Post #1782136
2026-04-27 18:56 UTC
I believe the following two must be kept _separate_ as much as possible, at least when _specifying_ the behavior of exponentiation with rational arguments:
(1) whether the result is a real number;
(2) whether both the real and imaginary parts of the result are rational.
(For the second item, of course, rational includes integer.)
For example, for
(expt 16/81 3/4)
both are true;
for
(expt 1/2 3/4)
only (1) is true;
for
(expt -1 1/2)
only (2) is true.
Anyway, I am just a side observer here who doesn't understand what you are driving at.
@simon_brooke @screwlisp
Replies (1)
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@simon_brooke@mastodon.scot 2026-04-27 19:21
@vnikolov @screwlisp OK, I'm going to take it on faith for now that the value of (expt 1/2 3/4) is irrational, because I don't have the headspace at present to work the proof. But I'm surprised -- it violates my naive intuition. What I'm trying to do with #PostScarcitySoftware is to think about how the software for the hardware of the deep future will work. Actually, it probably won't, of course. Actually, we'll probably burn the planet in the near future. But it's a fun thought experiment.