Fun with Marissa Mayer

Marissa Mayer is an epitome of all that’s wrong with Silicon Valley, and the world at large, increasingly influenced by it, culturally, in quite an undesirable way. She is an obvious pseudo-nerd (where here, nerd = really smart talented honest technical person) posing as one for marketing, like much of the SillyCon Valley elite. I’m not being “sexist,” for all that James Damore has triggered. There are women who are genuinely technically competent with good character, and Marissa does not seem to belong in that category. I had to be reminded of her again. How?

Well, I talk frequently with this girl who did undergrad (in CS and math) at MIT, who is now at Uber. She’s not that nerdy though.

In a group chat, she was like:
sigh it makes me worried about planning on staying at uber for 4 years
An uber (no-pun intended) nerd guy responds:
it’s ok to stay at one company if your career is actually progressing
if not then you should leave
Her:
i just wanna get promoted and then leave
but it’ll probably take all 4 years
Me (tongue-in-cheek, for those too autistic to detect sarcasm):
Her name why don’t you become the Marissa Mayer of Uber instead
The same uber nerd:
nobody likes Marissa Mayer
Another guy:
i think my name just noticed that they’re both female
with his superior pattern-matching mind
Me:

Uber nerd’s name, if you could, would you do Marissa Mayer

Him:
idk, she’s old
The other guy:
uber nerd’s name needs someone to intellectually stimulate him

Face recognition in China

I recently learned that face recognition, led by unicorns SenseTime and Megvii, has reached the level of accuracy and comprehensiveness that it is percolating into retail and banking, and moreover police are using it to detect suspects, or so various media articles say, like this one. Just Google “face recognition china.” I’m both surprised and impressed. Of course, in hindsight, what they did was mostly collect, aggregate, and organize enough data to train the deep learning models to the level that they can be put to production. The Chinese government has, after all, resident identity cards for all Chinese citizens with photos. I was certainly somewhat envious of the people involved in that in China, and I feel like such a failure compared to them, and that my life has been so boring and uneventful in comparison. Of course, whether I’m suited to do deep learning is another matter. After playing a bit with neural nets, including on the canonical MNIST data set, I sure was disappointed, and I understood immediately why this guy, who is doing a machine learning PhD at Stanford, had said to me that deep learning is very engineering heavy. I wish I had the enthusiasm and motivation for stuff like GPUs. As for that, all I’ve done was play with CUDA in a way so minor almost as if I did absolutely nothing. Again I don’t see myself as terribly suited towards engineering (I’m too much a purist at heart), but I might eventually be compelled to become interested in that, and once I do, I don’t think I’ll do badly. This also makes me wonder what I would’ve ended up like had I stayed in China. I’m sure I would’ve been weird there too, though I would also be more like everyone else. I wonder what I would have ended up majoring in there, and what I would’ve ended up doing afterwards. I’d like to think that I would have gotten a much better education and cultural experience there, though of course, the grass is always greener on the other side of the fence. For instance, in America, Asian quotas means you are judged relative to other Asians, but being in China means that automatically, and China, by virtue of having low resources per capita, is, needless to say, a grossly competitive society with fewer second chances, and thereby even harsher on late bloomers, though surely, the gaokao happens at age 18, whereas in America, grades start necessarily mattering at as early as age 14-5, when many are still very immature. I must acknowledge that as much as I dislike various aspects of the American education system, it is extremely generous, from what I see, relatively speaking, in tolerating failure at a young age. In China, you test into a specific department at a university, and once you’re in, it’s very hard to change, which means some land in majors they end up finding themselves unsuitable for. At age 18, it’s really hard to make such a decision, especially when you don’t really know anything about the actual content of the major, which is usually the case when one is a clueless kid. This is why I say that before you commit officially to an area, always try to learn something about it on your own beforehand to increase confidence that you actually have at least reasonable, and preferably high, talent for it.

On the broader topic of technology in China, it is needless to say that they are still quite a ways behind America and the advanced Western countries. Look at what the ZTE ban has done. China has its own CPUs but not the ecosystem for it. China still buys and deploys much of its most advanced military technology, including jet engines and surface-to-air missiles, an indicator that its indigenous versions of those are still seen as unproven, unreliable, and of lower quality, though surely they’ve made great strides on that the past decade. I stumbled on the video of this military parade held on August 1st, 2017 to mark the 90th anniversary of the Nanchang Uprising that showcased some of the latest developments. I didn’t like it all that much at first, with its overall presentation, the imagery and music in sync, kind of, how should I say it, corny, and I felt the music paled in comparison to the music of the Soviet Red Army, which is very hard to beat, at least based on my taste, though listening to the music again, I grew to like it more. Surely, I would characterize the whole thing as rather sinister, and representative portions of that would be this and this. Musically, the part that left the most memorable impression was this, and to be honest, I found the non-musical aspect of that part both awkward and sinister, especially coupled with the music. I’m sure many people in the West would view this parade as rather weird, or even effeminate, as much as I hate that stereotype of East Asians in America.

