## More on negative Chinese stereotypes

I talk with a guy who knows British race and intelligence researcher Richard Lynn, who prophesized back in 2001 in a book on eugenics that China will, with a combination of high IQ, size (both in land mass and population), and authoritarian government, eventually rule the world. I asked him what he thinks about that. His response was:

Chinese deeply incompetent and bad personality for innovation. But maybe if Western keeps importing blacks and Muslims…
It’s a good question and important

For more context on Lynn, I’ll copy directly from his book.

The nations of East Asia are likely to develop their economic, scientific, technological, and military strength during the twenty-first century by virtue of the high intelligence levels of their populations and the absence of any serious dysgenic processes. These countries have not allowed the growth of an underclass with high dysgenic fertility, and they have not permitted dysgenic immigration. China will continue its rapid economic development and will emerge as a new superpower in the early middle decades of the twentyfirst century. Chinese economic, scientific, and military strength is likely to be increased by the further development of the eugenic programs introduced in the 1980s and 1990s and particularly by the introduction of the new eugenics of embryo selection and the cloning of elites. As the power of the United States declines, China and Europe will emerge as the two superpowers. A global conflict will develop between them in which Europe will become progressively weakened by dysgenic forces and China progressively strengthened by eugenic programs. This conflict will eventually be won by China, which will use its power to assume control of the world and to establish a world state. This event will become known as “the end of history.” Once China has established a world state, it can be expected to administer this on the same lines as former colonial empires by appointing Chinese governors and senior military and administrative support staff in charge of the provinces of its world empire or by allowing nationals of its subject peoples to administer the provinces under Chinese supervision. The establishment of a Chinese world state will inevitably not be welcomed by the peoples of the rest of the world, who will become colonized populations governed by an oligarchy based in Beijing. There will be no democracy, and a number of freedoms will be curtailed, including freedom to publish seditious material and to have unlimited numbers of children. There will, however, be certain compensating benefits. There will be no more wars between independent nation states with the attendant dangers of the use of nuclear weapons and biological warfare. It will be possible to deal with the problems of dysgenic fertility, global warming, deforestation, the population explosion in the developing world, the AIDS epidemic, and similar global problems that cannot be tackled effectively in a world of independent nation states. Among the world state’s first objectives will be the reversal of dysgenic processes and the introduction of eugenic programs throughout the world. Over the longer term the world state will set up research and development programs for the use of genetic engineering to improve the human genome and to produce a new human species able to solve hitherto unsolvable problems and to colonize new planets. This will be the ultimate achievement of Galton’s vision of using eugenics to replace natural selection with consciously designed human selection.

This scenario for the twenty-first century, in which China assumes world domination and establishes a world eugenic state, may well be considered an unattractive future. But this is not really the point. Rather, it should be regarded as the inevitable result of Francis Galton’s (1909) prediction made in the first decade of the twentieth century, that “the nation which first subjects itself to a rational eugenical discipline is bound to inherit the earth” (p. 34).

And also an excerpt with reference to the perceived lack of personality conducive to innovation on the part of Chinese:

Once China has established the world state, it will be concerned with raising the prosperity of its subject populations, just as other colonial powers have been. One of its first measures to promote this objective will be to introduce worldwide eugenic programs. These will include programs of both positive and negative eugenics. With regard to negative eugenics, one of its first objectives will be to reverse the dysgenic fertility that appeared in Europe, the United States, and the rest of the economically developed world in the middle and later decades of the nineteenth century and persisted into the twentieth century and that developed later in most of the remainder of the world. It can be expected that in its European and North American provinces, the Chinese will introduce the same eugenic measures that had been pioneered in China, consisting of both the classical eugenics of parental licensing and the new eugenics of the mandatory use of embryo selection for conception. The Chinese may well also introduce the cloning of the elites of the European peoples. The Chinese will be aware that while they and other Oriental peoples have a higher average intelligence, the European peoples have a greater capacity for creative achievement, probably arising from a higher level of psychopathic personality, enabling them more easily to challenge existing ways of thinking and to produce creative innovations. This will be part of human genetic diversity that the Chinese will be keen to preserve and foster. They will regard the European peoples rather in the same way as the Romans regarded the Greeks after they had incorporated them into the Roman empire. Although the Romans had conquered the Greeks by their military superiority, they respected the Greeks for having developed a higher level of civilization than they themselves had been able to achieve. The Chinese will view their European subject peoples in a similar manner.

