“The antithesis is not so heterodox as it sounds, for every active mind will form opinions without direct evidence, else the evidence too often would never be collected.”
I already know, upon reading this sentence [source] that I’m going to be quoting it constantly.
It’s too perfect a rebuttal to the daily-experienced circumstance of people imagining that things—ideas, facts, heuristics, truisms—that are obvious to the people they consider politically “normal” [e.g., 2024 politically-cosmopolitan Americans, or LessWrong], must be or have been obvious to everyone of their cognitive intelligence level, at all times and in all places -
- or the converse, that what seems obvious to the people they consider politically “normal”, must be true.
Separately from how pithy it is, regarding the substance of the quote: it strikes me hard that of all people remembered by history who could have said this, the one who did was R.A. Fisher. You know, the original “frequentist”? I’d associated his having originated the now-endemic tic of “testing for statistical significance” with a kind of bureaucratic indifference to unfamiliar, “fringe” ideas, which I’d assumed he’d shared.
But the meditation surrounding this quote is a paean to the mental process of “asking after the actual causes of things, without assuming that the true answers are necessarily contained within your current mental framework”.
“That Charles Darwin accepted the fusion or blending theory of inheritance, just as all men accept many of the undisputed beliefs of their time, is universally admitted. [ . . . ] To modern readers [the argument from the variability within domestic species] will seem a very strange argument with which to introduce the case for Natural Selection [ . . . ] It should be remembered that, at the time of the essays, Darwin had little direct evidence on [the] point [of whether variation existed within species] [ . . . ] The antithesis is not so heterodox as it sounds, for every active mind will form opinions without direct evidence, else the evidence too often would never be collected.”
This comes on the heels of me finding out that Jakob Bernoulli, the ostensible great-granddaddy of the frequentists, believed himself to be using frequencies to study probabilities, and was only cast in the light of history as having discovered that probabilities really “were” frequencies.
“This result [Jakob Bernoulli’s discovery of the Law of Large Numbers in population statistics] can be viewed as a justification of the frequentist definition of probability: ‘proportion of times a given event happens’. Bernoulli saw it differently: it provided a theoretical justification for using proportions in experiments to deduce the underlying probabilities. This is close to the modern axiomatic view of probability theory.” [ Ian Stewart, Do Dice Play God, pg 34 ]
Bernoulli:
“Both [the] novelty [ of the Law of Large Numbers ] and its great utility combined with its equally great difficulty can add to the weight and value of all the other chapters of this theory. But before I convey its solution, let me remove a few objections that certain learned men have raised. 1. They object first that the ratio of tokens is different from the ratio of diseases or changes in the air: the former have a determinate number, the latter an indeterminate and varying one. I reply to this that both are posited to be equally uncertain and indeterminate with respect to our knowledge. On the other hand, that either is indeterminate in itself and with respect to its nature can no more be conceived by us than it can be conceived that the same thing at the same time is both created and not created by the Author of nature: for whatever God has done, God has, by that very deed, also determined at the same time.” [ Jakob Bernoulli’s “The Art of Conjecturing”, translated by Edith Dudley Sylla ]
It makes me wonder how many great names modern “frequentism” can even accurately count among its endorsers.
Edit:
Fisher on the philosophy of probability [ PLEASE click through, it’s kind of a take-your-breath-away read if you’re familiar with the modern use of “p-values” ]:
“Now suppose there were knowledge a priori of the distribution of μ. Then the method of Bayes would give a probability statement, probably a different one. This would supersede the fiducial value, for a very simple reason. If there were knowledge a priori, the fiducial method of reasoning would be clearly erroneous because it would have ignored some of the data. I need give no stronger reason than that. Therefore, the first condition [of employing the frequentist definition of probability] is that there should be no knowledge a priori.
[T]here is quite a lot of continental influence in favor of regarding probability theory as a self-supporting branch of mathematics, and treating it in the traditionally abstract and, I think, fruitless way [ . . . ] Certainly there is grave confusion of thought. We are quite in danger of sending highly-trained and highly intelligent young men out into the world with tables of erroneous numbers under their arms, and with a dense fog in the place where their brains ought to be. In this century, of course, they will be working on guided missiles and advising the medical profession on the control of disease, and there is no limit to the extent to which they could impede every sort of national effort.”
