All of wuthefwasthat's Comments + Replies

Ten small life improvements

clipmenu lets you configure the history amount - I set it to 1000. also you can save snippets to paste (accessed via a different hotkey) - e.g. your email address, email templates, common code snippets in developer console

also, a possible alternative to karabiner for vim users is wasavi, which lets you use vim in browser textareas

Games for Rationalists

I highly recommend Hanabi. It's a cooperative game about common knowledge.

More Cryonics Probability Estimates

There's another effect of "unpacking", which is that it gets us around the conjunction/planning fallacy. Minimally, I would think that unpacking both the paths to failure and the paths to success is better than unpacking neither.

3Eliezer Yudkowsky9yI wonder if that would actually work, or if the finer granularity basically just trashes the ability of your brain to estimate probabilities.
How do we really escape Prisoners' Dilemmas?

Well, for one thing, we don't know how many round there are, ahead of time.

Second order logic, in first order set-theory: what gives?

I don't think that's true. You may not believe that the set of functions is unique (in which case the notion of sets in bijection is no longer unique).

Zeckhauser's roulette

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.

[This comment is no longer endorsed by its author]Reply
0Quinn10yActually 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

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!

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

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

Utilitarians probably wasting time on recreation

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)

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

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

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.

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)

1CronoDAS10yAccording to what I've heard, working at Google is awesome. Go for it.
4Vaniver10yMy 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

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?

1juliawise10yHi there! There's been discussion of the trip on the Cambridge email list, which you can see on the meetup email archive [http://www.meetup.com/Cambridge-Less-Wrong-Meetup/messages/archive/].
No one knows what Peano arithmetic doesn't know

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_Vorobey10yIt'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/ [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
No one knows what Peano arithmetic doesn't know

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.

No one knows what Peano arithmetic doesn't know

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?

0cousin_it10yBut we want the oracle to be less helpful than the halting oracle... Anyway, the question is settled now, thanks a lot :-)
No one knows what Peano arithmetic doesn't know

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_it10yI'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...
No one knows what Peano arithmetic doesn't know

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_Vorobey10yAre 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_it10ySome 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 [http://mathoverflow.net/questions/34710/succinctly-naming-big-numbers-zfc-versus-busy-beaver] 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.
No one knows what Peano arithmetic doesn't know

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_Vorobey10yYeah, 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.
No one knows what Peano arithmetic doesn't know

Well, that argument only goes through if the other theory is recursively enumerable, so PA isnt as awesome as you make it sound.

6cousin_it10yAgreed. For example, we can't learn "all truths about the integers" by bootstrapping from PA in this way. But we can get all of formalist mathematics.
Do men have more partners than women?

Assuming 100% heterosexuality, and that there are roughly the same number of males and females, the average number of sexual partners should be the same for men and women, by a simple counting argument.

San Diego Meetup?

I'd be interested, and I should be able to make it any of those days. As a warning, I visit this site pretty occasionally and I don't post -- hopefully that's alright!

Where do meetings usually occur?

0Mercurial10yThere isn't really a "usually" as yet. We just had [http://lesswrong.com/meetups/1e] our first monthly meetup, and the locale worked out nicely (except that the VGA cable for the projector was apparently missing). And yes, it's fine that you don't visit the site often and don't post often. I don't really, either, and I poked around semi-casually for about a year before I made my first post. Last time there were some people there who had learned about Less Wrong for the first time that day!