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The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thoughts are certain signs and more or less clear images which can be "voluntarily" reproduced and combined. There is, of course, a certain connection between those elements and relevant logical concepts. It is also clear that the desire to arrive finally at logically connected concepts is the emotional basis of this rather vague play with the above-mentioned elements. . . . The above-mentioned elements are, in my case, of visual and some muscular type. Conventional words or other signs have to be sought for laboriously only in a secondary stage, when the mentioned associative play is sufficiently established and can be reproduced at will.
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Answer to a survey written by the French mathematician Jaques Hadamard, from Hadamard's An Essay on the Psychology of Invention in the Mathematical Field (1945). Reprinted in Ideas and Opinions (1954). His full set of answers to the questions can be read on p. 3 here.

 

Albert Einstein

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The Buddha said, "Elements come together and form this body. At the time of appearing, elements appear. At the time of disappearing, elements disappear. When elements appear, I do not say "I" appear. When elements disappear, I do not say "I" disappear. Past moments and future moments do not arise in sequence. Past elements and future elements are not in alignment. This is the meaning of ocean mudra samadhi."
Closely investigate these words by the Buddha. Attaining the way and entering realization does not necessarily require extensive learning or realization. Anyone can attain the way through a simple verse of four lines. Even scholars of extensive learning can enter realization through a one line verse.

 

Dogen

 

With his hands he unites heaven and earth, and the four elements that form the world are controlled by him.
The four symbols before him are the four letters of the name of God, the signs of the four elements, fire, water, air, earth."
I trembled before the depth of the mysteries A touched... The words I heard seemed to be littered by the Great Magician himself, and it was as though he spoke in me.
I was in deep trepidation and at moment I felt there was nothing, before me except the blue sky; but within me a window opened through which I could see unearthly things. and hear unearthly words.

 

P. D. Ouspensky

 

The main objection to the theory of pure visualization is our thesis that the non-Euclidean axioms can be visualized just as rigorously if we adjust the concept of congruence. This thesis is based on the discovery that the normative function of visualization is not of visual but of logical origin and that the intuitive acceptance of certain axioms is based on conditions from which they follow logically, and which have previously been smuggled into the images. The axiom that the straight line is the shortest distance is highly intuitive only because we have adapted the concept of straightness to the system of Eucidean concepts. It is therefore necessary merely to change these conditions to gain a correspondingly intuitive and clear insight into different sets of axioms; this recognition strikes at the root of the intuitive priority of Euclidean geometry. Our solution of the problem is a denial of pure visualization, inasmuch as it denies to visualization a special extralogical compulsion and points out the purely logical and nonintuitive origin of the normative function. Since it asserts, however, the possibility of a visual representation of all geometries, it could be understood as an extension of pure visualization to all geometries. In that case the predicate "pure" is but an empty addition, since it denotes only the difference between experienced and imagined pictures, and we shall therefore discard the term "pure visualization." Instead we shall speak of the normative function of the thinking process, which can guide the pictorial elements of thinking into any logically permissible structure.

 

Hans Reichenbach

 

Despite the amount of suffering, pain, misery, sorrow and travail which can exist in life, the reason for existence is the same reason as one has to play a game—interest, contest, activity and possession. The truth of this assertion is established by an observation of the elements of games and then applying these elements to life itself.

 

L. Ron Hubbard

 

Despite the amount of suffering, pain, misery, sorrow and travail which can exist in life, the reason for existence is the same reason as one has to play a game — interest, contest, activity and possession. The truth of this assertion is established by an observation of the elements of games and then applying these elements to life itself.

 

L. Ron Hubbard