254 



NATURE 



\Jan. 15, 1880 



14. I find it very difficult to represent my visualisation of 

 numerals diagrammatically. I scarcely ever see the lower numbers 

 written ; I simply know exactly where 6, 7, 4, &c, are to be 

 found. I cannot properly represent the crowding of numbers in 

 some places, nor the edgewise positions they occupy, nor can I 

 at all adequately express the compactness and yet extent of the 

 line. On either side of it there seems to be indefinite space. 

 But there is a boundary at I, beyond which I have to look for 

 minus quantities. After 108 the notion of place becomes hazy 

 and indistinct, though I can visualise the higher numbers in 

 respect to their position, if I make the effort. I think of a 

 million as very far off and high up. When multiplying for 

 example 5x6,! know instantly the spot where the product will 



15. From the very first I have seen numerals up to nearly 200, 

 range themselves always in a particular manner, and in thinking 

 of a number it always takes its place in the figure. The more 

 attention I give to the properties of numbers and their interpre- 

 tations, the less 1 am troubled with this clumsy framework for 

 them, but it is indelible in my mind's eye even when for a long 

 time less consciously so. The higher numbers are to me quite 

 abstract and unconnected with a shape. This rough and untidy 

 production is the best I can do towards representing what I see. 

 There was a little difficulty in the performance, because it is only 

 by catching oneself at unawares, so to speak, that one is quite sure 

 that what one sees is not affected by temporary imagination. But 

 ;t does not seem much like, chiefly because the mental picture 



be, and look to see what number it is. But if asked to multiply 

 14 x 17 I first go up to the place whereabouts I expect it will 

 be, and am baffled. I do not know where to look. In the 

 coloured parts, it is the place rather than the number that is 

 coloured, and the number is connected with colour because it 

 happens to be in that place. The brightness and darkness may 

 possibly in the lower numbers have some connection with the 

 events of my life, the numbers which correspond to years of my 

 age which were eventful, being as a rule much more distinct. 

 As a child I had great liking for the number six, arising I fancy 

 from a keen desire to be six years old. I had also an excessive 

 love for blue, so perhaps this accounts for the connection between 

 them. N.B. — I learnt arithmetic in a thorough old-fashioned 

 unintelligent style, the first step being to learn to count without 

 the least conception as to what the numbers meant. 



The writer of the foregoing has two sisters and a 

 brother. One of the sisters sees numerals in a differently 

 arranged diagram, and the figures themselves arc 

 coloured, (1) black, (2) white, (3) yellow, (4) red, (5) 

 greenish yellow, (6) blue, (7) black, (8) red, (9) grey, 

 (p) gold. The othe sister has a fainter, but still a 

 decided tendency to ee figures in a mental diagram. It 

 is without colour but has variations of shade. The 

 brother has a definite diagram of numbers arranged in a 

 line sloping upwards to the right as far as 120, 

 and absolutely devoid both of colour and variations of 

 shade. No trace of these colour-peculiarities has yet 

 been made out on either the father or the mother's 

 side, but there is a tendency in both father and mother to 

 visualise in diagrams. 



The effects of heredity are also strongly marked in the 

 next set of instances, consisting of two families of cousins. 

 A sister in the first family writes : — 



never seems on the flat but in a thick, dark grey atmosphere 

 deepening in certain parts, especially where I emerges, and about 

 20. How I get from 100 to 120 I hardlyknow, though if I could 

 require these figures a few times without thinking of them on 

 purpose, I should soon notice. About 200 1 lose all framework. 

 I do not see the actual figures very distinctly, but what there is 

 of them is distinguished from the dark by a thin whitish tracing; 

 It is the place they take and the shape they make collectively 

 which is invariable. Nothing more definitely takes its place than 

 a person's age. The person is usually there so long as his age is 

 jn mind. 



Another sister says : — 



16. I always see figures ascending in a directly perpendicular 

 line in front of my eye [according to the sketch and memo- 

 randum sent in illustration, which it is hardly necessary to 

 reproduce, the I stands opposite to the eye, and the scale reaches 

 vertically up to 1,000]. Then all becomes vague, but I know that 

 the thousands and tens of thousands are not in the same perpen- 

 dicular line, and I believe they turn to the left hand. 



A maternal aunt of these ladies " sees figures in a 

 diagram," which has not yet reached me, and the other 

 family that I am now about to mention are the children 

 of a maternal uncle. There are three sisters and a 

 brother who have the same faculty in varying degrees. 



The brother writes from Cambridge : — 



17. Numerals are always pictured by ine in a straight line 

 from left to right. They are black, on a ground varying in 

 illumination, which is bright up to 10, then getting very shady 

 from 10 to 20 ; 20 to 40, bright ; 40 to 60, moderate ; 60 to 80, 

 shady. Shadiest are from 10 to 20, 60 to 80 or 90, 1,000 to 



