This page contains affiliate links. As Amazon Associates we earn from qualifying purchases.
Language:
Form:
Genre:
Published:
  • 1883
Collection:
Buy it on Amazon FREE Audible 30 days

The teachers of many schools and colleges, some in America, have kindly questioned their pupils for me; the results are given in the two first columns of Plate I. It appears that the proportion of young people who see numerals in Forms is greater than that of adults. But for the most part their Forms are neither well defined nor complicated. I conclude that when they are too faint to be of service they are gradually neglected, and become wholly forgotten; while if they are vivid and useful, they increase in vividness and definition by the effect of habitual use. Hence, in adults, the two classes of seers and non-seers are rather sharply defined, the connecting link of intermediate cases which is observable in childhood having disappeared.

These Forms are the most remarkable existing instances of what is called “topical” memory, the essence of which appears to lie in the establishment of a more exact system of division of labour in the different parts of the brain, than is usually carried on. Topical aids to memory are of the greatest service to many persons, and teachers of mnemonics make large use of them, as by advising a speaker to mentally associate the corners, etc., of a room with the chief divisions of the speech he is about to deliver. Those who feel the advantage of these aids most strongly are the most likely to cultivate the use of numerical forms. I have read many books on mnemonics, and cannot doubt their utility to some persons; to myself the system is of no avail whatever, but simply a stumbling-block, nevertheless I am well aware that many of my early associations are fanciful and silly.

The question remains, why do the lines of the Forms run in such strange and peculiar ways? the reply is, that different persons have natural fancies for different lines and curves. Their handwriting shows this, for handwriting is by no means solely dependent on the balance of the muscles of the hand, causing such and such strokes to be made with greater facility than others. Handwriting is greatly modified by the fashion of the time. It is in reality a compromise between what the writer most likes to produce, and what he can produce with the greatest ease to himself. I am sure, too, that I can trace a connection between the general look of the handwritings of my various correspondents and the lines of their Forms. If a spider were to visualise numerals, we might expect he would do so in some web-shaped fashion, and a bee in hexagons. The definite domestic architecture of all animals as seen in their nests and holes shows the universal tendency of each species to pursue their work according to certain definite lines and shapes, which are to them instinctive and in no way, we may presume, logical. The same is seen in the groups and formations of flocks of gregarious animals and in the flights of gregarious birds, among which the wedge-shaped phalanx of wild ducks and the huge globe of soaring storks are as remarkable as any.

I used to be much amused during past travels in watching the different lines of search that were pursued by different persons in looking for objects lost on the ground, when the encampment was being broken up. Different persons had decided idiosyncracies, so much so that if their travelling line of sight could have scored a mark on the ground, I think the system of each person would have been as characteristic as his Number-Form.

Children learn their figures to some extent by those on the clock. I cannot, however, trace the influence of the clock on the Forms in more than a few cases. In two of them the clock-face actually appears, in others it has evidently had a strong influence, and in the rest its influence is indicated, but nothing more. I suppose that the complex Roman numerals in the clock do not fit in sufficiently well with the simpler ideas based upon the Arabic ones.

The other traces of the origin of the Forms that appear here and there, are dominoes, cards, counters, an abacus, the fingers, counting by coins, feet and inches (a yellow carpenter’s rule appears in one case with 56 in large figures upon it), the country surrounding the child’s home, with its hills and dales, objects in the garden (one scientific man sees the old garden walk and the numeral 7 at a tub sunk in the ground where his father filled his watering-pot). Some associations seem connected with the objects spoken of in the doggerel verses by which children are often taught their numbers.

But the paramount influence proceeds from the names of the numerals. Our nomenclature is perfectly barbarous, and that of other civilised nations is not better than ours, and frequently worse, as the French “quatre-vingt dix-huit,” or “four score, ten and eight,” instead of ninety-eight. We speak of ten, eleven, twelve, thirteen, etc., in defiance of the beautiful system of decimal notation in which we write those numbers. What we see is one-naught, one-one, one-two, etc., and we should pronounce on that principle, with this proviso, that the word for the “one” having to show both the place and the value, should have a sound suggestive of “one” but not identical with it. Let us suppose it to be the letter _o_ pronounced short as in “on,” then instead of ten, eleven, twelve, thirteen, etc., we might say _on-naught, on-one, on-two, on-three_, etc.

The conflict between the two systems creates a perplexity, to which conclusive testimony is borne by these numerical forms. In most of them there is a marked hitch at the 12, and this repeats itself at the 120. The run of the lines between 1 and 20 is rarely analogous to that between 20 and 100, where it usually first becomes regular. The ‘teens frequently occupy a larger space than their due. It is not easy to define in words the variety of traces of the difficulty and annoyance caused by our unscientific nomenclature, that are portrayed vividly, and, so to speak, painfully in these pictures. They are indelible scars that testify to the effort and ingenuity with which a sort of compromise was struggled for and has finally been effected between the verbal and decimal systems. I am sure that this difficulty is more serious and abiding than has been suspected, not only from the persistency of these twists, which would have long since been smoothed away if they did not continue to subserve some useful purpose, but also from experiments on my own mind. I find I can deal mentally with simple sums with much less strain if I audibly conceive the figures as on-naught, on-one, etc., and I can both dictate and write from dictation with much less trouble when that system or some similar one is adopted. I have little doubt that our nomenclature is a serious though unsuspected hindrance to the ready adoption by the public of a decimal system of weights and measures. Three quarters of the Forms bear a duodecimal impress.

I will now give brief explanations of the Number-Forms drawn in Plates I., II., and III., and in the two front figures in Plate IV.

DESCRIPTION OF PLATE I.

Fig. 1 is by Mr. Walter Larden, science-master of Cheltenham College, who sent me a very interesting and elaborate account of his own case, which by itself would make a memoir; and he has collected other information for me. The Number-Forms of one of his colleagues and of that gentleman’s sister are given in Figs. 53, 54, Plate III. I extract the following from Mr. Larden’s letter–it is all for which I can find space:–

[Illustration: PLATE I. _Examples of Number-Forms_.]

“All numbers are to me as images of figures in general; I see them in ordinary Arabic type (except in some special cases), and they have definite positions in space (as shown in the Fig.). Beyond 100 I am conscious of coming down a dotted line to the position of 1 again, and of going over the same cycle exactly as before, _e.g._ with 120 in the place of 20, and so on up to 140 or 150. With higher numbers the imagery is less definite; thus, for 1140, I can only say that there are no new positions, I do not see the entire number in the place of 40; but if I think of it as 11 hundred and 40, I see 40 in its place, 11 in its place, and 100 in its place; the picture is not single though the ideas combine. I seem to stand near 1. I have to turn somewhat to see from 30-40, and more and more to see from 40-100; 100 lies high up to my right and behind me. I see no shading nor colour in the figures.”

Figs. 2 to 6 are from returns collected for me by the Rev. A.D. Hill, science-master of Winchester College, who sent me replies from 135 boys of an average age of 14-15. He says, speaking of their replies to my numerous questions on visualising generally, that they “represent fairly those who could answer anything; the boys certainly seemed interested in the subject; the others, who had no such faculty either attempting and failing, or not finding any response in their minds, took no interest in the inquiry.” A very remarkable case of hereditary colour association was sent to me by Mr. Hill, to which I shall refer later. The only five good cases of Number-Forms among the 135 boys are those shown in the Figs. I need only describe Fig. 2. The boy says:–“Numbers, except the first twenty, appear in waves; the two crossing-lines, 60-70, 140-150, never appear at the _same time_. The first twelve are the image of a clock, and 13-20 a continuation of them.”

Figs. 7, 8, are sent me by Mr. Henry F. Osborn of Princeton in the United States, who has given cordial assistance in obtaining information as regards visualising generally. These two are the only Forms included in sixty returns that he sent, 34 of which were from Princeton College, and the remaining 26 from Vassar (female) College. Figs. 9-19 and Fig. 28 are from returns communicated by Mr. W.H. Poole, science-master of Charterhouse College, which are very valuable to me as regards visualising power generally. He read my questions before a meeting of about 60 boys, who all consented to reply, and he had several subsequent volunteers. All the answers were short, straightforward, and often amusing. Subsequently the inquiry extended, and I have 168 returns from him in all, containing 12 good Number-Forms, shown in Figs. 9-19, and in Fig. 28. The first Fig. is that of Mr. Poole himself; he says, “The line only represents position; it does not exist in my mind. After 100, I return to my old starting-place, _e.g._ 140 occupies the same position as 40.”

The gross statistical result from the schoolboys is as follows: –Total returns, 337: viz. Winchester 135, Princeton 34, Charterhouse 168; the number of these that contained well-defined Number-Forms are 5, 1, and 12 respectively, or total 18–that is, one in twenty. It may justly be said that the masters should not be counted, because it was owing to the accident of their seeing the Number-Forms themselves that they became interested in the inquiry; if this objection be allowed, the proportion would become 16 in 337, or one in twenty-one. Again, some boys who had no visualising faculty at all could make no sense out of the questions, and wholly refrained from answering; this would again diminish the proportion. The shyness in some would help in a statistical return to neutralise the tendency to exaggeration in others, but I do not think there is much room for correction on either head. Neither do I think it requisite to make much allowance for inaccurate answers, as the tone of the replies is simple and straightforward. Those from Princeton, where the students are older and had been specially warned, are remarkable for indications of self-restraint. The result of personal inquiries among adults, quite independent of and prior to these, gave me the proportion of 1 in 30 as a provisional result for adults. This is as well confirmed by the present returns of 1 in 21 among boys and youths as I could have expected.

I have not a sufficient number of returns from girls for useful comparison with the above, though I am much indebted to Miss Lewis for 33 reports, to Miss Cooper of Edgbaston for 10 reports from the female teachers at her school, and to a few other schoolmistresses, such as Miss Stones of Carmarthen, whose returns I have utilised in other ways. The tendency to see Number-Forms is certainly higher in girls than in boys.

Fig. 20 is the Form of Mr. George Bidder, Q.C.; it is of much interest to myself, because it was, as I have already mentioned, through the receipt of it and an accompanying explanation that my attention was first drawn to the subject. Mr. G. Bidder is son of the late well-known engineer, the famous “calculating boy” of the bygone generation, whose marvellous feats in mental arithmetic were a standing wonder. The faculty is hereditary. Mr. G. Bidder himself has multiplied mentally fifteen figures by another fifteen figures, but with less facility than his father. It has been again transmitted, though in an again reduced degree, to the third generation. He says: —

“One of the most curious peculiarities in my own case is the arrangement of the arithmetical numerals. I have sketched this to the best of my ability. Every number (at least within the first thousand, and afterwards thousands take the place of units) is always thought of by me in its own definite place in the series, where it has, if I may say so, a home and an individuality. I should, however, qualify this by saying that when I am multiplying together two large numbers, my mind is engrossed in the operation, and the idea of locality in the series for the moment sinks out of prominence.”

