Topic Quotes (12 quotes)
A hot topic of late, expressed most notably in Bernie Siegel’s best-selling books, has emphasized the role of positive attitude in combating such serious diseases as cancer. From the depths of my skeptical and rationalist soul, I ask the Lord to protect me from California touchie-feeliedom.
Biological disciplines tend to guide research into certain channels. One consequence is that disciplines are apt to become parochial, or at least to develop blind spots, for example, to treat some questions as “interesting” and to dismiss others as “uninteresting.” As a consequence, readily accessible but unworked areas of genuine biological interest often lie in plain sight but untouched within one discipline while being heavily worked in another. For example, historically insect physiologists have paid relatively little attention to the behavioral and physiological control of body temperature and its energetic and ecological consequences, whereas many students of the comparative physiology of terrestrial vertebrates have been virtually fixated on that topic. For the past 10 years, several of my students and I have exploited this situation by taking the standard questions and techniques from comparative vertebrate physiology and applying them to insects. It is surprising that this pattern of innovation is not more deliberately employed.
Definition of Mathematics.—It has now become apparent that the traditional field of mathematics in the province of discrete and continuous number can only be separated from the general abstract theory of classes and relations by a wavering and indeterminate line. Of course a discussion as to the mere application of a word easily degenerates into the most fruitless logomachy. It is open to any one to use any word in any sense. But on the assumption that “mathematics” is to denote a science well marked out by its subject matter and its methods from other topics of thought, and that at least it is to include all topics habitually assigned to it, there is now no option but to employ “mathematics” in the general sense of the “science concerned with the logical deduction of consequences from the general premisses of all reasoning.”
I have a good idea every two years. Give me a topic, I will give you the idea!
[Reputed to have been a remark made to the head of his department at Caltech.]
[Reputed to have been a remark made to the head of his department at Caltech.]
If [a man] is sent to a hospital, he is supplied with a topic of conversation, and often is boastful.
One of the most important choices any researcher makes is picking a significant topic to study. If you choose the right problem, you get important results that transform our perception of the underlying structure of the universe. If you don’t choose the right problem, you may work very hard but only get an interesting result.
Suppose then I want to give myself a little training in the art of reasoning; suppose I want to get out of the region of conjecture and probability, free myself from the difficult task of weighing evidence, and putting instances together to arrive at general propositions, and simply desire to know how to deal with my general propositions when I get them, and how to deduce right inferences from them; it is clear that I shall obtain this sort of discipline best in those departments of thought in which the first principles are unquestionably true. For in all our thinking, if we come to erroneous conclusions, we come to them either by accepting false premises to start with—in which case our reasoning, however good, will not save us from error; or by reasoning badly, in which case the data we start from may be perfectly sound, and yet our conclusions may be false. But in the mathematical or pure sciences,—geometry, arithmetic, algebra, trigonometry, the calculus of variations or of curves,— we know at least that there is not, and cannot be, error in our first principles, and we may therefore fasten our whole attention upon the processes. As mere exercises in logic, therefore, these sciences, based as they all are on primary truths relating to space and number, have always been supposed to furnish the most exact discipline. When Plato wrote over the portal of his school. “Let no one ignorant of geometry enter here,” he did not mean that questions relating to lines and surfaces would be discussed by his disciples. On the contrary, the topics to which he directed their attention were some of the deepest problems,— social, political, moral,—on which the mind could exercise itself. Plato and his followers tried to think out together conclusions respecting the being, the duty, and the destiny of man, and the relation in which he stood to the gods and to the unseen world. What had geometry to do with these things? Simply this: That a man whose mind has not undergone a rigorous training in systematic thinking, and in the art of drawing legitimate inferences from premises, was unfitted to enter on the discussion of these high topics; and that the sort of logical discipline which he needed was most likely to be obtained from geometry—the only mathematical science which in Plato’s time had been formulated and reduced to a system. And we in this country [England] have long acted on the same principle. Our future lawyers, clergy, and statesmen are expected at the University to learn a good deal about curves, and angles, and numbers and proportions; not because these subjects have the smallest relation to the needs of their lives, but because in the very act of learning them they are likely to acquire that habit of steadfast and accurate thinking, which is indispensable to success in all the pursuits of life.
The first effect of the mind growing cultivated is that processes once multiple get to be performed in a single act. Lazarus has called this the progressive “condensation” of thought. ... Steps really sink from sight. An advanced thinker sees the relations of his topics is such masses and so instantaneously that when he comes to explain to younger minds it is often hard ... Bowditch, who translated and annotated Laplace's Méchanique Céleste, said that whenever his author prefaced a proposition by the words “it is evident,” he knew that many hours of hard study lay before him.
The professor may choose familiar topics as a starting point. The students collect material, work problems, observe regularities, frame hypotheses, discover and prove theorems for themselves. … the student knows what he is doing and where he is going; he is secure in his mastery of the subject, strengthened in confidence of himself. He has had the experience of discovering mathematics. He no longer thinks of mathematics as static dogma learned by rote. He sees mathematics as something growing and developing, mathematical concepts as something continually revised and enriched in the light of new knowledge. The course may have covered a very limited region, but it should leave the student ready to explore further on his own.
This brings me to the final point of my remarks, the relation between creativity and aging, a topic with which I have had substantial experience. Scientific research, until it has gone through the grueling and sometimes painful process of publication, is just play, and play is characteristic of young vertebrates, particularly young mammals. In some ways, scientific creativity is related to the exuberant behavior of young mammals. Indeed, creativity seems to be a natural characteristic of young humans. If one is fortunate enough to be associated with a university, even as one ages, teaching allows one to contribute to, and vicariously share, in the creativity of youth.”
This topic brings me to that worst outcrop of the herd nature, the military system, which I abhor. That a man can take pleasure in marching in formation to the strains of a band is enough to make me despise him. He has only been given his big brain by mistake; a backbone was all he needed. This plague-spot of civilisation ought to be abolished with all possible speed. Heroism by order, senseless violence, and all the pestilent nonsense that goes by the name of patriotism–how I hate them! War seems to me a mean, contemptible thing: I would rather be hacked in pieces than take part in such an abominable business.
[E.H.] Moore was presenting a paper on a highly technical topic to a large gathering of faculty and graduate students from all parts of the country. When half way through he discovered what seemed to be an error (though probably no one else in the room observed it). He stopped and re-examined the doubtful step for several minutes and then, convinced of the error, he abruptly dismissed the meeting—to the astonishment of most of the audience. It was an evidence of intellectual courage as well as honesty and doubtless won for him the supreme admiration of every person in the group—an admiration which was in no wise diminished, but rather increased, when at a later meeting he announced that after all he had been able to prove the step to be correct.