
Martin Buber, in his Heruth: On Youth and Religion (1919)
A - F
From the Author's Preface to First Edition (1918)
Space—Time—Matter (1952)
Context: It was my wish to present this great subject as an illustration of the itermingling of philosophical, mathematical, and physical thought, a study which is dear to my heart. This could be done only by building up the theory systematically from the foundations, and by restricting attention throughout to the principles. But I have not been able to satisfy these self-imposed requirements: the mathematician predominates at the expense of the philosopher.
Martin Buber, in his Heruth: On Youth and Religion (1919)
A - F
§ 2.
Linear Associative Algebra (1882)
Context: The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks.
Source: Presidential Address British Association for the Advancement of Science, Section A (1910), p. 286; Cited in: Moritz (1914, 106): Modern mathematics.
“Great physics does not automatically imply complicated mathematics!”
[Martinus Veltman, Facts and mysteries in elementary particle physics, World Scientific, 2003, 981238149X, 15, https://books.google.com/books?id=CNCHDIobj0IC&pg=PA15]
The Nature of the Physical World (1928)
Context: The idealistic tinge in my conception of the physical world arose out of mathematical researches on the relativity theory. In so far as I had any earlier philosophical views, they were of an entirely different complexion.
From the beginning I have been doubtful whether it was desirable for a scientist to venture so far into extra-scientific territory. The primary justification for such an expedition is that it may afford a better view of his own scientific domain.
Preface http://www-groups.dcs.st-and.ac.uk/~history/Extras/Eddington_Gifford.html
Source: 1850s, An Investigation of the Laws of Thought (1854), p. 50
Remarks after the Solvay Conference (1927)
Context: I consider those developments in physics during the last decades which have shown how problematical such concepts as "objective" and "subjective" are, a great liberation of thought. The whole thing started with the theory of relativity. In the past, the statement that two events are simultaneous was considered an objective assertion, one that could be communicated quite simply and that was open to verification by any observer. Today we know that 'simultaneity' contains a subjective element, inasmuch as two events that appear simultaneous to an observer at rest are not necessarily simultaneous to an observer in motion. However, the relativistic description is also objective inasmuch as every observer can deduce by calculation what the other observer will perceive or has perceived. For all that, we have come a long way from the classical ideal of objective descriptions.
In quantum mechanics the departure from this ideal has been even more radical. We can still use the objectifying language of classical physics to make statements about observable facts. For instance, we can say that a photographic plate has been blackened, or that cloud droplets have formed. But we can say nothing about the atoms themselves. And what predictions we base on such findings depend on the way we pose our experimental question, and here the observer has freedom of choice. Naturally, it still makes no difference whether the observer is a man, an animal, or a piece of apparatus, but it is no longer possible to make predictions without reference to the observer or the means of observation. To that extent, every physical process may be said to have objective and subjective features. The objective world of nineteenth-century science was, as we know today, an ideal, limiting case, but not the whole reality. Admittedly, even in our future encounters with reality we shall have to distinguish between the objective and the subjective side, to make a division between the two. But the location of the separation may depend on the way things are looked at; to a certain extent it can be chosen at will. Hence I can quite understand why we cannot speak about the content of religion in an objectifying language. The fact that different religions try to express this content in quite distinct spiritual forms is no real objection. Perhaps we ought to look upon these different forms as complementary descriptions which, though they exclude one another, are needed to convey the rich possibilities flowing from man's relationship with the central order.
Source: In a letter addressed to George Stokes dated December 20, 1857, as quoted in Fluid Mechanics in the Next Century https://doi.org/10.1115/1.3101925 (1996), by Mohamed Gad-el-Hak and Mihir Sen.
Preface p. vi
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid