ations [II.viiif]. Of par ticular value is the observation that

certain expressions are comm onp laces if such a w arning w as not given

[e.g., I:186 n.8], the student with no broad acquaintance with the style of

Egyptian documents might be induced to take at automatic face value the

claim of the constru ctor of a Mid d le Kingd om w ater clock that never w as

mad e the like of it since the beginning of tim e [II.460], Clagetts cautiousdou bt notw ithstand ing (cf. below).

The title of Volume I (Knowledge and Order) translates a p air of cru cial

Egyptian words: rekh [...] and maat [...] [I:xi]. rekh/ know led ge refers to

the nor mative id eal the ability to measu re, count, and record of scribal

workmanship. maat/ ord er en com passes in on e d en sely packed con cep t

the notions of cosmic, political and social justice or order. Since Egyptian

science w as always the p reserve of th e scribal craft, and its scope w as

often to describe or up keep the order of the world , these two concepts werecertainly important aspects of the Egyptian intellectual achievement,

without whose development Egyptian science, rudimentary as it was,

wou ld have taken som e other form [I:xii].

The opening chapter of Section I (Know ledge) d escribes The Fruits

of Scribal Activity in Ancient Egypt [I:136, notes 3746]. Pp. 111 deal

with th e origin of writing and its first u ses until the introdu ction of year

names and some kind of rudimentary annaling (keeping track at least of

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the height of the yearly flood ing, importan t for tax determination) du ring

D.1 (c. 3000 BC). Then follows a presentation of material that portrays the

composition and tasks of the scribal profession and of positions that

presup posed scribal skills (includ ing lector pr iest, ph ysician, h our

watcher, and calculator), and of the various institutions that carried thehighest (i.e., m ost prestigious) levels of scribal know led ge: The Hou se

of Books, the Place of Records (both mentioned in Old Kingdom

sources), and the House of Life (Old Kingdom to Achaemenid or

Ptolemaic times). All in all, medicine and magic, astronomy (or star

gazing), determination of the time for religious festivals, rituals for

sacrifice, and knowledge of gods and temples, turn out to constitute a

netw ork; in as far as they w ere not taken care of by the sam e person , their

specialists w orked closely together.

The first d ocum ent of Section I is the Palerm o Stone, a D.5 d ocum ent

(c. 2400 BC) sur viving (incomp letely) in sun d ry p ieces, the m ost imp ortant

of which is now in the Palermo Museum. It contains annals for the first

5 dynasties, and show s how th e system of historical registration developed

over time: from around the beginnings of D.1, year names are recorded;

from som e point d ur ing the same d ynasty, even the yearly Nile height is

indicated; d uring D.2, the biennial censu s of the Wealth of the Land entersyear names; with D.4 (the dynasty of the great pyramids), genuine

chronicling registering several memorable events (predominantly but not

exclusively religious activities) for each year begins, while on the other

hand years are counted and not nam ed ind ividu ally.

Next follow various docum ents that illustrate the p osition, prestige and

tasks of high-level officials w ith a scribal backgrou nd in the Old Kingd om .

One of these is the funerar y biography th e early D.4 leading ad ministrator

Metjen, in w hich are includ ed qu otations from official d ocum ents whichimplies that a royal chancery provided with archives was functioning at

least since the end of D.3. A tale about wonders at the court of King

Cheop s, presumably comp osed during D.12 (19911783 BC), gives occasion

to the observations substantiated also in later sections that magic

pervaded the whole religious fabric of Egyptian society (at least at its top),

[that the] Egyptians attempted to achieve afterlife by means that were

fun d amentally magical, and fur ther [...] were concerned w ith preserving

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the cosmic order by those means [I:206].2

Tw o well-know n p ieces show different asp ects of scribal self-conscious-

ness as it was inculcated in Middle and New Kingd om scribal schools. One,

on Scribal Imm ortality, emph asizes the fame deriving from scribal

knowledge, which survives longer and more certainly than the funeraryservices of deceased kings not too far from the conviction of modern

scholars that honor and credit [should be given to predecessors] where

they are due. The other, the Satire of the trades, emphasizes the social

superiority of the scribal craft among those occupations that were open to

common people. Clagett gives no systematic treatment of the ed ucation of

scribes; the n otes to the latter d ocum ent together w ith scattered remarks

on Old Kingdom education [I:166, 188] shows, however, that he agrees

with the picture presented by Helmuth Brunner and John Baines 3: in the

Old Kingdom, sons of high officials might be brought up together with

the royal pr inces, and taught w ith them; or future scribes m ight be trained

as app rentices on the job; the scribal school as a par ticular institution is

a creation of the Midd le Kingd om. The ad vent of the Midd le Kingd om

thus marks the transition from very restricted to restricted literacy.

Those who wan t to know more m ay consult Brun ner and Baines.

The final docum ent from section I is an on om asticon, in its own w ord sexcogitated by the scribe of the sacred books in the Hou se of Life,

Amenope [I.247], presumably to be dated in the outgoing D.20, c. 1100 BC.

The list of entities p resents itself as a teaching for clearing the mind , for

instruction of the ignorant, and for learning all things th at exist, w hat Ptah

created , what Thoth copied d own (ibid.) in part a topos shared with the

Rhind mathematical Papyrus, introduced as Rules for enquiring into

2 One might add that the term translated magic (hike) is not only a practice, asmagic in our und erstanding, but also a substance of which the m agician may befull [e.g., I:335]; in the latter connection, an understanding close to mana iswarranted.

3 H elmu th Bru nner, A ltgyptische Erziehung (Wiesbaden: Otto Harrassow itz, 1957);John Baines, Literacy, Social Organization, and the Archaeological Record: TheCase of Early Egypt, in John Gledhill, Barbara Bender & Mogens Trolle Larsen(eds), State and Society. The Emergence and Development of Social Hierarchy and Political

Centralization, 192214 (One World Archaeology, 4. Lond on: Un w in Hym an, 1988).

