trentmkelly/LessWrong-43k huggingface dataset:
Solutions and Open Problems
by Manfred — 2014-03-15T06:53:36.039Z

Followup To: Approaching Logical Probability

Last time, we required our robot to only assign logical probability of 0 or 1 to statements where it's checked the proof. This flowed from our desire to have a robot that comes to conclusions in limited time. It's also important that this abstract definition has to take into account the pool of statements that our actual robot actually checks. However, this restriction doesn't give us a consistent way to assign numbers to unproven statements - to be consistent we have to put limits on our application of the usual rules of probability.

Total Ignorance

The simplest solution is to assign logical probabilities to proven statements normally, but totally refuse to apply our information to unproven statements. The principle of maximum entropy means that every unproven statement then gets logical probability 0.5.

There is a correspondence between being inconsistent and ignoring information. We could just as well have said that when we move from proven statements to unproven statements, we refuse to apply the product rule, and that would have assigned every unproven statement logical probability 0.5 too. Either way, there's something "non-classical" going on at the boundary between proven statement and unproven statements. If you are certain that 100+98=198, but not that 99+99=198, some unfortunate accident has befallen the rule that if (A+1)+B=C, A+(B+1)=C.

Saying 0.5 for everything is rarely suggested in practice, because it has some glaringly bad properties: if we ask about the last digit of the zillionth prime number, we don't want to say that the answer being 1 has logical probability 0.5, we want our robot to use facts about digits and about primes to say that 1, 3, 7, and 9 have logical probability 0.25 each.

Using Our Pool of Proof-Steps

The most obvious process that solves this problem is to assign logical probabilities by ignoring most of the starting information, but using as information all proven statements containing no variables (that is, can't regenerate a set of axioms that will require us to take infinite time). So if we prove that our prime number can't simultaneously end with 1 and 3, we'll never assign a combined probability to them greater than 1.

This is the most typical family of suggestions (of the ones that won't require infinite resources). See Benja, for example. Another phr

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What are you working on? March / April 2014
by VincentYu — 2014-03-15T03:45:10.855Z

This is the supposedly-bimonthly-but-we-keep-skipping 'What are you working On?' thread. Previous threads are here. So here's the question:

What are you working on?

Here are some guidelines:

Focus on projects that you have recently made progress on, not projects that you're thinking about doing but haven't started.

Why this project and not others? Mention reasons why you're doing the project and/or why others should contribute to your project (if applicable).

Talk about your goals for the project.

Any kind of project is fair game: personal improvement, research project, art project, whatever.

Link to your work if it's linkable.
Biomedical research, superstars, and innovation
by VipulNaik — 2014-03-14T22:38:40.340Z

As part of my work for Cognito Mentoring reviewing biomedical research as a career option (not much at the link there right now), I came across an interview with biomedical researcher John Todd of Cambridge University published by 80,000 Hours.

The whole interview is interesting, but one part of it struck me as interesting and somewhat hard to believe:

John would prefer a good person in his lab to an extra £0.5mn in annual funding. Generally, there are enough grants, so finding good people is a bigger constraint than money.

Here's the full context:

Our candidate does data analysis in finance, earning over $100,000 per year. They have an Economics degree for Chicago, and an Masters in Financial Engineering from University of California, LA, and reasonable programming skills. They’re planning to do an MD then PhD.

“This guy looks great. I’d love to hire him.” (when he has his MD, or even before).

“The MD and programming/statistics combo is lethal. Top of the world. There’s major demand.”

