Ask HN: Where did you top out in math classes?

Actually, there was a recent article on YC news about the large number of discoveries that were made independently at almost the same time.

Our made-for-tv histories usually show a lone scientist toiling away for years, making huge discoveries. But in reality, most discoveries are incremental. The stories we are taught about these discoveries are usually mythologized.

It is true that there is some level of creativity needed. But it's probably way more common than our histories would lead you to believe. The recurring theme you will hear from scientists is that "chance favors the prepared mind."

I'm not sure I ever had that reaction. I explored a few topics in different lectures in grad school which were pretty obtuse: ergodic theory, for example. I didn't get it, but I assumed it was because the topic wasn't suited to lectures, and after learning of the basic direction they were headed in and setting out myself, I found I could get pretty far.

I've seen others give up on some topic rather than the method they used to try to understand it. It's the equivalent of someone saying "I can't get math" because they're spending all of their time remembering formulae, or someone saying "I'm no good at programming" while spending their time reciting bubble sort line by line in preparation for the exam. Giving up on higher mathematics is like that. Almost always, there's some path to real understanding -- you just have to find it.

Are there any other quantifiable variables with such high predictive power? I'd be really interested if there were some other test that could better estimate the odds that someone would get a degree, earn lots of money, stay out of jail, vote often, delay having kids, etc.

It would be interesting to know more details, which I'm sure you can't divulge without violating someone's privacy. But it would be neat to find out if those people had other skills that correlate strongly with IQ, like the various digit-memorization/recitation tests, or reaction time. Were these people autistic? Were they taking a test in a language they didn't know too well?

They weren't autistic, and there didn't seem to be any strange behaviors socially, and they were quite inquisitive and swift on the uptake.

I once heard IQ defined as "ability to navigate bureaucracy, getting the answers others think correct in a manner testwriters imagined, and color in the lines" (paraphrased). This may have something to do with the phenomenon here.

The odds that someone would 'get a degree, earn lots of money, stay out of jail, vote often, delay having kids, etc.' seem to have more to do with successfully conforming to certain values of society's upper-middle class.

I think I'm capable of inventive thought, but I don't particularly want to get another degree, or earn much money, or delay having kids, or vote often, and the sort of things that one has to do to stay out of jail, are, honestly, quite often absurd, and I often rail against them.

And if you start to observe, closely, just how these things are tested, you'll start to get the impression that maybe bright people will find their ways through the cracks more than anticipated. There's an enormous weight given to quick answers -- time directly influences scoring. Linear answers are expected, and alternative interpretations are docked. There's often insufficient information in the questions, or it's based on a model of the world that's wrong. Domain knowledge like mathematics or vocabulary is brought into it. Analogies are made to hone in on one relationship from the many that could exist. Scorers of essays give insufficent weight to substance and too much to form -- despite their lipservice, they are indeed swayed by big words.

Even tests like GRE physics are bad. They claim to be testing rapid physical intuition, but in practice what divides good from poor scores is prior experience with 100 simple systems and the ability to get the factors of 2 and pi right with three minutes per question.

I think your quote comes from Cosma Shalizi. Thomas Sowell addressed that complaint years before by noting that most of the countries where you find that modern complexity are pretty nice places to live, whereas other places are hellholes. The correlation between IQ and income holds true for places outside of the US, too, so one might be tempted to think that a bureaucratic, find-objective-answers, fill-out-these-forms-in-triplicate society is better than most of the brutal alternatives.

"...seem to have more to do with successfully conforming to certain values of society's upper-middle class. I don't particularly want to get another degree, or earn much money, or delay having kids, or vote often, and the sort of things that one has to do to stay out of jail, are, honestly, quite often absurd, and I often rail against them."

My point is that, all else being equal, you could get a great job if you chose to, and that if you do illegal things, you apparently do them in such a way that you won't get caught. IQ seems to correlate with the ability to delay gratification, which itself seems to be a better predictor of success than IQ (sadly, it hasn't been tested in a rigorous, long-term way -- so it can't match the hundred or so years worth of data people have compiled on IQs).

One of the reasons that these tests emphasize time is that 'quickness' is a component of IQ. Francis Galton, the first guy to really study the subject, liked to think of things in that way -- and given that physical reaction time correlates so well with IQ, he had a point.

I agree that the essay part of standardized tests is messed up. Lots of the recent changes to tests seem to arise from political correctness. Test-makers found out that you can't design a test that has predictive value without getting politically incorrect results, like lots of men on the extremes, or lots of high-IQ Jews and Asians and low-IQ Mexicans and blacks. So they periodically adjust the scoring mechanism or the test to get bell curves closer to the same median and standard deviation (more focus on the median than the SD, since most of the people who complain about such things don't know what 'standard deviation' means). So keep that in mind when complaining about the essay, or the rebalanced scores, or the analogies (which were dropped from the SAT -- analogies happen to be more IQ-weighted than other categories of questions).