I subjoin a table, compiled by the help of Dr. Scripture's collection, which will broadly ill.u.s.trate the main points above mentioned. Some more detailed remarks may then follow.

TABLE OF PRINc.i.p.aL ARITHMETICAL PRODIGIES.

+-----------------------+---------------+---------------+---------------+

Name

Age when gift

Duration of

(alphabetically).

was observed.

gift.

Intelligence.

+-----------------------+---------------+---------------+---------------+

Ampere

4

?

eminent

Bidder

10

through life

good

Buxton

?

?

low

Colburn

6

few years

average

Dase [or Dahse]

boyhood

through life

very low

Fuller

boyhood

?

low

Gauss

3

?

eminent

Mangiamele

10

few years

average?

Mondeux

10

few years

low

Prolongeau

6

few years

low

Safford

6

few years

good

"Mr. Van R., of Utica"

6

few years

average?

Whately

3

few years

good

+-----------------------+---------------+---------------+---------------+

Now among these thirteen names we have two men of transcendent, and three of high ability. What accounts have they given us of their methods?

Of the gift of Gauss and Ampere we know nothing except a few striking anecdotes. After manifesting itself at an age when there is usually no continuous supraliminal mental effort worth speaking of, it appears to have been soon merged in the general blaze of their genius. With Bidder the gift persisted through life, but grew weaker as he grew older. His paper in Vol. XV. of the _Proceedings of the Inst.i.tute of Civil Engineers_, while furnishing a number of practical hints to the calculator, indicates also a singular readiness of communication between different mental strata. "Whenever," he says (p. 255) "I feel called upon to make use of the stores of my mind, they seem to rise with the rapidity of lightning." And in Vol. CIII. of the same _Proceedings_, Mr.

W. Pole, F.R.S., in describing how Mr. Bidder could determine mentally the logarithm of any number to 7 or 8 places, says (p. 252): "He had an almost miraculous power of seeing, as it were, intuitively what factors would divide any large number, not a prime. Thus, if he were given the number 17,861, he would instantly remark it was 33753.... He could not, he said, explain how he did this; it seemed a natural instinct to him."

Pa.s.sing on to the two other men of high ability known to have possessed this gift, Professor Safford and Archbishop Whately, we are struck with the evanescence of the power after early youth,--or even before the end of childhood. I quote from Dr. Scripture Archbishop Whately's account of his powers.

There was certainly something peculiar in my calculating faculty.

It began to show itself at between five and six, and lasted about three years.... I soon got to do the most difficult sums, always in my head, for I knew nothing of figures beyond numeration. I did these sums much quicker than any one could upon paper, and I never remember committing the smallest error. _When I went to school, at which time the pa.s.sion wore off, I was a perfect dunce at ciphering, and have continued so ever since._

Still more remarkable, perhaps, was Professor Safford's loss of power.

Professor Safford's whole bent was mathematical; his boyish gift of calculation raised him into notice; and he is now a Professor of Astronomy. He had therefore every motive and every opportunity to retain the gift, if thought and practice could have retained it. But whereas at ten years old he worked correctly in his head, in one minute, a multiplication sum whose answer consisted of 36 figures, he is now, I believe, neither more nor less capable of such calculation than his neighbours.

Similar was the fate of a personage who never rises above initials, and of whose general capacity we know nothing.

"Mr. Van R., of Utica," says Dr. Scripture on the authority of Gall, "at the age of six years distinguished himself by a singular faculty for calculating in his head. At eight he entirely lost this faculty, and after that time he could calculate neither better nor faster than any other person. _He did not retain the slightest idea of the manner in which he performed his calculations in childhood._"

Turning now to the stupid or uneducated prodigies, Dase alone seems to have retained his power through life. Colburn and Mondeux, and apparently Prolongeau and Mangiamele, lost their gift after childhood.