I do increasingly believe, as I’ve already written numerous times on this blog, that lack of creative potential of Chinese is way overstated. In the 20th century, they achieved a fair bit in terms of creativity at the highest levels, especially in STEM, in spite of very disadvantaged environmental circumstances. The Chinese did not develop modern science; I think though this has more to do with their having started later, civilization-wise, than the rest of the world due to limited scope and geographic obstacles than with their innate ability/personality. Agriculture and writing were independently developed in China substantially later than it was in Mesopotamia. I see an analogy here. Chinese often like to use the fact that Japan did not develop its own writing system to show contempt for this comparatively little country that Chinese themselves suffered so much from in modern times. This is clearly not because Japanese are less naturally talented (their IQ is about the same); they were basically too small to do so before Chinese characters were transmitted to them. There are actually quite a few Chinese who achieved at the highest levels of STEM (and even more Japanese), they are lesser known though due to their foreignness. As for names, there are quite a few, and one can easily find them online. I’ll go as far as Chen-Ning Yang in theoretical physics and Shing-Shen Chern in pure math.

Again, Chinese culture still lacks presence in the outside world, and China itself is still a developing country, though of course significant parts of China are basically at developed levels GDP wise. So even if Chinese are extremely good and creative, they have a harder time getting recognized and realizing their potential. This also has much to do with a relative lack of truly leading edge science culture and tradition in China, which will take some time. Transmission of knowledge from cultures and lands so far apart is by no means trivial.

We all know that it’s often not enough to be actually good. You also have to win politically. China is increasingly doing that. Its political system far apart from the norm set by the West is becoming increasingly credible to the dismay of many Western elites as China rises in economically, technologically, and militarily. The more powerful China becomes, the more easily Chinese will be able to advocate for themselves on the international stage and get recognized for their achievements. This reminds me of how many say Soviet scientists had to do better work than Western scientists to win the same big prizes, most of all the Nobel, because the West had the political sway to bias the committees to its favor somewhat. There is also, I guess, that the West can be very biased in who it promotes in the media. Like, the Nobel Peace Prize is a basically a complete joke, but there are people politically influential enough to make a big deal out of it.

What I believe is grossly under-recognized is how much creativity and daring it has taken for the Chinese to create their own, unique political system and maintain sufficient faith in it up to this day. In many ways, in this respect, the 90s, right after the Soviet collapse, when there was all this Francis Fukuyama end of history nonsense, was a nadir for China. But we’re now past that, and time seems to be on the side of the Chinese. I guess they will still need more people like me to advocate for these alternative perspectives to the extent that they becomes the new normal, in the international setting.

## On manipulating perceptions

My thoughts on the importance of perception management, in addition to actually being good, by way of a chat log.

dude I think the jewish domination of liberal media is just IQ
if white americans are 100 SD 15, ashkenazim are 115 SD 15
Then if you look at 130+
In the US you have a 30:1 ratio but among 130+ you would expect like
2:1
dude like 1/3 of the 130+ whites in the US are jews
jewish verbal is probably even > 115 since spatial is lower
also they are coastal and liberal

lol you idiot it has much to do with personality socioeconomics culture too

yeah i’m saying that
coastal and liberal
updating more

Lol also if Jewish verbal is so high why are Asians beating them at PSAT/SAT

stats?

English/culture

Read Myth of American Meritocracy by Unz

He has stats there

have you read Janet Mertz takedown

Yes I’ve skimmed through that

Unz overestimates harvard % jewish
and underestimates other things

Sure he probably does a little

wait like half the white people at mop are jewish
like half
Since it can be hard to tell by surname
dude I think chinese americans have a massive
verbal IQ
way higher than of mainland china
maybe even higher than ashkenazim
But they haven’t been here long enough
like Jews in the 50s
also a lot of them are not interested
in verbal professions

how trainable is verbal SAT?

