Open Thread: August 2009

Here's our place to discuss Less Wrong topics that have not appeared in recent posts. If something gets a lot of discussion feel free to convert it into an independent post.

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While I find I have benefitted a great deal from reading posts on OB/LW, I also feel that, given the intellectual abilities of the people involved, the site does not function as an optimally effective way to acquire the art of rationality. I agree that the wiki is a good step in the right direction, but if one of the main goals of LW is to train people to think rationally, I think LW could do more to provide resources for allowing people to bootstrap themselves up from wherever they are to master levels of rationality.

So I ask: What are the optimal software, methods, educational tools, problem sets, etc. the community could provide to help people notice and root out the biases operating in their thinking. The answer may be sources already extant, but I have a proposal.

Despite being a regular reader of OB/LW, I still feel like a novice at the art of rationality. I realize that contributing one's ideas is an effective way to correct one's thinking, but I often feel as though I have all these intellectual sticking points which could be rooted out quite efficiently--if only the proper tools were available. As far as my own learning methods go, assuming a realistic application of current technology, I would love something like the following:

An interactive (calibrated to respond to learner's demonstrated level of ability-- similar to the GRE) test with a set of 1000+ problems, wherein I could detect the biases operating in my thinking as I approach given questions and problems. Using such a technique, I believe I could train myself up to the point where I could more closely approximate what I remember Eliezer somewhere saying is going on when he approaches an argument: his brain is cycling through possible biases almost as automatically as it is controlling his autonomic nervous system.

[In terms of convenience, an added bonus would be to be able to look at questions through one of the standard flashcard applications available on the iphone (or other devices), so I could look at, say, a few (or a few dozen) questions whenever the urge struck me. I dream of such a tool someday even incorporating SuperMemo-type capabilities, wherein even experts are able to keep their knowledge fresh by having questions reappear based on optimal strategies for obviating long-term degradation of memories. I am interested in helping to develop such a learning tool.]

I welcome any input about how to proceed with such a plan. Although I am a PhD candidate/adjunct professor, I don’t know what the optimal technology for such a project would be. It does seem, though, that the technical demands necessary to get such a project off the ground need not be imposing.

Once such a project got off the ground, I believe the community could come together to provide effective questions and answers. As I see it, it would neither be necessary nor desirable for such a project to be created by a single person.

I believe there are many people for whom this could project could be valuable. We might find that, were such a tool to be implemented, at the very least, it might raise the level of discourse on LW. Beyond that, who knows. Thanks for your suggestions.

I think this is a great idea.

I'm aware of one simple technology which uses spaced repetition (items you remember or "get correct" taking longer to reappear, for optimal learning), is pre-existing and would be easy to use, which is that of flash card programs. There are a number of free ones out there, two of the best that I found are: Mnemosyne and Anki. I have been using Anki for about half a year now for learning vocabulary (largely for the GRE) and am very happy with it, wish I had discovered such programs earlier.

While they're pre-existing and easy to use (and to share and add "cards"), two imperfections stand out. First, I'm not aware of any functionality that lets you actually select an answer. You could look at the question and possible answers and then pick one mentally, but the "answer side" couldn't be customized to the selection you made. Secondly, you of course wouldn't be able to calibrate the questions to your level as the program won't know what you answered. You're able to select to repeat an item very soon, or after short, medium or long intervals (relative to how many times you've answered correctly, by your own scoring), but it's not quite the same.

I might be wrong and some existing flash card program might allow for the selection of answers. Or perhaps more promising Anki is open-source, so perhaps with only a bit of work we could build a quiz-version.

First, I'm not aware of any functionality that lets you actually select an answer. You could look at the question and possible answers and then pick one mentally, but the "answer side" couldn't be customized to the selection you made. Secondly, you of course wouldn't be able to calibrate the questions to your level as the program won't know what you answered. You're able to select to repeat an item very soon, or after short, medium or long intervals (relative to how many times you've answered correctly, by your own scoring), but it's not quite the same.

I don't understand. How do pseudo-multiple choice cards do any worse than a 'genuine' multiple-choice? And what do you mean by calibration? The calibration is done by ease of remembering, same as any card. Nothing stops you from saying (for Mnemosyne), 'if I get within 5% of the correct value, I'll set this at 5; 10%, 4, 20% 3, etc.'

It might well work to one's satisfaction. What I meant by calibration is that it wouldn't be able to give you a different new question based on what you answered; whether you get this question right or wrong, the series of questions awaiting you afterwards is exactly the same (unlike the GRE for example). And if the answer were numeric you could use an algorithm for when to repeat the card, yes. I had off hand imagined questions with discrete answers that had little distance relation.

OK... from the sound of it, it isn't really a good application for SRS systems. (They're focused on data, not skills - and thinking through biased problems would seem to be a skill, and something where you don't want to memorize the answer!)

However, probably one could still do something. Mnemosyne 2.0 is slated to have extensible card types; I've proposed a card type which will be an arbitrary piece of Python code (since it's running in an interpreter anyway) outputting a question and an answer.

My example was generating random questions to learn multiplication (in pseudocode, the card would look like 'x = getRandom(); y = getRandom(); question = print x "" y; answer = print x\y;'), but I think you could also write code that generated biased questions. For example, one could test basic probability by generating 3 random choices: 'Susan is a lawyer' 'Susan is a lawyer but not a sledge-racer' 'Susan is a lawyer from Indiana', and seeing whether the user falls prey to the conjunction fallacy.

(As a single card, it would get pushed out to the future by the SRS algorithm pretty quickly; but to get around this you could just create 5 or 10 such cards.)

This writer of this essay (seen on Reddit) is a true practical rationalist and role model for all of us.

It's not just because she made a good decision and didn't get emotionally worked up. She was able to look behind the human level and all its status and blame games, see her husband as a victim of impersonal mental forces (don't know if she knows evo psych, but she certainly has an intuitive grasp of some of the consequences) , and use her understanding to get what she wants. And she does it not in a manipulative or evil kind of way, but out of love and a desire to hold her family together.

