earthwormchuck163

Karma: 257

earthwormchuck163 Jan 8, 2013, 10:52 PM
0 points
in reply to: MarkusRamikin’s comment on: Rationality Quotes January 2013
Also, Kyubey clearly has pretty drastically different values from people, and thus his notion of saving the universe is probably not quite right for us.

earthwormchuck163 Jan 5, 2013, 9:50 PM
5 points
in reply to: Nick_Tarleton’s comment on: Second-Order Logic: The Controversy
If you take this objection seriously, then you should also take issue with predictions like “nobody will ever transmit information faster than the speed of light”, or things like it. After all, you can never actually observe the laws of physics to have been stable and universal for all time.

If nothing else, you can consider each as being a compact specification of an infinite sequence of testable predictions: “doesn’t halt after one step”, “doesn’t halt after two steps”,… “doesn’t halt after n steps”.

earthwormchuck163 Jan 5, 2013, 9:23 AM
4 points
in reply to: Qiaochu_Yuan’s comment on: Second-Order Logic: The Controversy

I don’t think ZFC can prove the consistency of ZF either, but I’m not a set theorist.

Also not a set theorist, but I’m pretty sure this is correct. ZF+Con(ZF) proves Con(ZFC) (see http://en.wikipedia.org/wiki/Constructible_universe), so if ZFC could prove Con(ZF) then it would also prove Con(ZFC).

earthwormchuck163 Dec 20, 2012, 11:51 PM
11 points
in reply to: lavalamp’s comment on: Standard and Nonstandard Numbers
< is defined in terms of plus by saying x<y iff there exists a such that y=z+x. + is supposed to be provided as a primitive operation as part of the data consisting of a model of PA. It’s not actually possible to give a concrete description of what + looks like in general for non-standard models because of Tenenbaums’s Theorem, but at least when one of x or y (say x) is a standard number it’s exactly what you’d expect: x+y is what you get by starting at y and going x steps to the right.

To see that x<y whenever x is a standard number and y isn’t, you need to be a little tricky. You actually prove an infinite family of statements. The first one is “for all x, either x=0 or else x>0”. The second is “for all x, either x=0 or x=1 or x>1″, and in general it’s “for all x, either x=0,1,..., or n, or else x>n”. Each of these can be proven by induction, and the entire infinite family together implies that a non-standard number is bigger than every standard number.

earthwormchuck163 Dec 20, 2012, 11:39 PM
16 points
in reply to: Eliezer Yudkowsky’s comment on: Standard and Nonstandard Numbers
It’s probably worth explicitly mentioning that the structure that you described isn’t actually a model of PA. I’d imagine that could otherwise be confusing for readers who have never seen this stuff before and are clever enough to notice the issue.

earthwormchuck163 Dec 20, 2012, 10:30 PM
1 point
in reply to: Benya’s comment on: Standard and Nonstandard Numbers
Okay. This is exactly what I thought it should be, but the way Eliezer phrased things made me wonder if I was missing something. Thanks for clarifying.

earthwormchuck163 Dec 20, 2012, 7:05 PM
4 points
in reply to: Benya’s comment on: Standard and Nonstandard Numbers

you can write a formula in the language of arithmetic saying “the Turing machine m halts on input i”

You get a formula which is true of the standard numbers m and i if and only if the m’th Turing machine halts on input i. Is there really any meaningful sense in which this formula is still talking about Turing machines when you substitute elements of some non-standard model?

earthwormchuck163 Dec 20, 2012, 6:55 PM
4 points
on: Standard and Nonstandard Numbers
Nice post, but I think you got something wrong. Your structure with a single two-sided infinite chain isn’t actually a model of first order PA. If x is an element of the two-sided chain, then y=2x=x+x is another non-standard number, and y necessarily lies in a different chain since y-x=x is a non-standard number. Of course, you need to be a little bit careful to be sure that this argument can be expressed in first order language, but I’m pretty sure it can. So, as soon as there is one chain of non-standard numbers, that forces the existence of infinitely many.

earthwormchuck163 Dec 18, 2012, 2:28 AM
12 points
in reply to: cousin_it’s comment on: Harry Potter and the Methods of Rationality discussion thread, part 17, chapter 86
I bet a large portion of the readership would have been disappointed if that didn’t happen.

And in this particular case, that was the only fast way for Alastor to gain enough respect for Harry’s competence that they could cooperate in the future. It wouldn’t have been consistent with his already established paranoia if he just believed Dumbledore & co.

I can imagine this getting old eventually, but imo it hasn’t happened yet.

earthwormchuck163 Oct 12, 2012, 10:15 PM
8 points
in reply to: Eliezer Yudkowsky’s comment on: Causal Diagrams and Causal Models
Were you trying to diet at the same time? Have you ever tried exercising more without also restricting your food intake?

Also, have you ever enjoyed exercising while doing it?

