The genius has limits. A simple answer, and undoubtedly true. But my assignment here is to reflect on the much more complex difference between intellectual giftedness and genius, using the latter term in its original sense, as socially recognized, outstandingly creative achievement. In this think-piece (which is just that, rather than a comprehensive review of the literature), I will focus on factors, many intriguing in and of themselves, that are characteristic of genius. My primary thesis is that the emergence of genius is best described using a multiplicative model.
I will argue that exceptional achievement is a multiplicative function of a number of different traits, each of which is normally distributed, but which in combination are so synergistic as to skew the resulting distribution of achieve ment. An extremely extended upper tail is thus produced, and it is within this tail that genius can be found. An interesting two-part question then arises: how many different traits are involved in producing extraordinary achievement, and what are they? The musings that follow provide some conjectures that can be drawn on to answer this critical question. As a subject for scientific study, the topic of genius, although immensely fascinating, is about as far from ideal as any phenom enon one can find. The literature on real genius can claim little besides biographical anecdotes and speculation, with this chapter contributing only more of the same. Whether the study of genius will ever evolve from a literary art form into a systematic science is itself highly speculative. The most promising efforts in this direction are those by Simonton (198 8 ) and Eysenck (1 9 9 5 ), with Eysenck’s monograph leaving little of potential scientific value that can be added to the subject at present, pending new empirical evidence.
Intelligence
Earlier I stated that genius has limits. But its upper limit, at least in some fields, seems to be astronomically higher than its lower limit. Moreover, the upper lim it of genius cannot be described as characterized by precocity, high intel ligence, knowledge and problem -solving skills being learned with speed and ease, outstanding academic achievement, honors and awards, or even intellec tual productivity. Although such attributes are commonly found at all levels of genius, they are not discriminating in the realm of genius. My point is perhaps most clearly illustrated by the contrast between two famous mathematicians who became closely associated with one another as “teacher” and “student.” T he reason for the quotation marks here will soon be obvious, because the teacher later claimed that he learned more from the student than the student had learned from him . G. H. Hardy was England’s leading mathematician, a professor at Cambridge University, a Fellow of the Royal Society, and the recipient of an honorary degree from Harvard. Rem ark ably precocious in early childhood, especially in m athem atics, he became an exceptionally brilliant student, winning a scholarship after another acknowledged the star graduate in mathematics at Cambridge, where he remained to become a professor of m athem atics. He also became a world-class mathematician. His longtime friend C. R Snow relates that Hardy, at the peak of his career, ranked himself fifth among the most important mathematicians of his day, and it should be pointed out that Hardy’s colleagues regarded him as an overly modest man (Snow, 1967). If the Study of Mathematically Precocious Youth (SMPY) had been in existence when Hardy was a schoolboy, he would have been a most prized and promising student in the program. One day Hardy received a strange-looking letter from Madras, India. It was full of mathematical formulations written in a quite unconventional—one might even say bizarre—form . The writer seemed almost mathematically illiter by Cambridge standards. It was signed “Srinivasa Ramanujan.” At first glance, Hardy thought it might even be some kind of fraud. Puzzling over this letter with its abstruse formulations, he surmised it was written either by some trickster or by someone sincere but poorly educated in m athem atics. Hardy sought the opinion of his most highly esteemed colleague, J. E. Littlewood, the other famous mathematician at Cambridge. After the two of them had spent several hours studying the strange letter, they finally realized, with excitement and absolute certainty, that they had “discovered” a major mathematical ge nius. The weird-looking formulas, it turned out, revealed profound m athe matical insights of a kind that are never created by ordinarily gifted mathematics. Hardy regarded this “discovery” as the single most important event in his life. Here was the prospect of fulfilling what, until then, had been for him only an improbable dream: of ever knowing in person a mathematician possibly of Gauss’s caliber. A colleague in Hardy’s department then traveled to India and persuaded Ramanujan to go to Cambridge, with all his expenses and a salary paid by the university. When the youth arrived from India, it was evident that, by ordinary standards, his educational background was meager and his almost entirely self taught knowledge of math was full of gaps. He had not been at all successful in school, from which he had flunked out twice, and was never graduated. To say, however, that he was obsessed by m athem atics is an understatement. As a boy in Madras, he was too poor to buy paper on which to work out his math prob lems. He did his prodigious mathematical work on a slate, copying his final results with red ink on old, discarded newspapers. While in high school, he thought he had made a stunning mathematical discovery, but he later learned, to his great dismay, that his discovery had already been made 150 years earlier by the great mathematician Euler. R am anu jan felt extraordinary shame for having “discovered” something that was not original, never considering that only a real genius could have created or even re created that discovery. At Cambridge, Ramanujan was not required to take courses or exams. That would have been almost an insult and a sure waste of time. He learned some essential things from Hardy, but what excited Hardy the most had nothing to do with Ramanujan’s great facility in learning the most advanced concepts and technical skills of mathematical analysis. Hardy himself had that kind of facility. What so impressed him was Ramanujan’s
uncanny mathematical intuition and capacity for inventing incredibly original and profound theorems. That, of course, is what real mathematical genius is all about. Facility in resolving textbook problem s and in passing difficult tests is utterly trivial when discussing genius. Although working out the proof of a theorem, unlike discovering a theorem , may take immense technical skill and assiduous effort, it is not itself a hallmark of genius. Indeed, Ramanujan seldom bothered to prove his own theorem s; proof was a technical feat that could be left to lesser geniuses. Moreover, in some cases, because of his spotty mathematical education, he probably would have been unable to produce a formal proof even if he had wanted to. But a great many important theorems were generated in his ob passively active brain. Often he seemed to be in another world. One might say that the difference between Ram anujan creating a theorem and a professional mathematician solving a complex problem with standard techniques of analysis
is like the difference between St. Francis in ecstasy and a sleepy vicar reciting the morning order of prayer. After his experience with Ramanujan, Hardy told Snow that if the word genius meant anything, he (Hardy) was not really a genius at all (Snow, 1967, p. 27). Hardy had his own hundred-point rating scale of his estimates of the “natural ability” of eminent mathematicians. Though regarding himself at the tim e as one of the world’s five best pure mathematicians, he gave himself a rating of only 25. The greatest mathematician of that period, David Hilbert, was rated 80. But Hardy rated Ramanujan 100, the same rating as he gave Carl Friedrich Gauss, who is generally considered the greatest mathematical genius the world has known. On the importance of their total contributions to mathematics, however, Hardy rated himself 35, Ramanujan 85, and Gauss 100. By this reckoning Hardy was seemingly an overachiever and Ramanujan an under achiever. Yet one must keep in mind that Ramanujan died at age thirty, Hardy at seventy, and Gauss at seventy-eight. of course, all geniuses are by definition extrem e overachievers, in the statistical sense. Nothing else that we could have known about them besides the monumental contributions we ascribe to their genius would have predicted such extraordinary achievement. In discussing Ramanujan's work, the Polish mathematician Mark Kac was forced to make a distinction between the “ordi nary genius” and the “magician.” He wrote: An ordinary genius is a fellow that you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what he has done, we feel certain that we, too, could have done it. It is different with the magicians. They are, to use mathematical jargon , in the orthogonal complement of where we are and the working of their minds is for all intents and purposes incomprehensible. Even after we understand what they have done, the process by which they have done it is completely dark. (Quoted in Kanigel, 1991, p. 28 1 ; Kanigel’s splendid biography of Ramanujan is highly recommended)
To come back to earth and the point of my meandering, genius requires giftedness (consisting essentially of g, often along with some special aptitude or talent, such as mathematical, spatial, musical, or artistic talent). But obviously there are other antecedents (to the magic of Ramanujan's “thinking processes”) that are elusive to us. Nonetheless, we do know of at least two key attributes, beyond ability, that appear to function as catalysts for the creation of that special class of behavioral products specifically indicative of genius. They are productivity and creativity.