It was Thanksgiving dinner that sealed it. My husband bowed his head humbly and said, “I’m thankful for my family.”

He was back.

And I saw what had been missing: pride. He’d lost pride in himself.

If I were that husband, I'd have tried to save my pride even if it meant abandoning the family, because once your pride is taken from you, it's only a matter of time before all the other good things in your life get taken as well.

The author believes that her husband lost pride not for a good reason, but because "[m]aybe that’s what happens when our egos take a hit in midlife and we realize we’re not as young and golden anymore." Do you disagree with her here? If not, how would getting a divorce have been a better solution than realizing that his wife was not the problem?

IMO the author is correct in her assessment. (Also for the record, I consider her actions admirable.)

I'm not saying that getting a divorce is necessarily preferable to staying in such a situation; only that I'd have done it if I saw absolutely no other way to regain pride. There are likely ways to regain pride that don't involve divorce, like the author's first suggestion of "go trekking in Nepal", and of course I'd consider those carefully first.

This has probably been requested before, and maybe I'm requesting it in the wrong place, but... Dear LW Powers-That-Be, any chance of a Preview facility for comments? It seems like I edit virtually every comment I make, straight after posting, for typos, missing words, etc. I find the input format awkward to proofread.

I recently had an idea that seemed interesting enough to post here: "Shut Up and Multiply!", the video game

The basic idea of this game is that before each level you are told some probabilities, and then when the level starts you need to use these probabilities in real time to achieve the best expected outcome in a given situation.

The first example I thought of is a level where people are drowning, and you need to choose who to save first, or possibly which method to use to try to save them, in order to maximize the total number of people saved.

Different levels could have different scenarios and objectives.

You are given time to examine the probabilities before the level starts, but once it starts you need to make your decisions in real-time.

Another twist: You see the actual outcome of your actions, randomly generated by the probability formulas. However, you aren't scored based on the actual outcome, but instead you are scored on the expected outcome of your actions, using the expected utility formula. I originally intended this to prevent people from getting a high score just by luck, or to prevent low scores caused by bad luck. Though I later realized that this doesn't actually fix the problem - you can still play repeatedly until, by luck, you happen to guess high-scoring actions. Still, I think it would be a good idea to show both scores.

Other random ideas:

The first few levels should be a tutorial. Showing how to do the calculations in order to maximize your expected score. Or there could be a separate turotial mode. Or maybe the game itself is a bad idea, but the tutorial might still be useful.

During each level you need to make your decisions as quickly as possible - the longer you wait the worse you score. Though maybe only some levels should be like this.

Later levels require more options to choose from, and more complex scenarios.

As much content as possible should be generated randomly, to prevent the game from being the same if you play it again.

Maybe the player could also be scored based on some calculations they do before the level starts? Or just integrate this with the tutorial?

And most importantly: Specifically design the game so that the player must learn to overcome some of the standard biases, in order to maximize their score. We should try to work in as many of these biases as possible. And also plenty of generally useful advice for working with probabilities.

So, now that I posted this idea, I'll let you decide what, if anything, we should do with this idea.

First, is this a stupid idea, that couldn't possibly work as described?

Or is it a good idea, but a low priority, compared to the other projects we're working on?

Should this be a group project? Does anyone volunteer to lead the project? Does anyone want to take on the project entirely on their own? Or should I lead the project, or work on it on my own?

What language would be best to implement this in? Flash? Java? PHP? Python? Something else?

I still haven't earned much karma on this site (only 1 point actually, when I originally posted this). Mainly because I don't expect to have anything original to say. And so I'm posting this here as a comment in the Open Thread, rather than making an actual post of it. If this comment gets enough upvotes for me to be able to make this into its own post, I plan to do so, unless someone objects. Or if anyone would like to take over the idea, please feel free to do so. I don't care about credit, and generally prefer to avoid it. Possibly by the flawed reasoning "credit = responsibility = blame", which I suppose might deserve a post of its own.

The first example I thought of is a level where people are drowning, and you need to choose who to save first, or possibly which method to use to try to save them, in order to maximize the total number of people saved.

I do competitive lifeguarding (possibly the world's weirdest recreational activity) and there is actually an event like this, called Priority Assessment or PA. Your team walks in and finds an area of the pool with a bunch of people drowning (for a team of 4 rescuers, usually it's about 12 victims.) The scoresheets are set up so that you get more points for rescuing the victims who are more likely to survive–i.e. non-swimmers and injured swimmers have a much higher point multiplier than unconscious, submerged victims. PA involves a lot of strategy–it's not always the teams of fast swimmers that win, although that helps. There is an optimal strategy, which has to be worked out in advance because it's a two-minute event.

I've been thinking about educational games as well. The main problem, it seems to me, is that trying to make learning fun for someone who isn't already interested and motivated is a waste of time because you're just trying to hide the teaching under a sugarcoating of computer game, and that never works. On the other hand trying to make learning fun for someone who is already interested and motivated is pointless, because they already want to learn and the game just adds needless hassle like completing levels in order to reach the next piece of knowledge, or whatever game mechanic you're using. It's a pity, because I think of the way games like Portal build up complex puzzles from simpler ones and use the level itself to ask the player leading questions, like a kind of visual/spatial socratic method, and I think there must be a way to use that to teach, espiecally mathematics where visual/spatial metaphors could easily translate into mathematical metaphors... but I just can't come up with a concrete version of the idea that wouldn't be boring or stupid.

Lately I've been thinking that the fastest way to get to grips with a new subject is probably just to memorise big chunks of information without trying to understand it, using techniques like a memory palace and spaced learning programs like Mnemosyne and Anki, then think about what you've learned later, and insight might strike you. This would be espiecally effective if you combined it with a social precommitment to teach your knowledge to someone else, or to take part in a competitive quiz.

Lately I've been thinking that the fastest way to get to grips with a new subject is probably just to memorise big chunks of information without trying to understand it, using techniques like a memory palace and spaced learning programs like Mnemosyne and Anki, then think about what you've learned later, and insight might strike you.

