Random Refutations

“(1) Parmenides-Leucippus: Leucippus takes the existence of motion as a partial refutation of Parmenides’s theory that the world is full and motionless. This leads to the theory of ‘atoms and the void’. It is the foundation of atomic theory.

(2) Galileo refutes Aristotle’s theory of motion : this leads to the foundation of the theory of acceleration, and later of Newtonian forces. Also, Galileo takes the moons of Jupiter and the phases of Venus as a refutation of Ptolemy, and thus as empirical support of the rival theory of Copernicus.

(3) Toricelli (and predecessors) : the refutation of ‘nature abhors a vacuum‘. This prepares for a mechanistic world view.

(4) Kepler’s refutation of the hypothesis of circular motion upheld till then (even by Tycho and Galileo), leads to Kepler’s laws and so to Newton’s theory.6

(5) Lavoisier’s refutation of the phlogiston theory leads to modern chemistry.

(6) The falsification of Newton’s theory of light (Young’s two- slit experiment). This leads to the Young-Fresnel theory of light. The velocity of light in moving water is another refutation. It prepares for special relativity.

(7) Oersted’s experiment is interpreted by Faraday as a refutation of the universal theory of Newtonian central forces and thus leads to the Faraday-Maxwell field theory.

(8) Atomic theory: the atomicity of the atom is refuted by the Thomson electron. This leads to the electromagnetic theory of matter, and, in time, to the rise of electronics. See Einstein’s and Weyl’s attempts at a monistic (‘unified’) theory of gravitation and electromagnetics.

(9) Michelson’s experiment (1881-1887-1902, etc.) leads to Lorentz’s Versuch einer Theorie der electrischen und optischen Erscheinungen in bewegten Körpern (1895: see §89). Lorentz’s book was crucially important to Einstein, who alluded to it twice in §9 of his relativity paper of 1905. (Einstein himself did not regard the Michelson experiment as very important.) Einstein’s special relativity theory is (a) a development of the formalism founded by Lorentz and (b) a different—that is, relativistic—interpretation of that formalism. There is no crucial experiment so far to decide between Lorentz’s and Einstein’s interpretations; but if we have to adopt action at a distance (non-locality: see Quantum Theory and the Schism in Physics, Vol. III of the Postscript, Preface 1982), then we would have to return to Lorentz.

Incidentally, it took years before physicists began to come to some agreement about the importance of Michelson’s experiments: I do not contend that falsifications are usually accepted at once (see the preceding section) not even that they are immediately recognised as potential falsifications.

(10) The ‘chance-discoveries’ of Roentgen and of Becquerel refuted certain (unconsciously held) expectations; especially Becquerel’s expectations. They had, of course, revolutionary consequences.

(11) Wilhelm Wien’s (partially) successful theory of black body radiation conflicted with the (partially) also very successful theories of SirJames Jeans and Lord Rayleigh. The refutation by Lummer and Pringsheim of the radiation formula of Rayleigh and Jeans, together with Wien’s work, leads to Planck’s quantum theory (see L.Sc.D., p. 108). In this, Planck refutes his own theory, the absolutistic interpretation of the entropy law, as opposed to a probabilistic interpretation similar to Boltzmann’s.

(12) Philipp Lenard’s experiments concerning the photoelectric effect conflicted, as Lenard himself insisted, with what was to be expected from Maxwell’s theory. They led to Einstein’s theory of light-quanta or photons (which were of course also in conflict with Maxwell), and thus, much later, to particle- wave dualism. (

(13) The refutation of the Mach-Ostwald anti-atomistic and phenomenalistic theory of matter: Einstein’s great paper on Brownian motion of 1905 suggested that Brownian motion may be interpreted as a refutation of this theory. Thus this paper did much to establish the reality of molecules and atoms. (14) Rutherford’s refutation of the vortex model of the atom.8 This leads directly to Bohr’s 1913 theory of the hydrogen atom, and thus, in the end, to quantum mechanics.

(14) Rutherford’s refutation of the vortex model of the atom.8 This leads directly to Bohr’s 1913 theory of the hydrogen atom, and thus, in the end, to quantum mechanics.

(15) Rutherford’s refutation (in 1919) of the theory that chemical elements cannot be changed artificially (though they may disintegrate spontaneously).

(16) The theory of Bohr, Kramers and Slater (see L.Sc.D., pp. 250, 243): this theory was refuted by Compton and Simon. The refutation leads almost at once to the Heisenberg-Born- Jordan quantum mechanics.

(17) Schrodinger’s interpretation of his (and de Broglie’s) theory is refuted by the statistical interpretation of matter waves (experiments of Davisson and Germer, and of George Thomson, for instance). This leads to Bom’s statistical interpretation.