Creativity
Although we can recognize creative acts and even quantify them after a fashion (MacKinnon, 1962), our understanding of them in any explanatory sense is practically nil. Yet one prominent hypothesis concerning creativity (by which I mean the bringing into being of something that has not previously existed) seems to me not only unpromising, but extremely implausible and probably wrong. It is also inherently unfalsifiable and hence fails Popper’s criterion for a useful scientific theory. I doubt that it will survive a truly critical examination. Because ruling out one explanation does further our understanding of creative ity, I will focus on this theory. I am referring here to what has been termed the ch an ce configuration theory of creativity (well explicated by Simonton, 1988, ch. 1). Essentially, it amounts to expecting that a computer that perpetually generates strictly ran dom sequences of all the letters of the alphabet, punctuation signs, and spaces will eventually produce Hamlet or some other work of creative genius. The theory insists that blind chance acting in the processes of m em ory searches for elements with which to form random combinations and permutations, from which finally there emerges some product or solution that the world considers original or creative. It is also essential that, although this generating process is operating entirely by blind chance, the random permutations produced thereby are subjected to a critical rejection/selection screening, with selective retention of the more promising products. This theory seems implausible, partly because of the sheer numerical explosion of the possible combinations and permutations when there are more than just a few elements. For example, the letters in the word permutation have 11! = 3 9 ,916,800 possible perm uta tions. To discover the “right” one by randomly permuting the letters at a continuous rate of one permutation per second could take anywhere from one second (if one were extremely lucky) up to one year, three thirty-day months, and seven days (if one were equally unlucky). Even then, these calculations assume that the random generating mechanism never repeated a particular permutation; otherwise it would take much longer. The combinatorial and permutation explosion resulting from an in
crease in the number of elements to be mentally manipulated and the exponen tially increased processing time are not, however, the worst problem s for this theory. The far greater problem is that, just as “nature abhors a vacuum,” the human mind abhors random ness. I recall a lecture by the statistician Helen M. Walker in which she described a variety of experiments showing that intelligent
people, no matter how sophisticated they are about statistics or how well they understand the meaning of randomness, and while putting forth their best conscious efforts, are simply incapable of selecting, combining, or permutation numbers, letters, words, or anything else in a truly random fashion. For exam ple, when subjects are asked to generate a series of random numbers, or repeat edly to make a random selection of N items from among a much larger number of different objects spread out on a table, or take a random walk, it turns out no one can do it. This has been verified by statistical tests of randomness applied to their performance. People even have difficulty simply reading aloud from a table of random numbers without involuntarily and nonrandom ly inserting other numbers. (Examples of this phenomenon are given in Kendall, 1948.) Thus, random ness (o r blind chance, to use the favored term in chance configuration theory) seems an unlikely explanation of creative thinking. This theory seems to have originated from what may be deemed an inappropriate analogy, namely the theory of biological evolution creating new living forms. According to the latter theory, a great variety of genetic effects is produced by random mutations and the screening out of all variations except those best adapted to the environment—that is, natural selection. But a genetic mutation, produced perhaps by a radioactive particle hitting a single molecule in the DNA at random and altering its genetic code, is an unfitting analogy for the neces sarily integrated action of the myriad neurons involved in the mental manip ulation of ideas.
The Creative Process The implausibility of randomness, however, in no way implies that creative thinking does not involve a great deal of “trial-and -error” mental manipula tion, though it is not at all random . The products that emerge are then critically sifted in light of the creator’s aim. The individuals in whom this mental manipulation process turns out to be truly creative most often are those who are relatively rich in each of three sources of variance in creativity: (1) ideational flu en cy, or the capacity to tap a flow of relevant ideas, them es, or images, and to play with them , also known as “brainstorming”; (2) what Eysenck (1995) has termed the individuals’ relevance horizon ; that is, the range or variety of ele m ents, ideas, and associations that seem relevant to the problem (creativity involves a wide relevance horizon); and (3) suspension of critical ju d g m en t. Creative persons are intellectually high risk takers. They are not afraid of zany ideas and can hold the inhibitions of self-criticism temporarily in abey ance. Both Darwin and Freud mentioned their gullibility and receptiveness to highly speculative ideas and believed that these traits were probably charac
teristic of creative thinkers in general. Darwin occasionally performed what he called “fool’s experiments,” trying out improbable ideas that most people would have instantly dismissed as foolish. Francis Crick once told me that Linus Pauling’s scientific ideas turned out to be wrong about 80 percent of the time, but the other 20 percent finally proved to be so important that it would be a mistake to ignore any of his hunches. I once asked another Nobel Prize winner, William Shockley, whose cre activity resulted in about a hundred patented inventions in electronics, what he considered the main factors involved in his success. He said there were two: (1) he had an ability to generate, with respect to any given problem , a good many hypotheses, with little initial constraint by previous knowledge as to their plausibility or feasibility; and (2) he worked much harder than most people would at trying to figure out how a zany idea might be shaped into something technically feasible. Some of the ideas that eventually proved most fruitful, he said, were even a physical impossibility in their initial conception. For that very reason, most knowledgeable people would have dismissed such unrealistic ideas immediately, before searching their imaginations for transformations that might make them feasible. Some creative geniuses, at least in the arts, seem to work in the opposite direction from that described by Shockley. That is, they begin by producing something fairly conventional, or even trite, and then set about to impose novel distortions, reshaping it in ways deemed creative. I recall a demonstration of this by Leonard Bernstein, in which he compared the early drafts of Beethoven’s Fifth Symphony with the final version we know today. The first draft was a remarkably routine-sounding piece, scarcely suggesting the familiar qualities of Beethoven’s genius. It was more on a par with the works com posed by his mediocre contemporaries, now long forgotten. But then two processes took hold: (1) a lot of “doctoring,” which introduced what for that time were sur prising twists and turns in the harmonies and rhythms, along with an ascetic purification, and (2) a drastic pruning and simplification of the orchestral score to rid it completely of all the “unessential” notes in the harmonic texture, all the “elegant variations” of rhythm , and any suggestion of the kind of filigree orna mentation that was so common in the works of his contemporaries. This resulted in a starkly powerful, taut, and uniquely inevitable-sounding master piece, which, people now say, only Beethoven could have written. But when Beethoven’s symphonies were first performed, they sounded so shockingly deviant from the prevailing aesthetic standards that leading critics declared him ripe for a madhouse. One can see a similar process of artistic distortion in a fascinating motion
picture using time-lapse photography of Picasso at work ( The Picasso Mystery). He usually begin by sketching something quite ordinary—for example, a com pletely realistic horse. Then he would begin distorting the figure this way and that, repeatedly painting over what he had just painted and imposing further, often fantastic, distortions. In one instance, this process resulted in such an utterly hopeless mess that Picasso Finally tossed the canvas aside, with a remark to the effect of “Now I see how it should go.” Then, taking a clean canvas, he worked quickly, with bold, deft strokes of his paintbrush, and there suddenly took shape the strangely distorted figure Picasso apparently had been striving for. Thus he achieved the startling aesthetic impact typical of Picasso’s art. It is exactly this kind of artistic distortion of perception that is never seen in the productions of the most extremely gifted idiot savants, whose drawings often are incredibly photographic, yet are never considered works of artistic genius. The greatest artists probably have a comparable gift for realistic draw ing, but their genius leads them well beyond such photographic perception. Other examples of distortion are found in the recorded performances of the greatest conductors and instrumentalists, the re-creative geniuses, such as Toscanini and Furtwangler, Paderewski and Kreisler. Such artists are not primarily distinguished from routine practitioners by their technical skill or virtuosity (though these are indeed impressive), but by the subtle distortions, within fairly narrow limits, of rhythm , pitch, phrasing, and the like, that they impose, consciously or unconsciously, on the works they perform . Differences between the greatest performers are easily recognizable by these “signatures.” But others’ attempts to imitate these idiosyncratic distortions are never subtle enough or consistent enough to escape detection as inauthentic; in fact, they usually amount to caricatures.
Psychosis
What is the wellspring of the basic elements of creativity listed above—idea tional fluency, a wide relevance horizon, the suspension of inhibiting self criticism , and the novel distortion of ordinary perception and thought? All of these features, when taken to an extreme degree, are characteristic of psychosis. The mental and emotional disorganization of clinical psychosis is, however,
generally too disabling to perm it genuinely creative or productive work, espe cially in the uncompensated individual. Eysenck, however, has identified a trait, or dimension of personality, term ed psychoticism , which can be assessed by means of the Eysenck Personality Questionnaire (Eysenck & Eysenck, 1991). Trait psychoticism , it must be emphasized, does not imply the psychiatric
diagnosis of psychosis, but only the predisposition or potential for the develop m ent of psychosis (Eysenck & Eysenck, 1976). In many creative geniuses, this potential for actual psychosis is usually buffered and held in check by certain other traits, such as a high degree of ego strength. Trait psychoticism is a constellation of characteristics that persons may show to varying degrees; such persons may be aggressive, cold, egocentric, im personal, impulsive, antisocial, unempathetic, tough-minded, and creative. This is not a charm ing picture of genius, perhaps, but a reading of the biographies of some of the world’s most famous geniuses attests to its veracity. By and large, geniuses are quite an odd lot by ordinary standards. Their spouses, children, and close friends are usually not generous in their personal recollections, aside from marveling at the accomplishments for which the per son is acclaimed a genius. Often the personal eccentricities rem ain long hidden from the public. Beethoven’s first biographer, for example, is known to have destroyed some of Beethoven’s letters and conversation books, presumably because they revealed a pettiness and meanness of character that seemed utterly inconsistent with the sublime nobility of Beethoven’s music. Richard Wagner's horrendous character is legendary. He displayed virtually all of the aforemen tioned features of trait psychoticism to a high degree and, to make matters worse, was also neurotic. Trait psychoticism is hypothesized as a key condition in Eysenck’s (1995) theory of creativity. Various theorists have also mentioned other characteristics, but some of these, such as self-confidence, independence, originality, and n o n conformity, to name a few, might well stem from trait psychoticism. (See Jackson & Rushton, 1987, for reviews of the personality origins of productivity and creativity.)
Productivity
A startling corollary of the multiplicative model of exceptional achievement is best stated in the form of a general law. This is Price’s Law, which says that if K persons have made a total of N countable contributions in a particular field, then N /2 of the contributions will be attributable to
(Price, 1963). Hence,
as the total number of workers ( K ) in a discipline increases, the ratio VTc/ K shrinks, increasing the elitism of the major contributors. This law, like any other, only holds true within certain limits. But within fairly homogeneous disciplines, Price’s Law seems to hold up quite well for indices of productivity— for example, in math, the empirical sciences, musical composition, and the frequency of performance of musical works. Moreover, there is a high rank-
order relationship between sheer productivity and various indices of the im portance of a contributor’s work, such as the frequency and half-life of scien tific citations, and the frequency of performance and staying power of musical com positions in the concert repertoire. (Consider such contrasting famous contemporaries as Mozart and Salieri; Beethoven and Hummel; and Wagner and Meyerbeer.) If productivity and importance could be suitably scaled, however, I would imagine that the correlation between them would show a scatter-diagram of the “twisted pear” variety (Fisher, 1959). That is, high productivity and triviality are more frequently associated than low productivity and high importance. As a rule, the greatest creative geniuses in every field are astoundingly prolific, although, without exception, they have also produced their share of trivia. (Consider Beethoven’s King Stephen Overture and Wagner's “United States Centennial M arch,” to say nothing of his ten published volumes of largely triv ial prose writings—all incredible contrasts to these composers’ greatest works.) But such seemingly unnecessary trivia from such geniuses is probably the inevitable effluvia of the mental energy without which their greatest works would not have come into being. On the other hand, high productivity is probably much more common than great importance, and high productivity per se is no guarantee of the importance of what is produced. The “twisted pear” relationship suggests that high productivity is a necessary but not suffi cient condition for making contributions of importance in any field. The im portance factor, however, depends on creativity—certainly an elusive attribute. What might be the basis of individual differences in productivity? The word motivation immediately comes to mind, but it explains little and also seems too intentional and self-willed to fill the bill. When one reads about famous creative geniuses one finds that, although they may occasionally have to force themselves to work, they cannot will themselves to be obsessed by the subject of their work. Their obsessive-compulsive mental activity in a particular sphere is virtually beyond conscious control. I can recall three amusing exam ples of this, and they all involve dinner parties. Isaac Newton went down to the cellar to fetch some wine for his guests and, while filling a flagon, wrote a mathematical equation with his finger on the dust of the wine keg. After quite a long tim e had passed, his guests began to worry that he might have had an accident, and they went down to the cellar. There was Newton, engrossed in his mathematical formulas, having completely forgotten that he was hosting a dinner party. My second example involves Richard Wagner. Wagner, while his guests as sembled for dinner, suddenly took leave of them and dashed upstairs. Alarmed
that something was wrong, his wife rushed to his room . Wagner exclaimed, “I'm doing it!”—their agreed signal that she was not to disturb him under any circumstances because some new musical idea was flooding his brain and would have to work itself out before he could be sociable again. He had a phenomenal m em ory for musical ideas that spontaneously surfaced, and could postpone writing them down until it was convenient, a tedious task he referred to not as com posing but as merely “copying” the music in his mind's ear. Then there is the story of Arturo Toscanini hosting a dinner party at which he was inexplicably morose and taciturn, just as he had been all that day and the day before. Suddenly he got up from the dinner table and hurried to his study; he returned after several minutes beam ing joyfully and holding up the score of Brahms's First Symphony (which he was rehearsing that week for the N BC Symphony broadcast the following Sunday). Pointing to a passage in the first movement that had never pleased him in past performances, he exclaimed that it had suddenly dawned on him precisely what Brahm s had intended at this troublesome point. In this passage, which never sounds “clean” when played exactly as written, Toscanini slightly altered the score to clarify the orchestral texture. He always insisted that his alterations were only the composer's true intention. But few would complain about his “delusions”; as Puccini once remarked, “Toscanini doesn’t play my music as I wrote it, but as I dreamed it.”
Mental Energy Productivity implies actual production or objective achievement. For the psychological basis of intellectual productivity in the broadest sense, we need a
construct that could be labeled m en tal energy. This term should not be co n fused with Spearman's g (for general intelligence). Spearman's theory of psy chom etric g as “mental energy” is a failed hypothesis and has been supplanted by better explanations of g based on the concept of neural efficiency (Jensen, 1993). The energy construct I have in mind refers to something quite different from cognitive ability. It is more akin to cortical arousal or activation, as if by a stimulant drug, but in this case an endogenous stimulant. Precisely what it consists of is unknown, but it might well involve brain and body chemistry. One clue was suggested by Havelock Ellis (1 904) in A Study of British Genius. Ellis noted a much higher than average rate of gout in the eminent subjects of his study; gout is associated with high levels of uric acid in the blood. So later investigators began looking for behavioral correlates of serum urate level (SU L), and there are now dozens of studies on this topic (reviewed in Jensen & Sinha, 1993). They show that SUL is only slightly correlated with IQ, but is more highly correlated with achievement and productivity. For instance,
among high school students there is a relation between scholastic achievement and SUL, even controlling for IQ (Kasl, Brooks, & Rodgers, 1970). The “over achievers” had higher SUL ratings, on average. Another study found a correla tion of + .3 7 between SUL ratings and the publication rates of university pro fessors (Mueller & French, 1974). Why should there be such a relationship? The most plausible explanation seems to be that the molecular structure of uric acid is nearly the same as that of caffeine, and therefore it acts as a brain stimulant. Its more or less constant presence in the brain, although affecting measured ability only slightly, consid erably heightens cortical arousal and increases mental activity. There are proba bly a number of other endogenous stimulants and reinforcers of productive behavior (such as the endorphins) whose synergistic effects are the basis of what is here called mental energy. I suggest that this energy, combined with very high f o r an exceptional talent, results in high intellectual or artistic productiv ity. Include trait psychoticism with its creative component in this synergistic mixture and you have the essential makings of genius. To summarize: Genius = High Ability X High Productivity AND High Creativity.
The theoretical underpinnings of these three ingredients are: —Ability = g = efficiency of information processing —Productivity = endogenous cortical stim u lation —Creativity = trait psychoticism
Other Personality Correlates
There are undoubtedly other personality correlates of genius, although some of them may only reflect the more fundamental variables in the formula given above. The biographies of m any geniuses indicate that, from an early age, they are characterized by great sensitivity to their experiences (especially those of a cognitive nature), the development of unusually strong and long-term interests (often manifested as unusual or idiosyncratic hobbies or projects), curiosity and exploratory behavior, a strong desire to excel in their own pursuits, th eo retical and aesthetic values, and a high degree of self-discipline in acquiring necessary skills (MacKinnon, 1962). The development of expert-level knowledge and skill is essential for any important achievement (Rabinowitz & Glaser, 1985). A high level of expertise
involves the automatization of a host of special skills and cognitive routines. Automatization com es about only as a result of an immense amount of prac tice (Jensen, 1990; Walberg, 1988). Most people can scarcely imagine (and are probably incapable of) the extraordinary amount of practice that is re quired for genius-quality performance, even for such a prodigious genius as Mozart. In their self-assigned tasks, geniuses are not only persistent but also re markably able learners. Ramanujan, for example, disliked school and played truant to work on math problems beyond the level of anything he was offered at school. Wagner frequently played truant so he could devote his whole day to studying the orchestral scores of Beethoven. Francis Galton, with an estimated childhood IQ of around 200 and an acknowledged genius in adulthood, abso lutely hated the frustrations of school and pleaded with his parents to let him quit. Similar examples are legion in the accounts of geniuses. In reading about geniuses, I consistently find one other important factor that must be added to the composite I have described so far. It is a factor related to the direction of personal ambition and the persistence of effort. This factor channels and focuses the individual’s mental energy; it might be described best as personal ideals or values. These may be artistic, aesthetic, scientific, theoret ical, philosophical, religious, political, social, economic, or moral values, or something idiosyncratic. In persons of genius, especially, this “value factor” seems absolutely to dominate their self-concept, and it is not mundane. People are often puzzled by what they perceive as the genius’s self-sacrifice and often egocentric indifference to the needs of others. But the genius’s value system, at the core of his or her self-concept, is hardly ever sacrificed for the kind of mundane pleasures and unimaginative goals com m only valued by ordinary persons. Acting on their own values—perhaps one should say acting out their self-images—is a notable feature of famous geniuses.
Characteristics of Genius: Some Conclusions
Although this chapter is not meant to provide an exhaustive review of the literature on geniuses and highly creative individuals, it has raised some consis tent them es that might be worthy of scientific study. I propose that genius is a multiplicative effect of high ability, productivity, and creativity. Moreover, many of the personality traits associated with genius can be captured by the label “psychoticism.” Although geniuses may have a predisposition toward such a disorder, they are buffered by a high degree of ego strength and intelligence. A number of the remaining personality correlates of genius may best be captured by the idea that genius represents an acting-out of its very essence.