Fig. 21 is that of Prof. Schuster, F.R.S., whose visualising powers are of a very high order, and who has given me valuable information, but want of space compels me to extract very briefly. He says to the effect:–

“The diagram of numerals which I usually see has roughly the shape of a horse-shoe, lying on a slightly inclined plane, with the open end towards me. It always comes into view in front of me, a little to the left, so that the right hand branch of the horse-shoe, at the bottom of which I place 0, is in front of my left eye. When I move my eyes without moving my head, the diagram remains fixed in space and does not follow the movement of my eye. When I move the head the diagram unconsciously follows the movement, but I can, by an effort, keep it fixed in space as before. I can also shift it from one part of the field to the other, and even turn it upside down. I use the diagram as a resting-place for the memory, placing a number on it and finding it again when wanted. A remarkable property of the diagram is a sort of elasticity which enables me to join the two ends of the horse-shoe together when I want to connect 100 with 0. The same elasticity causes me to see that part of the diagram on which I fix my attention larger than the rest.”

Mr. Schuster makes occasional use of a simpler form of diagram, which is little more than a straight line variously divided, and which I need not describe in detail.

Fig. 22 is by Colonel Yule, C.B.; it is simpler than the others, and he has found it to become sensibly weaker in later years; it is now faint and hard to fix.

Fig. 23. Mr. Woodd Smith:–

“Above 200 the form becomes vague and is soon lost, except that 999 is always in a corner like 99. My own position in regard to it is generally nearly opposite my own age, which is fifty now, at which point I can face either towards 7-12, or towards 12-20, or 20-7, but never (I think) with my back to 12-20.”

Fig. 24. Mr. Roget. He writes to the effect that the first twelve are clearly derived from the spots in dominoes. After 100 there is nothing clear but 108. The form is so deeply engraven in his mind that a strong effort of the will was required to substitute any artificial arrangement in its place. His father, the late Dr. Roget (well known for many years as secretary of the Royal Society), had trained him in his childhood to the use of the _memoria technica_ of Feinagle, in which each year has its special place in the walls of a particular room, and the rooms of a house represent successive centuries, but he never could locate them in that way. They _would_ go to what seemed their natural homes in the arrangement shown in the figure, which had come to him from some unknown source.

The remaining Figs., 25-28, in Plate I., sufficiently express themselves. The last belongs to one of the Charterhouse boys, the others respectively to a musical critic, to a clergyman, and to a gentleman who is, I believe, now a barrister.

DESCRIPTION OF PLATE II.

Plate II. contains examples of more complicated Forms, which severally require so much minuteness of description that I am in despair of being able to do justice to them separately, and must leave most of them to tell their own story.

Fig. 34 is that of Mr. Flinders Petrie, to which I have already referred (p. 66).

Fig. 37 is by Professor Herbert McLeod, F.R.S. I will quote his letter almost in full, as it is a very good example:–

“When your first article on visualised numerals appeared in _Nature_, I thought of writing to tell you of my own case, of which I had never previously spoken to any one, and which I never contemplated putting on paper. It becomes now a duty to me to do so, for it is a fourth case of the influence of the clock-face. [In my article I had spoken of only three cases known to me.–F. G.] The enclosed paper will give you a rough notion of the apparent positions of numbers in my mind. That it is due to learning the clock is, I think, proved by my being able to tell the clock certainly before I was four, and probably when little more than three, but my mother cannot tell me the exact date. I had a habit of arranging my spoon and fork on my plate to indicate the positions of the hands, and I well remember being astonished at seeing an old watch of my grandmother’s which had ordinary numerals in place of Roman ones. All this happened before I could read, and I have no recollection of learning the numbers unless it was by seeing numbers stencilled on the barrels in my father’s brewery.

“When learning the numbers from 12 to 20, they appeared to be vertically above the 12 of the clock, and you will see from the enclosed sketch that the most prominent numbers which I have underlined all occur in the multiplication table. Those doubly underlined are the most prominent [the lithographer has not rendered these correctly.–F. G.], and just now I caught myself doing what I did not anticipate–after doubly underlining some of the numbers, I found that all the multiples of 12 except 84 are so marked. In the sketch I have written in all the numbers up to 30; the others are not added merely for want of space; they appear in their corresponding positions. You will see that 21 is curiously placed, probably to get a fresh start for the next 10. The loops gradually diminish in size as the numbers rise, and it seems rather curious that the numbers from 100 to 120 resemble in form those from 1 to 20. Beyond 144 the arrangement is less marked, and beyond 200 they entirely vanish, although there is some hazy recollection of a futile attempt to learn the multiplication table up to 20 times 20.”

[Illustration: PLATE II. _Examples of Number Forms_.]

“Neither my mother nor my sister is conscious of any mental arrangement of numerals. I have not found any idea of this kind among any of my colleagues to whom I have spoken on the subject, and several of them have ridiculed the notion, and possibly think me a lunatic for having any such feeling. I was showing the scheme to G., shortly after your first article appeared, on the piece of paper I enclose, and he changed the diagram to a sea-serpent [most amusingly and grotesquely drawn.–F. G.], with the remark, ‘If you were a rich man, and I knew I was mentioned in your will, I should destroy that piece of paper, in case it should be brought forward as an evidence of insanity!’ I mention this in connection with a paragraph in your article.”

Fig. 40 is, I think, the most complicated form I possess. It was communicated to me by Mr. Woodd Smith as that of Miss L. K., a lady who was governess in a family, whom he had closely questioned both with inquiries of his own and by submitting others subsequently sent by myself. It is impossible to convey its full meaning briefly, and I am not sure that I understand much of the principle of it myself. A shows part only (I have not room for more) of the series 2, 3, 5, 7, 10, 11, 13, 14, 17, 18, 19, each as two sides of a square,–that is, larger or smaller according to the magnitude of the number; 1 does not appear anywhere. C similarly shows part of the series (all divisible by 3) of 6, 9, 15, 21, 27, 30, 33, 39, 60, 63, 66, 69, 90, 93, 96. B shows the way in which most numbers divisible by 4 appear. D shows the form of the numbers 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 41, 42-49, 81-83, 85-87, 89, 101-103, 105-107, and 109. E shows that of 31, 33-35, 37-39. The other numbers are not clear, viz. 50, 51, 53-55, 57-59. Beyond 100 the arrangement becomes hazy, except that the hundreds and thousands go on again in complete, consecutive, and proportional squares indefinitely. The groups of figures are not seen together, but one or other starts up as 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 2-1/3 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 is 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 _quatre est ma raison d’etre_.'”

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 the century.’ The growth of 80 was _sudden_, and has remained constant ever since.”

This is the only case known to me of a new stage in the development of a Number-Form being suddenly attained.

DESCRIPTION OF PLATE III.

Plate III. is intended to exhibit some instances of heredity. I have no less than twenty-two families in which this curious tendency is hereditary, and there may be many more of which I am still ignorant. I have found it to extend in at least eight of these beyond the near degrees of parent and child, and brother and sister. Considering that the occurrence is so rare as to exist in only about one in every twenty-five or thirty males, these results are very remarkable, and their trustworthiness is increased by the fact that the hereditary tendency is on the whole the strongest in those cases where the Number-Forms are the most defined and elaborate. I give four instances in which the hereditary tendency is found, not only in having a Form at all, but also in some degree in the shape of the Form.

Figs. 46-49 are those of various members of the Henslow family, where the brothers, sisters, and some children of a sister have the peculiarity.

Figs. 53-54 are those of a master of Cheltenham College and his sister.

Figs. 55-56 are those of a father and son; 57 and 58 belong to the same family.

Figs. 59-60 are those of a brother and sister.

The lower half of the Plate explains itself. The last figure of all, Fig. 65, is of interest, because it was drawn for an intelligent little girl of only 11 years old, after she had been closely questioned by the father, and it was accompanied by elaborate coloured illustrations of months and days of the week. I thought this would be a good test case, so I let the matter drop for two years, and then begged the father to question the child casually, and to send me a fresh account. I asked at the same time if any notes had been kept of the previous letter. Nothing could have come out more satisfactorily. No notes had been kept; the subject had passed out of mind, but the imagery remained the same, with some trifling and very interesting metamorphoses of details.

[Illustration: PLATE III. _Examples of an Hereditary Tendency to see Number-Forms_, _4 Instances where the Number Forms in same family are alike_ _3 Instances where the Number-Forms in same family are unlike_]

DESCRIPTION OF PLATE IV.

I can find room in Plate IV. for only two instances of coloured Number-Forms, though others are described in Plate III. Fig. 64 is by Miss Rose G. Kingsley, daughter of the late eminent writer the Rev. Charles Kingsley, and herself an authoress. She says:–

“Up to 30 I see the numbers in clear white; to 40 in gray; 40-50 in flaming orange; 50-60 in green; 60-70 in dark blue; 70 I am not sure about; 80 is reddish, I think; and 90 is yellow; but these latter divisions are very indistinct in my mind’s eye.”

She subsequently writes:–

“I now enclose my diagram; it is very roughly done, I am afraid, not nearly as well as I should have liked to have done it. My great fear, has been that in thinking it over I might be led to write down something more than what I actually see, but I hope I have avoided this.”

Fig. 65 is an attempt at reproducing the form sent by Mr. George F. Smythe of Ohio, an American correspondent who has contributed much of interest. He says:–

“To me the numbers from 1 to 20 lie on a level plane, but from 20 they slope up to 100 at an angle of about 25 deg. Beyond 100 they are generally all on a level, but if for any reason I have to think of the numbers from 100 to 200, or from 200 to 300, etc., then the numbers, between these two hundreds, are arranged just as those from 1 to 100 are. I do not, when thinking of a number, picture to myself the figures which represent it, but I do think instantly of the place which it occupies along the line. Moreover, in the case of numbers from 1 to 20 (and, indistinctly, from 20 up to 28 or 30), I always picture the number–not the figures–as occupying a right-angled parallelogram about twice as long as it is broad. These numbers all lie down flat and extend in a straight line from 1 to 12 over an unpleasant, arid, sandy plain. At 12 the line turns abruptly to the right, passes into a pleasanter region where grass grows, and so continues up to 20. At 20 the line turns to the left, and passes up the before-described incline to 100. This figure will help you in understanding my ridiculous notions. The asterisk (*) marks the place where I commonly seem to myself to stand and view the line. At times I take other positions, but never any position to the left of the (*), nor to the right of the line from 20 upwards. I do not associate colours with numbers, but there is a great difference in the illumination which different numbers receive. If a traveller should start at 1 and walk to 100, he would be in an intolerable glare of light until near 9 or 10. But at 11 he would go into a land of darkness and would have to feel his way. At 12 light breaks in again, a pleasant sunshine, which continues up to 19 or 20, where there is a sort of twilight. From here to 40 the illumination is feeble, but still there is considerable light. At 40 things light up, and until one reaches 56 or 57 there is broad daylight. Indeed the tract from 48 to 50 is almost as bad as that from 1 to 9. Beyond 60 there is a fair amount of light up to about 97, From this point to 100 it is rather cloudy.”

