School Daze:A Critical Review of the'African-American Baseline Essafor Science and Mathematics

WAlTER E ROWE

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These essays areriddled with pseudoscience

and pseudohistory. Theyshould not be used for thetraining of teachers or the

teaching 01 students.

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1II'IIe Iscllolarly' researcll displayed in .otllessays is too slloddy to serve as a .odel

for any teacller or student."

damental misunderstanding of the bio­logical relationships among the variousAfrican subpopulations. .

Even if it were true that the ancientEgyptians came from the same racialstock as sub-Saharan Africans, the dis­cussions of Egyptian science and mathe­matics in the "African-AmericanBaseline Essays" would still be worthlessfor the training ofpublic school teachers.Lumpkin's mathematics essay is merelyshoddy scholarship, while Adams's sci­ence essay unites pseudoscientific claimswith fanciful attempts at substantiation.

The science essay contains a num­ber of diagrams purporting to demon­strate the ancient Egyptians' extraordi­nary scientific and mathematicalsophistication. For example, Adamsreproduces as a full-page illustration asite plan of the Temple at Luxor with ahuman skeleton superimposed on it todemonstrate that the Egyptian archi­tects designed the temple so that itssubdivisions would conform to theproportions of the human body. A cur­sory glance at the diagram reveals thatwhile the skeleton's ankles and kneesdo indeed match crosswalls on theplan, none of the other joints (hips,wrists, elbows, or shoulders) corre­sponds to any significant feature of thetemple. That the builders intended acorrespondence between the templeand the human skeleton is renderedhighly unlikely by another fact: Theportion of the temple that is supposedto represent the cranium, rib cage,pelvis, and upper legs was built byAmenophis III; the remainder of thetemple was built by Ramses II, approx­imately two generations later (Bainesand Malek 1980).

Adams's science essay contains ahealthy dollop of Great Pyramid mys­ticism. According to Adams, the geom­etry of the Great Pyramid encodes asfollows:

the value of pi, the principle of thegolden section, the number of daysin the tropical year, the relativediameters of the earth at the equatorand the poles, and ratio metric [sic]distances of the planets from thesun, the approximate mean lengthof the earth's orbi t around the sun,the 26,OOO-year cycle of the

equinoxes, and the acceleration ofgravity.

One of the figures accompanying thescience essay also informs the readerthat the height of the Great Pyramidmultiplied by 109 yields 91,651,673miles, approximately the mean dis­tance from the earth to the sun.

This last assertion carries no weightas evidence that the Egyptians pos­sessed an unusual level of scientificknowledge. There is no reason to mul­tiply the pyramid height by 109 (otherthan to get the desired answer). If by

chance the height multiplied by somesimple factor did not give an approxi­mation of the mean distance from theearth to the sun, another multipliercertainly could have been found thatwould give the distance to the moon,to the nearest star, or to theAndromeda nebula. Writing the prod­uct to eight significant figures incor­rectly implies that the height of theGreat Pyramid is known with the sameprecision. Adams is evidently unfamil­iar with the concept of significant fig­ures (taught to high school physics andchemistry students).

Adams repeats a standard claim ofGreat Pyramid mysticism that the struc­ture encodes a number of mathematicalformulae. For example, the perimeter ofthe base divided by twice the heightsupposedly gives the value of pi (whichis 3.14159265). Indeed if one performsthis computation using the dimensionsof the Great Pyramid, one gets a goodestimate of pi (3.150685).

Pyramidologists like Adams charac­teristically restrict their attention to theGreat Pyramid and all but ignore otherEgyptian pyramids. Forty-seven royalpyramids are known to have existed.The heights and base dimensions of 22true pyramids belonging to this groupcan be determined with a reasonabledegree of accuracy (Baines and Malek1980). If these dimensions are used tocalculate pi, one obtains values ranging

SKEPTICAL INQUIRER • SEPTEMBER/OCTOBER 1995

from 2.58 to 4.42. Furthermore, thevalue of pi calculated from the dimen­sions of a pyramid depends on theslope of its sides. Extant Egyptianmathematical papyri reveal problemsdealing with the slopes of pyramidsand use four different values for theslopes (Gillings 1972).

