How should we reconstruct Perrin's argument?
Having examined Perrin's original exposition in his Atoms, I came to the conclusion that Mayo's reconstruction of Step 1 (establishing the complete irregularity of the Brownian motion) does not follow the order of the original, and hence misleading in some crucial respect. So let me present my own rendering, in the following.
Mayo rightly points out this:
Only by keeping in mind that a great many causal factors were ruled out experimentally before Perrin's tests (around 1910) can his experiments be properly understood. (Mayo 1996, 218)
And as I understand Perrin's argument, Perrin was almost convinced, before his experiments, that the Brownian motion is not caused by any external influence, such as air currents, because there were already an abundance of evidence for this conviction. Thus Perrin writes:
But in this case neighbouring particles move in approximately the same direction as the air currents and roughly indicate the conformation of the latter. The Brownian movement, on the other hand, cannot be watched for any length of time without it becoming apparent that the movements of any two particles are completely independent, even when they approach one another to within a distance less than their diameter (Brown, Wiener, Gouy). (Perrin 1990, 84)
The agitation cannot, moreover, be due to vibration of the object glass carrying the drop under observation, for such vibration, when produced expressly, produces general currents which can be recognized without hesitation and which can be seen superimposed upon the irregular agitation of the grains. (Perrin, 84)
In fact--and this is perhaps its strangest and most truly novel feature--the Brownian movement never ceases. Inside a small closed cell (so that evaporation may be avoided) it may be observed over periods of days, months, and years. It is seen in the liquid inclusions that have remained shut up in quarts for thousands of years. It is eternal and spontaneous. (Perrin, 85)
All these characteristics force us to conclude, with Wiener (1863), that "the agitation does not originate either in the particles themselves or in any cause external to the liguid, but must be attributed to internal movements, characteristic of the fluid state", movements which the grains follow more faithfully the smaller they are. We are thus brought face to face with an essential property of what is called a fluid in equilibrium; its apparent repose is merely an illusion due to the imperfection of our senses and corresponds in reality to a permanent condition of unco-ordinated agitation. (Perrin, 85-86)
However, despite this conviction and its general conformity to what the kinetic theory says, the kinetic theory "is nevertheless a hypothesis only" (88). That's why Perrin attempted to subject the question to a definite experimental test. But for this purpose, he had to extend the gas laws to dilute emulsions, and to particles larger than molecules in such emulsions (89-94). By preparing suitable materials (such as gamboge) for this inquiry, he obtained the affirmative answer, so that he now can go on to a quantitative inquiry as regards the Brownian motion. Then comes a series of experiments in which Perrin subjected the Einstein-Smoluchowski theory.
I have no objection to Mayo's reconstruction in terms of Step 1 amd Step 2; but I have an objection against Mayo's rendering of the alternative hypotheses at Step 1. According to Mayo, Perrin was to decide between the following two alternative hypotheses (Mayo 1996, 223; j is the null hypothesis)
j: The data from E approximates a random sample from the hypothesized Normal process M.
j': The sample displacements of data from E are characteristic of systematic (nonchance) effects.
And, for the sake of fairness, let us see what Mayo says on these hypotheses:
So ruling out hypothesis j' was the centerpiece of Perrin's work. Asking about j' came down to asking whether factors outside the liguid medium might be responsible for the observed motion of Brownian particles. The general argument in ruling out possible external factors--even without being able to list them all--was this: if Brownian motion were the effect of such a factor, then neighboring particles would be expected to move in approximately the same direction. In fact, however, a particle's movement was found to be independent of that of its neighbors. To sustain this argument, Perrin called up experimental knowledge gleaned from several canonical cases of ("real") chance phenomena. (Mayo 1996, 224; bold letters mine.)
Aside from other complaints (see How Mayo gets Severity), the contrast of key words in j and j' seems quite misleading, in view of the context of Perrin's experiments: random sample from the Normal process, and systematic effects. I have already suggested (Severity for Perrin?) that, if Mayo puts two key words (random and Normal) in the null hypothesis, we've got to consider four combinations:
- ramdom sample from the Normal process,
- random sample from a non-Normal process,
- non-random sample from the Normal process, and
- non-random sample from a non-Normal process.
But notice that Mayo interprets that Perrin was going to reject j' for sustaining his conviction (bold letters in the previous quotation) that there are no coordinated movements (due to external factors) among neighboring particles. This interpretation underlies the formulation of j'; and this causes a lot of trouble. My interpretation is different: given Perrin's conviction (supported by the predecessors' results) that no external influence is conceivable, he does not have to consider any systematic effect due to external influence; or even if he takes this possibility still into cnsideration, he can exclude this by separate experiments (indeed, some collaborator was checking the influence of temperature, for instance; see Perrin, 104, 122). So the remaining possibilities are deviations from irregularity due either to (a) bias of sampling or to (b) non-Normal process (distribution in the whole population). But (a) can be easily avoided by the manner of experiment, as Perrin's remark in other context shows (Mayo also quotes this):
In order not to be tempted to choose grains which happened to be slightly more visible than the rest (those, that is to say, which were slightly above the average size), which would raise the value of N a little, I followed the first grain that showed itself in the centre of the field of vision. (Perrin, 124)
That is, by following the rule of ramdom sampling, you can exclude the possibility of non-ramdom sample, i.e. (a). The manner Perrin paid enough attention to such considerations is well illustrated also by the following incident while he was trying to determine the Avogadro number:
In this way I obtained the value 69. A source of error has, however, been pointed out to me by M. Constantin. This young physicist noticed, during the course of some measurements on some preparations only a few microns thick, that the proximity of a boudary checked the Brownian movement. ... Working at a sufficient distance from the walls with the grains that I had used, he obtained the value [N = 64]; unfortunately the number of observations (about 100) was too small. These measurements will be repeated. (Perrin 1990, 124)
Thus, because of such practice of random sampling, and avoidance of systematic deviations, only the possibility of (b) remains (that is, 3 and 4 disappear from the preceding list). Then, it is clear that Mayo's formulation of j' is misleading (notice it contains the possibilities of non-statistical hypotheses), to say the least. It should be replaced by:
ªæj: The data from E approximates a random sample from a non-Normal process.
Here, "non-Normal" means a substantive deviation from a Normal distribution. Thus, only in this form, Mayo can claim (on the empirical basis) that "It is very probable that a few [experiments] would have shown differences statistically significant from what is expected under j''" (Mayo 1996, 231), because the falsity of j now corresponds to a non-Normal distribution; we may assume that Perrin was considering only statistical hypotheses, comparable to j, in his experiments. This is the crux Mayo should have stated clearly, but she has failed to do so. Finally, although this looks to be the most promising way for Mayo to adopt, the defect of her official definition of severity is not alleviated in the least; she has to use the revised (reletivized to a single alternative) version.
You can see how a careless (inappropriate) statement causes a lot of touble!
Reference
Mayo, Deborah (1996) Error and the Growth of Experimental Knowledge, The University of Chicago Press.
Perrin, J. (1990) Atoms, Ox Bow Press (reprint).
Last modified Jan. 27, 2003. (c) Soshichi Uchii