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Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
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Home > Category Index for Science Quotations > Category Index E > Category: Equivalence

Equivalence Quotes (6 quotes)

An amino acid residue (other than glycine) has no symmetry elements. The general operation of conversion of one residue of a single chain into a second residue equivalent to the first is accordingly a rotation about an axis accompanied by translation along the axis. Hence the only configurations for a chain compatible with our postulate of equivalence of the residues are helical configurations.
[Co-author with American chemist, ert B. Corey (1897-1971) and H. R. Branson]
'The Structure of Proteins: Two Hydrogen-bonded Helical Configurations of the Polypeptide Chain', Proceedings of the National Academy of Sciences of the United States of America (1951), 37, 206.
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Considering it as thus established, that heat is not a substance, but a dynamical form of mechanical effect, we perceive that there must be an equivalence between mechanical work and heat, as between cause and effect.
In 'On the Dynamical Theory of Heat, with Numerical Results Deduced from Mr. Joule's Equivalent of a Thermal Unit, and M. Regnault's Observations on Steam' (1851). In Mathematical and Physical Papers (1882-1911), Vol. 1, 175.
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I remember one occasion when I tried to add a little seasoning to a review, but I wasn’t allowed to. The paper was by Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: “The author discusses valueless measures in pointless spaces.”
In I Want to be a Mathematician: An Automathography (1985), 120.
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The precise equivalence of the chromosomes contributed by the two sexes is a physical correlative of the fact that the two sexes play, on the whole, equal parts in hereditary transmission, and it seems to show that the chromosomal substance, the chromatin, is to be regarded as the physical basis of inheritance. Now, chromatin is known to be closely similar to, if not identical with, a substance known as nuclein (C29H49N9O22, according to Miescher), which analysis shows to be a tolerably definite chemical compased of nucleic acid (a complex organic acid rich in phosphorus) and albumin. And thus we reach the remarkable conclusion that inheritance may, perhaps, be effected by the physical transmission of a particular chemical compound from parent to offspring.
In An Atlas of the Fertilization and Karyokinesis of the Ovum (1895), 4.
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There can never be two or more equivalent electrons in an atom, for which in a strong field the values of all the quantum numbers n, k1, k2 and m are the same. If an electron is present, for which these quantum numbers (in an external field) have definite values, then this state is ‘occupied.’
Quoted by M. Fierz, in article ‘Wolfgang Pauli’, in C. C. Gillispie (ed.), Dictionary of Scientific Biography (1974), Vol. 10, 423.
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Today, nothing is unusual about a scientific discovery's being followed soon after by a technical application: The discovery of electrons led to electronics; fission led to nuclear energy. But before the 1880's, science played almost no role in the advances of technology. For example, James Watt developed the first efficient steam engine long before science established the equivalence between mechanical heat and energy.
Edward Teller with Judith L. Shoolery, Memoirs: A Twentieth-Century Journey in Science and Politics (2001), 42.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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