Negative and Positive Selection

(Originally posted to my blog, The Rationalist Conspiracy; cross-posted here on request of Lukeprog.)

You’re the captain of a team, and you want to select really good players. How do you do it?

One way is through what I call positive selection. You devise a test – say, who can run the fastest – and pick the people who do best. If you want to be really strict, like if you’re selecting for the Olympics, you only pick the top fraction of a percent. If you’re a player, and you want to get selected, you have to train to do better on the test.

The opposite method is negative selection. Instead of one test to pick out winners, you design many tests to pick out losers. You test, say, who can’t run very well when it’s hot out, and get rid of them. Then you test who can’t run very well when it’s cold out, and get rid of them. Then you test running in the rain, and get rid of the losers there. And so on and so forth. When you’re strict with negative selection, you have lots and lots of tests, so that it’s very hard for any one person to pass through all the filters.

I think a big part of where American society’s gone wrong over the last hundred years is the ubiquitous use of negative selection over positive selection. (Athletics is one of the only exceptions. It’s apparently so important that people really care about performance – as opposed to, say, in medicine, where we exclude brilliant doctors if they don’t have the stamina to work ninety hours a week.) A single test can always be flawed; for example, IQ tests and SATs have many flaws. However, with negative selection, how badly you do is determined by the failure rate of every test combined. If you have twenty tests, and even one of them is so flawed it excludes good players, then your team will suck.

Elite college admissions is an example of a negative selection test. There’s no one way you can do really, really well, and thereby be admitted to Harvard. Instead, you have to pass a bunch of different selection filters: Are your SATs good enough? Are your grades good enough? Is your essay good enough? Are your extracurriculars good enough? Are your recommendations good enough? Failure on any one step usually means not getting admitted. And as competition has intensified, colleges have added more and more filters, like the supplemental applications top schools now require (in addition to the Common Application). It wasn’t always this way – Harvard used to admit primarily based on an entrance exam – until they discovered this let too many Jews in (no, seriously). More recently, the negative selection has been intensified by eliminating the SAT’s high ceiling.

Academia is another example of negative selection. To get tenure, first you have to get into a top PhD program. Then you have to graduate. Then you have to get a good recommendation from your advisor. Then you have to get a good postdoc. Then you have to get another good postdoc. Then you have to get a good assistant professorship. Then you have to get approved by the tenure committee. For the most part, if even one of those steps goes wrong – if you went to a second-tier PhD program, say – there’s no way to recover. Once you’re off the “track”, you’re off, and there’s no getting back on. It’s fail once, fail forever.

Grades are another example – A is a good grade, but there’s no excellent grade. There’s no grade that you only get if you’re in the top 0.1%. Hence, getting a really good GPA doesn’t mean excelling, so much as it means never failing. If you’re in high school and are taking six classes, if you fail one, your GPA is now 3.3 or less, regardless of how good you are otherwise.

In any field, at the top end, you tend to get a lot of variance. (Insert tales of the mad artist and mad mathematician.) Negative selection suppresses variance, by eliminating many of the dimensions on which people vary. Students at Yale are, for the most part, all strikingly similar – same socioeconomic class, same interests, same pursuits, same life goals, even the same style of dress. A lot of people tend to assume performance follows a bell curve, but in some cases, it’s more like a Pareto distribution: the top people do hundreds or thousands of times better than average. Hence, if you eliminate the small fraction of people at the very top, your performance is hosed. Fortunately for VC funds, the startup world is still positive selection.

Less obviously, a world with lots of negative selection might be a nasty one to live in. If you think of yourself as trying to eliminate bad, rather than encourage good, you start operating on the purity vs. contamination moral axis. Any tiny amount of bad, anywhere, must be gotten rid of, and that can lead to all sorts of nastiness. “When you are a Guardian of the Truth, all you can do is try to stave off the inevitable slide into entropy by zapping anything that departs from the Truth.  If there’s some way to pump against entropy, generate new true beliefs along with a little waste heat, that same pump can keep the truth alive without secret police.”

