News quotes Dr.
Anders Ericsson saying that anyone should be able to attain
prodigy-level performance in his discipline of choice. "This
may seem to be easily refuted by popular legends about geniuses
such as Mozart, Paganini and Gauss,
which report that they all showed exceptional skills in early
childhood before receiving a shred of formal instruction. But
Dr Ericsson points out that most of these stories are, indeed,
legends." A few comments are in order. Legend or not, the
precocities of the children described in "Mirror, mirror,
on the wall... " are real, and they're more precocious than
Gauss. Nor are they a product of their parents. "Genius will
out" even when these children are adopted shortly after birth,
and are given little or no encouragement by their foster parents.
I had a friend in high school who, as a child, never knew his
father's side of the family from whom his intelligence sprang.
One day, when he was three-and-a-half, his maternal uncle said,
"I wonder what the weather's going to be tomorrow?"
My three-and-a-half-year-old friend said, "The newspaper
says there will be inclement weather." That was when his
mother's side of the family learned that he had taught himself
to read. I know another phenomenal individual who was adopted
shortly after birth. His foster-parents were stunned when he began
to talk at 5 months, to read signs at 9 months, books at 15 months,
and French at age three. His foster-parents were afraid to encourage
this precocity because of stories they'd read about parents pushing
their children. In her book, "Gifted
Children: Myths and Realities", Ellen Winner tells
about three children, two of whom were artistic prodigies. The
third loved to draw as much as the two prodigies, but--
Dr. Winner cites the intriguing case of Charles, versus Eitan and Peter. All three boys were obsessed with drawing. However, Eitan and Peter were artistic prodigies, far ahead of their years, whereas Charles, in spite of all the drawing he did, never exceeded the norms for his age group."
With respect to the trainability of digit recall, Dr. Sam Renshaw (the "Dr. Renshaw" in James Thurber's "The Secret Life of Walter Mitty") had trained a couple of his Ohio State graduate students to remember more than 30 digits before I knew him in the early 50's. In the discussion of the Stanford Binet test that I read in 1945, it was observed that memory span for digits has a low correlation with IQ, but was included in the test because it's so easy to measure and it's not as culturally linked as some of the S-B's other items. (IQ tests are comprised of items that, individually, don't correlate terribly well with overall IQ, but that, in the aggregate, give a considerably better picture of innate learning and problem-solving ability. This is understandable because different sub tests measure different secondary components of intelligence.)
In his book, "Genius", pp. 69-74, Dr. Hans Eysenck discusses the trainability of memory span for digits and words. Dr. Eysenck says, "...few people can repeat more than 9 digits, letters, or words. Yet quite average IQ people can be taught to succeed at levels 20 S. D.'s above this level, equalling IQ levels of 400 or thereabouts!" He then cites six studies, beginning with those of Baltes and Kliegl (1982), "Plasticity and enhancement of intellectual Functioning to old age", in F. Kraik and S. E. Tretub, Aging and Cognitive Processes, pp. 353-89, New York, Plenum Press. The training techniques employed use either the association of numbers with non-numerical facts or objects or "helping the subject remember the actual sequence of the 'chunks reproduced", both of which are based upon the Method of Loci, "differing mainly in the amount of permanent knowledge they require" (p. 70).
"The sequential chunking of digits into historical events.(or concrete nouns) and the formation of images or thought associations between these to-be-remembered items and their corresponding landmarks does not put a heavy burden on working-memory subsystems such as the rehearsal loop or visuospatial scratch-pad (Baddeley, A. D., 1983, Working memory, Philosophical Transactions of the Royal Society of London, B302, 311-24).Only central executive functions which serve to integrate relevant knowledge are required. . Therefore, in the present models, expertise in memory span is not constituted by increasing short-term or working memory, but by invoking long-term memory encoding processes and permanent knowledge during encoding (as proposed by Chase and Ericsson, 1982, "Skill and Working Memory", in G. W. Bower, The Psychology of Learning and Motivation, Vol.16, Academic Press, New York). Once the memory experience has been acquired, capacity limitations in working memory functioning (e. g., in the capacity of the central executive to integrate short-term memory (STM) and long-term memory (LTM) processes) can be probed, for example, by manipulating the rate at which items to-be-remembered are presented (e. g. reducing presentation rates). Such a probe technique illustrates one theory-guided implementation of the testing-the-limits strategy.
"The results of such training, continued over lengthy periods, can be outstanding, depending upon the duration of training. ...Later studies used over 250 practice sessions with two subjects who achieved a digit spans of 82 and 68 respectively.
