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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