The Problem of Excess Genius

David Banks, Department of Statistics

Carnegie Mellon University, Pittsburgh PA 15213

The most important question we can ask of historians is "Why are some periods and places so astonishingly more productive than the rest?" It is intellectually embarrassing that this is almost never posed squarely -- I can think of only two articles (Gray, 1958 and 1961) and two books (Kroeber, 1944 and McClelland, 1961) that tackle this directly. But Gray is a lunatic, Kroeber waffles vaguely, and McClelland veers off into a fascinating but incomplete assessment. The question has never been the focus of professional attention in social history, although its answer would have thrilling implications for education, politics, science and art.

The Problem

Geniuses are not scattered uniformly through time and space. Some cultures have many more than one would expect, even after making sensible allowance for imperfect records, biased perspectives and such gross factors as famine, war, and the magnetic effect of libraries and patronage. Obvious clumps of geniuses occur in If the reader agrees that these three societies show such a remarkable excess of creative accomplishment that explanation is demanded, skip on to section 2. The remainder of this section is just a borderline pretentious argument to convince rational skeptics that random chance is an inadequate explanation for the intellectual inhomogeneity that history records. First, the three cities and times listed above are not unique -- there are many other accumulations, although these are particularly conspicuous. One can spend pleasant postprandial hours noting similar clusters in Weimar, Paris (twice), London (again), Vienna, Japan (late Heian period), Persia (just before Genghis Khan), the T'ang dynasty, and New York, at times that I hope most readers can discern for themselves. My sense is that there is a continuum of remarkability, from the three stellar cases listed first through the slightly humbler collections indicated in this paragraph, and the degree of remarkability shades imperceptibly into average societal behavior. (There are also major vacuums in intellectual achievement -- the Dark Ages were notoriously weak, and one should recall Orson Welles' comment that 500 years of Swiss peace produced only the cuckoo clock.)

But let us focus on the first list. Were general citizens asked to name famous Athenians, the handful of names produced would come entirely from the indicated period. Even were an academic interrogated, the list would surely lean (list?) towards this period (Euripides, Sophocles, Aeschylus, Aristophanes, Plato, Socrates, Thucydides, Herodotus, Xenophon, Anaxagoras, Demosthenes, Pericles, Aspasia, Alcibiades, Praxiteles, Phidias, Protagoras, Aristippus, Isocrates, Lysias, Lycurgos, Polygnotos, . . .). The suggested dates are obviously approximate, but I defy anybody to name an Athenian who amounted to anything that was born after 380 BCE (well, Kazantzakis will get a footnote, and if anyone were foolish enough to put forward Pseudo-Dionysius the Areopagite, I remind them that the extant writings are of Alexandrian origin).

So what happened to the cultural IQ of Athens over the last 23 centuries? The genetics didn't change appreciably (at least until 1398, when Nicopolis fell to the Turks). Why did such vitality stagnate?

Florence is almost as compelling. There is an early bump of productivity with Dante and Boccaccio and Giotto and Cimabue, but it faded out (perhaps as a subtle consequence of the the Black Plague). Then came a new lot, with Michelangelo, Leonardo Da Vinci, Machiavelli, Botticelli, Donatello, Politian, Mirandola, Lorenzo the Magnificent, and so forth. But before the birth of Cimabue (1240) and after the death of Galileo (1642), not much happened in the city. How was it that all its achievements were concentrated into such a relatively small proportion of its span? The question is particularly puzzling when one realizes that today, in all of Italy, the standard of education is higher, the promotion of merit is easier, and the population is enormously greater; nonetheless, there is no one that could seriously be compared to Dante or Leonardo or Michelangelo.

Elizabethan London is the third example. Marlowe and Shakespeare and Jonson and Raleigh and Bacon and Spenser laid the foundation for English writing, and there are a host of lesser luminaries whose hands helped. But their momentum ended with the coming of Cromwell (Milton stands alone). From the close perspective of college courses in the Restoration and Neoclassical periods, we can name many well-regarded writers (Dryden, Pope, Wycherly) before the Romantic poets burst forth, but the central point is that English talent isn't evenly sprinkled like pepper on potatoes; rather, it clots inhomogeneously.

If these litanies of names have not persuaded the skeptical reader that geniuses are sometimes superabundant, then a more formal debate is needed. To pursue that dialogue, I would ask such readers to decide how they would plan to calculate the numbers of geniuses they'd expect to see under their models, in order that we may compare their figures to the historical record. But for me, that smacks of straining at gnats when there are important camels to swallow.

There is much else one could say. It is interesting to compare the primary modes in which these societies operated (Athens did plays and philosophy, Florence did painting and sculpture, London did poetry and plays), and speculate upon the modern roles of television, performance art, and rap. Also, scientific progress seems slightly less likely to concentrate than do the arts and letters, and this can be tediously delineated at some future time.