Yet in spite of overall and in some cases critical backwardness, China is managing to unveil a face recognition system at a level of sophistication and scale, and also scariness/creepiness that many in America could only dream of. Surely, that was far from my expectation. Who knows. Maybe in a decade, China will have a nationwide genome database. I say this with the awareness that for anything of scale, there is a tremendous advantage to homogeneity and central organization. We already see, in the case of face recognition, China’s using this to compensate for its inferior technology as far as strict quality and capability is concerned.

As far as I can tell, Chinese and Chinese society place a strong emphasis on STEM and the society as a whole is far more scientifically literate than American society, which is advantageous for certain pro-STEM policies and government, though surely, China is still struggling to produce the best people in many areas, for which the corresponding elite subcultures in the West are difficult if not impossible to transmit. It will be very interesting to see what kind of novel stuff comes out of China organically over the next decade or so, especially as China seeks further to create its own distinct ecosystem, as opposed to remaining in many ways still a subsidiary of America and Russia. In any case, I am quite a fan of the political culture of China, and on the contrary, I am rather sick of the one in America.

More on population, eugenics, China

I had the pleasure of learning recently the name of the guy who is said to have proposed the one-child policy in China. His name is Song Jian, and he is a PhD in control theory from Moscow State who later became one of China’s top experts in missile guidance systems, rising up on the state apparatus through that. Well, it only became natural for him to develop a theory of population control that with his prestige and position was eventually put into implementation. In 1950, China’s population was 475 million. By 1975, that had risen to over 900 million, almost doubling in a quarter of a century.

Of course, it’s somewhat of a brutal policy. On this, I’ve seen some very kind and loving Americans who have adopted orphans from China, and most of them are female. Yes, there is due to this a gender imbalance, with necessarily means some men won’t be able to get married and have children, which will cause some social problems. Though it surely has its merits, in that it prevents genuinely dysfunctional people from having too many children. From this we can only expect that my generation of Chinese will have higher average IQ and overall ability than the generation of my parents, many of whom grew up with quite a few siblings.

Again, I am both surprised and pleased to hear that this infamous one-child policy originated from a hard (maybe even autistic, by today’s ridiculous standards 😉 ) scientist as opposed to some politician, though of course, once he became old, he essentially became a politician. By the way, I’m totally in favor of a totalitarian state run by people like him, me, and Hsu. I think with that, the world would become a much better place. I’m also pleased that Hsu, despite being a distant relative of Chiang Kai-shek, wishes the Chinese government could go more in that direction. In DNA Dreams, he was like

You have to remember that BGI is an independent, maverick organization, it’s not part of the Chinese government. People in the West, who we talked to, like even my colleagues at Oregon that I talked to about this project, they say, oh can’t the Chinese government just ORDER all the smart kids to show up, they’ll just order all the smart kids to spit in a tube and you’ll get their saliva, and I said well I wish that were the case.

I remember vividly how once when hanging out with some people, one of whom appeared in that documentary, right after that part was played, another guy cracked up. It’s like, Hsu is not only an IQ and genius obsessed freak, he’s also a pro-Chinese communist!!!!!! Well, not every uber high IQ person I’ve talked to agrees with him. One, a math PhD who knows quantum field theory and general relativity, believes that if Hsu’s vision does pan out, people will be more miserable, and we’ll have more genius misanthropes who end up like Robert Mercer. Another, on my telling him Hsu’s suggestion of the possibility of some regime’s eventually making IQs under 80 and expensive genetic diseases illegal, was like: his ideas scare me. I had also told him about Hsu’s opinion that any smart government would invest just as much in genomic prediction as it would on, say, a particle accelerator. Well, as a derivative of that, Hsu thinks that the Chinese government could get even smarter than it is right now. Oh yes, in DNA Dreams, Hsu also brought up the possibility of producing nice humans, honorable humans, caring humans, which means he’s not exclusively an IQ elitist, and is aware that a large number of people with those aforementioned traits not associated with brains is also beneficial and necessary for the world. Though Hsu can be pretty damn elitist and aggressive, I highly doubt he’s a psychopath with any malicious intent, and he is elitist and aggressive, I believe, in the right way. Not to mention that he’s also just very realistic, like most high IQ people, and at the same time ambitious enough to pursue his dream of using genomic prediction to create a better world. If only there were more people like Hsu in positions of power and influence.

