throwaway080383
Joined 8 years ago
Joined 8 years ago
Maybe I'm paranoid, but isn't it obvious how the whole Home Speaker story ends? "We're not spying on you, we're learning your behaviors to offer a better experience!"
How many Foxconn man-hours does it take to produce an iPhone, and what is the average hourly wage?
My point is that this is very similar to how elliptic curves are being counted here.
Fix any odd positive integer x, and consider its "twists" x{d}, which for positive d I define to be x*2^d. Every integer is of the form x{d} for a unique choice of x and d. Now, for fixed N, if I consider all "twists" for which d<N, the proportion which are even is (N-1)/N. Thus, as N tends to infinity, the proportion tends to 1.
If you only look at twists where |d| < N, you can ask "What proportion of these are rank zero, rank one, rank two, ...?" The Theorem in the paper is that as you let N go off to infinity, these proportions tend to 1/2, 1/2, 0, 0, 0, ... respectively.
Here's the thing: this does not correspond to a measure on the set of rational elliptic curves, and indeed, there is no reasonable way to define a uniform probability measure on a countable set. Consequently, statements like "half of all elliptic curves..." are kind of misleading and meaningless.
I do have to admit, it did not occur to me that the work week would still effectively enforce an "ordering" on longitudes which somehow takes the beauty out of it.
That is, I like the idea in principle, but I know it'll never happen.