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The Unparalleled Genius of John von Neumann (2019)

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Re: The Unparalleled Genius of John von Neumann (2019)

#31

Post by 1cvmask »

Regarding the coining of entropy is just an example of the creative genius of Von Neumann:

When Shannon first derived his famous formula for information, he asked von Neumann what he should call it and von Neumann replied “You should call it entropy for two reasons: first because that is what the formula is in statistical mechanises but second and more important, as nobody knows what entropy is, whenever you use the term you will always be at an advantage!

http://www.spatialcomplexity.info/what-von-neumann-said-to-s...

https://en.wikipedia.org/wiki/Entropy_(information_theory)

Re: The Unparalleled Genius of John von Neumann (2019)

#32

Post by Koshkin »

adamnemecek wrote: post #4
hintymad wrote: post #3

I often use von Neumann's quote, "Young man, in mathematics you don't understand things. You just get used to them.", to console myself when I have to read a math book multiple times to really understand something. The quote also has truth in it. I had no problem accepting that 0! = 1 only because I learnt that fact early in school. However, I struggled quite a bit to accept that span({}) = {0}, even though it is not…

I wonder if e.g. using constructive math would make things easier since every step of a constructive proof is understandable.

My understanding is that since any mathematical proof can (in principle) be reduced to manipulation with formal objects (symbols), it’s always “constructive.”

Re: The Unparalleled Genius of John von Neumann (2019)

#33

Post by hintymad »

ZephyrBlu wrote: post #14
hintymad wrote: post #3

I often use von Neumann's quote, "Young man, in mathematics you don't understand things. You just get used to them.", to console myself when I have to read a math book multiple times to really understand something. The quote also has truth in it. I had no problem accepting that 0! = 1 only because I learnt that fact early in school. However, I struggled quite a bit to accept that span({}) = {0}, even though it is not…

I've never seen that quote before, but it feels very human. I feel like there's an intuition which comes along with learning things. Or maybe learning is simply developing intuition. At some point things somehow just make sense in your mind because you've built up an intuition of how it works.

I learned it the hard way, as I hit a wall when taking a course on abstract algebra, that the only path to truly understanding college-level math is building solid intuition. Otherwise, the sheer number of definitions and theorems will just be overwhelming. Of course, intuition is as critical for pre-college math. It's just that we somehow get the intuition naturally probably because we get to experience all kinds of examples on a daily basis to hone our intuition unconsciously.

Re: The Unparalleled Genius of John von Neumann (2019)

#34

Post by Rochus »

djmips wrote: post #16
Rochus wrote: post #13

> von Neumann proposed a description for a computer architecture now known as the von Neumann architecture Well, he actually described an already existing design by Eckert and Mauchly under his name and this paper was illegally disclosed. For the ones interested in this and other fascinating stories about ENIAC, here is a good book: https://www.amazon.com/Eniac-Triumphs-Tragedies-Worlds-Compu... ; worth reading is al…

True but on the other hand, he kind of made computers 'open source'

> he kind of made computers 'open source'

The only "positive" (depeding on perspective) effect of his illegal and morally questionable action was that the patent was declared null and void due to the novelty-damaging effect of his report, among other issues supporting this outcome. The computers however did not become more "open source" because of this, just cheaper.

Re: The Unparalleled Genius of John von Neumann (2019)

#35

Post by pbsd »

inasio wrote: post #15
aeontech wrote: post #6

And he was only -51-, correction, 53 when he passed… One has to wonder what more he would have accomplished had he lived another 30 years or more. As an aside, are there many pure research institutes left? It seems like academic life is now mostly spent chasing grants and managing teaching load, and very very few people get to do pure research.

I heard or read a story from Freeman Dyson about a somewhat legendary conference where von Neumann was to present his version of Hilbert's problems, presumably about the new computing age, I think at the IAS. It was highly anticipated, but Dyson and everybody else present were shocked because von Neumann was in a state of advanced mental decline when he presented it, and people there agreed to pretend it hadn't happe…

This is probably the story in page 220 of [1], beginning at "Von Neumann got into trouble at the end of his life because he was really a frog but everyone expected him to fly like a bird.".

[1] http://www.uvm.edu/pdodds/files/papers/others/2009/dyson2009...