I agree the trainability of the SAT is overstated by people but cramming vocab is totally a thing, no
I dont trust unz statistics at all lol

Lol because Chinese-Americans know that verbal careers like law are rigged against them
So many strong ones are hesitant to enter
There’s a cultural affinity aspect to that as well

chinese prefer medicine or law
I think a lot of it also is that a society with a functional legal system is alien to most chinese people
his response: No

Haha he’s both right and wrong

but yeah law is jewish
but I mean jews are not pulling the strings or anything
like
they are smart verbally
And they tend to be coastal and liberal
The tribe is not jews, it’s coastal liberals
130+ secular coastal liberals are like half jewish
but they dont think of themselves as jewish but as secular coastal liberals
like NYT columnists are half jewish
because 130+ secular costal liberals in the US are half jewish

Lol lol

secular new york coastal liberals
it’s a majority easily

NYT columnists

like manhattan is 20% jewish

NYT is full of garbage

?
its pretty reliable
Sometimes they call Rouhani a “moderate” and I wince – he’s certainly better than ahmadenijad, but he’s no moderate … “pragmatist” is the right word

hmm?

See politically, the Anglo world is setting the standards right now

yes, I very much enjoy not living in a society with sesame credit

sesame credit?

yes

I don’t even know what that is

china could become an orwellian state

Oh that

isn’t that great

Orwellian state what does that even mean

It’s just this phrase for evil regime coined by the Anglo media based on the works of an Anglo writer, that’s all.
I’ve read 1984 and Animal Farm
They’re pretty good
Very hyperbolic of course, as is much media
I actually exchanged briefly with Unz

ok

Maybe I should ask him about what he thinks of Jews being subsumed into the white category in these racial classifications
What do you think of these IQ tests as actual measures of real, biological intelligence
They are very noisy for sure
Especially verbal, because exposure to language varies widely

on an individual level
noisy
on a group level good
they are measuring something important
Whether it’s 100% genetic I dont know
I doubt it

Lol when most Chinese kids’ parents don’t know English all that well
Heck I’m even unfamiliar with some of the more colloquial English language
People viewed me as funny for it in school

sure
what do you think about steven pinker
he’s one of my favorite people

No opinion of him
Also those tests are noisy predictors of actual ability on real things as well from my observation
The discrimination against Asians in admissions right now is likely partially premised on the perception that their test scores inflate their actual ability due to prep.
There is still the perception that Asians do well in school but don’t go on to do great things
Again it’s only a perception
Being good and being perceived as good are far from perfectly correlated.

I think there is discrimnation against asians
for being recent
for being perceived as grade grubbers

Yeah they’re also not rich or well-connected.

this perception is not wholly unjustified ofc
yeah also that
i am strongly opposed to ivy asian quotas

There is resistance towards Asians becoming successful in America
It’s a white country after all

eh

Anyhow, I think in a matter of time, the best young people in China will come here for grad school less and less.
America will become a place for China to send its second-rates.
I’ve written that China needs to get better at marketing

too right wing?
And I’ve read on Zhihu that in recent years, the Chinese who studied math in France have turned out better than the ones who came to US for grad school.

not china vs US

Lol math I think the best young people will still study abroad for a while.
There’s also engineering
Plenty of that China does well now.
I think in actual STEM ability/competence, China/Chinese still have much room for improvement, but now, they’re not bad, and the potential is there, with trends in favor of them.
It’s the whole game of manipulating perceptions that will take longer
Due to cultural difference and inertia
In that regard, it’s already been massively successful in just the last five years if you think about it
The media portrayal in the West has already drastically changed.
For instance, dismissiveness of Chinese tech companies is metamorphizing into fear.
I’m not gonna argue whether or not it’s gone to the other extreme
People can have different opinions on that
In any case, I don’t think China has transitioned to foundational innovator, that’ll take a while, but the increasing level of sophistication combined with the scale is certainly very formidable.
China still relies on US companies for its semiconductors/chips. She has not created a viable ecosystem for its homegrown ones yet. But that could well happen in a decade.
Then US will have even less bargaining chip.
Now, China can easily get away with what it’s doing to Taiwan largely because it is so much stronger economically, technologically, and militarily.

