but dont you think in terms of general education people's intuition should be much better? As for mathphobe - that is usally down to a failure of education and it can be overcome.

Maths matters in people lives - they have to decide on investing/pensions/etc etc where people make huge mistakes and where people are out to get them. They have to decide whether to take vaccines or not or whether to go to gyms or pubs. Thinking matters.

I think is totally wrong btw. I'd put DS's reaction on more like "give me some time with these peeple and I'll teach them how to think. They're not stupid, they've just been failed so far".

Even the "Pinker" reaction would be absurd, especially with respect to the second person I mentioned. That guy would outperform DS (and me) on any sort of intelligence test I can imagine. He is extraordinarily high-functioning. He doesn't need anyone to teach him how to think.

He simply made a mistake because (i) he wasn't familiar with the Monty Hall problem; (ii) probability brain teasers are not one of his hobbies; (iii) he was answering extemporaneously; the (iv) the wrong answer is superficially seductive, which is why so many people answer incorrectly.

In many ways, you are illustrating my point. The fact that this guy gave a wrong answer to the Monty Hall problem isn't indicative of a propensity to make errors in investing, deciding whether to take vaccines, etc.

Hell, it isn't even an explanation of why he is a poor card player. He is a poor card player because the stakes don't matter to him and he is easily bored, which leads to ill conceived efforts to run people over. Unprompted, he would admit that his poker play is suboptimal for exactly the reasons I described.

You got very lucky in your simulation as i have run the Monty Hall test prior and had the first 6 pick switches in a row be the wrong choice, and then by simulation 20 it started to balance a bit but was still 13-7 in favour of holding pat and not switching.

I realize over time the odds will prevail but in any given random test the odds are not so wide that you will be sure to prove it a winner. Many non believers would just declare you proved wrong with those first 6 misses and walk away.

Who said we ran the simulation six times?

Getting the Monty Hall Problem is not the type of intelligence that I am proud of. Its coming up with a simple explanation for it that virtually anyone can understand. Same with problems like why dealing it twice doesn't change EV. There is an instant simple explanation. But its not clear that your friend would have thought of it. Or, to give a more difficult example that came up a few years ago on this website, a roulette ball bounces one slat clockwise or counterclockwise based on coin flips until it has visited every number. Prove that all numbers, except the original of course, have an equal chance to be the last one visited. The mathematicians and physicists on the forum were either stumped or came up with complicated solutions. I came up with a two sentence solution that required no math. Then there was the time I was told that there was no way to put a poker type game on a poker table. I came up with one that day that eventual sold for thirty million.

So you are wrong that that I undervalue creative intelligence. I think that Deane Kamen is smarter than 99% of math or physics Phds. Being able to learn things quickly and accurately is a talent I am less impressed with. (The very best mathematicians and physicists have both.)

I use probability problems to show off because it is the only math where you don't have to know anything. It takes brilliance to be the first one to realize that ellipses are somehow connected to Fermat but it also takes years of study. I don't even know what a differential equation is. But 99% of those who do know cannot do logic puzzles as well as me or Kamen or Howard Lederer. And THAT's what grates on them. They know 100 times more than me but I still sometimes beat them when the goal mainly requires cleverness.

But with that being said, it is true that I have a lot more respect for those who study STEM type subjects, as opposed to others, regardless of their IQ, for one simple reason. They can't get away with being wrong (with some exceptions.) They get found out. In most other subjects two people can have highly differing views and they will both be accepted. Pretty sweet. And yes, that includes law.

Assuming that this is true, why do you think you're so good at these logic puzzles compared to those other folks? Also curious how you'd rate your level of intelligence (or cleverness or IQ or whatever you think is essentially important) relative to the general population. Top 1%? One in a million? Or even rarer?

I think you undervalue the type of intelligence you don’t have. Like if you haven’t figured out what a differential equation is, by simply knowing what a differential and equation are, you have really have no hope of getting above a 0 on a Putnam. And I think anybody who can get above a 0 on a Putnam is smarter than a guy who selectively picks out non math roulette analogies for a reason you basically describe. You can’t really get away on a Putnam, where you can forget about the millions of times you failed to solve a simple problem.

How does he teach calc without knowing what a differential equation is?

The Monty Hall problem is NOT a good example of a logic problem or a mini test of intelligence for the reasons you gave. But I never said it was. I said that coming up with a persuasive simple refutation is such a test. Meanwhile you contradicted your own point by admitting your friend could have been a good poker player if he wanted to. (But he wouldn't have completed a perfect math SAT as fast as my 16 year self. I'll stipulate to all your other assertions but not that.)

In any case regardless of whether well educated people are as stupid as you think I think they are, the fact remains that the majority of people are doomed to constantly make bad decisions or have incorrect opinions because they are susceptible to many of the thinking flaws that Pinker points out. Why won't any of you read the damn book? If you do, I'm sure some of your thoughts about it will change.

What's a differential?

I looked at a past Putnam at random and they had a problem regarding a complicated Nim type game that I solved. So, my average score would be above 0. (How hard is this test exactly? How many 2021 seniors in the state of New Jersey this year could go on to score above zero in your estimation? If you answered is higher than 5 then your opinion about me can't be right.)

If I had taken up math, my score would probably be low but not zero. But far fewer than half of those who outscored me would have been able to ace the SAT as fast as I did. Or the GRE.

