(Also H/T Ken.)
For the peanut gallery, what this means is how much math you’ve learned in life is almost as heritable as how intelligent you are. In other words, people who fall behind where their parents were in math almost always catch up somehow because the drive to do so is genetic, and people who get ahead of where their parents were in math fizzle out.
It’s not a perfect correlation. IQ is about 75% heritable and I still have a standard deviation on the average of my parents, which is unusual but not unheard of. But basically, if your parents took Calc 1 and then stopped it’s likely you will have the same math achievement level even if you’re separated from them at birth. As you’d expect, both of my parents took calc 4 (differential equations) and then stopped. I went very slightly further and then stopped. My siblings mostly stopped between calc 1 and calc 4.
Kid 1 – calc 2
Me – Partial differential equations (basically calc 5)
Kid 3 – precalc
Kid 4 – calc 2 (I think)
Kid 5 – calc 1 (I think)
Kid 6 – calc 4
Blacks are 13% of the population and most of them can’t perform 4th grade arithmetic as a consequence of verbal tilt on an 85 average IQ. And apparently, it’s so strongly genetic that it literally can’t be fixed.
Something else that occurred to me regarding Kid 3’s particularly low math achievement, despite his IQ (~125), is that another big difference comes from the split in the Openness dimension of the Big 5 personality model. On the one hand you have Aesthetic Interest, which is often much higher among women with high Openness. On the other hand you have Intellectual Interest, which is often much higher among men with high Openness. Kid 3 was, as a young adult, much higher in Aesthetic and basically uninterested in Intellect until his late twenties. I was the reverse, only recently (early thirties) having become interested in anything aesthetic or even the concept of “decorating”. And truthfully, it’s only because I’ve realized that aestheticism (and leading a balanced life in general) makes me better at intellectualizing, so in a roundabout way I’m still Intellect-maxing.
A good heuristic for this is autism quotient. It’s not perfect, but it’s pretty good.
This makes me want to learn higher math, just to see if I can (not now, whenever things are boring again).
Taking a class is a good way to be forced to do it. Another way (the right way) is to develop an organic interest in it as a form of brain-teasers (i.e. an addiction). And the last way is to discipline yourself to read a section of a math book every weekday and do the exercises.
You won’t need a textbook for the former.
For the middle option, I like the Paul Zeitz book: https://www.amazon.com/Art-Craft-Problem-Solving-3rd-ebook/dp/B01NALXA62/ref=sr_1_1?crid=24ZH1X6DS6VRD&keywords=paul+zeitz&qid=1664844470&qu=eyJxc2MiOiIyLjY1IiwicXNhIjoiMS45MiIsInFzcCI6IjEuNTAifQ%3D%3D&sprefix=paul+zeitz%2Caps%2C138&sr=8-1. Everyone always recommends the Polya book “How to Solve it” but I haven’t read it myself.
For the latter option, you can’t go wrong with the James Stewart books: https://www.amazon.com/Calculus-5th-James-Stewart/dp/053439339X
Re: Exercises, for whatever reason the least annoying way for me is to do them in my head as much as possible. I think this is a habit I picked up from homeschooling where you don’t have to show your work.
If you’re going to try that I’d recommend starting with the basics and go through Arthur Benjamin’s “Secrets of Mental Math” book, which has the added benefit of being somewhat useful. Then just get Schaum’s Outlines books for math you once knew (algebra, trig, etc.) and try to do the exercises in your head.
> Exercises, for whatever reason the least annoying way for me is to do them in my head as much as possible.
Ditto. My parents and teachers hated this though. Joke’s on them, they’re the ones using calculators now, I don’t need one.
Have written about this before: Everyone should learn how to use an abacus. Paper math is DUMB. Learn how to use an abacus, and you’ll be able to do 4×4 digit multiplications in your head. No savant abilities necessary.
Everyone recommends Polya, no one reads Polya. Same with Knuth’s Art of Computer Programming, Dragon Book, SICP, etc.