Giftedness and Genius: Important Differences Although giftedness (exceptional mental ability or outstanding talent) is a threshold trait for the emergence of genius, giftedness and genius do seem to be crucially different phenomena, not simply different points on a continuum . It has even been suggested that giftedness is in the orthogonal plane to genius. Thomas Mann (1 9 4 7 ), in his penetrating and insightful study of Richard Wag ner’s genius, for instance, makes the startling point that Wagner was not a musical prodigy and did not even seem particularly talented, in music or in anything else for that matter, compared to many lesser composers and poets. He was never skilled at playing any musical instrument, and his seriously focused interest in music began much later than it does for most musicians. Yet M ann is awed by Wagner's achievements as one of the world’s stupendous creative geniuses, whose extraordinarily innovative masterpieces and their ines capable influence on later composers place him among the surpassing elite in the history of music, in the class with Bach, Mozart, and Beethoven. It is interesting to note the words used by M ann in explaining what he calls Wagner's “vast genius”; they are not “giftedness” or “talent,” but “intelligence” and “will.” It is the second word here that strikes m e as most telling. After all, a high level of intelligence is what we mean by “gifted,” and Wagner was indeed most probably gifted in that sense. His childhood IQ was around 140, as estimated by Catherine Cox (1 9 2 6 ) in her classic, although somewhat flawed, study of three hundred historic geniuses. Yet that level of IQ is fairly com m on place on university campuses. We do not have to discuss such an awesome level of genius as Wagner's, however, to recognize that garden-variety outstanding achievement, to which giftedness is generally an accompaniment, is not so highly correlated with the psychometric and scholastic indices of giftedness as many people, even psychol ogists, might expect. At another symposium related to this topic, conducted more than twenty years ago, one of the speakers, who apparently had never heard of statistical regression, expressed fire alarm at the observation that far too many students who scored above the 99th percentile on IQ tests did not turn out, as adults, among those at the top of the distribution of recognized intellectual achievements. He was dismayed at many of the rather ordinary occupations and respectable but hardly impressive accomplishments displayed in midlife by the majority of the highly gifted students in his survey. A signifi can't number of students who had tested considerably lower, only in the top quartile, did about as well in life as many of the gifted. The speaker said the educational system was to blame for not properly cultivating gifted students. If
they were so bright, should they not have been high achievers? After all, their IQs were well within the range of the estimated childhood IQs of the three hundred historically eminent geniuses in C ox’s (1 9 2 6 ) study. Although educa tion is discussed in more detail below, the point here is that giftedness does not assure exceptional achievement; it is only a necessary condition. To reinforce this point, I offer an additional example that occurred on the very day I sat down to write this chapter. O n that day I received a letter from someone I had never met, though I knew he was an eminent professor of biophysics. He had read something I wrote concerning IQ as a predictor of achievement, but he was totally unaware of the present work. The coincidence is that my correspondent posed the very question that is central to my theme. He wrote;
I have felt for a long time that IQ , however defined, is only loosely related to men tal achievement. Over the years I have bumped into a fair nu m ber of MENSA people. As a group, they seem to be dilettantes seeking titillation bu t seem unable to think critically or deeply. They have a lot of motivation for intellectual play but little for doing anything worthwhile. One gets the feeling that brains were wasted on them . So, what is it that makes an intelligently productive person?
This is not an uncom m on observation, and I have even heard it expressed by m em bers of MENSA. It is one of their self-perceived problem s, one for which some have offered theories or rationalizations. The most typical is that they are so gifted that too many subjects attract their intellectual interest and they can never commit themselves to any particular interest. It could also be that indi viduals drawn toward m em bership in M ENSA are a selective subset of the gifted population, individuals lacking in focus. After all, most highly gifted individuals do not join MENSA. We must, then, consider some of the ways in which achieved em en t contrasts with ability if we are to make any headway in understanding the distinction between giftedness (i.e., mainly high g or special abilities) and genius. Genius involves actual achievement and creativity. Each of these characteristics is a quantitative variable. The concept of genius generally applies only when both of these variables characterize accomplishments at some extraordinary socially recognized level. Individual differences in countable units of achievement, un like measures of ability, are not normally distributed, but have a very positively skewed distribution, resembling the so-called J-curve. For example, the num ber of publications of members of the American Psychological Association, of research scientists, and of academicians in general, the number of patents of inventors, the number of compositions of composers, or the frequency of
composers’ works in the concert repertoire all show the same J-curve. M ore over, in every case, the J-curve can be normalized by a logarithmic transform a tion. This striking phenomenon is consistent with a multiplicative model of achievement, as developed and discussed above. That is, exceptional achieve m ent is a multiplicative function of a number of different traits, each of which may be normally distributed, but which in combination are so synergistic as to skew the resulting distribution of achievement. Thereby, an extremely extended upper tail of exceptional achievement is produced. Most geniuses are found far out in this tail. The multiplication of several normally distributed variables yields, there fore, a highly skewed distribution. In such a distribution, the mean is close to the bottom and the mode generally is the bottom . For any variable measured on a ratio scale, therefore, the distance between the median and the 99th percentile is much smaller for a normally distributed variable, such as ability, than for a markedly skewed variable, such as productivity. Indeed, this accords well with subjective impressions: the range of individual differences in ability (g or fluid intelligence) above the median level does not seem nearly so astounding as the above-median range of productivity or achievement. In conclusion, giftedness, a normally distributed variable, is a prerequisite for the development of genius. When it interacts with a number of other critical characteristics, which also are normally distributed, exceptional achievement is produced. Exceptional achievement, however, is a variable that is no longer norm al; it is highly skewed, with genius found at the tip of the tail.
Educational Implications
At this point in my highly speculative groping to understand the nature of genius as differentiated from giftedness, I should like to make some practical recommendations. First, I would not consider trying to select gifted youngsters explicitly with the aim of discovering and cultivating future geniuses. Julian Stanley’s decision (Stanley, 1977) to select explicitly for mathematical gifted ness—to choose youths who, in Stanley’s words, “reason exceptionally well mathematically”—was an admirably sound and wise decision from a practical and socially productive standpoint. The latent traits involved in exceptional mathematical reasoning ability are mainly high g plus high math talent (inde pendent of g). These traits are no guarantee of high productivity, much less of genius. But the threshold nature of g and m ath talent is so crucial to excelling in math and the quantitative sciences that we can be fairly certain that most of the productive mathematicians and scientists, as well as the inevitably few geniuses,
will com e from that segment of the population of which the SM PY students are a sample. Indeed, in Donald MacKinnon’s (1962) well-known study of large numbers of creative writers, mathematicians, and architects (certainly none of them a Shakespeare, Gauss, or Michelangelo), the very bottom of the range of intelligence-test scores in the whole sample was at about the 75th percentile of the general population, and the mean was at the 98th percentile (MacKinnon 8c Hall, 1972). However, it might eventually be profitable for researchers to consider searching beyond high ability per se and identify personality indices that also will aid in the prediction of exceptional achievement. The proportion of those gifted youths selected for special opportunities who are most apt to be productive professionals in their later careers would thereby be increased. Assuming that high achievement and productivity can be predicted at all, over and above what our usual tests of ability can predict, it would take extensive research indeed to discover sufficiently valid predictors to justify their use in this way. Lubinski and Benbow (1992) have presented evidence that a “theoretical orien tation,” as measured by the Allport, Vernon, and Lindzey Study of Values, might be just such a variable for scientific disciplines.
Conclusion
Certainly, the education and cultivation of intellectually gifted youths has never been more important than it is today, and its importance will continue to grow as we move into the next century. The preservation and advancement of civi lized society will require that an increasing proportion of the population have a high level of educated intelligence in science, engineering, and technology. Superior intellectual talent will be at a premium . Probably there will always be only relatively few geniuses, even among all persons identified as gifted. Yet this is not cause for concern. For any society to benefit from the fruits of genius requires the efforts of a great many gifted persons who have acquired high levels of knowledge and skill. For example, it takes about three hundred exceptionally talented and highly accomplished musicians, singers, set designers, artists, lighting directors, and stage directors, besides many stagehands, to put on a production of The Ring of the Nibelung, an artistic creation of surpassing genius. Were it not for the concerted efforts of these performers, the score of Wagner's colossal work would lie idle. The same is true, but on a much larger scale, in modern science and technology. The instigating creative ideas are seldom actualized for the benefit of society without the backup and follow through endeavors of a great many gifted and accomplished persons. Thus, a nation’s most important resource is the level of educated intelligence in its population; it determines the quality of life. It is imperative for society to cultivate all the high ability that can possibly be found, wherever it can be found.
References
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This essay by Arthur Jensen is from an old book .
The genius has limits. A simple answer, and undoubtedly true. But my
assignment here is to reflect on the much more complex difference
between intellectual giftedness and genius, using the latter term in its
original sense, as socially recognized, outstandingly creative achievement. In
this think-piece (which is just that, rather than a comprehensive review of the
literature), I will focus on factors, many intriguing in and of themselves, that
are characteristic of genius. My primary thesis is that the emergence of genius is
best described using a multiplicative model.