He probably wouldn’t need to do a PhD, because of the programming. After his MD, he could just apply to a lab. He should go into genomic medicine, which is what I do. Tailored therapeutics or stratified medicine will be played out for major health and economic benefits over the next 30 years. Check out Atul Butte at Stanford. He’s the perfect profile for this guy. He could be the new Butte”

£0.5mn is about USD 830,000 according to current foreign exchange rates. In other words, John Todd, the interviewee, indicated that a sufficiently good researcher was worth that much. Now, the question was framed in terms of additional funding, rather than reallocation of existing funds. But assuming that the existing funding for the biomedical research lab is at least one order of magnitude greater than the amount (£0.5mn) under discussion, I don't think it matters whether we're talking of using additional funding or reallocating existing funds. Essentially, I read John Todd as saying that he'd be willing to pay £0.5mn to attract a "good person" to his lab (actually, as framed, it could be interpreted as even more: he's willing to pay an ordinary salary for the person, plus forgo £0.5mn in additional funds, to hire the person). Note: I clarified with Ben Todd, the interviewer, that th...
High school students and effective altruism
by VipulNaik — 2014-03-14T19:04:38.727Z

The cluster of ideas underlying effective altruism is an important part of my worldview, and I believe it would be valuable for many people to be broadly familiar with these ideas. As I mentioned in an earlier LessWrong post, I was pleasantly surprised that many advisees for Cognito Mentoring (including some who are still in high school) were familiar with and interested in effective altruism. Further, our page on effective altruism learning resources has been one of our more viewed pages in recent times, with people spending about eight minutes on average on the page according to Google Analytics.

In this post, I consider the two questions:

Are people in high school ready to understand the ideas of effective altruism?

Are there benefits from exposing people to effective altruist ideas when they are still in high school?

1. Are people in high school ready to understand the ideas of effective altruism?

I think that the typical LessWrong reader would have been able to grasp key ideas of effective altruism (such as room for more funding and earning to give) back in ninth or tenth grade from the existing standard expositions. Roughly, I expect that people who are 2 or more standard deviations above the mean in IQ can understand the ideas when they begin high school, and those who are 1.5 standard deviations above the mean in IQ can understand the ideas by the time they end high school. Certainly, some aspects of the discussion, such as the one charity argument, benefit from knowledge of calculus. Both the one charity argument and the closely related concept of room for more funding are linked with the idea of marginalism in economics. But it's not a dealbreaker: people can understand the argument better with calculus or economics, but they can understand it reasonably well even without. And it might also work in reverse: seeing these applications before studying the formal mathematics or economics may make people more interested in mastering the mathematics or economics.

Of course, just because people can understand effective altruist ideas if they really want to, doesn't mean they will do so. It may be necessary to simplify the explanations and improve the exposition so as to make it more attractive to younger people. An alternative route would be to sneak the explanations into things young people are already engaging with. This could be an academic curriculum o...
Overcoming the Loebian obstacle using evidence logic
by Squark — 2014-03-14T18:34:21.761Z

In this post I intend to:

Briefly explain the Loebian obstacle and it's relevance to AI (feel free to skip it if you know what the Loebian obstacle is).

Suggest a solution in the form a formal system which assigns probabilities (more generally probability intervals) to mathematical sentences (and which admits a form of "Loebian" self-referential reasoning). The method is well-defined both for consistent and inconsistent axiomatic systems, the later being important in analysis of logical counterfactuals like in UDT.

Background

Logic

When can we consider a mathematical theorem to be established? The obvious answer is: when we proved it. Wait, proved it in what theory? Well, that's debatable. ZFC is popular choice for mathematicians, but how do we know it is consistent (let alone sound, i.e. that it only proves true sentences)? All those spooky infinite sets, how do you know it doesn't break somewhere along the line? There's lots of empirical evidence, but we can't prove it, and it's proofs we're interesting in, not mere evidence, right?

Peano arithmetic seems like a safer choice. After all, if the natural numbers don't make sense, what does? Let's go with that. Suppose we have a sentence s in the language of PA. If someone presents us with a proof p in PA, we believe s is true. Now consider the following situations: instead of giving you a proof of s, someone gave you a PA-proof p1 that p exists. After all, PA admits defining "PA-proof" in PA language. Common sense tells us that p1 is a sufficient argument to believe s. Maybe, we can prove it within PA? That is, if we have a proof of "if a proof of s exists then s" and a proof of R(s)="a proof of s exists" then we just proved s. That's just modus ponens.

There are two problems with that.

