Chapter VIII: Introduction (5)

"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."

"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'être_.'"

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.

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°. 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: Zwangmässige 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 _naïve_ 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."