Infinitesimal Quotes (5 quotes)
I also require much time to ponder over the matters themselves, and particularly the principles of mechanics (as the very words: force, time, space, motion indicate) can occupy one severely enough; likewise, in mathematics, the meaning of imaginary quantities, of the infinitesimally small and infinitely large and similar matters.
In Davis Baird, R.I.G. Hughes and Alfred Nordmann, Heinrich Hertz: Classical Physicist, Modern Philosopher (1998), 159.
It is going to be necessary that everything that happens in a finite volume of space and time would have to be analyzable with a finite number of logical operations. The present theory of physics is not that way, apparently. It allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore, if this proposition [that physics is computer-simulatable] is right, physical law is wrong.
International Journal of Theoretical Physics (1982), 21 Nos. 6-7, 468. Quoted in Brian Rotman, Mathematics as Sign (2000), 82.
The powers which tend to preserve, and those which tend to change the condition of the earth's surface, are never in equilibrio; the latter are, in all cases, the most powerful, and, in respect of the former, are like living in comparison of dead forces. Hence the law of decay is one which suffers no exception: The elements of all bodies were once loose and unconnected, and to the same state nature has appointed that they should all return... TIME performs the office of integrating the infinitesimal parts of which this progression is made up; it collects them into one sum, and produces from them an amount greater than any that can be assigned.
Illustrations of the Huttonian Theory of the Earth (1802), 116-7.
The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.
Elementary Mathematics From an Advanced Standpoint (1908). 3rd edition (1924), trans. E. R. Hedrick and C. A. Noble (1932), Vol. 1, 155.
We profess to teach the principles and practice of medicine, or, in other words, the science and art of medicine. Science is knowledge reduced to principles; art is knowledge reduced to practice. The knowing and doing, however, are distinct. ... Your knowledge, therefore, is useless unless you cultivate the art of healing. Unfortunately, the scientific man very often has the least amount of art, and he is totally unsuccessful in practice; and, on the other hand, there may be much art based on an infinitesimal amount of knowledge, and yet it is sufficient to make its cultivator eminent.
From H.G. Sutton, Abstract of Lecture delivered at Guy's Hospital by Samuel Wilks, 'Introductory to Part of a Course on the Theory and Practice of Medicine', The Lancet (24 Mar 1866), 1, 308
At the heart of science is an essential balance between two seemingly contradictory attitudes--an openness to new ideas, no matter how bizarre or counterintuitive they may be, and the most ruthless skeptical scrutiny of all ideas, old and new. This is how deep truths are winnowed from deep nonsense. -- Carl Sagan