First, there's no way to prove the sentence L:="for all s if R(s) then s", since it's not a PA-sentence at all. The problem is that "for all s" references s as a natural number encoding a sentence. On the other hand, "then s" references s as the truth-value of the sentence. Maybe we can construct a PA-formula T(s) which means "the sentence encoded by the number s is true"? Nope, that would get us in trouble with the liar paradox (it would be possible to construct a sentence saying "this sentence is false").

Second, Loeb's theorem says that if we can prov...
Can you escape Heat Death with MWI?
by DataPacRat — 2014-03-14T18:12:28.811Z

The universe is running down - there are only so many sources of negentropy that can be used for the work of life and intelligence. But thermodynamics is a statistical process, an average of a great many small processes. The standard model of MWI makes a certain hash of statistics - in a vanishingly small number of Everett branches, those statistical averages go right out the window: all the air in a room flies to one side, or an egg unscrambles itself.

In those universes in which life continues to survive after all the stars burn out, and all other known sources of useful energy have been turned into waste heat... might it be possible for said life to continue to survive in at least some timelines, by feeding on thermodynamic miracles?

And, at least as important, which forms of thermodynamic miracles are the most common, and which are most potentially useful? (After all, in any given volume of space ,a few electrons appearing out of relative nothingness is much more likely than an entire Boltzmann Brain appearing, and depending on how stable the matter-energy substrate that life at the time is using to maintain itself between miracles, said substrate might decay before some kinds of miracles ever occur...)

Edit: Question posed in recent 'Open Thread' at http://lesswrong.com/r/discussion/lw/jww/open_thread_1824_march_2014/api5
What attracts people to learning things that they consider neither interesting nor important?
by VipulNaik — 2014-03-14T17:32:43.188Z

A priori, it seems to me that one should engage in activities only if they satisfy at least one of these two conditions:

They are interesting: People receive direct hedonic value in the process of doing them.

They are important: People acquire relevant knowledge and skills that help them with other activities (some of that help could be through signaling).

But investigation we did in connection with our research at Cognito Mentoring led my collaborator Jonah and me to notice that a fair number of people seem attracted to learning things for the sake of learning, although they neither have an internal belief that learning the subject is important, nor a deep interest in learning that specific topic. Some of them then get frustrated that they're unable to make progress on their self-set learning goals, and this may harm their self-esteem (and put them off learning more important things later). Others may experience success that encourages them to learn more things, some of which may be interesting or important. Our page on managing your time generally advises against participating in and focusing on such activities, or at minimum critically considering whether the activities are sufficiently important to justify engaging in them even if one doesn't find them interesting.

However, Jonah and I may be missing important perspectives. I've heard claims that engaging in activities that are neither interesting nor important has intrinsic value -- it helps build character, makes one grow as a person, or it just might turn out to be important.

This school of thinking is reflected in diverse quarters. Tiger Mom Amy Chua famously forced her daughters to learn musical instruments to build their character, even though at least one of her daughters found it a terrible experience, and there was no reason to believe that the activity itself is important. The belief that one should try and learn new things is also widespread (albeit in a very different sort of way) in the rationalistic self-help community.

What's going on? Some possible explanations:

A mentality of trying and learning new things, including things that seem neither interesting nor important prima facie, might be crucial for learning new life habits and productivity hacks (see here and here for analysis by Dan Keys of CFAR that provides evidence in favor of this view).

Some people are very high in the openness t

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On the concept of "talent-constrained" organizations
by VipulNaik — 2014-03-14T16:42:11.713Z

Some people have claimed that organizations are often talent-constrained. In other words, they're not short on money, but they're not able to find talented people. Specifically, some people, such as biomedical researcher John Todd, have claimed they'd turn down large amounts of additional money in order to be able to hire superstars. Others have claimed that the effective altruism movement is talent-constrained.

I'll use talent-constrained in the following sense: an organization is talent-constrained if it's willing to turn down a substantial amount of additional money in order to be able to hire a superstar, and that additional money it's willing to turn down is enough to hire several people at the current salaries they offer.

