The
book also contains essays on Schrodinger, Fisher, Pauling, George Price, and Rashevsky.
Theoreticians as Professional Outsiders: The Modeling Strategies of John von Neumann and Norbert Wiener (Ehud Lamm in Biology Outside the Box: Boundary Crossers and Innovation in Biology, Oren Harman and Michael R. Dietrich (eds.))
Both von Neumann and Wiener were outsiders to biology. Both were inspired by biology and both proposed models and generalizations that proved inspirational for biologists. Around the same time in the 1940s von Neumann developed the notion of self reproducing automata and Wiener suggested an explication of teleology using the notion of negative feedback. These efforts were similar in spirit. Both von Neumann and Wiener used mathematical ideas to attack foundational issues in biology, and the concepts they articulated had lasting effect. But there were significant differences as well. Von Neumann presented a how-possibly model, which sparked interest by mathematicians and computer scientists, while Wiener collaborated more directly with biologists, and his proposal influenced the philosophy of biology. The two cases illustrate different strategies by which mathematicians, the “professional outsiders” of science, can choose to guide their engagement with biological questions and with the biological community, and illustrate different kinds of generalizations that mathematization can contribute to biology. The different strategies employed by von Neumann and Wiener and the types of models they constructed may have affected the fate of von Neumann’s and Wiener’s ideas – as well as the reputation, in biology, of von Neumann and Wiener themselves.
For and Against theory in biology:
... E.B. Wilson articulated the reserved attitude of biologists towards uninvited theoreticians. Wilson’s remarks at the Cold Spring Harbor Symposia on Quantitative Biology in 1934 were ostensibly about the “Mathematics of Growth” but it is impossible to fail to notice their tone and true scope. Wilson suggested orienting the discussion around five axioms or “platitudes” as he called them. The first two are probably enough to get his point across. Axiom 1 states that “science need not be mathematical,” and if that’s not bad enough, axiom 2 solidifies the reserved attitude towards mathematization by stating that “simply because a subject is mathematical it need not therefore be scientific.”
... While the idea of self-reproduction seems incredible, and some might even have thought it to involve a self-contradiction, with objects creating something as complex as they are themselves, von Neumann’s solution to the problem of self-reproduction was remarkably simple. It is based on two operations: (1) constructing an object according to a list of instructions, and (2) copying a list of instructions as is ... This procedure is trivial for anyone computer-literate to understand; it was a remarkable theoretical result in 1948. What, however, does it tell us about biology? It is often observed that von Neumann’s explanation, which involves treating the genetic material both as instructions and as data that is copied as-is, is analogous to the reproduction of cells, since DNA, the analogue of the instruction list, is passively replicated. Von Neumann compared the construction instructions that direct the automaton to genes, noting that genes probably do not constitute instructions fully specifying the construction of the objects their presence stimulates. He warned that genes are probably only general pointers or cues that affect development, a warning that alas did not curtail the “genetic program” metaphor that became dominant in years to come.
Von Neumann noted that his model explained how mutations that do not affect self- replication are possible. If the instruction list specifies not only the self-replicating automaton but also an additional structure, this structure will also be replicated. ...
... As Claude Shannon put it in a 1958 review of von Neumann’s contributions to automata theory, and specifically self-reproducing automata:
If reality is copied too closely in the model we have to deal with all of the complexity of nature, much of which is not particularly relevant to the self-reproducing question. However, by simplifying too much, the structure becomes so abstract and simplified that the problem is almost trivial and the solution is un-impressive with regard to solving the philosophical point that is involved. In one place, after a lengthy discussion of the difficulties of formulating the problem satisfactorily, von Neumann remarks: "I do not want to be seriously bothered with the objection that (a) everybody knows that automata can reproduce themselves (b) everybody knows that they cannot."
See also
On Crick and Watson and
Reliable Organization of Unreliable Components
6 comments:
Rashevsky's "Mathematical Biophysics" was extremely illuminating back when I was studying and doing biokinetics. But you should have included A. J. Lotka (a statistician and actuarian) and Volterra (a mathematician) in the list of contributors to biology.
That said, very few modern biologists have actually read these guys (well, Volterra writes in French), and biology as a whole remains largely innocent of mathematics.
Not biology, but a good example of a mathematician creating a revolution in different fields is Ed Thorpe, who invented counting cards in blackjack, true (market-neutral) hedge funds and the options-pricing formula later published by Black and Scholes, which Thorp very profitably kept to himself. His work has strong connections to information theory, particularly his work on Kelly Criterion and generalizations. He also collaborated in 1960-61 with Claude Shannon to make a computer that would fit in a shoe heel and allowed predicting moving roulette ball trajectories.
There is another recent example of the use of mathematics by an 'outsider' that springs to mind. Steven McIntyre was not a climatologist but he had a solid statistical background from mining research - of all things. For a while there he almost stood alone against the officious and arrogant climatologists. But climatology never attracted guys who were very good at math. In fact many of them are more or less innumerate.
But math is math no matter where it was learned and the battle was joined.
Von Neumann compared the construction instructions that direct the automaton to genes, noting that genes probably do not constitute instructions fully specifying the construction of the objects their presence stimulates. He warned that genes are probably only general pointers or cues that affect development, a warning that alas did not curtail the “genetic program” metaphor that became dominant in years to come.
NB.
Yeah, I remember Velikovsky standing alone against the officious and arrogant astronomers. Good times.
I am reading Norbert Wiener's cybernetics book right now. Incredible coincidence. Guess it goes to show that people who have similar interests in some fields probably have underlying similarities in brain architecture / personality that make them pursue similar interests in other unrelated fields.
I would also add Stuart Kaufman for theoretical biology. Haven't read him in detail but seems relevant.
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