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natu re, and for kn ow ing a ll that exists, [every] m ystery, ... every secret.4

Its over-all order is fairly systematic entities belonging to heaven, air,

water and land; offices and occupations in the other world (god, goddess,

blessed d ead) and the Egyptian cour t and state; classes of hu man beings;

towns of Egypt; buildings, their parts, and associated types of land;agricultural land and produ cts; etc. Within these groups, h owever, the

progress is often by association rather than by category, as pointed out

in Clagetts n otes. In view of the p rominent p lace w hich the use of lists

occup ies in discussion of th e relation between oral and literate culture5,

it is worth pointing out that this Egyptian list is thus very different in

character from the lists that constituted the backbone of proto-literate (and

later) Mesopotam ian scribal education; from the ear liest beginning, these

were ordered by category; they w ould never p ut on e type of land in a list

together with par ts of buildings, and another together w ith vegetables and

grain. In term s of Lurias d istinction betw een categorical classification

and situational thinking6, the Mesopotamian lists are of the former type

the type which Luria found in Soviet Central Asia in the 1930s to be

characteristic of kholkos activists, those engaged in the construction of

mod ern society; Amenopes catalogue of the world, on the other hand ,

comes closer to the later variety characteristic of the illiterate peasantswh o knew wh ich kind of land and wh ich produ cts belonged invariably

together in their traditional world.7 This character of Amenopes (and

4 Transl. T. Eric Peet, The Rhind Mathematical Papyrus, British Museum 10057 and10058, p. 33 (London: University Press of Liverpool, 1923).

5 See Jack Goody, The Domestication of the Savage Mind, pp. 74111 (Cambridge:Cambridge University Press, 1977). Pp. 99103 discuss the Egyptian onomastica.

6 Aleksand r R. Luria, Cognitive Development. Its Cultural and Social Foundations, 48ff(Cambrid ge, Mass., & Lond on: Ha rvard University Press, 1976; 1Moscow: Nau ka,1974).

7 John Wilson explains this hybrid character of the Egyptian lists by seeing themas a kind of cargo cult, probably an adaptation by ignorant Egyptians of w hatthey thou ght to be lexicograph y over in Asia. They th ough t that just m emorizingthe w ritings of these things in categories had something to d o w ith know ing andclassifying p hen omen a discu ssion contr ibution in Carl Kraeling & Robert McC.

Adams (eds), 1960. City Invincible, p. 104 (Chicago: University of Chicago Press,

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other) Egyptian lists agrees well with an observation made by Clagett

[I:239], viz that they correspond to Ptahs creation of the existing world

by the spoken w ord , not only according to the somew hat later Mem phite

theology but also to that part of Amenopes introduction that does not

repeat the commonplace of the Rhind Mathematical Papyrus: what Thoththe d ivine scribe copies dow n w ill be word s that create, not th ings created.

Just as much as a lexicon, the onomasticon is a ritual reenactment of that

creation. No similar idea seems ever to have been entertained by the

creators of the Mesopotam ian script.

The same intertw inement of d escription with magic and religion recur s

as the constant theme of section II, Order. In Clagetts words, during

the three thousand years of Pharaonic Egypt there was no natural

ph ilosophy or p hysics that w as separate from religion, myth, and magic

[I:263]. To the opinion of certain Egyptologist (exemplified by P. Derchain,

but the stance is not his alone) that the religion of the Egyptians

considered eminently practical people was no mysticism but physics

it is retorted that the physics in qu estion is un like any p hysics for which

w e now customarily use the term , since it regularly included contrad ictory

symbols to represent natural entities and events, expressed contendingforces by conflicting gods, made wholesale use of divine agencies to

describe creative acts, and everywh ere emp loyed magical terms and

pronou ncements to bring things into existence and to effect comm unication

between hu man and divine beings [I:373]. That contrad iction is not an

artefact produced by the modern compression of conflicting creeds into

a single Egyptian cosmology becomes clear in a passage from the

Mem phite Theology (docum ent II.9, [I:600]): [Ptahs] Enn ead is before him

as the semen an d hand s of Atum , for [it is said that] the Ennead of Atumcame into being by means of his semen and his fingers. But the Ennead

[of Ptah] is the teeth and lips in this mouth which pronounced the name

of everything [...] and which gave birth to the Ennead: the Ennead, indeed,

is the same set of nine gods in both cases; it may well, at the same time,

be the produ ct of Atums masturbation and result from Ptahs creative

1960).

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word , just as every major temple may stand on the first spot of firm land

that emerged from the primeval waters. According to Tertullians criterion

(credo quia absurdum) these are clearly mystical (or poetical) truths, to be

jud ged not according to th eir im m ed iate m eaning but from th eir con tr ibu-

tion to producing a meaningful life-world.A fairly long p assage in Chapter II [I:268279] is devoted to interpreta-

tions of this situation w here all the concepts w ere accepted to be valid

by the same theologians (Rudolf Anthes, quoted p. 271). Apart from

Anth es (who sees the contrad ictory explanations as sym bolic explanations

of that which cannot be understood directly by means of reason and

sensual experience p. 272), m ost w riters have been aston ishingly blind

to the character of religion in their own culture.8 Instead of inventing a

mythopoeic mode of thought which should characterize the ancient

Egyptian (and Mesopotamian) culture in general (Henry Frankfort) or a

many-valued logic (Hornu ng),9 Clagetts dow n-to-earth-position is

certainly more app ropriate: that the only branch of Egyptian though t where

something like natu ral philosophy reflection on the fund amen ts of natu ral

ph enom ena occurs is that of religion. That d id not preven t the Egyptian

scribal officials from having a very western view of the link between

measur able Nile height an d possible taxation level.Chapter II [I:263372, notes 373406] describes the variou s cosm ogon ies

connected to various m ain temp les On/ H eliopolis, Khm un / H ermop olis,

Memphis, Thebes (the New Kingdom Amon-Re cosmogony) together

with the monotheistic Aten cosmogony and the cosmogonies from the

8 Accord ing to E. Hornu ng, qu oted p . 273, the p rinciples of w estern logic w ould

consider it an impossible contradiction for the divine to appear to the believeras one and almost absolute, and then again as a bewildering multiplicity; trueenough, of course, when Muslim theology or Enlightenment Deism applies theprinciples of western logic to Trinity.