I will argue that exceptional achievement is a multiplicative function of a
number of different traits, each of which is normally distributed, but which in
combination are so synergistic as to skew the resulting distribution of achieve
ment. An extremely extended upper tail is thus produced, and it is within this
tail that genius can be found. An interesting two-part question then arises: how
many different traits are involved in producing extraordinary achievement, and
what are they? The musings that follow provide some conjectures that can be
drawn on to answer this critical question.
As a subject for scientific study, the topic of genius, although immensely
fascinating, is about as far from ideal as any phenom enon one can find. The
literature on real genius can claim little besides biographical anecdotes and
speculation, with this chapter contributing only more of the same. Whether the
study of genius will ever evolve from a literary art form into a systematic science
is itself highly speculative. The most promising efforts in this direction are
those by Simonton (198 8 ) and Eysenck (1 9 9 5 ), with Eysenck’s monograph
leaving little of potential scientific value that can be added to the subject at
present, pending new empirical evidence.
Intelligence
Earlier I stated that genius has limits. But its upper limit, at least in some fields,
seems to be astronomically higher than its lower limit. Moreover, the upper
lim it of genius cannot be described as characterized by precocity, high intel
ligence, knowledge and problem -solving skills being learned with speed and
ease, outstanding academic achievement, honors and awards, or even intellec
tual productivity. Although such attributes are commonly found at all levels of
genius, they are not discriminating in the realm of genius.
My point is perhaps most clearly illustrated by the contrast between two
famous mathematicians who became closely associated with one another as
“teacher” and “student.” T he reason for the quotation marks here will soon be
obvious, because the teacher later claimed that he learned more from the
student than the student had learned from him . G. H. Hardy was England’s
leading mathematician, a professor at Cambridge University, a Fellow of the
Royal Society, and the recipient of an honorary degree from Harvard. Rem ark
ably precocious in early childhood, especially in m athem atics, he became an exceptionally brilliant student, winning a scholarship after another acknowledged the star graduate in mathematics at Cambridge, where he remained to become a professor of m athem atics. He also became a world-class
mathematician. His longtime friend C. R Snow relates that Hardy, at the peak
of his career, ranked himself fifth among the most important mathematicians
of his day, and it should be pointed out that Hardy’s colleagues regarded him as
an overly modest man (Snow, 1967). If the Study of Mathematically Precocious
Youth (SMPY) had been in existence when Hardy was a schoolboy, he would
have been a most prized and promising student in the program.
One day Hardy received a strange-looking letter from Madras, India. It
was full of mathematical formulations written in a quite unconventional—one
might even say bizarre—form . The writer seemed almost mathematically illiter
by Cambridge standards. It was signed “Srinivasa Ramanujan.” At first
glance, Hardy thought it might even be some kind of fraud. Puzzling over this
letter with its abstruse formulations, he surmised it was written either by some
trickster or by someone sincere but poorly educated in m athem atics. Hardy
sought the opinion of his most highly esteemed colleague, J. E. Littlewood, the
other famous mathematician at Cambridge. After the two of them had spent
several hours studying the strange letter, they finally realized, with excitement
and absolute certainty, that they had “discovered” a major mathematical ge
nius. The weird-looking formulas, it turned out, revealed profound m athe
matical insights of a kind that are never created by ordinarily gifted mathematics.
Hardy regarded this “discovery” as the single most important event in his
life. Here was the prospect of fulfilling what, until then, had been for him only
an improbable dream: of ever knowing in person a mathematician possibly of
Gauss’s caliber.
A colleague in Hardy’s department then traveled to India and persuaded
Ramanujan to go to Cambridge, with all his expenses and a salary paid by the
university. When the youth arrived from India, it was evident that, by ordinary
standards, his educational background was meager and his almost entirely self
taught knowledge of math was full of gaps. He had not been at all successful in
school, from which he had flunked out twice, and was never graduated. To say,
however, that he was obsessed by m athem atics is an understatement. As a boy in
Madras, he was too poor to buy paper on which to work out his math prob
lems. He did his prodigious mathematical work on a slate, copying his final
results with red ink on old, discarded newspapers.
While in high school, he thought he had made a stunning mathematical
discovery, but he later learned, to his great dismay, that his discovery had
already been made 150 years earlier by the great mathematician Euler. R am anu
jan felt extraordinary shame for having “discovered” something that was not
original, never considering that only a real genius could have created or even re
created that discovery.
At Cambridge, Ramanujan was not required to take courses or exams.
That would have been almost an insult and a sure waste of time. He learned some essential things from Hardy, but what excited Hardy the most had nothing to do with Ramanujan’s great facility in learning the most advanced concepts and technical skills of mathematical analysis. Hardy himself had that kind of facility. What so impressed him was Ramanujan’s
uncanny mathematical intuition and capacity for inventing incredibly original and profound theorems. That, of course, is what real mathematical genius is all about. Facility in resolving textbook problem s and in passing difficult tests is utterly trivial when
discussing genius. Although working out the proof of a theorem, unlike discovering a theorem , may take immense technical skill and assiduous effort, it is
not itself a hallmark of genius. Indeed, Ramanujan seldom bothered to prove
his own theorem s; proof was a technical feat that could be left to lesser geniuses.
Moreover, in some cases, because of his spotty mathematical education, he
probably would have been unable to produce a formal proof even if he had
wanted to. But a great many important theorems were generated in his ob
passively active brain. Often he seemed to be in another world. One might say
that the difference between Ram anujan creating a theorem and a professional
mathematician solving a complex problem with standard techniques of analysis
is like the difference between St. Francis in ecstasy and a sleepy vicar reciting the
morning order of prayer.
After his experience with Ramanujan, Hardy told Snow that if the word
genius meant anything, he (Hardy) was not really a genius at all (Snow, 1967, p.
27). Hardy had his own hundred-point rating scale of his estimates of the
“natural ability” of eminent mathematicians. Though regarding himself at the
tim e as one of the world’s five best pure mathematicians, he gave himself a
rating of only 25. The greatest mathematician of that period, David Hilbert,
was rated 80. But Hardy rated Ramanujan 100, the same rating as he gave Carl
Friedrich Gauss, who is generally considered the greatest mathematical genius
the world has known. On the importance of their total contributions to mathematics, however, Hardy rated himself 35, Ramanujan 85, and Gauss 100. By this
reckoning Hardy was seemingly an overachiever and Ramanujan an under
achiever. Yet one must keep in mind that Ramanujan died at age thirty, Hardy at
seventy, and Gauss at seventy-eight.
of course, all geniuses are by definition extrem e overachievers, in the
statistical sense. Nothing else that we could have known about them besides the
monumental contributions we ascribe to their genius would have predicted
such extraordinary achievement. In discussing Ramanujan's work, the Polish
mathematician Mark Kac was forced to make a distinction between the “ordi
nary genius” and the “magician.” He wrote:
An ordinary genius is a fellow that you and I would be just as good as, if we were
only many times better. There is no mystery as to how his mind works. Once we
understand what he has done, we feel certain that we, too, could have done it. It is
different with the magicians. They are, to use mathematical jargon , in the orthogonal complement of where we are and the working of their minds is for all intents
and purposes incomprehensible. Even after we understand what they have done,
the process by which they have done it is completely dark. (Quoted in Kanigel,
1991, p. 28 1 ; Kanigel’s splendid biography of Ramanujan is highly recommended)
To come back to earth and the point of my meandering, genius requires
giftedness (consisting essentially of g, often along with some special aptitude or
talent, such as mathematical, spatial, musical, or artistic talent). But obviously
there are other antecedents (to the magic of Ramanujan's “thinking processes”)
that are elusive to us. Nonetheless, we do know of at least two key attributes,
beyond ability, that appear to function as catalysts for the creation of that
special class of behavioral products specifically indicative of genius. They are
productivity and creativity.
Creativity
Although we can recognize creative acts and even quantify them after a fashion
(MacKinnon, 1962), our understanding of them in any explanatory sense is
practically nil. Yet one prominent hypothesis concerning creativity (by which I
mean the bringing into being of something that has not previously existed)
seems to me not only unpromising, but extremely implausible and probably
wrong. It is also inherently unfalsifiable and hence fails Popper’s criterion for a
useful scientific theory. I doubt that it will survive a truly critical examination.
Because ruling out one explanation does further our understanding of creative
ity, I will focus on this theory.
I am referring here to what has been termed the ch an ce configuration
theory of creativity (well explicated by Simonton, 1988, ch. 1). Essentially, it
amounts to expecting that a computer that perpetually generates strictly ran
dom sequences of all the letters of the alphabet, punctuation signs, and spaces
will eventually produce Hamlet or some other work of creative genius. The
theory insists that blind chance acting in the processes of m em ory searches for
elements with which to form random combinations and permutations, from
which finally there emerges some product or solution that the world considers
original or creative. It is also essential that, although this generating process
is operating entirely by blind chance, the random permutations produced
thereby are subjected to a critical rejection/selection screening, with selective
retention of the more promising products. This theory seems implausible,
partly because of the sheer numerical explosion of the possible combinations
and permutations when there are more than just a few elements. For example,
the letters in the word permutation have 11! = 3 9 ,916,800 possible perm uta
tions. To discover the “right” one by randomly permuting the letters at a
continuous rate of one permutation per second could take anywhere from one
second (if one were extremely lucky) up to one year, three thirty-day months,
and seven days (if one were equally unlucky). Even then, these calculations
assume that the random generating mechanism never repeated a particular
permutation; otherwise it would take much longer.
