[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. (David Hilbert)

[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.

David Hilbert

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approach beyond geometry idea intuition intuitive large manifold mathematics outline possible presentation proof purpose should survey thus visual wealth facts

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The need for a fundamentally different approach to the study of physical processes at the molecular level motivated the development of relevant statistical methods, which turned out to be applicable not only to the study of molecular processes (statistical mechanics), but to a host of other areas such as the actuarial profession, design of large telephone exchanges, and the like. In statistical methods, specific manifestations of microscopic entities (molecules, individual telephone sites, etc.) are replaced with their statistical averages, which are connected with appropriate macroscopic variables. The role played in Newtonian mechanics by the calculus, which involves no uncertainty, is replaced in statistical mechanics by probability theory, a theory whose very purpose is to capture uncertainty of a certain type.

George Klir

Today every child knows what Merz is. But what is 'i'? I is the middle vowel of the alphabet and the designation for the consequence of Merz in relation to an intensive apprehension of the art form. For the shaping of the work of art Merz uses large ready-made complexes that count as material, to shorten as much as possible the path leading from the intuition to the actualization (Sichtbarmachung) of the artistic idea, so as to avoid heat loss through friction. i defines this path as o (i setzt diesen Weg = null). Idea, material, and work of art are the same. i apprehends the work of art in nature. Here the artistic shaping is the recognition of rhythm and expression in a part of nature. Thus, no loss through friction i. e., no disturbing distraction during creation occurs here.

Kurt Schwitters

You can imagine that it is not easy to describe this modern vision of the nature of things in any manner intelligible to those who have not our advantages. There is much in this vision which will remind you of your mystics; yet between them and us there is far more difference than similarity, in respect both of the matter and the manner of our thought. For while they are confident that the cosmos is perfect, we are sure only that it is very beautiful. While they pass to their conclusion without the aid of intellect, we have used that staff every step of the way. Thus, even when in respect of conclusions we agree with your mystics rather than your plodding intellectuals, in respect of method we applaud most your intellectuals; for they scorned to deceive themselves with comfortable fantasies.

Olaf Stapledon

I believe that it is possible by means of horizontal and vertical lines, constructed 'consciously' but not 'calculating', guided by a higher intuition and brought to harmony and rhythm – I believe that these fundamental aesthetic shapes – where necessary supplemented by lines in other directions or curved lines, make it possible to arrive at a work of art which is as strong as it is true. For anyone who sees more deeply, there is nothing vague about this; it is only vague for the superficial observer of nature. And 'chance' must be as far removed as 'calculation'. And for the rest it seems to me that it is necessary to keep breaking off the horizontal or vertical line: for if these directions were not countered by others, they would themselves come to signify something 'specific' and thus human.

Piet Mondrian

WHAT HAPPENS AFTER DEATH? When a human soul goes out of the body, some great mystery happens. For if it is guilty of sins, then there come hordes of demons, evil angels and dark forces, take that soul and drag it to their side. No one should be surprised at that, because if a man surrendered and fell prey to them while still alive in this world, will not they have even greater control over him and enslave him when he departs from this world? As for the other, the better part of people, something different happens to them. There are Angels around the holy servants of God in this life; the holy spirits surround them and protect them; and when their souls are separated from the body, the choir of Angels welcomes them into their fellowship, into a bright life, and thus leads them to the Lord.

Macarius of Egypt