My first reaction to claims of talent constraint is: why don't these organizations bid up the price of talent to the levels that they claim they're willing to forgo to hire that talent? There could be many possible answers. I'll explore the most salient here.

1. Talent constraint because of cash constraint

Some organizations are cash-constrained, so the ways they would use additional cash at the margin differs significantly from the ways they can reallocate existing cash. So, the fact that they'd be willing to forgo huge amounts of additional money in order to hire new talent doesn't necessarily mean that they can reallocate existing money to bid for superstar talent.

While I agree that this is a common situation, particularly for small organizations, I don't think that talent-constrained is the right description of this situation.

2. Genuine absence of talented people

In some cases, the talented people the organization needs are genuinely very rare. So it may so happen that the organization simply hasn't been approached by any person who'd be impressive enough to hire at a high wage. However, I don't find this explanation very convincing.

People decide whether or not to approach organizations based partly on publicly available information about how much those organizations pay. If the organizations in question don't pay most of their workers high salaries (presumably because these workers aren't superstars) then the superstars who are considering whether to apply to those organizations may believe they're not going to be paid high salaries, hence they may not bother to apply. If organizations care enough about hiring superstars, they need to...
New LW Meetup: Auckland
by FrankAdamek — 2014-03-14T16:02:32.264Z

This summary was posted to LW Main on March 7th. The following week's summary is here.

New meetups (or meetups with a hiatus of more than a year) are happening in:

Auckland Preliminary Meetup: 08 March 2014 02:00PM

Irregularly scheduled Less Wrong meetups are taking place in:

[Atlanta] March Meetup: Body Hacking!: 09 March 2014 08:07PM
Moscow, Meet up: 09 March 2014 04:00PM
Munich Meetup: 08 March 2014 02:00PM
Sydney Meetup - March: 26 March 2014 06:30PM
Tempe, AZ (ASU): 07 March 2014 06:30PM
Urbana-Champaign: Discussion: 09 March 2014 01:00PM
Utrecht: Effective Altruism: 07 March 2014 07:00PM

The remaining meetups take place in cities with regular scheduling, but involve a change in time or location, special meeting content, or simply a helpful reminder about the meetup:

Austin, TX: 08 March 2025 01:30PM
[Berlin] Community Weekend in Berlin: 11 April 2014 04:00PM
Brussels - Calibration and other games: 08 March 2014 01:00PM
Canberra: Meta-meetup + meditation: 28 March 2014 06:00PM
London Games Meetup 09/03, + Socials 02/03 and 16/02 : 09 March 2014 02:00PM
NYC Rationality Megameetup and Unconference: April 5-6: 05 April 2014 11:00AM
Salt Lake City UT — Open Possibilities and Improv Skills: 09 March 2014 02:00PM
Vienna Meetup : 15 March 2014 03:00PM
Washington DC Fun and Games Meetup: 09 March 2014 02:00PM
West LA—Expert At Vs. Expert On: 12 March 2014 06:00PM

Locations with regularly scheduled meetups: Austin, Berkeley, Berlin, Boston, Brussels, Cambridge UK, Canberra, Columbus, London, Madison WI, Melbourne, Mountain View, New York, Philadelphia, Research Triangle NC, Salt Lake City, Seattle, Toronto, Vienna, Washington DC, Waterloo, and West Los Angeles. There's also a 24/7 online study hall for coworking LWers.

If you'd like to talk with other LW-ers face to face, and there is no meetup in your area, consider starting your own meetup; it's easy (more resources here). Check one out, stretch your rationality skills, build community, and have fun!

In addition to the handy sidebar of upcoming meetups, a meetup overview is posted on the front page every Friday. These are an attempt to collect information on all the meetups happening in upcoming weeks. The best way to get your meetup featured is still to use the Add New Meetup feature, but you'll also have the benefit of having your meetup menti...
How much wealth is produced by high IQ people?
by JonahS — 2014-03-14T08:23:33.365Z

Cognito Mentoring aims to help high potential young people self-actualize. As a part of our investigation of where the greatest leverage points are, I've been investigating the aggregate wealth of high IQ people as a class. There's a paucity of good data, and it's very difficult to reason about these things in absence of it, so I'd appreciate any thoughts.