In a subsequent letter he adds:–

“I enclose a picture in perspective and colour of my ‘form.’ I have taken great pains with this, but am far from satisfied with it. I know nothing about drawing, and consequently am unable to put upon the paper just what I see. The faults which I find with the picture are these. The rectangles stand out too distinctly, as something lying on the plane instead of being, as they ought, a part of the plane. The view is taken of necessity from an unnatural stand-point, and some way or other the region 1-12 does not look right. The landscape is altogether too distinct in its features. I rather _know that there is_ grass, and that there are trees in the distance, than _see_ them. But the grass within a few feet of the line I see distinctly. I cannot make the hill at the right slope down to the plane as it ought. It is too steep. I have had my poor success in indicating my notion of the darkness which overhangs the region of eleven. In reality it is not a cloud at all, but a darkness.

“My sister, a married lady, thirty-eight years of age, sees numerals much as I do, but very indistinctly. She cannot draw a figure which is not by far too distinct.”

Most of those who associate colours with numerals do so in a vague way, impossible to convey with truth in a painting. Of the few who see them with more objectivity, many are unable to paint or are unwilling to take the trouble required to match the precise colours of their fancies. A slight error in hue or tint always dissatisfies them with their work.

Before dismissing the subject of numerals, I would call attention to a few other associations connected with them. They are often personified by children, and characters are assigned to them, it may be on account of the part they play in the multiplication table, or owing to some fanciful association with their appearance or their sound. To the minds of some persons the multiplication table appears dramatised, and any chance group of figures may afford a plot for a tale. I have collated six full and trustworthy accounts, and find a curious dissimilarity in the personifications and preferences; thus the number 3 is described as (1) disliked; (2) a treacherous sneak; (3) a good old friend; (4) delightful and amusing; (5) a female companion to 2; (6) a feeble edition of 9. In one point alone do I find any approach to unanimity, and that is in the respect paid to 12, as in the following examples:–(1) important and influential; (2) good and cautious–so good as to be almost noble; (3) a more beautiful number than 10, from the many multiples that make it up–in other words, its kindly relations to so many small numbers; (4) a great love for 12, a large-hearted motherly person because of the number of little ones that it takes, as it were, under its protection. The decimal system seemed to me treason against this motherly 12.–All this concurs with the importance assigned for other reasons to the number 12 in the Number-Form.

There is no agreement as to the sex of numbers; I myself had absurdly enough fancied that _of course_ the even numbers would be taken to be of the male sex, and was surprised to find that they were not. I mention this as an example of the curious way in which our minds may be unconsciously prejudiced by the survival of some forgotten early fancies. I cannot find on inquiring of philologists any indications of different sexes having been assigned in any language to different numbers.

Mr. Hershon has published an analysis of the Talmud, on the odd principle of indexing the various passages according to the number they may happen to contain; thus such a phrase as “there were three men who,” etc., would be entered under the number 3. I cannot find any particular preferences given there to especial numbers; even 7 occurs less often than 1, 2, 3, 4, and 10. Their respective frequency being 47, 54, 53, 64, 54, 51; 12 occurs only sixteen times. Gamblers have not unfrequently the silliest ideas concerning numbers, their heads being filled with notions about lucky figures and beautiful combinations of them. There is a very amusing chapter in _Rome Contemporaine_, by E. About, in which he speaks of this in connection with the rage for lottery tickets.

COLOUR ASSOCIATIONS.

Numerals are occasionally seen in Arabic or other figures, not disposed in any particular Form, but coloured. An instance of this is represented in Fig. 69 towards the middle part of the column, but as I shall have shortly to enter at length into the colour associations of the author, I will pass over this portion of them, and will quote in preference from the letter of another correspondent.

Baron von Osten Sacken, of whom I have already spoken, writes:–

“The localisation of numerals, peculiar to certain persons, is foreign to me. In my mind’s eye the figures appear _in front_ of me, within a limited space. My peculiarity, however, consists in the fact that the numerals from 1 to 9 are differently coloured; (1) black, (2) yellow, (3) pale brick red, (4) brown, (5) blackish gray, (6) reddish brown, (7) green, (8) bluish, (9) reddish brown, somewhat like 6. These colours appear very distinctly when I think of these figures separately; in compound figures they become less apparent. But the most remarkable manifestation of these colours appears in my recollections of chronology. When I think of the events of a given century they invariably appear to me on a background coloured like the principal figure in the dates of that century; thus events of the eighteenth century invariably appear to me on a greenish ground, from the colour of the figure 7. This habit clings to me most tenaciously, and the only hypothesis I can form about its origin is the following:–My tutor, when I was ten to twelve years old, taught me chronology by means of a diagram on which the centuries were represented by squares, subdivided in 100 smaller squares; the squares representing centuries had _narrow coloured borders_; it may be that in this way the recollection of certain figures became associated with certain colours. I venture this explanation without attaching too much importance to it, because it seems to me that if it was true, my _direct_ recollection of those coloured borders would have been stronger than it is; still, the strong association of my chronology with colour seems to plead in favour of that explanation.”

Figs. 66, 67. These two are selected out of a large collection of coloured Forms in which the months of the year are visualised. They will illustrate the gorgeousness of the mental imagery of some favoured persons. Of these Fig. 66 is by the wife of an able London physician, and Fig. 67 is by Mrs. Kempe Welch, whose sister, Miss Bevington, a well-known and thoughtful writer, also sees coloured imagery in connection with dates. This Fig. 67 was one of my test cases, repeated after the lapse of two years, and quite satisfactorily. The first communication was a descriptive account, partly in writing, partly by word of mouth; the second, on my asking for it, was a picture which agreed perfectly with the description, and explained much that I had not understood at the time. The small size of the Fig. in the Plate makes it impossible to do justice to the picture, which is elaborate and on a large scale, with a perspective of similar hills stretching away to the far distance, and each standing for a separate year. She writes:–

“It is rather difficult to give it fully without making it too definite; on each side there is a total blank.”

The instantaneous association of colour with sound characterises a small percentage of adults, and it appears to be rather common, though in an ill-developed degree, among children. I can here appeal not only to my own collection of facts, but to those of others, for the subject has latterly excited some interest in Germany. The first widely known case was that of the brothers Nussbaumer, published in 1873 by Professor Bruhl of Vienna, of which the English reader will find an account in the last volume of Lewis’s _Problems of Life and Mind_ (p. 280). Since then many occasional notices of similar associations have appeared. A pamphlet containing numerous cases was published in Leipsic in 1881 by two Swiss investigators, Messrs. Bleuler and Lehmann.[9] One of the authors had the faculty very strongly, and the other had not; so they worked conjointly with advantage. They carefully tabulated the particulars of sixty-two cases. As my present object is to subordinate details to the general impression that I wish to convey of the peculiarities of different minds, I will simply remark–First, that the persistence of the colour association with sounds is fully as remarkable as that of the Number-Form with numbers. Secondly, that the vowel sounds chiefly evoke them. Thirdly, that the seers are invariably most minute in their description of the precise tint and hue of the colour. They are never satisfied, for instance, with saying “blue,” but will take a great deal of trouble to express or to match the particular blue they mean. Fourthly, that no two people agree, or hardly ever do so, as to the colour they associate with the same sound. Lastly, that the tendency is very hereditary. The publications just mentioned absolve me from the necessity of giving many extracts from the numerous letters I have received, but I am particularly anxious to bring the brilliancy of these colour associations more vividly before the reader than is possible by mere description. I have therefore given the elaborately-coloured diagrams in Plate IV., which were copied by the artist directly from the original drawings, and which have been printed by the superimposed impressions of different colours from different lithographic stones. They have been, on the whole, very faithfully executed, and will serve as samples of the most striking cases. Usually the sense of colour is much too vague to enable the seer to reproduce the various tints so definitely as those in this Plate. But this is by no means universally the case.

Fig. 68 is an excellent example of the occasional association of colours with letters. It is by Miss Stones, the head teacher in a high school for girls, who, as I have already mentioned, obtained useful information for me, and has contributed several suggestive remarks of her own. She says:–

“The vowels of the English language always appear to me, when I think of them, as possessing certain colours, of which I enclose a diagram. Consonants, when thought of by themselves, are of a purplish black; but when I think of a whole word, the colour of the consonants tends towards the colour of the vowels. For example, in the word ‘Tuesday,’ when I think of each letter separately, the consonants are purplish-black, _u_ is a light dove colour, _e_ is a pale emerald green, and _a_ is yellow; but when I think of the whole word together, the first part is a light gray-green, and the latter part yellow. Each word is a distinct whole. I have always associated the same colours with the same letters, and no effort will change the colour of one letter, transferring it to another. Thus the word ‘red’ assumes a light-green tint, while the word ‘yellow’ is light-green at the beginning and red at the end. Occasionally, when uncertain how a word should be spelt, I have considered what colour it ought to be, and have decided in that way. I believe this has often been a great help to me in spelling, both in English and foreign languages. The colour of the letters is never smeared or blurred in any way. I cannot recall to mind anything that should have first caused me to associate colours with letters, nor can my mother remember any alphabet or reading-book coloured in the way I have described, which I might have used as a child. I do not associate any idea of colour with musical notes at all, nor with any of the other senses.”

She adds:–

“Perhaps you may be interested in the following account from my sister of her visual peculiarities: ‘When I think of Wednesday I see a kind of oval flat wash of yellow emerald green; for Tuesday, a gray sky colour; for Thursday, a brown-red irregular polygon; and a dull yellow smudge for Friday.'”

[Footnote 9: Zwangmaessige Lichtempfindungen durch Schall und verwandte Erscheinungen, von E. Bleuler und K. Lehmann. Leipsig, Fues’ Verlag (R. Reisland), 1881.]

The latter quotation is a sample of many that I have; I give it merely as another instance of hereditary tendency.

I will insert just one description of other coloured letters than those represented in the Plate. It is from Mrs. H., the married sister of a well-known man of science, who writes:–

“I do not know how it is with others, but to me the colours of vowels are so strongly marked that I hardly understand their appearing of a different colour, or, what is nearly as bad, colourless to any one. To me they are and always have been, as long as I have known them, of the following tints:–“

A, pure white, and like china in texture.

E, red, not transparent; vermilion, with china-white would represent it.

I, light bright yellow; gamboge.

O, black, but transparent; the colour of deep water seen through thick clear ice.

U, purple.

Y, a dingier colour than I.

“The shorter sounds of the vowels are less vivid and pure in colour. Consonants are almost or quite colourless to me, though there is some blackness about M.

