It is clear... that the concept of space can in no wise be generated by thought. ...Whoever maintains the contrary must undertake to derive the dimensions of space from the pure laws of thought—a problem which is at once seen to be impossible of solution.

— Hermann Grassmann Ausdehnungslehre (1844)

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Die lineare Ausdehnungslehre (1844) Einleitung, p. 20 seq. As quoted by John Stallo, The Concepts and Theories of Modern Physics (1881) Ch XIV. Metageometrical Space in the Light of Modern Analysis Riemann's Essay, p. 260.

More quotes by Hermann Grassmann

Geometry can in no way be viewed... as a branch of mathematics; instead, geometry relates to something already given in nature, namely, space. I... realized that there must be a branch of mathematics which yields in a purely abstract way laws similar to geometry.

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I define as a unit any magnitude that can serve for the numerical derivation of a series of magnitudes, and in particular I call such a unit an original unit if it is not derivable from another unit. The unit of numbers, that is one, I call the absolute unit, all others relative. Zero can never be a unit.

Ausdehnungslehre (1844)

I feel entitled to hope that I have found in this new analysis the only natural method according to which mathematics should be applied to nature, and according to which geometry may also be treated, whenever it leads to general and to fruitful results.

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It is clear... that the concept of space can in no wise be generated by thought. ...Whoever maintains the contrary must undertake to derive the dimensions of space from the pure laws of thought—a problem which is at once seen to be impossible of solution.

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