"The next grand extensions of mathematical physics will, in all likelihood, be furnished by quaternions." (Peter G Tait, "Note on a Quaternion Transformation", [communication read] 1863)
"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)
"From the earliest times man's apprehension of the causes and
connections of natural phenomena has been rendered uncertain and imperfect by
his wilfully ignoring the great fact that Natural Philosophy is an
experimental, and not an intuitive, science."
"It is very desirable to have a word to express the Availability for work of the heat in a given magazine; a term for that possession, the waste of which is called Dissipation. Unfortunately the excellent word Entropy, which Clausius has introduced in this connexion, is applied by him to the negative of the idea we most naturally wish to express. It would only confuse the student if we were to endeavour to invent another term for our purpose. But the necessity for some such term will be obvious from the beautiful examples which follow. And we take the liberty of using the term Entropy in this altered sense [...] The entropy of the universe tends continually to zero." (Peter G Tait, "Sketch Of Thermodynamics", 1868)
"If nothing more could be said of Quaternions than that they enable us to exhibit in a singularly compact and elegant form, whose meaning is obvious at a glance on account of the utter inartificiality of the method, results which in the ordinary Cartesian co-ordinates are of the utmost complexity, a very powerful argument for their use would be furnished. But it would be unjust to Quaternions to be content with such a statement; for we are fully entitled to say that in all cases, even in those to which the Cartesian methods seem specially adapted, they give as simple an expression as any other method; while in the great majority of cases they give a vastly simpler one. In the common methods a judicious choice of co-ordinates is often of immense importance in simplifying an investigation; in Quaternions there is usually no choice, for (except when they degrade to mere scalars) they are in general utterly independent of any particular directions in space, and select of themselves the most natural reference lines for each particular problem." (Peter G Tait, Nature Vol. 4, [address] 1871)
"It is true that, in the eyes of the pure mathematician, Quaternions have one grand and fatal defect. They cannot be applied to space of n dimensions, they are contented to deal with those poor three dimensions in which mere mortals are doomed to dwell, but which cannot bound the limitless aspirations of a Cayley or a Sylvester. From the physical point of view this, instead of a defect, is to be regarded as the greatest possible recommendation. It shows, in fact, Quaternions to be the special instrument so constructed for application to the Actual as to have thrown overboard everything which is not absolutely necessary, without the slightest consideration whether or no it was thereby being rendered useless for application to the Inconceivable." (Peter G Tait, [Presidential Address British Association for the Advancement of Science] 1871)
"There is nothing physical to be learned a priori. We have no
right whatever to ascertain a single physical truth without seeking for it
physically, unless it be a necessary consequence of other truths already
acquired by experiment, in which case mathematical reasoning is alone
requisite." (Peter G Tait, "Lectures on Some Recent Advances in Physical Science,
With a Special, Lecture on Force", 1876)
"There is a necessity for perfect definiteness of language in all truly Scientific work." (Peter G Tait, "On the Formula of Evolution", Nature, November 23, 1880)
"An exact or adequate conception of matter itself, could we obtain it, would almost certainly be something extremely unlike any conception of it which our senses and our reason will ever enable us to form. [...] The discovery of the ultimate nature of matter is probably beyond the range of human intelligence." (Peter G Tait, "Properties of Matter", 1890)
"To [the scientific man] the discovery of a new law of
nature, or even of a new experimental fact, or the invention of a novel
mathematical method, no matter who has been the first to reach it, is an event
of an order altogether different from, and higher than, those which are so
profusely chronicled in the newspapers." (Peter G Tait)
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