“Consider the mechanical adaptation of an instrument such as a microscope, when adjusted for distinct vision. If we imagine a derangement of the system by moving a little each of the lenses, either longitudinally or transversely, or by twisting through an angle, by altering the refractive index and transparency of the different components, or the curvature, or the polish of the interfaces, it is sufficiently obvious that any large derangement will have a very small probability of improving the adjustment, while in the case of alterations much less than the smallest of those intentionally effected by the maker or operator, the chance of improvement should be almost exactly one half (Fisher, R.A. 1930. The Genetical Theory of Natural Selection. Oxford Univ. Press. Oxford. p. 40.).”

There are several problems with Fisher’s analogy. Not the least of which is that it lacks the virtue of transparency, of a comparison that is readily apprehensible. It has one thing and one thing only going for it, in that unlike Darwin’s analogy, Fisher formalizes his design analogy with his famous “geometric model” of evolutionary adaptation. And unlike Darwin’s powerfully intuitive heuristic analogy, Fisher’s analogy, despite its formalization and having become a “central dogma” in population genetics, may, in the end, prove to be profoundly misleading.
It might be interesting to observe where Fisher may have gone wrong here, to explore Fisher’s equally influential analogy, which has heretofore received little critical attention, in comparison with Darwin’s analogy, which has been the source of much critical analysis, most of it bad. E.g., notice the many causal factors Fisher includes as possibly contributing to the magnitude of the effect. Yet the formalization does not include multiple factors, but assumes the effective independence (additivity) of factors, each contributing independently and each of small magnitude of effect. None of what was formalized seems to be suggested directly by the analogy!

It might be interesting to compare the fates of these two analogies so central to evolutionary theory.

See:

Towards a theory of evolutionary adaptation
Daniel L. Hartl & Clifford H. Taubes
Genetica 102/103: 525–533, 1998.
Copyright 1998 Kluwer Academic Publishers.
http://www.oeb.harvard.edu/hartl/lab/publications/pdfs/Hartl-98-Genetica.pdf

And for a nice historical review see also (and the citations therein):

THE GENETIC THEORY OF
ADAPTATION: A BRIEF HISTORY
H. Allen Orr
VOLUME 6 | FEBRUARY 2005 | 119-127
http://www.maths.lth.se/matematiklth/personal/mario/orr.pdf

And a simulation by the same author:

The evolutionary genetics of adaptation: a simulation study
Genet. Res., Camb. (1999), 74, pp. 207-214.

(This is available online.)

“Summary
It is now clear that the genetic basis of adaptation does not resemble that assumed by the
infinitesimal model. Instead, adaptation often involves a modest number of factors of large effect
and a greater number of factors of smaller effect. After reviewing relevant experimental studies, I
consider recent theoretical attempts to predict the genetic architecture of adaptation from ®rst
principles. In particular, I review the history of work on Fisher’s geometric model of adaptation,
including recent studies which suggest that adaptation should be characterized by exponential
distributions of gene effects. I also present the results of new simulation studies that test the
robustness of this finding. I explore the effects of changes in the distribution of mutational effects
(absolute versus relative) as well as in the nature of the character studied (total phenotypic effect
versus single characters). The results show that adaptation towards a fixed optimum is generally
characterized by an exponential effects trend.”

“Consider the mechanical adaptation of an instrument such as a microscope, when adjusted for distinct vision. If we imagine a derangement of the system by moving a little each of the lenses, either longitudinally or transversely, or by twisting through an angle, by altering the refractive index and transparency of the different components, or the curvature, or the polish of the interfaces, it is sufficiently obvious that any large derangement will have a very small probability of improving the adjustment, while in the case of alterations much less than the smallest of those intentionally effected by the maker or operator, the chance of improvement should be almost exactly one half (Fisher, R.A. 1930. The Genetical Theory of Natural Selection. Oxford Univ. Press. Oxford. p. 40.).”

There are several problems with Fisher’s analogy. Not the least of which is that it lacks the virtue of transparency, of a comparison that is readily apprehensible. It has one thing and one thing only going for it, in that unlike Darwin’s analogy, Fisher formalizes his design analogy with his famous “geometric model” of evolutionary adaptation. And unlike Darwin’s powerfully intuitive heuristic analogy, Fisher’s analogy, despite its formalization and having become a “central dogma” in population genetics, may, in the end, prove to be profoundly misleading.
It might be interesting to observe where Fisher may have gone wrong here, to explore Fisher’s equally influential analogy, which has heretofore received little critical attention, in comparison with Darwin’s analogy, which has been the source of much critical analysis, most of it bad. E.g., notice the many causal factors Fisher includes as possibly contributing to the magnitude of the effect. Yet the formalization does not include multiple factors, but assumes the effective independence (additivity) of factors, each contributing independently and each of small magnitude of effect. Little of what was formalized seems to be suggested directly by the analogy!