Re: The Unparalleled Genius of John von Neumann (2019)

#36

Post by sellyme »

hintymad wrote: post #3

I often use von Neumann's quote, "Young man, in mathematics you don't understand things. You just get used to them.", to console myself when I have to read a math book multiple times to really understand something. The quote also has truth in it. I had no problem accepting that 0! = 1 only because I learnt that fact early in school. However, I struggled quite a bit to accept that span({}) = {0}, even though it is not…

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

Not quite in the same weight class as von Neumann, but Matt Parker's "There's a trick for dealing with that in mathematics, called 'not really worrying about it'" when discussing results that don't mesh with our intuitive understanding is another nice one.

Re: The Unparalleled Genius of John von Neumann (2019)

#37

Post by hintymad »

Koshkin wrote: post #32
adamnemecek wrote: post #4

Earlier quoted context omitted.

I wonder if e.g. using constructive math would make things easier since every step of a constructive proof is understandable.

My understanding is that since any mathematical proof can (in principle) be reduced to manipulation with formal objects (symbols), it’s always “constructive.”

Not really. Check out the proof of Hilbert's Nullstellensatz. He got tons of criticism for proving the existence of a relation without constructing that relation.

Re: The Unparalleled Genius of John von Neumann (2019)

#38

Post by Groxx »

pointedset wrote: post #10
hintymad wrote: post #3

I often use von Neumann's quote, "Young man, in mathematics you don't understand things. You just get used to them.", to console myself when I have to read a math book multiple times to really understand something. The quote also has truth in it. I had no problem accepting that 0! = 1 only because I learnt that fact early in school. However, I struggled quite a bit to accept that span({}) = {0}, even though it is not…

Yes, those two facts about zero/empty cases (and so many more) are definitely related, and this class of facts is one of my favourites! Usually, if you're dealing with something algebraic in flavour (which is a very vague concept, sorry), there will be a sensible way to define the zero/empty case. This is often a good test of whether you have a uniform concept that works for all n without corner cases. It almost irri…

Yeah, it took a while to sink into my head that many of these "wait, why is span({}) = {0}?" kinds of cases have answers that sum up as "because anything else means other rules are inconsistent, and the whole thing is either less useful or useless". It's "arbitrary", but it's either the only useful option, or sometimes a simple(st) one of many.

Even just one number theory course helped a lot, since it brought that kind of consistency into its own concept, where [this set of rules] forms a ring, and [this set] forms a field, etc.

Re: The Unparalleled Genius of John von Neumann (2019)

#39

Post by Frost1x »

Guthur wrote: post #26

I think John von Neumann was a genius but I also think that at the time there was also confluence of great minds across mathematics and science in general which likely feed into and accelerated the advancements. Maybe it's still happening but we no longer hear the names, though potentially it was also just one of those alignments of possibilities.

I often wonder if there are points in human understanding where there is an opportunistic amount of existing knowledge, current exploration of knowledge, and sets of ideas floating around that lead to these sorts of surges of shared ideas and principles in disciplines.

While it's no doubt from accounts Nuemann was brilliant, I've observed other brilliant people who I feel could be ground breaking minds given the right set of circumstances.

A bit of nature vs nurture, environment vs natural talent. I feel as though humanity often has the Neumann, Einstein, Euler, Ramanujan, etc. but need the right set of circumstances to really shine through. They could just be outliers but when you see a collection of these sort of minds during a time period, I can't help but think there is an environmental factor enabling it. Even people as brilliant as Newton had some equivilance in Leibnez with the invention of calculus (Newton was clearly above and beyond though).

Re: The Unparalleled Genius of John von Neumann (2019)

#40

Post by sellyme »

Guthur wrote: post #26

I think John von Neumann was a genius but I also think that at the time there was also confluence of great minds across mathematics and science in general which likely feed into and accelerated the advancements. Maybe it's still happening but we no longer hear the names, though potentially it was also just one of those alignments of possibilities.

> Maybe it's still happening but we no longer hear the names

We do hear the names, it's just difficult to recognise which ones are going to be the names that echo for generations.

I would be completely unsurprised if articles like this were written about Tao in 50 years' time.

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