## More on Asian stereotypes

I just stumbled upon this wonderful essay by Gwydion Madawc Williams on why the Ming voyages led by Zheng He (郑和) led to nothing. The quote of it particularly memorable to me was this:

The separation of craft and education as represented by China’s illiterate shipwrights was indeed a genuine weakness in the Chinese system.  Christian Europe always remembered that St Peter had been a fisherman and St Paul a tent-maker, and it was quite acceptable for learned people to also be involved in manufacturing.  The weakness of Confucianism was not so much that it rated agriculture and craft above merchant trade, but that it insisted on the educated being a learned caste distanced from all of these matters.

Again, it’s the Asian stereotype of being a study hard grind lacking in practical, hands-on skills and “well-roundedness” and “social skills” and all that that admissions officers use to justify denying Asian applicants. I’ll say that from what I know, that is still very limited, Confucianism was very much like that. The quote that epitomized this was: 劳心者治人，劳力者治于人, which translates to roughly “the worker of the mind governs, the physical worker is governed.” The whole imperial examination system essentially created an upper class of bookworms for whom any form of hands on labor was beneath. To be a true 君子, gentlemen, you were supposed to study the classics and write poetry and engage in all that Confucian bull shit. I myself don’t have a very high opinion of Confucianism. It’s too conservative for me, with all the emphasis on ritual and filial piety. It discouraged any form of innovation outside the system, outside what was already there, which is partly why China could not make the giant leaps in science that the West did. I’ve read some of the Analects of Confucius and know some of the quotes, and I don’t think Confucius was a deep philosopher at all; there is little actual substance in what he said. On the other hand, Mo Tzu was a much further reaching, more scientific, and surprisingly modern thinker, and had China followed his path instead of banishing his school of thought into obscurity, the world would be completely different now, with China likely having made many more leaps of progress than it had actually done. I’ll say that the West was able to escape the shackles of Christianity, but China could not by itself escape those of Confucianism, until its dire situation, with reached its nadir in 1900, forced it too.

Apparently, the elite college admissions officers aren’t terribly good at filtering out the real Asian grinds either, as I know one who went to Princeton, who I found ridiculous. He said that all he did in college was study, and even though he majored in math, he hardly knew any. Like, he didn’t know what a topological space is. When I went ice skating with him and some others, he was near the edge the whole time, and he characterized my skating backwards (not well at all) as “scary.” I told him I’m not very athletic and wasn’t even any good, unlike the girl he was dating at that time, who could do spins among other fancy “figure skating” things she was trying out. I did show him the video taken of this 360 somersault I did off a 15 feet cliff in Hawaii, into the water, which was the first time I had done anything like that. He was like: “that’s so scary.” I honestly didn’t know what to say. To justify himself, he was like: “Chinese parents only want their kids to study.” I told him that in China, there are some very athletic people who attend special sports schools. On that, he was like: “but those aren’t normal people.” I also remember when we went camping once, everybody else got drunk, so I got to drive that kid’s BMW back. He had told us that his father does business in Beijing, which might explain why he drives that kind of car. He came to US at age 4. His Chinese is absolutely awful though, and he doesn’t realize it. He will of course say: “I already know enough. Some people can’t even speak it.” 怎么说那，不仅是个书呆子，而且是个书都读不好的书呆子，连这样的sb还都被Princeton录取了。I’ve talked with one of my very smart Asian friends about this, and he was like: “but he’s socially normal, unlike us.” And more recently: “Maybe they do accept Asian grinds, just not the ones with bad social skills.”

From what I’ve seen, there are plenty of super conformist Asian grinds like him, but there are also many who aren’t, who are actually smart and interesting, like myself (or at least I hope). I think what he said about Chinese parents is somewhat true actually; after all, I saw many growing up. They do see academics as a way to get ahead more so than others, largely because in China, to get out of your rural village and/or not be stuck with a working class job, you had to do sufficiently well on the gaokao to get into a good major at a good university. It’s funny that I’ve actually seen a ton of ignorant, narrow-minded, and risk-averse uncool tiger Chinese parents. And I have also seen some extremely impressive ones, not just academically. There is again quite a wide range and variety.

