Rich Lawler has an insightful comment:
It's interesting to note that a few of the most insightful observations about the evolutionary process were first promulgated verbally, then later proven mathematically (unlike H-W equilibrium). These include runaway sexual selection (first adumbrated by Fisher, then shown mathematically possible by Lande and Kirkpatrick), the handicap principle (first adumbrated by Zahavi, then--finally--shown to be mathematically possible by Grafen), and, of course, natural selection (first adumbrated by what's-his-face, then formalized by Wright, Fisher, and later Price, among others). And of course, all of these topics were debated back-n-forth until the math made them more clear.
I think the key here is the reference to evolutionary process, dynamics which span time and space beyond intuitive conceptualization. Verbal "lock & key" models are often sufficient to communicate the biophysical processes at work when an enzyme and substrate interact. A graphical illustration of a biophysical process is clear as the visual mapping is can be precise and accurate; the primary actors here are material. Not so for something as abstract as "fitness." Verbal descriptions of moments about distributions of abstract concepts are not sufficiently precise to allow for fruitful theoretical inference beyond the most elementary level. Of course, a non-mathematical idea can, and usually does, serve as the seed for future growth of formal theory. But when the subject is by its nature complex formalism is often simplest route.
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Hmmm. And what, exactly and in full generality, do you mean by fitness?
I wonder if there isn't a confirmation bias here. Consider all the ideas about evolutionary process first promulgated verbally that turned out to be crap. Orthogenesis. Recapitulation. Naive group selectionism. Saltationism. Polygenism.
I won't count use inheritance, because it actually is described well mathematically and may work for cultural evolution.
Evolutionary biology has a lot of recycling of common-sensical insights, and a lot of "new rediscoveries" of what Darwin said 150 years ago. This is all because of the propensity for verbal argumentation.
A more subtle problem is that words change their meanings. "Fitness," mentioned in the previous comment is a good example. I think Dobzhansky did better at verbal argumentation than almost anyone, but it is fairly easy to put words into even his mouth. Dawkins did a masterful job of putting Williams and Hamilton into English, but hardened them in the process. When you consider Gould's big volume, or Mayr's History of Biological Thought, they do far worse justice to the originals, scrambling some ideas beyond recognition. The problem is that words are too easily changed for the interpreter's convenience.
I don't think saltationism is crap. Overstated at the time, sure. Macromutations that give rise to major innovations and changes in body plans are on the upper end of a spectrum of degrees of phenotypic effect, from mutations of no effect to small effect to large effect. There is room for both Goldschmidt and Fisher.
A mathematical model with incorrect assumptions may prevail while a contradictory but commonsensical verbal argument is discarded. And perhaps that is part of the reason for the tradition of anti-saltationist bias.
My question on fitness wasn't rhetorical and unfortunately hasn't yet been answered. It's not a matter of ambiguity or change of meaning, although that has happened too, but a case where mathematical precision in a too-restricted domain has proved positively misleading in several ways when extended beyond that domain.
To anyone: what, exactly and in full generality, do you mean by fitness?
that's a long answer, and no one is obligated to satisfy your curiosity.
I know the literature on fitness and have contributed to it.
The point of my question is to suggest that the subject requires thought outside its usual mathematical straitjacket, and to hope that this will be more widely done, in contrast to the perspective expressed in this blog. A verbal argument can be as tight as a symbolic one; both can be misused. In theories as in faces, beauty can be an artifact.
A verbal argument can be as tight as a symbolic one; both can be misused. In theories as in faces, beauty can be an artifact.
leigh, like most verbal arguments this doesn't quantify the extent of misuse. and i basically reject that a verbal argument can be as tight as a formal one, because when people express themselves in language there are always implicit points which are left unsaid. verbal arguments are best when assumptions and viewpoints are shared, but when they are not math (or a somewhat turgid formal presentation) is necessary to make explicit where everyone stands.