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.
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
Athens, from about 440 BCE to 380 BCE,
Florence, from about 1440 to 1490,
London, from about 1570 to 1640.
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
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
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.
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.
Hegel, in his The Philosophy of Right, proposed the Zeitgeist theory
of genius. But this, at best, is description masquerading as
explanation. As good empirics, we seek a more specific understanding
of the problem.
Kroeber (1944) listed many cases of apparent accumulation, and lists
all the obvious factors (economy, education, world leadership, etc.)
that might play a role. His perspective is anthropological and
psychological, and he weaves in a fashionable amount of Toynbee. But
he confesses that he is unsatisfied with his treatment, and I concur.
Gray (1958, 1961) believes that geniuses arrive according to
numinously perfect mathematical cycles. He identifies three distinct
periodicities, and shows that when all simultaneously peak, high
culture hits the jackpot; when all three trough, the world's culture
is comparable to an Alabama high school's. The man is insane. (Readers
who disagree with this casual dismissal of his lifework are invited to
respond, but I shan't waste essay space on empty scholarly courtesy.)
McClelland (1961) counted the numbers of achievement images (e.g.,
"the farmer wrests his livelihood from the soil" vs. "the farmer sows
and reaps his sustenance") that appear in samples of text from periods
of artistic creativity and periods of artistic decline. He finds
statistically significant differences, argues that these reflect
important psychological differences, and speculates that the engine of
cultural enrichment is emphasis upon individual success.
Asimov (1951) suggested that psychohistorical forces could cause the
cultural florescences, but, after all, this is only science fiction.
And he never specifies the mechanisms that drive the advanced
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:
Prosperity. They submit that a florescent culture needs the economic
wherewithal to support the arts.
Peace. They suggest that a climate of peace is also conducive to
philosophical, artistic and (perhaps) scientific progress. (But recall
Welles' comment on Switzerland.)
Freedom. They believe that artistic freedom from state or religious
control enables new growth.
Social Mobility. They think that when class distinctions are
relatively permeable, then there is greater inducement for artists to
The Paradigm Thing. They suppose that when a new medium or perspective
arises, then art flourishes until the vein of originality is worked
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
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.
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 minutiž 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.
Asimov, I. (1951). Foundation, Panther: London.
Gray, C. E. (1958). "An Analysis of Graeco-Roman Development,"
American Anthropologist, 60, 15-27.
Gray, C. E. (1961). "An Epicyclical Model for Western Civilization,"
American Anthropologist, 63, 1036-1054.
Hayes, J. R. and Simon, H. A. (1985). "Three Problems in Teaching
Problem Solving Skills," Thinking and Learning Skills, Vol. 2, edited
by J. W. Sega and R. Glases, Erlbaum: Hillsdale, NJ.
Kroeber, A. L. (1944). Configurations of Culture Growth, University of
California Press: Berkeley.
Lopez, R. S. (1970). The Three Ages of the Italian Renaissance,
University Press of Virginia: Charlottesville.
McClelland, D. (1961). The Achieving Society, D. Van Nostrand:
Wilson, C. (1965). England's Apprenticeship, 1603-1763, St. Martin's
Press: New York.
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