9 As one m ight perhap s gu ess, Horn un g u ses the notion of logical polyvalency asa poetical metaphor (probably without knowing so), and not according to itstechnical meaning e.g., that the god whom I address in this very moment issup erior to th e god s, he is more than they are. But in this sense, many-valuedlogic is as western as binary logic, one being the preserve of the theological

faculty (and poetry) and the oth er of th e p hilosophical faculty.

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Roman period (temple of Esna). Differences and temporal development

are pointed out, but also the existence of a set of fun d amental ideas that

run through all the different narratives the existence before creation of

an am orph ous Abyss of primeval waters, from w hich a creator god (or

corporation of eight gods) first fashions his own form and makes landemerge, and then goes on with the creation of other gods (by spitting, by

masturbation, by speaking, on the pottery-wheel, by craftwork) and the

world in general with its inhabitants and its order (maat) as observed

by Clagett [I:265f], this imagery reflects the two pervad ing natu ral features

of Egypt: the overw helming im portance of the Nile and its ann ual flooding

and the ever-present sun as a continuing source of light and heat. Also

recurrent is the idea that abysm al chaos is not sup pressed but only pushed

back, and that it remains an ever-present threat which (at least in some

versions) is eventually going to engulf the ordered world.

The last p art of the chap ter d eals w ith cosmology, with w hat kind

of world resulted [from creation], w hat sort of visible and invisible beings

popu lated this w orld, and wh at w as the nature of the forces which were

believed to keep the w orld and its parts fun ctioning harmoniously and

of those which were dangerous and threatened the desired harmony of

the cosmos [I:328] with the n atu re of the god s (includ ing their possiblehistorical origin in fetishes and animal forms but only ambiguous

iconograp hic evidence for such a process exists); w ith the relation between

gods and magic (a substance or magical force, we remember, not only

a powerful practice); with the question of human immortality and the

topography of the Netherworld (not yet exclusively nether in the Old

Kingdom); with the position of the king between gods and ordinary

hu man s; w ith the interpretation of d reams throu gh semantic analogy, or

contrast, but also through ph onological similarity or pun ning no innocentamu sement but another aspect of the p ower of the creative w ord.

The documents that constitute the second part of Section II provide

the general exposition with concrete body and substance, even though,

as Clagett observes in his introd uction to th e Coffin texts [I:435], it is

obvious that I hav e only skim med the cosmogonic and cosm ological ideas

from this extensive collection and the reader will certainly find further

stud y of it of great profit if he w ishes to gain furth er know ledge of ancient

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Egyp tian religious th ought. They illustrate not only the relation betw een

continuity and chan ge regarding the ideas that are expressed bu t also the

developments of intellectual style. The earliest texts, the Pyramid Texts

(Document II.1) from the royal tombs of late D.5 and D.6 (23502180 BC)

are collections of ind ividual statemen ts or spells, presenting them selvesas Words to be Spoken, with no overall coherence and no single, all-

embr acing title. They reflect spells u sed in bu rial and offering ritu als, and

their oral character is everywhere evident [I:407f]. The Coffin Texts

(Document II.2), written inside the coffins of nobles from the late Old and

the Midd le Kingd om , are not very d ifferent in character as far as the spells

themselves are concerned ; the Midd le Kingdom specimens, how ever, start

giving titles to the single sp ells, often w ritten in red ink [I:433f,455]; orality

is clearly on th e wane after the establishm ent of the school institution an d

the concomitant shift from very restricted to restricted literacy.

The Coffin Texts reflect what has been spoken of as a democratization

of Egyptian religion at the end of the Old Kingdom, after which even

common mortals and not only the king were allowed identification with

the resu rrected Osiris. Clagett rightly considers the term extravagant [I:430]:

those who procured for themselves the right to immortality were not

commoners but those same nobles w ho had seized effective p ower andconfiscated royal benefits in the breakdow n of Old Kingd om centralization.

(In th e long ru n, it is tru e, w hat star ted as a narrow ly oligarchic revolution

spread to somew hat broader circles).

The so-called Book of the Dead(Docum ent II.3, early N ew Kingd om and

onwards), various collections of Spells for going forth by day (i.e., for

allowing the deceased to leave the tomb in any form in which he wished

to leave it [I:451]) still contain m uch m aterial that goes back to the ear ly

collections. The literate character of the texts, how ever, becomes even moreobvious. Not only have red-ink titles become the rule: as behoves a

scholarly tradition, the spells are am ply provided w ith explanatory scholia;

w hat emerged as a technical tool has achieved th e char acter of theological

theory, w hile still retaining its instru m ental function (as strikingly revealed

by the presence of a spell that shall prevent the heart or bad conscience

of the deceased to betray him when confronted with Osiris the great

Judge[I:458]).

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This character of theological or cosmological treatises is even more

outspoken in other New Kingdom texts like the Book of Amduat (the

Netherw orld), the Litany of Re and the Book of the Divine Cow (Documents

II.46) and in the Memphite Theology (Document II.9), an archaizing

work known in a copy from c. 700 BC and probably not much earlier (inany case not earlier than mid-New Kingdom). Whereas the chest of

w ritings brou ght to the scene when the D.5 Vizier Washp tah fell sudd enly

ill (Docum ent I.4) is likely to have contained casuistic med ical papyri an d

spells to be used by the lector-priest (sum m oned by the King together w ith

the chief p hysician), the N ew Kingdom and later H ouse of Life is likely

to have p ossessed such d escriptive or eschatological works along w ith the

magical evergreens and hym ns (an intermed iate category from this point

of view even they only become literature when oral culture is

waning).10

Astronomy, which was deliberately left out from cosmology as

considered in Section II, is treated together with calendars and clocks (long-

and short-term time-keeping) in Section III (= Volume Two). Indeed, the

only apparently astronomical element of the cosmologies the description

of the stations of the nocturnal voyage of the Sun-god Re through theNetherworld in the Book of Amduat is not only devoid of concrete

astronomical detail but also in a curious contrast to more astronomical

ideas about this nocturnal voyage (see below).

