Computation

There’s a natural question that arises when working with computers and math enough: what is computation? Informally, it seems pretty straightforward to answer that, but I was never satisfied by the explanations and kept thinking there must be a better definition out there somewhere. It turns out there isn’t. Not…

Does size matter?

Why is the observable universe so small? Or, why is it so big?

Immortality

So it turns out you will never die. I know, I was surprised too. To be a little more precise, it is—regrettably—possible and probably inevitable to go through the process of dying, to have it seem like everything is ending… but it never actually will. My argument is based on…

On generating primes with periodic continued fractions

This week’s been spent investigating properties of continued fractions, specifically the periodic species which arise when dealing with where . Notation     The bracketed string on the left expands as shown, with each element included until reaching and repeating from , indefinitely. Values The first 25 terms of for…

Factorials vs. Power Sets

Wanted to jot this down as food for thought before I forgot. And so I did. So we have factorials, denoted with a suffix, e.g. , or more generally     Among many other things, represents the number of possible permutations of a set of unique elements, that is, the…

Empirical evidence for the Axiom of Choice

Near as I can figure, the go-to framework for mathematics these days is Zermelo-Fraenkel set theory, with or without the Axiom of Choice (denoted as ZF or ZFC, respectively). The Axiom of Choice (AC) was contentious in its day, but the majority of mathematicians now accept it as a valid…