February 14, 2006

Genius germs: preliminary evidence, part II

II. Measuring creativity and genius
(Part I here, III & IV to follow.)

Before Part III discusses how germs could contribute to genius, we must define "genius" and build a model for "creativity." Informally, a "genius" has smarts, "thinks outside the box," and shows Herculean output. So, we would look for them among revolutionary figures in the arts & sciences. We formally define a "genius" as someone who shows up in the upper 5 "deciles" by Index Score in comprehensive rankings of eminence. The bible of such rankings is Charles Murray's Human Accomplishment, to which we refer. He consulted many encyclopedias of the arts & sciences, determined who was mentioned most and given most space across all volumes, and rank-ordered the figures by raw score, w/ the raw score of the top figure set to 100 (e.g., Michelangelo in Western Art). Several top 20s are here. "Decile" here is not frequency-based but refers to Index Score. So for Western Music (see previous link), Mozart and Beethoven have an Index Score at least 90, so they are in the 9th decile; Bach and Wagner are in the 8th; etc. Murray began at 800 BC and ended at 1950, covering the entire globe for the sciences, while creating separate categories for the arts (e.g., Western Lit and Japanese Lit).

The rankings do not reflect mere fashion because the plots of how many figures are in the 1st through 9th deciles model a hyperbolic curve (one that approaches its asymptote much faster than a bell curve), just as happens in the clear case of rankings of excellence in sports -- Murray (p. 101) shows a similar curve for percentage of golfers who have won varying numbers of victories in the Majors in golf. That is, of those who showed up at all, most won 1 to 3 Majors, after which the curve levels off; almost no one won 5 - 18 Majors. Since victory in the Majors reflects overall excellence rather than fashion or speciality in one narrow aspect of golf (such as driving), curves which resemble it in the arts & sciences can be assumed to reflect overall excellence as well.

Murray stopped at 1950 to dampen "epochcentric bias" -- the tendency to overemphasize the importance of the recent past. The most recent figures' scores could reflect such bias to some degree, but since few of them show up in the upper 5 deciles anyway, this will not impact our discussion of genius. Disclaimers: 1) Before dismissing Murray's approach based on my whirlwind summary, read the book first (which is accessible; reviews here, here, and here). 2) We can agree that Mozart was a more aesthetically excellent composer than Bizet (Index Scores 100 vs 10, respectively), even if one finds Bizet more agreeable to one's tastes.

So what makes a genius mind? Dean Simonton is the authority on psychologically modeling genius, and to recapitulate, a genius is one w/ exceptional intelligence (psychometric g), "outside the box" creativity, and an untiring work ethic. As for work ethic, we interpret this as a high score on the Conscientiousness factor of Big Five personality tests. But hard-working though geniuses are, we assume the primary factor in accounting for genius isn't Conscientiousness but the combination of smarts plus creativity. Ah, but that raises (not begs) the question: is "creativity" independent of "intelligence" like "athleticism" is? John Carroll's Human Cognitive Abilities, a massive summary of psychometrics, including tests of g and creativity, shows that as yet there is no evidence that creativity is independent of g -- in fact, the available data suggest that the two are highly intertwined, and since g is the primary factor on all mental tests, our default assumption is that "creativity" is really just another "flavor of g." Carroll (p. 428):

It appears to require a considerable degree of general cognitive ability [i.e., g] for an individual to be able to make high-scored responses to tests of factor FO [i.e., "originality" or "creativity" factor]. . . .[T]hese data provide no evidence for or against the hypothesis that there is a threshold of intelligence above which there is little relationship between intelligence and creativity. . .

Here is a visual of his meta-analysis: one general factor at the apex (General), a handful of broad "flavors of g" like auditory (Broad), along w/ myriad specific abilities such as pitch perception (Narrow). So, we assume that what we call "creativity" is either a Broad ability or is distributed among Broad and Narrow abilities. Recently, Linda Gottfredson dissected claims by Robert Sternberg that "practical intelligence" (something like common sense) was a cognitive ability largely independent of g (for pdf, Ctrl F dissecting). She found that there was no evidence that it was independent (most of the samples Sternberg examined were biased toward high IQ, rather than examining the general population), and plenty of evidence that common sense is largely explained by g. Absent compelling contrary evidence, we assume the same holds for creativity's purported independence of g. As an aside, we introduce our own term for "flavor of g," which gets more to the point: we call Carroll's Broad & Narrow abilities "shadows of g," meant to suggest both the various shapes the single g factor casts, as well as the analogy to Platonic Forms and their myriad Particular instances.

Now, as a former IQ skeptic, I must reassure those I've upset w/ the suggestion that the ineffable quality "creativity" is a mere shadow of g, which many (falsely) mistake for nitty-gritty analysis. We start w/ two run-of-the-mill IQ question types that require "outside the box" thinking, and then we formalize the creative thought process. First the questions (answers & remarks at the bottom of the post). Consider the following sequence of numbers, and then fill in the blank w/ the next number:

23, 57, 1113, 1719, 2329, ____ ?

Now, consider the sequence of pictures here, then choose the next picture.