Section III (introduced by Chapter III, [II:1129, notes 131165]) thus

brings us to the heart of what would normally be considered Egyptian

science, starting with the intricate question of calendars. Well-known

10 A selection of hymns constitute Document II.7; Documents II.8 and II.11 areexcerp ted from texts that reflect the continu ing p opu larity of spells and m agic (the4th c. BC Book of Knowing the Creations of Re and the Felling of Apep, and the N ewKingdom Harris Magical Papyrus). The former excerpt, however, is essentiallya piece of descriptive theology, w hile the latter consists of hym ns.

The Mesopotamian record provides an interesting parallel to the Egyptianliterarization of hym ns: hymns (and proverbs) are written d own for the first timein the Fara period (26th c. BC), precisely when scribes turn up in the sources asa p articular (and very self-conscious) craft d istinct from the m anagers of tem ple

estates, at the turn from very restricted to restricted literacy.

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is the civil calendar w ith a year of 12 months of 30 d ays each (subd ivid ed

into three ten-day weeks) and 5 extra epagomenal days 365 days in

total; almost as familiar is the notion that it was originally geared to the

heliacal rising of Sirius (Egyptian Sothis), and therefore begun in

42414238 BC or 27812778 BC (13211318 BC being obviou sly too late)11 throughout the Pharaonic p eriod, the Sothic year determined by this

heliacal rising remained very close to 365.25 days, for which reason the

app earance of Sirius is delayed by one d ay every four years with regard

to the civil calendar (so, approximately, are the yearly flooding and the

seasons). Clagett presents the wh ole discussion since Edu ard Meyer

exposed the details of the calendar in 1904 and opted (in agreement with

the accepted Egyptian chronology of his tim es) for the earliest date. Clagett

espouses Neugebauers arguments [II:31f]:12 Observations made over a

single year will reveal that an astronomical, i.e., lunar, month is 29 days

as often as 30, and the observations of 40 years will demonstrate these to

fall 10 days short of the Sirius rising; measured w ith an astronom ical gauge,

the civil year is so crude that this cannot be its origin. If the origin is

agricultural, however, 365 days will result automatically from averaging

over a coup le of decades the time between successive Nile flood ings; on

the other hand , only observation of this quite irregular ph enomenon m ad eover several centuries would allow significantly higher precision. Even

the structure of three seasons (inu nd ation emergen ce [of agricultural

land, and sowing] low water/ harvest) is obviously agricultural in

reference and highly u nlikely to be astronom ical in origin (if fitted to on e

solstice or equinox, any u niform three-season scheme w ill by necessity miss

the other). The year of 365 days an d an ad ministrative month of 30 days

are likely to have been adopted around the beginning of D.1 (around or

11 Bernard Grun, The Time-Tables of History, (Lond on: Tham es and H ud son, 1975),indeed tells 4241 BC to be the first exactly dated year in history on this account!

12 Since Meyer s version is still widely accepted outside the circle of narrowspecialists, they d eserve to be repeated. Neu gebauer s full d iscussion is foun d inDie Bedeutungslosigkeit der Sothisperiodefr die lteste gyptische Chronologie,

Acta Orientalia17 (1938), 169195, and The Origin of the Egyptian calend ar, Journalof Near Eastern Studies 1 (1942), 396403; both are reprinted in N eugebauer,

A stronomy and Hist ory, pp. 169203. New York etc.: Springer, 1983.

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slightly before 3000 BC), the form er in the belief that it fitted the agricultural

year; as the d iscrepancy between th e behaviour of the Nile and this year

became too obvious, the Sothis rising as harbinger of the flooding was

introduced as the official beginning of the year around 2780 BC, and

remained so in terminology even w hen obviously not so in fact. Since theearliest plau sible evid ence for the u se of a year of exactly 365 days is from

late D.4 (c. 2470 BC) and the earliest definite proofs from early D.5 (c.

2440 BC) [II:28f], to be certain abou t these conclusions would be foolhard y,

since w e h ave piled conjecture u pon conjecture [II:33].13

As a parallel show ing that a 30-d ays mon th introduced for administra-

tive p ur poses is conceivable, Neu gebauer pointed to the later p ractice of

Babylonia. It is worth ad ding that this Mesopotamian administrative m onth,

kept w ell apart from the norm al lunar m onth, has now been follow ed back

to the Jemdet Nasr period, i.e., to the late fourth millennium BC.14 This

is exactly the phase where elements of Mesopotamian culture (certain

characteristic artistic motifs, certain features of temple architecture, perhap s

some basic ideas about writing that served the development of extant

Egyptian m arks into a rud imentary script) and even some Mesopotamian

13 A postscript, A Petroglyph Discovered at Nekh en w ith Possible AstronomicalSignificance [II:497506], contains a paper by James O. Mills about a probablyPredynastic graffito from u pp er Egypt. Along w ith other marks, a nu mber incisionsarranged in an arc might (thus Mills) record the changing direction of sunset orsunrise; ifthe rock in w hich the gra ffito is encarved has been rotated by som e 10,one of the extreme incisions w as originally in the direction of winter solstice su nset;Mills asserts (with Clagetts polite consent) that this would constitute evidence that

the Predyn astic Egyptians knew about the 365 days year; the reviewer would object,firstly, that Neu gebauers argum ent against an astronomical origin of this year holdseven in th is case; second ly, that no necessary (nor just p lausible) link exists betw eenthe observation of extreme azimuth s and the counting of days. Azimuth observa-tions, heliacal risings and similar phenomena are in fact alternatives that allowcultures without a fixed calendar to predict the arrival of the new season. Thus,e.g., Hesiod, Works and days, verse 383f, in Paul Mazon (ed., trans.), Hsiode, p.100 (Paris: Les Belles Lettres, 1928).

14 See Robert K. Englu nd , Adm inistrative Timekeeping in An cient Mesop otam ia.

Journal of the Economic and Social Hist ory of the Orient 31 (1988), 121185.