“Some association with U in the words blue and purple may account for that colour, and possibly the E in red may have to do with that also; but I feel as if they were independent of suggestions of the kind.

“My first impulse is to say that the association lies solely in the sound of the vowels, in which connection I certainly feel it the most strongly; but then the thought of the distinct redness of such a [printed or written] word as ‘_great_’ shows me that the relation must be visual as well as aural. The meaning of words is so unavoidably associated with the sight of them, that I think this association rather overrides the primitive impression of the colour of the vowels, and the word ‘_violet_’ reminds me of its proper colour until I look at the word as a mere collection of letters.

“Of my two daughters, one sees the colours quite differently from this (A, blue; E, white; I, black; O, whity-brownish; U, opaque brown). The other is only heterodox on the A and O; A being with her black, and O white. My sister and I never agreed about these colours, and I doubt whether my two brothers feel the chromatic force of the vowels at all.”

I give this instance partly on account of the hereditary interest. I could add cases from at least three different families in which the heredity is quite as strongly marked.

Fig. 69 fills the whole of the middle column of Plate IV., and contains specimens from a large series of coloured illustrations, accompanied by many pages of explanation from a correspondent, Dr. James Key of Montagu, Cape Colony. The pictures will tell their own tale sufficiently well. I need only string together a few brief extracts from his letters, as follows:–

“I confess my inability to understand visualised numerals; it is otherwise, however, with regard to colour associations with letters. Ever since childhood these have been distinct and unchanging in my consciousness; sometimes, although very seldom, I have mentioned them, to the amazement of my teachers and the scorn of my comrades. A is brown. I say it most dogmatically, and nothing will ever have the effect, I am convinced, of making it appear otherwise! I can imagine no explanation of this association. [He goes into much detail as to conceivable reasons connected with his childish life to show that none of these would do.] Shades of brown accompany to my mind the various degrees of openness in pronouncing A. I have never been destitute in all my conscious existence of a conviction that E is a clear, cold, light-gray blue. I remember daubing in colours, when quite a little child, the picture of a jockey, whose shirt received a large share of E, as I said to myself while daubing it with grey. [He thinks that the letter I may possibly be associated with black because it contains no open space, and O with white because it does.] The colour of R has been invariably of a copper colour, in which a swarthy blackness seems to intervene, visually corresponding to the trilled pronunciation of R. This same appearance exists also in J, X, and Z.”

The upper row of Fig. 69 shows the various shades of brown, associated with different pronunciations of the letter A, as in “fame,” “can,” “charm,” and “all” respectively. The second, third and fourth rows similarly refer to the various pronunciations of the other vowels. Then follow the letters of the alphabet, grouped according to the character of the appearance they suggest. After these come the numerals. Then I give three lines of words such as they appear to him. The first is my own name, the second is “London,” and the third is “Visualisation.” Proceeding conversely, Dr. Key collected scraps of various patterns of wall paper, and sent them together with the word that the colour of the several patterns suggested to him. Specimens of these are shown in the three bottom lines of the Fig. I have gone through the whole of them with care, together with his descriptions and reasons, and can quite understand his meaning, and how exceedingly complex and refined these associations are. The patterns are to him like words in poetry, which call up associations that any substituted word of a like dictionary meaning would fail to do. It would not, for example, be possible to print words by the use of counters coloured like those in Fig. 69, because the tint of each influences that of its neighbours. It must be understood that my remarks, though based on Dr. Key’s diagrams and statements as on a text, do not depend, by any means, wholly upon them, but on numerous other letters from various quarters to the same effect. At the same time I should say that Dr. Key’s elaborate drawings and ample explanations, to which I am totally unable to do justice in a moderate space, are the most full and striking of any I have received. His illustrations are on a large scale, and are ingeniously arranged so as to express his meaning.

Persons who have colour associations are unsparingly critical. To ordinary individuals one of these accounts seems just as wild and lunatic as another, but when the account of one seer is submitted to another seer, who is sure to see the colours in a different way, the latter is scandalised and almost angry at the heresy of the former. I submitted this very account of Dr. Key to a lady, the wife of an ex-governor of one of the most important British possessions, who has vivid colour associations of her own, and who, I had some reason to think, might have personal acquaintance with the locality where Dr. Key lives. She could not comprehend his account at all, his colours were so entirely different to those that she herself saw.

I have now completed as much as I propose to say about the quaint phenomena of Visualised Forms of numbers and of dates, and of coloured associations with letters. I shall not extend my remarks to such subjects as a musician hearing mental music, of which I have many cases, nor to fancies concerning the other senses, as none of these are so noteworthy. I am conscious that the reader may desire even more assurance of the trustworthiness of the accounts I have given than the space now at my disposal admits, or than I could otherwise afford without wearisome iteration of the same tale, by multiplying extracts from my large store of material. I feel, too, that it may seem ungracious to many obliging correspondents not to have made more evident use of what they have sent than my few and brief notices permit. Still their end and mine will have been gained, if these remarks and illustrations succeed in leaving a just impression of the vast variety of mental constitution that exists in the world, and how impossible it is for one man to lay his mind strictly alongside that of another, except in the rare instances of close hereditary resemblance.

VISIONARIES.

In the course of my inquiries into visual memory, I was greatly struck by the frequency of the replies in which my informants described themselves as subject to “visions.” Those of whom I speak were sane and healthy, but were subject notwithstanding to visual presentations, for which they could not account, and which in a few cases reached the level of hallucinations. This unexpected prevalence of a visionary tendency among persons who form a part of ordinary society seems to me suggestive and well worthy of being put on record. The images described by different persons varied greatly in distinctness, some were so faint and evanescent as to appear unworthy of serious notice; others left a deep impression, and others again were so vivid as actually to deceive the judgment. All of these belong to the same category, and it is the assurance of their common origin that affords justification for directing scientific attention to what many may be inclined to contemptuously disregard as the silly vagaries of vacant minds.

The lowest order of phenomena that admit of being classed as visions are the “Number-Forms” to which I have just drawn attention. They are in each case absolutely unchangable, except through a gradual development in complexity. Their diversity is endless, and the Number-Forms of different persons are mutually unintelligible. These strange “visions,” for such they must be called, are extremely vivid in some cases, but are almost incredible to the vast majority of mankind, who would set them down as fantastic nonsense; nevertheless, they are familiar parts of the mental furniture of the rest, in whose imaginations they have been unconsciously formed, and where they remain unmodified and unmodifiable by teaching. I have received many touching accounts of their childish experiences from persons who see the Number-Forms, and other curious visions of which I have spoken or shall speak. As is the case with the colour-blind, so with these seers. They imagined at first that everybody else had the same way of regarding things as themselves. Then they betrayed their peculiarities by some chance remark that called forth a stare of surprise, followed by ridicule and a sharp scolding for their silliness, so that the poor little things shrank back into themselves, and never ventured again to allude to their inner world. I will quote just one of many similar letters as a sample. I received it, together with much interesting information, immediately after a lecture I gave to the British Association at Swansea, in which I had occasion to speak of the Number-Forms. The writer says:–

“I had no idea for many years that every one did not imagine numbers in the same positions as those in which they appear to me. One unfortunate day I spoke of it, and was sharply rebuked for my absurdity. Being a very sensitive child I felt this acutely, but nothing ever shook my belief that, absurd or not, I always saw numbers in this particular way. I began to be ashamed of what I considered a peculiarity, and to imagine myself, from this and various other mental beliefs and states, as somewhat isolated and peculiar. At your lecture the other night, though I am now over twenty-nine, the memory of my childish misery at the dread of being peculiar came over me so strongly that I felt I must thank you for proving that, in this particular at any rate, my case is most common.”

The next sort of vision that flashes unaccountably into existence is the instant association in some persons of colour with sound, which was spoken of in the last chapter, and on which I need not say more now.

A third curious and abiding fantasy of certain persons is invariably to connect visualised pictures with words, the same picture to the same word. These are perceived by many in a vague, fleeting, and variable way, but to a few they appear strangely vivid and permanent. I have collected many cases of this peculiarity, and am much indebted to the authoress, Mrs. Haweis, who sees these pictures, for her kindness in sketching some of them for me, and for permitting me to use her name in guarantee of their genuineness. She says:–

“Printed words have always had faces to me; they had definite expressions, and certain faces made me think of certain words. The words had _no_ connection with these except sometimes by accident. The instances I give are few and ridiculous. When I think of the word Beast, it has a face something like a gargoyle. The word Green has also a gargoyle face, with the addition of big teeth. The word Blue blinks and looks silly, and turns to the right. The word Attention has the eyes greatly turned to the left. It is difficult to draw them properly because, like Alice’s ‘Cheshire cat,’ which at times became a grin without a cat, these faces have expression without features. The expression of course” [note the _naive_ phrase “of course.”–F.G.] “depends greatly on those of the letters, which have likewise their faces and figures. All the little a’s turn their eyes to the left, this determines the eyes of Attention. Ant, however, looks a little down. Of course these faces are endless as words are, and it makes my head ache to retain them long enough to draw.”

Some of the figures are very quaint. Thus the interrogation “what?” always excites the idea of a fat man cracking a long whip. They are not the capricious creations of the fancy of the moment, but are the regular concomitants of the words, and have been so as far back as the memory is able to recall.

When in perfect darkness, if the field of view be carefully watched, many persons will find a perpetual series of changes to be going on automatically and wastefully in it. I have much evidence of this. I will give my own experience the first, which is striking to me, because I am very unimpressionable in these matters. I visualise with effort; I am peculiarly inapt to see “after-images,” “phosphenes,” “light-dust,” and other phenomena due to weak sight or sensitiveness; and, again, before I thought of carefully trying, I should have emphatically declared that my field of view in the dark was essentially of a uniform black, subject to an occasional light-purple cloudiness and other small variations. Now, however, after habituating myself to examine it with the same sort of strain that one tries to decipher a signpost in the dark, I have found out that this is by no means the case, but that a kaleidoscopic change of patterns and forms is continually going on, but they are too fugitive and elaborate for me to draw with any approach to truth. I am astonished at their variety, and cannot guess in the remotest degree the cause of them. They disappear out of sight and memory the instant I begin to think about anything, and it is curious to me that they should often be so certainly present and yet be habitually overlooked. If they were more vivid, the case would be very different, and it is most easily conceivable that some very slight physiological change, short of a really morbid character, would enhance their vividness. My own deficiencies, however, are well supplied by other drawings in my possession. These are by the Rev. George Henslow, whose visions are far more vivid than mine. His experiences are not unlike those of Goethe, who said, in an often-quoted passage, that whenever he bent his head and closed his eyes and thought of a rose, a sort of rosette made its appearance, which would not keep its shape steady for a moment, but unfolded from within, throwing out a succession of petals, mostly red but sometimes green, and that it continued to do so without change in brightness and without causing him any fatigue so long as he cared to watch it. Mr. Henslow, when he shuts his eyes and waits, is sure in a short time to see before him the clear image of some object or other, but usually not quite natural in its shape. It then begins to change from one form to another, in his case also for as long a time as he cares to watch it. Mr. Henslow has zealously made repeated experiments on himself, and has drawn what he sees. He has also tried how far he is able to mould the visions according to his will. In one case, after much effort, he contrived to bring the imagery back to its starting-point, and thereby to form what he terms a “visual cycle.” The following account is extracted and condensed from his very interesting letter, and will explain the illustrations copied from his drawings that are given in Plate IV.