Raed and understaend the classics. (Lol, now that I look I have the Dragon Book 1st ed in the bookshelf right behind me.)
Polya suffers somewhat from “The 100 mental models of Charlie Munger” style, which is that there are just too many disparate techniques to keep track of and get good at. Consulting a recent edition, it’s a 50-page intro essay followed by about 200 pages of heuristics. Well, maybe a math grind can master them all.
I sympathise with kid 3. I was (am) of the same outlook. I might also be a SD above my parents’ average, and I don’t have any first degree cousins that are within a SD (no one’s above). There’s certainly a few second-degree cousins, one I’d even rank higher. No first degree adult contenders (uncles, aunts, etc) but there are many of the second degree that measure up. I’m only 130-140, though.
Friend 1 : Qualified for IMO Prelims (national training / elimination rounds) when he was 11. Shortlisted for the penultimate roster when he was 14, didn’t get selected, lost interest, and now watches anime and puts in 10% of his attention into his CS career
Friend 2 : “friend”. Was a short retard, imagine Jonah Hill in Superbad. Got some hormone therapy or something, went to Germany for his masters (cuz its FREE) and is in line for German citizenship and will work with water and infrastructure. RIP Germany. Hobbies: watching professional wrestling. Last I heard he was unironically worshipping Schwab’s WEF.
Friend 3 : Average dude, earns more than friend 1.
Friend 4 : Bottom of the pile for many years. Never got more than a B- in anything in school. Masters from a mid-tier state school, now working at a tier-2 IT firm. Earns more than Friend 3.
Friend 5 : Above average in school, opportunist. BS’d resume, got into Jewgle. Earns more than friend 4.
Friend 6 : Wamen. TM, somehow had her university invent an award for her. Cookie-cutter headgirl. Interested in a PhD. No personal interest in field. Earns less than friend 4.
Friend 7 : Wamen. Also headgirl, but no M. No special math skillz but insanely conscientious. Training to write high-reliability software for physics simulation or something.
Friend 8 : Wamen. Not a headgirl but smaht, aesthetics over gruntwork. Unemployed.
Math skillz: 1 > 7 > 8 > 5 > 3 > 6 > 4 > 2
Sibling math scores: 8 > 1 > 7 > 5 > 6 > 3 > 2
(4 doesn’t have siblings)
Tracks with dysfunction increasing with IQ.
> Tracks with dysfunction increasing with IQ.
In my family it correlates bigly with fertility (negatively).
Math is heritable, this page proves it: https://en.wikipedia.org/wiki/List_of_Jewish_mathematicians
Reminds me of the refutation of the popular application of the ‘regression to the mean’ statistic to IQ, by Bruce Charlton.
Also, visual abilities are heritable. Myopia isn’t, but growth plates and pressure on the eyeball is. And mental visualization increases with minor losses in visual acuity.
We all know I have the highest openness out of anyone youve acquainted yourself with aeoli!
Aeoli you can censor my comment but the truth is still out there!
I think you don’t understand how comment moderation works.
Indeed it is
just admit it Aeoli you are an autist scoundrel.
Caught me again.
i believe you have benevolent intent but it is hidden by layers of being an autist scoundrel unfortunately.
Koanic was right (again)
EXCLUSIVE: Her Majesty the Queen has always been seen as a level-headed leader, but her fascination with the mysterious snow beasts led her to meet one man who claimed to have been taken hostage by a family of Bigfoots
…so you see, with svante pääbo getting noble prize for neanderthards, Edenism will soon become cringe and every internet e-celeb will soon be part neanderthal (like and donate to my bomb shelter). When you win you lose. never bet on neanderthal. Hopefully we get to keep melonboons SC and ooga booga cannibal rapist headhunters to ourselves.
I sure do be hoping Vladimir Biden and Joe Putin hastens the process of collapsing europe together Faster so I don’t have to witness such cringes. Bring on the salted cobalt warheads.