jack ma is a smart guy
but I mean

Nobody wants to piss off the powerful, because there’s much to lose.

china’s system doesnt make too much room for jack ma and yitang zhang
The lack of political freedom is a big obstacle here

Lol Jack Ma isn’t smart IQ wise
Struggled to get into a college
He has other qualities

The lack of political freedom is a big problem for innovation

Hahaha
Elaborate on that one

Name a totalitarian society that was innovative
Germany under the Kaiser wasn’t really totalitarian

Uh, USSR?

all their jewish scientists moved to america and israel
Because they prevented them from leaving
They didn’t have much in the way of tech

Uh, Sputnik?

low tech
very low tech
there won’t be a chinese steve jobs

Sure computer technology they were behind, because semi-conductors and integrated circuits were invented in America
Lol Steve Jobs is mostly marketing

shockley
eugenics
chinese bill gates

And what you say about Sputnik is ridiculous
First satellite in orbit
That was back in 1957 silly
You don’t think Ren Zhengfei is as impressive as Steve Jobs?
Huawei
So much of the global telecommunications infrastructure
Now their phones, which US is banning.

So
Lol what if China once it has the resources starts a huge propaganda/PR war
China has a ton of young people with nothing to do.
Have them troll the YouTube comments, drown out all the anti-communist Chinese.
Numbers do matter
The Chinese government could also incentivize more people in the West to start blogs supportive of Chinese ideology.
Try to buy out US media outlets
You don’t think China once it is advantaged in resources can start playing the game of manufacturing consent as well

## A revisit of the drama behind the Poincaré

I recall back in 2008, when I first cared enough to learn about mathematicians, I read a fair bit of the media articles on the proof of the Poincaré conjecture. At that time, I was clueless about math, and these mathematicians seemed to me like these otherworldly geniuses. I do remember thinking once to myself that maybe it would be kind of cool to part of that world. Except at that time, I was way too dumb, and maybe I still am. However, now I actually have some idea of what math research is about, unlike back then, when my conception of math and mathematicians was more of a naive popular one.

## Understanding Human History

I had the pleasure to read parts of Understanding Human History: An Analysis Including the Effects of Geography and Differential Evolution by Michael H. Hart. He has astrophysics PhD from Princeton, which implies that he is a serious intellectual, though it doesn’t seem like he was quite so brilliant that he could do good research in theoretical physics, though an unofficial source says he worked at NASA and was a physics professor at Trinity University who picked up a law degree along the way. I would estimate that intellectually, he is Steve Hsu level, perhaps a little below, though surely in the high verbal popularization aspect, he is more prolific, as evidenced by that book, among many others, such as one on the 100 most influential historical figures. He is active in white separatist causes (heh) and appears to have had ties with the infamous and now deceased Rushton.

## On questioning authority

A couple years ago, my friend who won high honors at the Intel Science Talent Search told me that he was talking this guy who created some app that allows you to schedule a Uber ride for later, who was also at/near the top of the same science competition, who is extraordinarily versatile and prolific. I watched a little of a video of a TED talk he gave, wherein he explained what one can learn from ancient Hebraic texts. Overall, I wasn’t terribly terribly impressed by it, though it was quite eloquently delivered. Mostly because with those types of things, one is too free to interpret and thus, the lessons/messages given were overly generic so as to make them almost meaningless, one of which was how the Bible teaches the importance of questioning authority, with reference to the refusal to bow to the golden image of King Nebuchadnezzar by Shadrach, Meshach, and Abednego as an exemplary.

## Censorship in America

I’ve had the pleasure of reading the comments on Disqus of Bob Sykes, a baby boomer who, according to himself, has been an engineering professor for 37 years, at OSU if I remember correctly. He comments mostly on military technology, China, North Korea, race relations in America, and other political issues both internal and external to America. You can tell easily that he has some rather “radical” views. Like, he believes in segregation, to the extent that he thinks we should have segregated colleges. Now is he actually serious or is he employing the humor of hyperbole. He will also say:

Face the facts: the Anthem, Pledge, Flag, Declaration and Constitution are WASP male symbols. Blacks, Jews, Asians and Mexicans are not and cannot be Americans. America is and always will be WASP country.