In another section of the scienceessay Adams discusses what he calls"psychoenergetics," saying, "Theancient Egyptians were known theworld over as the masters of 'magic'(psi): precognition, psychokinesis,

remote viewing and other underdevel­oped human capabilities." Accordingto Adams, psi was an exact science thatwas used to preserve the world orderand protect the pharaoh. However, ifthe Egyptians were such powerfulmagicians, why were they conqueredby the Persians? Why were ten revoltsagainst the Ptolemies unsuccessful?

Adams subsequently informs read­ers that ancient Egyptian doctors werealso experts in the healing techniquenow known as Therapeutic Touch.Readers of SKEPTICAL INQUIRER willbe familiar with the unsubstantiatedclaims of the advocates of this fringemedical therapy. Adams is deeply con­fused about the distinction betweenscience and pseudoscience.

Adams also has a penchant for wildextrapolation from limited data. Hediscusses a small model of a bird foundin a tomb at Saqqara in 1898. When areplica of this model was made frombalsa wood and a horizontal stabilizer(not present in the original) added, thereplica was able to glide a short dis­tance (Messiha et al. 1984). However,balsa wood is roughly 20 times lessdense than the sycamore wood fromwhich the original artifact was made;consequently, the aerodynamic perfor­mance of the balsa wood replica wassignificantly different from that of theoriginal. From this incompetent exer­cise in experimental archaeology,

29

IITlte science anel lIIatltelllatics essays elistortflte Itistory of flte franslllission of Islalllicscience anel lIIafltelllafics fo Europe. II

Adams leaps to speculations about theancient Egyptians' use of transport andrecreational gliders. The articles thatAdams cites here were not written byprofessional Egyptologists.

Beatrice Lumpkin's treatment ofEgyptian mathematics is marginally bet­ter than Adams's discussion of Egyptianscience. It still violates the canons of his­torical scholarship in a number of ways.Lumpkin frequently cites her own fic­tional writings as authorities to substan­tiate her assertions. She also frequentlyomits facts, especially when those factsdo not support her conclusions.

For example, Lumpkin states thatthe Egyptian value of pi was betterthan the biblical or Mesopotamianvalue of pi equal to three. Nine esti­mates of the value of pi were calculatedbefore A.D. 1000 . Of these, the Egyp­tian value was the second most inaccu­rate (Beckmann 1971). The use of avalue of pi equivalent to 3.125 hasbeen found in a Babylonian cuneiform

tablet. This tablet is discussed inGeorge Sarton's A History of Science(1966), a source cited by Lumpkinelsewhere in her mathematics essay.

There are grounds for doubting thatthe Egyptians had an understanding ofthe concept of pi (Bunt et al. 1976).The Rhind mathematical papyrusshows how the Egyptians calculated thearea ofa circle from its diameter. To getthe area, 1/9 of the diameter is first cal­culated; this fraction is subtracted fromthe value of the diameter; and the resultis then squared. This is equivalent tousing a value of pi equal to 256/81.This procedure for calculating the areaof a circle appears to have been devel­oped empirically (Gillings 1972).

Beware of Greeks

When Adams and Lumpkin attempt todeal with later historical periods thanancient Egypt, their accuracy as histo-

30

rians should be better because Greekscience and mathematics are betterdocumented than Egyptian scienceand mathematics. Adams has difficultygetting even the most basic facts cor­rect about Alexander the Great andAlexandria:

In fact, the Greeks called Egypt theseat of scientific knowledge and sentmany of its [sic] most brilliant schol­ars there to study such as Thales,Dernocritus, and Pythagoras. Per­haps it was this reason Alexandermade Alexandria, Egypt, the capitalof his empire after he conqueredEgypt in 325 B.C.

