Last week, when I posted about the Mathematical Universe Hypothesis (MUH), I noted that it has the same problem as the Block Universe Hypothesis (BUH): It needs to account for its apparent out-of-the-box complexity. In his book, Tegmark raises the issue, but doesn’t put it to bed.
He invokes the notion of Kolmogorov complexity, which, in a very general sense, is like comparing things based on the size of their ZIP file. It’s essentially a measure of the size of information content. Unfortunately, his examples raised my eyebrows a little.
Today I thought I’d explore why. (Turns out I’m glad I did.)
Happy Tau Day! It’s funny. I feels like I’ve written a lot of posts about pi plus few about it’s bigger sibling, tau. Yet the reality is that I’ve only ever written one Tau Day post, and that was back in 2014. (As far as celebrating Pi Day, I’ve only written three posts in eight years: 2015, 2016, & 2019.)
What I’m probably remembering is mentioning pi a lot here (which is vaguely ironic in that I won’t eat pie — mostly I don’t like cooked fruit, but there’s always been something about pie that didn’t appeal — something about baking blackbirds in a crust or something).
It’s true that I am fascinated by the number.
The ultimate goal is a consideration of how to create a working model of the human mind using a computer. Since no one knows how to do that yet (or if it’s even possible to do), there’s a lot of guesswork involved, and our best result can only be a very rough estimate. Perhaps all we can really do is figure out some minimal requirements.
Given the difficulty we’ll start with some simpler software models. In particular, we’ll look at (perhaps seeming oddity of) using a computer to model a computer (possibly even itself).
The goal today is to understand what a software model is and does.