2026/01/15

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2026-01-16 00:31:21 +0100 <monochrom> 2-colourability is polynomial-time, 3-colourability is NP-complete.
2026-01-16 00:31:10 +0100 <int-e> bitstream adds additional observations for each natural number.
2026-01-16 00:30:54 +0100 <monochrom> SillyType is countable, BitStream is uncountable.
2026-01-16 00:30:51 +0100 <int-e> jreicher: NO!
2026-01-16 00:30:35 +0100 <jreicher> monochrom: hang on, are you now saying bitstream is countable? I was hoping that, having proved SillyType is countable, you'd now prove bitstream is uncountable.
2026-01-16 00:30:22 +0100 <monochrom> Generally there are multiple instance when switching from 1 to 2, or 2 to 3, or 3 to 4 makes breaking changes.
2026-01-16 00:30:04 +0100merijn(~merijn@host-cl.cgnat-g.v4.dfn.nl) merijn
2026-01-16 00:29:56 +0100__monty__(~toonn@user/toonn) (Quit: leaving)
2026-01-16 00:29:51 +0100k0zy(~user@user/k0zy) k0zy
2026-01-16 00:29:51 +0100k0zy(~user@75-164-179-179.ptld.qwest.net) (Changing host)
2026-01-16 00:29:43 +0100k0zy(~user@75-164-179-179.ptld.qwest.net)
2026-01-16 00:29:37 +0100 <int-e> Sure. It's morally finite ("morally" being the view where you don't have bottoms)
2026-01-16 00:29:36 +0100 <monochrom> But intuitively I'm not surprised. Expressing natural numbers in unary requires n units of memory for n; "merely" switching to binary, that drops down to lg n.
2026-01-16 00:28:51 +0100 <jreicher> And so SillyType is countable, yes?
2026-01-16 00:27:29 +0100 <monochrom> I map 0 to the infinite stream z = I z, 1 to bottom, 2 to I bottom, 3 to I (I bottom), etc.
2026-01-16 00:26:51 +0100 <jreicher> Every proof I sketch out results in an inconsistency.
2026-01-16 00:26:25 +0100 <jreicher> No, prove away, please. I'd like to understand.
2026-01-16 00:26:11 +0100 <monochrom> I can prove them, but if you're asking for intuition, I think I don't have any.
2026-01-16 00:25:59 +0100 <jreicher> Surely they're either both countable, or both uncountable, depending on your "definitions"
2026-01-16 00:25:35 +0100 <jreicher> I still don't understand why anyone would say SillyType is countable but BitStream is uncountable.
2026-01-16 00:20:22 +0100 <EvanR> imaginary numbers are real and real numbers are fictional
2026-01-16 00:20:08 +0100 <monochrom> My beef is that "imaginary number" is a misnomer. But I digress.
2026-01-16 00:20:04 +0100 <jreicher> Fictionalists unite
2026-01-16 00:19:48 +0100 <EvanR> lol
2026-01-16 00:19:43 +0100 <int-e> EvanR: "real number" is a misnomer :P
2026-01-16 00:19:40 +0100 <EvanR> I'm doing vibes there
2026-01-16 00:19:29 +0100 <jreicher> I'm really not doing vibes, so I don't know why you keep saying that
2026-01-16 00:19:26 +0100 <EvanR> at least approximately
2026-01-16 00:19:21 +0100 <EvanR> well you know where infinitesimals are
2026-01-16 00:19:08 +0100 <EvanR> if were doing vibes, this kind of defeats the point of the real line, and the idea of quantity or ordering
2026-01-16 00:19:05 +0100merijn(~merijn@host-cl.cgnat-g.v4.dfn.nl) (Ping timeout: 245 seconds)
2026-01-16 00:19:04 +0100 <jreicher> I'm pretty sure non-standard analysis does this with asserting the existence of infinitisimals
2026-01-16 00:18:19 +0100 <jreicher> yes of course. :)
2026-01-16 00:18:11 +0100 <EvanR> at least approximately
2026-01-16 00:17:49 +0100 <EvanR> but it would seem kind of odd that these objects don't "sit" somewhere on the real line xD
2026-01-16 00:17:34 +0100 <EvanR> I don't doubt you can throw exotic objects in
2026-01-16 00:15:49 +0100 <jreicher> I never have
2026-01-16 00:15:43 +0100 <dolio> So you can't assume that real numbers are the same things as expansions.
2026-01-16 00:15:43 +0100Googulator(~Googulato@2a01-036d-0106-29ac-fd48-b0ea-63d3-602a.pool6.digikabel.hu) (Quit: Client closed)
2026-01-16 00:15:39 +0100Googulator69(~Googulato@2a01-036d-0106-29ac-fd48-b0ea-63d3-602a.pool6.digikabel.hu)
2026-01-16 00:15:12 +0100 <jreicher> I'm not confused about that. Every bitstream can be interpreted as a numeral corresponding to a number. But that says nothing about the converse, especially since nothing stops you from throwing in all kinds of exotic objects to the set you want to call "the reals"
2026-01-16 00:15:08 +0100 <dolio> Yeah, like I said, there's a paper about a topos where the reals are countable. But the diagonal argument holds in every topos.
2026-01-16 00:14:38 +0100 <EvanR> if you didn't guess already the argument in the paper is answering "no" to its title... like betteridge's law
2026-01-16 00:14:36 +0100trickard_(~trickard@cpe-84-98-47-163.wireline.com.au)
2026-01-16 00:14:22 +0100trickard_(~trickard@cpe-84-98-47-163.wireline.com.au) (Read error: Connection reset by peer)
2026-01-16 00:14:20 +0100merijn(~merijn@host-cl.cgnat-g.v4.dfn.nl) merijn
2026-01-16 00:13:49 +0100 <EvanR> if you keep getting confused thinking stream of bits means "oh reals", and reals means "oh, just a binary expansion", then that equivocation is the point of this old paper
2026-01-16 00:12:35 +0100 <EvanR> that's specifically about reals
2026-01-16 00:12:26 +0100 <EvanR> that was being discussed
2026-01-16 00:12:19 +0100 <EvanR> you brought up chaitin