Alexander did not make Alexandria thecapital of his empire. Alexander actuallynever saw the Alexandria to which hegave his name; he ruled from Babylonand Susa until his death. These factsare readily verifiable in the writings ofancient historians, such as Plutarchand Arrian. And contrary to the claimsof both Adams and Lumpkin,

Alexandria was not an Egyptian city. Itwas founded as a Greek colony and wasnot legally part of Egypt. In antiquity itwas commonly referred to as"Alexandria near Egypt" (Sarton 1966;Fraser 1972).

Adams's version of Egypt under therule of the Ptolemies is similarly a far­rago of misinformation:

Frequently, it is assumed that, dur­ing the Hellenistic period of Greekrule, the African character of Egyptwas negligible, however, to the con­trary, the Greeks practiced a policyof assimilation, marrying Egyptianwomen and even adopting Egyptianreligion.

All of this is demonstrably false. Therewas no such policy of assimilation. Infact, for many generations the Greeksin Egypt disapproved of marriages withnative Egyptians. It was also many gen­erations before native Egyptians held

SKEPTICAL INQUIRER • SEPTEMBER/OaOBER 1995

high government offices or militarycommands. The Greek and Mace­donian presence in Egypt has beencompared to that of the Boers in SouthAfrica and whites in the antebellumU.S. South (Bevan 1968; Lewis 1986).

The intellectual elite of Alexandriaduring the first century after the deathof Alexander-the most creative peri­od of Hellenistic mathematics and sci­ence-was composed almost exclusivelyof Macedonians and Greeks from out­side of Egypt. Manerho, the historianto whom we owe the division ofEgyptian history into dynasties, is theonly identifiable Egyptian intellectualduring this period (Sarton 1966; Fraser1972).

Beatrice Lumpkin fulminatesagainst the supposed racism of thewriters of mathematics textbooks:

Euclid of Alexandria, one of thegreatest mathematicians of this era,lived and died in Egypt. There is nosuggestion that he ever left Africa.Yet he is pictured in textbooks as afair European Greek, not as anEgyptian. We have no pictures ofthese mathematicians, but we couldat least visualize them honestly incostumes, complexions, and featurestrue to the peoples and their times.

It is highly improbable that Euclidwas a native Egyptian. He wrote inGreek and his name is a commonGreek one. This name was sufficientlycommon in antiquity that Euclid themathematician was confused with thephilosopher Euclid of Megara (Heath1926). It is also likely that Euclid livedfor a time in Athens. The mathematicalcommentator Proclus preserves a tradi­tion that Euclid was a Platonist(Morrow 1970). At the time of Euclidthe books of Plato had not yet begunto circulate widely, making it likelythat Euclid lived at some time inAthens and attended Plato's Academy.T. L. Heath, the leading expert onGreek mathematics and Euclid in par­ticular, believed that Euclid must havestudied at some time in Athens becauseit was only in Plato's Academy that hecould have learned the mathematicsthat later appeared in the Elements(Heath 1926).

IIAccorcling to AelalllS, psi \Vas an exact sciencefltat \Vas usecl to preserve flte \Vorlel orcler anel

protect flte pltaraolt."

Euclid's Elements is also firmly a

part of Greek mathematical traditions.

Three earlier Greek mathematicians

are known to have written similar ele­

ments of geometry (Morrow 1970).Significantly, one of these works was

the mathematics manual written by

Theudius of Magnesia for use byPlato's Academy (Heath 1926). Lump­

kin is glowing in her praise of theElements: "The logical arrangement of

this work is so masterful the Elementsdominated the teaching of geometryfor 2,000 years." The abstraction of theElements is Platonic, while the methodof exposition (definition, common

notion, postulate, and theorem) is

Aristotelian (Heath 1926; Bunt et al.

1976). The extant Egyptian mathe-

matical papyri have only the remotestsimilarity in form and content toEuclid's Elements.