The combinatorial and permutation explosion resulting from an in
crease in the number of elements to be mentally manipulated and the exponen
tially increased processing time are not, however, the worst problem s for this
theory. The far greater problem is that, just as “nature abhors a vacuum,” the
human mind abhors random ness. I recall a lecture by the statistician Helen M.
Walker in which she described a variety of experiments showing that intelligent
people, no matter how sophisticated they are about statistics or how well they
understand the meaning of randomness, and while putting forth their best
conscious efforts, are simply incapable of selecting, combining, or permutation
numbers, letters, words, or anything else in a truly random fashion. For exam
ple, when subjects are asked to generate a series of random numbers, or repeat
edly to make a random selection of N items from among a much larger number
of different objects spread out on a table, or take a random walk, it turns out no
one can do it. This has been verified by statistical tests of randomness applied to
their performance. People even have difficulty simply reading aloud from a
table of random numbers without involuntarily and nonrandom ly inserting
other numbers. (Examples of this phenomenon are given in Kendall, 1948.)
Thus, random ness (o r blind chance, to use the favored term in chance
configuration theory) seems an unlikely explanation of creative thinking. This
theory seems to have originated from what may be deemed an inappropriate
analogy, namely the theory of biological evolution creating new living forms.
According to the latter theory, a great variety of genetic effects is produced by
random mutations and the screening out of all variations except those best
adapted to the environment—that is, natural selection. But a genetic mutation,
produced perhaps by a radioactive particle hitting a single molecule in the DNA
at random and altering its genetic code, is an unfitting analogy for the neces
sarily integrated action of the myriad neurons involved in the mental manip
ulation of ideas.
The Creative Process
The implausibility of randomness, however, in no way implies that creative
thinking does not involve a great deal of “trial-and -error” mental manipula
tion, though it is not at all random . The products that emerge are then critically
sifted in light of the creator’s aim. The individuals in whom this mental manipulation process turns out to be truly creative most often are those who
are relatively rich in each of three sources of variance in creativity: (1) ideational
flu en cy, or the capacity to tap a flow of relevant ideas, them es, or images, and to
play with them , also known as “brainstorming”; (2) what Eysenck (1995) has
termed the individuals’ relevance horizon ; that is, the range or variety of ele
m ents, ideas, and associations that seem relevant to the problem (creativity
involves a wide relevance horizon); and (3) suspension of critical ju d g m en t.
Creative persons are intellectually high risk takers. They are not afraid of
zany ideas and can hold the inhibitions of self-criticism temporarily in abey
ance. Both Darwin and Freud mentioned their gullibility and receptiveness to
highly speculative ideas and believed that these traits were probably charac
teristic of creative thinkers in general. Darwin occasionally performed what
he called “fool’s experiments,” trying out improbable ideas that most people
would have instantly dismissed as foolish. Francis Crick once told me that Linus
Pauling’s scientific ideas turned out to be wrong about 80 percent of the time,
but the other 20 percent finally proved to be so important that it would be a
mistake to ignore any of his hunches.
I once asked another Nobel Prize winner, William Shockley, whose cre
activity resulted in about a hundred patented inventions in electronics, what he
considered the main factors involved in his success. He said there were two: (1)
he had an ability to generate, with respect to any given problem , a good many
hypotheses, with little initial constraint by previous knowledge as to their
plausibility or feasibility; and (2) he worked much harder than most people
would at trying to figure out how a zany idea might be shaped into something
technically feasible. Some of the ideas that eventually proved most fruitful, he
said, were even a physical impossibility in their initial conception. For that
very reason, most knowledgeable people would have dismissed such unrealistic
ideas immediately, before searching their imaginations for transformations
that might make them feasible.
Some creative geniuses, at least in the arts, seem to work in the opposite
direction from that described by Shockley. That is, they begin by producing
something fairly conventional, or even trite, and then set about to impose novel
distortions, reshaping it in ways deemed creative. I recall a demonstration of
this by Leonard Bernstein, in which he compared the early drafts of Beethoven’s
Fifth Symphony with the final version we know today. The first draft was a
remarkably routine-sounding piece, scarcely suggesting the familiar qualities of
Beethoven’s genius. It was more on a par with the works com posed by his
mediocre contemporaries, now long forgotten. But then two processes took
hold: (1) a lot of “doctoring,” which introduced what for that time were sur
prising twists and turns in the harmonies and rhythms, along with an ascetic
purification, and (2) a drastic pruning and simplification of the orchestral score
to rid it completely of all the “unessential” notes in the harmonic texture, all the
“elegant variations” of rhythm , and any suggestion of the kind of filigree orna
mentation that was so common in the works of his contemporaries. This
resulted in a starkly powerful, taut, and uniquely inevitable-sounding master
piece, which, people now say, only Beethoven could have written. But when
Beethoven’s symphonies were first performed, they sounded so shockingly
deviant from the prevailing aesthetic standards that leading critics declared him
ripe for a madhouse.
One can see a similar process of artistic distortion in a fascinating motion
picture using time-lapse photography of Picasso at work ( The Picasso Mystery).
He usually begin by sketching something quite ordinary—for example, a com
pletely realistic horse. Then he would begin distorting the figure this way and
that, repeatedly painting over what he had just painted and imposing further,
often fantastic, distortions. In one instance, this process resulted in such an
utterly hopeless mess that Picasso Finally tossed the canvas aside, with a remark
to the effect of “Now I see how it should go.” Then, taking a clean canvas, he
worked quickly, with bold, deft strokes of his paintbrush, and there suddenly
took shape the strangely distorted figure Picasso apparently had been striving
for. Thus he achieved the startling aesthetic impact typical of Picasso’s art.
It is exactly this kind of artistic distortion of perception that is never seen
in the productions of the most extremely gifted idiot savants, whose drawings
often are incredibly photographic, yet are never considered works of artistic
genius. The greatest artists probably have a comparable gift for realistic draw
ing, but their genius leads them well beyond such photographic perception.
Other examples of distortion are found in the recorded performances of
the greatest conductors and instrumentalists, the re-creative geniuses, such as
Toscanini and Furtwangler, Paderewski and Kreisler. Such artists are not primarily distinguished from routine practitioners by their technical skill or virtuosity (though these are indeed impressive), but by the subtle distortions,
within fairly narrow limits, of rhythm , pitch, phrasing, and the like, that they
impose, consciously or unconsciously, on the works they perform . Differences
between the greatest performers are easily recognizable by these “signatures.”
But others’ attempts to imitate these idiosyncratic distortions are never subtle
enough or consistent enough to escape detection as inauthentic; in fact, they
usually amount to caricatures.
Psychosis
What is the wellspring of the basic elements of creativity listed above—idea
tional fluency, a wide relevance horizon, the suspension of inhibiting self
criticism , and the novel distortion of ordinary perception and thought? All of
these features, when taken to an extreme degree, are characteristic of psychosis.
The mental and emotional disorganization of clinical psychosis is, however,
generally too disabling to perm it genuinely creative or productive work, espe
cially in the uncompensated individual. Eysenck, however, has identified a trait,
or dimension of personality, term ed psychoticism , which can be assessed by
means of the Eysenck Personality Questionnaire (Eysenck & Eysenck, 1991).
Trait psychoticism , it must be emphasized, does not imply the psychiatric
diagnosis of psychosis, but only the predisposition or potential for the develop
m ent of psychosis (Eysenck & Eysenck, 1976). In many creative geniuses, this
potential for actual psychosis is usually buffered and held in check by certain
other traits, such as a high degree of ego strength. Trait psychoticism is a
constellation of characteristics that persons may show to varying degrees; such
persons may be aggressive, cold, egocentric, im personal, impulsive, antisocial,
unempathetic, tough-minded, and creative. This is not a charm ing picture of
genius, perhaps, but a reading of the biographies of some of the world’s most
famous geniuses attests to its veracity.
By and large, geniuses are quite an odd lot by ordinary standards. Their
spouses, children, and close friends are usually not generous in their personal
recollections, aside from marveling at the accomplishments for which the per
son is acclaimed a genius. Often the personal eccentricities rem ain long hidden
from the public. Beethoven’s first biographer, for example, is known to have
destroyed some of Beethoven’s letters and conversation books, presumably
because they revealed a pettiness and meanness of character that seemed utterly
inconsistent with the sublime nobility of Beethoven’s music. Richard Wagner's
horrendous character is legendary. He displayed virtually all of the aforemen
tioned features of trait psychoticism to a high degree and, to make matters
worse, was also neurotic.
Trait psychoticism is hypothesized as a key condition in Eysenck’s (1995)
theory of creativity. Various theorists have also mentioned other characteristics,
but some of these, such as self-confidence, independence, originality, and n o n
conformity, to name a few, might well stem from trait psychoticism. (See
Jackson & Rushton, 1987, for reviews of the personality origins of productivity
and creativity.)