My whole experience with the American school system

I accidentally stuffed my face last night and found myself too uncomfortable from that to do anything productive, to my great disappointment. So I verged onto non-technical topics again, and in particular, I reflected somewhat on my personal experience growing up as a Chinese immigrant kid in America, and I write this with a hope that it might be inspiring to others with a similar background.

I came in first grade not knowing a word of English, but at least I knew the alphabet. As for learning English, it didn’t help that my first grade ESL teacher was a woman parents from Taiwan who was likely born in the US, who spoke Mandarin. I remember she would tell me that my Chinese was more proper than hers, as she really only learned it in college. Well, as you can guess, because I could speak Chinese to her if needed, I didn’t even know English all that well even after a year. I remember there were kids in that class from a variety of places, from Russia to Japan to Colombia. I wasn’t very well behaved, and near the end of the year, when we were watching some Disney movie, she actually put tape on my mouth.

I had forgotten like all my written Chinese by end of third grade, including how to write my Chinese name. But that summer there, I was able to relearn some of that.

My parents didn’t really give me much pressure academically. I would expect that they were very busy themselves. So throughout grade school, much of my life consisted of playing and watching basketball and baseball, and also stuff like Pokémon, and also piano practice, which I initially disliked but grew to like as became somewhat good at it, by a low standard. My teachers could tell that I was smart, especially at math, but I was quite hyperactive and poorly behaved.

No offense, but where I was, most of the kids and parents I encountered were pretty fucking dumb and ignorant. They seemed content with a chill, mediocre life, the bliss of ignorance. The other kids could sort of tell I was smart, but I was also pretty fucking socially weird. In third, fourth, and sixth grade, the teachers invited me to this “games club,” which I later found was designated for kids identified by the teacher to be deficient in social skills.

I wasn’t in any gifted program. I was actually not even able to test into one, because my verbal IQ was apparently way too low. So I felt like I was inferior compared to kids in gifted programs, but by now, I’ve basically far surpassed basically all of them.

My junior high which was 7th to 9th grade absolutely sucked. The teachers were really fucking stupid. The math was bull shit with graphing calculators, and the history class was full of stupid political indoctrination. I got low grades in 9th grade English and history, one because I was super immature and impulsive, and another because that teacher, who was an idiot far-right (American style) scumbag, absolutely hated me. It certainly affected my self-esteem very negatively. I was problematic in a way yes, but I dare say much was because I had far more latent IQ/talent than the other students that nobody had nurtured in me.

High school was better but still pretty shitty. I was in this IB program much of which was an utter waste of time and was really at quite a joke of a level academically. I had already realized that, doing math contests and such. However, even there, because my foundation was so shitty, I did not progress anywhere as efficiently as I could have. On the other hand, most of those kids in the full IB program thought they were doing so well, because they were in it, and getting good grades, not considering that most got As. The truth is of course that most of those kids, the way they were, had no future in anything serious. Another positive thing to happen for me then was that I started reading various stuff online I found interesting, including in Chinese, on my own. The more I learned, the more I realized how much of a joke the American school system is. It is ridden with the worst type of political indoctrination and scant on actual intellectual substance.

Now, most other advanced countries have an education system where students test into high schools based on their ability. There is much more academic preparation provided at the early stages, and more popularization of serious academic contests like the AMCs. There is also a system of vocational education for those who are less academically inclined, which is great, because practical skills should not be underrated. In contrast, American schools are too concerned with the self-esteem of students to tell them that they are basically garbage, academically, and they are falling short in terms of providing alternatives to prepare them for the real world. The result of course is that their self-esteem will become eventually utterly wrecked in college and the real world where people care more about your actual ability and work and don’t really give a damn about how hard you tried. Of course, now college in America has become a joke too, and so overpriced. On that, Charles Murray is completely right that most students in college right now in America would be better served learning some practical vocational skills as opposed to studying bullshit liberal arts.

I was quite socially clueless in high school, and I was not even that aware of the discrimination against Asians in college admissions. My parents were anything but savvy about the college admissions process in America. Expectedly, high school was full of morons padding their resumes with substance-less stuff just for that. I absolutely hated that, and I cared more about actually learning some serious stuff. That includes math, physics, algorithms, Chinese, history (that was not the brainwash taught in class). Okay, I was a joke at basically all of them but far better than almost all my classmates. There were I think three kids in my year who were accepted to Yale but to me they were the stereotypical superficial well-rounded conformist well-socialized types, and one was an athlete. Another was a very superficial whitewashed Asian who even had a non-Asian surname that I later learned was changed officially when he was a kid. Now I know what he was really up to.

