Stephan Wolfram: 100 Years Since Principia Mathematica
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Stephan Wolfram: 100 Years Since Principia Mathematica
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Re: Stephan Wolfram: 100 Years Since Principia Mathematica
#2In case you're interested, about halfway down is the usually quoted result (*110.643) that 1+1=2. I'm often asked why it took so long (it's over 80 pages into volume 2) to prove something so trivially, and obviously true, and recently I've come up with an example that demonstrates the idea.
I'll try to write about it later when I get a bit more time.
Re: Stephan Wolfram: 100 Years Since Principia Mathematica
#3In case you're interested, about halfway down is the usually quoted result (*110.643) that 1+1=2. I'm often asked why it took so long (it's over 80 pages into volume 2) to prove something so trivially, and obviously true, and recently I've come up with an example that demonstrates the idea. I'll try to write about it later when I get a bit more time.
Amusing fact is it didn't take long at all, compared to some later approaches ;) http://mathoverflow.net/questions/14356/bourbakis-epsilon-ca...
And a twist you might find worthy a mention in your forthcoming essay, http://mathoverflow.net/questions/40920/what-if-current-foun...
Re: Stephan Wolfram: 100 Years Since Principia Mathematica
#4There's a Principia Mathematica anniversary symposium at Trinity College, Cambridge this weekend.
Re: Stephan Wolfram: 100 Years Since Principia Mathematica
#5In case you're interested, about halfway down is the usually quoted result (*110.643) that 1+1=2. I'm often asked why it took so long (it's over 80 pages into volume 2) to prove something so trivially, and obviously true, and recently I've come up with an example that demonstrates the idea. I'll try to write about it later when I get a bit more time.
An interesting project that is developing an updated version of this idea is Metamath: http://us.metamath.org/index.html
Re: Stephan Wolfram: 100 Years Since Principia Mathematica
#6First:
In 1903, he published The Principles of Mathematics: Volume 1 (no volume 2 was ever published) [...]
[...] it did not hurt the whole impression that it took until more than 80 pages into volume 2 [...]Re: Stephan Wolfram: 100 Years Since Principia Mathematica
#7First: In 1903, he published The Principles of Mathematics: Volume 1 (no volume 2 was ever published) [...] Later: [...] it did not hurt the whole impression that it took until more than 80 pages into volume 2 [...]
Volume 2 of Principia Mathematica, not Principles of Mathematics.
Re: Stephan Wolfram: 100 Years Since Principia Mathematica
#8It's interesting that Wolfram makes a quick foray into computer science to bash type systems. (I think he couldn't be more wrong)
"To resolve this, Russell introduced what is often viewed as his most original contribution to mathematical logic: his theory of types—which in essence tries to distinguish between sets, sets of sets, etc. by considering them to be of different “types”, and then restricts how they can be combined. I must say that I consider types to be something of a hack. And indeed I have always felt that the related idea of “data types” has very much served to hold up the long-term development of programming languages. (Mathematica, for example, gets great flexibility precisely from avoiding the use of types.)"
Re: Stephan Wolfram: 100 Years Since Principia Mathematica
#9There's a Principia Mathematica anniversary symposium at Trinity College, Cambridge this weekend. http://www.srcf.ucam.org/principia/
Sorry I miss clicked and downvoted you instead of upvoting; the interface prevents me from rectifying this error.
Re: Stephan Wolfram: 100 Years Since Principia Mathematica
#10In case you're interested, about halfway down is the usually quoted result (*110.643) that 1+1=2. I'm often asked why it took so long (it's over 80 pages into volume 2) to prove something so trivially, and obviously true, and recently I've come up with an example that demonstrates the idea. I'll try to write about it later when I get a bit more time.
An interesting project that is developing an updated version of this idea is Metamath: http://us.metamath.org/index.html
That is interesting - I think the idea that looms over the whole essay is that we have computers that do logic and can fit those logical operations together, we should be able to give a computer some basic axioms and see what theorems it can construct. Et voila!, there it is. Mention of such a project would have fit the essay well.