The roulette problem can be done by math. Just like the problem of a freezout between x dollars and y dollars can be done with or without math. You don't think that finding a cute logic explanation shows intelligence as much as the ability to slog through a problem that requires a lot of knowledge as well as intelligence. I know some big names who disagree.

Not a fan of Thomas Kuhn, I see.

I doubt that your average humanities professor was attracted to the humanities because he or she wanted to avoid being characterized as wrong. A lot of humanities scholarship involves PhDs arguing about who is right and who is wrong about some esoteric topic.

Practicing litigators get constant feedback from courts and juries on whether they are right or wrong. The difference, I guess, is that it is relatively easy to avoid internalizing losses. Because you are acting as an advocate, you often know going in that you have the worse argument and are likely to lose. And the decisionmakers get it wrong a decent percentage of the time.

I never said the bolded and I am not certain it is true. His tolerance for boredom is very low and it would be difficult for him to find games at stakes that would matter to him. I suspect that most great poker players have a relatively high capacity for boredom.

I have no way of knowing the answer to this question. I assume that he got a perfect score on the math SAT unless he made a clerical error. And as I said, he is the fastest processor I have ever met in my thirty years as an adult. But there is always someone who is better at everything.

I am sure that you can infer from my posting history that I value logic-based decision-making. Based on your description of the book, I suspect that Pinker overstates his point in places for rhetorical effect, but I doubt that I would quibble much with a book that advocates for a logic-based worldview.

I haven't read the book because I am busy and I am reading other things.

That’s not what I said, or at least meant. I don’t trust your subjective estimations of your own cleverness based on anecdotes when you don’t have something more objective like Putnam scores to back it up. I’ve also discussed stuff like basic logic with you and in my estimation you failed to pick it up as quickly as an average math major at an elite school would have. Those people are far from world class so it’s highly likely you’re overestimating your skills through a mix of ignorance, hubris and a psychological desire to believe.

Or put another way, I can tell you about the time at a seminar that Jacob Lurie said a calculation would take too much time to do at the board and I correctly pointed out that we basically already did it in the previous section, we just needed a minor tweak based on a symmetry argument. This of course means nothing and leaves out the millions of times he or people at his level beat me to the punch.

Eh tu Brutus? You know what I meant.

No one. That is not my point.

Your point seemed to be that you quickly demonstrated thru the bet (even giving odds) that Monty Hall switch choice was the correct one.

I then game MY example and said after 6 straight 'wins' where the person who stuck with their pick won defying the thin odds, many would quit and declare themselves proven correct.

Even as you expanded out to 20 simulations where it was only then just balancing many would not see it as indicative of needing to switch. Even if you projected my example out to 40 so the 'switch' choice was 'winning' it would not be seen as a definitive margin any more than the initial 6 the other way should.


So I was not being critical, but just pointing out for anyone who thinks they will simply and quickly demonstrate the Monty Hall switch to prove it to a skeptic that you might, rightly, need to run a hundred or more simulations to really illustrate the proof otherwise you are taking a really thin odds gamble that could convince them otherwise.

I could win this argument with more details but it would be counterproductive. So I will just end it say that there were several high school classmates who went on to major in math at elite universities who would dispute your conclusions.

I guess. But it's a simple game. You can do dozens of simulations pretty quickly. I don't remember how many we did. But he started losing money quickly, probably more quickly than the actual edge. And once he started losing money, he gave the question a little more thought and realized that he was on the wrong side of the bet.

I have no idea why you quoted me and launched into some random soliloquy about slippery slops, but at the level I teach at this is basically entirely wrong. Students that try to treat learning university level mathematics as an exercise in rote memorization without understanding are doomed to failure, and one of the key things as teachers is to help transition them away from these learning behaviours.

Did you go to Bronx Science or something? Not many high schools have several students in a class go on to do math at elite universities.

I’ve honestly never met a grown man who gives a rip about his SAT score.

@cuepee

You should perhaps be aware that most of us have gone through that stage years/decades ago.

On slippery slopes, if I may lick my own boots for moment, I did once make an enjoyable post pointing out that DS's argument that a slippery slope didn't apply in a particular problem looked reasonable but had to be rejected because if we were going to allow it there then ....

Honestly, I don't. My point was that his failings as a poker player were not attributable to a poor understanding of probability, an inability to estimate odds in his head under time pressure, or an inability to understand the concept of optimized multi-step play based on incomplete information.

I'm not sure that I know what anyone else in the world got on the SAT (other than DS on the math section).

Watching DS pat himself on the back about how smart he thinks he is at logic puzzles will never cease to amuse me. What a sad thing to have at the absolute core of your identity. I particularly like all the chatting about what math and physics PhD from someone who doesn't know what a differential equation is (but claims to be top 5% practioner at calculus???). I didn't understand the kind of intellectual skills (hint: it's not silly logic puzzles) that make a good PhD in math until I was actually doing a PhD in math.

I am not disagreeing. The thin odds play and bet can work in your favor, just like betting on an even distribution of heads or tails can.

I am just saying, I learned, to my not so great surprise, the first time I tried it that with such thin odds, the chance of it skewing against you at the onset, and even significant skews (your are unlucky, or 'running bad') can easily happen.

Now if I am explaining the Monty Hall gambit, I would not demonstrate it to prove it due to 'running bad' risk and would instead just describe why it works and tell them to google to the simulations.