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Thursday, October 11, 2018

William Thomson and the philosophy of mathematics


Photo source: Wikimedia Commons, Herbert von Herkomer


William Thomson (1824-1907) was an Irish physicist best known for his contributions to the first and second laws of thermodynamics. Thomson is also known as Lord Kelvin. Mathematician E. W. Hobson said,


"The man of true Physical instincts, endowed with the great faculty of scientific imagination, possessed for example by Lord Kelvin in a very remarkable degree, is for ever imagining models which shall enable him by their working to represent and depict the course of actual physical processes." (Mathematics, from the points of view of the Mathematician and of the Physicist, 1912)


The rest of this post is some quotes from Thomson.


Mathematics and reality


"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be." (Lecture on Electrical Units of Measurement, 1883)


"Nothing can be more fatal to progress than a too confident reliance upon mathematical symbols; for the student is only too apt to take the easier course, and consider the formula and not the facts as the physical reality." (Treatise on Natural Philosophy with Peter Guthrie Tait, 1867)


"I am never content until I have constructed a mechanical model of the subject I am studying." (Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light, 1904)


Pure mathematics


"Mathematics is the only true metaphysics." (Quoted in The Life of William Thomson by Silvanus Philips Thompson)


"Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense." (Quoted in The Life of William Thomson by Silvanus Philips Thompson)


Matter and force


"If, then, the motion of every particle of matter in the universe were precisely reversed at any instant, the course of nature would be simply reversed forever after." (The Kinetic Theory of the Dissipation of Energy, 1874)


"In general the actions which we see ever taking place around us are complex, or due to the simultaneous action of many causes." (Treatise on Natural Philosophy with Peter Guthrie Tait, 1867)


"We cannot, of course, give a definition of matter which will satisfy the metaphysician, but the naturalist may be content to know matter as that which can be perceived by the senses, or as that which can be acted upon by, or can exert, force." (Treatise on Natural Philosophy with Peter Guthrie Tait, 1867)


Scientific method


"In all cases when a particular agent or cause is to be studied, experiments should be arranged in such a way as to lead if possible to results depending on it alone... (Treatise on Natural Philosophy with Peter Guthrie Tait, 1867)