Fig. 70. The first image that spontaneously presented itself was a cross-bow (1); this was immediately provided with an arrow (2), remarkable for its pronounced barb and superabundance of feathering. Some person, but too indistinct to recognise much more of him than the hands, appeared to shoot the arrow from the bow. The single arrow was then accompanied by a flight of arrows from right to left, which completely occupied the field of vision. These changed into falling stars, then into flakes of a heavy snowstorm; the ground gradually appeared as a sheet of snow where previously there had been vacant space. Then a well-known rectory, fish-ponds, walls, etc., all covered with snow, came into view most vividly and clearly defined. This somehow suggested another view, impressed on his mind in childhood, of a spring morning, brilliant sun, and a bed of red tulips: the tulips gradually vanished except one, which appeared now to be isolated and to stand in the usual point of sight. It was a single tulip, but became double. The petals then fell off rapidly in a continuous series until there was nothing left but the pistil (3), but (as is almost invariably the case with his objects) that part was greatly exaggerated. The stigmas then changed into three branching brown horns (4); then into a knob (5), while the stalk changed into a stick. A slight bend in it seems to have suggested a centre-bit (6); this passed into a sort of pin passing through a metal plate (7), this again into a lock (8), and afterwards into a nondescript shape (9), distantly suggestive of the original cross-bow. Here Mr. Henslow endeavoured to force his will upon the visions, and to reproduce the cross-bow, but the first attempt was an utter failure. The figure changed into a leather strap with loops (10), but while he still endeavoured to change it into a bow the strap broke, the two ends were separated, but it happened that an imaginary string connected them (11). This was the first concession of his automatic chain of thoughts to his will. By a continued effort the bow came (12), and then no difficulty was felt in converting it into the cross-bow, and thus returning to the starting-point. Fig. 71. Mr. Henslow writes:–

“Though I can usually summon up any object thought of, it not only is somewhat different from the real thing, but it rapidly changes. The changes are in many cases clearly due to a suggestiveness in the article of something else, but not always so, as in some cases hereafter described. It is not at ail necessary to think of any particular object at first, as something is sure to come spontaneously within a minute or two. Some object having once appeared, the automatism of the brain will rapidly induce the series of changes. The images are sometimes very numerous, and very rapid in succession: very frequently of great beauty and highly brilliant. Cut glass (far more elaborate than I am conscious of ever having seen), highly chased gold and silver filigree ornaments; gold and silver flower-stands, etc.; elaborate coloured patterns of carpets in brilliant tints are not uncommon.

“Another peculiarity resides in the extreme restlessness of my visual objects. It is often very difficult to keep them still, as well as from changing in character. They will rapidly oscillate or else rotate to a most perplexing degree, and when the characters change at the same time a critical examination is almost impossible. When the process is in full activity, I feel as if I were a mere spectator at a diorama of a very eccentric kind, and was in no way concerned with the getting up of the performance.

“When a succession of images has been passing, I sometimes _determine_ to introduce an object, say a watch. Very often it is next to impossible to succeed. There is an evident struggle. The watch, pure and simple, will not come; but some hybrid structure appears–something round, perhaps–but it lapses into a warming-pan or other unexpected object.

“This practice has brought to my mind very clearly the distinction between at least one form of automatism of the brain and volition; but the strength of the former is enormous, for the visual objects, when in full career of the change, are _imperative_ in their refusal to be interfered with.

“I will now describe the cases illustrated. Fig. 71. I thought of a gun. The _stock_ came into view, the metal plate on the end very distinct towards the left (1). The wood was elaborately carved. I cannot recall the pattern. As I scrutinised it, the stock oscillated up and down, and _crumpled up_. The metallic plate sank inwards: and the stock contracted so that it looked not unlike a tuning-fork (2). I gave up the stock and proceeded cautiously to examine the lock. I got it well into view, but no more of the gun. It turned out to be an old-fashioned flint-lock. It immediately began to nod backwards and forwards in a manner suggestive of the beak of a bird pecking. Consequently it forthwith became converted into the head of a bird with a long curved beak, the knob on the lock (3) becoming the head of the bird. I then looked to the right expecting to find the barrel, but the snout of a saw-fish with the tip _distinctly_ broken off appeared instead. I had not thought either of a _flint_-lock or of a saw-fish: both came spontaneously.

“Fig. 72. I have several times thought of a rosebud, as Goethe is said to have been able to see one at will, and to observe it expand. The following are some of the results:–The bud appeared unexpectedly a moss rosebud. Its only abnormal appearance was the inordinately elongated sepals (1). I tried to _force_ it to expand. It enlarged but only partially opened (2), when all of a sudden it burst open and the petals became reflexed (3).[10]

“Fig. 73. The spontaneous appearance of a poppy capsule (1) dehiscing as usual by ‘pores,’ but with inordinately long and arching valves over the pores. These valves were eminently suggestive of hooded flowers. Hence they changed to a whorl of _salvias_ (2). Each blossom now gyrated rapidly in a vertical plane. Concentrating observation on _one_ rotating flower, it became a ‘rotating haze,’ as the rapid motion rendered the flower totally indistinct. The ‘haze’ now shaped itself into a circle of moss with a deep funnel-like cavity. This was suggestive of a bird’s nest. It became lined with _hair_, but the nest was a _deep_, pointed cavity. A nest was suggestive of eggs. Hence a series appeared (4); the two rows meeting in one at the apex appears to have arisen from the _perspective_ view of the nest. The eggs all disappeared but one (5), which increased in size; the bright point of light now shone with great intensity like a star; then it gradually grew dimmer and dimmer till it disappeared into the usual hazy obscurity into which all [my] visual objects ultimately vanish.”

I have a sufficient variety of cases to prove the continuity between all the forms of visualisation, beginning with an almost total absence of it, and ending with a complete hallucination. The continuity is, however, not simply that of varying degrees of intensity, but of variations in the character of the process itself, so that it is by no means uncommon to find two very different forms of it concurrent in the same person. There are some who visualise well, and who also are seers of visions, who declare that the vision is not a vivid visualisation, but altogether a different phenomenon. In short, if we please to call all sensations due to external impressions “_direct”_ and all others “_induced_” then there are many channels through which the “_induction_” of the latter may take place, and the channel of ordinary visualisation in the persons just mentioned is different from that through which their visions arise.

The following is a good instance of this condition. A friend writes: —

“These visions often appear with startling vividness, and so far from depending on any voluntary effort of the mind, [10] they remain when I often wish them very much to depart, and no effort of the imagination can call them up. I lately saw a framed portrait of a face which seemed more lovely than any painting I have ever seen, and again I often see fine landscapes which bear no resemblance to any scenery I have ever looked upon. I find it difficult to define the difference between a waking vision and a mental image, although the difference is very apparent to myself. I think I can do it best in this way. If you go into a theatre and look at a scene–say of a forest by moonlight–at the back part of the stage you see every object distinctly and sufficiently illuminated (being thus unlike a mere act of memory), but it is nevertheless vague and shadowy, and you might have difficulty in telling afterwards all the objects you have seen. This resembles a mental image in point of clearness. The waking vision is like what one sees in the open street in broad daylight, when every object is distinctly impressed on the memory. The two kinds of imagery differ also as regards voluntariness, the image being entirely subservient to the will, the visions entirely independent of it. They differ also in point of suddenness, the images being formed comparatively slowly as memory recalls each detail, and fading slowly as the mental effort to retain them is relaxed, the visions appearing and vanishing in an instant. The waking visions seem quite close, filling as it were the whole head, while the mental image seems farther away in some far-off recess of the mind.”

[Footnote 10: The details and illustrations of four other experiments with the image of a rosebud have been given me. They all vary in detail.]

The number of sane persons who see visions no less distinctly than this correspondent is much greater than I had any idea of when I began this inquiry. I have received an interesting sketch of one, prefaced by a description of it by Mrs. Haweis. She says:–

“All my life long I have had one very constantly-recurring vision, a sight which came whenever it was dark or darkish, in bed or otherwise. It is a flight of pink roses floating in a mass from left to right, and this cloud or mass of roses is presently effaced by a flight of ‘sparks’ or gold speckles across them. The sparks totter or vibrate from left to right, but they fly distinctly upwards; they are like tiny blocks, half gold, half black, rather symmetrically placed behind each other, and they are always in a hurry to efface the roses; sometimes they have come at my call, sometimes by surprise, but they are always equally pleasing. What interests me most is that, when a child under nine, the flight of roses was light, slow, soft, close to my eyes, roses so large and brilliant and palpable that I tried to touch them; the _scent_ was overpowering, the petals perfect, with leaves peeping here and there, texture and motion all natural. They would stay a long time before the sparks came, and they occupied a large area in black space. Then the sparks came slowly flying, and generally, not always, effaced the roses at once, and every effort to retain the roses failed. Since an early age the flight of roses has annually grown smaller, swifter, and farther off, till by the time I was grown up my vision had become a speck, so instantaneous that I had hardly time to realise that it was there before the fading sparks showed that it was past. This is how they still come. The pleasure of them is past, and it always depresses me to speak of them, though I do not now, as I did when a child, connect the vision with any elevated spiritual state. But when I read Tennyson’s _Holy Grail_, I wondered whether anybody else had had my vision, ‘Rose-red, with beatings in it.’ I may add, I was a London child who never was in the country but once, and I connect no particular flowers with that visit. I may almost say that I had never seen a rose, certainly not a quantity of them together.”

A common form of vision is a phantasmagoria, or the appearance of a crowd of phantoms, sometimes hurrying past like men in a street. It is occasionally seen in broad daylight, much more often in the dark; it may be at the instant of putting out the candle, but it generally comes on when the person is in bed, preparing to sleep, but by no means yet asleep. I know no less than three men, eminent in the scientific world, who have these phantasmagoria in one form or another. It will seem curious, but it is a fact that I know of no less than five editors of very influential newspapers who experience these night visitations in a vivid form. Two of them have described the phenomena very forcibly in print, but anonymously, and two others have written on cognate experiences.