I for the most part agree with what he says, when taken less literally and with some de-magnifications perhaps. He’s also pretty fucking funny. (If not, I wouldn’t be reading him ;))

I did see this morning this comment of his:

For almost a generation, Chinese students have dominated enrollments in our major STEM departments. They are an absolute majority of the students enrolled in most STEM programs today, especially mathematics and computers, engineering, physics and chemistry. And that is true even of our most elite STEM schools like MIT.

This has been a nearly zero-cost endeavor for the Chinese. At any decent STEM program all (as in ALL) of the graduate students are supported by the research programs they work for. That includes tuition, fees and a comfortable stipend. Support for graduate students is what distinguishes good graduate program from a mediocre one. The good ones have ample externally funded research programs; the mediocre ones don’t.

This investment shows up in many areas. China can put men into space; we can’t. China has many more super computers than we do, and they have the fastest supercomputers. Those machines are entirely home grown, from the chips to the operating systems. China also has the largest and most diverse manufacturing sector in the world and the largest infrastructure sector. Its nearest rival in terms of manufacturing diversity (but not size) is Russia. If China does succeed in integrating Eurasia into one economy, they will be the de facto world hegemon, and we will be a region power.

And I drafted and submitted a response:

You seem to overestimate China and Chinese in STEM a bit, though surely, the American mainstream tends to downgrade it. I know and talk with a guy, a very talented MIT student, who thinks rather lowly of China. Pollution, human rights, very few top mathematicians and scientists, yada yada yada. It is surely the case that even now most of the very elite STEM people of Chinese descent are in America, working in American universities or benefiting the American economy massively in American companies. It also does appear that at the highest levels, Chinese are still very underrepresented in many fields.

America is still quite a ways ahead in terms of sophistication of technology. You say China’s supercomputers are homegrown entirely, including the chips, but China’s best chip, the Loongson, is still far from the level that Intel has. Also, China has been struggling to manufacture high quality jet engines, which it has to buy from Russia, and in that, America, with Pratt and Whitney, is a generation ahead. These are examples of the most difficult technologies where China is still quite behind.

In a field I’m more familiar with, computer science, there’s no way China is anywhere close overall. See http://dubfuture.blogspot.c…. Almost all the important and foundational software systems, from the widely used programming languages, to Linux, to distributed systems, to git, have been developed in the West, and China is merely using them. I don’t see many Chinese, including those in America, creating complex, widely used open source tools yet.

China also is nowhere near competitive in the global automobile market.

So, too many glaring weaknesses. In China, people see themselves as scientifically and technologically behind, though that’s been changing. They even believe to a non-negligible extent that the Chinese education and system is ill for creativity, which seems to me way overblown, which the American mainstream promulgates, as did the professor who wrote the essay linked above.

I’ve gone through all my schooling in America, and I read Chinese online regularly, so I know a bit about China including its education and STEM, and this gives me an unusual double lens. I honestly think that American STEM education up to the undergrad level is a complete joke, and I realized this on a gradual basis. I eventually realized, starting from high school, that I had to learn on my own, as the school system by itself produces people who are not at all competitive. The American high school and college admissions system and even college is full of inane, time-wasting artificial nonsense. It has much to do with that the fact that students are simply too dumb nowadays, without selection at the high school level, which is done in most other advanced countries, including China, including Germany. There is also a ton of ideological BS within the American system, one that prides itself in vacuous democracy and freedom of speech; I’ve gone through American English and history classes to know the nightmare.

I do think though that in America, there is a sizable contingent who manage to really excel in spite of this morass, through independent learning and research, and by the graduate level, the American system is for the most part top notch. At the very top, the non-Chinese still have an edge, and that arguably extends to the younger generation as well.