Previous Answers

Having posed the problem, let's proceed to a catalogue of some of the stock answers that have been given previously. The following four can be rejected out of hand. Except for McClelland, these treatments suffer from vagueness. We want explanations that make sense, and which can be corroborated by specific historical research.

What type of explanation is adequate? My sense is that high points in cultural history require the confluence of many factors; some of these are more important than others. When all or most of the factors coincide, then one has a Periclean Athens, Laurencian Florence or Elizabethan London. When only several factors combine, the cultural eruption is more humble -- one gets Goethe's Weimar, or the Lake Poets. Things trail off gradually; if virtually none of the factors obtains, then we call it a Dark Age. From this perspective, the sought-for answer is a list of factors that facilitate/militate the occurrence of genius, with some understanding of their relative importance. In a crudely statistical way (retrodiction rather than prediction), one can test hypothetical factors by determining whether their presence is associated with higher measurements on some suitable index of a society's florescence.

In general, it is statistically (and epistemologically) impossible for the historical record to suggest the factors (this entails technical statistical details; epexegesis is deferred). The researcher must make clever guesses, which are then corroborated by the record. The next section describes factors that have been proposed, and various strategies for discovering plausible factors.

Searching for Factors

When I beard social historians at cocktail parties, they usually dismiss the problem of explaining excess genius as complex and ill-posed. But when coaxed into conversation, several ideas for facilitating factors come forward: All of these are good ideas, and superficially plausible. But most contradict the historical record.

To be specific, the prosperity suggestion fails for Athens, Florence and London. Athens spent its boom period in combat with Sparta; the income from the Delian League went to the fleet. Athenian farmers could not tend their crops (cf. The Acharnians), and such staples as grain had to be imported. Similarly, quatrocento Florence was poor compared to pre-plague Florence. The Medici bank had about half the capital of the Peruzzi bank in 1340, and Lopez (1970) documents other indications of reduced standards of living. A symptom of this desperation was the revolt of the populo minuto, which pushed the Medici into prominence. And Elizabethan London suffered "dearness without scarcity" (inflation); this fell most heavily on the aristocracy and the very poor. Then the wool trade collapsed, England entered "the worst economic depression in history" (Wilson, 1965), and Parliament anxiously debated means of averting a Bellum Rusticum.

Regarding the peace hypothesis, it clearly fails for Athens. Florence was torn by internal factions (e.g., il popolo grosso vs. il popolo minuto, the assassination of Giuliano de Medici, Savonarola). London had to contend with the Armada, the war with Spain in Holland, and internal religious dissent.

Regarding artistic freedom, the Athenian plays were written for religious festivals, and the prize was awarded according to the taste of respectable, pious and civic-minded judges (this caused Aristophanes and Euripides no end of trouble). In Florence, art was commissioned largely by the Church, sometimes by a patron, and had to voice themes prescribed in the contract. In London, note that Shakespeare's plays avoid all mention of religion and contemporary politics; Marlowe and Jonson were similarly cautious (in literature, not in their personal lives).

Regarding social mobility, this hypothesis seems borne out by our three primary examples. Athens and Florence were both devaluing the aristocracy and promoting mercantilism. In London, the early part of the period clearly shows the rise of the middle class.

Regarding the emergence of a new paradigm, this is difficult to judge concisely. Much of the problem involves distinguishing a perturbation from an innovation. Did the introduction of a second on-stage character in Athenian plays represent a new paradigm? Was Plato's decision to record philosophical discussion a minor influence on the content of the debate? Similarly, in Florence, painting and sculpture were well-established before the peak occurred, but the invention of perspective and the rediscovery of the classical period may have constituted a paradigm shift. Finally, in London, the key change seems to have been that small groups of strolling players discovered they could pack a hall in a city, and people would stroll to them. This enabled more elaborate props and larger companies, while pressing the need for a larger repertoire. But this kind of change is not especially Kuhnian in spirit, and the problem merits more lengthy consideration.

One could propose other factors. It seems to me that each of the three societies under consideration enjoyed a substantial military victory in the generation preceding their florescence. Athenians whose names shine today are reported to have prided themselves on being the sons of the men who fought at Marathon. Florence was not a military force (the Italian city-states relied upon mercenary condottieri in time of war) but in 1254 they conquered Pisa and Lucca. This secured an outlet to the sea, which was essential to their economic expansion. And in 1588, England conquered the Spanish Armada. This made the seas safe for colonial empire, and was a watershed for British morale.

Also, the great minds in each of these societies tended to hang out together. Socrates spoke with everyone. The playwrights talked shop, and the orators honed themselves upon each other. In Florence, artists trained under an apprentice system that pulled talents together, and Vasari describes frequent visits by the greats to each other's studios. Leonardo and Michelangelo held a public contest over The Battle of Anghiari; meanwhile, the poets and philosophers clubbed together at Lorenzo's mansion. In London, much of the theater circle met for drinks at the Mermaid Tavern, and one expects that their common profession ensured their lives crossed even more regularly. Aubrey reports that Bacon visited the Mermaid Tavern too, and doubtless Bacon knew Raleigh, who was sufficiently friendly with Marlowe to rise to the Shepherd/Nymph bait. Does the social intercourse of good minds produce great minds?