"Thus, given suitable training, perfectly ordinary people with ordinary IQs can achieve extraordinary results with minimal training. It is not difficult to see that the alleged extraordinary feats of race-track tipsters and others, achieved over many years of practice (rather than hours) appear remarkable, and are not correlated with IQ. The application of everyday training and reward can never be compared with unpractised achievements, like the digit span test."
Dr, Eysenck discusses "Z", a musical idiot savant, who practised nine hours a day, and who had extraordinary musical knowledge and skills. He goes on to say,
"Again, musical ability of the executive kind is largely separate from IQ, i. e., the ability to think abstractly, to learn easily and solve cognitive problems."
Dr. Eysenck mentions Luria's study of S. V. Sherewshewski, and "Hunter's account of the British mathematician, C. Aitken". He says,
"Numbers to devoted mathematicians are not just sequences of digits, as they might be to most people; they acquire individuality, and are remembered, and used, as such. Mathematicians do not have to be taught the tricks used by Baltes and his colleagues; the knowledge of chunks, automatization and the development of strategies develop automatically, based upon high motivation and long periods of intensive learning and motivation.
"In the same way, chess masters do not deal with the individual places of the pieces, but with positions, i. e., chunks involving many pieces simultaneously. Thus when pieces are distributed randomly on the chess board, and subjects are allowed to view them for a limited period, chess masters are no better than others at remembering the positions occupied by the pieces. But if the pieces actually illustrate meaningful positions, chess masters produce very much higher scores. To them this is not a meaningless collection of so many different pieces, but the position arrived at after 25 moves in the Capablanca-Tartakover match of 1925. Thus they have to remember one item, not hundreds, as must the unfortunate novice.
"Some 50,000 chunks, about the same magnitude as the recognition vocabulary of college-educated readers*, may be required for expert mastery of a given field. The highest achievement in scientific disciplines, however, may require a memory store of a million chunks--probably the equivalent of 70 hours of concentrated effort each week for a decade even for a talented scholar. Without chunking, the whole process would be utterly impossible.
"Child prodigies and exceptionally early achievers, to quote the title of an interesting book by Radford (1990, ), seem to be able to curtail this prolonged expenditure of mental energy; a Mozart, Newton, or Einstein, by combining outstandingly high IQ, special abilities, motivation and creativity may get by with less, and achieve outstanding success at an extraordinarily early age. But even for them a long period of information acquisition is needed before creativity can emerge to restructure the chunks now available. Because not only do we have to transmute the material in question into chunks, these chunks themselves are tied together with pretty pink ribbons, and the most difficult task of the genius is to undo these ties, and fit the chunks together in a different pattern.
"To summarise, intelligence, which may be defined as innate, general cognitive ability, is a necessary but not a sufficient factor in the genesis of genius. Special abilities (verbal, visuo-spatial, numerical, musical, etc.), persistence, personality qualities and other factors are also required, and probably interact synergistically (multiplicatively) with intelligence, thus producing the typically J-shaped curved distribution of eminence defined in terms of achievement--very few geniuses, a small number of eminent people, and a large number of ordinary people with no claims to eminence. Precise IQ values of geniuses studied in the past should not be taken too seriously; there are many reasons to doubt their accuracy or meaningfulness. However, the fact of unusually high intelligence in these people cannot be doubted, even if no precise estimate can be given. The existence of large numbers of very high IQ people who are very far from being geniuses demonstrate the fact that factors other than IQ play a large part in producing the geniuses."
* - Dr. Eysenck's vocabulary guideline of 50,000 words of recognition vocabulary for college graduates seems high to me. Of course, in England, in the 50's, only about 2% of the population graduated from college. Still, my estimate of the vocabulary of the average individual (IQ = 100) would be about 25,000 to 30,000 words, based upon a tabulation of the words in the Webster Collegiate Dictionary, and for the average U. S. college graduate, might be 35,000 to 40,000. For example, opening that dictionary to page 800, I find:nitrogen narcosis, nitrogen trichloride, nitroglycerin, nitros- or nitroso, nitrosamine, nitrous, nitrous acid, nitrous oxide, nitty-gritty, nitwit, nix, nix, nix, nix, nixie, Nixie, nizam, no, no, no, no, Noh, no-account, Noachian, Noah, nob, nobble, nobby, Nobelist, nobellium, nobility, noble, noble, noble gas, nobleman, noblesse oblige, noblewoman, nobody, nocent,... In looking at these words, one sees multiple entries for similar words, like noble, nobility, nobleman, and noblewoman, so the number of independent root words may be quite a bit smaller than the number of dictionary entries that one can recognise. Another way to size this is to consider the 3,500 key words listed in Barron's "How to Prepare for the SAT I (More than 5,000,000 copies sold)". The pre-1995 SAT went up to a deviation IQ of 168, and the re-centered SAT probably has a ceiling in the upper 150's. A list of the words on Page 200 yields latitude, laud, lavish, lax, leaven, lechery, leery, legacy, legend, legerdemain, leniency, lethargic, levitate, levity, levy, lewd, lexicographer, lexicon, liability, liaison, lbel, libretto, licentious, lilliputian, limber, limpid, linchpin, lineage... One telling point: since most of our printed material is aimed toward people with IQ's in the 100-120 range, vocabulary choices that lie outside this range must needs be few and far between. It must be quite challenging to build an abnormally large vocabulary in a restricted cultural ambiance. I would guess that vocabulary size relates to IQ in an approximately linear fashion, but because of the rapid roll-off in frequency of occurrence of words that are less-commonly used, the underlying difficulty of acquiring a large vocabulary may be an exponential function of the "difficulty" (infrequency of appearance) of the words involved.