By the way, how much discrimination do you see against Chinese in hard STEM fields (that does not include biology, in which it most certainly does exist). A friend of mine, a pure American, suspects that there is some pro-Jewish bias in academia right now in America, and that even in something like math, those mainland Chinese have to be better than those Jews to obtain equivalent positions. It’s hard to say. It does seem that Jews produce the most revolutionary thinkers and scientists if you look at the giants of math and theoretical physics. On the other hand, within the younger generation, Chinese are dominating the contests and Olympiads, which are 100% objective, fair contests. One ought to remember that in the older generation, China was quite poor and the Chinese came as immigrants with no money in a very foreign culture, a stark contrast to what the Jews, who are basically white European, have experienced. I’ve seen many very intelligent Jews say complete nonsense about China, more or less echoing the braindead mainstream American media, and I’ll go as far as to say that the Chinese cognitive elite does appear to be far less “full of shit.” It could be that the older generation of Chinese, to the extent that it underperformed, did so mostly out of discrimination and/or lack of resources and opportunity, or it could be that there is a relative dearth of Chinese talent wise at the very highest (say +4, +5 sigma) levels. We’ll see.

And Disqus marked it as spam!

Was it the Disqus system itself or was it some moderator of whatever forum this was, who decided that my writing was too un-PC to be publicized?

## Innate mathematical ability

This morning I had the great pleasure of reading an article on LessWrong on innate ability by Jonah Sinick. Jonah has been one of my greatest influences and inspirations, having interacted with him substantially. He is unusual in one of the best ways possible. I would not be surprised if he goes on to do something extraordinary.

When I catch up with Jonah, I like to talk with him about math, mathematicians, and IQ, which happens to be what that article of his on LessWrong is about. 😉 That article resonates with me deeply because I myself had similar experiences as he did. It is hypothesized by me that I was also twice exceptional, albeit in different ways, with its effects compounded by my unusual background, all of which mediocrities within the American public school system are not good at dealing with in an effectual way.

This writing of Jonah has brought forth reflections in my own mind with regard to mathematical ability, development, and style. I’ll say that as a little kid under 6, I was very good at arithmetic and even engaged in it obsessively. However, by age 8, after two years of adjusting to life in America starting off not knowing a word of English, I had forgotten most of that. I was known to be good at math among the normal normal students; of course, that doesn’t mean much. In grade school, I was not terribly interested in math or anything academic; I was more interested in playing and watching sports, particularly basketball and baseball.

I didn’t have any mathematical enrichment outside of school other than this silly after school math olympiad program. Nonetheless, I managed to test into two year accelerated math once I reached junior high, not that it means anything. In junior high, we were doing this stupid “core math” with graphing calculators and “experiments.” I didn’t realize that I was actually a joke at math until I failed miserably at the state mathcounts contest, having not prepared for it, unlike all those other tiger mommed Asian kids, who to me seemed way beyond me at that time. It only occurred to me that I might have some real talent for math when I made the AIME in 10th grade, taking the AMCs for the first time, being one of four in my high school of about 2000 to do so. I thought it was fun solving some of those math contest problems, which were more g-loaded, with an emphasis on the pattern recognition side.

It was after that I started to read up on the history of mathematics and mathematicians. I taught myself some calculus and was fascinated by it, not that I understood it very well. But I could easily sense that this was much more significant than many of those contrived contest problems, and soon, I began to lose interest in the contest stuff. It was also after that that I learned about proving things, which the American public school math doesn’t teach. I finally realized what mathematics is really about.

Like Jonah, I had some difficulties with careless errors and mental organization. I don’t think my raw intellectual horsepower was very high back in high school, but fortunately, it has improved substantially since then that it is for the most part no longer the major impediment.

I took calculus officially in 11th grade, and it was a breeze for me. I could easily compute the areas and volumes and such but the entire time, I felt quite dissatisfied, because I could not actually understand that stuff at a rigorous, theoretical level as I poured through our textbook that went up to vector calculus during lecture, which was rather inane, expected if one considers the mismatch between cognitive threshold relative to the distribution of ability of the students. I knew from reading online the rich world of math far beyond what we were covering, most of which I was not intellectually mature enough to access at that time. However, I vividly remember during summer after 11th grade, while attending a math summer program, I was able to comfortably write out the delta epsilon definition of limit with understanding of why it was reasonably defined that way. Still, I would say I was still quite weak in terms of both my mathematical maturity and overall intellectual ability. There were too many things I wasn’t aware of, including the g factor, that I easily would have been had I been higher in verbal ability, which would have enabled me to read, absorb, and internalize information much more rapidly and broadly. In contrast, Jonah had discovered independently, or so he says, the lack of free will at the age of 7!