On the whole the ignorant prodigies seldom appear to have been conscious of any continuous logical process, while in some cases the separation of the supraliminal and subliminal trains of thought must have been very complete. "Buxton would talk freely whilst doing his questions, that being no molestation or hindrance to him."[29] Fixity and clearness of inward visualisation seems to have been the leading necessity in all these achievements; and it apparently mattered little whether the mental blackboard (so to say) on which the steps of the calculation were recorded were or were not visible to the mind's eye of the supraliminal self.

I have been speaking only of visualisation; but it would be interesting if we could discover how much actual mathematical insight or inventiveness can be subliminally exercised. Here, however, our materials are very imperfect. From Gauss and Ampere we have, so far as I know, no record. At the other end of the scale, we know that Dase (perhaps the most successful of all these prodigies) was singularly devoid of mathematical grasp. "On one occasion Petersen tried in vain for six weeks to get the first elements of mathematics into his head."

"He could not be made to have the least idea of a proposition in Euclid.

Of any language but his own he could never master a word." Yet Dase received a grant from the Academy of Sciences at Hamburg, on the recommendation of Gauss, for mathematical work; and actually in twelve years made tables of factors and prime numbers for the seventh and nearly the whole of the eighth million,--a task which probably few men could have accomplished, without mechanical aid, in an ordinary lifetime. He may thus be ranked as the only man who has ever done valuable service to Mathematics without being able to cross the a.s.s's Bridge.

No support is given by what we know of this group to the theory which regards subliminal mentation as necessarily a sign of some morbid dissociation of physical elements. Is there, on the other hand, anything to confirm a suggestion which will occur in some similar cases, namely, that,--inasmuch as the addition of subliminal to supraliminal mentation may often be a completion and integration rather than a fractionation or disintegration of the total individuality,--we are likely sometimes to find traces of a more than common activity of the _right_ or less used cerebral hemisphere? Finding no mention of ambidexterity in the meagre notices which have come down to us of the greater "prodigies," I begged the late Mr. Bidder, Q.C., and Mr. Blyth, of Edinburgh (the well-known civil engineer and perhaps the best living English representative of what we may call the calculating diathesis), to tell me whether their left hands possessed more than usual power. And I find that in these--the only two cases in which I have been able to make inquiry--there is somewhat more of dextro-cerebral capacity than in the ma.s.s of mankind.

We may now pa.s.s on to review some further instances of subliminal co-operation with conscious thought;--first looking about us for any cases comparable in _definiteness_ with the preceding; and then extending our view over the wider and vaguer realm of creative and artistic work.

But before we proceed to the highly-specialised senses of hearing and sight, we must note the fact that there are cases of subliminal intensification of those perceptions of a less specialised kind which underlie our more elaborate modes of cognising the world around us. The sense of the _efflux of time_, and the sense of _weight_, or of muscular resistance, are amongst the profoundest elements in our organic being. And the sense of time is indicated in several ways as a largely subliminal faculty. There is much evidence to show that it is often more exact in men sleeping than in men awake, and in men hypnotised than in men sleeping. The records of spontaneous somnambulism are full of predictions made by the subject as to his own case, and accomplished, presumably by self-suggestion, but without help from clocks, at the precise minute foretold. Or this hidden knowledge may take shape in the imagery of dream, as in a case published by Professor Royce, of Harvard,[30] where his correspondent describes "a dream in which I saw an enormous flaming clock-dial with the hands standing at 2.20. Awaking immediately, I struck a match, and upon looking at my watch found it was a few seconds past 2.20."

Similarly we find cases where the uprush of subliminal faculty is concerned with the deep organic sensation of muscular resistance. We need not postulate any direct or supernormal knowledge,--but merely a subliminal calculation, such as we see in the case of "arithmetical prodigies," expressing itself supraliminally, sometimes in a phantasmal picture, sometimes as a mere "conviction," without sensory clothing.[31]

Pa.s.sing on here to subliminal products of _visual_ type, I am glad to be able to quote the following pa.s.sage which seems to me to give in germ the very theory for which I am now contending on the authority of one of the most lucid thinkers of the last generation.