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artefacts (cylind er seals, ceram ic vessels) turn up in Egypt.15 Administra-

tive needs being perhaps analogous,16 independent invention of a

counterfactual month remains a possibility; but the possibility of borrow ing

from a culture with wh ich D.1 Egyp t was in dem onstrable contact supp orts

Neugebauers idea.Older than the civil calend ar is a lun ar calend ar, w hose traces are found

in the sequences of temp le festivals, and w hich remained in use as liturgical

year. According to Richard A. Parker, it intercalated an extra month in the

year w henever the Sothic rising took p lace w ithin the last 11 d ays of the

year; Clagett scrutinizes the sources on wh ich th is elaborate theory is built,

and concludes that Parkers opinion that the old lunar calendar was

intercalary m ay be correct (though not certainly so), but th at (1) the use

of the Sothic heliacal rising, that (2) the intercalary month (if it existed)

was nam ed Thoth, and that (3) the lunar calend ar in schematized form

is that given in the Ebers calendar and in the astronomical ceilings of

Senmuts tomb and the Ramesseum 17 are all unproved and indeed

untenable [II:21f].

A later lunar calendar is described in a papyrus from AD 144 or later

(P. Carlsberg 9); as Clagett quotes Parker, it is the only tru ly math ematical

astronomical Egyptian text yet pu blished [II:23f].18

The papyrus istranslated and further d iscussed as Docum ent III.9; it d escribes a 25 years

15 B. G. Trigger, The Rise of Egyp tian Civilization, in B. G. Trigger et al., AncientEgypt. A Social History , 170, here 36f (Cambrid ge: Cambridge University Press,1983).

16 Perhaps analogous, but hardly the same. In proto-literate Mesopotamia, the30-days calend ar wa s used to determ ine fod d er rations for animals (and w orkers?)

within a h ighly bu reaucratic economy ; the bienn ial coun ting of the Wealth of theLand (introduced moreover during D.2, it seems) suggests nothing similar.

17 The Ebers Calendar and the astronomical ceilings are among the documentstranslated and discussed later in the volume.

18 Evidently, this assertion is only true if Egyptian means in the tradition ofPharaonic Egypt, allowing us to exclud e not only the Almagestbut also m aterialof pu rely Babylonian origin; but this exclusion remains Clagetts sen sible choice,which also allow s him to leave out th e late astrological texts, mainly based as they

are on Greco-Babylonian syncretism cf. [II.129].

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intercalation cycle, wh ich makes the lunar year agree w ith the Egyptian

civil year w ith an error of only 1 d ay in c. 500 years. As it tu rns out, the

most likely time for the construction of the cycle is 357 BC. It thu s anted ates

the Macedonian conqu est an d the establishmen t of H ellenistic scientists

in Egypt; the basic idea is likely to have been borrowed from Babylonia(Egypt was under Achaemenid rule from 525 to 404 BC, and again from

343 to 332 BC), and schematic intercalation was used in Babylonia well

before that), but the terminology of the schem e is purely Egyp tian and thu s

evidence that the idea was fully naturalized. Only Egyptians (not even

foreign conquerors of Egypt) are also likely to have encountered the

problem of fitting together the Egyptian liturgical year an d the Egyptian

civil year.

The last year treated in the volum e is a conjecture: the fixed Sothic year

of 365.25 days, w hich in the op inion of man y Egyptologists mu st have been

known to and used by the Egyptians. Clagett discusses the purported

evidence (much of it is in Documents III.2 and III.10), and argues con-

vincingly that ability to predict when the actual Sothic rising would take

place in given year (almost self-evident, and w ell documen ted thou gh w ith

un know n p recision since the Mid dle Kingd om) d oes not entail the use of

a corresponding year; nor does the wording of the Decree of Canopus[II:326329], an abortive attem pt to chan ge the length of the civil year into

365.25 days, suggest that such a calender already existed.

Clocks are of three very d ifferent kind s: star clocks, w ater clocks, and

sundials. Star clocks can be followed from D.910, and are likely to be an

Old Kingdom invention they are rendered though defectively on coffin

lids, and the un derlying system h as been d eciphered by N eugebauer an d

Parker. In the D.912 version, they make use of a set of stars or groups

of stars (the decans) whose heliacal risings fall in the beginning of the36 weeks of the civil calend ar (with some fur ther comp lication d ue to

the epagom enal days, and an au tomatic outd ating because of the d iscrep-

ancy betw een the civil and th e sid ereal year); ifall decans had h ad the same

latitude (which was not the case), their longitudes would thus differ by

c. 10. The first h our lasted from the beginning of comp lete d arkness to

the next rise of a decan; the following ten hou rs w ere marked by successive

decanal risings; the remaining time to the beginning of dusk counted as

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a tw elfth h our. At the beginning of a week, the first 11 hour s wou ld thus

be approximately equal; around summer solstice, even the twelfth hour

wou ld not be very different at the first d ay of a week; around winter

solstice, it would be very much longer (and obviously so even to an

Egyptian stargazer, wh o w ould observe the r ise of several extra d ecans);the hours of the Old Kingdom night were thus neither seasonal hours

nor equinoctial hours, nor were they meant to be equal divisions of the

period of darkness of the actual night; they marked stations of the Sun

du ring its nocturn al voyage through th e Netherw orld, and constituted n o

metrology. Correspond ingly, hou rs w ere originally only d ivisions of the

night (corresponding, we may assume, to particular liturgical duties19);

only later wou ld the d ay be d ivid ed by analogy in its own 12 hou rs [II:49].

That the copies of the decanal clocks on coffin lids are imperfect is

cogently explained by Clagett by their funeral purp ose: these clocks were

not actual aids for observation but symbolic [II.56]. The acceptance of

unequal hours may be seen in the same light: if certain acts had to be

performed at hou rs d efined by the rise of decans, equal d ivision w ould

be a pointless and pedantic Verschlimmbesserung. Within the religious

sph ere, tru th is sym bolic and hen ce a matter of acceptance and consensus.

A characteristic form ulation d ue to a Muslim trad itional scholar regard ingthe direction of prayer w as reported by David King (personal com m unica-

tion): When the Proph et was in Medina, he prayed toward the South; wh at

w as good enou gh for the Prophet is good en ough for me [even if I hap pen

to live in the Magh reb]!. Islam had no needfor mathematicians who might

determine the astronomically correct prayer direction (pace numerous

historians of mathem atics); but it m ight serve as a p retext for math ema-

tician s like al-Khw arizm who wanted to be useful to their community.20

There is thu s no reason to be aston ished by that lack of care for horologicalprecision which Clagett shows to persist until the end (without being

19 The earliest extant description of the duties of the stargazer tells these to beattending to the guiding (or introduction) of festivals and giving all people theirhours (6th c. BC, quoted [II:491]).