A near relative of my own saw phantasmagoria very frequently. She was eminently sane, and of such good constitution that her faculties were hardly impaired until near her death at ninety. She frequently described them to me. It gave her amusement during an idle hour to watch these faces, for their expression was always pleasing, though never strikingly beautiful. No two faces were ever alike, and no face ever resembled that of any acquaintance. When she was not well the faces usually came nearer to her, sometimes almost suffocatingly close. She never mistook them for reality, although they were very distinct. This is quite a typical case, similar in most respects to many others that I have.[1]

A notable proportion of sane persons have had not only visions, but actual hallucinations of sight, sound, or other sense, at one or more periods of their lives. I have a considerable packet of instances contributed by my personal friends, besides a large number communicated to me by other correspondents. One lady, a distinguished authoress, who was at the time a little fidgeted, but in no way overwrought or ill, assured me that she once saw the principal character of one of her novels glide through the door straight up to her. It was about the size of a large doll, and it disappeared as suddenly as it came. Another lady, the daughter of an eminent musician, often imagines she hears her father playing. The day she told me of it the incident had again occurred. She was sitting in her room with her maid, and she asked the maid to open the door that she might hear the music better. The moment the maid got up the hallucination disappeared. Again, another lady, apparently in vigorous health, and belonging to a vigorous family, told me that during some past months she had been plagued by voices. The words were at first simple nonsense; then the word “pray” was frequently repeated; this was followed by some more or less coherent sentences of little import, and finally the voices left her. In short, the familiar hallucinations of the insane are to be met with far more frequently than is commonly supposed, among people moving in society and in good working health.

I have now nearly done with my summary of facts; it remains to make a few comments on them.

The weirdness of visions lies in their sudden appearance, in their vividness while present, and in their sudden departure. An incident in the Zoological Gardens struck me as a helpful simile. I happened to walk to the seal-pond at a moment when a sheen rested on the unbroken surface of the water. After waiting a while I became suddenly aware of the head of a seal, black, conspicuous, [12] and motionless, just as though it had always been there, at a spot on which my eye had rested a moment previously and seen nothing. Again, after a while my eye wandered, and on its returning to the spot the seal was gone. The water had closed in silence over its head without leaving a ripple, and the sheen on the surface of the pond was as unbroken as when I first reached it. Where did the seal come from, and whither did it go? This could easily have been answered if the glare had not obstructed the view of the movements of the animal under water. As it was, a solitary link in a continuous chain of actions stood isolated from all the rest. So it is with the visions; a single stage in a series of mental processes emerges into the domain of consciousness. All that precedes and follows lies outside of it, and its character can only be inferred. We see in a general way that a condition of the presentation of visions lies in the over-sensitiveness of certain tracks or domains of brain action and the under-sensitiveness of others, certain stages in a mental process being represented very vividly in consciousness while the other stages are unfelt; also that individualism is changed to dividualism.

[Footnote 12: See some curious correspondence on this subject in the _St. James’ Gazette_, Feb. 10, 15, and 20, 1882.]

I do not recollect seeing it remarked that the ordinary phenomena of dreaming seem to show that partial sensitiveness is a normal condition during sleep. They do so because one of the most marked characteristics of the dreamer is the absence of common sense. He accepts wildly incongruous visions without the slightest scepticism. Now common sense consists in the comprehension of a large number of related circumstances, and implies the simultaneous working of many parts of the brain. On the other hand, the brain is known to be imperfectly supplied with blood during sleep, and cannot therefore be at full work. It is probable enough, from hydraulic analogies, that imperfect irrigation would lead to partial irrigation, and therefore to suppression of action in some parts of the brain, and that this is really the case seems to be proved by the absence of common sense during dreams.

A convenient distinction is made between hallucinations and illusions. Hallucinations are defined as appearances wholly due to fancy; illusions, as fanciful perceptions of objects actually seen. There is also a hybrid case which depends on fanciful visions fancifully perceived. The problems we have to consider are, on the one hand, those connected with “_induced_” vision, and, on the other hand, those connected with the interpretation of vision, whether the vision be _direct_ or _induced_.

It is probable that much of what passes for hallucination proper belongs in reality to the hybrid case, being an illusive interpretation of some induced visual cloud or blur. I spoke of the ever-varying patterns in the optical field; these, under some slight functional change, may become more consciously present, and be interpreted into fantasmal appearances. Many cases could be adduced to support this view.

I will begin with illusions. What is the process by which they are established? There is no simpler way of understanding it than by trying, as children often do, to see “faces in the fire,” and to carefully watch the way in which they are first caught. Let us call to mind at the same time the experience of past illnesses, when the listless gaze wandered over the patterns on the wall-paper and the shadows of the bed-curtains, and slowly evoked the appearances of faces and figures that were not easily laid again. The process of making the faces is so rapid in health that it is difficult to analyse it without the recollection of what took place more slowly when we were weakened by illness. The first essential element in their construction is, I believe, the smallness of the area covered by the glance at any instant, so that the eye has to travel over a long track before it has visited every part of the object towards which the attention is directed generally. It is as with a plough, that must travel many miles before the whole of a small field can be tilled, but with this important difference–the plough travels methodically up and down in parallel furrows; the eye wanders in devious curves, with abrupt bends, and the direction of its course at any instant depends on four causes: (1) on the easiest sequence of muscular motion, speaking in a general sense, (2) on idiosyncrasy, (3) on the mood, and (4) on the associations current at the moment. The effect of idiosyncrasy ft excellently illustrated by the “Number-Forms,” where we observe that a very special sharply-defined track of mental vision is preferred by each individual who sees them. The influence of the mood of the moment is shown in the curves that are felt appropriate to the various emotions, as the lank drooping lines of grief, which make the weeping willow so fit an emblem of it. In constructing fire-faces it seems to me that the eye in its wanderings tends to follow a favourite course, and it especially dwells upon the marks that happen to coincide with that course. It feels its way, easily diverted by associations based on what has just been noticed, until at last, by the unconscious practice of a system of “trial and error,” it hits upon a track that will suit–one that is easily run over and that strings together accidental marks in a way that happens to form a well-connected picture. This fancy picture is then dwelt upon; all that is incongruous with it becomes disregarded, while all deficiencies in it are supplied by the fantasy. The latest stages of the process might be represented by a diorama. Three lanterns would converge on the same screen. The first throws an image of what the imagination will discard, the second of that which it will retain, the third of that which it will supply. Turn on the first and second, and the picture on the screen will be identical with that which fell on the retina. Shut off the first and turn on the third, and the picture will be identical with the illusion.

Turner the painter made frequent use of a practice analogous to that of looking for fire-faces in the burning coals; he was known to give colours to children to daub in play on paper, while he keenly watched for suggestive but accidental combinations.

I have myself had frequent experience of the automatic construction of fantastic figures, through a practice I have somewhat encouraged for the purpose, of allowing my hand to scribble at its own will, while I am giving my best attention to what is being said by others, as at small committees. It is always a surprise to me to see the result whenever I turn my thoughts on what I have been subconsciously doing. I can rarely recollect even a few of the steps by which the drawings were made; they grew piece-meal, with some almost forgotten notice, from time to time, of the sketch as a whole. I can trace no likeness between what I draw and the images that present themselves to me in dreams, and I find that a very trifling accident, such as a chance dot on the paper, may have great influence on the general character of any one of these automatic sketches.

Visions, like dreams, are often mere patchworks built up of bits of recollections. The following is one of these:–

“When passing a shop in Tottenham Court Road, I went in to order a Dutch cheese, and the proprietor (a bullet-headed man whom I had never seen before) rolled a cheese on the marble slab of his counter, asking me if that one would do. I answered ‘Yes,’ left the shop, and thought no more of the incident. The following evening, on closing my eyes, I saw a head detached from the body rolling about slightly on a white surface. I recognised the face, but could not remember where I had seen it, and it was only after thinking about it for some time that I identified it as that of the cheesemonger who had sold me the cheese on the previous day. I may mention that I have often seen the man since, and that I found the vision I saw was exactly like him, although if I had been asked to describe the man before I saw the vision I should have been unable to do so.”

Recollections need not be combined like mosaic work; they may be blended, on the principle of composite portraiture. I suspect that the phantasmagoria may be in some part due to blended memories; the number of possible combinations would be practically endless, and each combination would give a new face. There would thus be no limit to the dies in the coinage of the brain.

I have found that the peculiarities of visualisation, such as the tendency to see Number-Forms, and the still rarer tendency to associate colour with sound, is strongly hereditary, and I should infer, what facts seem to confirm, that the tendency to be a seer of visions is equally so. Under these circumstances we should expect that it would be unequally developed in different races, and that a large natural gift of the visionary faculty might become characteristic not only of certain families, as among the second-sight seers of Scotland, but of certain races, as that of the Gipsies.

It happens that the mere acts of fasting, of want of sleep, and of solitary musing, are severally conducive to visions. I have myself been told of cases in which persons accidentally long deprived of food became for a brief time subject to them. One was of a pleasure party driven out to sea, and not being able to reach the coast till nightfall, at a place where they got shelter but nothing to eat. They were mentally at ease and conscious of safety, but all were troubled with visions that were half dreams and half hallucinations. The cases of visions following protracted wakefulness are well known, and I have collected a few of them myself. I have already spoken of the maddening effect of solitariness: its influence may be inferred from the recognised advantages of social amusements in the treatment of the insane. It follows that the spiritual discipline undergone for purposes of self-control and self-mortification, have also the incidental effect of producing visions. It is to be expected that these should often bear a close relation to the prevalent subjects of thought, and although they may be really no more than the products of one portion of the brain, which another portion of the same brain is engaged in contemplating, they often, through error, receive a religious sanction. This is notably the case among half-civilised races.

The number of great men who have been once, twice, or more frequently, subject to hallucinations is considerable. A list, to which it would be easy to make large additions, is given by Brierre de Boismont (_Hallucinations_, etc., 1862), from whom I translate the following account of the star of the first Napoleon, which he heard, second-hand, from General Rapp:–

“In 1806 General Rapp, on his return from the siege of Dantzic, having occasion to speak to the Emperor, entered his study without being announced. He found him so absorbed that his entry was unperceived. The General seeing the Emperor continue motionless, thought he might be ill, and purposely made a noise. Napoleon immediately roused himself, and without any preamble, seizing Rapp by the arm, said to him, pointing to the sky, ‘Look there, up there.’ The General remained silent, but on being asked a second time, he answered that he perceived nothing. ‘What!’ replied the Emperor, ‘you do not see it? It is my star, it is before you, brilliant;’ then animating by degrees, he cried out, ‘it has never abandoned me, I see it on all great occasions, it commands me to go forward, and it is a constant sign of good fortune to me.'”

Napoleon was no doubt a consummate actor, ready and unscrupulous in imposing on others, but I see no reason to distrust the genuineness of this particular outburst, seeing that it is not the only instance of his referring to the guidance of his star, as a literal vision and not as a mere phrase, and that his belief in destiny was notorious.