I made some incremental advances in my math knowledge from reading and thinking outside of school the next year. As for contest math, I almost made the USAMO. Though I had improved, I was still not terribly quick and careful with solving contest style problems and doing computations. I think close to graduation, I also solved some Putnam problems.

Only in undergrad did I learn real math more seriously, but even there, nothing too advanced. US undergrad is a joke, and I also was one, just to a lesser extent than most of my “peers.” Almost certainly, Jonah, based on he’s told me, had gained much deeper and broader knowledge at the same stage, from the reading works of giants like Euler and Riemann.

I’ve noticed how there are a lot of Chinese-(American) kids really into those high school math contests, and they now also dominate USAMO and Putnam (though careful, as in the latter, there you’ve got some of Chinese internationals drawn from the elite from China). I will say that at the lower levels, many of those kids have some pretty low taste and an inability to think outside the system that would enable them to discover the existence of real math, as opposed to this artificial math game that they enjoy playing or are pressured to doing so for college. Though those contests have a high pattern recognition component to them, there is not really much depth or substantial math knowledge. It is also my belief, with reference to Jonah’s article, that math contests are mostly M loaded while real math is more V loaded. So this behavior is consistent with the lopsidedness in favor of M and perhaps also short term working memory of Chinese students. It has also been Jonah’s belief that controlling for g, these contests select for low taste and value judgement, and I surely identify with that perspective. So maybe college admissions are somewhat fair to assess an Asian penalty?

Of the thesis of Jonah’s article, a representative figure is Terry Tao. There, Jonah also pointed out that Tao’s research in math is more concrete and problem solving oriented by pure math standards, in line with what appears to be the same lopsided (modulo the absolute level, as Terry is a far far outlier) cognitive profile of his based on testing at age 9 and 10. Again, people enjoy what they are best at, and though, Terry Tao is almost certainly at least +3 sigma at verbal, he is far more rare, at least +5 sigma, a real übermensch, in the (in some sense dual) pattern recognition component, which means he leans towards the areas of math more loaded on the latter. I have heard the saying that even other Fields medalists are intimidated by Terry Tao. The breadth and volume and technical power of his work is almost unrivaled and otherworldly. The media makes it seem like Terry is a league above even the other Fields medalists. However, Jonah seems to believe that the deepest and most leading of mathematicians are the ones who are more theory builders, who create through leaps of insight and synthesis new fields and directions that keep mathematicians busy for decades, and even centuries. That would be say Grothendieck or SS Chern, and an ability that is more loaded on verbal ability, crudely speaking. Again, I have felt the same. This might explain why the advantage of Chinese students is not anywhere near as pronounced in math research as in contests, and why some people say that generally speaking, the Chinese mathematicians are more problem solving and technical than theoretical, more analysis than algebra. Likewise, we can predict the opposite for Jews who are skewed in favor of verbal. A corollary of this would be that the Jews produce the deepest thinkers, adjusted somewhat for population, which is almost certainly the case, if you look at the giants of mathematics and theoretical physics.

I’ll conclude with the following remark. I used to revere somewhat those who placed very highly on those contests, until I realized that many of them are actually somewhat weak in terms of deep understanding and thinking at a more theoretical level. Yes, I have met MOSPers who got destroyed by real math and who are not very intellectually versatile, with glaring weaknesses; I was quite surprised initially that even I seemed to be smarter if not a lot than some of them. Once upon a time, I couldn’t understand those who appeared very strong at real math (and often also science and/or engineering and/or humanities) who struggled with more concrete math and/or contest-style problem solving, like Jonah, who has written on LessWrong of his difficulties with accuracy on the trivial math SAT. I’ve met this other guy, who I thought was an idiot for being unable to perform simple computations, who is leagues beyond me in the most abstract of math, who writes prolifically about partially V-loaded areas of math like model theory. Now, the more metacognitive me has awakened to the reality that I may never by deficit of my neurobiology be able to fathom and experience what they’re capable of. After all, there are plenty I am almost certain are and are essentially doomed to be very delusional by nature relative to me, and since I’m at the far tail but not quite so much, there are bound to be people who view me the same. I can only hope that I can become more like them through some combination of exposure and organic neurobiological growth, but I as a realist will not deem that very likely.