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I asked my father to read this and give his thoughts.

He says that positive selection only works well when you have a very good idea what you need to select for. If you're sending an athlete to the Olympics but the event he'll have to compete in will be chosen at random, you can't just choose the one with the best time on the 800 meter dash, because the event might end up being something like archery, fencing, or weightlifting. And you certainly wouldn't want to send a non-swimmer. If you need a generalist, seeing how well someone does at jumping through a wide variety of arbitrary hoops might really be the best test you can practically implement.

(Now I'm wondering just how good or bad the 800 meter dash actually is at predicting levels of success at unrelated sports. For example, could you tell the difference between an NHL-quality ice hockey player and one that plays on a minor league team just by looking at their times on the 800 meter dash?)

Assuming a significantly large distribution of athletes sent by other rational managers, where all athletes are bound to the same rules of random event selection, I would still send the best possible specialist in a single discipline in this case, because without certainty that all other rational managers know certainly that some generalists will be better in everything than other generalists and that each one is confident that theirs is best, I conclude that some of them attempt a gamble of probabilities and send a specialist, and thus I also send a specialist to maximize my chances of winning.

After all, there are higher chances of the event being my athlete's specialty than there are chances of every single other athlete being less good at it if I pick a generalist, unless the number of possible events is large enough to outweigh the number of athletes. Throw in irrational managers and the possibility of other managers having information unavailable to you, and your father's argument seems very weak.

Now, of course, I'm probably attacking something that wasn't meant to be a strong defensible argument. However, I feel very strongly about the point that negative selection is wrong in many contexts it is currently used in (which I support), as well as the point that positive selection is so difficult and utterly impractical in so many cases (which I want to pound into tiny bits of forgotten wrongness).

I'm not sure where I'm going with this, however. I strongly agree with the article's statements, but my attempts to formulate any further useful thought seem to come up short.

Well, the sports analogy was my own interpretation of what he said.

Game theory question time: you and N other players are playing a dice rolling game. Each player has the choice of rolling a single twenty-sided die, or rolling five four-sided dice. The player with the highest total wins. (Ties are broken by eliminating all non-tying players and then playing again.) Now, rolling 5d4 has an expected score of 12.5 and rolling 1d20 has an expected score of 10.5, so when N=2, it's obviously better to roll 5d4. However, when N becomes sufficiently large, someone is going to roll a 20, so it's better to pick the 20-sided die, which gives you a 1 in 20 chance of rolling a 20 instead of a 1 in 1024 chance of getting five 4s. For exactly what value of N does it become better?

Edit: Fixed stupid math mistakes. That'll teach me to post after staying up all night!

Insightful question, if you ask me, though solving for N feels a lot more like a straight up actuary-level math problem than Game Theory to me. My maths above basic calculus is generally foggy, so I'd appreciate any corrections or nitpicks someone more fluent here might have.

Essentially, you have to solve when (odds of having highest result when rolling d20) >= (odds of having highest result when rolling 5d4). To simplify, let's assume that all players are perfectly rational, and thus at N and higher will all roll 1d20. This still leaves you the problem of calculating N's odds of rolling higher than you for both rolls, which is a simpler reformulation of the above parentheses.

For any roll result Y, there is (y/20)^N probability that you "win" here, assuming ties count as wins (or at least are preferable to losses). This means that with N=1 (you're playing against one other person), you will win 52.5% of the time (and so will your opponent, because that 2.5% is for ties) when rolling 1d20.

Your odds of winning naturally decrease if you roll 1d20 such that for N=2 you have 35.875% chances of winning, and so on in a proportional manner since the odds are always even for everyone.

Where it gets more interesting is when you are playing an unfair game where you have to equate your total odds of winning when playing 1d20 vs d20s to those when playing 5d4 vs d20s. Since the math here is kind of foggy and hard to combine into one big formula, I've thrown the data at a spreadsheet (to calculate the sum of the odds of any N rolling higher than you for each roll Y multiplied by your odds of obtaining Y), and it turns out that at N=3 the 5d4 roll dips just below the odds of winning with 1d20 by about 0.2%.

