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Everyone is capable of, and can benefit from, mathematical thinking

quantamagazine.org

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Re: Everyone is capable of, and can benefit from, mathematical thinking

#401

Post by tptacek »

cutemonster wrote: post #399
tptacek wrote: post #377

Earlier quoted context omitted.

Current estimates of the "heritability" of intelligence are far, far lower than "0.7 or 0.8"; they're probably below 0.1, and that's before digging into what "heritability" means, which is not generally what people think it does. I'd guess the person you're responding to has thought more carefully about this issue than the median HN commenter has.

> Current estimates of the "heritability" of intelligence are far, far lower than "0.7 or 0.8"; they're probably below 0.1 Sources please, if you have time? I tried to find something supporting what you wrote, but wasn't able to (this far). Instead I found this from 2015: Thinking positively: The genetics of high intelligence , https://pmc.ncbi.nlm.nih.gov/articles/PMC4286575/ They've studied men in Sweden during 40…

My sibling comment (unsuprisingly) goes into more depth and with more sourcing. The 0.4 result you've cited is from 2015, which is in the phlogiston era of this science given what we've learned since 2018. As he has aptly demonstrated: his authorities are sound, and he has thought carefully about this matter --- respectfully, far more than you seem to have. That's OK! We're just commenting on a message board. I wouldn't even bring it up, except that you've decided to make his grasp on the subject a topic of debate.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#402

Post by hosh »

FractalHQ wrote: post #290
hosh wrote: post #268

Earlier quoted context omitted.

There's a lot of interesting discrete math that can supercharge programming at different levels of scale. What's pretty cool is that it reveals a layer of understanding when I watch my toddlers learn math from counting. One of the interesting things is being able to exactly describe how something is an anti-pattern, because you have a precise language for describing constraints.

I would love to learn about some of these anti-pattern proofs if you have any examples or references you can share!

I don't have proofs. I haven't gone into any level of rigor with any of this.

Here is a recent example: https://files.spritely.institute/papers/petnames.html

The idea of a naming system can be (1) decentralized, (2) globally unique, (3) human meaningful. It talks about the onion DID names which achieves decentralized and globally-unique, and proposes a petname system that maps local names to achieve all three when combined with the onion names.

It sounds similar to me to the mathematical concept of an atlas. Atlases originally came about trying to map a non-Euclidian topology to a local, Euclidian topology. No Euclidian topology can fully describe the non-Euclidian topology, but a set of those can, and together would form an atlas.

Someone with more math chops than I can prove (or disprove) that the petname system forms an atlas over the set of globally-unique names (identifiers). The biggest anti-pattern I can see coming out of it is when people using this attempt to make the local petnames globally unique instead of working with it as a local mapping that can never fully describe the global space of unique names.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#403

Post by cutemonster »

davidbessis wrote: post #394
cutemonster wrote: post #372

Earlier quoted context omitted.

> they do know something about math ... that it requires a certain "attitude" Of course. That does not mean that intelligence doesn't play a (big) role. > Starting from Descartes and his famous "method", continuing with Newton, Einstein, Grothendieck all these guys insisted that they were special because of this "attitude" and not because of what people call "intelligence" That doesn't make sense. Back when they were…

Dear cutemonster, I know this reply may not suffice to convince you, but unfortunately I won't be able to argue forever. Did you ever consider the possibility that you might be the one living in a bubble? FYI, the concept of innate talent predated IQ tests and twin studies by many millenia. Two of the authors I'm citing in my book (Descartes and Grothendieck) believed that innate talent existed and they both declared…

> Did you ever consider the possibility that you might be the one living in a bubble?

You're wrong about that, but you couldn't have know. I've lived in far more different places with more different people, than most people you've met.

> innate talent predated IQ tests and twin studies by many millenia

That's why I wrote it hadn't been well studied, not that it hadn't been studied at all.

> You're declaring that

Of course not. I'm not the source.

> incredibly smart people were wrong about their own domains, which is a pretty bold claim to make. What do you have in support of this claim? A fake Einstein quote?

That's from a letter Einstein wrote 1926 to Bohr. He wrote in German, that quote is a paraphrase in English.

