252 



NATURE 



\Jan. 15, i ! 



VISUALISED NUMERALS 



I HAVE lately been occupied in eliciting the degree 

 and manner in which different persons possess the 

 power of seeing images in their mind's eye, and am 

 collecting a large and growing store of materials, partly 

 of verbal answers made by friends to my inquiries, but 

 principally by means of written replies to a printed list 

 of question 5 that I am distributing. The subject bears 

 in many ways upon psychological and ethnological studies, 

 and I should be glad if the present memoir upon one 

 particular branch of it should induce correspondents to 

 furnish me with authentic information of the kind I seek. 

 The various ways in which numerals are visualised is 

 but a small subject, nevertheless it is one that is curious 

 and complete in itself. My data in respect to it are 

 already sufficiently numerous to be worth recording, and 

 they will serve to show that parallel results admit of being 

 arrived at in other directions. 



I may begin by mentioning one or two general expe- 

 riences. 1 have been astonished to find how superior 

 women usually are to men in the vividness of their mental 

 imagery and in their powers of introspection. Though 

 I havejadmirable/eturnsfroirf many men, I have frequently 

 found others, even of the highest general ability, quite 

 unable for some time to take in the meaning of such 

 simple questions as these. " Think of some definite 

 object, — say your breakfast table, as you sat down to it 

 this morning, and consider carefully the picture that rises 

 before your mind's eye. Is the image dim, or fairly 

 clear? Is its brightness comparable to that of the actual 

 scene ? Are the objects sharply defined ? Are the colours 

 quite distinct and natural, &c. ? " On the other hand, I 

 find the attention of women, especially women of ability, 

 to be instantly aroused by these inquiries. They eagerly 

 and carefully address themselves to consider their modes 

 of thought, they put pertinent questions, they suggest 

 tests, they express themselves in well-weighed language 

 and with happy turns of expression, and they are evidently 

 masters of the art of introspection. I do not rind any 

 peculiar tendency to exaggeration in this matter either 

 among women or men ; the only difference I have 

 observed between them is that the former usually show an 

 unexpected amount of intelligence, while many of the 

 latter are as unexpectedly obtuse. The mental difference 

 between the two sexes seems wider in the vividness of 

 their menial imagery and the power of introspecting it, 

 than in respect to any other combination of mental facul- 

 ties of which I can think. 



Another general experience is that the power of seeing 

 vivid images in the mind's eye has little connection with 

 high or low ability or any other obvious characteristic, so 

 that at present I am o;ten puzzled to guess from my 

 geneial knowledge of a friend, whether he will prove on 

 inquiry to have the faculty or not. I have instances in 

 which the highest ability is accompanied by a large 

 measure of this gift, and others in which the faculty 

 appears to be almost wholly absent. It is not possessed 

 by all artists, nor by all mathematicians, nor by all 

 mechanics, nor by all men of science. It is certainly 

 not possessed by all metaphysicians, who are too apt to 

 put forward generalisations based solely on the experi- 

 ences of their own special ways of thinking, in total 

 disregard of the fact that the mental operations of other 

 men may be conducted in very different ways to their own. 

 I have much to say on this and cognate topics which I 

 pass by on the present occasion, that I may at once proceed 

 to the subject of this paper. The first section of it is of 

 minor interest and may be quickly dismissed. It is 

 the power of mentally seeing numerals, of holding them 

 fast in the field of view, of perusing them when there, and 

 of working sums by mental imagery in the same form as 

 that in which they are usually carried on with pen and 

 paper. 



Here is a well marked case of the power of visualising 



numerals. The writer is an office-bearer of one of our 

 scientific societies : — 



1. If words such as fifty-six bespoken, I most clearly, easily 

 and instantly visualise the figures. I do so almost automatically. 

 I perceive that when I speak the word "thousand " or hear it 

 spoken, the figures at once group themselves together. I find it 

 quite impossible to think of the date of a year without remem- 

 bering and visualising the figures, though I express myself in 

 words. The figures are always printed; in type and size they 

 resemble those commonly used for the headings of newspapers. 

 I cannot, how ever, appreciate a back-ground, the figures appear 

 simply in space. I think that by practice and concentration I 

 could hold fast many figures. 



The next is by a friend who has a most tenacious 

 memory for numerical administrative details : — 



2. I can see and mentally retain many figures, and can multiply 

 four figures by four figures without practice, the operation 

 proceeding visibly in my mind like a sum upon paper. 



The following is by a school-boy who is a near relation 

 of a man of the highest mark in science : — 



3. I can visualise a fairly long line of figures, and I do mental 

 sums by putting down the working of them in my mind's eye, up 

 to square roots with two figures in the root, and in algebra, 

 to simple quadratics. 



A schoolmistress writes : — 



4. I can retain several figures in my mental view and work 

 examples, seeing every fiyure in the process. 



A late Fellow of Trinity College, Cambridge, states : — 



5. All arithmetical processes performed mentally, are exactly 

 the processes I should perform on paper. 



It must not, however, be imagined for a moment, that 

 the processes of mental arithmetic arc necessarily wholly 

 dependent on the faculty of visualising numerals. Here 

 is a good instance to the contrary. The writer is the 

 author of a valuable work on a branch of Mental Philo- 

 sophy : — 



6. The numerals are merely ideal sounds [to me], not ideal sights 

 in any way. I have, or used to have, very considerable pi 



of mental arithmetic aid mental algebra, but always used in 

 thought ihe sounds of the signs. In the process I always forgot 

 every step as soon as 1 had reached the result of tint step. 



This last sentence is exceedingly suggestive, and 

 reminds one that many so-called " unconscious " acts are 

 not really unconscious, but are acts characterised by an 

 exceedingly brief and evanescent period of consciousness. 



The processes of mental arithmetic are commonly 

 dependent on the representation of more than one sense, 

 as in the following instance : — 



7. I can multiply with effort four figures by four ; but partly 

 only by images, chiefly by memory. 



I am as yet unable to determine the percentage of persons 

 who possess in the various degrees, the power of visual 

 numerals, because my returns are chiefly derived from 

 persons who are exceptionally gifted. An excellent way 

 of obtaining average returns to psychological questions 

 would be by the help of schoolmasters, who have an 

 admirable field of psychological research immediately 

 before them, which they wholly neglect. If a hundred 

 boys in a large school could be set simultaneously to 

 answer such questions as those I am putting, after their 

 masters had cl arly explained their purport to them, and 

 had taken common precautions to insure independent 

 replies, and to sift away lax and untrustworthy state- 

 ments, the thing would be effected by a single stroke, and 

 both bovs and masters would enjoy the satisfactory 

 feeling of having accomplished a substantial piece of 

 scientific research. 



I have many curious cases of colour association with 

 the various numerals, but shall only give a very few 

 instances of them, and those incidentally, in the present 

 paper. I shall also abstain at present from speaking 

 of the many different ways in which dates, days of the 

 week, and months of the year are apt to be visualised. 