Both require unusual thinking (as explained below), and the picture sequence is the type tested on Ravens Progressive Matrices, the most highly g-loaded IQ test. Therefore, we see no problem w/ viewing creativity as a shadow of g. A question type frequently tested on creativity tests asks the person to devise a novel use for an existing tool, say a cup. Again, this sort of "What if I tried this?" thinking is what's needed to solve a brainteasing Ravens problem.

To formalize creativity, we begin w/ Dean Simonton's model of creativity as a metaphorical Darwinian process. (I read his work after thinking about this topic, so I was disappointed to find that I'd been scooped on the rough outline of the model. I suppose I can console myself w/ "Great minds think alike!") For overviews, browse his publication list (for pdf, Ctrl F 195), or read Origins of Genius: Darwinian Perspectives on Creativity here. Essentially, he believes geniuses are capable of unconsciously generating greater quantity & remoteness of variations on an underlying idea, among which they consciously select the "fittest" -- the one likely to bear the most artistic or scientific fruit. The underlying idea is like the initial genotype, the variations are blind like random mutations producing novel genotypes, and the artist's choice plays the role of natural selection. He has the generation of random variations doing most of the work; the idea is that geniuses are better at this stage of the process than the rest of us.

However, coming from a linguistics background, I find the mental generation of random variations simple. To mention just two models, Optimality Theory (OT) in phonology tries to model how the sound of a word that's stored in our mental dictionary surfaces when it's pronounced from our mouths. Take the plural word "dogs." Simplifying notation, this could be pronounced with an "s" sound or a "z" sound at the end; in reality, it has a "z" sound. The mental dictionary form is the genotype which is fed to a function (called GEN) which returns the infinite set of variations on that form -- e.g., "dogs," "dogz," "digs," "bladiblabla," ad infinitum. This infinite "candidate set" is then fed to another function (called EVAL) which processes (at the unconscious level) each member in parallel and marks each member that violates certain rank-ordered constraints (which are like selection pressures). The candidate that incurs the fewest violations of higher-ranked constraints is chosen as the "fittest" form. In our example, "dog-z" wins because the "g" and "z" sounds agree w/ each other on the value of voicing (whether or not your vocal chords vibrate), a highly ranked constraint in English, whereas the "g" and "s" sound don't agree in "dog-s."

Though OT and natural selection are isomorphic in many ways, the metaphor should not be taken too far, as pronounced forms do not breed and spread throughout the population. The key point is that the infinite set of blind variations is easy to get: just supply a form to the GEN function, and it'll mutate each constituent sound in every imaginable way, as well as add or delete sounds. The heavy lifting is done by the EVAL (or selection) function; it must simultaneously juggle all candidates and check the constraint ranking to see which is the most fit.

Second, a standard model for the semantics of questions is that the meaning of a question is simply the (in principle, infinite) set of possible answers; the job of the responder is to single out the answer from that set. For the curious, see the right-hand side of page 4 in this handout (pdf) by Paul Hagstrom. So, "What is the President's name?" means the infinite set of possible names; the responder then picks out the correct name from the list. Again, the key point is that generating an infinite set of blind variations is easy -- simply replace "What is the President's name?" with the infinite set of sentences "The President's name is x" for all names x. The heavy lifting is done by the responder who searches the list and singles out the answer.

We now apply these theoretical approaches to modeling creativity. (Note: for the empirical support for such a model, read Simonton's work. We present here what we view as an improvement on Simonton's cognitive model.) We view the creative "problem" as identical to a question, e.g., "What shall I paint?" This problem is fed into a function we'll call GEN, which returns the infinite set of answers -- but because not all answers are satisfactory solutions, this set is best visualized as the "idea landscape," on analogy w/ the fitness landscape concept in evolutionary biology, where peaks & valleys represent fitness maxima and minima, respectively. In reality, an answer to "what to paint" likely has many more dimensions than two plus a fitness indicator, but for ease of presentation, we treat them as ordered pairs plus a fitness indicator. An algorithm we'll call INIT ("initial") takes in this landscape and returns a randomly chosen finite cluster of starting points to investigate. These starting points are then fed into a hill climbing algorithm called PON ("pondering"), which in parallel maps each point to a higher adjacent point until it reaches a local maximum. These local maxima represent the conceptual statues hewn from the conceptual marble. The finished product results after, e.g., putting pen to paper to flesh out these outlines -- which in turn may illuminate other starting points to investigate -- and choose the best result.

So what separates these processes run by a genius mind from those run by an ordinary mind? A naive first guess might be that the INIT and PON algorithms are simply run continuously, so that geniuses have more random starting points to investigate, increasing the odds that one of them will be worthwhile. But this would imply that geniuses merely think longer about a problem. Moreover, unlike the EVAL function in OT, the PON selection algorithm is a largely conscious process and is thus subject to constraints on attention and number of items being mentally juggled at once. We therefore introduce the following to restrict how INIT chooses its cluster of starting points for PON to make climb hills -- the idea is that the cluster is a "spotlight" of attention defined by a center C and radius R (roughly, "focus" and "scope," respectively). By hypothesis, natural selection has hard-wired the default search locations for these to correspond to "obvious" solutions; for example, in the problem of "Who shall I mate with?" the C for males is wired to focus on the female region of the landscape, with R set to a small radius (lest he consider males as well).

