JF Ptak Science Books Quick Post
"When I imagine a triangle, even though such a figure may exist nowhere in the world except in my thought, indeed may never have existed, there is nonetheless a certain nature or form, or particular essence, of this figure that is immutable and eternal, which I did not invent, and which in no way depends on my mind.--Rene Descartes, Meditations on First Philosophy (1641) tr. John Cottingham, Descartes: Meditations on First Philosophy (1986)
This is the lovely response by the great mathematician J.J, Sylvester to Thomas Huxley's muckety comment on the lack of imnagination in the mathematical sciences. Huxley's remarks were made at a meeting of the British Association for the Advancement of Science, stating that (Mathematics) "is that study which knows nothing of observation, nothing of induction, nothing of experiment, nothing of causation"1 This quote is taken from Sylvester's quick and elegant responses in two articles in Nature, December 30, 1869 (231-3) and January 6, 1870 (pp 261-3), as "A Plea for the Mathematician" and "A Plea for the Mathematician II".
"For Sylvester, the ability to be able to imagine what the experience of space would be like in dimensions other than three is sufficient to establish the empirical basis of geometry--the three-dimensional Euclidean is not the science of space in general, but the science of the space of our experience."--Fact and Feeling: Baconian Science and the Nineteenth-Century Literary ...by Jonathan Smith, pp 181-182
Ex nihilo nihil fit/Nothing comes out of nothing.--R Descartes, Principia philosophiae, Part I, Article 49
The original papers are available on this blog's bookstore section.