Edit: Just to be clear, this isn’t supposed to be advice, implicit or otherwise. I’m just curious.

earthwormchuck163 Oct 12, 2012, 10:12 PM
3 points
in reply to: Eliezer Yudkowsky’s comment on: The Fabric of Real Things
You can account for a theory where neurons cause consciousness, and where consciousness has no further effects, by drawing a causal graph like

(universe)->(consciousness)

where each bracketed bit is short-hand for a possibly large number of nodes, and likewise the → is short for a possibly large number of arrows, and then you can certainly trace forward along causal links from “you” to “consciousness”, so it’s meaningful. And indeed for the same reason that “the ship doesn’t disappear when it crosses the horizon” is meaningful.

We reject epiphenomenal theories of consiousness because the causal model without the (consciousness) subgraph is more simpler than the one with it, and we have no evidence for the latter to overcome this prior improbability. This is of course the exact same reason why we accept that the ship still exists after it crosses the horizon.

earthwormchuck163 Oct 12, 2012, 9:42 PM
0 points
in reply to: Eliezer Yudkowsky’s comment on: The Fabric of Real Things
In a universe without causal structure, I would expect an intelligent agent that uses an internal causal model of the universe to never work.

Of course you can’t really have an intelligent agent with an internal causal model in a universe with no causal structure, so this might seem like a vacuous claim. But it still has the consequence that

P(intelligence is possible|causal universe)>P(intelligence|acausal universe).

earthwormchuck163 Oct 12, 2012, 8:59 PM
2 points
in reply to: Eliezer Yudkowsky’s comment on: The Fabric of Real Things

My cousin is psychic—if you draw a card from his deck of cards, he can tell you the name of your card before he >looks at it. There’s no mechanism for it—it’s not a causal thing that scientists could study—he just does it.

I believe that your cousin can, under the right circumstances, reliably guess which card you picked. There are all sorts of card tricks that let one do exactly that if the setup is right. But I confidently predict that his guess is not causally separated from the choice of card.

To turn this into a concrete empirical prediction: Suppose that I have your cousin repeat his trick several times (say 100) for me, and each time I eliminate any causal interaction between the the deck and your cousin that I can think of. Then I predict with probability ~1 that, within several rounds, your cousin will not be able to guess which card I draw.

If this prediction turns out to be wrong, and your cousin can still reliably guess which card I drew even when we are in lead boxes on opposite sides of the planet, then I will gladly discard my model of reality, since it will have predicted a true state of affairs to be impossible.

Even this wouldn’t be enough to prove your cousin’s power is acausal, since there are conceivable causal influences that I couldn’t eliminate easily.For example, maybe we live in a computer simulation that runs standard physics all the time, except for a high-level override which configures your cousin’s visual cortex to a see a picture of every card that anyone draws from a deck. But I would certainly require evidence at least that strong before even considering the possibility that your cousin can guess cards acausally.

it’s not a causal thing that scientists could study

A scientist is just a person who learns about things by looking at them (ie causally interacting with them), plus some social conventions to make up for human fallibility. Do you claim that the social conventions of science stop one from learning about this thing by looking at it, or that one cannot learn about this thing by looking at it at all. If the former, then again I confidently predict that you are wrong. If the latter, then I can only ask how you learned about the thing, if not by looking at it.

Same thing when I commune on a deep level with the entire universe in order to realize that my partner truly loves >me.

You mean to say that your confidence that your partner loves you is not a result of your direct interactions with em? How terrible!

earthwormchuck163 Oct 2, 2012, 8:50 PM
11 points
on: The Useful Idea of Truth
The pictures are a nice touch.

Though I found it sort of unnerving to read a paragraph and then scroll down to see a cartoon version of the exact same image I had painted inside my head, several times in a row.

earthwormchuck163 Oct 2, 2012, 8:22 PM
4 points
in reply to: Armok_GoB’s comment on: The Useful Idea of Truth
I would like to thank you for bringing my attention to that sentence without any context.

earthwormchuck163 Sep 18, 2012, 10:38 PM
1 point
on: The Nanny State Didn’t Show Up, You Hired It [LINK]
Thanks for reminding me that I should be following this guy.

earthwormchuck163 Aug 23, 2012, 1:05 AM
1 point
in reply to: A1987dM’s comment on: Rationality Quotes August 2012
No, but mistaking your approximation for the thing you are approximating is.

earthwormchuck163 Aug 22, 2012, 9:23 PM
1 point
in reply to: A1987dM’s comment on: Rationality Quotes August 2012
I thought that was what I just said...

earthwormchuck163 Aug 22, 2012, 3:35 AM
1 point
in reply to: Strange7’s comment on: Rationality Quotes August 2012
Instrumental values are just subgoals that appear when you form plans to achieve your terminal values. They aren’t supposed to be reflected in your utility function. That is a type error plain and simple.

earthwormchuck163 Aug 10, 2012, 3:16 AM
2 points
in reply to: Wei Dai’s comment on: From the “weird math questions” department...
Okay, I concede. I recognize when I’ve been diagonalized.