20 The traditional scholars w ere not imp ressed: David King has found only one

medieval mosque with astronomically determined orientation (in Fatimid Egypt).

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astonished), nor a fortiori to be scand alized as Borchard t in wh at Clagett

characterizes as a patronizing and distasteful remark [II:423] about the

Egyptian failure to und erstan d that tim e is money. The interesting p roblem

is rather to understand why a certain interest in precision did develop after

all; professionalization of stargazer p riests (hour-watchers, as they w erecalled until Ptolemaic times [II:58]) and their environment seems to be

the answer (cf. below on Am enem het), rath er than techn ological needs like

the determination of w orking time (as seen in late third millennium

Mesopotamia).

A first adjustment seems to have taken place during late D.12 [II:56].

At that moment the original decan system will have gone so much out

of phase that m any decans m ay have been invisible du ring the m onth

w here they were m eant to wor k; revision in this situation will hav e been

compulsory even for religious purposes. At the same time, however, a

rather different system had developed, making use of meridian transits

instead of heliacal risings; because of the different latitude of the old

decans, most of the decans had to be, and were indeed replaced: stars

w hose heliacal risings differ by 10 days (or wh ose risings du ring the sam e

night differ by 40 minutes) may well culminate at the same time, perhaps

even in reverse order. The introd uction of this new system thu s representsa fairly rad ical break with the trad ition, and presup poses the constru ction

of a new canon based on fresh observations. The same holds for the

Ramesside star clock dep icted in royal tombs from D.19 but ap parently

constructed around 1470 BC. H ere, the year is d ivided into half-months

instead of weeks; the beginning of each hour is determined by the

passage of a par ticular star over one of seven lines, of which the central

one is the meridian.21 The whole period of darkness is thus, it seems,

21 The seven lines is an interpretation thou gh su pp orted by the draw n d iagrams:the verbal text tells that the star is on the left shou lder, on th e left ear, op p ositethe heart [i.e., central], etc. There has been some discussion of the actualtechnique whether a string frame was used or the stargazer was actuallyconfronting a partner (or a statue); both possibilities are suggested by the tombcopies of the clocks [Fig. III.19ab]; a th ird in terp retation, p rop osed by E. M. Bru ins,is analyzed [II:145f] and in the en d characterized as su rely [...] a p erverse theory.

It may be ad ded that the Egyptian canonical system for representing the

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meant to be d ivided equally an d w ith fair precision (as far as it could be

calibrated by means of a water clock, we may assume). Once again the

inherited system is thus broken up and reorganized empirically.

By 1470 BC, outflow w ater clocks w ere already well-know n, and they

are likely to have been used for calibrating the Ram essid e star clock. Likethe Babylonian water clocks, the early Egyptian specimens are of the

outflow type; but w hereas the Babylonian clocks m easured the w eight of

water that had flown out (which would permit a periodical refilling in

order to keep the w ater level app roximately constant w hether it was don e

we d o not know ), the Egyptian specimens measure the w ater level; in order

to compensate for the decrease of the outflow w ith decreasing water height,

they were shaped as inverted truncated cones (flower pots), and not

meant to run empty one, found in Karnak and constructed in the early

14th c. BC, is discussed in detail [II:66ff] and depicted. Clagett, following

earlier w orkers, discusses w hether its slope is optimal and conclud es with

Borchard t from the m athem atical mod el used in a ll d iscussions of ancient

w ater clocks that the w alls shou ld h ave been somew hat steep er [II:76]. As

a run-away physicist, the reviewer w ill observe that this model presup poses

that energy losses d ue to su rface tension and the effects of ad hesion can

be neglected; this is a reasonable assum ption a s long as the w ater leavesin a jet, bu t certainly no longer w hen it starts dr ipp ing (as d oes the Karn ak

clock, see [II:69]). Surface tension w ill slow d ow n the outflow, to an extent

that depends on adhesion effects and the actual geometry of the orifice;

only emp irical tests can d ecide w hether the Egyptian clock w as better than

the one p roposed by the mathematical mod el.22

hu man body (etc.) mad e essential and standard ized use of square grids cf. ErikIversen, Canon and Proportion in Egyptian Art. (Warm inster, England : Aris & Phillips,21975; 11955). In itself, metaphorical use of parts of the human body for theirpositions within a grid is thus not excluded.

22 To the objection that this is unlikely or would at best be accidental, since theEgyptians had no means of determining whether their hours were equal or not(R. W. Sloley, quoted [II:70], but an oft-repeated claim) it may be replied that theyhad : another w ater clock w hich was refilled after the lapse of one h our. Whetherthe interest of some clock bu ild er in precision w as large enough to inspire this idea

is a d ifferent qu estion.

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The Karnak clock contains several scales corresponding to months of

d ifferent lengths; the m onth nam es on the scales are about on e mon th off,

which means that the clock was copied from an earlier specimen from

around 1500 BC. This date corresponds to a very interesting text included

as Document III.15: the funerary autobiography of Amenemhet, a highofficial of the late 16th c. BC w ho, w hile read ing in all of the books of the

divine w ord found that the longest n ight w as 14 if the shortest was 12

hours [II:459]; Clagett suggests in a note that the 14 be understood as

fingers in a water clock and not as a number of some universal time

unit certainly justified, since even the winter night is divided into 12

hou rs in the correspond ing water clocks. He also tells of having constru cted

a water clock with corresponding scales in honour of King Amenhotep

I Never was made the like of it since the beginning of time. The

somewh at op aqu e final passage seems to claim that it was p recise for all

seasons. As m entioned above, never ... since the beginning of time w as

a comm onp lace, and therefore not necessarily to be taken to the letter; nor

is it quite clear how much of Amenemhets discovery was made in books

and on the scales of existing water clocks and how much by his own

observation; in any case it is obvious that the constru ction of a w ater clock

at least as precise as anything kn own w as an object of pride, and that theclock itself was w orth being offered to the king; since the text still speaks

of night h ours on ly, insp iration from n on-liturgical (or non -astronomical)

time measurement seems absent.