If this is true and you aren't too much of an outlier, it would go a decent way to explain the failure of a good chunk of educational theory in the past few centuries.

If this is true and you aren't too much of an outlier, it would go a decent way to explain the failure of a good chunk of educational theory in the past few centuries.

The basic idea works for me, but I think Tom's simplifying it. It's not about "add to Anki with 0% understanding" vs "gain 100% understanding when first learning"; instead, it's more like "add to Anki with 80% understanding" vs "gain 90% understanding, having had to spend several hours for the extra 10%."

Far too many people tend to get hung up over that one thing in a chapter that they can't understand. More often than not, it's something they could understand perfectly if they just said "meh" and read a few pages ahead, but no; they just stay stuck on that one spot, thinking "wtf is this??!!"

Also, far too many people read books word-by-word when they could get essentially the same amount of information by skimming over the pages. Anki helps here, as it forces you to extract the relevant pieces of information from the text, (or at least stuff that looks important) instead of letting you comfortably wade through a wall of text and believe you've understood it.

(It seems, on first glance, that these two paragraphs contradict each other, but they actually don't. The third one is talking about stuff that looks easy but actually isn't, the second one's talking about stuff that looks difficult, but wouldn't if you'd just read ahead.)

Also, you generally don't have to wait until later for insight into whatever you've failed to understand... More often than not, insight strikes even as you're adding the cards.

I'd suggest making it so you get scored by the number of people you save, but the game is long enough that luck doesn't make a difference.

I wonder if it would be a good idea to give it multiple scores. For example, lives saved, life-years saved, quality-adjusted life-years saved, etc.. This way, you won't have as many problems with people disagreeing with the scoring system.

Alternately, you could just have it so you could change the scoring mode in the options part. It would also act somewhat as a difficulty setting. It would get harder when you have to weigh a destitute child, who will live longer, vs. a middle-class adult, who will be happier.

Reading that, it occurred to me that in all the computer games I've played, it is possible to totally succeed. Kill every monster, pick up every piece of treasure, solve every puzzle, gain the perfect score. (I have not actually played all that many, but I also read some of the games press and it seems to be the usual case.) Even the old arcade games fit the pattern: you can't win them, only endure as long as possible, but until then your goal is to impeccably handle every challenge that comes at you.

Are there any games in which this is deliberately made impossible? For example, PeerInfinity's suggestion of trying to save drowning people, in a scenario that makes it impossible to save all of them (and which is varied every time you play the game, so you can't simply search out the optimal walk-through). Military operations in a city, fighting door-to-door, with innocent civilians everywhere whose lives matter in game terms.

I'm not sure the suggestion of a game in which one cannot 'get the top score' makes sense. It seems contradictory - 'is there an optimal path through the game which is not the optimal path through the game?'

Can you have games where the 'path' to a top score, the optimal play, varies from game to game? Sure. Not every game carries it to quite the extent of Nethack, but most do it to some extent. Non-random games like go or chess are generally the exception, and they can be trivially randomized. But each specific game can be seen as ultimately deterministic: given the output of the random number generator this time, the ideal path is such-and-such. You, the player, may not know it, but that's your fault.

Can you have games which deceive the player about what the best possible score is? Sure. The original Donkey Kong promises that you can play indefinitely; but go too high and the game will always crash. The upper bound is not where one thought it was. Or there are political games in which one tries to prevent 9/11 (IIRC); of course, the game must sooner or later defeat you, like those old arcade games.

What would it mean for a game to have scores players couldn't reach? If in Mario, there is code to paint a picture of a 1-UP on a corner of the screen surrounded by unbreakable blocks, then in what sense is the player missing out on 1k points (or whatever). If a cut scene depicts a hostage dying, then how 'could' I have saved it? What if I can choose between a cut scene depicting hostage A dying, and hostage B? What if it's in-game, and there's a timer or rescuing A triggers the death of B?

Or what if there is a trove of 1 million points coded in, but the only access is to type in a true contradiction? Would the world record holder for Mario really be missing 1 million points off his score just because he can't come up with one? (Yes, there is a number equal to his score+1 million; but there's an infinite number of integers. What makes score+1 million special? All the lower number are special because it's possible to manipulate a given blob of code to display characters we interpret as those lower numbers; but we can't get it to emit any images of higher numbers, and that's that.)

I'm not sure the suggestion of a game in which one cannot 'get the top score' makes sense.

It can make sense if the game does not have a one-dimensional score. World Of Warcraft, The Sims, Second Life, D&D... Life itself, for that matter.

If you choose one sub-game, then there's optimal play for that; if you switch between them, then there's still optimal play, it's just you need to weight it if there is no canonical ultimate score (just like with utilities).

If there aren't any scores or sense of progress at all, I question whether it's a game at all, or whether it merely bears a Wittgensteinian family resemblance. If you and I push around piled pieces on a Go board just for the pleasure of watching the piles build and collapse and form swirling patterns, we're doing something entertaining (maybe) but who would call it a game? To call life itself a game is to either commit a tired weak metaphor, or to drain the word game of all meaning.

The Unpleasant Truth Party Game

I wanted to make this idea a new post, but apparently I need karma for that. So I'll just put it here:

The aim is to come up with sentences that are informative, true and maximally offensive. Each of the participants comes up with a sentence. The other participants rate the sentence for two values, how offensive it is on a scale from 0 (perfectly inoffensive) to 1 (the most unspeakable thing imaginable), and how informative it is from 0 (complete gibberish or an utterly obvious untruth) to 1 (immensely precise and true beyond question). As with any real-world probabilities, exact 0 and 1 should probably be avoided, but anything arbitrarily close to them is fair.

Each sentence is scored by it's offensiveness score Q and its truthfulness score P. The total score of the sentence is P * Q. This will give a higher score the more the statement is both true and offensive.

Coming up with absolute probabilities and calculating the score formula might be a bit hard for a tabletop game. A variation could have the players just ordering the sentences on offensiveness and truthfulness tracks, assign 1 to the top item each, 2 to the next and so on, multiply the two values for each sentence. In this variant, the lowest score wins.