It might be interesting to compare the fate of these two analogies.

See:

Towards a theory of evolutionary adaptation
Daniel L. Hartl & Clifford H. Taubes
Genetica 102/103: 525–533, 1998.
Copyright 1998 Kluwer Academic Publishers.
http://www.oeb.harvard.edu/hartl/lab/publications/pdfs/Hartl-98-Genetica.pdf

And for a nice historical review see also (and the citations therein):

THE GENETIC THEORY OF
ADAPTATION: A BRIEF HISTORY
H. Allen Orr
VOLUME 6 | FEBRUARY 2005 | 119-127
http://www.maths.lth.se/matematiklth/personal/mario/orr.pdf

And a simulation by the same author:

The evolutionary genetics of adaptation: a simulation study
Genet. Res., Camb. (1999), 74, pp. 207-214.

(This is available online.)

“Summary
It is now clear that the genetic basis of adaptation does not resemble that assumed by the
infinitesimal model. Instead, adaptation often involves a modest number of factors of large effect
and a greater number of factors of smaller effect. After reviewing relevant experimental studies, I
consider recent theoretical attempts to predict the genetic architecture of adaptation from ®rst
principles. In particular, I review the history of work on Fisher’s geometric model of adaptation,
including recent studies which suggest that adaptation should be characterized by exponential
distributions of gene effects. I also present the results of new simulation studies that test the
robustness of this finding. I explore the effects of changes in the distribution of mutational effects
(absolute versus relative) as well as in the nature of the character studied (total phenotypic effect
versus single characters). The results show that adaptation towards a fixed optimum is generally
characterized by an exponential effects trend.”

Ah, but the interesting question is: What makes it reasonable?

In every system of thought a degree of faith is required. This was famously formalized by mathematician Kurt Godel when he actually tried to establish Bertrand Russel and Alfred North Whitehead’s aim in Prinicipia Mathematica that significant ultimate truths could be established without any sort of self-reference or faith.

When mapping mathematical analogies to physical systems, or describing one system as an anology to another, my math professor said their is no way to prove the analogy is accurate or demonstrate the absolute efficacy of the analogy. One can falsify the fidelity of an analogy, but one can not formally prove it. This is actually consistent with the Popperian conception of science.

Thus anaologies are accepted by and large by faith, but they are open to falsification. There really is no “confidence” level in the conclusion. The sun has risen every day of my life. I expect the analogy of the past to be reasonably applicable to tomorrow, but there is no guarantee the sun will rise tomorrow and that a thousand years of analogical expectation will hold.

Salvador

“I’m guessing that at some point (now or in your class) you’re going to use this in analyzing and evaluating ID.”

I am indeed, although I’m not sure where or when. This is an ongoing project, and as I indicated in the essay, I haven’t reached clarity on all of it myself.

We’ve induced that all green apples are sour. Now we want an explanation for why that is. So we posit the generalization:

“All green fruit is sour.”

This is not an induction. This is a hypothesis, that we can then go out and test. And we find out that honeydew mellon falsifies our hypothesis. So we abandon our hypothetical generalization, and look for some other generalization that will “cover” the fact that all green apples are sour.

I think it probably gets more complicated when we come up with competing hypotheses that explain or “cover” our original inductive generalizations.

By the way. I’m guessing that at some point (now or in your class) you’re going to use this in analyzing and evaluating ID. Am I wrong?

Thanks for the response, Professor. And I appreciate the effort you put into your logical analysis. I’m not aware that anyone has ever really attempted a thoroughgoing formal logical analysis of analogical arguments. And if not it truly is a significant neglect. Usually logical analyses of “illogical” arguments are in the endeavor to correct common logical errors in argumentation. But an analogical argument really is something else altogether.

(Man! Absence makes the heart grow fonder and I never really appreciated how much I releid [LOL] upon Bill Gates clunky spellchecker and the MS version of the English language.)

Thanks for the comments, and for the tip about subscripts.
And yes, I agree with your evaluation of the status of analogies in science, and especially your analysis of Darwin’s analogy between artificial and natural selection in Ch. 1 & 2 of the Origin. I have had my students in Evolution analyze his argument from analogy, and some have come to the same conclusion that you do.

In the context of the essay, therefore, I would say that Darwin’s argument is perhaps abductive (in the second sense used by Peirce), in that he “abducts” both artificial and natural selection under the more general covering law of “selection” (which, BTW, he wanted to call “preservation” but did not because of its connotations of intentional action in nature).

However, I really have to question your analogy:

MS = POS

In my opinion,

MS = AOE

where

MS = MicroSoft

and

AOE = axis of evil

;-)