The Karnak clock assumes the change of the length of night to be

uniform from solstice to solstice in the id iom u sed to d iscuss Babylon ian

astronom y, it constitutes a zigzag-function (which shou ld not be taken as

evidence of a borrowing, cf. note 25). Fragments of clocks from the

Hellenistic period shows that the quest for increasing regularizationcontinued [II:73f]: they p ut the shortest night at 11, the equinoctial night

at 12 and the longest at 13, and make the increases and not the lengths

follow a zigzag function; this is a second -order approxima tion and should

be better but since the true ratio is rather 14:10, the method behind the

supposed improvement is obviously bookish a rational reconstruction

and not empirical.

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A pap yru s from Oxyrynchus (third c. CE) reveals something about the

kind of books that are likely to have inspired this reconstruction [II:75f].

It comp utes the volumes of w ater correspond ing to su ccessive hour s; for

this it assum es the volum e of a trun cated cone to be the m id-cross-section

times the height; the area of a circle to be 1/ 4arcdiameter; and the arcto be 3 diameters. All three formula are used in that Near Eastern

practitioners tradition which is reflected in the practical geometry of the

Old Babylonian school; taken singly, each of the three formulae would

prove nothing; but their occur rence together leaves n o reasonable d oubt

about the inspiration for the computation.

During the Hellenistic period,23 inflow w ater clocks also begin to tu rn

up ; once again, they should be better in theory than the outflow type, and

may have been believed to be so, since they provide th e obvious answ er

to the problem of un equal flow of w hich the Egyptians were d emonstrably

aware. Once again, however, no real improvement is obtained [II:78f];

firstly, the old 14:12 ratio is conserved; second ly, the only preserved

specim en has misun d erstood the zigzag principle and m akes the increases

follow an inverse zigzag-function.

Daytime, originally including twilights, was divided by analogy into

12 hours, which were measured by two types of instruments. So-calledshad ow clocks m ay be referred to alread y in a Midd le Kingdom text, but

the oldest specimen is from c. 1450 BC. They measure the length of the

shadow, more precisely the east-west component of that shadow.24 A

description from c. 1300 BC (Document III.16, [II:465f], cf. [II:84f]) shows

that the d ivision points of the scale are found by mean s of a mathem atical

construction, not empirically (their distances decrease un iformly25).

N othing in the description nor in the incomp lete specimen s that have been

23 Clagett analyses the interp retation of a temp le d ecoration pu rp orted ly ind icatingthe u se of inflow clocks alread y du ring D.18 (mid-third m illennium BC) and sh owsthat it is entirely fanciful [II:82f].

24 Other types were developed in the late period [II:9395].

25 That is, they follow a zigzag function, and the positions themselves thu s thesum mation of such a functions; there is hence no need w hatsoever to ascribe theuse of second -order app roximations in the Hellenistic water clocks to Mesopotam ian

inspiration.

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foun d suggests a correction for the changing length of the d ay. Nor w as

there any obvious need for such a correction with four marks before noon

and four after n oon the m odel wou ld automatically ensure that the day

had 12 hours; one before sunrise, one between su nrise and the first m ark,

etc. Clagett describes how the m odel could be equipp ed so as to p rodu ceequal hours [II:91] by means of a device suggested by Borchardt. He

comm ents, how ever, that one cannot emph asize too strongly [...] that there

is no actual evidence that su ch a bevelled crossbar w as used , and I susp ect

that the apparent ind ifference of the an cient Egyptians to the exact divisions

into equal hours of any of their clocks makes their use of this device

unlikely;26 he has more immediate sympathy for a device by which

Bru ins wou ld take the seasonal variation of the solar height into consider-

ation, but points out that this is the most coherent of the translations but

is the one which has been most widely altered from what can be read in

the text, and politely rem ind[s] the read er that it is not always p ru d ent

to correct the text to fit the readers fancy [II:467].

Even sundials, registering the direction of the shadow of a horizontal

gnom on on a v ertical surface, can equally be traced to the New Kingd om,

the oldest being from c. 1220 BC. In this specimen, the angles between hou r

lines change so irregularly that it is not even worth discussing whetherit attempted to measure equal hours but like the shadow clocks, the

model ensures that the day (here, from sunrise to sunset, since such are

the divisions) would always be of 12 hours. An apparently Hellenistic

specimen (with the Egyptian month names given in Greek) is precise

enou gh to allow analysis, and reveals itself to be another a-pr iori construc-

tion whatever the season, morning and evening h ours are too long, and

noon h ours too short, as shown in a d rawing borrowed from Borchardt

[Fig. III.57].As pointed out by Clagett [II:98], the many attempts at improvement

and app arent systematization to wh ich comes also attemp ts to d escribe

the changing lengths of day and night in terms of a scheme of 24 equal

26 The reviewers immediate impression was that Borchardts invention was of kindthat might be expected in 18th-c. instrument making: ingenious yet simple, and

in need of trigonometric calibration.

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hours [II:98106] did not entail any theoretical unification; apart from

the probable use of water clocks to calibrate the Ramesside star clock, no

use seems to have been made of the fact that the different devices measured

the same thing (as revealed by the independ ent a-priori constru ctions used

in the different techniques). In an ad-hoc distinction, we may say thatprogress was mainly technological in character (as cars, railways and

airplanes may be imp roved ind epend ently of each other, even thou gh all

provide transportation), not oriented toward theoretical unification into a

single coherent metrology. It is characteristic that a 3d-c. BC description

of the d uties of an astronomer (d ocum ent III.18) still specifies that he is

one who divides the hours of the two times (i.e., day as well as night)

[II:495].