The pa.s.sage occurs in an article by Sir John Herschel on "Sensorial Vision," in his _Familiar Lectures on Scientific Subjects_, 1816. Sir John describes some experiences of his own, "which consist in the involuntary production of visual impressions, into which geometrical regularity of form enters as the leading character, and that, under circ.u.mstances which altogether preclude any explanation drawn from a possible regularity of structure in the retina or the optic nerve."[32]

Twice these patterns appeared in waking daylight hours,--with no illness or discomfort at the time or afterwards. More frequently they appeared in darkness; but still while Sir John was fully awake. They appeared also twice when he was placed under chloroform; "and I should observe that I never lost my consciousness of being awake and in full possession of my mind, though quite insensible to what was going on....

Now the question at once presents itself--What _are_ these Geometrical Spectres? and how, and in what department of the bodily or mental economy do they originate? They are evidently not dreams. The mind is not dormant, but active and conscious of the direction of its thoughts; while these things obtrude themselves on notice, and by calling attention to them, _direct_ the train of thought into a channel it would not have taken of itself.... If it be true that the conception of a regular geometrical pattern implies the exercise of thought and intelligence, it would almost seem that in such cases as those above adduced we have evidence of a _thought_, an intelligence, working within our own organisation distinct from that of our own personality." And Sir John further suggests that these complex figures, entering the mind in this apparently arbitrary fashion, throw light upon "the suggestive principle" to which "we must look for much that is determinant and decisive of our volition when carried into action." "It strikes me as not by any means devoid of interest to contemplate cases where, in a matter so entirely abstract, so completely devoid of any moral or emotional bearing, as the production of a geometrical figure, we, as it were, seize upon that principle in the very act, and in the performance of its office."

From my point of view, of course, I can but admire the ac.u.men which enabled this great thinker to pierce to the root of the matter by the aid of so few observations. He does not seem to have perceived the connection between these "schematic phantasms," to borrow a phrase from Professor Ladd,[33] and the hallucinatory figures of men or animals seen in health or in disease. But even from his scanty data his inference seems to me irresistible;--"we have evidence of a _thought_, an intelligence, working within our own organisation, distinct from that of our own personality." I shall venture to claim him as the first originator of the theory to which the far fuller evidence now accessible had independently led myself.

Cases observed as definitely as those just quoted are few in number; and I must pa.s.s on into a much trodden--even a confusedly trampled--field;--the records, namely, left by eminent men as to the element of subconscious mentation, which was involved in their best work. Most of these stories have been again and again repeated;--and they have been collected on a large scale in a celebrated work,--to me especially distasteful, as containing what seems to me the loose and extravagant parody of important truth. It is not my business here to criticise Dr. Von Hartmann's _Philosophy of the Unconscious_ in detail; but I prefer to direct my readers' attention to a much more modest volume, in which a young physician has put together the results of a direct inquiry addressed to some Frenchmen of distinction as to their methods especially of imaginative work.[34] I quote a few of the replies addressed to him, beginning with some words from M. Sully Prudhomme,--at once psychologist and poet,--who is here speaking of the subconscious clarification of a chain of abstract reasoning. "I have sometimes suddenly understood a geometrical demonstration made to me a year previously without having in any way directed thereto my attention or will. It seemed that the mere spontaneous ripening of the conceptions which the lectures had implanted in my brain had brought about within me this novel grasp of the proof."

With this we may compare a statement of Arago's--"Instead of obstinately endeavouring to understand a proposition at once, I would admit its truth provisionally;--and next day I would be astonished at understanding thoroughly that which seemed all dark before."

Condillac similarly speaks of finding an incomplete piece of work finished next day in his head.

Somewhat similarly, though in another field, M. Rette, a poet, tells Dr.

