NUMBER FORMS. 507 



forms as are shown in Figs. 13, 15, and 16. Nevertheless, it is 

 probable that all strongly eye-minded people, if they do not visu- 

 alize the alphabet in any other way, visualize it as they do other 

 things, in the form in which they had usually seen it. 



Concerning the stability of number forms, any one may have 

 his doubts removed by a few tests separated by months or years. 

 In almost every case it will be found that, no matter how compli- 

 cated the form may be, the subject, after one, 

 two, or three years, will draw from his mental « etc - 



picture of it a copy differing in no essential p 25 



respect from the original copy. The number p 24 



form represented in Fig. 3 was given to me in p 22 



1889. In October, 1892, I requested of the 21 



young man by letter a second copy, and in p ^~ 



reply received one precisely like the first. p 18 



Other tests gave similar results. Galton testi- ■_, Jg 



fies to the unchangeable character of number ■ 

 forms in all cases where they are well defined. e ^ 13 



It is true, however, that they sometimes disap- 12 



pear entirely. They are found to be more 123L5G780 10 

 common among children than adults. It is F *. 



probable that in children who are not natu- 

 rally vivid visualizers, or in cases where it does not serve any 

 useful purpose, the form fails to survive. One case of such a 

 lapse I have found in an adult. 



The general character of number form is such that a person 

 having one can not think of the related numbers without seeing 

 them in a definite visual picture. A form or outline rises invol- 

 untarily before his mind. In some cases the seer can describe it 

 as definitely located in space in relation to his own body. It is 

 two feet long or six inches long. It stares him in the face or lies 

 at his feet. It recedes to the right or left, or into the distance. 

 Others can not answer the question as to the location. In most 

 cases, though not in all, no individual number can be thought of 

 without seeing it in its appropriate place in the usual outline. 

 Sometimes the form seems to be useful to its possessor in compu- 

 tations, particularly in addi- 

 I2345 6789 10 1112 13 14 15 16 etc, tion and subtraction. Inother 

 f io> 8- cases it seems to have no use 



at all further than that of all 

 mental imagery, which will be considered below. It has been 

 suggested that it is by means of a number form, or at least by a 

 clear visualization of numbers, that the arithmetical prodigies 

 accomplish their remarkable computations. Though it has been 

 shown that many of them do visualize the numbers, and men- 

 tally see the different steps of their problem, yet this alone offers 



