On Facebook, in response to this article that's been circulating today for some inscrutable reason, one A. Melaragni said: Apparently the guy is just talking about our own galaxy; there are BILLIONS AND BILLIONS of galaxies in the universe. Not to mention that even if other life doesn't exist in…

Three new recent discoveries. First, it turns out that you can generate a complete list of primes in the following fashion. Using %n% where %p + q = 2n%, let %n = 2% and find any Goldbach partitions %p, q%; if %max(q in bb Q)% is not in set %bb P%, add…

As usual, the main ideas here are wildly speculative, written down as food for thought. I am not claiming to be a cosmetologist or astrologer. For the purposes of this post, let's suppose that the universe is ultimately discrete. By this, I mean that when you get down to its…

I've been trying to visualize the problem in many different ways, tables and graphs and geometry and anything else that seems plausible. Here's one I nailed down this morning that's concise and readily graspable for any coder. First, ignore the %2%. It just gets in the way. And then we…

Shit, I made the mistake of thinking about them, and now I'm back on it. We'll try the opposite tack this time, though: proving that it's impossible to solve in polynomial time. Stream of consciousness begins: Consider the unconstrained case where %S% is the set of integers provided, of finite…

I have spent time working on almost every impossible problem there is. This is a lie, but it is rooted in a kernel of truth. I remember my very first impossible problem. When I was eight or nine, my dad gave me a word problem about firemen and houses or…