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Christian or atheist - in the end we all believe in infinite torture forever. Welcome!
I think you're leaving out a substantial number of people who don't believe in infinite anything.
This was an attempt at humor. Usually when people start sentences with "Whatever religion we adhere to..." they are going to utter a platitude ending with "...we all believe in love/life/goodness". The intended joke was to come about through a subversion of the audience's expectation. It was also meant to poke fun at all the torture discussions here lately, though perhaps that's already been done to death.
Creative idea, poor execution. You'd have to combine it with several other such platitude parodies before other people would interpret your joke correctly.
It might not work in another month or two, but the idea of "contrived infinite-torture scenarios" has high salience for LW readers right now. I got the joke immediately.
Just because you didn't get the joke doesn't mean he did it wrong. I got the joke, and he was saying it to me, so I believe the joke was performed correctly, given his target audience! ^_^
The problem, I'd say, would be an assumption of shared prior experience - but humor in general tends to make that assumption, whether it's puns which assume a shared experience with lingual quirks, friend in-jokes which are directly about shared experiences, or genre humor which assumes a shared experience in that genre. This was genre humor.
While transparent communication is wonderful for rational discussion, I would conjecture that humor is inherently about the irrational links our minds make between disparate information with similar qualities.
I got the joke, but I guess I just didn't think it was funny. That may be because I've been pretty annoyed with all the infinite torture discussions that have been going on; I think the idea is laughably implausible, and don't understand the compulsion people seem to have to keep talking about it, even after being informed that they are causing other people horrible nightmares by doing so.
I think everyone believes in infinite something, even if it's infinite nothingness, or infinite cosmic foam, but I understand your meaning. ^_^
I don't. I believe that there are things that can only be described in terms of stupendously huge numbers, but I believe that everything that exists can be described without reference to infinities.
Really, when I think about how incomprehensibly enormous a number like BusyBeaver(3^^^3) is, I have trouble believing that there is some physical aspect of the universe that could need anything bigger. And if there is, well, there's always BusyBeaver(3^^^^3) waiting in the wings.
Eliezer calls this infinite-set atheism, which is as good a name as any, I suppose.
See also: Finitism
Concepts don't have to be about "reality", whatever that is (not a mathematically defined concept for sure).
Infinities exist as concepts, yes. They're even useful in math. But I have never encountered anything that exists (for any reasonable definition of "exists") that can't be described without an infinity. MWI describes a preposterously large but still finite multiverse, as far as I understand it. And if our physical universe is infinite, as some have supposed, I haven't seen proof of it.
Really, like any other form of atheism, infinite-set atheism should be easy to dispel. All anyone has to do to change my mind is show me an infinite set.
Unfortunately, observations don't have epistemic power, so we'd have to live with all possible concepts. Besides, it's quite likely that reality doesn't in fact contain any infinities, in which case it's not possible to show you an infinity, and you are just demanding particular proof. :-)
Wait... he's already saying he believes reality doesn't contain any infinities...
And you say that you can't show proof to the contrary because it's likely reality doesn't contain any infinities...
I don't think I followed you there.
I distinguish between "believing in X" and "believing reality contains X". I grew to dislike the non-mathematical concept of reality lately. Decision theory shouldn't depend on that.
My disbelief in infinities extends only to reality; I make no claims about the question of their existence elsewhere.
Considering your brain is finite, I don't think you're entitled to that particular proof.
(Perhaps you're just saying it would be a sufficient but not a necessary proof, in which case...okay, I guess.)
That's not the only proof I'd accept, but given that I do accept conceptual infinities, I don't think my brain is necessarily the limiting factor here.
Another form of acceptable evidence would be some mathematical proof that begins with the laws of physics and demonstrates that reality contains an infinity. I'm not sure if a similar proof that demonstrates that reality could contain an infinity would be as convincing, but it would certainly sway me quite a bit.
I'm not sure I understand. Part of it is the use of BusyBeaver - I'm familiar with Busy Beaver as an AI state machine, not as a number. Second: So you say you do not believe in infinity ... but only inasmuch as physical infinity? So you believe in conceptual infinity?
The BusyBeaver value I'm referring to is the maximum number of steps that the Busy Beaver Turing Machine with n states (and, for convenience, 2 symbols) will take before halting. So (via wikipedia), BB(1) = 1, BB(2) = 6, BB(3) = 21, BB(4) = 107, BB(5) >= 47,176,870, BB(6) >= 3.8 × 10^21132, and so on. It grows the fastest of all possible complexity classes.
OK, have to make technical corrections here. Busy Beaver is not a complexity class, complexity classes do not grow. Busy Beaver function grows faster than any computable function, but I doubt it's the "fastest" at anything, seeing as you can always just take e^BB(n), e.g.
Ugh, thank you. I seem to have gotten complexity classes and algorithmic complexity mixed up. Busy Beaver's algorithmic complexity grows asymptotically faster than any computable function, so far as considerations like Big-O notation are concerned. In those sorts of cases, I think that even for functions like e^BB(n), the BB(n) part dominates. Or so Wikipedia tells me.
ETA: cousin_it has pointed out that there uncomputable functions which dominate Busy Beaver.
Sure, but my point is it's not the "fastest" of anything unless you want to start defining some very broad equivalences...
As Eliezer pointed out on HN, there is a way to define numbers that dominate BB values as decisively as BB dominates the Ackermann function, but you actually need some math knowledge to make the next step, not just stack BB(BB(...)) or something. (To be more precise, once you make the step, you can beat any person who's "creatively" using BB's and oracles but doesn't know how to make the same step.) And after that quantum leap, you can make another quantum leap that requires you to understand another non-trivial bit of math, but after that leap he doesn't know what to do next, and I, being a poor shmuck, don't know either. If you want to work out for yourself what the steps are, don't click the link.
Ah, excellent, so I'm not so far off. Then what's 3^^^3, then?
3^^^^3 on Less Wrong wiki.
Oh, good golly gosh, that gets big fast. Thank you!
( chuckles warmly ) don't worry - I got the joke. ^_^ Although I'm rather in a minority in my view of Hell as something other than torture, but hey, there's plenty of time for that! Thank you for the welcome!