trentmkelly/LessWrong-43k huggingface dataset:
Formalized math: dream vs reality
by cousin_it — 2009-07-09T20:51:04.087Z

(Disclaimer: this post is intended as an enthusiastic introduction to a topic I knew absolutely nothing about till yesterday. Correct me harshly as needed.)

We programmers like to instantly pigeonhole problems as "trivial" and "impossible". The AI-Box has been proposed as candidate for the simplest "impossible" problem. Today I'd like to talk about a genuinely hard problem that many people quickly file as "trivial": formalizing mathematics. Not as in, teach the computer to devise and prove novel conjectures. More like, type in a proof for some simple mathematical fact, e.g. the irrationality of the square root of 2, and get the computer to verify it.

Now, if you're unfamiliar with the entire field, what's your best guess as to the length of the proof? I'll grant you the generous assumption that the verifier already has an extensive library of axioms, lemmas and theorems in elementary math, just not this particular fact. Can you do it in one line? Two lines? (Here's a one-liner for humans: when p/q is in lowest terms, p2/q2 is also in lowest terms and hence cannot reduce to 2.)

While knowledgeable readers chuckle to themselves and the rest frantically calibrate, I will take a moment to talk about the dream...

Since the cutting edge of math will obviously always outrun any codification effort, why formalize proofs at all? Robert S. Boyer (of Boyer-Moore fame) spelled out his vision of the benefits in the QED Manifesto in 1993: briefly, a machine-checkable repository of humanity's mathematical knowledge could help math progress in all sorts of interesting ways, from educating kids to publishing novel results. It would be like a good twin of Cyc where the promises actually make sense.

But there could be more than that. If you're a programmer like me, what word first comes to your mind upon imagining such a repository? Duh, "refactoring". Our industry has a long and successful history of using tools for automated refactorings, mechanically identifying opportunities to extract common code and then shove it around with guaranteed conservation of program behavior. Judging from our experiences in shortening large ad-hoc codebases, this could imply a radical simplification in all areas of math at once!

Import Group Theory. Analyze. Duplicate Code Spotted: 119 Instances. Extract? Yes or No.

...Or so goes the dream.

You ready with that estimate? Here's a page com...
Recommended reading for new rationalists
by XFrequentist — 2009-07-09T19:47:02.279Z

This has been discussed in passing several times, but I thought it might be worthwhile to collect a list of recommended reading for new members and/or aspiring rationalists. There's probably going to be plenty of overlap with the SingInst reading list, but I think the purposes of the two are sufficiently distinct that a separate list is appropriate.

Some requests:

A list of blog posts can be collected at another point in spacetime; for now, please stick to books, book sections, or essays1.

Please post a single suggestion per comment, so upvoting can determine the final list for the eternal fame of wikihood.

Please limit yourself to no more than 3-5 suggestions. We could probably all think of dozens, try and think what would actually be the best for the purposes of this site.

Please only suggest an entry if you've read it. Judgement Under Uncertainty, while certain to make the list, should be put there by someone who has invested the time and waded through it (i.e. someone other than me).

Please say why you're suggesting it. What did you learn from it? What is its specific relevance to rationality? (ETA)

Happy posting!

PS - Is there a "New Readers Start Here" page, or something similar (aside from "About")? I seem to remember someone talking about one, but I can't find it.

1"Everything Eliezer has ever written (since 2001)... twice!" while likely a highly beneficial suggestion for every single human being in existence, is not an acceptable entry. A Technical Explanation of Technical Explanation is fine. If you're not sure whether to classify something as "an essay" or "a blog post", there is a little-known trick to distinguish the two: essays contain small nuggets of vanadium ore, and blog posts contain shreds of palladium. Alternatively, just use your best judgement.
Revisiting torture vs. dust specks
by cousin_it — 2009-07-08T11:04:39.325Z

In line with my fine tradition of beating old horses, in this post I'll try to summarize some arguments that people proposed in the ancient puzzle of Torture vs. Dust Specks and add some of my own. Not intended as an endorsement of either side. (I do have a preferred side, but don't know exactly why.)

The people saying one dust speck is "zero disutility" or "incommensurable utilities" are being naive. Just pick the smallest amount of suffering that in your opinion is non-zero or commensurable with the torture and restart.

Escalation argument: go from dust specks to torture in small steps, slightly increasing the suffering and massively decreasing the number of people at each step. If each individual change increases utility, so does the final result.

Fluctuation argument: the probability that the universe randomly subjects you to the torture scenario is considerably higher than 1/3^^^3 anyway, so choose torture without worries even if you're in the affected set. (This doesn't assume the least convenient possible world, so fails.)

Proximity argument: don't ask me to value strangers equally to friends and relatives. If each additional person matters 1% less than the previous one, then even an infinite number of people getting dust specks in their eyes adds up to a finite and not especially large amount of suffering. (This assumption negates the escalation argument once you do the math.)