In the ordering game, getting a good position on either track should beat an average position, 4 2 = 8 < 3 3 = 9.

Could this be made into an actually playable game? How many sessions could you play and still have a social circle?

meh. The "say something maximally offensive" game is nothing new, and I'm not sure there's a lot to be gained here.

It isn't just shock value; it isn't just "say something maximally offensive".

Could this be made into an actually playable game? How many sessions could you play and still have a social circle?

Once it starts getting personal, it's all over. A game I used to play with my friends was just debating random propositions (I once defended with considerable success the proposition that puppies are tender and delicious.) I think this was as useful simply to see what pleased the onlookers the most, and there was little chance that someone might say something like 'John's acne is truly grotesque'. How many non-personal, awful truths does anyone know, or could people agree on?

This (IIRC) imported Overcoming Bias post has mangled text encoding ("shōnen anime than shōjo", including a high control character; the structure suggests that this is UTF-8 data reinterpreted as some other encoding, then converted to HTML character references). This suggests that there may be a general problem, in which case all the imported OB posts should be fixed en masse.

Indeed, as Psy-Kosh suggests, that's a LW original.

Perhaps it would have helped if Eliezer had used waapuro-style romanization, or modified Hepburn, as is right and proper (when kana are not acceptable).

IIRC, that one isn't imported but is an LW original and was never on OB. I don't think I've seen such artifacts on any of the imported posts that I've looked at anyways.

The built-in editor for top-level posts is a little buggy. The first time I tried to edit a draft, it mangled the <pre> sections. From then on, I re-pasted every edit.

This comment doesn't really go anywhere, just some vague thoughts on fun. I've been reading A Theory of Fun For Game Design. It's not very good, but it has some interesting bits (have you noticed that when you jump in different videogames, you stay in there air for the same length of time? Apparently game developers all converged on an air time that feels natural, by trial and error). At one point the author asserts that having to think things through consciously is boring, but learning and using unconscious skills is fun. So a novice chess player gets bored quickly having to think through all the moves, while an expert 'just sees' the right moves, and has fun. It made me think of the concept of flow and of Alan Kay's work on Squeak and Etoys, making learning more fun and intuitive with computers (particularly learning mathematics) I think it's called constructionist learning.

It does seem though that we don't have much of a theory of fun, most of the stuff we know we learn through trial and error. If we had a decent model of fun we might be able to make boring learning activities fun, which would help with motivation and akrasia and so on.

I think Flow is one of the most important ideas to have come out of psychology. My hypothesis for why it's not more widely known is that the creator's name is so difficult to spell and pronounce.

My belief is that the learning part of your brain sends a signal to the decision-making part, when the former is experiencing a type of stimulus that is highly learnable. That signal is treated by the decision making part in the same way as a more typically pleasant signal (food, sex, etc) would be. Flow is thus an evolutionary adaptation that makes us seek experiences that help us learn more rapidly (the underlying assumption being that not all stimuli are equally learnable).

I think Flow is pretty good as a theory of fun, or as a theory of fun-from-learning. Flow is the best way to learn. The problem is that not all ideas can be learned in a way that meets the Flow criteria (rapid feedback, ability to experiment, clear goals, challenge keyed to ability level). So the interesting questions in my view are how to rephrase learning problems in such a way that one can enter Flow states when approaching those problems.

I think Flow is one of the most important ideas to have come out of psychology. My hypothesis for why it's not more widely known is that the creator's name is so difficult to spell and pronounce.

It's a sad comment on academia and humanity that this hypothesis is not the least bit implausible.

We totally need an article about Flow. Who's up for writing one?

A few years ago I had developed a theory of game playing and low pressure social group interaction which starts at a similar place as Koster's. I was able to take that starting point about play and patterns and produce empirically testable hypotheses with formal mathematical models of what is happening during play.

And then I stopped working on it because I couldn't seem to get across the concept that learning and fun might be related well enough. Now that I've had a chance to read his book, I might have to reconsider.

Imagine you find a magic lamp. You polish it and, as expected, a genie pops out. However, it's a special kind of genie and instead of offering you three wishes it offers to make you an expert in anything, equal to the greatest mind working in that field today, instantly and with no effort on your part. You only get to choose one subject area, with "subject area" defined as anything offered as a degree by a respectable university. Also if you try to trick the genie he'll kick you in the nads*.

So if you could learn anything, what would you learn?

*This example is in no way intended to imply that women are less worthy of the right to be attacked by genies. Neither is it intended to imply that there could never be a female genie. That would be stupid. Where else could baby genies come from?

Mathematics

Its the foundation for everything else I want to learn. I don't know why I didn't major in it- other than concerns for a paycheck.

The nice thing about mathematics is that you can easily do it outside of school and independently, and when you do it as a mature adult, you do it because you love it and for no other reason. You are free to use better texts than you could as a student, so if you want to brush up on calculus, you can use Spivak or Courant rather than being forced to use low-quality texts that are optimized for the convenience of the professor rather than the insight of the student. There are also so many learning resources available now that weren't available when I was a student -- things like wikipedia, planet math, and physicsforums.com, not to mention software like Octave and Sage.

I'd like to add that one of the nice things about mathematics as a choice is that you can avoid credentialing issues. I'm sure we've all read Hanson on how most of the value of a college degree is in that the college is certifying your abilities, and stamping you.

If you chose world-class ability in economics/financial trading, say, and you are a poor student, then what are you going to do with it? You can't make a killing on the market to prove your abilities; you can't go work as an intern for a firm to prove your knowledge, etc.

Similarly with genetics. If I suddenly gained world-class genetic knowledge, I cannot walk up to Cold Spring Harbor and ask them to let me use some multi-million dollar equipment for a year because I have this awesome bit of research I'd like to do. I simply don't have any proof that I'm not a random bozo who has memorized a bunch of textbooks and papers. I'd have to get lucky and convince a professor or somebody to take me on as an assistant and slowly build up my credentials until I can do the bit of research that will irrefutably establish me as a leading luminary.