There is a phenomenon I’ve witnessed, which is that if a person is extremely strong at X and merely above average at Y, then that person will seem weak at Y, even compared to another person about as good at Y but less lopsided. It seems a natural human cognitive bias to think this way. This is in fact applied rather perversely to Asians in stereotyping. For example, Asian students are perceived as weak at language and humanities because they are generally stronger at STEM. We all know that in fact math IQ and verbal IQ (which we can use crudely as proxies for STEM ability and humanities ability respectively) are highly correlated, which makes it highly unlikely that a STEM star is actually legitimately weak at humanities. He might not be interested in reading novels and such but that’s rather different. There is also that humanities is more cultural exposure loaded with a much higher subjective element to it, with much less of a uniform metric. It actually seems to me based on personal experience that is by no means representative that in terms of precise use of language and the learning of foreign languages, mathematicians and theoretical physicists are at or near the top in terms of ability. On this, I will give an opposing perspective that I identify with somewhat, which is that even if you’re very strong at Y, having an X that you are significantly more talented at is a weakness for Y, because engaging in Y deprives the joy derived from engaging in the X, which often leads to loss of interest over time. Maybe this is why employers shy from hiring people who they deem “overqualified?” On this, I have thought of how possibly the lopsided cognitive profile in East Asians (with what is likely at least 2/3 SD differential between math/visuo-spatial and verbal, normalizing on white European scores) predisposed the thinking of the elite (assuming that lopsidedness is preserved at the far tail) as well as the development of that society at large in certain ways, some of which may have been not the most conducive for, say, the development of theoretical science. This is of course very speculative, and I would actually hypothesize that the far tail cognitive elite among East Asians is more balanced in terms of the math/visuo-spatial and verbal split, given the great extent to which the imperial examination system, which tested almost exclusively literary things, selected for V at the tail instead of for M.

On the aforementioned bias, I’ll give another illustrative example. I once said to this friend of mine, a math PhD student, not Asian, how there’s the impression that people who are weaker academically tend to be better at certain practical things, like starting restaurants and businesses. We sure all know there are plenty who weren’t good at school but were very shrewd and successful at business, at practical things. That guy responded with reference to Berkson’s paradox. He said something like: “That’s because you are unlikely to see those who are bad at both. They tend to be in prison or in the lower classes.” I could only agree.

I’ll conclude with another more dramatic example. I used to, when I knew nothing about the subject, think that people who were really at math were weirdos and socially awkward. For one, there was this kid in my high school who was way better than me at math at the time, who was incredibly autistic. Also, summer after 10th grade, I saw Beautiful Mind, which depicts the mathematician as mentally crazy. Now I would bet the incidence of schizophrenia among the mathematically gifted is lower than it is in the whole population. It just happens that certain combinations of extreme traits are vastly more noticeable or exposed by the media to the public (a mathematician or physicist may think of this as weighing those with such combinations with a delta function, or something along that direction at least). I wasn’t quite aware of that at that time though. Only later, after meeting more math people did I realize that math people are not actually that socially out of it in general, far from it, at least once they’re past a certain age, by which they will have had the chance to interact with more people like them and form their own peer group.

It is my hope that people can be more cognizant of these biases described in this blog post.

## 四海翻腾云水怒，五洲震荡风雷激

The China striding into that spotlight is not guaranteed to win the future. In this fragmenting world, no one government will have the international influence required to continue to set the political and economic rules that govern the global system. But if you had to bet on one country that is best positioned today to extend its influence with partners and rivals alike, you wouldn’t be wise to back the U.S. The smart money would probably be on China.

## On China

I’m talking to that 犹太IMO金牌 again. I first asked him if he knew the Riesz representation theorem, the statement of which I saw today. He said he used to. Then I brought up Shizuo Kakutani, who was quite a genius mathematician, who created some generalization of the aforementioned theorem or something like that. His daughter Michiko is also a distinguished writer. On that I said:

Lol I haven’t gotten to meet many Japanese
They don’t emigrate much nowadays, so patriotic
They’re so well organized and efficient
Produces lots of top mathematicians too

He responded with “china weak.” And “china deserved to get fucked by japan.”