## Math sunday

I had a chill day thinking about math today without any pressure whatsoever. First I figured out, calculating inductively, that the order of $GL_n(\mathbb{F}_p)$ is $(p^n - 1)(p^n - p)(p^n - p^2)\cdots (p^n - p^{n-1})$. You calculate the number of $k$-tuples of column vectors linear independent and from there derive $p^k$ as the number of vectors that cannot be appended if linear independence is to be preserved. A Sylow $p$-group of that is the group of upper triangular matrices with ones on the diagonal, which has the order $p^{n(n-1)/2}$ that we want.

I also find the proof of the first Sylow theorem much easier to understand now, the inspiration of it. I had always remembered that the Sylow $p$-group we are looking for can be the stabilizer subgroup of some set of $p^k$ elements of the group where $p^k$ divides the order of the group. By the pigeonhole principle, there can be no more than $p^k$ elements in it. The part to prove that kept boggling my mind was the reverse inequality via orbits. It turns out that that can be viewed in a way that makes its logic feel much more natural than it did before, which like many a proof not understood, seems to spring out of the blue.

We wish to show that the number of times, letting $p^r$ be the largest $p$th power dividing $n$, that the order of some orbit is divided by $p$ is no more than $r-k$. To do that it suffices to show that the sum of the orders of the orbits, $\binom{n}{p^k}$ is divided by $p$ no more than that many times. To show that is very mechanical. Write out as $m\displaystyle\prod_{j = 1}^{p^k-1} \frac{p^k m - j}{p^k - j}$ and divide out each element of the product on both the numerator and denominator by $p$ to the number of times $j$ divides it. With this, the denominator of the product is not a multiple of $p$, which means the number of times $p$ divides the sum of the orders of the orbits is the number of times it divides $m$, which is $r-k$.

Following this, Brian Bi told me about this problem, starred in Artin, which means it was considered by the author to be difficult, that he was stuck on. To my great surprise, I managed to solve it under half an hour. The problem is:

Let $H$ be a proper subgroup of a finite group $G$. Prove that the conjugate subgroups of $H$ don’t cover $G$.

For this, I remembered the relation $|G| = |N(H)||Cl(H)|$, where $Cl(H)$ denotes the number of conjugate subgroups of $H$, which is a special case of the orbit-stabilizer theorem, as conjugation is a group action after all. With this, given that $|N(H)| \geq |H|$ and that conjugate subgroups share the identity, the union of them has less than $|G|$ elements.

I remember Jonah Sinick’s once saying that finite group theory is one of the most g-loaded parts of math. I’m not sure what his rationale is for that exactly. I’ll say that I have a taste for finite group theory though I can’t say I’m a freak at it, unlike Aschbacher, but I guess I’m not bad at it either. Sure, it requires some form of pattern recognition and abstraction visualization that is not so loaded on the prior knowledge front. Brian Bi keeps telling me about how hard finite group theory is, relative to the continuous version of group theory, the Lie groups, which I know next to nothing about at present.

Oleg Olegovich, who told me today that he had proved “some generalization of something to semi-simple groups,” but needs a bit more to earn the label of Permanent Head Damage, suggested upon my asking him what he considers as good mathematics that I look into Arnold’s classic on classical mechanics, which was first to come to mind on his response of “stuff that is geometric and springs out of classical mechanics.” I found a PDF of it online and browsed through it but did not feel it was that tasteful, perhaps because I’m been a bit immersed lately in the number theoretic and abstract algebraic side of math that intersects not with physics, though I had before an inclination towards more physicsy math. I thought of possibly learning PDEs and some physics as a byproduct of it, but I’m also worried about lack of focus. Maybe eventually I can do that casually without having to try too hard as I have done lately for number theory. At least, I have not the right combination of brainpower and interest sufficient for that in my current state of mind.