Or how about physics? If I specialize in experimental or practical physics, I have the same chicken-and-egg problem; if I specialize in theoretical, then I run the risk of simply being ignored, or written off as a crank (and the better my contribution, the more likely I am to be seen as a crank!).

But with mathematics, I can just crank out a bunch of theorems and send in a paper. If people are still unconvinced, being a mathematical genius, I can just formalize it and send in a Coq/Isabelle/Twelf file consisting solely of the proof.

While mathematics certainly appears to me to be more of a meritocracy than the sciences, it's still the case that the notion of proof has changed over time -- and continues to change (witness Coq and friends) --, as have standards of rigor and what counts as mathematics. There are social and other non-mathematical reasons that influence how and why some ideas are accepted while others are rejected only to be accepted later, and vice versa.

It's an interesting question whether this will always be the case or if it will converge on something approaching unanimously accepted truth and aesthetic criteria. Personally, I think mathematics is intrinsically an artistic endeavor and that the aesthetic aspect of it will never disappear. And where there is aesthetics, there is also politics and other sausage-making activities...

While mathematics certainly appears to me to be more of a meritocracy than the sciences, it's still the case that the notion of proof has changed over time -- and continues to change (witness Coq and friends) --, as have standards of rigor and what counts as mathematics.

The gold standard of what is a proof and what is not was achieved with the first-order predicate calculus a century ago and has not changed since. Leibniz' dream has been realised in this area. However, no-one troubles to explicitly use the perfect language of mathematical proof and nothing else, except when the act of doing so is the point. It is enough to be able to speak it, and thereafter to use its idioms to the extent necessary to clearly communicate one's ideas.

On the other hand, what proofs or theorems mathematicians find important or interesting will always be changing.

I don't really think the question is whether mathematics is more meritocratic - it's an economic question of credentialing. You need credentialing when you cannot cheaply verify performance. If I had a personal LHC and wrote a paper based on its results, I don't think anyone would care too much about whether I have 2 PhDs or just a GED - the particle physicists would accept it. But of course, nobody has a personal LHC.

With mathematics, with formal machine-checkable proofs, the cost of verification is about as low as possible. How long does it take to load a Coq proof and check it? A second or two? Then all someone needs to do is take a look at my few premises; either the premises are dodgy (which should be obvious), or they're common & acceptable (in which case they know I'm a math genius), or I'm exploiting a Coq flaw (in which case I'm also a math genius). Once they rule out #1, I'm golden and can begin turning the genie's gift to good account.

By meritocracy, I meant what you explain by credentialing: the idea that the work alone is absolutely sufficient to establish itself as genius or crackpottery or obvious or uninteresting or whatever, that who you are, who you know, where you went to school and who your advisors were, which conferences you've presented at, the time and culture in which you find yourself, whether you're working in a trendy sub-discipline, etc., that all that is irrelevant.

How much of mathematics is machine-checkable now? My (possibly mistaken) understanding was that even the optimists didn't expect most of existing mathematics for decades at least. And how will we formalize the new branches of mathematics that have yet to be invented? They won't spring forth fully formed as Coq proofs. Instead, they'll be established person-to-person at the whiteboard, explained in coffee shops and over chinese food in between workshop sessions. And much, much later, somebody will formalize the radically revised descendant of the original proof, when the cutting edge has moved on.

I'll know you're right and I'm wrong if I ever begin to hear regular announcements of important new theorems being given in machine-checkable format by unaffiliated non-professionals and their being lauded quickly by the professionals. And that is the easier task, since it is the creation of new branches and the abstraction and merging of seemingly unrelated or only distantly related branches that is the heart of mathematics, and that seems even less likely to be able to be submitted to a theorem prover in the foreseeable future.

How much of mathematics is machine-checkable now?

I'm not sure how one would measure that. The Metamath project claims over 8k proofs, starting with ZFC set theory. I would guess that has formalized quite a bit.

I'll know you're right and I'm wrong if I ever begin to hear regular announcements of important new theorems being given in machine-checkable format by unaffiliated non-professionals and their being lauded quickly by the professionals.

I think that only follows if genius outsiders really do need to break into mathematics. Most math is at the point where outsiders can't do Fields-level work without becoming in the process insiders. Consider Perelman with Poincare's conjecture - he sounds like an outsider, but if you look at his biography he was an insider (even just through his mother!).

This is what I thought everyone was going to say. I don't see why you'd be concerned about the paycheck though, a strong mathematics background could land you a job as a banker or trader or something. But looking at your upvotes it seems like plenty of people agree with you.

My next question would be what you'd like to have a basic introduction to. Plenty of LW posts tend to assume a grounding in subjects like maths, economics or philosophy - which is fine, this is a community for informed people - but it probably shrinks LW's audience somewhat, and certainly shrinks the pool of people who are able to understand all the posts. We probably miss this because nobody's going to jump into the middle of a thread and say, "I lack the education to understand this." espiecally not a casual reader.

My upvotes are probably due to the fact that I said mathematics, rather than any agreement concerning my potential lack of paycheck. I know that a mathematics background could supply me a paycheck at this point in my life, but I was urged against it by some other people when I was choosing my major.

Basic introduction to? Is this in addition to the expertise I got from the genie, or if the genie was only offering me a basic introduction? Do I only get to choose one? Gee that's hard. I'm pretty much working on having a basic introduction to everything already. So, given my existing basic introductions... I think I'd like to get a basic introduction to quantum physics... but that's kind of cheating because I'd have to know a lot of physics and mathematics in the basic intro. I choose that one because I want to know it for purely vain reasons, and it would be nice to save the time of learning it for more "useful" studies.

This blog definitely is going to appeal to a minority of people. I personally do not have the proper education to follow the bayesian/frequentist debate, though I want to hear about it. I think that the healthy practice of linking to information is fantastic, as well as the lesswrong wiki. That way if you know what the person is talking about, you don't have to follow the link, but if you need to learn, it's right there at your fingertips.

