A Quote by Arthur Cayley

Not that the propositions of geometry are only approximately true, but that they remain absolutely true in regard to that Euclidean space which has been so long regarded as being the physical space of our experience.

Arthur Cayley

Quote Topics

Absolutely Been Being Experience Geometry Long Only Our Physical Propositions Regard Regarded Remain Space True Which

Quote Author

Arthur Cayley
British - Mathematician
August 16, 1821 - January 26, 1895

The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.

Hans Reichenbach

The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry.

John Maynard Keynes

I believe that all centers that appear in space - whether they originate in biology, in physical forces, in pure geometry, in color - are alike simply in that they all animate space. It is this animated space that has its functional effect upon the world, that determines the way things work, that governs the presence of harmony and life.

Christopher Alexander

The truth us that other systems of geometry are possible, yet after all, these other systems are not spaces but other methods of space measurements. There is one space only, though we may conceive of many different manifolds, which are contrivances or ideal constructions invented for the purpose of determining space.

Paul Carus

...the differential element of non-Euclidean spaces is Euclidean. This fact, however, is analogous to the relations between a straight line and a curve, and cannot lead to an epistemological priority of Euclidean geometry, in contrast to the views of certain authors.

Hans Reichenbach

Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces, which our senses determine by its position to bodies, and which is vulgarly taken for immovable space.

Isaac Newton

If we can avoid disaster for the next two centuries, our species should be safe as we spread into space. If we are the only intellegent beings in the galaxy we should make sure we survive and continue. . . . Our only chance of long-term survival is not to remain inward looking on planet Earth but to spread out into space. We have made remarkable progress in the last hundred years. But if we want to continue beyond the next hundred years, our future is in space.

Stephen Hawking

The validity of mathematical propositions is independent of the actual world-the world of existing subject-matters-is logically prior to it, and would remain unaffected were it to vanish from being. Mathematical propositions, if true, are eternal verities.

Cassius Jackson Keyser

Despite the campaign rhetoric, the bureaucracies-big business and big government-are here to stay. The centralization effort cannot be checked. but it can be rationally directed towards our species goal: Space Migration, which in turn offers the only way to re-attain individual freedom of space-time and the small-group social structures which obviously best suit our nervous systems. It is another paradox of neuro-genetics that only in space habitats can humanity return to the village life and pastoral style for which we all long.

Timothy Leary

Our time here is magic! It's the only space you have to realize whatever it is that is beautiful, whatever is true, whatever is great, whatever is potential, whatever is rare, whatever is unique, in. It's the only space.

Ben Okri

True ecstasy is stepping out of the bondage of the time-bound, space-bound world. We long to be free of fear and limitation. We hunger to experience our infinite, unbounded Self.

Deepak Chopra

Freedom, individualism and being yourself so long as you don't hurt another's physical person or property: The true artist is a man who believes absolutely in himself, because he is absolutely himself.

Oscar Wilde

Space expands or contracts in the tensions and functions through which it exists. Space is not a static, inert thing. Space is alive; space is dynamic; space is imbued with movement expressed by forces and counterforces; space vibrates and resounds with color, light and form in the rhythm of life.

Hans Hofmann

Even when we're with someone we love, we're foolish enough to think of her body and soul as being separate. To stand before the person we love is not the same as loving her true self, for we are only apt to regard her physical beauty as the indispensable mode of her existence. When time and space intervene, it is possible to be deceived by both, but on the other hand, it is equally possible to draw twice as close to her real self.

Yukio Mishima

It has frequently been said that we never desire what we think absolutely inapprehensible: it is however true that some of our sharpest agonies are those in which the object of desire is regarded as both possible and imaginary.