College was much better. It was a flagship state school, and I didn’t mix well with most of the kids there, who I again felt were mostly drones and tools, but there were certainly some really sharp ones, and a few who I had genuine chemistry with. I did of course waste some time on general ed courses. On the more positive end, I could in that environment learn more serious math and science, and also engineering. Because I majored in math and computer science though, I would say that there was very little natural science or real engineering. Moreover, I could meet people from all over the place, including graduate students who had attended elite schools for undergrad, and also talk with international students from China there. The latter partially motivated to improve my Chinese further, to the point that reading it online felt basically as natural as reading English. From that, I also learned more about Chinese culture and the Chinese education system. I felt I was finally seriously shedding away the tremendous damage the American education system had imparted on me, the more socially acceptable it became to detach from that crowd. Though it was much better than high school, I was still not terribly content with the curriculum or the people around me. I felt I was learning too little actual math and especially science, as virtually zero of the latter was required for computer science majors. The computer science majors thought they were really good because they were in this supposedly very competitive program, bound to get six figure jobs in industry, and they were fine at programming, but really, their level of IQ, on average, was quite low. They absolutely sucked at math and had no concept of how to prove anything. There were of course exceptions who mostly kept to themselves. Like this kid who wrote his own compiler for a subset of Java in Haskell early sophomore year, which he taught himself. At programming, I was pretty garbage, lacking the engineering sense at that time, but I was not bad at algorithms, given my math ability. Overall, I am rather disappointed with my college experience. Because my starting point was so low, and because many of the students were dull but studious and conforming enough (to get better grades than I did), I became easily content and cocky at times, and also frustrated. I can blame both my lack of ability and maturity and also lack of fit of the whole educational experience to a guy like me. I sort of kept some distance from most of the other students. Again, many were tools, who I had little desire to be around. Of course, they will excel in the typical tech job, but that’s another matter. In fact, they may well have life much more easy than I do.

Summer after junior year was a major turning point for me. Through a superconnector of high achieving students many if not most at elite places like MIT and Harvard, I met and began chatting online with a few people at Caltech, MIT, and the likes. I expected them to be brilliant or at least solid academically but reality was disappointing, though almost certainly, they were below average ones at those places. However, there was one guy from a top Canadian school and another from a more mediocre state school who were both freakishly smart and competent. I looked up to both of them greatly. I was inspired by a few of them to enter competitive programming, with one of them’s being an IOI medalist, and with some practice on TopCoder, I managed to lead a team the following year to place in the top 10 in ACM regionals.

Something else that happened was that I sort of discovered Marxist literature online, partially inspired by my genius Russian friend, who was also quite a misfit, very defiant of the whole American cultural and political value system. Ironically, he’s actually doing his PhD now at a place famous for American blue-bloods, and he does not express a high opinion in general of the undergrads there, many who are not actually talented but are from well-off families who know how to game the whole system. Given my heritage, Marxist literature necessarily means learning more about the whole culture and tradition created by the Chinese communists, which I found quite fascinating and inspiring. Of course, I also learned some Russian stuff. As I did, I felt ever more indignant with respect to all the historical and political lies promulgated and normalized in American society by the media, lauded as a free one, but in reality, controlled largely by what one can crudely characterize as destroyers of civilization. In the process, I fell in love with Soviet music, which is of much higher artistic quality and substance than the trash kids listen to nowadays. It even idealistically inspired me to fight for a better world. Of course, now I know how hard that is, but I am not giving up just yet.

In college, there was of course pressure to conform, to act in a socially acceptable way, to not be too strange. That means not being openly elitist and critical the way I am right now. That also means not acting in a way that is too un-American. I’m a guy who came here in first grade, not an international student from China. In some sense, it’s not right for me to not be like all those ABCs. It kind of sucks to grow up as an Asian immigrant kid in America. It sucks even more if you’re actually nerdy/smart and culturally/politically sane, like I am. You feel like there is something wrong with you, but of course, now I am confident that that is not true, and that it is in fact American society/culture that is becoming ever more fucked up. Michael O Church can attest to this.