It appears that stars of this kind, so frequently spoken of in history, and so well known as a metaphor in language, are a common hallucination of the insane. Brierre de Boismont has a chapter on the stars of great men. I cannot doubt that visions of this description were in some cases the basis of that firm belief in astrology, which not a few persons of eminence formerly entertained.

The hallucinations of great men may be accounted for in part by their sharing a tendency which we have seen to be not uncommon in the human race, and which, if it happens to be natural to them, is liable to be developed in their overwrought brains by the isolation of their lives. A man in the position of the first Napoleon could have no intimate associates; a great philosopher who explores ways of thought far ahead of his contemporaries must have an inner world in which he passes long and solitary hours. Great men may be even indebted to touches of madness for their greatness; the ideas by which they are haunted, and to whose pursuit they devote themselves, and by which they rise to eminence, having much in common with the monomania of insanity. Striking instances of great visionaries may be mentioned, who had almost beyond doubt those very nervous seizures with which the tendency to hallucinations is intimately connected. To take a single instance, Socrates, whose _daimon_ was an audible not a visual appearance, was, as has been often pointed out, subject to cataleptic seizure, standing all night through in a rigid attitude.

It is remarkable how largely the visionary temperament has manifested itself in certain periods of history and epochs of national life. My interpretation of the matter, to a certain extent, is this–That the visionary tendency is much more common among sane people than is generally suspected. In early life, it seems to be a hard lesson to an imaginative child to distinguish between the real and visionary world. If the fantasies are habitually laughed at and otherwise discouraged, the child soon acquires the power of distinguishing them; any incongruity or nonconformity is quickly noted, the visions are found out and discredited, and are no further attended to. In this way the natural tendency to see them is blunted by repression. Therefore, when popular opinion is of a matter-of-fact kind, the seers of visions keep quiet; they do not like to be thought fanciful or mad, and they hide their experiences, which only come to light through inquiries such as these that I have been making. But let the tide of opinion change and grow favourable to supernaturalism, then the seers of visions come to the front. The faintly-perceived fantasies of ordinary persons become invested by the authority of reverend men with a claim to serious regard; they are consequently attended to and encouraged, and they increase in definition through being habitually dwelt upon. We need not suppose that a faculty previously non-existent has been suddenly evoked, but that a faculty long smothered by many in secret has been suddenly allowed freedom to express itself, and to run into extravagance owing to the removal of reasonable safeguards.

NURTURE AND NATURE.

Man is so educable an animal that it is difficult to distinguish between that part of his character which has been acquired through education and circumstance, and that which was in the original grain of his constitution. His character is exceedingly complex, even in members of the simplest and purest savage race; much more is it so in civilised races, who have long since been exempted from the full rigour of natural selection, and have become more mongrel in their breed than any other animal on the face of the earth. Different aspects of the multifarious character of man respond to different calls from without, so that the same individual, and, much more, the same race, may behave very differently at different epochs. There may have been no fundamental change of character, but a different phase or mood of it may have been evoked by special circumstances, or those persons in whom that mood is naturally dominant may through some accident have the opportunity of acting for the time as representatives of the race. The same nation may be seized by a military fervour at one period, and by a commercial one at another; they may be humbly submissive to a monarch, or become outrageous republicans. The love of art, gaiety, adventure, science, religion may be severally paramount at different times.

One of the most notable changes that can come over a nation is from a state corresponding to that of our past dark ages into one like that of the Renaissance. In the first case the minds of men are wholly taken up with routine work, and in copying what their predecessors have done; they degrade into servile imitators and submissive slaves to the past. In the second case, some circumstance or idea has finally discredited the authorities that impeded intellectual growth, and has unexpectedly revealed new possibilities. Then the mind of the nation is set free, a direction of research is given to it, and all the exploratory and hunting instincts are awakened. These sudden eras of great intellectual progress cannot be due to any alteration in the natural faculties of the race, because there has not been time for that, but to their being directed in productive channels. Most of the leisure of the men of every nation is spent in rounds of reiterated actions; if it could be spent in continuous advance along new lines of research in unexplored regions, vast progress would be sure to be made. It has been the privilege of this generation to have had fresh fields of research pointed out to them by Darwin, and to have undergone a new intellectual birth under the inspiration of his fertile genius.

A pure love of change, acting according to some law of contrast as yet imperfectly understood, especially characterises civilised man. After a long continuance of one mood he wants to throw himself into another for the pleasure of setting faculties into action that have been long disused, but not yet paralysed by disuse, and which have become fidgety for employment. He has so many opportunities for procuring change, and has so complex a nature that he easily learns to neglect a more deeply-seated feeling that innovation is wicked, and which is manifest in children and barbarians. To a civilised man the varied interests of civilisation are temptations in as many directions; changes in dress and appliances of all kinds are comparatively inexpensive to him owing to the cheapness of manufactures and their variety; change of scene is easy from the conveniences of locomotion. But a barbarian has none of these facilities: his interests are few; his dress, such as it is, is intended to stand the wear and tear of years, and all weathers; it is relatively very costly, and is an investment, one may say, of his capital rather than of his income; the invention of his people is sluggish, and their arts are few, consequently he is perforce taught to be conservative, his ideas are fixed, and he becomes scandalised even at the suggestion of change.

The difficulty of indulging in variety is incomparably greater among the rest of the animal world. If a pea-hen should take it into her head that bars would be prettier than eyes in the tail of her spouse, she could not possibly get what she wanted. It would require hundreds of generations in which the pea-hens generally concurred in the same view before sexual selection could effect the desired alteration. The feminine delight of indulging her caprice in matters of ornament is a luxury denied to the females of the brute world, and the law that rules changes in taste, if studied at all, can only be ascertained by observing the alternations of fashion in civilised communities.

There are long sequences of changes in character, which, like the tunes of a musical snuff-box, are regulated by internal mechanism. They are such as those of Shakespeare’s “Seven Ages,” and others due to the progress of various diseases. The lives of birds are characterised by long chains of these periodic sequences. They are mostly mute in winter, after that they begin to sing; some species are seized in the early part of the year with so strong a passion for migrating that if confined in a cage they will beat themselves to death against its bars; then follow courtship and pairing, accompanied by an access of ferocity among the males and severe fighting for the females. Next an impulse seizes them to build nests, then a desire for incubation, then one for the feeding of their young. After this a newly-arisen tendency to gregariousness groups them into large flocks, and finally they fly away to the place whence they came, goaded by a similar instinct to that which drove them forth a few months previously. These remarkable changes are mainly due to the conditions of their natures, because they persist with more or less regularity under altered circumstances. Nevertheless, they are not wholly independent of circumstance, because the period of migration, though nearly coincident in successive years, is modified to some small extent by the weather and condition of the particular year.

The interaction of nature and circumstance is very close, and it is impossible to separate them with precision. Nurture acts before birth, during every stage of embryonic and pre-embryonic existence, causing the potential faculties at the time of birth to be in some degree the effect of nurture. We need not, however, be hypercritical about distinctions; we know that the bulk of the respective provinces of nature and nurture are totally different, although the frontier between them may be uncertain, and we are perfectly justified in attempting to appraise their relative importance.

I shall begin with describing some of the principal influences that may safely be ascribed to education or other circumstances, all of which I include under the comprehensive term of Nurture.

ASSOCIATIONS.

The furniture of a man’s mind chiefly consists of his recollections and the bonds that unite them. As all this is the fruit of experience, it must differ greatly in different minds according to their individual experiences. I have endeavoured to take stock of my own mental furniture in the way described in the next chapter, in which it will be seen how large a part consists of childish recollections, testifying to the permanent effect of many of the results of early education. The same fact has been strongly brought out by the replies from correspondents whom I had questioned on their mental imagery. It was frequently stated that the mental image invariably evoked by certain words was some event of childish experience or fancy. Thus one correspondent, of no mean literary and philosophical power, recollects the left hand by a mental reference to the rocking-horse which always stood by the side of the nursery wall with its head in the same direction, and had to be mounted from the side next the wall. Another, a politician, historian, and scholar, refers all his dates to the mental image of a nursery diagram of the history of the world, which has since developed huge bosses to support his later acquired information.

Our abstract ideas being mostly drawn from external experiences, their character also must depend upon the events of our individual histories. For example, the spoken words house and home must awaken ideas derived from the houses and the homes with which the hearer is, in one way or other, acquainted, and these could not be the same to persons of various social positions and places of residence. The character of our abstract ideas, therefore, depends, to a considerable degree, on our nurture.

I doubt, however, whether “abstract idea” is a correct phrase in many of the cases in which it is used, and whether “cumulative idea” would not be more appropriate. The ideal faces obtained by the method of composite portraiture appear to have a great deal in common with these so-called abstract ideas. The composite portraits consist, as was explained, of numerous superimposed pictures, forming a cumulative result in which the features that are common to all the likenesses are clearly seen; those that are common to a few are relatively faint and are more or less overlooked, while those that are peculiar to single individuals leave no sensible trace at all.

This analogy, which I pointed out in a Memoir on Generic Images, [11] has been extended and confirmed by subsequent experience of the process. One objection to my view was that our so-called generalisations are commonly no more than representative cases, our recollections being apt to be unduly influenced by particular events, and not by the totality of what we have seen; that the reason why some one recollection has prevailed is that the case was sharply defined, or had something unusual about it, or that our frame of mind was at the time of observation susceptible to that particular kind of impression. I have had exactly the same difficulties with the composites. If one of the individual portraits has sharp outlines, or if it is unlike the rest, or if the illumination is temporarily strong, it will assert itself unduly in the result. The cases seem to me exactly analogous. I get over my photographic difficulty very easily by throwing the sharp portrait a little out of focus, by eliminating such portraits as have exceptional features, and by toning down the illumination to a standard intensity.

[Footnote 11: “Generic Images,” _Proc. Royal Institute_, Friday, April 25, 1879, partly reprinted in the Appendix.]

PSYCHOMETRIC EXPERIMENTS.

When we attempt to trace the first steps in each operation of our minds, we are usually baulked by the difficulty of keeping watch, without embarrassing the freedom of its action. The difficulty is much more than the common and well-known one of attending to two things at once. It is especially due to the fact that the elementary operations of the mind are exceedingly faint and evanescent, and that it requires the utmost painstaking to watch them properly. It would seem impossible to give the required attention to the processes of thought, and yet to think as freely as if the mind had been in no way preoccupied. The peculiarity of the experiments I am about to describe is that I have succeeded in evading this difficulty. My method consists in allowing the mind to play freely for a very brief period, until a couple or so of ideas have passed through it, and then, while the traces or echoes of those ideas are still lingering in the brain, to turn the attention upon them with a sudden and complete awakening; to arrest, to scrutinise them, and to record their exact appearance. Afterwards I collate the records at leisure, and discuss them, and draw conclusions. It must be understood that the second of the two ideas was never derived from the first, but always directly from the original object. This was ensured by absolutely withstanding all temptation to reverie. I do not mean that the first idea was of necessity a simple elementary thought; sometimes it was a glance down a familiar line of associations, sometimes it was a well-remembered mental attitude or mode of feeling, but I mean that it was never so far indulged in as to displace the object that had suggested it from being the primary topic of attention.

