High V, Low M
I sent the message below to a social scientist I know who (like many, perhaps understandably) is confused about Stephen J. Gould's status as an evolutionary theorist. Many Gould readers are surprised to learn that his main expertise was the paleontology of snails and that he struggled with higher mathematics. When I first encountered Gould's essays as a kid, I concluded that there was just no there there. He was all literary flourish and little depth.
Which brings me to an observation I've been meaning to write about. It is that high verbal ability (which Gould certainly had) is useful for appearing to be smart, or for winning arguments and impressing other people, but it's really high math ability that is useful for discovering things about the world -- that is, discovering truth or reasoning rigorously. The importance of math ability manifests in two distinct ways:
1. Powerful (deep) models of Nature (e.g., electrodynamics or evolutionary theory) are themselves mathematical. Most of the incredible progress in our understanding of the universe is just not available to people who do not understand math. For example, we can talk until we are blue in the face about the Uncertainty Principle, but there is no precise understanding without actual equations.
2. The statistical techniques used to analyze data obtained in a messy, complex world require mathematical ability to practice correctly. In almost all realistic circumstances hypothesis testing is intrinsically mathematical. It is quite easy to fool yourself statistically if you don't have strong math ability, but rather are simply following cookbook recipes.
High verbal ability is useful for more than just impressing others -- it typically implies a certain facility with concepts and relationships between ideas -- but high V alone is a dangerous thing. The most confused people I meet in the academy tend to be high V, low (modest) M types.
More on the V / M split in this longitudinal study of gifted children (SMPY / SVPY -- see esp. figure 4).
Gould on Gould (NY Review of Books, March 29 1984):
See Human capital mongering: M-V-S profiles for further explanation of this figure.
Which brings me to an observation I've been meaning to write about. It is that high verbal ability (which Gould certainly had) is useful for appearing to be smart, or for winning arguments and impressing other people, but it's really high math ability that is useful for discovering things about the world -- that is, discovering truth or reasoning rigorously. The importance of math ability manifests in two distinct ways:
1. Powerful (deep) models of Nature (e.g., electrodynamics or evolutionary theory) are themselves mathematical. Most of the incredible progress in our understanding of the universe is just not available to people who do not understand math. For example, we can talk until we are blue in the face about the Uncertainty Principle, but there is no precise understanding without actual equations.
2. The statistical techniques used to analyze data obtained in a messy, complex world require mathematical ability to practice correctly. In almost all realistic circumstances hypothesis testing is intrinsically mathematical. It is quite easy to fool yourself statistically if you don't have strong math ability, but rather are simply following cookbook recipes.
High verbal ability is useful for more than just impressing others -- it typically implies a certain facility with concepts and relationships between ideas -- but high V alone is a dangerous thing. The most confused people I meet in the academy tend to be high V, low (modest) M types.
More on the V / M split in this longitudinal study of gifted children (SMPY / SVPY -- see esp. figure 4).
Gould on Gould (NY Review of Books, March 29 1984):
"I am hopeless at deductive sequencing... I never scored particularly well on so-called objective tests of intelligence because they stress logical reasoning ..."This is from the email I sent to a colleague:
Gould appeals to high V low M people who do not actually understand evolutionary theory at a mathematical level. He never made any important contribution to evolutionary theory other than as a popularizer.
Note this is distinct from his deliberate obfuscation of topics like IQ in Mismeasure of Man. He wrote some incorrect things there about factor and statistical analysis, but perhaps those distortions were intentional. See The Mismeasure of Science: Stephen Jay Gould versus Samuel George Morton on Skulls and Bias.
Paul Krugman:
Now it is not very hard to find out, if you spend a little while reading in evolution, that Gould is the John Kenneth Galbraith of his subject. That is, he is a wonderful writer who is beloved by literary intellectuals and lionized by the media because he does not use algebra or difficult jargon. Unfortunately, it appears that he avoids these sins not because he has transcended his colleagues but because he does does not seem to understand what they have to say; and his own descriptions of what the field is about - not just the answers, but even the questions - are consistently misleading. His impressive literary and historical erudition makes his work seem profound to most readers, but informed readers eventually conclude that there's no there there. (And yes, there is some resentment of his fame: in the field the unjustly famous theory of "punctuated equilibrium", in which Gould and Niles Eldredge asserted that evolution proceeds not steadily but in short bursts of rapid change, is known as "evolution by jerks").
What is rare in the evolutionary economics literature, at least as far as I can tell, is references to the theorists the practitioners themselves regard as great men - to people like George Williams, William Hamilton, or John Maynard Smith. This is serious, because if you think that Gould's ideas represent the cutting edge of evolutionary theory (as I myself did until about a year and a half ago), you have an almost completely misguided view of where the field is and even of what the issues are.
http://www.pkarchive.org/theory/evolute.html
John Maynard Smith:
"Gould occupies a rather curious position, particularly on his side of the Atlantic. Because of the excellence of his essays, he has come to be seen by non-biologists as the preeminent evolutionary theorist. In contrast, the evolutionary biologists with whom I have discussed his work tend to see him as a man whose ideas are so confused as to be hardly worth bothering with, but as one who should not be publicly criticized because he is at least on our side against the creationists. All this would not matter, were it not that he is giving non-biologists a largely false picture of the state of evolutionary theory."
John Tooby:
"Although Gould characterizes his critics as "anonymous" and "a tiny coterie," nearly every major evolutionary biologist of our era has weighed in in a vain attempt to correct the tangle of confusions that the higher profile Gould has inundated the intellectual world with. The point is not that Gould is the object of some criticism -- so properly are we all -- it is that his reputation as a credible and balanced authority about evolutionary biology is non-existent among those who are in a professional position to know...
These [major evolutionary biologists] include Ernst Mayr, John Maynard Smith, George Williams, Bill Hamilton, Richard Dawkins, E.O. Wilson, Tim Clutton-Brock, Paul Harvey, Brian Charlesworth, Jerry Coyne, Robert Trivers, John Alcock, Randy Thornhill, and many others."
http://cogweb.ucla.edu/Debate/CEP_Gould.html
Richard Lewontin:
"Steve and I taught evolution together for years and in a sense we struggled in class constantly because Steve, in my view, was preoccupied with the desire to be considered a very original and great evolutionary theorist. So he would exaggerate and even caricature certain features, which are true but not the way you want to present them. For example, punctuated equilibrium, one of his favorites. He would go to the blackboard and show a trait rising gradually and then becoming completely flat for a while with no change at all, and then rising quickly and then completely flat, etc. which is a kind of caricature of the fact that there is variability in the evolution of traits, sometimes faster and sometimes slower, but which he made into punctuated equilibrium literally. Then I would have to get up in class and say “Don’t take this caricature too seriously. It really looks like this…” and I would make some more gradual variable rates. Steve and I had that kind of struggle constantly. He would fasten on a particular interesting aspect of the evolutionary process and then make it into a kind of rigid, almost vacuous rule, because—now I have to say that this is my view—I have no demonstration of it—that Steve was really preoccupied by becoming a famous evolutionist."
https://johnhawks.net/weblog/topics/history/biology/lewontin-wilson-gould-interview-2015.html
See Human capital mongering: M-V-S profiles for further explanation of this figure.