Edit: Oh right, and I can't contribute to quantum physics discussions very well either.

"subject area" defined as anything offered as a degree by a respectable university

Hard to choose between Science and Math, but I'll take Math.

Hey, B.Sc is a degree, right?

Biology, specifically brain-related neurosci.

I never could get far studying it because of the immense squick factor, but if I could just KNOW all of it via genie, the squick ought to go away because then it'd be just so much brain bits. Kind of like how intimidating complex and austere symbols become just regular greek letters after learning to read math.

I want to know foreign languages, especially Japanese, but I find them much harder to learn than other things, due to the sheer amount of brute force memorization required to learn vocabulary.

The other thing I would consider is this.

This example is in no way intended to imply that women are less worthy of the right to be attacked by genies. Neither is it intended to imply that there could never be a female genie. That would be stupid. Where else could baby genies come from?

You're solving the wrong problem by including this asterisk. It's easy to just call the genie "it" - which you already did above - and pick a different action - "rip off your arms" would work as well.

I read this and at first I was like, "Damn! Not only did my anti-sexism plan fail, it made me even more sexist!" but then I was all, "No way! I'm going to find a bunch of evidence that genies can't be neuter! That'll show 'em! Show all of them." but then I read the Wikipedia article and it goes, "The pre-Islamic Zoroastrian culture of ancient Persia believed in jaini/jahi, evil female spirits thought to spread diseases to people." and I was totally like, "God fucking damnit! That's like... sexism squared!"

Well you might have won this round, Yudkowsky. But you haven't seen the last of me!

Incidentally, being kicked in the crotch isn't exactly pleasant for women, either...

Yes, but he didn't say "crotch", he said "nads". Female gonads (ovaries) are internal, so we could be kicked in the nads in the same sense as it is possible to kick someone "in", say, the kidney. It's just not a traditional target.

::reads that again::

::investigates definitions of "nads"::

Wow.

I have just been owned.

Consider me extremely impressed. Having been soundly outmatched in the battle of nitpicking, I am hereby reduced to making fawning fanboy puppy dog noises.

::takes deep breath::

oh-my-god-i'm-not-worthy-can-I-have-your-autograph-will-you-marry-me-teach-me-oh-great-master-squee-etc-etc...

::runs out of breath::

Phew. I hope I got that out of my system. Let's see...

::still has the completely ridiculous urge to propose marriage::

Guess not.

::sighs::

I have now acquired yet another pointless Internet crush. Oh well, nothing to do but try to ignore it...

No, I will not marry you. I do, however, accept Internet crushes and encourage you to accordingly familiarize yourself with my works of fiction and tell all your friends about them. :)

You can have my autograph if you commission a work of art.

Hello, I went through the archive of your magical girl comic. I'm gonna keep my eye on it.

The way the premise is presented is nonsensical, but that's a-ok in the genre, and I suspect you just wanted to through the setup quickly. Girls' publicity is a nice twist to the trope, and I hope you'll explore it thoroughly. I really like the tiny dragons - my favorite strip involves them. Oh, and the fact that the girls are not lawful stupid (a too common disorder among magical girls) is a big, big plus.

On the flipside, I think you should work on backgrounds and perspective more. Especially Datekaln - painting its sky solid green doesn't do it justice. At least make a reusable texture like you did with Earth's sky presumably.

Thanks for the feedback. Everybody loves the pagets and everybody loves that page - I should change the title to "Pagets Are Cute (and some silly humans sometimes do things)."

Backgrounds are very tedious and unrewarding to draw, so my progress on them is slow. I'll mess with possible simple textures for Datékaln's sky, though, since that's easy. (Earth's sky is just the Photoshop cloud filter.)

For personal interest, neuroscience (and the genie would wave his wand, and I would be V. Ramachandran). For benefit to society, probably genetics (or do colleges offer degrees in AI?)

I'd also like to see if I could use the genie to answer one of the great questions of the ages. I guess it all depends on how the "expert" thing is implemented. For example, if the genie created a great expert in quantum mechanics, would the expert simply know and understand facts about quantum mechanics, or would they also be such an expert as to have the correct opinion on the Copenhagen vs. many worlds question? After all, Tom did say "an expert equivalent to the greatest mind today", and there are minds that are pretty sure they know the answer to that question, so the mind that has the correct opinion on it must be greater than an equivalent mind that doesn't. That means if I wake up and find myself believing Many Worlds, I have very strong evidence that Many Worlds is correct.

If I thought that plan would work, I'd probably choose Philosophy. I might get kicked in the 'nads, but for the chance to have genie-approved answers all the great philosophical questions at once, it'd be worth it.

I'd pick neurology, assuming that doesn't cause my brain to implode.

I would go for whatever could make me the most money with the pure skill that they teach in school. In most professions, it seems like you need either some talent at sales or self-promotion or just luck to be successful, in addition to whatever skill you supposedly have. I think that maybe being the world's greatest computer engineer or something like that would probably get you paid millions without having do much other than be amazing at what you do.

My initial thinking was cardiac surgeon or something like that, but on further reflection I think that is about the worst choice possible. You have this amazing skill, but what do you do with it? Do you have to go to medical school and get easy As before you can get licensed to use it? That would really suck.

I'd have to agree with "math", given that the ability granted includes not just comprehensive knowledge, but extreme ability to make novel important and fundamental discoveries in the field.

(How is babby genie formed? (Sorry, couldn't resist))

Does this apply only to theoretical expertise, or could I choose (say) vocal music and then totally win on American Idol?

I checked with the genie and he said fine. Not very rationalist-y of you, though.

I'm more likely to become massively rich by being a fantastic singer than I am to become massively rich by being a fantastic philosopher, or even a fantastic economist. My education-related values change some if I don't have to invest time or effort in acquiring the expertise. That said, I don't think I'll pick singing. I think I'll pick creative writing.

I'm more likely to become massively rich by being a fantastic singer than I am to become massively rich by being a fantastic philosopher, or even a fantastic economist.