However, if we want to compute for xDf die for N, with K possible ways to roll (which was 2 here), then the math yet eludes me. I've figured it out or been told what it was several times, but I just can't seem to ever memorize this when I can only barely remember integration anyway when I don't use it.

Edit: For those curious, here's the spreadsheet mentioned above with all the raw data and brute-force formulas.

Your analysis also assumes there's no difference between second place and last place.

Yes, the reward system is very important in choosing the right strategy. If the first place gives you gold, and all other places give you nothing, use positive selection. If the last places gives you problem, and all other places give you nothing, use negative selected. Other point of view: if being average is good, play safe by using negative selection; if being average is bad, aim for greatness (and accept a certain risk of failure) by using positive selection.

So the question is what exactly do we want in elite colleges or academia (examples from the article)? I guess for elite colleges it is better to play safe. If your students are above average and everyone knows it, they don't have to be exceptional -- your diploma will help them get a decent job, which is why they pay you. A few bad apples could ruin your marketing. With academia, for an average university it is probably better to have "safe" professors who do their jobs, get grants, and don't cause scandals; even if the price is having less Nobel-price winners.

Yes, that it does, or at least it assumes that the difference is trivial within this decision scheme and the expected utility returns of a specialist are higher than the expected utility of a generalist even when taking second place into account.

I don't think the right way to do this is not either positive or negative selection (those terms really suggest a false dichotomy, don't they?). As has been pointed out elsewhere, what's here being called "positive" is really "or", and what's here being called "negative" is really "and".

But there are lots more ways to combine the data into a single number then just "apply a cutoff to each one, and then apply some operation to the resulting booleans". The appropriate sort of selection is not positive or negative, but rather, whatever will be used in the actual competition. (And if it's unknown, apply expected utility, etc.)

Now I'm wondering just how good or bad the 800 meter dash actually is at predicting levels of success at unrelated sports. For example, could you tell the difference between an NHL-quality ice hockey player and one that plays on a minor league team just by looking at their times on the 800 meter dash?

This (among other prior information) suggests to me that extreme levels of performance at different tests are probably negatively correlated, but I would not be surprised if there were events out there where extreme levels of performance on other tests are correlated with better (but not extreme) levels of performance on that test.

Unless you sample at random from the whole population, that's a Berkson's fallacy.

Berkson's fallacy.

Upvoted for this link. I wish I had known this term back in the Amanda Knox days -- this fallacy (or rather, the reverse of it -- failing to take into account conditional dependence of a priori independent events) is a version of the main probability-theoretic error of that case.

This fallacy may also explain why people tend to assign 50% percent probability to the odds of the second child being a boy in the classic puzzle.

Thanks for the link! I think a careful statement of my claim avoids that fallacy.

The claimed data:

  1. Body shape is relevant to performance in particular events (say, the 800 meter dash)- for example, Michael Phelps is shaped well for swimming.
  2. Extreme performance in that event will generally require a body shape optimized for that event.
  3. Extreme performance in different events correspond to different body shapes.

Stated carelessly, it seems likely to me that if I know you're an Olympic-level athlete, I'll have some estimate that you can play Olympic-level basketball; but then when you tell me that you're a Olympic-level wrestler, I can lower my probability estimate that you would be able to play Olympic-level basketball.

But if I condition on knowing you're an Olympic athlete, and then try to drop that condition without being careful, then I can get into trouble (this fallacy, specifically). So instead, let's start off with some (really low) probability that a person chosen uniformly at random can play Olympic-level basketball, and then update on the knowledge that they're an Olympic wrestler- we should increase our estimate based on their general level of athleticism, and then decrease our estimate based on their probable body shape. I think the effect of the body shape will be stronger than the effect of general athleticism, and so they will actually be negatively correlated.