Real-world analogy: we don't decide to pay one penny each to collectively save one starving African child, so choose torture. (This is resolved by the proximity argument.)

Observer splitting: if you split into 3^^^3 people tomorrow, would you prefer all of you to get dust specks, or one of you to be tortured for 50 years? (This neutralizes the proximity argument, but the escalation argument also becomes non-obvious.)

Oh what a tangle. I guess Eliezer is too altruistic to give up torture no matter what we throw at him; others will adopt excuses to choose specks; still others will stay gut-convinced but logically puzzled, like me. The right answer, or the right theory to guide you to the answer, no longer seems so inevitable and mathematically certain.

Edit: I submitted this post to LW by mistake, then deleted it which turned out to be the real mistake. Seeing the folks merrily discussing away in the comments long after the deletion, I tried to undelete the post somehow, but not...
Causality does not imply correlation
by Richard_Kennaway — 2009-07-08T00:52:28.329Z

It is a commonplace that correlation does not imply causality, however eyebrow-wagglingly suggestive it may be of causal hypotheses. It is less commonly noted that causality does not imply correlation either. It is quite possible for two variables to have zero correlation, and yet for one of them to be completely determined by the other.

The causal analysis of statistical information is the subject of several major books, including Judea Pearl's Causality and Probabilistic reasoning in intelligent systems, and Spirtes et al's Causation, Prediction, and Search. One of the axioms used in the last-mentioned is the Faithfulness Axiom. See the book for the precise formulation; informally put it amounts to saying that if two variables are uncorrelated, then they are causally independent. As support for this, the book offers a theorem to the effect that while counterexamples are theoretically possible, they have measure zero in the space of causal systems, and anecdotal evidence that people find fault with causal explanations violating the axiom.

The purpose of this article is to argue that this is not the case.

The counterexample consists of just two variables A and B. The time series data can be found here, a text file in which each line contains a pair of values for A and B. Here is a scatter-plot:

The correlation is not significantly different from zero. Consider the possible causal relationships there might be between two variables, assuming there are no other variables involved. A causes B; B causes A; each causes the other; neither causes the other. Which of these describes the relationship between A and B for the above data?

The correct answer is that none of the four hypotheses can be rejected by these data alone. The actual relationship is: A causes B. Furthermore, there is no noise in the process. A is varying randomly, but B is deterministically caused by A and nothing else, and not by a complex process either. The process is robust: it is not by an accident that the correlation is zero. Every physical process that is modelled by the very simple mathematical relation at work here (to be revealed below) has the same property.

Because I know the process that generated these data, I can confidently predict that it is not possible for anyone to discover from them the true dynamical relation between A and B. So I'll make it a little ea

...
Can self-help be bad for you?
by Tom_Talbot — 2009-07-07T20:40:44.330Z

From the NHS Behind the Headlines blog:

“Self help makes you feel worse,” BBC News has reported. It says that the growing trend of using self-help mantras to boost your spirits may actually have a detrimental effect. The news comes from Canadian research, which found that people with low self-esteem felt worse after repeating positive statements about themselves.

Although positive self-statements are widely believed to boost mood and self-esteem, they have not been widely studied, and their effectiveness has not been demonstrated. This experimental study sought to investigate the contradictory theory that these statements can be harmful.

The researchers had a theory that when a person feels deficient in some way, making positive self-statements to improve that aspect of their life may highlight the discrepancy between their perceived deficiency and the standard they would like to achieve. The researchers carried out three studies in which they manipulated positive self-statements and examined their effects on mood and self-esteem.

Something about the hypothesis sounds familiar:

This experimental research among a group of Canadian university students has found that positive statements may reinforce that positivity among those with high self-esteem, and make them feel even better. But it causes those with low self-esteem to feel worse and to have lower self-esteem.

The researchers say that this theory is based on the idea of ‘latitudes of acceptance’, i.e. messages that reinforce a position close to one’s own are more likely to be persuasive than messages that reinforce a position far from one’s own. As they suggest, if a person believes that they are unlovable and keeps repeating, "I’m a lovable person", they may dismiss this statement and possibly reinforce their conviction that they are unlovable.

What do you think? Is this plausible, or is it an attempt to shoehorn one of those trendy heuristics-and-biases-related hypotheses into a study on self-esteem? If you accept the validity of the study and its conclusion, does it influence LW's Rationalists Should Win self-help philosophy? What if it is literally true that some people are more lovable and some less, and that this has unavoidable effects on self-esteem? Do low self-esteem rationalists need different techniques from those with high s...
An interesting speed dating study
by CronoDAS — 2009-07-07T07:09:42.080Z

I recently found an article in the New York Times that talks about a speed dating study that is going to be published in an upcoming issue of the journal Psychological Science. Given the usual state of science journalism, the fact that the article includes links that let me find a press release about the upcoming paper and a 20-page PDF file containing the paper itself was very helpful.

