It's been so long since we released the last FoC episode that it disappeared behind Slack's horizon. Well, happy new year, here's an episode we recorded back in September!! It's been kinda nuts for the past few months, so sorry for the radio silence. FoC Episode 74 • Is the Whole Universe a Computer™? Jack Copeland, Mark Sprevak, and Oron Shagrir ask this question in chapter 41 of their book, The Turing Guide. They split this question in two, first asking whether the universe itself is a computer, then whether the universe could even be computed. These are lofty, unanswerable questions, sure, but they encroach on our territory — philosophy, automata, nonsense. So, in our usual reverent style and with attentive pacing, the three of us explore the paper, the questions, the answers they choose to highlight, and even share a few perfectly reasonable answers of our own.

I just want to say: I enjoy how long and haphazard the podcast is.

There are dozens of us! Dozens!

Coincidentally Sean Carroll just shared his related thoughts: https://www.preposterousuniverse.com/podcast/2025/01/06/300-solo-does-time-exist

For two interesting mathematical podcast takes on the (non-)distinction between continuous and discrete, with bonus connections to reals vs rationals and determinism: • https://kpknudson.com/my-favorite-theorem/2019/3/12/episode-38-robert-ghrist • https://kpknudson.com/my-favorite-theorem/2019/7/10/episode-44-james-propp

And on the aside about Zelda games, I cannot recommend the Parallel Worlds https://www.romhacking.net/hacks/197/ ROM hack enough. I'd say Parallel Worlds is the Majora's Mask of "A Link to the Past". Entirely new experience using the existing engine. Two things I remember fondly... Instead of just handing it out, you get to work to get your sword. And the platforming puzzles! What platforming? But you can't jump in "A Link to the Past"! There isn't a jump button, but there is an existing tool that you can use.

@Josh Bleecher Snyder From the transcript of the first episode:

If I exponentiate the left hand side of the complex plane, what do I get? I get the region in the plane with modulus less than 1.

I think this makes sense, and it's wild. Thanks for sharing that!

I just finished listening to the episode (loved the ending!), and I think I can pretty definitely say that the universe is not computable(TM). The most basic examples of quantum mechanics contradict this. The outcome of the double-slit experiment or the Stern-Gerlach experiment, or the time between decay events in a radioactive material is, as far as we currently know, completely, truly random. This doesn't exclude the possibility of the universe being a computer, just like how the electrons and silicon atoms making up a CPU are fundamentally quantum-mechanical but they are still acting as a Turing machine. I was a little bit disappointed overall by how little quantum mechanics and quantum computers were discussed, though I understand if you feel out of your depth there :)

There are a few ways to interpret what’s going on with quantum mechanics. I don’t know of a consensus on which one’s right or how to tell. Others here will know better. Roughly I think it breaks out this way. Either quantum indeterminacy is… • genuinely random or • decided by hidden magic we don’t know understand or • preserved distributing over the environment giving rise to many worlds. I hear that the math is cleanest for many worlds. For random resolution, it’s hard to tell when exactly it happens. Hidden magic would be the most satisfying if the magic could be reduced to some mechanism.

I would say that's a reasonably good description. Wikipedia seems to list quite a few additional interpretations for QM, most of which I hadn't heard of. But yeah, basically there is no consensus, which is kind of funny as the 100th anniversary of QM is celebrated this year. In practice most people do math according to the Copenhagen interpretation, which would be the "genuinely random" option. I don't know much about many worlds, but I think it's not been ruled out basically because it's so simple and it does explain everything. Many people (myself included) find it pretty unsatisfying.

I don't know whether it's still up to date, but Quantum Mechanics and Experience is (was?) a good exposition.