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sbi | 12 years ago | on: Firefox 23 is available

I see that Mozilla is now signing hashes of Firefox downloads with a 4096-bit RSA key. But the key used to sign firefox-23.0.tar.bz2 (id 0x057CC3EB15A0A4BC) is only self-signed and was created three weeks ago. It's not on pgp.mit.edu. Is there any actual way to "validate the authenticity of these keys in an out-of-band manner" as the KEYS file recommends?

sbi | 13 years ago | on: You are dangerously bad at cryptography

Two notes: factoring polynomials over finite fields isn't hard (look up the Berlekamp algorithm or Cantor-Zassenhaus for starters). Second, I believe the system you've described doesn't satisfy your property (b). Quantities such as M[1]C[0] - C[1]M[0] + M[0]^2 and C[1]M[2] - C[2]M[1] + M[1]^2 - M[0]M[2] are congruent to 0 mod p; compute them over the integers and then take the gcd. By computing enough of these you should recover the prime p. Once you have p, recovering z is very easy (e.g., take the gcd of C and C'-M, where C' is the derivative of C).

sbi | 13 years ago | on: How many draws of a random number [0,1] are needed to sum to 1

This is a pretty solution, and it gives you the probability generating function for free: by some power series manipulation, the pgf of the number of draws needed is g(z) = 1 + (z-1)*exp(z). So you can show fairly easily that Var(draws needed) = 3e - e^2, for example ...

sbi | 13 years ago | on: The Mathematical Hacker

I don't want to put words in hazov's mouth here but Gödel is a total nonsequitor here. This thread isn't about formal set theory. The question is not whether mathematics can be axiomatized in a satisfactory way in first-order logic, but what it is mathematicians study. Since not everything in mathematics is obviously related to geometry or numbers, it is hard to write a satisfactory definition; just look at the difficulty that, say, Wikipedians have had trying to cook up a canonical one. But saying that mathematics is just about rigor or abstract structures makes just about everything mathematical. Not all scholars are mathematicians. And if mathematicians just study abstract structures, what's so special about, say, elliptic PDE, or Fourier analysis, or commutative algebra?

sbi | 13 years ago | on: The Mathematical Hacker

I respectfully beg to differ that "mathematics isn't about numbers or even proofs." Why are the math books on my shelves full of numbers and proofs? What was it I was wasting my time on in graduate school? This sort of definition (really a non-definition) is so vague that it robs mathematics of its character. Is mathematics important merely because many people believe that mathematicians are clever?

sbi | 13 years ago | on: The Mathematical Hacker

Well,

     lround(exp(lgamma(...)))
is just about the worst way to use lgamma. If long ints are signed 64 bit integers, then the largest factorial you can store is 20!. You might as well look it up in an array. But you frequently need ratios of factorials (and values of the gamma function more generally) when doing statistical computing and lgamma is invaluable.

sbi | 13 years ago | on: Why math is painful to read

This is an old chestnut. Mathematical notation is terse because mathematics doesn't consist entirely of notation! Look at any book or research paper; you'll find a great deal of text surrounding equations. Comparing this to code is nonsensical. Unless you're reading something in WEB, you are much more likely to encounter code than comments. There are certainly some unfortunate conventions and cruft in mathematics, but every generation of mathematicians rewrites in part what it inherited from its forebears.

sbi | 13 years ago | on: Wind Map

The Euler characteristic of a compact orientable genus g surface X is nonzero if g is not 1 (the general formula is 2-2g), so the Euler class e(TX) of the tangent bundle TX of X is nonzero. This implies that TX cannot have a continuous nowhere-vanishing section. If it did, e(TX) would be 0. The single-holed torus is the only orientable compact surface that possesses a continuous nonvanishing vector field.

sbi | 13 years ago | on: Are functional languages inherently slow?

How relevant are numerical benchmarks when comparing languages? In practice you'll probably use BLAS, LAPACK, etc. for numerical computing and get on with it; you're unlikely to write code that is both faster and numerically stable.

sbi | 13 years ago | on: Ubuntu is coming back to Dell Laptops

On my E520, I was getting about 2 to 2.5 hours under similar conditions (I have the 6 cell battery, however) in Debian; under Windows I get 4-5 hours.

sbi | 13 years ago | on: Ubuntu is coming back to Dell Laptops

What is the battery life going to be like? I grudgingly installed Windows 7 on my (Lenovo) laptop after using Unix exclusively for 15 years simply because the battery lasts twice as long on Windows.

For what it's worth, I bought a Dell Inspiron Mini 10v with Ubuntu Hardy preinstalled 2.5 years ago. It didn't suspend/resume properly and video out was flaky. It died after two years of use (with strange electrical problems). I don't think I'll buy a Dell in the future.

sbi | 14 years ago | on: C# to take a breaking change in version 5

Thanks for pointing that out. I would have guessed that the original form would desugar to

  map(lambda i: (lambda: i), xrange(10))
but apparently it doesn't.
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