RANT#20: S.1: Now the real object of true naturalists ... (is) but to find out the connection of known phenomena, and by deductive reasoning, to obtain a knowledge of hithterto unknown phenomena. ...
S.4: I had occasion, just lately,to use the word "naturalist." ... It must, however, be noted that the naturalist, as at present generaly understood, is a student of living nature only. He has certainly no exclusive right to so excellent a name. On the other hand, the physicist is a student of inanimate nature, in the main, so that he has no exclusive right to the name, either. Both are naturalists. ... Then about the other set of men. Are they not essentially students of the properties of matter, and therefore materialists. That "materialist is the right name is obvious at a glance. ... For my part I always admired the old-fashioned term "natural philosopher." It was so dignified, and raised up visions of the portraits of ... usually highly respectable-looking elderly gentlemen, with very large bald heads and much wrapped up about the throats, sitting in their studies pondering calmly over the secrets of nature revealed to them by their experiemnts. ...
S.7: I shall, therefore, in the next place make a few remarks upon mathematical investigatons in general, a subject upon which there are many popular delusions current, even amongst people who, one would think, should know better. ...
S.8:There are men of a certain type of mind who are never wearied with gibing at mathematics, at mathematicians, and at mathematical methods of inquiry. ... Plainly, then, the anti-mathematician must belong to the same class of the paradoxer, whose characteristic is to be wise in his ignorance, whereas the really wise man is ignorant in his wisdom. ... What is of greater importance is that the anti-mathematicians sometimes do a deal of mischief. For there are many of a neutral frame of mind, little acquainted themselves with mathematical methods, who are sufficiently impressible to be easily taken in by the gibers and to be prejudiced thereby; and, should they possess some mathematical bent, they may be hindered by their prejudice from giving it fair development. We cannot all be Newtons or Laplaces, but that there is an immense amount of moderate mathematical talent lying latent in the average man I regard as a fact; and even the moderate development implied in a working knowldge of simple algebraical equations can, with common-sense to assist, be not the only the means of valuable mental discipline, but even be of commercial importance (which goes a long way with some people), ...
S.9:"Mathematics is gibberish." Little need be said about this statement. It is only worthy of the utterly iliterate. "What is the use of it?" ... Now, similar remarks to thse I have often heard from fairly intelligent and educated people. They don't see the use of it, that is plain. That is nothing; what is to the point is that they conclude that it is of no use.... But what is the use of it, then? Well, it is quite certain that if a person has no mathematical talent whatever he had really better be doing something "useful", that is to say, something else than mathematics, (inventing a dynamo, for instance), ... This is quite a personal question. Every mind should receive fair development (in good directions) for what it is capable of doing fairly well. People who do not cultivate their minds have no conception of what they lose. They become mere eating and drinking and money-grabbing machines. And yet they seem happy! There is some merciful dispensation at work, no doubt....
S.10:Mathematical reasoning is, fundamentally, not different from reasoning in general. And as by the exercise of the reason discoveries can be made, why not by mathematical reasoning? Whatever were Newton and the long array of mathematical materialists who followed him doing all the time? Making discoveries, of course, largely assisted by their mathematics.I say nothing of the pure mathematicians. Their discoveries are extensions of the field of mathematics itself - a perfectly limitless field. I refer only to students of Nature on its material side, who have employed mathematics expressly for the purpose of making discoveries....
S.11:Mathematics is reasoning about quantities. ... If there be something which cannot be reduced to a quantity...then that something cannot be accurately reasoned about, because it is in part unknown. ... The unknown is not necessarily unknowable; ... But there must be an ultimate limit, because we are a part of Nature, and cannot go beyond it. Beyond this limit, the Unknown becomes the Unknowable, which it is of little service to discuss, though it will always be a favourite subject of speculation. ... The assumption of a special act of creation, either now or at any time is merely a confession of ignorance. We have no evidence of any such disconinutities. ...
S.12:It is exceedingly remarkable that the scientific spirit (asking how it is done), which is so active and widespread at the present day, should be of such recent orign. With few exceptions, it hardly existed amongst the Ancients (who would be more appropriately termed the Youngsters). Now, in the development of our knowledge of the workings of Nature out of the tremondously complex assemblage of phenomena presented to the scientific inquirer, mathematics plays in some respects a very limited, in others a very important part. ... facts are of not use, considered as facts. They bewilder by their number and their apparent incoherency. ... Theory is the essence of facts. Without theory scientific knowledge would be only worthy of the madhouse. ...
S.14:It will have been observed that I have said next to nothing upon the study of pure mathematics; this is a matter with which we are not concerned. But that I have somewhat dilated (and I do not think needlessly) upon the adantages attending the use of mathematical methods by the materials to assist him in his study of the laws governing the material universe, by the proper co-ordination of known and the discovery of unknown (but not unknowable) phenomena.
Clearly this is not my rant - it is however my exact feelings. This polemic was taken from the first chapter of "Electromagnetic Theory" by (maverick Englishman) Oliver Heaviside and published in 1893! He was self educated after age 16 and though he is a scientific giant as little known as his contemporary the (American Yale Professor) J. Willard Gibbs, it is they who are credited with establishing the modern form of Vector Analysis in their real work of phenomenal (cis?) physics. It should be noted that the emphasis throughout is mine.
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