Productivity
A startling corollary of the multiplicative model of exceptional achievement is
best stated in the form of a general law. This is Price’s Law, which says that if K
persons have made a total of N countable contributions in a particular field,
then N /2 of the contributions will be attributable to
(Price, 1963). Hence,
as the total number of workers ( K ) in a discipline increases, the ratio VTc/ K
shrinks, increasing the elitism of the major contributors. This law, like any
other, only holds true within certain limits. But within fairly homogeneous
disciplines, Price’s Law seems to hold up quite well for indices of productivity—
for example, in math, the empirical sciences, musical composition, and the
frequency of performance of musical works. Moreover, there is a high rank-
order relationship between sheer productivity and various indices of the im
portance of a contributor’s work, such as the frequency and half-life of scien
tific citations, and the frequency of performance and staying power of musical
com positions in the concert repertoire. (Consider such contrasting famous
contemporaries as Mozart and Salieri; Beethoven and Hummel; and Wagner
and Meyerbeer.)
If productivity and importance could be suitably scaled, however, I would
imagine that the correlation between them would show a scatter-diagram of the
“twisted pear” variety (Fisher, 1959). That is, high productivity and triviality
are more frequently associated than low productivity and high importance. As
a rule, the greatest creative geniuses in every field are astoundingly prolific,
although, without exception, they have also produced their share of trivia.
(Consider Beethoven’s King Stephen Overture and Wagner's “United States
Centennial M arch,” to say nothing of his ten published volumes of largely triv
ial prose writings—all incredible contrasts to these composers’ greatest works.)
But such seemingly unnecessary trivia from such geniuses is probably the
inevitable effluvia of the mental energy without which their greatest works
would not have come into being. On the other hand, high productivity is
probably much more common than great importance, and high productivity
per se is no guarantee of the importance of what is produced. The “twisted
pear” relationship suggests that high productivity is a necessary but not suffi
cient condition for making contributions of importance in any field. The im
portance factor, however, depends on creativity—certainly an elusive attribute.
What might be the basis of individual differences in productivity? The
word motivation immediately comes to mind, but it explains little and also
seems too intentional and self-willed to fill the bill. When one reads about
famous creative geniuses one finds that, although they may occasionally have to
force themselves to work, they cannot will themselves to be obsessed by the
subject of their work. Their obsessive-compulsive mental activity in a particular
sphere is virtually beyond conscious control. I can recall three amusing exam
ples of this, and they all involve dinner parties. Isaac Newton went down to the
cellar to fetch some wine for his guests and, while filling a flagon, wrote a
mathematical equation with his finger on the dust of the wine keg. After quite a
long tim e had passed, his guests began to worry that he might have had an
accident, and they went down to the cellar. There was Newton, engrossed in his
mathematical formulas, having completely forgotten that he was hosting a
dinner party.
My second example involves Richard Wagner. Wagner, while his guests as
sembled for dinner, suddenly took leave of them and dashed upstairs. Alarmed
that something was wrong, his wife rushed to his room . Wagner exclaimed,
“I'm doing it!”—their agreed signal that she was not to disturb him under any
circumstances because some new musical idea was flooding his brain and
would have to work itself out before he could be sociable again. He had a
phenomenal m em ory for musical ideas that spontaneously surfaced, and could
postpone writing them down until it was convenient, a tedious task he referred
to not as com posing but as merely “copying” the music in his mind's ear.
Then there is the story of Arturo Toscanini hosting a dinner party at which
he was inexplicably morose and taciturn, just as he had been all that day and the
day before. Suddenly he got up from the dinner table and hurried to his study;
he returned after several minutes beam ing joyfully and holding up the score of
Brahms's First Symphony (which he was rehearsing that week for the N BC
Symphony broadcast the following Sunday). Pointing to a passage in the first
movement that had never pleased him in past performances, he exclaimed that
it had suddenly dawned on him precisely what Brahm s had intended at this
troublesome point. In this passage, which never sounds “clean” when played
exactly as written, Toscanini slightly altered the score to clarify the orchestral
texture. He always insisted that his alterations were only the composer's true
intention. But few would complain about his “delusions”; as Puccini once
remarked, “Toscanini doesn’t play my music as I wrote it, but as I dreamed it.”
Mental Energy
Productivity implies actual production or objective achievement. For the psychological basis of intellectual productivity in the broadest sense, we need a
construct that could be labeled m en tal energy. This term should not be co n
fused with Spearman's g (for general intelligence). Spearman's theory of psy
chom etric g as “mental energy” is a failed hypothesis and has been supplanted
by better explanations of g based on the concept of neural efficiency (Jensen,
1993). The energy construct I have in mind refers to something quite different
from cognitive ability. It is more akin to cortical arousal or activation, as if by a
stimulant drug, but in this case an endogenous stimulant. Precisely what it
consists of is unknown, but it might well involve brain and body chemistry.
One clue was suggested by Havelock Ellis (1 904) in A Study of British
Genius. Ellis noted a much higher than average rate of gout in the eminent
subjects of his study; gout is associated with high levels of uric acid in the blood.
So later investigators began looking for behavioral correlates of serum urate
level (SU L), and there are now dozens of studies on this topic (reviewed in
Jensen & Sinha, 1993). They show that SUL is only slightly correlated with IQ,
but is more highly correlated with achievement and productivity. For instance,
among high school students there is a relation between scholastic achievement
and SUL, even controlling for IQ (Kasl, Brooks, & Rodgers, 1970). The “over
achievers” had higher SUL ratings, on average. Another study found a correla
tion of + .3 7 between SUL ratings and the publication rates of university pro
fessors (Mueller & French, 1974).
Why should there be such a relationship? The most plausible explanation
seems to be that the molecular structure of uric acid is nearly the same as that of
caffeine, and therefore it acts as a brain stimulant. Its more or less constant
presence in the brain, although affecting measured ability only slightly, consid
erably heightens cortical arousal and increases mental activity. There are proba
bly a number of other endogenous stimulants and reinforcers of productive
behavior (such as the endorphins) whose synergistic effects are the basis of
what is here called mental energy. I suggest that this energy, combined with very
high f o r an exceptional talent, results in high intellectual or artistic productiv
ity. Include trait psychoticism with its creative component in this synergistic
mixture and you have the essential makings of genius.
To summarize:
Genius = High Ability X High Productivity AND High Creativity.
The theoretical underpinnings of these three ingredients are:
—Ability = g = efficiency of information processing
—Productivity = endogenous cortical stim u lation
—Creativity = trait psychoticism
Other Personality Correlates
There are undoubtedly other personality correlates of genius, although some of
them may only reflect the more fundamental variables in the formula given
above. The biographies of m any geniuses indicate that, from an early age, they
are characterized by great sensitivity to their experiences (especially those of a
cognitive nature), the development of unusually strong and long-term interests
(often manifested as unusual or idiosyncratic hobbies or projects), curiosity
and exploratory behavior, a strong desire to excel in their own pursuits, th eo
retical and aesthetic values, and a high degree of self-discipline in acquiring
necessary skills (MacKinnon, 1962).
The development of expert-level knowledge and skill is essential for any
important achievement (Rabinowitz & Glaser, 1985). A high level of expertise
involves the automatization of a host of special skills and cognitive routines.
Automatization com es about only as a result of an immense amount of prac
tice (Jensen, 1990; Walberg, 1988). Most people can scarcely imagine (and
are probably incapable of) the extraordinary amount of practice that is re
quired for genius-quality performance, even for such a prodigious genius as
Mozart.
In their self-assigned tasks, geniuses are not only persistent but also re
markably able learners. Ramanujan, for example, disliked school and played
truant to work on math problems beyond the level of anything he was offered at
school. Wagner frequently played truant so he could devote his whole day to
studying the orchestral scores of Beethoven. Francis Galton, with an estimated
childhood IQ of around 200 and an acknowledged genius in adulthood, abso
lutely hated the frustrations of school and pleaded with his parents to let him
quit. Similar examples are legion in the accounts of geniuses.
In reading about geniuses, I consistently find one other important factor
that must be added to the composite I have described so far. It is a factor related
to the direction of personal ambition and the persistence of effort. This factor
channels and focuses the individual’s mental energy; it might be described best
as personal ideals or values. These may be artistic, aesthetic, scientific, theoret
ical, philosophical, religious, political, social, economic, or moral values, or
something idiosyncratic. In persons of genius, especially, this “value factor”
seems absolutely to dominate their self-concept, and it is not mundane. People
are often puzzled by what they perceive as the genius’s self-sacrifice and often
egocentric indifference to the needs of others. But the genius’s value system, at
the core of his or her self-concept, is hardly ever sacrificed for the kind of
mundane pleasures and unimaginative goals com m only valued by ordinary
persons. Acting on their own values—perhaps one should say acting out their
self-images—is a notable feature of famous geniuses.