Historians of mathematics consider

the Egyptian influence on Greek math­ematics to be minimal. This influence

was confined to the very elementarygeometry of the time of Thales, to

practical methods of calculation (the

branch of mathematics the Greeks

called "logistika") and to the proto­

algebra of Diophantus. The Greeks

borrowed much more heavily from themathematics of Mesopotamia (Heath

1921; Eves 1971; Fraser 1972).

Who Is Al-Khwarizmi and WhyIs He In 'African-AmericanBaseline Essays'?

Wnen she reaches the Middle Ages, the

period of Islamic mathematical domi­

nance, Beatrice Lumpkin enthuses: "In

summarizing the contribution of the

African Muslim mathematicians, espe­cially those ofthe Nile Valley, an authoris overwhelmed by an embarrassmentof riches." [Emphasis added.] The

"African-American Baseline Essays"section on mathematics discusses eightIslamic mathematicians: Al-Khwar­

izmT, Abu Karnil, ibn Yiinus, ibn al­

Haytharn, Omar Khayyam, Nasir

Eddin, Al-KashT, and Al Qasadi. Of

these, only Abu Karnil and ibn Yilnus

can be considered in any sense African.

Beyond his appellation as the

"Egyptian calculator," virtually noth­

ing is known ofAbu Karnil's life (Levey

1980). Ibn Yunus lived and worked in

Cairo in the tenth century (Goldstein

1965; King 1980). Of the remainingIslamic mathematicians, only ibn al­

Haytham had an association withAfrica. Ibn al-Haytham (known to

Europeans as Alhazen) was educated inBaghdad; he came to Egypt to partici­

pate in an unsuccessful project to dam

the Nile River (Vernet 1965; Sabra

1980; Hogendijk 1985).The origins of the remaInIng

Islamic mathematicians mentioned in

the mathematics essay are well known:

AI-Khwarizml-Urgench in formerUSSR (Berggren 1986).

Omar Khayyam-Nishapur (now inIran) (Berggren 1986).

Nasir Eddin-Khorasan in Persia(Eves 1971).

Al-Kashi-v-Kashan (90 miles northof Isfahan) (Berggren 1986).

AI-Qasadi-Granada (mathematicsbaseline essay).

Lumpkin and Adams get many ofthe facts about the lives and works of

Islamic mathematicians and scientistswrong. Both Lumpkin and Adamsmention the Dar al-Hikma (House of

Wisdom) established by the Fatimid

rulers of Egypt in Cairo. Both essayauthors have ibn al-Haytharn workingin the Dar al-Hikma; however, the

only institution in Cairo with which

ibn al-Haytham is known to have been

associated is the al-Azhar Mosque

(Sabra 1980). Lumpkin also describesibn Yiinus working in the Dar al­

Hikma. This is highly unlikely: The

Dar al-Hikma was founded in A.D.

1005; ibn Yiinus made his last astro­nomical observation in A.D. 1003; and

died in A.D. 1009 (Sourdel 1965; King

1980). The article on the Dar al­

Hikma in the Encyclopedia of Islam(Sourdel 1965) does not mention the

name of a single Islamic scientist Inconnection with the Dar al-Hikma.

SKEPTICAL INQUIRER • SEPTEMBER/OCTOBER 1995

The Transmission ofIslamic Mathematics andScience to Europe

The science and mathematics essaysdistort the history of the transmission

of Islamic science and mathematics to

Europe. According to both Adams and

Lumpkin, Europeans learned aboutEgyptian, Hindu, and Arabic mathe­matics and science through the transla­

tions of Constantinus Africanus (born

in Carthage in North Africa). As

Beatrice Lumpkin describes it, Con­

stantinus "brought a precious cargo of

manuscripts to Salerno, where a school

was founded to translate and study the

Arabic works." Characteristically,

Lumpkin neglects to tell readers whatmanuscripts he brought to Salerno.Adams is similarly uninformative. The

works that Constantinus Africanus

translated were the medical treatises of

Galen, Hippocrates, the Persian doctor

Haly Abbas, and the Jewish physician

Isaac Israeli (Castiglioni 1941; Crom­bie 1959).