I think my last statement in the grandparent- that extreme levels of performance on a specific test should correlate with better performance on some 'general athleticism' test- is true when you compare extreme individuals to random individuals, but less true (or perhaps not true) when comparing extreme individuals to good individuals. The NHL ice hockey player is probably not much more 'athletic' than a minor league hockey player, but probably is more 'hockey-shaped.'

But now that I've stated that last paragraph, I'm thinking of counterevidence- like the famous birth month effect for Canadian hockey players. Early training appears to have a huge impact on whether or not someone hits extreme levels of performance, but I think both NHL players and minor league players started early. So maybe it is biological talent that differentiates many of them. Hmm. I should probably stop speculating about sports.

If you put an Olympic-level wrestler on a college (American) football team, how well would they do? Michael Jordan did tolerably well during his year as a minor league baseball player.

Tolerably well for minor league, but remember that his father had envisioned him as a major league baseball player, so presumably he'd practiced and done well at the sport when he was younger. There are probably selection effects on Michael Jordan in particular to be good at baseball out of the set of NBA players; most never try to transition to baseball at all.

One of the most important social structures of modern society is the corporation - a framework for large groups of people to band together and get absolutely huge projects done. In this framework, the structure itself is more important than individual excellence at most levels. To a lesser extent, the same applies to academia and even "society as a whole".

In that context, I think preferring negative selection to positive makes sense: a genius data-entry clerk is less helpful than an insubordinate data-entry clerk is disruptive.

And remember that we have side routes so real geniuses (of some kinds) can still make it: set up their own company, start their own political party, start publishing their work online, design games in their basement, and so on.

And remember that we have side routes so real geniuses (of some kinds) can still make it: set up their own company, start their own political party, start publishing their work online, design games in their basement, and so on.

This is a really good point. It's good to have low barriers to this sort of thing. For instance, if you need to hire a lawyer and an accountant to set up your own company, then a genius cookie baker can't set up their own cookie shop unless they also have the money or connections to get the help of a lawyer and an accountant.

I'm not sure that it's the corporate structure that makes negative selection more useful in the data entry case. It's not the fact that the data-entry clerk is part of a large organisation that means that a slightly incompetent data-entry clerk is more disruptive than a genius-level one is helpful. Rather it's the fact that data-entry is a relatively low skill job and with relatively little room for excelling above mere competence. Leaving the corporation wholly out of it, and imagining a person doing data entry in complete isolation, the most helpful data-entry clerk would still be selected by making sure they weren't terrible, but weren't necessarily brilliant, at typing and remaining attentive etc. I think this idea is supported by the fact that for higher level/skill positions, one probably would want to employ more positive selection.

If your point was specifically that insubordination (and not just slight incompetence in general) is more harmful than genius-level work is helpful, then I guess that, in an obvious sense, the harm of insubordination is due to the corporate nature of work (since you can't be insubordinate outside of a group hierarchy). But then I'm not sure that insubordination-worries requires negative selection, or at least not a wide range of negative selection tests. Sure, you might want to include a negative selection test along the lines of 'are they likely to do the opposite of what they're told on a whim occasionally?', but it's an open question whether the rest of your criteria would be negative or positive.

The point I should have made clear was that data-entry clerks don't exist outside of corporations, because in isolation they're useless. More generally, mass production has been made possible by the production-line paradigm: break down the undertaking into tiny discrete jobs and assign a bunch of people to doing each one over and over again.

Once you get that kind of framework, exceptionally good workers aren't very helpful, because the people to either side of them in the production line aren't necessarily going to keep up. You just need to shut up and do your job, the same as everyone else.

At the high levels - the people wielding their collective underlings as a tool, rather than the people who are part of that tool - this obviously no longer works.

Important note: all of the above, including my original comment, is 100% psuedo-intellectual wank, since I've never been part of a corporation, never taken a business management course or seminar, and never conducted or read a study on the efficacy of various business practices.

This was my favorite post on your blog and I'm glad you posted it here.

I agree. I stumbled across this one a week ago or so - without knowing the author was associated with LW - loved it, and have been thinking about it off and off since. I'm glad to see it again. I feel like I should probably start reading your blog regularly..

