A Quote by Hans Reichenbach

We must... maintain that mathematical geometry is not a science of space insofar as we understand by space a visual structure that can be filled with objects - it is a pure theory of manifolds.

Hans Reichenbach

Quote Topics

Filled Geometry Maintain Mathematical Must Objects Pure Science Space Structure Theory Understand Visual

Quote Author

Hans Reichenbach
Philosopher
September 26, 1891 - April 9, 1953

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

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

One thing that you and I know is language. Another thing that you and I know is how objects behave in perceptual space. We have a whole mass of complex ways of understanding what is the nature of visual space. A proper part of psychology ought to be, and in recent years has been, an effort to try to discover the principles of how we organize visual space. I would say that the same is true of every domain of psychology, of human studies.

Noam Chomsky

In order to understand the phenomena in a certain plasma region, it is necessary to map not only the magnetic but also the electric field and the electric currents. Space is filled with a network of currents which transfer energy and momentum over large or very large distances. The currents often pinch to filamentary or surface currents. The latter are likely to give space, as also interstellar and intergalactic space, a cellular structure.

Hannes Alfven

We've been surrounded by images of space our whole lives, from the speculative images of science fiction to the inspirational visions of artists to the increasingly beautiful pictures made possible by complex technologies. But whilst we have an overwhelmingly vivid visual understanding of space, we have no sense of what space sounds like.

Honor Harger

From a mathematical standpoint it is possible to have infinite space. In a mathematical sense space is manifoldness, or combinations of numbers. Physical space is known as the 3-dimension system. There is the 4-dimension system, the 10-dimension system.

Charles Proteus Steinmetz

It is clear that Economics, if it is to be a science at all, must be a mathematical science ... simply because it deals with quantities... As the complete theory of almost every other science involves the use of calculus, so we cannot have a true theory of Economics without its aid.

William Stanley Jevons

There is nothing mysterious about space-time. Every speck of matter, every idea, is a space-time event. We cannot experience anything or conceive of anything that exists outside of space-time. Just as experience precedes all awareness and creative expression, the visual language of our photographs should ever more strongly express the fourth dimensional structure of the real world.

Wynn Bullock

I think the universe is pure geometry - basically, a beautiful shape twisting around and dancing over space-time.

Antony Garrett Lisi

In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.

Jean-Victor Poncelet

Small objects, like the Walkman first and then the iPod, create bubbles of space around us that enable us to have a metaphysical space that is much bigger than our physical space.

Paola Antonelli

(Game theory is) essentially a structural theory. It uncovers the logical structure of a great variety of conflict situations and describes this structure in mathematical terms. Sometimes the logical structure of a conflict situation admits rational decisions; sometimes it does not.

Anatol Rapoport

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

Space, space: architects always talk about space! But creating a space is not automatically doing architecture. With the same space, you can make a masterpiece or cause a disaster.

Jean Nouvel

I reject what I see as flat-footed accounts of the fundamental structure of the world, where we somehow assume that, because ordinary experience involves middle-sized objects in space and time, that fundamental reality must be essentially like that.