You insist that there is something a machine cannot do. If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.
John Von NeumannRead
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.
Interpretation
Scientific models aim to describe phenomena rather than explain them in absolute terms.
In this quote, John Von Neumann emphasizes that the primary function of scientific models is not to provide explanations or interpretations of the underlying reality, but to effectively describe and predict observed phenomena. He highlights that the value of a mathematical model is determined by its predictive power and its ability to work across various scenarios, thus illustrating the pragmatic nature of scientific inquiry.
In practice
In a scientific conference discussing the role of mathematics in science.
You insist that there is something a machine cannot do. If you tell me precisely what it is a machine cannot do, then I can always make a machine which will do just that.
Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.
Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number - there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method.
It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in 5 years.
Technological possibilities are irresistible to man. If man can go to the moon, he will. If he can control the climate, he will.
I would like to make a confession which may seem immoral: I do not believe absolutely in Hilbert space any more.
Of course, we would love to know more about the exact moment of Big Bang, but interposing an outside intelligence does nothing to add to that knowledge, as we still know nothing about the creation of that intelligence.
Testing shows the presence, not the absence of bugs.
The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.
There are no miracles in agricultural production.
A black hole really is an object with very rich structure, just like Earth has a rich structure of mountains, valleys, oceans, and so forth. Its warped space whirls around the central singularity like air in a tornado.
For me, arguably the story of telomeres and telomerase began thousands of years ago, in the cornfields of the Maya highlands of Central America.
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