It is no exaggeration to state that the classic culture of Tlön comprises only one discipline: psychology. All others are subordinated to it. I have said that the men of this planet conceive the universe as a series of mental processes which do not develop in space but successively in time.

Mountcastle discovered that tactile sensation is made up of several distinct modalities; for example, touch includes... hard pressure on the skin as well as a light brush... He found that each distinct submodality has its own private pathway within the brain and that this segregation is maintained at each relay...

Two other sciences in the same way will accurately treat of 'size': geometry, the part that abides and is at rest, [and] astronomy, that which moves and revolves.

[O]ur purpose is to give a presentation of geometry... in its visual, intuitive aspects. With the aid of visual imagination we can illuminate the manifold facts and problems... beyond this, it is possible... to depict the geometric outline of the methods of investigation and proof, without... entering into the details... In this manner, geometry being as many-faceted as it is and being related to the most diverse branches of mathematics, we may even obtain a summarizing survey of mathematics as a whole, and a valid idea of the variety of problems and the wealth of ideas it contains. Thus a presentation of geometry in large brushstrokes... and based on the approach through visual intuition, should contribute to a more just appreciation of mathematics by a wider range of people than just the specialists.

Tactile space separates us from objects, as opposed to visual space, which separates objects from one another. I have spent my life trying to paint the former kind.

Geometry is to the plastic arts what grammar is to the art of the writer.

Visual forms are not perceived differently from colors or brightness. They are sense qualities, and the visual character of geometry consists in these sense qualities.

[T]he increases of optics, geography and other sciences... are also due to the application of the more intricate geometry to philosophical matters. Hence has been made clear the curvature of the rays of light in the same medium; hence the causes of extraordinary s have been laid bare; hence, given one surface of a lens, another may be determined by means of which a ray entering the lens with given position will have a given position in emerging from it; hence in geography the excess of the normal diameters of the axis over the axis is found, and also the al figure of any planet; hence the varying gravity of the same body in different parts of the Earth, and the varying length of an isochronous pendulum according to the latitude of its place, and then indeed, after the due correction, the construction of a universal measure and of a perfect .

Euclidean geometry can be easily visualized; this is the argument adduced for the unique position of Euclidean geometry in mathematics. It has been argued that mathematics is not only a science of implications but that it has to establish preference for one particular axiomatic system. Whereas physics bases this choice on observation and experimentation, i.e., on applicability to reality, mathematics bases it on visualization, the analogue to perception in a theoretical science. Accordingly, mathematicians may work with the non-Euclidean geometries, but in contrast to Euclidean geometry, which is said to be "intuitively understood," these systems consist of nothing but "logical relations" or "artificial manifolds". They belong to the field of analytic geometry, the study of manifolds and equations between variables, but not to geometry in the real sense which has a visual significance.

"In an ever-more complex world, Mandelbrot argues, scientists need both tools: image as well as number, the geometric view as well as the analytic. The two should work together. Visual geometry is like an experienced doctor's savvy in reading a patient's complexion, charts, and X-rays. Precise analysis is like the medical test results-the raw numbers of blood pressure and chemistry. "A good doctor looks at both, the pictures and the numbers. Science needs to work that way too," he says."

There is the science of pure geometry, in which there are many geometries, , , non-Euclidean geometry... [etc.]. Each... is a , a pattern of ideas... judged by the interest and beauty of... pattern. It is a map or picture, the... product of many hands, a partial and imperfect copy (yet exact so far as it extends) of a section of mathematical reality. But... there is one thing... of which pure geometries are not pictures, and that is the spatio-temporal reality of the physical world. ...[T]hey cannot be, since earthquakes and eclipses are not mathematical concepts.

In order to see the difference which exists between... studies,—for instance, history and geometry, it will be useful to ask how we come by knowledge in each. Suppose, for example, we feel certain of a fact related in history... if we apply the notions of evidence which every-day experience justifies us in entertaining, we feel that the improbability of the contrary compels us to take refuge in the belief of the fact; and, if we allow that there is still a possibility of its falsehood, it is because this supposition does not involve absolute absurdity, but only extreme improbability.
In mathematics the case is wholly different... and the difference consists in this—that, instead of showing the contrary of the proposition asserted to be only improbable, it proves it at once to be absurd and impossible. This is done by showing that the contrary of the proposition which is asserted is in direct contradiction to some extremely evident fact, of the truth of which our eyes and hands convince us. In geometry, of the principles alluded to, those which are most commonly used are—
I. If a magnitude is divided into parts, the whole is greater than either of those parts.
II. Two straight lines cannot inclose a space.
III. Through one point only one straight line can be drawn, which never meets another straight line, or which is parallel to it.
It is on such principles as these that the whole of geometry is founded, and the demonstration of every proposition consists in proving the contrary of it to be inconsistent with one of these.

La géométrie est aux arts plastiques ce que la grammaire est à l'art de l'écrivain.

The term `geometry'...refers to a pattern of processing within our brains related to our spatial and visual senses, more than it refers to a separate content area of mathematics.