Veering from the default settings is not inconceivable, so we posit Flexibility Constants for the C and the R (FC-C and FC-R). A low value for an FC indicates low tolerance for deviation from the default, and similarly for a high value. We propose a simple method to quantify them: namely, as the expected value of fitness loss due to allowed deviation from the "obvious" solution (expressed as a percent, thus from 0 - 100). So for the mating problem in male brains, if the C were flexible enough to focus on the male terrain rather than the female (it could still survey it, but would not bother generating starting points there), then the FC-C would be 80 for this problem, since gay men have on average 80% fewer kids than straights. By contrast, pursuing the "obvious" solution would entail an FC-C of 0, since by following the cumulative wisdom endowed by natural selection, one doesn't expect to have fewer kids. Thus, the FC-C and FC-R are 0 for adaptive problems in normal individuals, e.g. "who to mate with" or "what to eat."

Consequently, for fitness-neutral problems, e.g. "what to paint," the FCs may well describe a bell curve centered around, say, 50 rather than be so lopsidedly biased toward 0. The variance in FC-C (again, how tolerant one is to focus on unusual regions) we interpret as the variance in g and perhaps the Openness factor in the Big Five personality model. See here (pdf) for evidence that at least among college students, g correlates +0.43 w/ Objective Openness (openness to ideas, actions, and values, not fantasy, aesthetics, or feelings). The variance in FC-R (again, how wide the scope of consideration is, or how many starting points are being mentally juggled) we interpret as the variance in Digit Span measured on, e.g., the Wechsler IQ test. So, geniuses are expected to have remarkable values for FC-C and FC-R in fitness-neutral problems: tentatively, 3 SD above the median of practicing artists & scientists.

As with other aspects of personality & intelligence, variance here is due to a combination of genes and environment -- such as germs affecting the brain. In Part III, we will briefly examine how germs could affect cognitive ability in ways less obvious than, e.g., aggression caused by rabies.

Answers: The next number is 3137. Each term is a pair of consecutive prime numbers. Thus, the person must shed inhibitions that there is an arithmetic operation between each term (say, adding or multiplying), as well as the inhibition that the numbers are atomic rather than glued together.

The next picture is B. Each color moves one ring outward until it reaches the outer ring, at which point it loops back to the center. This requires seeing a ripple-like movement among three "snapshots." One must also shed the inhibition that the ripple must continue in the direction it started, like a real ripple, rather than be caught in a loop.


  1. John S Bolton2/15/06, 1:26 AM

    One statement I often use against openness-valorization is that this is what a parasite would direct us to say to others, if it had only to be transmitted. If it could make us say only two words, these would be 'value openness'. If one such parasite lineage were to spread and impart greatly enhanced intelligence in the manner suggested, as by valuing also intellectual openness, yet somehow without destroying discrimination, and the impulse towards higher purities; wouldn't it cause epidemics with high mortality from other, faster-killing microbes or ideas?

  2. John S Bolton2/15/06, 1:35 AM

    When an evangelical mystic accosts you, and you indicate that his irrationality is of no interest to you, does he not reply 'be open', 'be more open' or 'be open-minded'? Already you know that what he wants you to be open to, will close the door of openness to anything else behind it; while commanding you to spread his directive of valuing openness to the next victim, along with any other doctrines which are additional. Like the parasite which had only to command you to say to the next victim, 'value openness', there need be no additional message beyond this absolute minimum one.

  3. John S Bolton2/15/06, 2:02 AM

    I'm sure this is not what is to be proposed; but suppose that a microbe could generate some improbable openness of mentality. Would not the newly-infected soon become permanently mentally disabled from lack of sleep, if indeed they retained their openness to messages or information which was broadcast their way, such as advertising? Would the program be something like; 'be open, then with speed, close off totally'. Such a program would favor something like Islam, but there have been no geniuses in that culture for 1000 years perhaps, on the level you're referring to. There is a contradiction here, as in Allan Bloom's saying "openness to closedness is what we teach". The infectious agent needs you to be open just long enough to receive it, after which it needs you to stay alive long enough to transmit, commanding someone else to be open, after which next transmission, it needs you to live not necessarily any longer.

  4. Hi,

    Interesting series. I'm looking forward to getting to some of the conclusions.

    Re: creativity, I would slightly disagree with your approach of modeling it. I think the FC-C and FC-R system works well for well-defined, "outside-the-box yet inside-the-box" problems such as those on IQ tests, and in that sense creativity and g are very correlated and linear. Your approach works surprisingly well on modeling how such problems are solved by different people.

    However, a lot of creativity rests not only on novel solutions to pre-defined problems, but novel formulations of problems, and of what problems exist. And these other factors do not lend themselves very well to representation in a simple shared fitness landscape.

    In short, I like your method, but it doesn't capture all of how creativity functions. I'm not sure whether this criticism will be relevant to your conclusion.


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