John Von Neumann citáty

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John Von Neumann

Datum narození: 28. prosinec 1903
Datum úmrtí: 8. únor 1957

John von Neumann byl maďarský matematik židovského původu, který značnou měrou přispel k oborům jako jsou kvantová fyzika, funkcionální analýza, teorie množin, ekonomika, informatika, numerická analýza, hydrodynamika, statistika, a mnoho dalších matematických disciplín.

Citáty John Von Neumann

„Věda se nesnaží o vysvětlení, stěží se pokouší interpretovat, převážně sestavuje modely. Modelem se myslí matematický konstrukt, který spolu s jistou verbální interpretací popisuje pozorované jevy.“

„If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.“

„Young man, in mathematics you don't understand things. You just get used to them.“

„It is just as foolish to complain that people are selfish and treacherous as it is to complain that the magnetic field does not increase unless the electric field has a curl. Both are laws of nature.“

„There's no sense in being precise when you don't even know what you're talking about“

„Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.“

„The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work - that is correctly to describe phenomena from a reasonably wide area. Furthermore, it must satisfy certain esthetic criteria - that is, in relation to how much it describes, it must be rather simple.“

„The other line of argument, which leads to the opposite conclusion, arises from looking at artificial automata. Everyone knows that a machine tool is more complicated than the elements which can be made with it, and that, generally speaking, an automaton A, which can make an automaton B, must contain a complete description of B, and also rules on how to behave while effecting the synthesis. So, one gets a very strong impression that complication, or productive potentiality in an organization, is degenerative, that an organization which synthesizes something is necessarily more complicated, of a higher order, than the organization it synthesizes. This conclusion, arrived at by considering artificial automaton, is clearly opposite to our early conclusion, arrived at by considering living organisms.“ Theory Of Self Reproducing Automata

„Furthermore, it's equally evident that what goes on is actually one degree better than self-reproduction, for organisms appear to have gotten more elaborate in the course of time. Today's organisms are phylogenetically descended from others which were vastly simpler than they are, so much simpler, in fact, that it's inconceivable, how any kind of description of the latter, complex organism could have existed in the earlier one. It's not easy to imagine in what sense a gene, which is probably a low order affair, can contain a description of the human being which will come from it. But in this case you can say that since the gene has its effect only within another human organism, it probably need not contain a complete description of what is to happen, but only a few cues for a few alternatives. However, this is not so in phylogenetic evolution. That starts from simple entities, surrounded by an unliving amorphous milieu, and produce, something more complicated. Evidently, these organisms have the ability to produce something more complicated than themselves.“ Theory Of Self Reproducing Automata

„Anybody who looks at living organisms knows perfectly well that they can produce other organisms like themselves. This is their normal function, they wouldn't exist if they didn't do this, and it's not plausible that this is the reason why they abound in the world. In other words, living organisms are very complicated aggregations of elementary parts, and by any reasonable theory of probability or thermodynamics highly improbable. That they should occur in the world at all is a miracle of the first magnitude; the only thing which removes, or mitigates, this miracle is that they reproduce themselves. Therefore, if by any peculiar accident there should ever be one of them, from there on the rules of probability do not apply, and there will be many of them, at least if the milieu is reasonable. But a reasonable milieu is already a thermodynamically much less improbable thing. So, the operations of probability somehow leave a loophole at this point, and it is by the process of self-reproduction that they are pierced.“ Theory Of Self Reproducing Automata

„Kurt Gödel's achievement in modern logic is singular and monumental – indeed it is more than a monument, it is a landmark which will remain visible far in space and time.... The subject of logic has certainly completely changed its nature and possibilities with Gödel's achievement." —John von Neumann“

„In any conceivable method ever invented by man, an automaton which produces an object by copying a pattern, will go first from the pattern to a description to the object. It first abstracts what the thing is like, and then carries it out. It's therefore simpler not to extract from a real object its definition, but to start from the definition.“ Theory Of Self Reproducing Automata

„In this sense, an object is of the highest degree of complexity if it can do very difficult and involved things.“ Theory Of Self Reproducing Automata

„A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so.“

„An element which stimulates itself will hold a stimulus indefinitely.“

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