4 T. H. Pear, Number-Forms 



'' The essential parts of my number-form are shown in 

 Fig. C (i). There is an incomplete circle, round which the 

 numbers i to 12 are placed equidistantly. This is simply a 

 clock face, but there is always a gap between 12 and i, 

 not filled in. The numbers from 12 to 20 are arranged in a 

 straight line sloping down from 12 and away from it. 

 The numbers from 20 to 100 are arranged in a series of 

 semi-circles ^ of 10, round a semi-circle, so that 100 is on the 

 same level as 20. But the number-form is not all on one 

 plane, and in Fig. C (2) I have attempted to show exactly 

 how it appears to me. The whole scheme is visible at 

 onoe, and I appear to be looking down on it from above, 

 along a line of sight indicated by the arrowed and dotted line. 

 Thus 20 is lower down than 12, and 36 is the lowest of all 

 the numbers. The numbers 36 to 100 are increasingly 

 higher up, the number 100 being on the same level as 20, 

 but much farther away. The plane of the semi-circle on 

 which the semi-circles of numbers from 20 to 100 lie is 

 inclined at an angle to the plane of the numbers 12 to 20, 

 so that the number 36, besides being the lowest of the 

 numbers is also the farthest away to the left. 



*' When thinking of any number from i to 100, I 

 immediately visualize it in its place in this scheme. For 

 numbers higher than 100 the visualization varies according 

 to the character of the number. For instance, 400 has the 

 same position as 4, 900 as 9, 1200 as 12, 1700 as 17, 2000 as 

 20, and so on. But for numbers like 425 there is a general 

 tendencv to split the number-form into two parts, first 

 visualizing 4, then 25. For numbers sufficently near to 100, 

 say 337, I visualize at once three complete schemes and the 

 position of 37 in the fourth scheme. But as the numbers get 

 higher, as, for instance, 876, I visualize 8 and a diminutive 

 scheme between 8 and 9 in which the position of 76 is 

 visualized. In the higher numbers, such as 4678, the 

 splitting of the visualization is always complete ; I visualize 

 the position of 46 and 78.^ 



1. An important emendation of the word senii-circle, added subsequently 

 by Prof. Tattersall, appears on p. 5. I have thought it best to give the 

 original term here. 



2. (Added subsequently.) " The relative scale in which one is thinking 

 often determines the position of a number in the number-form. For instance, 

 it is usual to think of salaries in tenns of hitndred'i of pounds, and so in 

 visualizing the 2000 in a salary of that dimension it becomes 20 hundreds 

 and has the position of 20. On the other hand, populations of places are 

 usually thought of in terms of thousands, and the 2000 in such a case would 

 have the position of 2." 



