The Unparalleled Genius of John von Neumann (2019)
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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)
#2Who doesn’t like being greeted by Medium’s dickbar?
Re: The Unparalleled Genius of John von Neumann (2019)
#3I 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 that different from 0!=1 and I knew multiple explanations. It seems the later one learns a new concept, the longer it takes to accept it.
Re: The Unparalleled Genius of John von Neumann (2019)
#4I 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.
Re: The Unparalleled Genius of John von Neumann (2019)
#5OT but when I open an article like this in Firefox's reader view, it often displays each image twice, first a blurry version and then the actual image. This is frustrating when I want to print a long article from reader view as I have to go through and delete all the blurry duplicate images first using developer tools (given that I don't want to waste ink or paper). Is there a better way I can fix or work around this?
I'm also interested because, as my username implies, I'm learning web dev and I would like to ensure if possible that any websites I make don't have this issue for people wanting to print pages from them.
Re: The Unparalleled Genius of John von Neumann (2019)
#6And 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.
Re: The Unparalleled Genius of John von Neumann (2019)
#7First the article about Dirac and Feynman, and now this article about von Neumann. Cantor's Paradise has been a revelation to me.
It reminds me of my teenage years when I was a young student of mathematics and voraciously devoured the MacTutor History of Mathematics archive: https://mathshistory.st-andrews.ac.uk/
Thank you, Jorgen Veisdal.
My only appeal to you is that you not put these articles behind the Medium paywall. But if you are earning significant income via Medium, I retract my appeal.
Re: The Unparalleled Genius of John von Neumann (2019)
#8It staggers me that in an age of incredible innovation and technology- we still have no idea what biologically separates a man like this from the rest of us.
I'd like to take the idyllic position of (somewhat irresponsibly) hoping that some level of genius can be fostered and created in anyone from a young age.. But when I read articles like this I feel the compulsive need to sit back in my chair and ponder just how much more primitive my mind is in comparison to a man like John's.
Re: The Unparalleled Genius of John von Neumann (2019)
#9"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."
— John von Neumann
Re: The Unparalleled Genius of John von Neumann (2019)
#10I 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 irritates me when I read a book or a paper and they say that the zero/empty case is "by convention". I almost want to yell, "no! it's because that's how you make the definition uniform!"
Addition is usually defined as a binary operation, a+b, but really it should be defined as an n-ary operation; associativity tells us that doing "two layers" of addition should boil down to doing a single layer of addition on the concatenated list of operands. That forces 0-ary addition to be zero, which can always be added to the list of operands without affecting the result.
Something similar happens with empty products (which explains the factorial), empty spans, etc. In all cases, the trick is to figure out, what is the equivalent of associativity? What "syntactic" operations on the inputs (for example, concatenating a list of lists of operands) correspond to operations on the outputs (you can get the total sum by first computing partial sums)?
A fun puzzle, if you enjoy this kind of thing: what's the determinant of the 0x0 matrix (over your favourite field or ring)? For all (square) sizes, the determinant of the zero matrix is zero, but the determinant of the identity matrix is one, and the 0x0 matrix is kind of both. So which pattern should win? Which one is stronger? I know my own answer ;)