Ancient Egypt and Bad Math: Morton’s Research Ran Rife with Errors

This blog is based on text from Chapter 29 of my book, a pdf of which is posted on this webpage. Detailed footnotes and citations are presented in the pdf. The author does not support racism, eugenics, or even the existence of biologically distinct human races. However, to maintain historical accuracy, this blog uses outdated and sometimes offensive ethnic terms found in historic documents. No offense is intended.

Samuel George Morton’s Crania Aegyptiaca is a case study in his staggeringly bad employment of basic mathematics. Within Crania Aegyptiaca, Morton published the craniological measurements of a set of 100 skulls from Egypt, most of which were ancient Egyptians. Morton summarized his findings on these skulls in the table shown below.

Egypt Blog 1The above table contains a blatant error regarding the Semitic (or Arabic) skulls, three of which are from Thebes. According to Morton, the smallest of the three Semitic Thebans is 79 cubic inches, and the mean is also 79 cubic inches. This is mathematically impossible. Furthermore, four of the five means values presented in the sixth column do not actually generate the mean reported in the seventh column, which I shall call the second mean.
In 2011, I recalculated second means in the above table. Figure 2 below presents the means and second means reported by Morton in 1844 along with the corrected second means. This figure shows that four of the five second means reported by Morton were lower than they should have been. Morton’s Pelasgic Form, Semitic Form, and Negro Form were all incorrectly inflated by 3 cubic inches. Morton’s Egyptian Form was boosted up one inch.

Egypt Blog 2After I found the above-noted errors, I decided to recreate Morton’s 1844 Table using Morton’s raw data, which he published in Crania Aegyptiaca. The internal volumes of the 100 skulls he measured are included in a 15-page inventory within the book. Recreating this table was no simple task because Morton was not consistent with the terms he used to describe the ethnicity of the skulls he measured. For example, his Ethnographic Divisions Table (Figure 2) does not describe any skulls as being mixed race. However, on page 19 of Crania Aegyptiaca, he presented a table (Figure 3 below) describing five of his 100 skulls as mixed. My challenge was to find out to which Ethnographic Division these five mixed skulls were assigned within Morton’s Ethnographic Division Table.

Egypt Blog 3To complicate matters even more, the above table refers to mixed skulls, but the term mixed is not used in the 15-page inventory. Furthermore, on page 7 of Crania Aegyptiaca, Morton describes Skull No. 795 as “Egyptian blended with the Negroid form?” indicating that Morton regarded it as having mixed ethnicity. And yet on page 31, this same skull is included in a listing of “Egyptian Group” skulls. On page 8, Morton describes Skull No. 802 as “Egypto-Pelasgic Form,” but it is included in a list of “Pelasgic Group” skulls on page 30. Morton’s inconsistent definitions make his inventory and his tables unclear and confusing. However, I was able to deduce what skulls Morton measured and how he classified them by combining all the information presented in his 15-page inventory, along with tables on pages 19 and 21, and the listing of skulls in the Pelasgic, Egyptian, and Negroid Groups, found on pages 30 and 31. (I spent a few weeks just sorting out this Gordian knot, a testament to either my obsessiveness or thoroughness. Take your pick.)

Figure 4 shows a spreadsheet with all the information I gathered from the tables and text within Crania Aegyptiaca. The final column of Figure 4 presents the ethnicities I was able to deduce from Morton’s information. I was fortunate in that I was able to cross reference all of Morton’s lists and tables, and from them assign every mixed skull to one of the categories on Morton’s Ethnographic Divisions table. I cannot fathom why Morton published his information in such a convoluted manner. His organization system defies common sense. It was only with the aid of a computer datasheet that I was able to untangle it all, and finally account for each of his 100 skulls.

Egypt Blog 4aEgypt Blog 4b

Using the data listed in Figure 4 above, I re-created Morton’s Ethnographic Division Table as shown below in Figure 5.

Egypt Blog 5Ultimately, I was able to determine that Morton’s 1844 Ethnographic Tables contained 13 mathematical errors, as shown above in Figure 5. There are a total of 65 units of data (numbers) listed on this table. Thus, the 13 errors indicate that 20 percent of the information on this table is in error. Stanton (1960), Gould (1978), Michael (1988), and Lewes (2011) all failed to note the errors on this table, including the blatantly incorrect mean for the three Semitic skulls from Thebes. We all spent hours and hours gazing our eyeballs directly at Morton’s table and none of us noticed that the mean for the Semitic-Thebans was utterly impossible. That fact is somewhat distressing, and Lord knows I was as guilty as the rest. It is also distressing to realize that Morton, who was held in such high esteem by his colleagues, could have generated a table in which approximately one fifth of the data was in error.

There have been those who have argued that Morton’s craniological research is a diagnostic example of bias, unconscious bias, science correcting itself, or science failing to correct itself. To them, I would argue that his research is so flawed that it is not a good example of anything… save a man who did sloppy work.

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