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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
by A_D_E_P_T 3y ago
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.)
- 082349872349872 3y agoFor that matter, all inconsistent structures ought to also "exist" — they're just indistinguishably boring, for inconsistency leads to triviality?
- A_D_E_P_T 3y agoEverything 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.