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R. A. Fisher, Scientific Method, and the Tower of Babel, Pt. 1 February 2, 2013

Posted by Will Thomas in Uncategorized.
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Fisher1924

R. A. Fisher in 1924

For a paper Chris Donohue and I have been working on, I have been delving into the historiography on statistician and genetic theorist R. A. Fisher (1890-1962). The main thing I was trying to do was to make sense of the last third of Fisher’s touchstone book The Genetical Theory of Natural Selection (1930), which is a protracted eugenic explanation for why civilizations decline.  When I first got onto this topic, I consulted Greg Radick about it, and he directed me to Stephen Jay Gould’s 1991 essay, “The Smoking Gun of Eugenics” (reprinted in Gould’s Dinosaur in a Haystack collection), in which Gould takes apart both Fisher’s civilizational theory as well as his 1950s-era arguments against claims that smoking leads to cancer.

If you’re interested in the specifics of Fisher’s arguments, do read Gould’s essay, or, better still, read the original.  Suffice it here to say that Gould claims Fisher made bogus arguments on account of his commitment to eugenics (with a similar story for smoking). This is true, as far as it goes, but I wanted to find a “higher-order” explanation for Fisher’s civilizational theory, which would account for why he thought his arguments made sense.  Fisher, after all, was a famous proponent of methodological rigor, and even prima facie his arguments about civilizational decline were, shall we say, less than rigorous.

If you’re interested in my take, you’ll have to wait until 2014 for the edited volume our essay will be in to come out (hooray for academic publishing; if you’re really interested, please do contact me for a draft copy).  But the general approach I took was to delve into Fisher’s ideas about scientific methodology.  Below the fold I take a meandering tour through these ideas, and the scattered historiography on them.

The main reason I wanted to do some research on Fisher was because of his manuals Statistical Methods for Research Workers (1925), and The Design of Experiments (1935).  These are pertinent to my work on operations research and decision theory, as well as to my more recent work on agricultural expertise (Fisher wrote both books partially from his experiences helping design agricultural experiments at the Rothamsted Experimental Station, where he worked from 1919 to 1933).  What is interesting is that neither of these works, nor his later Statistical Methods and Scientific Inference (1956), is a full treatise of scientific methodology.

All of these works were, essentially, devoted to inductive reasoning and hypothesis testing.  For Fisher, the sine qua non of scientific knowledge was experience.  The security of that knowledge could be ascertained through the statistical analysis of experimental tests where pertinent variables were controlled either physically or statistically.  For a recent discussion of Fisher’s commitment to randomization and statistical control of experimental bias, see Nancy S. Hall, “R. A. Fisher and His Advocacy of Randomization,” Journal of the History of Biology 40 (2007): 295-325.

A plan for a controlled agricultural experiment, from: R. A. Fisher and W. A. MacKenzie, “Studies in Crop Variation. II. The Manural Response of Different Potato Varieties,” Journal of Agricultural Science 13 (1923): 311-320.

A plan for a controlled agricultural experiment, from: R. A. Fisher and W. A. MacKenzie, “Studies in Crop Variation. II. The Manural Response of Different Potato Varieties,” Journal of Agricultural Science 13 (1923): 311-320.

Of course, Fisher was aware that there was more to scientific practice than empiricism.  For him, though, there had to be a definable distinction between speculation and experience, because mistaking mere speculation for scientific knowledge opened the door to dogmatism.  On this point, I found Harry M. Marks, “Rigorous Uncertainty: Why RA Fisher is Important,” International Journal of Epidemiology 32 (2003): 932-937 helpful.  The piece has some very interesting discussion of the ideological significance that Fisher attached to inductivism, particularly its importance to intellectual freedom—a concern that only grew more pronounced in the postwar era (Lysenko and all that).

Fisher_old

An older Fisher

Marks observes that similar issues were at the core of Fisher’s postwar methodological disputes with statistical theoreticians Jerzy Neyman (1894-1981) and Abraham Wald (1902-1950).  Fisher made the ideological resonance he saw in this issue very explicit in his 1955 paper, “Statistical Methods and Scientific Induction,” Journal of the Royal Statistical Society B 17: 69-78, in which he linked his rivals’ theories to the technologized pragmatism of the Soviet Union and the United States, which privileged “speeding production, or saving money” rather than “drawing correct conclusions”.*

Backing up a bit: these postwar methodological disputes were basically extensions of Fisher’s lifelong campaign against “inverse probability,” or, as it is now generally known, Bayesian probability.  Briefly: in Bayesian probability, an a priori probability distribution (say if there are three possible outcomes to an experiment, one might suppose that each has an equal probability of being the result) is modified following trials.  For Fisher, whose position is often referred to as “frequentist”, any a priori distribution was an arbitrary imposition on an experimental interpretation, and could not therefore count as scientific knowledge—in trials, any valid conclusions had to follow purely from experience.

