All of wuthefwasthat's Comments + Replies

Oops, sorry! I misread. My bad. I would agree that they are all equivalent.

Zeckhauser's roulette

You reject the claim, but can you point out a flaw in their argument?

I claim that the answers to E, F, and G should indeed be the same, but H is not equivalent to them. This should be intuitive. Their line of argument does not claim H is equivalent to E/F/G - do the math out and you'll see.

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0Quinn13y

Actually my revised opinion, as expressed in my reply to Tyrell_McAllister, is that the authors' analysis is correct given the highly unlikely set-up. In a more realistic scenario, I accept the equivalences A~B and C~D, but not B~C. I really don't know what you have in mind here. Do you also claim that cases A, B, C are equivalent to each other but not to D?

Zeckhauser's roulette

Harry Potter and the Methods of Rationality discussion thread, part 9

I agree that you should pay the same amount.

It feels as though you should be willing to pay twice as much in case 2, since you remove twice as much "death mass". At this point, one might be confused by the apparent contradiction. Some are chalking it up to intuition being wrong (and the problem being misinformed) and others are rejecting the argument. But both seem clearly correct to me. And the resolution is simple - notice that your money is worth half as much in case 1, since you are living half as often!

Utilitarians probably wasting time on recreation

Harry's patronus also blocks a killing curse, in Azkaban (in HPMoR)

wuthefwasthat13y100

I think realistically, most people burn out if they don't spend some time relaxing. If your argument had been more extreme, it might argue that people should sacrifice a couple of hours of sleep each day as well, right? But it's plausible that for most people, going off of 6 hours of sleep per day will decrease their cognitive ability and productivity drastically. Or that exercising 1 hour a day has sufficient physical and mental health benefits to justify it. Could some amount of recreation be worth it? I think so. I think I couldn't function withou... (read more)

Richard_Kennaway13y100

Everyone is wasting some time. Nobody is being perfectly altruistic, and making the best choices at all times. I don't think anyone ever thought they were...

Scientists have shown that we only use 10% of our time!

Utilitarians probably wasting time on recreation

Less Wrong mentoring thread

I think you can make $5/hr with Mechanical Turk.

Less Wrong mentoring thread

I was in a similar situation as you, 4 years ago. I worked a fair bit harder, learned WAY more, and had a WAY better time in college. To be fair, my work ethic is still not very good, but I pretty much get A's in the classes I care about and B's in the ones I don't.

I suspect that you will be fine - you're probably smart enough that college won't be as hard as you might think, and you'll also be more motivated to dig up good work habits if you really need/want to.

wuthefwasthat13y40

I'm in my last year of studying CS/Math as an undergradate at MIT (I'm going to do a Master's next year though). I'd really like some advice about what I should do after I graduate - Grad school? Industry? Any alternative?

I care a fair amount about reducing xrisk, but I am also fairly skeptical that there is much I can do about it right now.

I have job offers with Google and some tech start-ups, and I suspect I could get a job in finance if I tried. I personally have some desire to start a tech company one day. I'm not sure what the tradeoff between... (read more)

1CronoDAS13y

According to what I've heard, working at Google is awesome. Go for it.

4Vaniver13y

My recommendation would be working at Google, or possibly one of the startups. Finding a job that fits your temperament is great for satisfaction- many doctors make the mistake of going into the field they find academically fascinating rather than the one that has a practice they'll enjoy. (That is, they don't look at what hours a job will require, whether they'll have to be on call, how many patients they'll have / how much time each patient will take, etc.) If you go to graduate school / do research, it will mostly be thinking about problems for extended periods of time. Ability to code is not very relevant, though it's important in industry. You shouldn't worry about being third rate- the intellectual bar for PhDs is around 5th rate (though you need other strengths to make up for that).

East Coast Megameetup II: Electric Boogalloo

http://en.wikipedia.org/wiki/Arbitrage

I'm in the Cambridge area, and haven't been attending meetups, but this seems like the most awesome possible way to start. What is the mailing list/point of contact to work things out with Cambridge meet-up guys?

1juliawise13y

Hi there! There's been discussion of the trip on the Cambridge email list, which you can see on the meetup email archive.

The Allais Paradox

wuthefwasthat13y10

Soundness: a semantic claim that given a specific notion of "true" as applies to a statement, e.g. truth in the model N of natural numbers, all the axioms of the theory are true. Automatically implies both consistency and omega-consistency. Requires a notion of the "intended model" or a "standard model" for the theory in which we consider the truth of propositions. For example, soundness is meaningless to talk about in the case of ZFC, which doesn't have an intended model.

I looked it up, and it seems like what you're referr... (read more)

0Anatoly_Vorobey13y

It's just a different meaning of the word "soundness". The soundness you're talking about is really a property of a deductive system in first-order logic, as you point out. The soundness I'm talking about is a property of a theory w.r.t. a particular notion of truth defined for first-order formulas (and it's usually defined by fixing a structure and an interpretation, in that structure, of the logic's constant/function/relation symbols; in other words, a model). You're right that sometimes, when talking about the model N, it's referred to as "arithmetic soundness", but the modifier is not at all required. E.g. search for "a theory T is sound" on Google as a phrase, with quotation marks, to see usage examples. Or search for "sound" in this post: http://rjlipton.wordpress.com/2011/03/30/random-axioms-and-gdel-incompleteness/ Compare with the word "completeness", which, I'm sure you're aware, is also notoriously ambiguous: in "Godel's completeness theorem" and "Godel's incompleteness theorems" it refers to two totally different kinds of completeness. The difference between them is similar, though not identical, to the one between soundness as a property of a first-order logic and soundness as a property of a theory. Well, not quite. Why do you think that omega-consistency guarantees that? What is it about omega-consistency that guarantees anything to be true? It only speaks of things that are provable/nonprovable. Let me try to be a bit more detailed. You actually need your theory S (the one you have an oracle for, be it PA or something else) to uphold two separate requirements: 1. When S proves a sentence of the form "Exists x such that T halts after x steps", you need that sentence to be true. This sentence is a Sigma1 sentence (let me know if I need to detail that further). 2. When there is a true sentence of the form "this is a run of T that ends after N steps" (which is a Sigma0 sentence), you need S to be able to prove it. This is what the original post me