The SAT as an indicator

The Relationship Between the Scholastic Assessment Test and General Cognitive Ability found a correlation of 0.82 between IQ and SAT scores based on 1979 data. Some people have claimed that the SAT has become less g-loaded in recent years, but a large fraction of the most intellectually impressive people who I know in my age group scored 1600 on a scale of 1600.

Longitudinal studies of high IQ children

Who Rises to the Top? Early Indicators (2013) find that people who scored at the 1 in 10k level on the SAT for < 13 year olds had median income of $80k at age 33. This is about 2.5x median income for Americans in general (of all ages), and at the 90th percentile of income for 33 year olds (). There's a confounding factor which is that plausibly people who took the SAT before age 13 came from unrepresentatively wealthy and well-educated families.

The maximum income reported out of the sample of 225 was $1.4 million. I wasn't able to find information on how this compares with other 33 year olds. The income is at about the 99.9th percentile for Americans in general (all ages). On the face of things this doesn't seem impressive, but maybe income of outliers rises dramatically over time.

Tech entrepreneurs

Bill Gates famously scored 1590 on the SAT, at a time when many fewer people scored 1600 than people did in subsequent years. He also solved a notable problem in combinatorics as a a college sophomore.

Jeff Bezos graduated summa cum laude from Princeton in computer science

Zuckerberg took a graduate course in computer science as a high school student.

Drew Houston (Dropbox founder) started programming at age 5 and scored 1600 on the SAT.

Steve Jobs tested at the 10th grade level in 4th grade.

This is broadly consistent with "top tech entrepreneurs" having IQ ~145+ (99.8th percentile).

Gates made ~ $100 billion, Jobs would have been ~$100 billion with 20% equity in Apple. Ellison ~$48 B Page $32.3 B, Bezos $32 Brin $32 B, Zuckerberg $28 B, for about $4...
On not diversifying charity
by DanielLC — 2014-03-14T05:14:08.909Z

A common belief within the Effective Altruism movement that you should not diversify charity donations when your donation is small compared to the size of the charity. This is counter-intuitive, and most people disagree with this. A Mathematical Explanation of Why Charity Donations Shouldn't Be Diversified has already been written, but it uses a simplistic model. Perhaps you're uncertain about which charity is best, charities are not continuous, let alone differentiable, and any donation is worthless unless it gives the charity enough money to finally afford another project, your utility function is nonlinear, and to top it all off, rather than accepting the standard idea of expected utility, you are risk-averse.

Standard Explanation:

If you are too lazy to follow the link, or you just want to see me rehash the same argument, here's a summary.

The utility of a donation is differentiable. That is to say, if donating one dollar gives you one utilon, donating another dollar will give you close to one utilon. Not exactly the same, but close. This means that, for small donations, it can be approximated as a linear function. In this case, the best way to donate is to find the charity that has the highest slope, and donate everything you can to it. Since the amount you donate is small compared to the size of the charity, a first-order approximation will be fairly accurate. The amount of good you do with that strategy is close to what you predicted it would do, which is more than you'd predict of any other strategy, which is close to what you'd predict for them, so even if this strategy is sub-optimal, it's at least very close.

Corrections to Account for Reality:

Uncertainty:

Uncertainty is simple enough. Just replace utility with expected utility. Everything will still be continuous, and the reasoning works pretty much the same.

Nonlinear Utility Function:

If your utility function is nonlinear, this is fine as long as it's differentiable. Perhaps saving a million lives isn't a million times better than saving one, but saving the millionth life is about as good as the one after that, right? Maybe each additional person counts for a little less, but it's not like the first million all matter the same, but you don't care about additional people after that.

In this case, the effect of the charity is differentiable with respect to the donation, and the utility i...