On that, I was like:

Haha
China was super weak back then
Of course, the situation has reversed/is reversing
China is still behind Japan in many advanced areas, but it’s just a matter of time
Japan lost to America in WWII
China on the other hand could defeat America in the Korean War
Thanks to communist ideology

He said that “china did not defeat america.” I responded:

It was a stalemate whatever
But China proved it could get even with number one in the world
When she was still very behind
In any case, in the war in North Korea, America clearly lost, America had to flee
If China had better logistics and equipment probably could’ve taken over the entire Korean peninsula
Because of the Korean War, many of those top Chinese in STEM in America returned
There were negotiations as America knew if they let them return these people would serve their enemy
People contrast that to the brain drain after reforms
The younger generation of Chinese do not have the type of selfless patriotism that the older generation did
Lol you don’t like China
I think America lost its best chance to bring China down, that was during the 89 protests
That was actually kind of close
It’s quite remarkable that China recovered so well. When you’re down, it’s really hard to get back up.
In any case, by 1970s, people in China knew that the most difficult/critical period was past.
And that China had succeeded at it
It’s like earning money, the beginning is the hardest, once you’re rich and high up, it’s almost impossible to fail

He says: “fuck china. china anti human rights.” It’s funny how so many people say that, and I believe privately, or not so much, many in the world have a rather low opinion of China. Though I’m Chinese, I wouldn’t say I really care; it’s just a perception as far as I can tell, not something that can be objectively defined. When I grew up in America, I kept hearing this negative stuff about China and was wondering what was going on. Back a decade ago, China was much less developed than now, and perhaps because of that, the bashing sometimes feels to have subsided quite a bit now compared then, but maybe not, considering that even a guy like him will say that. Whether he genuinely believes it, that is another matter.

On this, I’ll give some of my thoughts. Recall that I said in my chat with him: “when you’re down, it’s really hard to get back up.” This is in general, it applies to individuals as well, with unemployment and such. In the context of the chat, I was referring to the century from 1850 to 1950, when China kept being beaten and made little progress when the rest of the world was advancing rapidly, including China’s foe from the East, Japan. Back then, many intellectuals desperate believed China to be hopeless and on that, even advocated the abolishment of Chinese characters. I believe China was very fortunate to get out of that, as it could have easily been much worse. The international situation, in particular the world’s having been exhausted after WWII destruction, gave China the opportunity to win the civil war, ending a century of violent internal strife that had severely hampered development. The Korean War did much to help Chinese regain their confidence. It proved Chinese military ability for the first time in modern history, much needed at the time, and America blundered by letting China do so. The 1950s was a golden period for China, during which with Soviet aid, China modernized essentially, developing the industrial foundation that even after the Soviet Union withdrew its support for China, though it had a significant negative effect on development, China was able to do okay. In the 60s, the international situation was very unfavorable for China, but by 1970, China was high up enough in terms of capability that America had no choice but to recognize it, seeing that there was no way the old regime in Taiwan could retake the mainland. At that time, China was still extremely poor standard of living wise, but there was already a fair degree of technological sophistication. China was also very lucky not to suffer the demise that the Soviet Union did that is literally impossible to recover from. Why that did not happen, why America did not succeed in 1989 in bringing China down, is a very complex question. The Chinese elite were not as foolish as the Soviet ones. Since then, China has made tremendous progress in terms of developing economics and standard of living and also STEM, and though of course, China is still behind in certain areas, it is only a matter of time as many believe before the gap closes. Throughout the last 60+ years, these “experts” have doubted the PRC, but the PRC keeps proving them wrong. Maybe these “experts” should stop deluding themselves on many matters.

It is interesting how many very intelligent people in the West, including the person I mentioned in this very post, believes some rather peculiar notions on China related matters. It still puzzles me where they’re coming from with all that. They can not like China or see China as a threatening competitor (and I won’t be offended by that, as people are entitled to their own view), but they should still try to be objective, as unpleasant as the facts may be for them to bear. Penalizing someone or downgrading someone’s ability or accomplishment out of an antipathy for that person’s background or political/religious beliefs is the act of a little person, an insecure person. Also, when you discriminate against someone and they still beat you, it’ll only make them more formidable and yourself more insecure.