Look here: https://en.wikipedia.org/wiki/Bohr%E2%80%93Einstein_debates, And, about him being mistaken, quoting that article:

"As mentioned above, Einstein's position underwent significant modifications over the course of the years. In the first stage, Einstein refused to accept quantum indeterminism [...]" -- indicating that, at some points, he had the wrong beliefs, right.

Here's the quote explained further: https://hsm.stackexchange.com/questions/5937/why-did-einstei...

> It's true that a number of people have been fooled by twin studies, most notably Steven Pinker, in Chapter 19 of the Blank Slate (did you read it?)

> You see, Pinker ... Bouchard's 1990 ... The Bell Curve's Charles Murray ... thinks ... structurally flawed

No, didn't read that book. Continuing in another comment.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#404

Post by cutemonster »

tptacek wrote: post #401
cutemonster wrote: post #399

Earlier quoted context omitted.

> Current estimates of the "heritability" of intelligence are far, far lower than "0.7 or 0.8"; they're probably below 0.1 Sources please, if you have time? I tried to find something supporting what you wrote, but wasn't able to (this far). Instead I found this from 2015: Thinking positively: The genetics of high intelligence , https://pmc.ncbi.nlm.nih.gov/articles/PMC4286575/ They've studied men in Sweden during 40…

My sibling comment (unsuprisingly) goes into more depth and with more sourcing. The 0.4 result you've cited is from 2015, which is in the phlogiston era of this science given what we've learned since 2018. As he has aptly demonstrated: his authorities are sound, and he has thought carefully about this matter --- respectfully, far more than you seem to have. That's OK! We're just commenting on a message board. I would…

> he has thought carefully about this matter --- respectfully, far more than you seem to have

He was wrong in his guesses about me and what I've read, and wrong about the quote too (see sibling comment).

> is from 2015 ... what we've learned since 2018

You're saying the graph is somehow invalid, because of newer GWAS related research?

The blog he links to looks biased to me. Are there two camps that don't get along: looking at DNA (GWAS), vs looking at twin studies etc ... yes seems so. I'll reply to both of you in another comment

Re: Everyone is capable of, and can benefit from, mathematical thinking

#405

Post by cutemonster »

tptacek wrote: post #397
davidbessis wrote: post #394

Earlier quoted context omitted.

Dear cutemonster, I know this reply may not suffice to convince you, but unfortunately I won't be able to argue forever. Did you ever consider the possibility that you might be the one living in a bubble? FYI, the concept of innate talent predated IQ tests and twin studies by many millenia. Two of the authors I'm citing in my book (Descartes and Grothendieck) believed that innate talent existed and they both declared…

Some of the stuff on Gusev's substack is pretty startling, and I highly recommend it. Thank you for taking the time to comment here!

> > twin studies and they have taken in serious beating in the past decade, especially in light of GWAS.

Here's a twin study from 2015, newer than the books (Clean Slate etc) and papers you (David) mentioned.

"Thinking positively: The genetics of high intelligence" https://pmc.ncbi.nlm.nih.gov/articles/PMC4286575/

Figure 3 indicates that intelligence is pretty strongly inherited, and they arrive at 0.44.

Now you're saying that that doesn't matter because of GWAS? Sounds a bit hand-wavy to me.

> > Sasha Gusev's Substack as an entry point: https://theinfinitesimal.substack.com

Blog post looks biased. So there's a controversy: https://en.wikipedia.org/wiki/Missing_heritability_problem

And there's two camps:

https://www.clearerthinking.org/post/the-missing-heritabilit...

(I like that article!)

And the two of you (Davind and Thomas) seem to be in the "The DNA Proponents" camp. The other is "The Twin Study Advocates" camp.

I guess now I'm in "The middle ground" camp, no longer in the "Twin Study Advocates".

Thanks for that. Maybe I'll check back in 10 years later and see what has happened.

Re: Everyone is capable of, and can benefit from, mathematical thinking

#406

Post by tptacek »

cutemonster wrote: post #405
tptacek wrote: post #397

Earlier quoted context omitted.

Some of the stuff on Gusev's substack is pretty startling, and I highly recommend it. Thank you for taking the time to comment here!