Adams explicitly charges Europeanscientists with plagiarizing the discover­ies of Islamic scientists. For example, heasserts that ibn al-Haytham discovered

the refraction of light and that credit forthis discovery has been falsely ascribed

to Isaac Newton. Not unexpectedly,

Adams cites no authority for this extra­

ordinary statement. The mathematical

law governing the relation between the

angle of incidence and the angle ofrefraction is commonly known as Snell's

Law (after the seventeenth-centuryDutch physicist Willebrord Snell). Ibn

al-Haytham came close to discoveringthis law, but ultimately failed to do so(Al-Daffa' 1977).

According to Adams, Newton also

has been improperly credited with the

discovery of the law of gravity, saying it

actually was discovered by Al-Khazin,

Adams has confused Al-Khazin, a

Sabaean mathematician and astron-

31

orner of Persian ongln (Dold­Samplonius 1980), with al-Khazinf ,the author of the Book ofthe Balance ofWisdom. In mathematician al­Khazinf 's theory ofweights, the weightof a body varies according to its dis­tance from the center of the world.Accordingly, objects at the center ofthe world weigh nothing. This is a farcry from Newton's inverse square lawfor the force of gravity acting betweentwo masses. At this point, the readerwill probably not be surprised to learnthat al-KhazinI was actually aByzantine Greek (Hall 1980).

Adams also charges that the work ofthe astronomer al-Batrani' was stolenby Copernicus. Copernicus did indeeduse some of al-BattanI 's astronomicalobservations (Hartner 1980; Duncan1976); Copernicus clearly acknowl­edged this use. In Book One of On theRevolutions of the Heavenly SpheresCopernicus explicitly cites al-Battanfas the source of the erroneous estimatethat the sun's diameter is only ten timesthat of Venus (Duncan 1976).

Finally, Adams asserts that theworks of al-BlrunT were plundered byboth Galileo and Francis Bacon.Unless these Western scientists wereable to read Arabic (which is doubtful)they could scarcely have taken any oftheir ideas directly from his works.None of al-BlrunT's books were trans­lated in to European languages duringthe Middle Ages or the Renaissance.Many have never been so translated.Having been born south of the AralSea in Khwarizrn, al-Bi runf was notAfrican. There is irony in HunterHavelin Adams III invoking the nameofal-BTruni . In the words ofone biog­rapher, "BlrunI had a remarkablyopen mind, but his tolerance was notextended to the dilettante, the fool, orthe bigot" (Kennedy 1980).

Conclusion

The science and mathematics essays inthe "African-American BaselineEssays" are riddled with pseudoscienceand pseudohistory. As tools for thetraining of public school teachers theyare not merely worthless, but are likely

32

to prove pernICIOUS. Their fallaciousmodes of reasoning may dull the criti­cal faculties of readers. The "scholarly"research displayed in both essays is tooshoddy to serve as a model for anyteacher or student. The essays willcontribute to the growing tribalizationof American culture. A purported goalof the "African-American BaselineEssays" is to "eliminate personal andnational ethnocentrism so that oneunderstands that a specific culture isnot intrinsically superior or inferior toanother." This statement is nothingbut cant. Throughout the science andmathematics essays the genuineachievements of Greek, Arab, Persian,and European scientists and mathe­maticians are ruthlessly pillaged, andcredit for them assigned to blackAfrican cultures on the flimsiest ofgrounds.

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Berggren, J. L. 1986. Episodes in theMathematicsof Medieval Islam. New York: Springer­Verlag.

Bevan, Edwyn Robert. 1968. The House ofPtolemy: A History of Egypt Under thePtolemaic Dynasty. Chicago: Argonaut, Inc.,Publishers. (A reissue of the 1927 edition.)

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