Really good post...it makes a point that is completely new to me, which is always nice.

It does occur to me that the current (negative selection) system would reward "hard work" more, relative to "talent", than a positive selection system. (In quotation marks because those are both metrics that are hard to measure separately from one another.) Someone who is very conscientious and hard-working is likely to compensate for wherever areas they're weaker, in terms of "natural talent", however you define that.

My first, emotional reaction to your post was "I would be screwed in a positive selection system!" As someone who's above average in a lot of areas, not really exceptional in any, and obsessively hard-working enough that it's a running joke among my friends, I like the current system just fine (although I'm not in academia.) I don't know if conscientiousness would have a bigger long-term effect on results than innate brilliance; it probably depends on what field you're talking about.

My intuition says that a positive selection system would probably be a good idea in fields where there is big variance in natural ability, i.e. math or physics, and less so in fields like medicine where a lot of "talent" depends on how willing you are to work hard and keep improving over your whole career.

Negative selection may be good, actually, for the vast majority of people who are ultimately going to be mediocre.

It seems like it may hurt the occasional genius... but then again, there are a lot more people who think they are geniuses than really are geniuses.

My first reaction was pretty much identicle, right now you can do well at almost anything purely based on conscientiousness, including video games, work, school, and social interaction. I don't know of any good way to measure general talent, but when I learn most things I tend to be quite bad at them until I enter tsukoku naritai mode. Perhaps this should influence my career decision somewhat, its hard to tell if talent or effort is more crucial for programming.

Perhaps this should influence my career decision somewhat, its hard to tell if talent or effort is more crucial for programming.

Effort. Always assume effort. Talent will speed up the learning process in the early stages, is likely to make effort easier (because it is more fun) and at the extreme upper ends of of performance probably gives a higher limit. But in general effort plus social politics skill will determine your career success.

Despite what they are taught likely to be about themselves, what they might think of themselves, and what western culture expects of them, programmers are more creative artists than analytic engineers.

The difference is most tangible from the management perspective since motivating programmers is less like motivating chemical, mechanical, or any other sort of engineer and more like motivating commercial artists with less pretense, who were never led to believe they were meant for something greater. Dissatisfaction from programmers grows in much the same way it grows in commercial artists as well, though they programmer is less likely to specifically identify his or her complaint and the artist is more likely to complain about having sold his or her soul.

Common responses to criticism of work among programmers align more with those among artists than those among engineers. Again, I learned this from a managerial perspective.

The most important advice that may be given to starting artists (excluding all the low-hanging fruit advice that is best for everyone in general, of course) isn't about discovering your own inner talent or anything similar, instead it is about discipline: "Ideas are not swords you can brandish about in triumph. What matters most is the Sit Down, Shut Up And Get It Done. Only there will you find the true steel for your craft. Only there, will you know if you are worth the words out of your mouth."

its hard to tell if talent or effort is more crucial for programming.

I would suggest talking to some programmers.

My intuition is that there's something of innate talent involved in programming, so that you can divide people into two populations: those whose brain makeup causes them to find programming intuitive and fascinating and cool, and those to whom it just doesn't make sense. If you're considering it as a career, presumably you fall into the first category. Beyond that, I would guess that conscientiousness is the biggest predictor–my one-semester programming elective was enough to show me that it's really time-consuming.

But I'm not a programmer by specialty. An unusual percentage of LWers are, though, so maybe someone can give you advice?

"The Camel Has Two Humps", which IIRC has been linked here before, does purport to find a bimodal distribution between people who can and can't program. I'm not at all sure if that has anything to do with inborn talent, though, at least beyond basic general intelligence.

At various points in my career I've found reasons to teach people programming skills, and my n=1 impression is that the ability to internalize basic programming has little to do with personality (though conscientiousness helps, and I suspect openness to experience might too) and a lot to do with the student's level of comfort with mathematical thinking. Not necessarily advanced math (you don't need anything more complicated than algebra to program except in specialized domains), but you do need to be very comfortable with a certain level of abstraction. I suspect that might have more to do with the distribution in the linked paper than the "geek gene" concepts I've heard tossed around elsewhere: at the level of the math prerequisites for CS 1 it's still possible to do well by solving problems mechanistically without a good grasp of the abstractions involved, but that won't cut it in computer science. And it'd probably be difficult to teach that in a semester.