It's always fun to see what empirical facts might change one's assessment. Philosophers, ever since Thales at least, haven't been known for wealth but - Are you sure becoming one of the greatest economists in the world wouldn't be likely to make you massively rich?

I'm sure we both agree that the average economist makes more than your average singer (and median too); but have you considered that superstar economists can still make more than superstar singers?

Michael Jackson is one of the wealthiest singers of all time (wealthiest?), yet he died with maybe 500 million USD in assets; there were hedge fund folks who made several times that in 2008 alone. And he doesn't hold a candle to Warren Buffett. Or consider Lawrence Summers. Despite a career largely spent in government or academia, his world-class status means that he can do things like pick up a >5million USD a year salary working less than a day a week. We may argue that these kind of financial bonuses are obscene and unfair, but economists and other financial types reap them nevertheless...

I'm sure that extraordinary expertise at economics would enable people with the right mindset to make large amounts of money, but the obvious avenues (e.g. spending all day trading stocks) would not interest me, and I'd be unlikely to value the money enough to put up with them in the quantity necessary to become massively rich. If I magically acquired extraordinary expertise at economics, I'd probably mess around with it until I had enough money to hand the reins to a less-skilled accountant to handle and invest for me and keep me in housing and groceries for the rest of my life. I'd be more comfortably upper-middle-class than rich. It's possible that my extraordinary expertise at economics would also inform me of fun ways to make money with it, but none spring immediately to my unskilled-at-economics mind.

Its quite a leap to go from economist to hedge fund manager. Their skill sets are not at all the same. The best way to make bank if you are a brilliant economist is: 1) make a fundamental contribution to economics, especially related to finance. 2) win nobel prize or at least have your contribution adopted by industry. 3) get paid millions to "consult" or "advise" hedge fund managers who will use your name to attract investors and probably never ask you to do actual work.

Its quite a leap to go from economist to hedge fund manager.

Not for our genie!

EDIT: also, I think trading skills are covered under either economics or another college major, so the genie can give you them.

So you pick the area with the highest expected monetary payoff? I'm not sure that skills in singing or creative writing serve that end, since the competition is so intense and the selection process for successful singers and writers seems somewhat arbitrary and random.

I see what you mean about the amount of effort required changing which area you would pick, and that was part of what I was getting at. I wonder how many of us choose to study a particular subject because it's easier than the alternatives, then rationalise it later as what we really wanted. If effort wasn't a factor and you could have chosen to study anything, what would it have been? If we on Less Wrong find ways to make learning easier, what will you do?

Creative writing might not serve that end, but it's hardly the longest of long shots, and moreover, writing creatively is something I enjoy, unlike doing math or working on hard science or whatever. So even if I don't wind up writing bestselling books and making a billion dollars, I can still have fun writing excellent books. It's a tradeoff between expected monetary payoff, and the enjoyability of the task to turn the skill into the payoff.

I'm studying philosophy because most of the time, studying philosophy is fun. It's not consistently easy, and it's not going to make me a lot of money now or later, but it entertains me. If effort wasn't a factor I could study, oh, medicine, and be a brilliant physician, or law and be a brilliant lawyer, but I don't expect that (even effort aside) I would enjoy the study or practice of those fields.

So you wouldn't pick instant expertise in philosophy because that would take the fun out of it. Do you think that if studying philosophy was easier, it would be less fun? I'm not convinced because no matter how much of an expert you are, there's still more to learn. The genie is offering you the chance to be at the cutting edge of your field.

So you wouldn't pick instant expertise in philosophy because that would take the fun out of it.

No. I'm saying that fun is my motivation for studying philosophy, because when I decide how to invest years of my life, I want to choose fun investments. Your genie opens up the options of choosing to (productively) invest directly in the practice, rather than the study, of various fields. There are fields that I think I would enjoy being an expert in that I would not enjoy the process of studying to become an expert in, especially when you consider that intrinsic talent/motivation/etc. might block me from acquiring expertise in some fields that the genie could make me brilliant at. Some of those fields might also net me money. Bypassing a potentially-unfun studying step makes several of them more appealing than philosophy.

OK, I see where you're coming from. Learning to play the violin is frustrating, but it's probably fun once you can do it.

So if we could find a way to make learning easier, hypothetically speaking, you would use that opportunity to be a better generalist rather than further specialising in your chosen area? That's interesting because specialists are usually better paid. I wonder if that's a common point of view.

LWers are generalists, in general. Most of us know some psychology, some economics, some philosophy, some programming and so on. But I wonder what Less Wrong would be like if we all specialised, while remaining united by the pursuit of rationality. I think Robin Hanson said something similar in that post where he compared us to survivalists, trying to learn everything and failing to reap the benefits of specialisation and cooperation.

Anyway sorry for rambling like this. I tend to use these open threads as an opportunity to think out loud, and nobody's told me to shut up yet so I just keep going.

If learning, in general, became easier for me, I would learn more, in general. I don't think I'd use it to do more philosophy; I think I'd use it to do the same amount of philosophy in less time.

If learning became a whole lot easier, I'd probably study foreign languages in my spare time. The ability to communicate in more languages would open up more learning potential than most other tasks.

On the subject of advice to novices, I wanted to share a bit I got out of Understanding Uncertainty. This is going to seem painfully simple to a seasoned bayesian, but it's not meant for you. Rather, it's intended for someone who has never made a probability estimate before. Say a person has just learned about the bayesian view of probability and understands what a probability estimate is, actually translating beliefs into numerical estimates can still seem weird and difficult.

The book's advice is to use the standard balls-in-an-urn model to get an intuitive sense of the probability of an event. Imagine an urn that contains fifty red balls and fifty white balls. If you imagine drawing a ball at random from that urn, you get an intuitive sense for an event that has fifty percent probability. Now either increase or decrease the number of red balls in the urn (while correspondingly altering the number of white balls so that the total number of balls still sums to one hundred) until the intuitive probability of drawing a red ball seems to match your intuitive probability of the event occuring. The number of red balls in the urn equals your (unexamined, uncorrected) probability estimate for the event.