Oops sorry! Ignore what I said there. Anyways, the axioms aren't necessarily r.e., but as far as I can tell, they don't need to be.

I'm a little out of my depth here, so sorry if my comments don't make sense.

I'm not an expert either, so I'm probably just being unclear

That's supposed to be a r.e. set of axioms, not a single axiom, right? I can easily imagine the program that successively prints the axioms R(x) for all x in L, but how do you enumerate the axioms not R(x) for all x not in L, given that L is only r.e. and not recursive? Or am I missing some easy way to have the whole thing as a single axiom without pulling in the machinery for running arbitrary programs and such?

The... (read more)

0cousin_it13y

But we want the oracle to be less helpful than the halting oracle... Anyway, the question is settled now, thanks a lot :-)

wuthefwasthat13y40

I believe the answer to your question is yes. I'm going to just interpret "formal system" as "first order theory", and then try to do the most straightforward thing.

Take a language L of intermediate degree, as constructed via the priority method. I'd like to just take the strings (or numbers) in this language to be the theory's axioms. So let the theory have some 1-ary relation, call it R, as well as +, and constants 0 and 1. Assert that everything has a successor, just to get the "natural numbers" (without having multipl... (read more)

2cousin_it13y

I'm a little out of my depth here, so sorry if my comments don't make sense. That's supposed to be a r.e. set of axioms, not a single axiom, right? I can easily imagine the program that successively prints the axioms R(x) for all x in L, but how do you enumerate the axioms not R(x) for all x not in L, given that L is only r.e. and not recursive? Or am I missing some easy way to have the whole thing as a single axiom without pulling in the machinery for running arbitrary programs and such? On second thought, maybe we don't need the second part. Just having R(x) for all x in L could be enough. I don't completely understand why there won't be an accidental smart thing among all the silly things...

Sure. You actually need something a bit stronger than soundness, in that you want omega-consistency, right?

I still don't agree/understand with what you two are saying about having the standard integers as a model, or interepreting PA with its own axioms, though (or anything along the lines of needing to contain PA). I think this argument holds as long as the other formal system is recursively enumerable, and if PA is omega-consistent.

0Anatoly_Vorobey13y

Are you confusing soundness with consistency? omega-consistency is much weaker than soundness. Consistency: a syntactic claim that it's impossible to derive a contradiction. Doesn't require a notion of truth to be useful. Omega-consistency: a syntactic claim that it's impossible to prove certain statements together. Doesn't need a notion of truth, but is motivated by the standard model of natural numbers. Soundness: a semantic claim that given a specific notion of "true" as applies to a statement, e.g. truth in the model N of natural numbers, all the axioms of the theory are true. Automatically implies both consistency and omega-consistency. Requires a notion of the "intended model" or a "standard model" for the theory in which we consider the truth of propositions. For example, soundness is meaningless to talk about in the case of ZFC, which doesn't have an intended model. Look at this sentence from the argument: "If the oracle says yes, you know that the statement is true for standard integers because they're one of the models of PA, therefore N is a standard integer, therefore T halts." If the oracle for a formal system S says "yes" on a given statement S that encodes the proposition "a Turing machine T will halt on this input", this means that S proves this proposition. It does not mean that the proposition is true and T will in fact halt! For that to be true, you need the formal system S to be sound. S could easily be omega-consistent and not sound, in which case it'll lie to you (example, assuming you believe PA to be consistent: the formal system.

1cousin_it13y

Some parts of my post were just wrong, they're edited now. But other parts use the unspoken assumption that there's such a thing as "standard integers" (or, equivalently, there's such a thing as "Turing machines") and the axioms of PA are true statements about that thing. That seems to imply omega-consistency, but the whole argument is so informal that I can't tell for sure. It could be formalized somehow, I guess, but that was not the intent. In the words of Liron Shapira, I'm talking about Turing machines as "their own meta-level thing", so statements about their halting or non-halting are to be interpreted as "facts of the matter" outside any formal system. The "standard integers" exist in the same limbo. That's where the handwavy reasoning about SSS...S0 comes from. Yeah I know that's weird.

wuthefwasthat13y40

The halting oracle's uncomputability degree is the smallest possible uncomputable degree, so no.

What? That's false. See http://en.wikipedia.org/wiki/Turing_degree#Post.27s_problem

ETA: Also, not sure what you are saying about soundness... =/

1Anatoly_Vorobey13y

Yeah, retracted above. Don't know what I was thinking. Suppose PA is inconsistent. Then a provability oracle for PA always answers "yes", and is completely useless as a halting problem oracle. Debugging cousin_it's argument with this example helps to see where he relies on PA being sound, that is, anything proved by PA being a true statement about N.