Characteristics of Genius: Some Conclusions
Although this chapter is not meant to provide an exhaustive review of the
literature on geniuses and highly creative individuals, it has raised some consis
tent them es that might be worthy of scientific study. I propose that genius is
a multiplicative effect of high ability, productivity, and creativity. Moreover,
many of the personality traits associated with genius can be captured by the
label “psychoticism.” Although geniuses may have a predisposition toward such
a disorder, they are buffered by a high degree of ego strength and intelligence. A
number of the remaining personality correlates of genius may best be captured
by the idea that genius represents an acting-out of its very essence.
Giftedness and Genius: Important Differences
Although giftedness (exceptional mental ability or outstanding talent) is a
threshold trait for the emergence of genius, giftedness and genius do seem to be
crucially different phenomena, not simply different points on a continuum . It
has even been suggested that giftedness is in the orthogonal plane to genius.
Thomas Mann (1 9 4 7 ), in his penetrating and insightful study of Richard Wag
ner’s genius, for instance, makes the startling point that Wagner was not a
musical prodigy and did not even seem particularly talented, in music or in
anything else for that matter, compared to many lesser composers and poets.
He was never skilled at playing any musical instrument, and his seriously
focused interest in music began much later than it does for most musicians. Yet
M ann is awed by Wagner's achievements as one of the world’s stupendous
creative geniuses, whose extraordinarily innovative masterpieces and their ines
capable influence on later composers place him among the surpassing elite in
the history of music, in the class with Bach, Mozart, and Beethoven.
It is interesting to note the words used by M ann in explaining what he calls
Wagner's “vast genius”; they are not “giftedness” or “talent,” but “intelligence”
and “will.” It is the second word here that strikes m e as most telling. After all, a
high level of intelligence is what we mean by “gifted,” and Wagner was indeed
most probably gifted in that sense. His childhood IQ was around 140, as
estimated by Catherine Cox (1 9 2 6 ) in her classic, although somewhat flawed,
study of three hundred historic geniuses. Yet that level of IQ is fairly com
m on place on university campuses.
We do not have to discuss such an awesome level of genius as Wagner's,
however, to recognize that garden-variety outstanding achievement, to which
giftedness is generally an accompaniment, is not so highly correlated with the
psychometric and scholastic indices of giftedness as many people, even psychol
ogists, might expect. At another symposium related to this topic, conducted
more than twenty years ago, one of the speakers, who apparently had never
heard of statistical regression, expressed fire alarm at the observation that far
too many students who scored above the 99th percentile on IQ tests did not
turn out, as adults, among those at the top of the distribution of recognized
intellectual achievements. He was dismayed at many of the rather ordinary
occupations and respectable but hardly impressive accomplishments displayed
in midlife by the majority of the highly gifted students in his survey. A signifi
can't number of students who had tested considerably lower, only in the top
quartile, did about as well in life as many of the gifted. The speaker said the
educational system was to blame for not properly cultivating gifted students. If
they were so bright, should they not have been high achievers? After all, their
IQs were well within the range of the estimated childhood IQs of the three
hundred historically eminent geniuses in C ox’s (1 9 2 6 ) study. Although educa
tion is discussed in more detail below, the point here is that giftedness does not
assure exceptional achievement; it is only a necessary condition.
To reinforce this point, I offer an additional example that occurred on the
very day I sat down to write this chapter. O n that day I received a letter from
someone I had never met, though I knew he was an eminent professor of
biophysics. He had read something I wrote concerning IQ as a predictor of
achievement, but he was totally unaware of the present work. The coincidence
is that my correspondent posed the very question that is central to my theme.
He wrote;
This is not an uncom m on observation, and I have even heard it expressed by
m em bers of MENSA. It is one of their self-perceived problem s, one for which
some have offered theories or rationalizations. The most typical is that they are
so gifted that too many subjects attract their intellectual interest and they can
never commit themselves to any particular interest. It could also be that indi
viduals drawn toward m em bership in M ENSA are a selective subset of the
gifted population, individuals lacking in focus. After all, most highly gifted
individuals do not join MENSA.
We must, then, consider some of the ways in which achieved em en t contrasts
with ability if we are to make any headway in understanding the distinction
between giftedness (i.e., mainly high g or special abilities) and genius. Genius
involves actual achievement and creativity. Each of these characteristics is a
quantitative variable. The concept of genius generally applies only when both of
these variables characterize accomplishments at some extraordinary socially
recognized level. Individual differences in countable units of achievement, un
like measures of ability, are not normally distributed, but have a very positively
skewed distribution, resembling the so-called J-curve. For example, the num
ber of publications of members of the American Psychological Association, of
research scientists, and of academicians in general, the number of patents
of inventors, the number of compositions of composers, or the frequency of
composers’ works in the concert repertoire all show the same J-curve. M ore
over, in every case, the J-curve can be normalized by a logarithmic transform a
tion. This striking phenomenon is consistent with a multiplicative model of
achievement, as developed and discussed above. That is, exceptional achieve
m ent is a multiplicative function of a number of different traits, each of which
may be normally distributed, but which in combination are so synergistic as to
skew the resulting distribution of achievement. Thereby, an extremely extended
upper tail of exceptional achievement is produced. Most geniuses are found far
out in this tail.
The multiplication of several normally distributed variables yields, there
fore, a highly skewed distribution. In such a distribution, the mean is close to
the bottom and the mode generally is the bottom . For any variable measured on
a ratio scale, therefore, the distance between the median and the 99th percentile
is much smaller for a normally distributed variable, such as ability, than for a
markedly skewed variable, such as productivity. Indeed, this accords well with
subjective impressions: the range of individual differences in ability (g or fluid
intelligence) above the median level does not seem nearly so astounding as the
above-median range of productivity or achievement.
In conclusion, giftedness, a normally distributed variable, is a prerequisite
for the development of genius. When it interacts with a number of other critical
characteristics, which also are normally distributed, exceptional achievement is
produced. Exceptional achievement, however, is a variable that is no longer
norm al; it is highly skewed, with genius found at the tip of the tail.
Educational Implications
At this point in my highly speculative groping to understand the nature of
genius as differentiated from giftedness, I should like to make some practical
recommendations. First, I would not consider trying to select gifted youngsters
explicitly with the aim of discovering and cultivating future geniuses. Julian
Stanley’s decision (Stanley, 1977) to select explicitly for mathematical gifted
ness—to choose youths who, in Stanley’s words, “reason exceptionally well
mathematically”—was an admirably sound and wise decision from a practical
and socially productive standpoint. The latent traits involved in exceptional
mathematical reasoning ability are mainly high g plus high math talent (inde
pendent of g). These traits are no guarantee of high productivity, much less of
genius. But the threshold nature of g and m ath talent is so crucial to excelling in
math and the quantitative sciences that we can be fairly certain that most of the
productive mathematicians and scientists, as well as the inevitably few geniuses,
will com e from that segment of the population of which the SM PY students are
a sample. Indeed, in Donald MacKinnon’s (1962) well-known study of large
numbers of creative writers, mathematicians, and architects (certainly none of
them a Shakespeare, Gauss, or Michelangelo), the very bottom of the range of
intelligence-test scores in the whole sample was at about the 75th percentile
of the general population, and the mean was at the 98th percentile (MacKinnon
8c Hall, 1972).
However, it might eventually be profitable for researchers to consider
searching beyond high ability per se and identify personality indices that also
will aid in the prediction of exceptional achievement. The proportion of those
gifted youths selected for special opportunities who are most apt to be productive professionals in their later careers would thereby be increased. Assuming
that high achievement and productivity can be predicted at all, over and above
what our usual tests of ability can predict, it would take extensive research
indeed to discover sufficiently valid predictors to justify their use in this way.
Lubinski and Benbow (1992) have presented evidence that a “theoretical orien
tation,” as measured by the Allport, Vernon, and Lindzey Study of Values,
might be just such a variable for scientific disciplines.
Conclusion
Certainly, the education and cultivation of intellectually gifted youths has never
been more important than it is today, and its importance will continue to grow
as we move into the next century. The preservation and advancement of civi
lized society will require that an increasing proportion of the population have a
high level of educated intelligence in science, engineering, and technology.
Superior intellectual talent will be at a premium . Probably there will always be
only relatively few geniuses, even among all persons identified as gifted. Yet this
is not cause for concern. For any society to benefit from the fruits of genius
requires the efforts of a great many gifted persons who have acquired high levels
of knowledge and skill. For example, it takes about three hundred exceptionally
talented and highly accomplished musicians, singers, set designers, artists,
lighting directors, and stage directors, besides many stagehands, to put on a
production of The Ring of the Nibelung, an artistic creation of surpassing
genius. Were it not for the concerted efforts of these performers, the score of
Wagner's colossal work would lie idle. The same is true, but on a much larger
scale, in modern science and technology. The instigating creative ideas are
seldom actualized for the benefit of society without the backup and follow through endeavors of a great many gifted and accomplished persons. Thus, a nation’s most important resource is the level of educated intelligence in its
population; it determines the quality of life. It is imperative for society to
cultivate all the high ability that can possibly be found, wherever it can be
found.
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