Astronomy is the last topic of Volume Two, which more specifically

deals with the description of the heaven and the ideas about the movem ent

of the stars when they were invisible. In agreement with this, Clagett often

reminds the reader that an Egyptian astronomer was actually a

stargazer. The main material, apart from the decanal clocks, is constituted

by the astron omical ceilings of tom bs and ceilings and similar d ocum ents,

wh ere the arran gement of the various astronomical elements d eveloped

into an almost standard form that we can with some looseness call theAncient Egyptian Celestial Diagram while recognizing that there are

about six families of the standard form [II:108]. To this standard diagram

comes from 200 BC onwards rectangular, elliptic and circular zodiacs, in

which elements of Greco-Babylonian and direct Babylonian origin are

integrated with traditional Egyptian constellations and with yet another

kind of decans, which have lost any actual function and represent the

deities of the dual year, the combined lunar-civil year (Neugebauer &

Parker, quoted [II:476]).27The star diagrams are, precisely, diagrams and not maps; as Clagett

formulates (observing that the Zodiacs are not even that but decorational

and reverential), they are elements th at w ould be astronomically useful

to the deceased in his life in the Otherworld [II:479], collecting the

27 They are thus not identical with the decans that entered Greek and later

astrology, which are 10-divisions of the Zodiacal signs.

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timetelling decanal stars in one half of the ceiling and the useless

circumpolar constellations in the other. But no faithfulness was aimed at

(nor achieved!) that w ould allow u s to identify m ore than a few of the stars

they contain.

One of the theological treatises of Section II, we remember, told thenocturnal voyage of the sungod Re through that Otherworld which after

the Old Kingd om became a N etherw orld on ly. The d escription of the transit

decanal clock contained in the Book of Nut (Document III.12, cf. [II:57f])

and the d ram atic text in Seti Is cenotap h (Docum ent III.13) also tell that

the decanal stars, like Sirius, spend 70 days in the Netherworld (the time

wh ere they are below the horizon d uring n ight, as we w ould say); then,

for 80 d ays, they rise before d awn but do not culminate before coming

invisible; d uring th e ensu ing 120 days they w ork, i.e., serve to mark th e

hou r by their culmination. During 90 days they h ave alread y culminated

before sunset; w hen these are finished, they d ie again an d go the N ether-

world.

This might seem, if not modern then at least Ptolemaic the Sun

and the stars pass the visible heaven and then go below the Earth; bu t this

is a misunderstanding, as explained in the dramatic text: the stars go

to the Netherworld as other persons who die; but they do so for 70consecutive days, not every night. And the heav en, of course, is no sphere

surround ing the Earth but the Godd ess N ut standing on h er hands and

feet, head toward the west and hind par t in the east, a sow w ho eats her

piglets [II:399]. This name she has deserved because she swallows the

Sun and the setting stars, who then pass through her body (above their

visible path) and are reborn in the east. Clagett tells [II:396] that he has

includ ed this text, essentially myth ological in character and content an d

lacking all but trivial astronom ical d etail, in a volum e d evoted largelyto technical d etail in ord er to un d erline once m ore that such scientific

know ledge that the ancient Egyptians acquired w as p resented integrally

with religion, myth, and magic, and that that knowledge has been

tran smitted to us almost exclusively in religiou s docum ents. We may ad d,

however, that the very content of the document, the topographic visualiz-

ation of the movement of the heavenly bodies, shows that there was no

easy transformation of this world picture into one presup posing a heavenly

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sphere. The Egyptian star diagrams fit their topographical imagination;

star maps as w e know th em from the Ptolem aic Midd le Ages (not to speak

of star globes) are meaningless in this context.

In conclusion we may observe that Clagett has produced two richvolumes which differ from much history of Egyptian science by taking

Egyp tology seriously, as an integrated stud y of Egyptian culture. But their

fund am ental app roach also differs from that of mu ch Egyp tology in a w ay

that can only please a historian. In the w ord s of a group of highly inform ed

insiders,

Ancient Egyp t has proved remarkably resistant to the writing of history whichis not traditional in character; which is not, in other word s, concerned p rimarilywith the ordering of kings and the chron icling of their d eeds. [....] For one thing,the very completeness of the chronological listing of kings which severalgenerations of mod ern scholars have given u s creates an image of knowledgein detail which other kinds of evidence cannot match. The abundance of royalart an d architecture comp oun ds the p roblem w ith an illusion of familiarity.28

This illusion of familiarity reflects itself in the default theory that

everything w hose later origin cannot be dem onstrated w ill go back at least

to the early Old Kingdom. In one recent formulation,

Il convient de rappeler que ce que lon connaissait au Moyen Empire tait unsavoir labore bien ava nt, prob ablement d s le dbu t d e lAncien Emp ire. Cesavoir vnrable se retrouve intact pendant toute lhistoire gyptienne, jusquedan s les pap yrus grecs d e lpoqu e byzantine, sans changem ent ni am liorationnotables, comm e le p rouve le p apyrus dAkhmim.29

28 B. G. Trigger et al, Ancient Egypt, xi (note 15).

29 Sylvia Couchoud, Mathmatiques gyptiennes. Recherches sur les connaissancesmathmatiques de lgypte pharaonique, 11 (Paris: Le Lopard dOr, 1993). Thisformulation is extreme, it is true, since the Papyrus Akhmm does bear witnessto considerable change though w ithin a rather stable framew ork, and because themod est pu blished material ind icates that the unit fraction system with its strict canonwas notdeveloped in the late Old Kingd om (according to a personal commu nicationfrom Jim Ritter, u np ub lished ma terial proves th is defin itely). But similar ideas areexpressed by scholars of high standing thu s Walther Friedrich Reineke, Gedan kenzum vermutlichen Alter d er mathematischen Kenntnisse im alten gypten.

Zeitschrift fr gypt ische Sprache und A ltertumskunde 105 (1978), 6776.

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Withou t being polemical, Clagett points to several instances of this same

peren nializing presu pposition e.g. [I:495f] when it w as conclud ed from

the unspecific words of the D.25 Memphite Theology (viz that it was

copied from a worm-eaten original) that the original composition was

w ritten either in Archaic times or at least no later than the Old Kingd om.As it should be clear from the preceding pages, Clagetts own approach

is w holly different: he d oes not d eny the existence of that continu ity which

gives sense to the whole project of describing three millennia of ancient

Egyptian science; but as a true historian he tries to characterize it in its

relation to, and interplay w ith the actual intellectual prod ucts w hich grew

out of this soil, neither postulating continuity to be self-evident nor

id entifying the quasi-perennial soil w ith the changing crop.

24