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Number-Forms
99
the number is thought of. The form has no background, and is always seen
in front. No Arabic or other figures are seen with it. Experiments were
made as to the time required to get these images well in the mental view,
by reading to the lady a series of numbers as fast as she could visualise
them. The first series consisted of twenty numbers of two figures each—
thus, 17, 28, 13, 52, etc.; these were gone through on the first trial in 22
seconds, on the second in 16, and on the third in 26. The second series
was more varied, containing numbers of one, two, and three figures—thus
121, 117, 345, 187, 13, 6, 25, etc., and these were gone through in three
trials in 25, 25, and 22 seconds respectively, forming a general result of
23 seconds for twenty numbers, or 4 seconds per number? A noticeable
feature in this case is the strict accordance of the scale of the image with
the magnitude of the number, and the geometric regularity of the figures.
Some that I drew, and sent for the lady to see, did not at all satisfy her eye
as to their correctness.
I should say that not a few mental calculators work by bulks rather
than by numerals; they arrange concrete magnitudes symmetrically in
rank and file like battalions, and march these about. I have one case where
each number in a Form seems to bear its own weight.
Fig. 45 15 a curious instance of a French Member of the Institute,
communicated to me by M. Antoine d’Abbadie (whose own Number-
Form is shown in Fig. 44):
“He was asked, why he puts 4 in so conspicuous a place; he replied, ‘You see that such
a part of my name (which he wishes to withhold) means 4 in the south of France, which is
the cradle of my family; consequently quare est ma raison d'être.' "
Subsequently, in 1880, M. d’Abbadie wrote: —
“I mentioned the case of a philosopher whose, 4, 14, 24, etc., all step out of the rank in
his mind’s eye. He had a haze in his. mind from 60, I believe [it was 50.— F. G.], up to 80;
but latterly 80 has sprung out, not like the sergeants 4, 14, 24; but like a captain, farther out
still, and five or six times as large as the privates 1, 2, 3, 5, 6, etc. ‘Were I superstitious,’
said he, ‘I should conclude that my death would occur in the 80th year of
