"Every process has laws, known or unknown, according to which it must take place. A consciousness of them is so far from being necessary to the process, that we cannot discover what they are, except by analyzing the results it has left us." (Lord William T Kelvin , "An Outline of the Necessary Laws of Thought", 1866)
"Nothing can be more fatal to progress than a too confident reliance on mathematical symbols; for the student is only too apt to take the easier course, and consider the formula not the fact as the physical reality." (William T Kelvin & Peter G Tait, "Treatise on Natural Philosophy", 1867)
"Accurate and minute measurement seems to the nonscientific imagination a less lofty and dignified work than looking for something new. But nearly all the grandest discoveries of science have been but the rewards of accurate measurement and patient long contained labor in the minute sifting of numerical results." (William T Kelvin, "Report of the British Association For the Advancement of Science" Vol. 41, 1871)
"Simplification of modes of proof is not merely an indication of advance in our knowledge of a subject, but is also the surest guarantee of readiness for farther progress." (William T Kelvin, "Elements of Natural Philosophy", 1873)
"All that is shown to the eye; and one of the most beautiful results of mathematics is the means of showing to the eye the law of variation, however complicated, of one independent variable." (William T Kelvin, [Presidential Address] 1883)
"[…] when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of science." (William T Kelvin, "Electrical Units of Measurement", 1883)
"There cannot be a greater mistake than that of looking superciliously upon the practical applications of science. The life and soul of science is its practical application; and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind." (William T Kelvin, "Electrical Units of Measurement", 1883)
"I have no satisfaction in formulas unless I feel their arithmetical magnitude." (William T Kelvin, [lecture] 1884)
"The scientific man sees and feels beauty as much as any mere observer - as much as any artist or painter. But he also sees something underlying that beauty; he wishes to learn something of the actions and forces producing those beautiful results." (William T Kelvin, "The Bangor Laboratories", 1885)
"I do think [...] that you would find it would lose nothing by omitting the word 'vector' throughout. It adds nothing to the clearness or simplicity of the geometry, whether of two dimensions or three dimensions. Quaternions came from Hamilton after his really good work had been done; and, though beautifully ingenious, have been an unmixed evil to those who have touched them in any way, including Clerk Maxwell." (William T Kelvin, [Letter to Robert B Hayward] 1892)
"Symmetrical equations are good in their place, but "vector" is a useless survival, or offshoot, from quaternions, and has never been of the slightest use to any creature. Hertz wisely shunted it, but unwisely he adopted temporarily Heaviside’s nihilism. He even tended to nihilism in dynamics, as I warned you soon after his death. He would have grown out of all this, I believe, if he had lived. He certainly was the opposite pole of nature to a nihilist in his experimental work, and in his Doctorate Thesis on the impact of elastic bodies." (William T Kelvin, [footnote in Letter to George F FitzGerald] 1896)
"I never satisfy myself until I can make a mechanical model of a thing. If I can make a mechanical model, I understand it." (William T Kelvin, 1904)
"A scientific theory is a tool and not a creed." (William T Kelvin)
"Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense." (William T Kelvin)
"Mathematics is the only good metaphysics." (Lord William T Kelvin)
"Paradoxes have no place in science. Their removal is the substitution of true for false statements and thoughts." (William T Kelvin, "On Sun's Heat", [Lecture])
"Science is bound, by the everlasting vow of honour, to face fearlessly every problem which can be fairly presented to it." (William T Kelvin)
"When you are face to face with a difficulty, you are up against a discovery." (William T Kelvin)
"When you call a thing mysterious, all that means is that you don't understand it." (William T Kelvin)
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