A third possible factor is education. In each of the three societies, education tended to be as personal as a punch in the nose. In Athens, the upper class had tutors and the lower classes shopped for their educations among various freelance teachers. In Florence, the upper class had tutors and the masses learned as apprentices. In England, the upper class had tutors and the commoners learnt to write plays and poetry from each other, insofar as I can tell. All three of these systems emphasize individual instruction over the currently popular cattle drive approach. And there is ancillary evidence (cf. the lives of Wiener, Maxwell, Dirac, Russell, Mill, Malthus, Arnold, Feynman) that tutoring is enormously effective.

One can postulate many other factors. For example, it is suggestive that all three of Athens, Florence, and London had populations near 300,000. Also, all three had relatively democratic styles of government, and all three's florescences were ended by right-wing revolutions (the Rule of the 400, Savonarola, and Cromwell). Finally, each of the three were in the process of reinventing their language -- Periclean Athens defined the conventions of Attic Greek, Dante made Tuscan the foundation of modern Italian, and the linguistic gap from Chaucer to Shakespeare is enormously larger than the gap from Shakespeare to us (but this could be due to selection bias, since language might gel around great writings, rather than great writings arise from volatile language).

There is never any shortage of hypotheses. The useful trick is to know how to test them. In this case, one could rank a sample of cities in terms of their cultural IQ, and then decide whether the hypothesized factor obtains for each of the cities. If the factor is more common for the florescent cities than for the average or below average cities, then the hypothesis is supported (this can be made formally statistical). To an extent, this style of reasoning is what is used in this section, except that I haven't elaborated the comparison by listing cities which have made meager cultural contributions.

The Individual

There is an alternative strategy for studying the problem of excess genius. Instead of focusing upon the society that produced them, one can study the minuti┼ż of geniuses' lives, looking for commonalities that might suggest cultural forces. For example, if a study of many geniuses finds that disproportionate numbers were tutored, then one might guess that creative societies were those in which tutoring was a prevalent means of education.

Hayes and Simon (1985) report a study of composers. After sifting through much biographical material, they conclude that a minimum of ten years of serious study is required before anyone begins to produce important music. And subsequent research suggests that this ten year rule applies to many different disciplines, including mathematics, chess and poetry (though possibly not philosophy). Allen Newell is alleged to have proffered an explanation of this regularity:

Greatness is relative, and humans compete against other humans. If intelligence is not a major factor, and if ten years represents the amount of time an exceptionally dedicated human is willing to invest, then, ceteris paribus, world class geniuses will be those who've marinated in a subject for ten years.

Clearly, the controversial element in this line of research is its underemphasis of the importance of native intelligence and skill.

In a similar mood, I undertook a study of 100 eminent men and women of Victorian science and letters. With the help of 11 undergraduates, I compiled a database that recorded 56 traits for each of the people chosen. We then applied a laundry list of semi-sophisticated statistical procedures to look for hidden patterns in the data. One particular question of interest was whether there were biographical traits that discriminated the artists from the scientists.

To give a better flavor of the project, the first twenty people in the database are: Arthur Conan Doyle, Andrew Lang, Matthew Arnold, Jane Austen, Charles Babbage, James Barrie, Jeremy Bentham, Sir Richard Francis Burton, Charlotte Bronte, Thomas Carlyle, Arthur Cayley, Charles Lamb, Samuel Taylor Coleridge, Charles Darwin, Thomas DeQuincey, Benjamin Disraeli, Charles Dodgson, Elizabeth Barrett Browning, Robert Browning, and Michael Faraday. (The list is only partially alphabetical, for technical reasons related to the software and our occasional use of initials to distinguish some subjects.)

Similarly, some of the biographical traits that were examined included birth order, family status, number of spouses, number of siblings, age at father's death, age at mother's death, whether or not the subject loved the father, ditto the mother, whether the subject was thrifty, whether the subject was gay, an estimate of the subject's sexual appetite, an estimate of the subject's precocity, a description of the kind of schooling the subject received, the intensity of the subject's religiosity, whether the subject had a sense of humor, whether the subject drank, the age at which the subject first produced good work, and so forth.

Unfortunately, the results of the analyses so far have been unilluminating. It appears that Romantic poets tended to have been raised by their mothers, and that scientists tended to come from happy, stable families. However, the statistical support for both of these conclusions is small (a=0.05), and the reliance upon undergraduates for the gathering of information ensures that, despite substantial efforts at data cleaning, the accuracy of the records is not beyond question.


The problem of excess genius is one of the most important questions I can imagine, but very little progress has been made. It surprises me that essentially no scholarly effort has been directed towards it. I warmly solicit any suggestions from readers that may help me to clarify my own confusion and uncertainty regarding this.


The Autodidact's Journal