“The antithesis is not so heterodox as it sounds, for every active mind will form opinions without direct evidence, else the evidence too often would never be collected.”
I already know, upon reading this sentence [source] that I’m going to be quoting it constantly.
It’s too perfect a rebuttal to the daily-experienced circumstance of people imagining that things—ideas, facts, heuristics, truisms—that are obvious to the people they consider politically “normal” [e.g., 2024 politically-cosmopolitan Americans, or LessWrong], must be or have been obvious to everyone of their cognitive intelligence level, at all times and in all places -
- or the converse, that what seems obvious to the people they consider politically “normal”, must be true.
Separately from how pithy it is, regarding the substance of the quote: it strikes me hard that of all people remembered by history who could have said this, the one who did was R.A. Fisher. You know, the original “frequentist”? I’d associated his having originated the now-endemic tic of “testing for statistical significance” with a kind of bureaucratic indifference to unfamiliar, “fringe” ideas, which I’d assumed he’d shared.
But the meditation surrounding this quote is a paean to the mental process of “asking after the actual causes of things, without assuming that the true answers are necessarily contained within your current mental framework”.
Fisher:
“That Charles Darwin accepted the fusion or blending theory of inheritance, just as all men accept many of the undisputed beliefs of their time, is universally admitted. [ . . . ] To modern readers [the argument from the variability within domestic species] will seem a very strange argument with which to introduce the case for Natural Selection [ . . . ] It should be remembered that, at the time of the essays, Darwin had little direct evidence on [the] point [of whether variation existed within species] [ . . . ] The antithesis is not so heterodox as it sounds, for every active mind will form opinions without direct evidence, else the evidence too often would never be collected.”
This comes on the heels of me finding out that Jakob Bernoulli, the ostensible great-granddaddy of the frequentists, believed himself to be using frequencies to study probabilities, and was only cast in the light of history as having discovered that probabilities really “were” frequencies.
“This result [Jakob Bernoulli’s discovery of the Law of Large Numbers in population statistics] can be viewed as a justification of the frequentist definition of probability: ‘proportion of times a given event happens’. Bernoulli saw it differently: it provided a theoretical justification for using proportions in experiments to deduce the underlying probabilities. This is close to the modern axiomatic view of probability theory.” [ Ian Stewart, Do Dice Play God, pg 34 ]
Bernoulli:
“Both [the] novelty [ of the Law of Large Numbers ] and its great utility combined with its equally great difficulty can add to the weight and value of all the other chapters of this theory. But before I convey its solution, let me remove a few objections that certain learned men have raised. 1. They object first that the ratio of tokens is different from the ratio of diseases or changes in the air: the former have a determinate number, the latter an indeterminate and varying one. I reply to this that both are posited to be equally uncertain and indeterminate with respect to our knowledge. On the other hand, that either is indeterminate in itself and with respect to its nature can no more be conceived by us than it can be conceived that the same thing at the same time is both created and not created by the Author of nature: for whatever God has done, God has, by that very deed, also determined at the same time.” [ Jakob Bernoulli’s “The Art of Conjecturing”, translated by Edith Dudley Sylla ]
It makes me wonder how many great names modern “frequentism” can even accurately count among its endorsers.
Edit:
Fisher on the philosophy of probability [ PLEASE click through, it’s kind of a take-your-breath-away read if you’re familiar with the modern use of “p-values” ]:
“Now suppose there were knowledge a priori of the distribution of μ. Then the method of Bayes would give a probability statement, probably a different one. This would supersede the fiducial value, for a very simple reason. If there were knowledge a priori, the fiducial method of reasoning would be clearly erroneous because it would have ignored some of the data. I need give no stronger reason than that. Therefore, the first condition [of employing the frequentist definition of probability] is that there should be no knowledge a priori.
[T]here is quite a lot of continental influence in favor of regarding probability theory as a self-supporting branch of mathematics, and treating it in the traditionally abstract and, I think, fruitless way [ . . . ] Certainly there is grave confusion of thought. We are quite in danger of sending highly-trained and highly intelligent young men out into the world with tables of erroneous numbers under their arms, and with a dense fog in the place where their brains ought to be. In this century, of course, they will be working on guided missiles and advising the medical profession on the control of disease, and there is no limit to the extent to which they could impede every sort of national effort.”
[ R.A. Fisher, 1957 ]