Last but not least, I’ll reiterate again that Anglo culture is still dominant across the globe, as a legacy of British colonialism as well as subsequent American supremacy. With that said, international discourse will necessarily be biased towards the interests of that group, an obvious fact that apparently still needs to be noted, and a rationalist would apply some correction to account for the bias. On the other hand, Chinese language and culture is still alien to most of the world, and a derivative of that is that there is much vital information accessed little outside of China of much more validity than what the Anglo media chooses to promulgate. I know that there are ones keen on using such means to alter political opinion and whatnot, so as to bring down a regime they don’t like, as was done in Ukraine in 2014, but these are rogue tactics that will eventually reflect badly on its instigators. Plus, time and time again, Chinese have proved not foolish enough to fall for these tricks.

## 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.

## 两首诗

### Чанша

В день осенний, холодный
Я стою над рекой многоводной,
Над текущим на север Сянцзяном.
Вижу горы и рощи в наряде багряном,
Изумрудные воды прозрачной реки,
По которой рыбачьи снуют челноки.
Вижу: сокол взмывает стрелой к небосводу,
Рыба в мелкой воде промелькнула, как тень.
Всё живое стремится сейчас на свободу
В этот ясный, подёрнутый инеем день.
Увидав многоцветный простор пред собою,
Что теряется где-то во мгле,
Задаёшься вопросом: кто правит судьбою
Всех живых на бескрайной земле?
Мне припомнились дни отдалённой весны,
Те друзья, с кем учился я в школе…
Все мы были в то время бодры и сильны
И мечтали о будущей воле.
По-студенчески, с жаром мы споры вели
О вселенной, о судьбах родимой земли
И стихами во время досуга
Вдохновляли на подвиг друг друга.
В откровенных беседах своих молодёжь
Не щадила тогдашних надменных вельмож.
Наши лодки неслись всем ветрам вопреки,
Но в пути задержали нас волны реки…

## 华罗庚

朋友们：

1950年2月归国途中

## 老代中国科学家与诗词

How not woven the fabric of the universe
Spliced with craft
Comes together as one
Wide and broad with unparalleled mystery
Nature loves geometry
Fiber bundles describe four forces
Long unsolved problems
Euclid Gauss Riemann Cartan Chern

## Some speculations on the positive eugenics effects on the far right tail of intelligence of the Chinese population of the imperial examination system

Over the past few months, I had read casually on the imperial examination system (科举) out of curiosity. My knowledge of it, the system that very much defined pre-modern Chinese society, is still very limited and vague, but now I at least know what 进士 and 秀才 are, along with some classical Chinese, background indispensable for understanding that system. I hope, if time permits, to learn more about this over the next year, on the side.

It has occurred to me that the imperial examination system, while doing much to prevent China from developing modern science as the West had for cultural reasons, did select for intelligence at the far tail. The reason is simple. The tests, which were very g-loaded, conferred those who scored highly on them wealth, position, and status that enabled them to have more children, and those from families who scored highly married those from similar families. Over time, there emerged an elite subpopulation with very high base genotypic IQ, one that results in those born from such families to regress not to the overall Chinese mean but to the high mean of that subpopulation. This is consistent with the fact that in the 20th century and probably even today, a disproportionately high percentage of top scholars, scientists, engineers, and even revolutionaries and political leaders of Chinese descent can be traced back to those elite 科举 families, based on the many examples I have seen. I’ll not give specific examples for now; they can easily be found by anyone who reads Chinese.

I will conclude with a note that is likely to be very relevant. Brian Bi, about a year ago, made this following IQ map of China by province.

You can also view it here.

First of all, the data may not be very accurate; I’ll have to check on its source. But for now, let’s assume that it is. Then, what’s most noticeable is the high average of Zhejiang, consistent with the number of mathematical and scientific geniuses of Zhejiangnese ancestry relative to the number of those with ancestry of other provinces, adjusted for province population of course. Examples are numerous: Shiing-Shen ChernWu WenjunFeng KangYitang Zhang, etc for math. There is also, in another field, Qian Xuesen. Too many to name. Brian Bi and I have wondered the cause of this. It is plausible that the aforementioned effect was much more pronounced in Zhejiang than in other provinces in China. Of course, there is a probably substantial environmental effect here too. So I guess to satisfy this curiosity, I might study some Zhejiangnese history as well.

Aside from prominence in science, Zhejiangnese are stereotyped in China for being really entrepreneurial. They are now one of the most prosperous provinces in China, needless to say. They are, to put it simply, a super breed among Chinese, to my superficial view.