So intimate is the union between Mathematics and Physics that probably by far the larger part of the accessions to our mathematical knowledge have been obtained by the efforts of mathematicians to solve the problems set to them by experiment, and to create for each successive class phenomena a new calculus or a new geometry, as the case might be, which might prove not wholly inadequate to the subtlety of nature. Sometimes the mathematician has been before the physicist, and it has happened that when some great and new question has occurred to the experimentalist or the observer, he has found in the armory of the mathematician the weapons which he needed ready made to his hand. But much oftener, the questions proposed by the physicist have transcended the utmost powers of the mathematics of the time, and a fresh mathematical creation has been needed to supply the logical instrument requisite to interpret the new enigma.
Henry John Stephen SmithRelated topics
calculus case enigma experiment far found fresh geometry great knowledge mathematician mathematics might nature observer physicist prove question ready requisite set subtlety utmost experimentalist questionsRelated quotes
Dear Mr. Rosenberg - I was very surprised this morning that you refused to give me 2,000 fr. especially given that I had told you that my wife was gravely ill in Berlin and that I needed to leave immediately. You probably thought it was a tale I was telling you in order to shave some money off the sum that you owe me; to prove to you that this is not the case, I enclose with this letter a telegram that I received this morning. Strong though the crisis may be and as strongly as you may have applied the brakes, it is not possible that you are not able to find 1,000 fr. for a painter with whom you have done business for six years now and who (I dare hope) enjoys all your esteem; especially given that the said painter tells you that his wife is seriously ill and that he needs to leave.
I should tell you that in general the way you act in these times of crises is not particularly heroic.
Giorgio de Chirico
This consideration must alter the form of our proposed inquiry; for the question being thus at least partly decided, since it is ascertained that we have rays of heat which give no light, it can only become a subject of inquiry whether some of these heat-making rays may not have a power of rendering objects visible, superadded to their now already established power of heating bodies. This being the case, it is evident that the onus probandi [burden of proof] ought to lie with those who are willing to establish such an hypothesis, for it does not appear that Nature is in the habit of using one and the same mechanism with any two of our senses. Witness the vibration of air that makes sound, the effluvia that occasion smells, the particles that produce taste, the resistance or repulsive powers that affect the touch-all these are evidently suited to their respective organs of sense.
William Herschel
One should view the present situation – the status quo – as being maintained by certain conditions or forces. A culture – for instance, the food habits of a certain group at a given time – is not a static affair but a live process like a river which moves but still keeps to a recognizable form...Food habits do not occur in empty space. They are part and parcel of the daily rhythm of being awake and asleep; of being alone and in a group; of earning a living and playing; of being a member of a town, a family, a social class, a religious group... in a district with good groceries and restaurants or in an area of poor and irregular food supply. Somehow all these factors affect food habits at any given time. They determine the food habits of a group every day anew just as the amount of water supply and the nature of the river bed determine the flow of the river, its constancy or change.
Kurt Lewin
So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premisses which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of Principia Mathematica, they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary.
Bertrand Russell
I would summarize the Keynesian view in terms of four points:1. Economies sometimes produce much less than they could, and employ many fewer workers than they should, because there just isn't enough spending. Such episodes can happen for a variety of reasons; the question is how to respond.
2. There are normally forces that tend to push the economy back toward full employment. But they work slowly; a hands-off policy toward depressed economies means accepting a long, unnecessary period of pain.
3. It is often possible to drastically shorten this period of pain and greatly reduce the human and financial losses by "printing money”, using the central bank's power of currency creation to push interest rates down.
4. Sometimes, however, monetary policy loses its effectiveness, especially when rates are close to zero. In that case temporary deficit spending can provide a useful boost. And conversely, fiscal austerity in a depressed economy imposes large economic losses.
Paul Krugman