I remember my friend Johnny von Neumann used to say, 'with four parameters I can fit an elephant and with five I can make him wiggle his trunk.'

There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.

The most spectacular thing about Johnny [von Neumann] was not his power as a mathematician, which was great, or his insight and his clarity, but his rapidity; he was very, very fast. And like the modern computer, which no longer bothers to retrieve the logarithm of 11 from its memory (but, instead, computes the logarithm of 11 each time it is needed), Johnny didn't bother to remember things. He computed them. You asked him a question, and if he didn't know the answer, he thought for three seconds and would produce and answer.

Running overtime is the one unforgivable error a lecturer can make. After fifty minutes (one microcentury as von Neumann used to say) everybody's attention will turn elsewhere.

John von Neumann gave me an interesting idea: that you don't have to be responsible for the world that you're in. So I have developed a very powerful sense of social irresponsibility as a result of von Neumann's advice. It's made me a very happy man ever since. But it was von Neumann who put the seed in that grew into my active irresponsibility!

There are two kinds of people in the world: Johnny Von Neumann and the rest of us.

John von Neumann draws attention to what seemed to him a contrast. He remarked that for simple mechanisms, it is often easier to describe how they work than what they do, while for more complicated mechanisms, it is usually the other way around.

He [John von Neumann] had the invaluable faculty of being able to take the most difficult problem and separate it into its components, whereupon everything looked brlliantly simple.

All stable processes we shall predict. All unstable processes we shall control. Describing John von Neumann's aspiration for the application of computers sufficiently large to solve the problems of meteorology, despite the sensitivity of the weather to small perturbations.

... The approach of von Neumann and Connes to the use of non-commutative algebra in physics is naive, the situation is much more complicated.

...where were answers to the truly deep questions? Religion promised those, though always in vague terms, while retreating from one line in the sand to the next. Don't look past this boundary, they told Galileo, then Hutton, Darwin, Von Neumann, and Crick, always retreating with great dignity before the latest scientific advance, then drawing the next holy perimeter at the shadowy rim of knowledge.

Pascal and C are special-purpose languages for manipulating the registers and memory of a von Neumann-style computer.

Robert von Neumann taught painting, and when I finally got into a painting class of his, he reacted in much the same way.

Those two teachers [Kathleen Blackshear and Robert von Neumann] were just fantastic, I thought. They never directed you in a single direction, but they just encouraged you to think for yourself.

In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, "How many arbitrary parameters did you use for your calculations?" I thought for a moment about our cut-off procedures and said, "Four." He said, "I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk." With that, the conversation was over.

If you didn't know what you were trying to do, [Robert von Neumann] wouldn't say a word. He would just turn and walk away. So you very quickly learned to think that you'd better be attempting to do something in that painting class.

It was a figure painting class, where you had a model, and [Robert von Neumann ] would wander around and he'd come up behind someone and say, "Well, what are you trying to do?" And if you told him what you were trying to do, he would then proceed to discuss this with you and suggest things that you might look at and ways in which you could improve what you were attempting to do, etc - never worked on your painting, never touched your painting but talked extensively about what you were trying to do.

My greatest concern was what to call it. I thought of calling it 'information,' but the word was overly used, so I decided to call it 'uncertainty.' When I discussed it with John von Neumann, he had a better idea. Von Neumann told me, 'You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.'

Von Neumann languages do not have useful properties for reasoning about programs. Axiomatic and denotational semantics are precise tools for describing and understanding conventional programs, but they only talk about them and cannot alter their ungainly properties. Unlike von Neumann languages, the language of ordinary algebra is suitable both for stating its laws and for transforming an equation into its solution, all within the "language."

The two teachers that I had in the Art Institute who affected me the most were Kathleen Blackshear and Robert von Neumann; Kathleen Blackshear because she taught a class called design - I can't remember, design something, and in this class - it met once a week - we would do work centered around some theme, word or subject or technique or whatever, and bring it in for a three-hour discussion. And Kathleen was able, in watching and looking at our work, to direct us to all kinds of things which might relate to what we were trying to do, but she never attempted to tell us what to do.

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