Now, this conflict is one of the most celebrated and contentious episodes in the history of statistics.  In case Fisher’s position seems obviously correct from my brief description, here’s xkcd.com‘s fine take on the subject:

frequentists_vs_bayesians

Unsurprisingly, there is a lot of scattered material on this issue, but your best one-stop-shop is probably David Howie’s Interpreting Probability (2002), which concentrates especially on Fisher’s 1930s-era disputes with Harold Jeffreys (1891-1989).

Now, despite the fact that Fisher was a champion of inductivism, he was also a great deductive statistician.  For Fisher’s thoughts on deductive reasoning, Marks points us to Fisher’s 1932 lecture, “The Bearing of Genetics on Theories of Evolution,” in which Fisher extolled his mathematical accomplishments in The Genetical Theory of Natural Selection reconciling Darwin’s natural selection mechanism with Mendelian genetics.

In his lecture, Fisher offered a strikingly different portrait of scientific method from that found in his manuals.  Invoking the Biblical legend of the Tower of Babel, he observed that a “common metaphor represents the labours of men of science as the construction of a gigantic edifice, upon the wings and annexes of which workers in different branches of natural knowledge are engaged. The various methods and techniques in which we have been trained correspond to the crafts of the different classes of artisans, the stone-cutters, masons, plasterers, sculptors, and painters, whose co-operation is needed to produce a finished and habitable building.”

The Confusion of Tongues, by Gustave Doré (1865)

The Confusion of Tongues, by Gustave Doré (1865)

Fisher went on to compare the disaster God inflicted at Babel to the fragmentation of scientific methodology, offering an unusually naturalistic take on how the division of language came to be:

We are not told exactly in what manner the confusion of tongues originated ; whether by a sudden and miraculous transmutation in the word-centre of each individual, he began forthwith and, all unconscious of the change, to express his ideas in a babbling jargon, meaningless to his fellows ; or whether, as the work progressed, groups of workers so concentrated their attention upon special parts of the building, and on the particular technical problems of their crafts, that they gradually came to use words unintelligible outside their own little circle ; or, still worse, to use the old words with meanings quite unknown to the workers on the floor above, until their old common language had been lost irrevocably.

Typically, Fisher cast himself as something of a hero in his lecture, bridging the “unnatural separation of mathematics from biology,” both in his work at Rothamsted, and in his work reconciling genetics with evolution.  And, importantly, his accomplishment represented a reconciliation of mathematical deduction with inductive science:

Deductive and inductive reasoning … are the means by which alone we can ascertain whether or not a new slab of observational fact will fit into its place in our edifice; and the mathematical expression of such reasoning is the only effective cement which we possess, by which such new facts can be held fast as parts of a coherent structure.

Ultimately, though, Fisher’s ideas about the reassembly of the deductive and the inductive into a more unified methodology were never so clearly articulated as his ideas about statistical inference.  In Pt. 2, we look at some scholars’ views of Fisher’s deductivism.

*For more on the relationship between “scientific” knowledge and the problem of limited testing opportunity from an anti-Fisherian perspective, see my post “Decision, Risk, and Values: The Philosophy of Churchman and Ackoff,” which is a brief excerpt from my book manuscript.

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Comments»

1. Michael Robinson - February 2, 2013

This is interesting Will. I’ve been reading work by James Frazer (Golden Bough) on methods of of anthropology — specifically the idea that field workers should limit themselves to data collection while armchair theorists (i.e. Frazer) should do the crunching and interpreting.This idea was accepted by Frazer’s disciple in Africa, John Roscoe, who spent decades studying the culture of Buganda in East Africa. What’s striking to me is how obvious Roscoe’s interpretive claims are in his work (in this case, claims that Fisher would have applauded, a genetic theory of civilization advances in Africa). Neither Frazer nor Roscoe seem to be bothered by these glaring acts of theorizing. Was it invisible to them? Or did they separate (consciously or not) the talking of theory from the doing of anthropology? Not sure.

Will Thomas - February 2, 2013

Michael, good to hear from you! The main purpose of Chris’s and my paper is to highlight theories of civilization as what Chris likes to call a genre of argument. Basically, throughout the 19th century, and well into the 20th, it was extremely common for “men of science” (or really any scholarly figure) to attempt to develop theories that explained why civilizations developed the features that they did. Sometimes these theories were fully developed; other times they seem to randomly appear within works on, say, linguistics. Fisher dealt with the problem of civilization in a very direct manner, but in his half of the paper Chris looks at its more oblique place in plant-breeder Luther Burbank’s highly idiosyncratic works.

So, our overall aim is to show that the appearance of this genre in an individual’s works should not be regarded as an isolated extravagance, but as their participation in a very prominent scholarly tradition. Argumentation in this tradition obeyed certain rules, which doesn’t really map onto what we would properly consider a “scientific” argument. For them, theorizing was what ambitious scholars did; they would not have considered it a “glaring act”. (See Martin Rudwick on “Theories of the Earth” in his Bursting the Limits of Time; it’s a very good discussion of a very similar genre.)