Chabaneix that he falls asleep in the middle of an unfinished stanza, and when thinking of it again in the morning finds it completed. And M.

Vincent d'Indy, a musical composer, says that he often has on waking a fugitive glimpse of a musical effect which (like the memory of a dream) needs a strong immediate concentration of mind to keep it from vanishing.

De Musset writes, "On ne travaille pas, on ecoute, c'est comme un inconnu qui vous parle a l'oreille."

Lamartine says, "Ce n'est pas moi qui pense; ce sont mes idees qui pensent pour moi."

Remy de Gourmont: "My conceptions rise into the field of consciousness like a flash of lightning or like the flight of a bird."

M. S. writes: "In writing these dramas I seemed to be a spectator at the play; I gazed at what was pa.s.sing on the scene in an eager, wondering expectation of what was to follow. And yet I felt that all this came from the depth of my own being."

Saint-Saens had only to listen, as Socrates to his Daemon; and M. Ribot, summing up a number of similar cases, says: "It is the unconscious which produces what is vulgarly called inspiration. This condition is a positive fact, accompanied with physical and psychical characteristics peculiar to itself. Above all, it is impersonal and involuntary, it acts like an instinct, when and how it chooses; it may be wooed, but cannot be compelled. Neither reflection nor will can supply its place in original creation.... The bizarre habits of artists when composing tend to create a special physiological condition,--to augment the cerebral circulation in order to provoke or to maintain the unconscious activity."

In what precise way the cerebral circulation is altered we can hardly at present hope to know. Meantime a few psychological remarks fall more easily within our reach.

In the first place, we note that a very brief and shallow submergence beneath the conscious level is enough to infuse fresh vigour into supraliminal trains of thought. Ideas left to mature unnoticed for a few days, or for a single night, seem to pa.s.s but a very little way beneath the threshold. They represent, one may say, the first stage of a process which, although often inconspicuous, is not likely to be discontinuous,--the sustenance, namely, of the supraliminal life by impulse or guidance from below.

In the second place, we see in some of these cases of deep and fruitful _abstraction_ a slight approach to duplication of personality. John Stuart Mill, intent on his _Principles of Logic_, as he threaded the crowds of Leadenhall Street, recalls certain morbid cases of hysterical _distraction_;--only that with Mill the process was an integrative one and not a dissolutive one--a gain and not a loss of power over the organism.

And thirdly, in some of these instances we see the man of genius achieving spontaneously, and unawares, much the same result as that which is achieved for the hypnotic subject by deliberate artifice. For he is in fact co-ordinating the waking and the sleeping phases of his existence. He is carrying into sleep the knowledge and the purpose of waking hours;--and he is carrying back into waking hours again the benefit of those profound a.s.similations which are the privilege of sleep. Hypnotic suggestion aims at co-operations of just this kind between the waking state in which the suggestion, say, of some functional change, is planned and the sleeping state in which that change is carried out,--with benefit persisting anew into waking life.

The hypnotic trance, which is a _developed_ sleep, thus accomplishes for the ordinary man what ordinary sleep accomplishes for the man of genius.

The coming chapters on Sleep and Hypnotism will ill.u.s.trate this point more fully. But I may here antic.i.p.ate my discussion of _dreams_ by quoting one instance where dreams, self-suggested by waking will, formed, as one may say, an integral element in distinguished genius.

The late Robert Louis Stevenson, being in many ways a typical man of genius, was in no way more markedly gifted with that integrating faculty--that increased power over all strata of the personality--which I have ascribed to genius, than in his relation to his dreams (see "A Chapter on Dreams" in his volume _Across the Plains_). Seldom has the essential a.n.a.logy between dreams and inspiration been exhibited in such a striking way. His dreams had always (he tells us) been of great vividness, and often of markedly _recurrent_ type. But the point of interest is that, when he began to write stories for publication, the "little people who managed man's internal theatre" understood the change as well as he.

