Mathematical journeys into fictional worlds (2021) [pdf] | Hacker News Reader

Mathematical journeys into fictional worlds (2021) [pdf]

gresham.ac.uk

37 pointstmtvl11 comments

You can actually see the lecture at https://www.youtube.com/watch?v=MLSqJYQgC-c

Too bad they didn't release the following one, I wanted to read about Perec and Borges...

More recently, Permutation City by Greg Egan and Neverness by David Zindell are all about mathematical journeys in fictional worlds. It's hard to discuss what they mean without getting pretty deep into the philosophical implications of simulated worlds, though, so they're less useful as pen-and-paper exercises and more interesting as references on contemporary philosophy.

It's been a long time since I last read Permutation City and I was browsing its Wikipedia page to refresh my memory and I loved this description: "there is no difference, even in principle, between physics and mathematics".

https://en.wikipedia.org/wiki/Permutation_City

As the Wikipedia page alludes, Egan, and this book in particular, was surely the inspiration for Tegmark's Mathematical Universe Hypothesis; the notion that all logically/mathematically consistent structures exist on some level, our universe among them.

(Though in truth the Pythagoreans of 2500 BC -- those adherents to what can rightly be called the first universalizing European religion -- believed much the same thing. Egan and the Pythagoreans, but not Tegmark, also considered the nature of time in such a scenario; eternal recurrence was a Pythagorean idea.)

For that matter, all inconsistent structures ought to also "exist" — they're just indistinguishably boring, for inconsistency leads to triviality?

Everything that you can imagine, no matter how trivial, is a consistent notion that can be expressed mathematically as a true logical proposition. This includes an empty room, a Platonic solid, physical entropy, whatever. As Wittgenstein once noted, "logically consistent statements which are a priori true are possibilities which ensure their own truth."

What stands in opposition to this? The logically nonsensical – the incomputable. This includes anything discrete that can't be simulated, even in principle. These things cannot exist even in an infinite mathematical universe; for everything in such a universe is emergent, but such things cannot emerge.

Isn’t that referred to as the Dust Theory?

I just finished Permutation City for the first time since it’s come up on HN a few times so I thought I’d give it a read. (Mild spoiler alert) I found that once everything was in the autoverse I stopped caring about the characters’ copies. Maybe that’s an intended perspective, or maybe it says something about me.

Related ongoing thread:

A mathematician who finds poetry in math and math in poetry - https://news.ycombinator.com/item?id=39589102 - March 2024 (12 comments)

I knew giants couldn't exist because they'd collapse under their own weight, but it's interesting what challenges Lilliputians face.

see also https://www.damtp.cam.ac.uk/user/gold/pdfs/purcell.pdf (for the challenges of Lilliputians specifically) and https://en.wikipedia.org/wiki/On_Being_the_Right_Size (in general).

and if they were big enough we'd have a hard time communicating with them because their eardrums wouldn't resonate with our vocal frequencies

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