The thing that wasn't replicated was their attempt at a predictive test of the distribution (based on a particular explanation they thought applied), not the existence of the distribution itself, which is something that was observed in grade patterns in CS compared to other subjects (though I don't know how rigorously established it is).

Isn't the predictive part the interesting thing? I wasn't aware that bimodal grade distributions were unique to CS.

Well, their original paper claimed that (eg) math grades are typically a bell curve, whereas CS grades are typically bimodal (with examples from one university). But again, I'm not sure if this is something that's been rigorously demonstrated.

Good to know. I thought it had a bit of a questionable odor to it, but I wasn't able to find any replications in the brief time I spent looking into it.

I don't think it has much to do with personality either, except, like you said, willingness to work hard (especially if you're someone who starts out finding it very difficult.) But I think that a lot of people, even people who can work up to the level of calculus in math, go at it with the mindset of "memorize that Formula X gives Answer Y" instead of trying to understand how and why Formula X relates to the underlying structure of the problem so that it's obvious that it should give answer Y, but gives Answer Z in a different context... You can get by with memorizing formulas in math classes, at least the way they're currently taught and tested. It's a lot harder to get by with that habit that when you're programming.

(On the whole, the people I've known whose minds appear to work like this aren't noticeably "lower" intelligence, however you define that. They just don't think of math as something where they should be applying the analytic part of their mind.)

Your intuition relating to "innate talent" is wrong. There is nothing innate about any of the "talents" required for programming, other than what generally comes with the package of most human brains. This might be a simple question of wording though, as if you change the words to "inner" talent, I would be more inclined to agree.

Simply put, unless a person is simply incapable of mental change and learning, then they will be able to "learn" and self-adjust into "obtaining" the "talents" required. However, this usually requires much more effort than people (read: the small sample size of the people I know who are not programmers but have attempted to learn how to program, which amounts to eight individuals) are willing to put forth, hence the common misconception that there is this "innate talent" that you simply must have to become a programmer.

I was using 'innate' means "something present in a person's brain and/or skill-set when they start trying to learn how to program." It might have something to do with how open-minded they've been in the past to learning new ideas, because if they've been open to that, then they'll have a wider base of knowledge and practice thinking about problems at a certain level of abstraction. I don't think it's necessarily innate as in "determinable at birth"–in fact, that seems really unlikely to me, but what I know about the subject doesn't allow me to distinguish those possibilities. (The phrase 'inner talent' is one I've never heard used before and would not have thought to use, so I don't know exactly what area it would cover.)

Do you agree that some people will start learning programming and find it easy, intuitive, and immediately fun, and not have to put in a lot of conscious effort, whereas others will need to lean much more on their capacity for mental change and learning? This is what I'm talking about.

Yes, on that I agree. I suppose I was more disagreeing on the choice of word than on the concept of something being already there in some and lacking in others. The dictionary definitions (referring to Dictionary.com and my old pocket dict) of "innate" all seem utterly inappropriate for this usage.

However, I'll still nitpick on the point of conscious effort. My "definition" of inner talent is that of an abstract representation of the "source" of the talent in question. An "outer" talent is one where, to explain by example, a person's genetic profile is directly favorable to athletics by producing the required muscle mass more efficiently with less prodding, and recovering from exercising damage more easily, and so on. By contrast, an "inner" talent is one where synergies, "affinities" in the system, side-routes, or other indirect or invisible. I always fail to find the words to explain complex dynamics where various seemingly-unrelated things converge to the same location to push in the same direction, but that's about the kind of psychological or physical events I'm trying to refer to with "inner" talents.