(18) Anderson’s discovery of the positron (1932) refutes a lot: the theory of two elementary particles — protons and electrons — is refuted; conservation of particles is refuted; and Dirac’s own original interpretation of his predicted positive particles (he thought they were protons) is refuted. Some theoretical work of about 1930-31 is thereby corroborated.

(19) The electrical theory of matter elaborated by Einstein and Weyl, and held implicitly — and at any rate, pursued — by Einstein to the end of his life (since he interpreted the unified field theory as a theory of two fields, gravitation and electromagnetics),is refuted by the neutron and by Yukawa’s theory of nuclear forces: the Yukawa Meson. This gives rise to the theory of the nucleus.
(20) The refutation of parity conservation. (See Allan Franklin, Stud. Hist. Philos. Sci. 10, 1979, p. 201.)”
That is an interesting list of scientific refutations provided by Popper himself. Popper  was right to suggest that the new theories highlighted above were not direct results of the refutations. The refutations merely created new problem situations which stimulated imaginative and critical thought by thinking men. But this initial stage of conceiving a new theory is not susceptible for logical analysis.”The question how it happens that a new idea occurs to a man  … may be of great interest  to empirical psychology ; but it is irrelevant to the logical analysis of scientific knowledge” (See Popper, K., The  Logic of Scientific Discovery,1934,  p. 7). That is because the latter does not concern with quid facti but with quid juris.
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R.I.P. George E.P. Box


Last Thurs­day (28 March 2013), George Box passed away at the age of 93. He was one of the great sta­tis­ti­cians of the last 100 years, and leaves an aston­ish­ingly diverse legacy.

When I teach fore­cast­ing to my sec­ond year com­merce stu­dents, we cover Box-​​Cox trans­for­ma­tions, Box-​​Pierce and Ljung-​​Box tests, and Box-​​Jenkins mod­el­ling, and my stu­dents won­der if it is the same Box in all cases. It is. And we don’t even go near his work on response sur­face mod­el­ling, design of exper­i­ments, qual­ity con­trol or ran­dom num­ber gen­er­a­tion. Occa­sion­ally, a stu­dent won­ders if box­plots are also due to GEP Box, but they were the brain­child of his good friend John W Tukey.

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The beauty of piecewise polynomials

It always amazes me  what beautiful objects may be created by very simple mathematical equations…piecewise

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I would definitely add to the list the following paper which Rob Tibshirani was too modest to include:
R Tibshirani (1996) – Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society. Series B (Methodological), 267-288

Normal Deviate


Today we have a guest post by my good friend Rob Tibshirani. Rob has a list of nine great statistics papers. (He is too modest to include his own papers.) Have a look and let us know what papers you would add to the list. And what machine learning papers would you add? Enjoy.

9 Great Statistics papers published after 1970
Rob Tibshirani

I was thinking about influential and awe-inspiring papers in Statistics and thought it would be fun to make a list. This list will show my bias in favor of practical work, and by its omissions, my ignorance of many important subfields of Statistics. I hope that others will express their own opinions.

  1. Regression models and life tables (with discussion) (Cox 1972). A beautiful and elegant solution to an extremely important practical problem. Has had an enormous impact in medical science. David Cox…

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Error Statistics Philosophy

A SPANOSby Aris Spanos

Few statisticians will dispute that R. A. Fisher (February 17, 1890 – July 29, 1962) is the father of modern statistics; see Savage (1976), Rao (1992). Inspired by William Gosset’s (1908) paper on the Student’s t finite sampling distribution, he recast statistics into the modern model-based induction in a series of papers in the early 1920s. He put forward a theory of optimal estimation based on the method of maximum likelihood that has changed only marginally over the last century. His significance testing, spearheaded by the p-value, provided the basis for the Neyman-Pearson theory of optimal testing in the early 1930s. According to Hald (1998)

“Fisher was a genius who almost single-handedly created the foundations for modern statistical science, without detailed study of his predecessors. When young he was ignorant not only of the Continental contributions but even of contemporary publications in English.” (p. 738)

What is…

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A useful trick…

An Ergodic Walk

I came across some references to “Bernstein’s trick” in some papers I was reading, but had to do a little digging to find out what it really meant. Suppose you have independent and identically distributed random variables Xi for i = 1, 2, … n, taking values in [-1, 1], and with E[Xi] =…. Our goal is to bound

Pr[ (1/n) ∑ Xi > a ] .

The Bernstein trick is to multiply both sides by a dummy variable t and exponentiate both sides:

Pr[ (1/n) ∑ Xi > a ] = Pr[ exp(t ∑ Xi) > exp(a n t) ] ,

Now we use the Markov inequality on the random variable exp(t ∑ X_i):

Pr[ exp(t ∑ Xi) > exp(a n t) ] ≤ exp(- a n t) E[ exp(t ∑ Xi) ],

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