Spiked Math is a webcomic by a mathematician, with jokes about math, physics and the culture around them.
HN commenters link individual comics as related or favorite jokes, including ones about IQ test sequences, and praise the site's calculus captcha for comments.
> > A program is a piece of a text.
> But, a program is more than a text, it is a structure, parsed from text with the rules of the language .
Yes, you are right. By "text" I actually meant "term" or "abstract syntax tree".
> Execution of the program is when we give it some input and run it. So there would be similarly an input to proofs. Proof would need to be "proven correct" for EVERY valid input, that is what compiler does for programs, proving the result of the program must be of its declared result-type.
Not necessarily, not all programs require input and similarly not all proofs require input. But yes, for most cases you're right: Just as the program "output a prime number larger than <>" requires an input, so does a proof of the statement "there is a prime number larger than <>".
> But a proof which proves anything is not really a proof as said by someone, it corresponds to a non-halting program. So in this sense doesn't a proof ALWAYS require that we "run" it, to prove that it terminates, and thus is a valid proof actually?
Indeed, in general, running a proof and observing that it terminates is one way to ensure that it's a valid proof. However, all the proof systems (logics) used in mathematical practice correspond, under Curry–Howard correspondence, to programming languages in which any well-typed program terminates. (These programming languages are therefore in some sense quite impoverished; they are definitely not Turing-complete. However they are still…
We like to include sequences that appear on IQ tests. It’s always
been one of my goals to help people do these silly tests.
Yessssss! Those damn "IQ" questions:
http://spikedmath.com/062.html
We also get them with some regularity in Freenode's ##math. It's a FAQ. "Here's a list of numbers, what's the formula?" Sometimes we're able to send the person to Sloane's and be done with it.
Other times...
Many of the examples in The Pi Manifesto are wrong. See the rebuttal I posted last year:
http://tauday.com/tau-manifesto#sec-the_pi_manifesto_a_rebuttal
Indeed, the author of The Pi Manifesto essentially rebutted his own work in March of last year:
http://spikedmath.com/fact-005.html
One of the comics I read requires you to solve a simple calculus problem before you can comment, as a pseudo-captcha.
http://spikedmath.com/
Comic version: http://spikedmath.com/445.html
Follow up: http://mrburkemath.blogspot.com/2011/05/coffee-logic.html
related: http://spikedmath.com/334.html
(there's also a followup, at http://spikedmath.com/335.html )