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I Can See the Ellipsoid from the Inside: Girtonian Responses to Francis Galton’s Survey on Mental Imagery

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Notes

  1. Galton published his findings between 1880 and 1883 in Nature [13], Journal of the Anthropological Institute [14], Mind [15], Fortnightly Review [16], Proceedings of the Royal Institution of Great Britain [17], and finally his own monograph [18, 19].

  2. Galton further extended the results of his questionnaire to hypothesize about differences between “races,” speculating that the French “are able to foresee effects with unusual clearness”; singling out the “much underrated Bushmen of South Africa” whose drawings of animals suggest that “the artist had a clear image in his mind’s eye of what he was about to draw, and was able, in some degree, to project it”; and finally noting that “the Eskimos are geographers by instinct, and appear to see vast tracts of country mapped out in their heads.” Galton’s conception of racial difference is such that he drew conclusions about those outside of England based solely on their external production without any documented knowledge of their corresponding mental processes.

  3. All extant correspondence and completed surveys on mental imagery have been digitized by University College London and are available for public perusal through their digital collections (https://digital-collections.ucl.ac.uk/).

  4. Further information on the Mathematical Tripos in the nineteenth century can be found in [4, 8, 38].

  5. Remarkably, Scott’s survey response for Galton is dated January 23, 1880—the final day of the examination.

  6. Marks’s early life is documented in detail in the biography Hertha Ayrton: A Memoir, by Evelyn Sharp.

  7. The Natural Sciences Tripos had been inaugurated in 1851. Herschel’s duties as science mistress involved directing the college’s new chemical laboratory and teaching “elementary mathematics to some students who came up wholly unprepared for taking the mathematics in the Little Go Exam” [27]. The “Little Go” was the name for the previous examination at Cambridge that tested elementary mathematics, Latin, and ancient Greek. In the 1870s and 1880s, Girton College students were expected to take the exam as a “compulsory matriculation requirement for all degree candidates” [37, p. 31].

  8. The arithmetical lessons that Sir John Herschel gave to his older daughters are available at the Harry Ransom Center of the University of Texas at Austin and might shed further light on what Constance studied.

  9. On the profligate use of paper by students studying for the Tripos, see [38, p. 132].

  10. The Irish mathematician George Salmon (1819–1904) was the author of the popular textbook A Treatise on Conic Sections.

  11. See, for instance, [30].

  12. Isabella’s letter is also quoted by Burbridge, who identifies in a footnote that Isabella was “probably one of the many daughters of Sir John Herschel” [6, footnote 74]. Isabella (1831–1893) played a substantial role in organizing and copying the family papers (see the Herschel family papers at the Harry Ransom Center at the University of Texas).

  13. Bain founded the journal Mind in 1876.

  14. As historian Ruth Cowan recounts, by 1885, Galton had “long since forgotten all the formulas for the conic sections” and wrote to J. D. Hamilton Dickson, a tutor at Cambridge, regarding fitting an ellipse to his data [7, p. 523].

  15. Contemporary researchers note that any observed effects are actually gender differences, “because in the vast majority of studies comparing the use of mental imagery in men and women the participants are categorized on the basis of their outward appearance and behaviour rather than on the basis of their biological characteristics” [31, p. 271].

  16. Before he was Hertha Ayrton’s husband, William E. Ayrton wrote to Galton on March 4, 1880, with a brief description of his own training in mathematics:

    To the present day I can remember on what part of the blackboard at University College the late Prof. De Morgan wrote down certain equations, and certainly some portion of my success as a mathematical student arose from my diagrammatically collating in my note-books mathematical proofs [2].

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Years Ago features essays by historians and mathematicians that take us back in time. Whether addressing special topics or general trends, individual mathematicians or “schools,” the idea is always the same: to shed new light on the mathematics of the past. Submissions are welcome. They should be uploaded to http://tmin.edmgr.com.

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Lorenat, J. I Can See the Ellipsoid from the Inside: Girtonian Responses to Francis Galton’s Survey on Mental Imagery. Math Intelligencer 44, 153–160 (2022). https://doi.org/10.1007/s00283-021-10131-4

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