According to most studies and in accordance with popular stereotypes, men are normally less selective than women when it comes to evaluating potential romantic partners - in general, it appears that men are more likely to want to date any given woman than women are to want to date any given man. In a typical speed dating experiment, men and women rate potential partners as either a "yes" or a "no" depending on whether or not they want to see that person again. Men almost always rate a larger percentage of women as a "yes" than women do men, and, according to this paper, this is a fairly robust finding that generalizes over many different contexts. The usual explanation of this phenomena is based on evolutionary psychology: a female has a lot more to lose from a bad mate choice than a male does. If there were a biological, genetic basis for this tendency, it should be difficult to come up with an experimental setup in which women are less selective and men are more selective.

However, that's not the case at all. This study demonstrates that a small, seemingly trivial change in the speed dating ritual results in a (partial) reversal of the normal results. You see, in practically every speed dating setup, when it is time to interact with a new partner, men physically leave their seat and move to the table where the next woman is sitting, while the women remain seated and wait for the men to approach them. The authors of this study had the men remain still and had the women change seats, and found that this was all it took to wipe away the usual pattern: when the women were required to physically approach while the men remained still, the women became less selective then the men, reporting greater romantic interest and "yes"ing partners at a higher rate. "Rotaters" also reported greater self-confidence than "sitters", regardless of gender.

I suggest that you go read the paper, or at least the press release, yourself; my summary doesn't really do it justice, and I'm leaving the impli...
The Dangers of Partial Knowledge of the Way:  Failing in School
by Gordon Seidoh Worley — 2009-07-06T15:16:41.776Z

I lost the Way, even when I didn't know what I was trying to follow, when I learned a Dangerous Truth about school. This is a brief recounting of how I lost the Way, came back, and what I believe we can learn from this. I hope you find it instructive.

I suffered from insomnia as a child. Not because of any traumatic events or abuse (if anything I had an exceptionally comfortable childhood), but because I would lay awake in bed, staring into the darkness and worrying about school. I worried that I wouldn't complete assignments, that I would fail in subjects, and that terrible things would happen if I didn't make straight As. None of my fears were well founded, though: I was never at any serious risk of failing to complete an assignment, getting anything worse than a B for a quarter grade in a subject, or having indeterminate terrible things happen to me. I experienced this anxiety in part because I was suffering from undiagnosed obsessive-compulsive disorder and in part because I believed that the most important thing in life was to succeed in school. If school was a game, I was playing to win.

I continued in this mode all the way until I entered high school (9th grade in Florida, USA). Since it's not significant to this post I'll omit most of the details, but the short story is that I did not enjoy high school for a multitude of reasons, not least of which was that I felt held back by teachers and administrators who didn't want me advancing my learning too far past the level they were trying to teach.1 I don't think most of them were being malicious, but had their hands forced by an educational system that is more concerned with average performance and improving the results of underperforming students than allowing exceptional students to succeed. Looking back, if I'd had more guts I would have pushed to take my GED and gone to early college, but instead I wallowed in my high school's educational mire until I had wasted nearly all of four years.

Having finished my four year sentence to secondary education and graduating with high marks and my belief in the educational system still intact, I began college hopeful that I would find a better learning environment, and with only a few exceptions, I did. I enjoyed most of my classes, even if I did sleep through the middle 2/3rds of nearly ever cl...
Can chess be a game of luck?
by Rune — 2009-07-06T03:08:32.930Z

Gil Kalai, a well known mathematician, has this to say on the topic of chess and luck:

http://gilkalai.wordpress.com/2009/07/05/chess-can-be-a-game-of-luck/

I didn't follow his argument at all, but it seems like something other LW posters may understand, so I decided to post it here. Do comment on his arguments if you agree or disagree with him.
Media bias
by PhilGoetz — 2009-07-05T16:54:37.819Z

No, I don't mean that the news media are biased politically. I mean that authors are biased by the media they use.

I'm learning about support vector machines (SVMs). There are a lot of books and articles written on SVMs. There are also a whole lot of video lectures on SVMs at videolectures.net (see "kernel methods").

People go into much greater detail in lectures than in text. I like to work with text. I'd like to have a text on SVMs that goes into as much detail as videos on SVMs usually do, and works out the ideas behind the concepts as thoroughly, but no such text exists. For some reason, giving a 5-hour lecture series in which you describe the motivations, applications, and work out the mathematical details is acceptable; but writing a text of the same level of detail, which might take only 2 hours to read, is not.

