A Quote by Hermann Weyl
Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind.
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Besides language and music, it [mathematics] is one of the primary manifestations of the free creative power of the human mind, and it is the universal organ for world understanding through theoretical construction. Mathematics must therefore remain an essential element of the knowledge and abilities which we have to teach, of the culture we have to transmit, to the next generation.
Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent to a pair of ears. Mathematics can only be "seen" with the "eyes of the mind". It is as if we had no sense of hearing, so that only someone able to sight read music would be able to appreciate its patterns and harmonies.
When we talk mathematics, we may be discussing a secondary language built on the primary language of the nervous system.
The question for the ultimate foundations and the ultimate meaning of mathematics remains open; we do not know in which direction it will find its final solution nor even whether a final objective answer can be expected at all. "Mathematizing" may well be a creative activity of man, like language or music, of primary originality, whose historical decisions defy complete objective rationalization.
May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.
Mathematics never reveals man to the degree, never expresses him in the way, that any other field of human endeavour does: the extent of the negation of man's corporeal self that mathematics achieves cannot be compared with anything. Whoever is interested in this subject I refer to my articles. Here I will say only that the world injected its patterns into human language at the very inception of that language; mathematics sleeps in every utterance, and can only be discovered, never invented.
One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics.
Our species is the only creative species, and it has only one creative instrument, the individual mind and spirit of man. Nothing was ever created by two men. There are no good collaborations, whether in music, in art, in poetry, in mathematics, in philosophy. Once the miracle of creation has taken place, the group can build and extend it, but the group never invents anything. The preciousness lies in the lonely mind of a man.
For all the sublimity of art, physics, music, mathematics, and other manifestations of human genius, everything depends on the mundane, frustrating, often debased vocation known as politics (and its most exacting subspecialty - statecraft). Because if we don't get politics right, everything else risks extinction.
Music is the language of God. God's language, music, is not like mathematics or geometry. It is a language of love. If we love music, that is enough.
When I dream about music, or think about music, by myself, I try to be as free as possible and allow my creative mind full reign.
Either mathematics is too big for the human mind or the human mind is more than a machine.
For loving, working, and creative people to throw off the yoke of power it is necessary to abolish power itself, not merely to make the yoke comfortable. Where some have power, others do not, and the two classes persist. A free society is where all have power-power over and responsibility for their own lives, power and reason to respect the lives of others. This is also a society without classes, a society of human beings, not rulers and the ruled.
I'm chasing a kind of language that can be unburdened by people's expectations. I think music is the primary model-how close can you get this language to be like music and communicate feeling at the base level in the same way a composition with no words communicates meaning? It might be impossible. Language is always burdened by thought. I'm just trying to get it so it can be like feeling.
We are spectacular splendid manifestations of life. We have language. We have affection. And finally, and perhaps best of all, we have music.
The primary imagination I hold to be the living power and prime agent of all human perception, and as a repetition in the finite mind of the eternal act of creation in the infinite I Am.
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