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Jack Abbot

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The intelligence recedes, no more a tool of learning - because knowledge is based on experience - but a tool of the outside world it is deprived of knowing. It tries to contact other minds by telepathy; it becomes the Ancestor. Words and Numbers come to hold mystic significance: they were invented by some arcane magic older than man. The line between the word and the thing vanishes; the intervals of numbers in infinity collapse with infinity.

 
Jack Abbot

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I shall here present the view that numbers, even whole numbers, are words, parts of speech, and that mathematics is their grammar. Numbers were therefore invented by people in the same sense that language, both written and spoken, was invented. Grammar is also an invention. Words and numbers have no existence separate from the people who use them. Knowledge of mathematics is transmitted from one generation to another, and it changes in the same slow way that language changes. Continuity is provided by the process of oral or written transmission.

 
Carl Eckart
 

These primitive propositions ... suffice to deduce all the properties of the numbers that we shall meet in the sequel. There is, however, an infinity of systems which satisfy the five primitive propositions. ... All systems which satisfy the five primitive propositions are in one-to-one correspondence with the natural numbers. The natural numbers are what one obtains by abstraction from all these systems; in other words, the natural numbers are the system which has all the properties and only those properties listed in the five primitive propositions

 
Giuseppe Peano
 

The idea of infinity cannot be expressed in words or even described, but it can be apprehended through art, which makes infinity tangible. The absolute is only attainable through faith and in the creative act. (p39)

 
Andrei Tarkovsky
 

We can imagine that Thamus [or Amun: this is a reference to a discussion on the value of writing in Plato's Phaedrus] would also have pointed out to Gutenberg, as he did to Theuth, that the new invention would create a vast population of readers who "will receive a quantity of information without proper instruction... with the conceit of wisdom instead of real wisdom"; that reading, in other words, will compete with older forms of learning. This is yet another principle of technological change we may infer from the judgment of Thamus: new technologies compete with old ones — for time, for attention, for money, for prestige, but mostly for dominance of their world-view. This competition is implicit once we acknowledge that the medium contains an ideological bias. And it is a fierce competition, as only ideological competitions can be. It is not merely a matter of tool against tool — the alphabet attacking ideographic writing, the printing press attacking the illuminated manuscript, the photograph attacking the art of painting, television attacking the printed word. When media make war against each other, it is a case of world-views in collision.

 
Neil Postman
 

Numbers instill a feeling for the lie of the land, and furnish grist for the mathematical mill that is the physicist's principal tool.

 
Hans Christian von Baeyer
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