21–30 of 38 posts
I'm impressed it took Wolfram until the third paragraph to mention A New Kind of Science .
The post by Wolfram is a great discussion of logic and the philosophy of mathematics throughout the 20th century. Yet the top comment on HN is a snark, tribal bashing of the author.
Earlier quoted context omitted.
The post by Wolfram is a great discussion of logic and the philosophy of mathematics throughout the 20th century. Yet the top comment on HN is a snark, tribal bashing of the author.
These snarks appear because of Wolfram's writing style, he comes off as a kind of Steve Jobs who he himself is the product he is selling. Though at least this one is lighter than usual.
That's the whole point. If you read it without thinking "Wolfram wrote this therefore it will be self-centered", then it sounds perfectly fine. The GP's snark was merely appealing to people's confirmation bias. It's a high-level version of that high-school classic: "I'll pick on that kid to show I'm part of the group".
Besides, it's depressingly ironic that a community producing a deluge of "How my startup achieved X in Y months" complains about this post being self-centered.
Read it! It's a good essay!
Earlier quoted context omitted.
These snarks appear because of Wolfram's writing style, he comes off as a kind of Steve Jobs who he himself is the product he is selling. Though at least this one is lighter than usual.
Though at least this one is lighter than usual. That's the whole point. If you read it without thinking "Wolfram wrote this therefore it will be self-centered", then it sounds perfectly fine . The GP's snark was merely appealing to people's confirmation bias. It's a high-level version of that high-school classic: "I'll pick on that kid to show I'm part of the group". Besides, it's depressingly ironic that a community…
Your analogy works, except its Wolfram who does the bullying, not the other way around.
It'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 c…
It is a strange comment. The type theories used in programming languages, certainly in those based on the λ-cube, descend from simple type theory (via the simply-typed λ-calculus), which Russell discarded in favour of his ramified theory of types. I also wonder why Wolfram, originally a mathematician, doesn't even mention the Curry-Howard correspondence, which seems to me a fairly important result linking mathematics…
I also like this page as a more basic introduction to type systems: http://blogs.perl.org/users/ovid/2010/08/what-to-know-before...
Earlier quoted context omitted.
These snarks appear because of Wolfram's writing style, he comes off as a kind of Steve Jobs who he himself is the product he is selling. Though at least this one is lighter than usual.
Though at least this one is lighter than usual. That's the whole point. If you read it without thinking "Wolfram wrote this therefore it will be self-centered", then it sounds perfectly fine . The GP's snark was merely appealing to people's confirmation bias. It's a high-level version of that high-school classic: "I'll pick on that kid to show I'm part of the group". Besides, it's depressingly ironic that a community…
But Wolfram seems incapable of talking about any subject without shoehorning in some reference to his own works. Even when expected, it's a jarring, unnecessary interruption; a wild swing from a reasonably interesting article on mathematical history to unabashed self-promotion.
The snark wasn't intended as an offering to Hacker New group-think, but rather borne out of a genuine frustration at Wolfram's style of writing. I find it very difficult to read anything he says, because I'm continually awaiting that moment when he will pause, smile cheesily at the proverbial camera, and explain how amazing his products are.
In 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.
Please do... In my freshman year of college, I asked my real analysis professor why 1+1=2 and he failed to provide an edifying explanation. He did, however, commend me for asking -- I think it earned me some brownie points, which I redeemed by asking for extra clarification on more course-related topics later in the quarter. Anyway, it's always bothered me so if I can learn something about it then I would love to!
If we use Dedekind's recursive definition of addition, and the definitions 1=S(0) and 2=S(S(0)), then:
S(0) + S(0) = S(S(0)+0) = S(S(0))
I know the computer proof assistant Isabelle/HOL, inspired by the Principia Mathematica, can prove simple theorems about arithmetic using a "rewrite" system similar to what I've done above.
It'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 c…
It is a strange comment. The type theories used in programming languages, certainly in those based on the λ-cube, descend from simple type theory (via the simply-typed λ-calculus), which Russell discarded in favour of his ramified theory of types. I also wonder why Wolfram, originally a mathematician, doesn't even mention the Curry-Howard correspondence, which seems to me a fairly important result linking mathematics…
In the 1920s Frank Ramsey proved that the theory of ramified types + "The Axiom of Reducibility" is equivalent to the theory of simple types: http://en.wikipedia.org/wiki/Type_theory#Simple_theory_of_ty...
The history I've heard is that ramified types were abandoned after this, since simple type theory is easier and has the same expressive power.
I see this almost happening daily on HN with the huge interest in new languages especially functional languages. By almost I mean these are mostly descendants of either Lisp or ML and they are based on the same logic. I'm not sure if you would gain anything by hard-wiring a language into one of the other multitude of axiomatic systems. It would be an intellectual challenge to first select an appropriate system, and then construct a useful language. And it would be hard to recruit people to use it enough to provide useful feedback.
Earlier quoted context omitted.
It is a strange comment. The type theories used in programming languages, certainly in those based on the λ-cube, descend from simple type theory (via the simply-typed λ-calculus), which Russell discarded in favour of his ramified theory of types. I also wonder why Wolfram, originally a mathematician, doesn't even mention the Curry-Howard correspondence, which seems to me a fairly important result linking mathematics…
>No one uses ramified type theory these days, at least not that I am aware In the 1920s Frank Ramsey proved that the theory of ramified types + "The Axiom of Reducibility" is equivalent to the theory of simple types: http://en.wikipedia.org/wiki/Type_theory#Simple_theory_of_ty... The history I've heard is that ramified types were abandoned after this, since simple type theory is easier and has the same expressive pow…
José Ferreirós in The Princeton Companion to Mathematics mentions his name as well, albeit without much detail. Chwistek seems a fascinating character: like his contemporary Witkacy, he was an artist as well as a logician, and according to the biography of Alfred Tarski by the Fefermans [2], was appointed to a professorship at Lvov in 1930 which Tarski was also in the running for; apparently a letter of recommendation from Russell was the decisive factor (see p. 67 of the aforementioned).
Bernard Linsky seems to have written a chapter on Chwistek and type theory in The Golden Age of Polish Philosophy. You can read the first page [3] but I haven't been able to find the entire thing online.
[1] http://en.wikipedia.org/wiki/Leon_Chwistek
[2] http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=052...
I'm impressed it took Wolfram until the third paragraph to mention A New Kind of Science .
I also thought it was kind of a dick move to wait until the end to admit that he didn't understand the symbols in principia_1b1.jpg. This is actually a pet peeve of mine in mathematics writing in general, introducing ambiguity and not resolving it until several pages or paragraphs later. It's really alienating. =(