When he lay down to prepare himself for sleep, he no longer sought amus.e.m.e.nt, but printable and profitable tales; and after he had dozed off in his box-seat, his little people continued their evolutions with the same mercantile designs.... For the most part, whether awake or asleep, he is simply occupied--he or his little people--in consciously making stories for the market....

The more I think of it, the more I am moved to press upon the world my question: "Who are the Little People?" They are near connections of the dreamer's, beyond doubt; they share in his financial worries and have an eye to the bank book; they share plainly in his training; ... they have plainly learned like him to build the scheme of a considerate story and to arrange emotion in progressive order; only I think they have more talent; and one thing is beyond doubt,--they can tell him a story piece by piece, like a serial, and keep him all the while in ignorance of where they aim....

That part [of my work] which is done while I am sleeping is the Brownies' part beyond contention; but that which is done when I am up and about is by no means necessarily mine, since all goes to show the Brownies have a hand in it even then.

Slight and imperfect as the above statistics and observations admittedly are, they seem to me to point in a more useful direction than do some of the facts collected by that modern group of anthropologists who hold that genius is in itself a kind of nervous malady, a disturbance of mental balance, akin to criminality or even to madness.

It is certainly not true, as I hold, either that the human race in general is nervously degenerating, or that nervous degeneration tends to a maximum in its most eminent members. But it can be plausibly maintained that the proportion of nervous to other disorders tends to increase. And it is certain that not nervous degeneration but nervous change or development is now proceeding among civilised peoples more rapidly than ever before, and that this self-adaptation to wider environments must inevitably be accompanied in the more marked cases by something of nervous instability. And it is true also that from one point of view these changes might form matter for regret; and that in order to discern what I take to be their true meaning we have to regard the problem of human evolution from a somewhat unfamiliar standpoint.

The nervous system is probably tending in each generation to become more complex and more delicately ramified. As is usual when any part of an organism is undergoing rapid evolutive changes, this nervous progress is accompanied with some instability. Those individuals in whom the hereditary or the acquired change is the most rapid are likely also to suffer most from a _perturbation which masks evolution_--an occasional appearance of what may be termed "nervous sports" of a useless or even injurious type. Such are the fancies and fanaticisms, the bizarre likes and dislikes, the excessive or aberrant sensibilities, which have been observed in some of the eminent men whom Lombroso discusses in his book on the Man of Genius. Their truest a.n.a.logue, as we shall presently see more fully, lies in the oddities or morbidities of sentiment or sensation which so often accompany the development of the human organism into its full potencies, or precede the crowning effort by which a fresh organism is introduced into the world.

Such at least is my view; but the full acceptance of this view must depend upon some very remote and very speculative considerations bearing upon the nature and purport of the whole existence and evolution of man.

Yet however remote and speculative the thesis which I defend may be, it is not one whit remoter or more speculative than the view which, _faute de mieux_, is often tacitly a.s.sumed by scientific writers.

In our absolute ignorance of the source from whence life came, we have no ground for a.s.suming that it was a purely planetary product, or that its unknown potentialities are concerned with purely planetary ends. It would be as rash for the biologist to a.s.sume that life on earth can only point to generations of further life on earth as it would have been for some cosmic geologist to a.s.sume--before the appearance of life on earth--that geological forces must needs const.i.tute all the activity which could take place on this planet.

Since the germ of life appeared on earth, its history has been a history not only of gradual _self-adaptation_ to a known environment, but of gradual _discovery_ of an environment, always there, but unknown. What we call its primitive simple irritability was in fact a dim panaesthesia; a potential faculty, as yet unconscious of all the stimuli to which it had not yet learnt to respond. As these powers of sensation and of response have developed, they have gradually revealed to the living germ environments of which at first it could have no conception.

It is probable, to begin with, that the only environment which the vast majority of our ancestors knew was simply hot water. For the greater part of the time during which life has existed on earth it would have been thought chimerical to suggest that we could live in anything else.