It would be interesting to know how general knowledge varies with IQ. Here, although there's "common knowledge", there's no well-defined lexicon the way there is with words.
A related topic is that of speed of learning. Dr. Arthur Jensen, in his book, "The g Factor", Praeger, Westport, CT, London, 1998, p. 274, says,
"It is well-known that different individuals need very different amounts of time to learn something to the same level of mastery, and some individuals are able to learn things that other individuals, given the same conditions of learning, are not able to learn at all.
"Some people acquire knowledge (i. e., learning what) and skills (i. e., learning how) some ten to twenty times faster than others. In a typical school situation, the fastest learners acquire knowledge and skills some five times faster than the slowest learners. By the time students reach their last year in high school, there are some who are still having seemingly insurmountable trouble with long division and fractions while some others are learning calculus These differences cannot be attributed merely to differences in opportunity, interest, or motivation. Laboratory experiments, in which the conditions of learning are highly controlled, have shown that individuals differ in the upper limit of complexity of the tasks or concepts that they are able to learn to a criterion of mastery, given any amount of time.(!)"
On page 276, Dr. Jensen has written
"Certain kinds of learning tasks, of course, are more g-loaded than others. Concept learning and the acquisition of learning sets )i. e., generalised learning-to-learn), for example, are more g loaded than rote learning, trial-and-error learning, and perceptual motor skills learning.
Dr. Jensen also mentions studies performed in the 1940s that looked for correlations between IQ and total-time-to-learn. These studies showed low correlations (and in some cases, negative correlations), but it's now understood that this was because the tests measured the subjects' abilities to rote-mechanically learn nonsense syllables, and because the tests employed "gain scores", defined as the number of trials required to master the problem (a statistically problematical procedure). Later studies, based upon school learning situations and meaningful material revealed the dramatic differences cited above. Bright students basically teach themselves by rapidly educing relationships that less-intelligent students infer slowly, if at all.
In my own experience, I learn best when I have a framework or "filing system" set up for knowledge of any particular sort, that involves patterns and conceptual frameworks anchored with otherwise-disparate facts. Of course, disparate facts provide the working material for "aha!" moments and the intercorrelations that lead to working models.
So how are we to put this all together?
(1) In his book "Straight Talk About Mental Tests", The Free Press Division of Macmillan Publishing Company, 1982, pg.31, Dr. Jensen says that there is practically no relationship between the learning of simple motor skills and IQ. Similarly, where students have to fall back on trial-and-error, there is little difference in learning time between fast learners and slow learners.
(2) learning-speed ratios as high as 20-to-1 may be found between the fastest learners and slow learners in the development of conceptual understanding, and the construction of knowledge frameworks. (In other words, learning speeds are improving exponentially (?) with rising IQ.
(3) There are relationships and insights that the brightest among us will perceive that others of us will never correctly apprehend. (We may get the wrong answer.)
In other words, it would seem to me as though it's in the areas of conceptual learning and problem-solving that intelligence particularly makes its presence known.
What might this mean about the mastery of a field? To me, it suggests that given sufficient long-term effort and focus, someone with a somewhat-above-average mentality can master the field at the journeyman level. In fields that require the rote-mechanical learning of new information, intelligence would not be as important as in, perhaps, mathematics and physics. On the other hand, someone who's brighter could learn faster, and will be best able to generate the leaps of intuition and the meaningful connections that are so important to human progress.
Of course, I would expect other traits to play crucial roles, such as persistence and focus. It takes awhile to gain the background to effect blazing leaps of intuition. It's also important to back up when you've made a mistake, to learn the literature in your chosen field, and to avoid an I-know-it-all attitude when, in fact, you don't.
Dr. Ericsson knows all of this, too. It would be interesting to explore this further with him, as well as with his critics.