One feature of this tradition we highlight is its employment of highly heterogeneous forms of evidence and mechanisms. Thus, while Fisher’s theories of genetics featured in his thinking of civilization, his civilizational theory was not presented as a logical consequence of his genetical theory, but, in fact, was highly derivative of previous considerations of the problem.

Followers of this blog will recognize that this is mainly Chris’s concern, but it was fun and productive for us to join our interests together. I’ll send you a copy of our paper,

Will

2. Joachim - February 9, 2013

From perusing Fisher’s chapters on human society, his protracted arguments could, IMHO, be distilled as follows:

1. Problem: Leading civilizations often declined (e.g., Roman, Greek) despite being superior over their neighbors in weaponry, agriculture etc.
2. In these civilizations, belonging to the ruling classes correlated with having fewer children (he calls it the “social promotion of infertility”).
3. Fisher’s solution: Social promotion of fertility can avert the decline and lead to a permanent civilization.

The only thing that I cannot tell is whether Fisher thought of 1. and 2. as observations, hence of the whole argument as an induction, or whether he thought of 1. and 2. as premises, hence of the whole as a deduction.

Will Thomas - February 9, 2013

Hi Joachim,

Thanks for the comment. Those are certainly the main points of his argument. I don’t think it quite fits in the inductive/deductive scheme. Chris and I feel he inherited a more archaic form of argument, which is related to Whewell’s notion of “consilience”; the burden was to posit a explanation for a general phenomenon which is more coherent and answers objections better than competing explanations. We also think that he viewed the efficacy of his proposed explanation as empirical evidence (albeit not rigorously inductive) for his reconciliation of Mendelism and Darwinism. This will all be developed much more extensively in our paper.

Also, I was unaware of your blog—thanks for the link!

3. David Duffy - February 21, 2013

“…directed me to Stephen Jay Gould’s 1991 essay, “The Smoking Gun of Eugenics” (reprinted in Gould’s Dinosaur in a Haystack collection), in which Gould takes apart both Fisher’s civilizational theory as well as his 1950s-era arguments against claims that smoking leads to cancer.”

I’m never that impressed by Gould on these matters eg

http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001071

or more generally

http://www.psych.utoronto.ca/users/reingold/courses/intelligence/cache/carroll-gould.html

Haldane’s review of _The genetical theory…_ in Ann Eugenics is pretty amusing on the chapters on eugenics.

As regards smoking, I see this more as a controversialist stand of a pipe smoker, rather than necessarily a coherent scientific theory. Though, one of the early applications of the Swedish Twin Registry, set up in the 1960s, was to test whether there was a genetic correlation between smoking and cancer susceptibility (it would have to have been awfully big).

Will Thomas - February 24, 2013

Hi David, thanks for the comment.

Gould’s tendency was to explain Bad Science in terms of some mixture of ideological bias and bad methodology failing to prevent its intrusion. The object, therefore, was to locate those things wherever they were to be found.

I think this did lead Gould to make some simplistic accusations, but I don’t like to be too hard on him, mainly because he had a huge scientific and popular audience, and did a great service in combating reckless uses of scientific evidence in public discourse. Even professional historians are not always careful on this score—though they should, of course, hold themselves to a high standard, and also shouldn’t be afraid to challenge Gould’s accounts even though they serve a good cause.

On the smoking point, Gould’s criticism is mainly that Fisher’s rhetoric was too forceful, where Fisher’s rhetoric seems to have been motivated by his belief that anti-smoking advocates’ rhetoric was too forceful, as well as a general willingness to err toward personal freedom (particularly given his fondness for his pipe). Still, my overall impression is that Gould explains the issues at play in that controversy pretty well.

Finally, do you have a citation for the Haldane review? It didn’t crop up in my research. I took a quick look around for it and couldn’t find it, but would definitely be interested in reading it over.

4. Ross Upshur - March 27, 2013

I would be reluctant to attribute Fisher’s stance on smoking simply to his pipe habit or his .desire to be controversial. Austin Bradord Hill and Richard Doll are and the results of observational studies informing and directing policy are of concern. In his polemic Cigarettes, Cancer and Statistics,he is quite blunt about the requirements of randomization, control and replication. He writes: It is not the fault of Hill or Doll that they cannot produce evidence in which a thousand children of teen age have been laid under a banthat they shall never smoke and a thousand more chosen at random from the same age group have been under a compulsion to smoke at least thirty cigarettes a day. If that type of experiment could be done, there would be no difficulty.
Of course this has never been done, and when I ask during lectures if any one would like to join me in conducting this study and getting ethics approval, laughter ensues.
Yet his point stands, and it is highly germane to how we interpret and weigh evidence in an era of evidence based approaches to health care.
Thank you for the insightful essay on Fisher. I instruct my students to read him and try to refute him. It is much harder than they thin!

5. – 10 links for February 2013 - April 13, 2013

[...] via Analogy part 1 and part 2 R. A. Fisher, Scientific Method, and the Tower of Babel part 1 and part 2 Small things: The discovery of a microscopic world shook the foundations of theology and [...]


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