AlephNeil

Karma: 885

AlephNeil Aug 1, 2011, 12:39 AM
3 points
on: Why no uniform weightings for ensemble universes?
What interests me about the Boltzmann brain (this is a bit of a tangent) is that it sharply poses the question of where the boundary of a subjective state lies. It doesn’t seem that there’s any part X of your mental state that couldn’t be replaced by a mere “impression of X”. E.g. an impression of having been to a party yesterday rather than a memory of the party. Or an impression that one is aware of two differently-coloured patches rather than the patches themselves together with their colours. Or an impression of ‘difference’ rather than an impression of differently coloured patches.

If we imagine “you” to be a circle drawn with magic marker around a bunch of miscellaneous odds and ends (ideas, memories etc. but perhaps also bits of the ‘outside world’, like the tattoos on the guy in Memento) then there seems to be no limit to how small we can draw the circle—how much of your mental state can be regarded as ‘external’. But if only the ‘interior’ of the circle needs to be instantiated in order to have a copy of ‘you’, it seems like anything, no matter how random, can be regarded as a “Boltzmann brain”.

AlephNeil Jul 31, 2011, 11:53 PM
0 points
on: Why no uniform weightings for ensemble universes?

Every now and then I see a claim that if there were a uniform weighting of mathematical structures in a Tegmark-like ’verse—whatever that would mean even if we ignore the decision theoretic aspects which really can’t be ignored but whatever—that would imply we should expect to find ourselves as Boltzmann mind-computations

The idea is this: Just as most N-bit binary strings have Kolmogorov complexity close to N, so most N-bit binary strings containing s as a substring have Kolmogorov complexity at least N—length(s) + K(s) - somethingsmall.

And now applying the analogy:

N-bit binary string <---> Possible universe

N-bit binary string containing substring s <---> Possible universe containing a being with ‘your’ subjective state. (Whatever the hell a ‘subjective state’ is.)

we get:

N-bit binary string containing substring s with Kolmogorov complexity >= N—length(s) + K(s) - O(1) <---> A Boltzmann brain universe.

We don’t seem to be experiencing nonsensical chaos, therefore the argument concludes that a uniform weighting is inadequate and an Occamian weighting over structures is necessary

I’ve never seen ‘the argument’ finish with that conclusion. The whole point of the Boltzmann brain idea is that even though we’re not experiencing nonsensical chaos, it still seems worryingly plausible that everything outside of one’s instantaneous mental state is just nonsensical chaos.

What an ‘Occamian’ weighting buys us is not consistency with our experience of a structured universe (because a Boltzmann brain hypothesis already gives us that) but the ability to use science to decide what to believe—and thus what to do—rather than descend into a pit of nihilism and despair.

AlephNeil Jul 7, 2011, 10:25 PM
3 points
in reply to: Morendil’s comment on: How to annoy misanthropes and bleeding-hearts

Hmm, are you interpreting the results as “boo CEOs” then?

I’m only interpreting the result as “boo this fictional CEO”.

How would you modify the experiment to return information closer to what was sought?

Well, what Knobe is looking for is a situation where subjects make their ‘is’ judgements partly on the basis of their ‘ought’ judgements. Abstractly, we want a ‘moral proposition’ X and a ‘factual proposition’ Y such that when a subject learns X, they tend to give higher credence to Y than when they learn ¬X. Knobe takes X = “The side-effects are harmful to the environment” and Y = “The effect on the environment was intended by the CEO”.

(My objection to Knobe’s interpretation of his experiment can thus be summarised: “The subjects are using Y to express a moral fact, not a ‘factual fact’.” After all, if you asked them to explain themselves, in one case they’d say “It wasn’t intentional because (i) he didn’t care about the effect on the environment, only his bottom line.” In the other they’d say “it was intentional because (ii) he knew about the effect and did it anyway.” But surely the subjects agree on (i) and (ii) in both cases—the only thing that’s changing is the meaning of the word ‘intentional’, so that the subjects can pass moral judgement on the CEO.)

To answer your question: I’m not sure that genuine examples of this phenomenon exist, except when the ‘factual’ propositions concern the future. If Y is about a past event, then I think any subject who seems to be exhibiting the Knobe effect will quickly clarify and/or correct themselves if you point it out. (Rather like if you somehow tricked someone into saying an ungrammatical sentence and then told them the error.)

AlephNeil Jul 7, 2011, 6:05 PM
18 points
in reply to: AlanCrowe’s comment on: How to annoy misanthropes and bleeding-hearts

Instead, the moral character of an action’s consequences also seems to influence how non-moral aspects of the action – in this case, whether someone did something intentionally or not – are judged.