Some person will have no particular skill or strength that is directly beneficial towards chopping wood, but once they try, suddenly a bunch of unrelated past experiences or other points about their current self help them catch on quickly to just the right way of holding the axe and establishing their footing and swinging and so on.

What I want to make a point for is that both the processes of awakening an inner talent or slowly going through all the steps from nothing can be either conscious or unconscious. This will depend on many factors that may not be obvious.

I agree that I probably shouldn't have used the word 'innate'; given the meanings people associate with it, it was more likely to confuse people than help. Maybe "prior talent" or something similar?

My "definition" of inner talent is that of an abstract representation of the "source" of the talent in question. An "outer" talent is one where, to explain by example, a person's genetic profile is directly favorable to athletics by producing the required muscle mass more efficiently with less prodding, and recovering from exercising damage more easily, and so on. By contrast, an "inner" talent is one where synergies, "affinities" in the system, side-routes, or other indirect or invisible. I always fail to find the words to explain complex dynamics where various seemingly-unrelated things converge to the same location to push in the same direction, but that's about the kind of psychological or physical events I'm trying to refer to with "inner" talents.

I think I understand the concept you're trying to convey, but I find that youre're using the words 'inner' and 'outer' in a very unconventional way that I've never heard before, which is also likely to confuse.

Simply put, unless a person is simply incapable of mental change and learning, then they will be able to "learn" and self-adjust into "obtaining" the "talents" required. However, this usually requires much more effort than people (read: the small sample size of the people I know who are not programmers but have attempted to learn how to program, which amounts to eight individuals) are willing to put forth

This is an untestable claim. How would you distinguish between your claim being wrong and a person not putting out enough effort?

I fail to see how it is untestable. It might be impractical to test, but if the survival of all humans suddenly depended on their future programming skills (e.g. because a dictatorial alien appears and decides to kill off any human they can't use in their programming slave workshops), it would certainly be tested, as far as I can tell.

I also didn't really define my usage of the word "effort" very clearly or unambiguously, which is intentional: I'm not in the best position to determine/figure out the exact line at which the scope of the term "effort" should be drawn for the statement to be solid.

The alternative, however, being that a person simply cannot learn and obtain talents, would imply that some individuals have a meta-talent for obtaining talents, as it's been demonstrated before that people can (and often will in extreme situations or environments) adjust in such a manner. This, to me, seems much more complex than "Everything can be learned, including talents and how to obtain talents", so by Occam's Razor I prefer to believe the former.

I don't know to what degree innate talent is important in programming ability. I tend to agree that most people would be capable of learning to lot of things that are generally thought to require innate talent.

However, I'm not sure that "effort" is the most important hurdle stopping the learning from happening. First, people may not even believe that they can learn - they go from finding something hard to understand to assuming that they aren't the sort of person that is good at this. Secondly, they have to find out what to learn. In the case of programming an average set of lecture notes or a "teach yourself language X" probably won't do the job. A really good textbook may - but it won't quickly diagnose misunderstandings, which a good tutor will (I lectured and tutored computer science and programming for a number of years).

Then you need the effort.

Yes, I attempted to infer this when saying that it requires "much more effort". First, they need to make an effort to be more aware of themselves, then to be able to learn and develop new mental models of their own accord on things of their choosing, in a conscious manner.

Then, they need to, as you say, find out what to learn. This can be achieved through the effort of looking for resources (including "human resources") that can help you figure it out or give you the right information.

Notice that at every step, there is effort required. You might call it a "meta-effort", in a sense, since you also need to make the effort of doing effort, but I like to simplify and just say that it's a lot of effort that most people aren't willing to make. After all, I'm usually explaining this to the very people who aren't, in an ultimate play to get them to either start gearing up for a long trek into Better-Person-Hood or give up about becoming a programmer/researcher/etc.

If you define "talent" as a product of your current ability to produce and visualize mental models of complex systems, especially "from nothing", then it is the most defining factor for the higher maximum awesomeness of programs you can code at present.

This "talent" can be enhanced and self-improved through effort, however, in a very similar manner to making oneself more "luminous".

[-]brilee
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