I must add, that I found the experiments to be extremely trying and irksome, and that it required much resolution to go through with them, using the scrupulous care they demanded. Nevertheless the results well repaid the trouble. They gave me an interesting and unexpected view of the number of the operations of the mind, and of the obscure depths in which they took place, of which I had been little conscious before. The general impression they have left upon me is like that which many of us have experienced when the basement of our house happens to be under thorough sanitary repairs, and we realise for the first time the complex system of drains and gas and water pipes, flues, bell-wires, and so forth, upon which our comfort depends, but which are usually hidden out of sight, and with whose existence, so long as they acted well, we had never troubled ourselves.

The first experiments I made were imperfect, but sufficient to inspire me with keen interest in the matter, and suggested the form of procedure that I have already partly described. My first experiments were these. On several occasions, but notably on one when I felt myself unusually capable of the kind of effort required, I walked leisurely along Pall Mall, a distance of 450 yards, during which time I scrutinised with attention every successive object that caught my eyes, and I allowed my attention to rest on it until one or two thoughts had arisen through direct association with that object; then I took very brief mental note of them, and passed on to the next object. I never allowed my mind to ramble. The number of objects viewed was, I think, about 300, for I had subsequently repeated the same walk under similar conditions and endeavoured to estimate their number, with that result. It was impossible for me to recall in other than the vaguest way the numerous ideas that had passed through my mind; but of this, at least, I am sure, that samples of my whole life had passed before me, that many bygone incidents, which I never suspected to have formed part of my stock of thoughts, had been glanced at as objects too familiar to awaken the attention. I saw at once that the brain was vastly more active than I had previously believed it to be, and I was perfectly amazed at the unexpected width of the field of its everyday operations. After an interval of some days, during which I kept my mind from dwelling on my first experiences, in order that it might retain as much freshness as possible for a second experiment, I repeated the walk, and was struck just as much as before by the variety of the ideas that presented themselves, and the number of events to which they referred, about which I had never consciously occupied myself of late years. But my admiration at the activity of the mind was seriously diminished by another observation which I then made, namely, that there had been a very great deal of repetition of thought. The actors in my mental stage were indeed very numerous, but by no means so numerous as I had imagined. They now seemed to be something like the actors in theatres where large processions are represented, who march off one side of the stage, and, going round by the back, come on again at the other. I accordingly cast about for means of laying hold of these fleeting thoughts, and, submitting them to statistical analysis, to find out more about their tendency to repetition and other matters, and the method I finally adopted was the one already mentioned. I selected a list of suitable words, and wrote them on different small sheets of paper. Taking care to dismiss them from my thoughts when not engaged upon them, and allowing some days to elapse before I began to use them, I laid one of these sheets with all due precautions, under a book, but not wholly covered by it, so that when I leaned forward I could see one of the words, being previously quite ignorant of what the word would be. Also I held a small chronograph, which I started by pressing a spring the moment the word caught my eye, and which stopped of itself the instant I released the spring; and this I did so soon as about a couple of ideas in direct association with the word had arisen in my mind. I found that I could not manage to recollect more than two ideas with the needed precision, at least not in a general way; but sometimes several ideas occurred so nearly together that I was able to record three or even four of them, while sometimes I only managed one. The second ideas were, as I have already said, never derived from the first, but always direct from the word itself, for I kept my attention firmly fixed on the word, and the associated ideas were seen only by a half glance. When the two ideas had occurred,

I stopped the chronograph and wrote them down, and the time they occupied. I soon got into the way of doing all this in a very methodical and automatic manner, keeping the mind perfectly calm and neutral, but intent and, as it were, at full cock and on hair trigger, before displaying the word. There was no disturbance occasioned by thinking of the forthcoming revulsion of the mind the moment before the chronograph was stopped. My feeling before stopping it was simply that I had delayed long enough, and this in no way interfered with the free action of the mind. I found no trouble in ensuring the complete fairness of the experiment, by using a number of little precautions, hardly necessary to describe, that practice quickly suggested, but it was a most repugnant and laborious work, and it was only by strong self-control that I went through my schedule according to programme. The list of words that I finally secured was 75 in number, though I began with more. I went through them on four separate occasions, under very different circumstances, in England and abroad, and at intervals of about a month. In no case were the associations governed to any degree worth recording, by remembering what had occurred to me on previous occasions, for I found that the process itself had great influence in discharging the memory of what it had just been engaged in, and I, of course, took care between the experiments never to let my thoughts revert to the words. The results seem to me to be as trustworthy as any other statistical series that has been collected with equal care.

On throwing these results into a common statistical hotch-pot, I first examined into the rate at which these associated ideas were formed. It took a total time of 660 seconds to form the 505 ideas; that is, at about the rate of 50 in a minute, or 3000 in an hour. This would be miserably slow work in reverie, or wherever the thought follows the lead of each association that successively presents itself. In the present case, much time was lost in mentally taking the word in, owing to the quiet unobtrusive way in which I found it necessary to bring it into view, so as not to distract the thoughts. Moreover, a substantive standing by itself is usually the equivalent of too abstract an idea for us to conceive properly without delay. Thus it is very difficult to get a quick conception of the word “carriage,” because there are so many different kinds–two-wheeled, four-wheeled, open and closed, and all of them in so many different possible positions, that the mind possibly hesitates amidst an obscure sense of many alternatives that cannot blend together. But limit the idea to say a laudau, and the mental association declares itself more quickly. Say a laudau coming down the street to opposite the door, and an image of many blended laudaus that have done so forms itself without the least hesitation.

Next, I found that my list of 75 words gone over 4 times, had given rise to 505 ideas and 13 cases of puzzle, in which nothing sufficiently definite to note occurred within the brief maximum period of about 4 seconds, that I allowed myself to any single trial. Of these 505 only 289 were different The precise proportions in which the 505 were distributed in quadruplets, triplets, doublets, or singles, is shown in the uppermost lines of Table I. The same facts are given under another form in the lower lines of the Table, which show how the 289 different ideas were distributed in cases of fourfold, treble, double, or single occurrences.

TABLE I.
RECURRENT ASSOCIATIONS.
================+=================================================+ Total Number of | | Associations. | Occurring in | |————————————————-+ | Quadruplets. | Triplets. | Doublets. | Singles.| 505 | 116 | 108 | 114 | 167 | —————-+————–+————+———–+———+ Per cent . 100 | 23 | 21 | 23 | 33 | ================+==============+============+===========+=========+ Total Number of | | Different | Occurring | Associations. +————————————————-+ | Four times. |Three times.| Twice. | Once. | —————-+————–+————+———–+———+ 289 | 29 | 36 | 57 | 167 | —————-+————–+————+———–+———+ Per cent . 100 | 10 | 12 | 20 | 58 | ================+==============+============+===========+=========+

I was fully prepared to find much iteration in my ideas but had little expected that out of every hundred words twenty-three would give rise to exactly the same association in every one of the four trials; twenty-one to the same association in three out of the four, and so on, the experiments having been purposely conducted under very different conditions of time and local circumstances. This shows much less variety in the mental stock of ideas than I had expected, and makes us feel that the roadways of our minds are worn into very deep ruts. I conclude from the proved number of faint and barely conscious thoughts, and from the proved iteration of them, that the mind is perpetually travelling over familiar ways without our memory retaining any impression of its excursions. Its footsteps are so light and fleeting that it is only by such experiments as I have described that we can learn anything about them. It is apparently always engaged in mumbling over its old stores, and if any one of these is wholly neglected for a while, it is apt to be forgotten, perhaps irrecoverably. It is by no means the keenness of interest and of the attention when first observing an object, that fixes it in the recollection. We pore over the pages of a _Bradshaw_, and study the trains for some particular journey with the greatest interest; but the event passes by, and the hours and other facts which we once so eagerly considered become absolutely forgotten. So in games of whist, and in a large number of similar instances. As I understand it, the subject must have a continued living interest in order to retain an abiding place in the memory. The mind must refer to it frequently, but whether it does so consciously or unconsciously is not perhaps a matter of much importance. Otherwise, as a general rule, the recollection sinks, and appears to be utterly drowned in the waters of Lethe.

The instances, according to my personal experience, are very rare, and even those are not very satisfactory, in which some event recalls a memory that had lain _absolutely_ dormant for many years. In this very series of experiments a recollection which I thought had entirely lapsed appeared under no less than three different aspects on different occasions. It was this: when I was a boy, my father, who was anxious that I should learn something of physical science, which was then never taught at school, arranged with the owner of a large chemist’s shop to let me dabble at chemistry for a few days in his laboratory. I had not thought of this fact, so far as I was aware, for many years; but in scrutinising the fleeting associations called up by the various words, I traced two mental visual images (an alembic and a particular arrangement of tables and light), and one mental sense of smell (chlorine gas) to that very laboratory. I recognised that these images appeared familiar to me, but I had not thought of their origin. No doubt if some strange conjunction of circumstances had suddenly recalled those three associations at the same time, with perhaps two or three other collateral matters which may be still living in my memory, but which I no not as yet identify, a mental perception of startling vividness would be the result, and I should have falsely imagined that it had supernaturally, as it were, started into life from an entire oblivion extending over many years. Probably many persons would have registered such a case as evidence that things once perceived can never wholly vanish from the recollection, but that in the hour of death, or under some excitement, every event of a past life may reappear. To this view I entirely dissent. Forgetfulness appears absolute in the vast majority of cases, and our supposed recollections of a past life are, I believe, no more than that of a large number of episodes in it, to be reckoned perhaps in hundreds of thousands, but certainly not in tens of hundreds of thousands, that have escaped oblivion. Every one of the fleeting, half-conscious thoughts that were the subject of my experiments, admitted of being vivified by keen attention, or by some appropriate association, but I strongly suspect that ideas which have long since ceased to fleet through the brain, owing to the absence of current associations to call them up, disappear wholly. A comparison of old memories with a newly-met friend of one’s boyhood, about the events we then witnessed together, show how much we had each of us forgotten. Our recollections do not tally. Actors and incidents that seem to have been of primary importance in those events to the one have been utterly forgotten by the other. The recollection of our earlier years are, in truth, very scanty, as any one will find who tries to enumerate them.

My associated ideas were for the most part due to my own unshared experiences, and the list of them would necessarily differ widely from that which another person would draw up who might repeat my experiments. Therefore one sees clearly, and I may say, one can see _measurably_, how impossible it is in a general way for two grown-up persons to lay their minds side by side together in perfect accord. The same sentence cannot produce precisely the same effect on