Stupid Knobe effect. Obviously the subjects’ responses were an attempt to pass judgement on the CEO. In one case, he deserves no praise, but in the other he does deserve blame [or so a typical subject would presumably think]. The fact that they were forced to express their judgement of moral character through the word ‘intentional’, which sometimes is a ‘non-moral’ quality of an action, doesn’t tell us anything interesting.

AlephNeil Jul 2, 2011, 8:55 PM
7 points
in reply to: Normal_Anomaly’s comment on: [LINK] Charlie Stross: Federov’s Rapture
Merely saying it wouldn’t be so bad, as long as there was some substance behind the assertion.

But basically his argument boils down to this:

“If you dunk two wooden boards with wires poked through them into soapy water and then lift them out, the soaps films between the wires are the solution to an NP-hard problem. But creating the boards and wires and dunking them can be done in polynomial time. So as long as physics is Turing computable, P = NP.”

This is a fantastically stupid argument, because you could easily create a simulation of the above process that appeared to be just as good at generating the answers to this problem as the real soap films. But if you gave it a somewhat difficult problem, what would happen is that it would quickly generate something which was nearly but not quite a solution, and there’s no reason to think that real soap films would do better.

The fact that Bringsjord got as far as formalising his argument in modal logic and writing it up, without even thinking of the above objection, is quite incredible.

AlephNeil Jul 2, 2011, 8:26 PM
4 points
in reply to: Normal_Anomaly’s comment on: [LINK] Charlie Stross: Federov’s Rapture
Yeah well, it’s Selmer P = NP Bringsjord. He’s a complete joke!

AlephNeil Jul 2, 2011, 7:56 PM
0 points
in reply to: cousin_it’s comment on: Born rule or universal prior?
I think what mathemajician means is that if the stream of data is random (in that the bits are independent random variables each with probability ¹⁄₂ of being 1) then Solomonoff induction converges on the uniform measure with high probability (probability 1, in fact).

I’m sure you knew that already, but you don’t seem to realize that it undercuts the logic behind your claim:

The universal prior implies you should say “substantially less than 1 million”.

AlephNeil Jul 2, 2011, 7:44 PM
0 points
in reply to: cousin_it’s comment on: Born rule or universal prior?
O(BB^-1) (or whatever it is) is still greater than O(1) though, and (as best I can reconstruct it) your argument relies on there being a constant penalty.

AlephNeil Jun 30, 2011, 4:17 PM
1 point
on: Born rule or universal prior?
I think you’re implicitly assuming that the K complexity of a hypothesis of the form “these n random bits followed by the observations predicted by H” equals n + (K-complexity of H) + O(1). Whereas actually, it’s n + (K-complexity of H) + O(log(n)). (Here, the log(n) is needed to specify how long the sequence of random bits is).

So if you’ve observed a hugely long sequence of random bits then log(n) is getting quite large and ‘switching universe’ hypotheses get penalized relative to hypotheses that simply extend the random sequence.

This makes intuitive sense—what makes a ‘switching universe’ unparsimonious is the arbitrariness of the moment of switching.

(Btw, I thought it was a fun question to think about, and I’m always glad when this kind of thing gets discussed here.)

ETA: But it gets more complicated if the agent is allowed to use its ‘subjective present moment’ as a primitive term in its theories, because then we really can describe a switching universe with only a constant penalty, as long as the switch happens ‘now’.

AlephNeil Jun 19, 2011, 5:22 AM
7 points
in reply to: PhilGoetz’s comment on: When is further research needed?
The mathematical result is trivial, but its interpretation as the practical advice “obtaining further information is always good” is problematic, for the reason taw points out.

A particular agent can have wrong information, and make a poor decision as a result of combining the wrong information with the new information. Since we’re assuming that the additional information is correct, I think it’s reasonable to also stipulate that all previous information is correct.

Actually, I thought of that objection myself, but decided against writing it down. First of all, it’s not quite right to refer to past information as ‘right’ or ‘wrong’ because information doesn’t arrive in the form of propositions-whose-truth-is-assumed, but in the form of sense data.* It’s better to talk about ‘misleading information’ rather than ‘wrong information’. When adversary A tells you P, which is a lie, your information is not P but “A told me P”. (Actually, it’s not even that, but you get the idea.) If you don’t know A is an adversary then “A told me P” is misleading, but not wrong.

Now, suppose the agent’s prior has got to where it is due to the arrival of misleading information. Then relative to that prior, the agent still increases its expected utility whenever it acquires new data (ignoring taw’s objection).

(On the other hand, if we’re measuring expectations wrt the knowledge of some better informed agent then yes, acquiring information can decrease expected utility. This is for the same reason that, in a Gettier case, learning a new true and relevant fact (e.g. most nearby barn facades are fake) can cause you to abandon a true belief in favour of a false one.)