> > twin studies and they have taken in serious beating in the past decade, especially in light of GWAS. Here's a twin study from 2015, newer than the books (Clean Slate etc) and papers you (David) mentioned. "Thinking positively: The genetics of high intelligence" https://pmc.ncbi.nlm.nih.gov/articles/PMC4286575/ Figure 3 indicates that intelligence is pretty strongly inherited, and they arrive at 0.44. Now you're s…

The "warring camps" framing is very overstated. Greenberg, who doesn't practice in this space, believes it to be a vital concern, but giants in the twin-study practitioner field freely cite GWAS results, including the EA studies.

A 2015 twin study result is basically a citation to the phlogiston era of polygenic population-wide genetic surveys. Heritability estimates of that vintage basically define away indirect genetic effects, which subsequent work appears to have very clearly established; the work now is on characterizing and bounding it, not asking whether it's real.

"Blog post looks biased" is not a good way to address this unless you actually practice in the space, like the author does, and are in conversation with other practitioners in the space, like the author is. You find lots of --- let's generally call them pop science writers --- knee-jerk responding to the new rounds of heritability numbers, but those same authors often wrote excitedly about how GWAS results would bolster their priors in the years before the results were published. It's worth paying attention to the backgrounds of the people writing about this stuff!

I substantially rewrote this comment, which was sprawling; the original is preserved here: https://gist.github.com/tqbf/b118ec9f9e69e0f3f61003c152d0d44...

Re: Everyone is capable of, and can benefit from, mathematical thinking

#407

Post by tptacek »

cutemonster wrote: post #404
tptacek wrote: post #401

Earlier quoted context omitted.

My sibling comment (unsuprisingly) goes into more depth and with more sourcing. The 0.4 result you've cited is from 2015, which is in the phlogiston era of this science given what we've learned since 2018. As he has aptly demonstrated: his authorities are sound, and he has thought carefully about this matter --- respectfully, far more than you seem to have. That's OK! We're just commenting on a message board. I would…

> he has thought carefully about this matter --- respectfully, far more than you seem to have He was wrong in his guesses about me and what I've read, and wrong about the quote too (see sibling comment). > is from 2015 ... what we've learned since 2018 You're saying the graph is somehow invalid, because of newer GWAS related research? The blog he links to looks biased to me. Are there two camps that don't get along:…

No. (Replied to your other reply.)

Re: Everyone is capable of, and can benefit from, mathematical thinking

#408

Post by cutemonster »

nolamark wrote: post #353
sdeframond wrote: post #336

Earlier quoted context omitted.

What about Frank Lentini ? https://en.m.wikipedia.org/wiki/Frank_Lentini

Seems like he has more than the average number of legs as well. The fact that he has a wiki page, and that many folks with born without or who have lost legs (~500,000/year Americans experience limb loss or are born with a limb difference https://amputee-coalition.org/resources/limb-loss-statistics... ) do not, suggest that the number of people with 2. So the average is still less than 2. For better or worse, number…

He must have been an amazing person. I imagine one easily gets bullied, when looking that different. But, from Wikipedia:

> Lentini was so respected among his peers that he was often called "The King".

Re: Everyone is capable of, and can benefit from, mathematical thinking

#409

Post by anticensor »

Tainnor wrote: post #352
llm_trw wrote: post #306

Earlier quoted context omitted.

In arithmetic. There is a lot more to math than arithmetic.

Square roots are fundamental to (real and complex) analysis and to algebra (in the study of polynomials), so the two major branches of modern mathematics.

Also fundamental to geometry (pythagorean equation and others).

Re: Everyone is capable of, and can benefit from, mathematical thinking

#410

Post by davidbessis »

cutemonster wrote: post #403
davidbessis wrote: post #394

Earlier quoted context omitted.

Dear cutemonster, I know this reply may not suffice to convince you, but unfortunately I won't be able to argue forever. Did you ever consider the possibility that you might be the one living in a bubble? FYI, the concept of innate talent predated IQ tests and twin studies by many millenia. Two of the authors I'm citing in my book (Descartes and Grothendieck) believed that innate talent existed and they both declared…

> Did you ever consider the possibility that you might be the one living in a bubble? You're wrong about that, but you couldn't have know. I've lived in far more different places with more different people, than most people you've met. > innate talent predated IQ tests and twin studies by many millenia That's why I wrote it hadn't been well studied, not that it hadn't been studied at all. > You're declaring that Of c…

I was alluding to the quote relevant to the current debate: "Genius is 1% talent and 99% hard work" — which you incorrectly attributed to Einstein.
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