Perhaps this is because writers are motivated to keep pagecounts low. But pagecount no longer matters with electronic articles. Yet writers still don't want to explain things thoroughly. They certainly aren't saving their readers any time by leaving out intermediate steps. A longer article would take less time to read (and possibly less time to write). Another problem with the pagecount theory is that texts routinely include footnotes and appendices, contributing to the pagecount; yet relegate them to the back of the book, as if embarassed of them, despite the fact that this makes them very difficult to use.

It's especially bad in math, in which writers have a long tradition of deliberately concealing difficult steps and leaving them "as an exercise to the reader". For some reason it is considered bad form to write out all of the steps in a proof, even if adding one or two lines could save the reader five minutes of puzzling. I read an electronic article yesterday where the author said, "These two equations are actually equivalent. Do you see why?"

I think people have adopted a set of cultural biases about what is appropriate in lectures vs. in writing by simply counting observations, without thinking about the systematic sample bias. Speakers speak the way they've seen other speakers speak, without recollecting that most of those speakers were instructors. Technical writers, meanwhile, are picking up their cues from authors of textbooks, which are writt...
The enemy within
by Roko — 2009-07-05T15:08:05.874Z

I read an article from the economist subtitled "The evolutionary origin of depression" which puts forward the following hypothesis:

As pain stops you doing damaging physical things, so low mood stops you doing damaging mental ones—in particular, pursuing unreachable goals. Pursuing such goals is a waste of energy and resources. Therefore, he argues, there is likely to be an evolved mechanism that identifies certain goals as unattainable and inhibits their pursuit—and he believes that low mood is at least part of that mechanism. ...

[Read the whole article]

This ties in with Kaj and PJ Eby's idea that our brain has a collection of primitive, evolved mechanisms that control us via our mood. Eby's theory is that many of us have circuits that try to prevent us from doing the things we want to do.

Eliezer has already told us about Adaptation-Executers, not Fitness-Maximizers; evolution mostly created animals which excecuted certain adaptions without really understanding how or why they worked - such as mating at a certain time or eating certain foods over others.

But, in humans, evolution didn't create the perfect the perfect consequentialist straight off. It seems that evolution combined an explicit goal-driven propositional system with a dumb pattern recognition algorithm for identifying the pattern of "pursuing an unreachable goal". It then played with a parameter for balance of power between the goal-driven propositional system and the dumb pattern recognition algorithms until it found a level which was optimal in the human EEA. So blind idiot god bequeathed us a legacy of depression and akrasia - it gave us an enemy within.

Nowadays, it turns out that that parameter is best turned by giving all the power to the goal-driven propositional system because the modern environment is far more complex than the EEA and requires long-term plans like founding a high-technology startup in order to achieve extreme success. These long-term plans do not immediately return a reward signal, so they trip the "unreachable goal" sensor inside most people's heads, causing them to completely lose motivation.

However, some people seem to be naturally very determined; perhaps their parameter is set slightly more towards the goal-driven propositional system than average. These people rise up from council flats to billionaire-dom and celebrity status. People like Alan Sugar....
Not Technically Lying
by Psychohistorian — 2009-07-04T18:40:02.830Z

I'm sorry I took so long to post this. My computer broke a little while ago. I promise this will be relevant later.

A surgeon has to perform emergency surgery on a patient. No painkillers of any kind are available. The surgeon takes an inert saline IV and hooks it up to the patient, hoping that the illusion of extra treatment will make the patient more comfortable. The patient asks, "What's in that?" The doctor has a few options:

"It's a saline IV. It shouldn't do anything itself, but if you believe it's a painkiller, it'll make this less painful.

"Morphine."

"The strongest painkiller I have."

-The first explanation is not only true, but maximizes the patient's understanding of the world.
-The second is obviously a lie, though, in this case, it is a lie with a clear intended positive effect: if the patient thinks he's getting morphine, then, due to the placebo effect, there is a very real chance he will experience less subjective pain.
-The third is, in a sense, both true and a lie. It is technically true. However, it's somewhat arbitrary; the doctor could have easily have said "It's the weakest painkiller I have," or "It's the strongest sedative I have," or any other number of technically true but misleading statements. This statement is clearly intended to mislead the hearer into thinking it is a potent painkiller; it promotes false beliefs while not quite being a false statement. It's Not Technically Lying. It seems that it deserves most, if not almost all, the disapproval that actually lying does; the truth does not save it. Because language does not specify single, clear meanings we can often use language where the obvious meaning is false and the non-obvious true, intentionally promoting false beliefs without false statements.

Another, perhaps more practical example: the opening two sentences of this post. I have been meaning to write this for a couple weeks, and have failed mostly due to akrasia. My computer broke a few months ago. Both statements are technically true,1 but the implied "because" is not just false, but completely opposite the truth - it's complex, but if my computer had not broken, I would probably never have written this post. I've created the impression of a quasi-legitimate excuse without actually saying anything false, because our conventional use of language filled in the gaps that would have been lies.

The distinction between tell...