Once you teach a person how to put numbers on their beliefs, you've helped them make a first step in overcoming bias, because numbers are easy to write down and check, and easy to communicate to other people. They can also begin to quantify their biases. Anyone can learn to repeat the phrase, "The availability heuristic causes us to estimate what is more likely by what is more available in memory, which is biased toward vivid, unusual, or emotionally charged examples." (guessing the teacher's password) but it takes a rationalist to ask: how much, on average, does the availability heuristic reduce the accuracy of my beliefs? Where does it rank on the list of biases, in terms of the inaccuracy it causes?

Thanks, if this is what you're saying it is, it's something I've been looking for. :-)

A very common belief here is that most human behaviour is based on Paleolithic genes, and only trivial variations are cultural (memetic), coming from fresh genes, or from some other sources.

But how strong is the evidence of Paleogenes vs memes vs fresh genes (vs everything else)?

Fresh genes are easy to test - different populations would have different levels of such genes, so we could test for that.

An obvious problem with Paleogenes is that there aren't really that many genes to work with. Also, do we know of any genetic variations that alter these behaviours? If preference for large breasts was genetic, surely there might be a family somewhere with some mutation which would prefer small breasts. Do we have any evidence of that?

So I suspect memes might be much more important relative to Paleogenes than we tend to assume.

I think we can fairly easily come up with examples of things that are regarded as attractive in some cultures and not others.

For example, tanned skin. Back in the "olden days" in Europe, pale skin was considered the ideal. The much-desired "fair maiden" in old tales is literally one with light-colored skin that is kept out of the sun so it doesn't tan. Today, in the U.S. at least, skin with a slightly bronze tan is often considered the ideal.

This may or may not have to do with social class. Prior to industrialization, lower class people would be tanned from working outside on farms, while higher class people (nobility, etc.) could stay inside and keep their skin nice and pale. Once poor people switched from working on farms to working in indoor factories, they, too, had pale skin, while the wealthier could afford to waste time sitting in the sun getting a tan. "Find signals of high status attractive" might be a genetically influenced trait (I'd be surprised if it weren't) but genes don't seem to determine exactly how people signal high status.

Plenty of behavior has genetic influences, but people learn an awful lot from their environment, too. When a dog is trained to roll over on command, is that a genetic behavior? If it is, then so is everything and it becomes a meaningless category.

If preference for large breasts was genetic, surely there might be a family somewhere with some mutation which would prefer small breasts. Do we have any evidence of that?

Brain-coding phenomena like sexual preferences seem to be built from large collections of genes that are interconnencted with other systems, such that there aren't many possible mutations that would undo the feature without wreaking havoc elsewhere in the phenotype as well.

In fact, the universality of such preferences across neurologically intact humans is evidence that they come from Paleogenes rather than memes or fresh genes, either of which can more easily be altered without deleterious effects elsewhere.

I'm not saying Paleogenes are not a possible explanation, but I haven't seen much in terms of such evidence like:

  • I don't think it's so common for people to go around the world, and actually verify that people in statistically significant number of virtually isolated tribes do have preferences for larger breasts etc. So universality is more postulated than actually empirically found. Even if you find extremely common behaviour, it can still be memetic, as a lot of memes are copied from parents to children. How many behaviours are empirically known to be universal?
  • Mutations to such genes would be non-lethal, and some would only mildly reduce inclusive fitness. We have plenty of genetic diseases in the population affecting more important genes. So how come we haven't discovered mutations in the wild that alter genes controlling this supposedly genetic behaviour.
  • We know very few genes obviously linked with behaviour, and saying it's coded by emergent interaction of multiple genes is just handwaving away the problem. There's a pretty low ceiling of how much can be straightforwardly coded this way, and I'd expect some serious evidence of some mechanism of complex genetically coded behaviour.

http://the10000yearexplosion.com/

The 10000 year Explosion shows very good evidence that this isn't quite true; many significant genetic adaptations are indeed far more recent and have been developping faster since the end of the Paleolithic.

It's also an enjoyable read.

A very common belief here is that most human behaviour is based on Paleolithic genes, and only trivial variations are cultural (memetic), coming from fresh genes, or from some other sources.

...

If preference for large breasts was genetic, surely there might be a family somewhere with some mutation which would prefer small breasts. Do we have any evidence of that?

Maybe there is also disagreement about what is and isn't a trivial variation.

If preference for large breasts was genetic, surely there might be a family somewhere with some mutation which would prefer small breasts. Do we have any evidence of that?

On the other hand, do we have disconfirming evidence? (Would we expect to have noticed?)

All such evidence would be expected to come from different times or from isolated communities, today vast majority of the world population lives in one connected memetic soup. Unfortunately I don't know enough about anthropology to give particularly convincing evidence.

Wikipedia search suggests some cultures don't care much about breasts at all, what you can consider weak evidence against Paleogenetic explanation.

Wikipedia search suggests some cultures don't care much about breasts at all, what you can consider weak evidence against Paleogenetic explanation.

Weak, yeah. After all, Westerners consider the face to be a great part of a person's sex appeal, and it's very important in sex (kissing, oral sex, etc.) - yet they don't cover it up. Do they not care?

What's really needed is data showing that breast size or proportions are uncorrelated with reproductive success, or at least with ratings of attractiveness.

Sure:

"All conventional theories of cultural evolution, of the origin of humans, and what makes us so different from other species. All other theories explaining the big brain, and language and tool use and all these things that make us unique, are based upon genes. Language must have been useful for the genes. Tool use must have enhanced our survival, mating and so on. It always comes back, as Richard Dawkins complained all that long time ago, it always comes back to genes.

The point of memetics is to say, "Oh no it doesn't." There are two replicators now on this planet. From the moment that our ancestors, perhaps two and a half million years ago or so, began imitating, there was a new copying process. Copying with variation and selection. A new replicator was let loose" [...] - Sue Blackmore.