* Yes yes, I know statements like this are philosophically contentious, but within LW they’re assumptions to work from rather than be debated.

AlephNeil Jun 18, 2011, 2:45 PM
0 points
in reply to: Will_Sawin’s comment on: When is further research needed?
It’s true for anyone who understands random variables and expectations. There’s a one line proof, after all.

AlephNeil Jun 18, 2011, 8:26 AM
1 point
on: When is further research needed?
Or in other words, the expectation of a max of some random variables is always greater or equal to the max of the expectations.

You could call this ‘standard knowledge’ but it’s not the kind of thing one bothers to commit to memory. Rather, one immediately perceives it as true.

AlephNeil Jun 15, 2011, 11:17 PM
1 point
in reply to: Ronny Fernandez’s comment on: Induction, Deduction, and the Collatz Conjecture: the Decidedly Undecidable Propositions.

What I’m really asking is, if some statement turns out to be undecidable for all of our models,

Nitpick: you don’t mean “models” here, you mean “theories”.

does that make that conjecture meaningless

Why should it?

or is undecidable somehow distinct from unverifiable.

Oh… you’re implicitly assuming a 1920s style verificationism whereby “meaningfulness” = “verifiability”. That’s a very bad idea because most/all statements turn out to be ‘unverifiable’ - certainly all laws of physics.

As for mathematics, the word ‘verifiable’ applied to a mathematical statement simply means ‘provable’ - either that or you’re using the word in a way guaranteed to cause confusion.

Or perhaps by “statement S is verifiable” what you really mean is “there exists an observation statement T such that P(T|S) is not equal to P(T|¬S)”?

AlephNeil Jun 12, 2011, 3:58 AM
0 points
in reply to: TimFreeman’s comment on: St. Petersburg Mugging Implies You Have Bounded Utility
You can find it here though.

AlephNeil Jun 9, 2011, 7:12 AM
4 points
in reply to: PhilosophyFTW’s comment on: Identity Isn’t In Specific Atoms

You don’t get to infer P from Q which is probably false, and then assert P with conviction.

What if I were to put P = “there is no such thing as absolute simultaneity” and Q = “special relativity”?

Or P = “the earth orbits the sun” and Q = “Newton’s theory of gravity”?

AlephNeil Jun 8, 2011, 4:23 PM
0 points
in reply to: CarlShulman’s comment on: St. Petersburg Mugging Implies You Have Bounded Utility

Hyperreals or some other modification to the standard framework (see discussion of “infinity shades” in Bostrom) are necessary in order to say that a 50% chance of infinite utility is better than a 1/3^^^3 chance of infinite utility.

No it isn’t, unless like Hayek you think there’s something ‘not blindingly obvious’ about the ‘modification to the standard framework’ that consists of stipulating that probability p of infinite utility is better than probability q of infinite utility whenever p > q.

This sort of ‘move’ doesn’t need a name. (What does he call it? “Vector valued utilities” or something like that?) It doesn’t need to have a paper written about it. It certainly shouldn’t be pretended that we’re somehow ‘improving on’ or ‘fixing the flaws in’ Pascal’s original argument by explicitly writing this move down.

AlephNeil Jun 8, 2011, 4:13 PM
−1 points
in reply to: CarlShulman’s comment on: St. Petersburg Mugging Implies You Have Bounded Utility
Alan Hajek’s article is one of the stupidest things I’ve ever read, and a depressing indictment on the current state of academic philosophy. Bunch of pointless mathematical gimmicks which he only thinks are impressive because he himself barely understands them.

AlephNeil Jun 6, 2011, 12:53 AM
0 points
in reply to: Tyrrell_McAllister’s comment on: Nature: Red, in Truth and Qualia
That may be right, but I don’t see how it conflicts with my (throwaway) remark.

“Quale” works better than “qualia” because (i) it sounds more like the word “claw” and (ii) it’s singular whereas ‘qualia’ is plural.

AlephNeil Jun 3, 2011, 9:59 PM
0 points
in reply to: [deleted]’s comment on: About addition and truth
Why is the difference relevant? I honestly can’t imagine how someone could be in the position of ‘feeling as though 2+2=4 is either necessarily true or necessarily false’ but not ‘feeling as though it’s necessarily true’.

(FWIW I didn’t downvote you.)

AlephNeil Jun 3, 2011, 9:44 PM
3 points
in reply to: [deleted]’s comment on: About addition and truth

If I say “37460225182244100253734521345623457115604427833 + 52328763514530238412154321543225430143254061105 = 8978898869677433866588884288884888725858488938” it should not immediately strike you as though I’m asserting a necessary truth that cannot possibly be otherwise.

It immediately strikes me that what you’re asserting is either necessarily true or necessarily false, and whichever it is it could not be otherwise.