If the difficulty of a physiological problem is mathematical in essence, ten physiologists ignorant of mathematics will get precisely as far as one physiologist ignorant of mathematics and no further.
I’m going to be unfair here—there is a limit to how much specificity one can expect in a brief quote but:
In what sense is the difficulty “mathematical in essence”, and just how ignorant of how much mathematics
are the physiologists in question? Consider a problem where the exact solution of the model equations
turns out to be an elliptic integral—but where the practically relevant range is adequately represented by
a piecewise linear approximation, or by a handful of terms in a power series. Would ignorance of the
elliptic integral be a fatal flaw here?
Speaking as someone who is neither the OP nor Norbert Wiener, I think even the task of posing an adequate mathematical model should not be taken for granted. Thousands of physiologists looked at Drosophila segments and tiger stripes before Turing, thousands of ecologists looked at niche differentiation before Tilman, thousands of geneticists looked at the geological spread of genes before Fisher and Kolmogorov, etc. In all these cases, the solution doesn’t require math beyond an undergraduate level.
Also, concern over an exact solution is somewhat misplaced given that the greater parts of the error are going to come from the mismatch between model and reality and from imperfect parameter estimates.
Norbert Wiener
I’m going to be unfair here—there is a limit to how much specificity one can expect in a brief quote but: In what sense is the difficulty “mathematical in essence”, and just how ignorant of how much mathematics are the physiologists in question? Consider a problem where the exact solution of the model equations turns out to be an elliptic integral—but where the practically relevant range is adequately represented by a piecewise linear approximation, or by a handful of terms in a power series. Would ignorance of the elliptic integral be a fatal flaw here?
Speaking as someone who is neither the OP nor Norbert Wiener, I think even the task of posing an adequate mathematical model should not be taken for granted. Thousands of physiologists looked at Drosophila segments and tiger stripes before Turing, thousands of ecologists looked at niche differentiation before Tilman, thousands of geneticists looked at the geological spread of genes before Fisher and Kolmogorov, etc. In all these cases, the solution doesn’t require math beyond an undergraduate level.
Also, concern over an exact solution is somewhat misplaced given that the greater parts of the error are going to come from the mismatch between model and reality and from imperfect parameter estimates.