Alfred North Whitehead (1861-1947) - was an English mathematician and philosopher. He is best known as the defining figure of the philosophical school known as process philosophy.
He corresponded with Thompson intermittently between 1906 and 1945.
D'Arcy's philosophical consideration of the Three Dimensional space
It is interesting to consider different ways Thompson thought about the world. His letter to Whitehead (ms20371) [in 1918] shows a more philosophical side of his thinking.
In the letter D'Arcy debated the definitions (and understanding) of Space and Dimensions. He questioned the three dimensional understanding of reality (i.e. if we were effected only by molecular forces, but not by gravity, we would know nothing about a vertical dimension).
D'Arcy said in the letter that he had considered the same question with Joseph Larmor and had asked him the question raised by Peter Guthrie Tait:
given a symmetrical individual in symmetrical space, how on earth could you ever teach him what right and left meant.
Larmor had answered this question of Thompson's :
If you fix a body in space by two points, it will always come back, at length, by rotation, to the same position as before.
However, D'Arcy was not satisfied with this answer. He had read about an elliptical space where this does not follow.
However, the archive does not contain Whitehead's answer to this letter, and it is not clear if there ever was one.
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Eric Harold Neville
Alfred North Whitehead