Now, after college. I got to meet some way more interesting, smart people, learn way more interesting things. I could fully distance myself from the uninspiring people I went to school with. This includes people from all over the world, across all age groups, with much deeper and more varied expertise. That includes IMO and IOI medalists, top finishers on the Putnam contest, people in top or good grad schools, some of whom are really impressive, and some of whom are nowhere near the level that they may look on paper superficially. My cultural, historical, political, and linguistic knowledge went up quite another level. Of course, I also saw more first hand from working how the world actually works, which really only parents will tell you. On this, Michael O Church loves to say how it’s the moderately privileged kids whose parents are in mostly meritocratic places like medicine and academia who can be sheltered enough to be naive. In contrast, underprivileged kids need to be street smart just to survive, while genuinely privileged kids know how rigged the system is and how to game it. I felt so much more free because I finally found more like-minded people with whom I could talk openly without fear of how I might be perceived. I was able to in the process re-mould myself into the organic me as opposed to the me under the yoke of a specific educational system.

Finally, I shall speak specifically on growing up Asian in the American education system. Overall, it’s a pretty shitty cultural experience. They’re not really American, no matter how hard they try, yet they lose the ability to be a genuine Asian. Fortunately, I shielded myself from that largely on my own initiative. It wasn’t always easy, but in the long run, that was quite a wise choice, and I encourage more people with same background as me to do the same. Learn from the good aspects of America, not from the toxic ones. Do this with any culture, any system. Also, exposure to genuine Chinese culture can shield you from the pseudo one presented by the American media that has done so much to confuse the thinking and damage the self-esteem of people like me, but not like me.

Reflecting on my experience, I really wished that I could have gotten a much better education. American education really is pretty shitty, especially for actually smart people, if you’re not very well situated in terms of schools and parents. Of course, later on, it gets much better.

I’ll conclude by going on a tangent. That is, my *anti-Semitism* that kicked off recently. What started it? And I also ask myself: am I simply taking out bitterness with my own educational and cultural experience, and also my own failures, on another group, instead of taking responsibility for them myself? Yes and no. Anyhow, I consider it not anti-Semitic, more like realistic, and in fact, I have interacted substantially with and highly regard many from that group. It is without doubt a remarkably high achieving group, often spectacularly so. This math PhD also well-versed in physics I talk to was also saying to me recently how Jewish accomplishment in mathematics and physics is absolutely overwhelming, which is indisputable. Of course, there’s also a darker side. I think I might have been inspired by this really smart guy who is a white Gentile (later atheist) American who doesn’t actually think I’m insane, or at least I hope not. Because once he was like:

You know what you should do? Become one of those food workers where rich Jews eat. Nobody cares about those people.

I actually told this to someone else, who was like: “that’s because they run things. If you ran things, you’d be the same.” When I told that guy about that, he was like:

counterpoint: other people have run things
some corruption is expected
Even the worst of the colonialist era was tempered
a lot of people were actually trying to do good
civilize the savages, that whole thing
that’s not saying there weren’t atrocities
because there were

And I was like, wow

So you’re saying the Jews now are worse
Than whites during the whole age of white/European imperialism/colonialism.
How much do whites regret letting Jews seize the positions of power

Him:

yes
norms have become nicer
so they can’t pull the old school shit
and more importantly
you’re not going to see the megadeaths from plague

Me:

So your argument is roughly that the calibration has to be much different now relative to the colonialist era, and Jews, by the current calibration, are pretty shitty.
About as shitty as the Belgians were in the Congo eh?

Him:

the belgians self-corrected
I mean, after killing a whole bunch of people
somebody said it was pretty fucked up
and the whole thing kinda fell apart
if we didn’t live in a post-colonial culture
they’d genuinely believe
that goyim are as cattle
and that they should do whatever it takes to ensure their rule persists
also the jews don’t want to exterminate
they need goyim to rule over
a world run by whites is one where half want to conquer and half want to help
a world run by chinese or japanese is one where they’d be rich and on top but mostly leave other people alone
other than getting money from them
a world run by jews is one where they’d systematically extinguish any hope of ending it
ITT anyone smart who’s not a jew would be a threat

Me (critically):

But plenty of smart Asians/whites have had Jewish advisors who strongly supported them
Recognized and cultivated their talent

Him:

this is a world with Jews who can openly be in power
not slink about in the shadows

Me:

That’s kind of theoretically impossible because Jews are too few
See because of that, they can only engage in deception
They’re evolved for that

Him:

look at Israel
they might be “evolved for deception” as you say
but that’s not stopping them from carrying out an effective, slow-motion genocide
which alone is scary
because sure, you can have one Hitler
you can have one Stalin
but you have multiple generations of Jews who are determined to exterminate the palestinians
you can’t have that kind of value alignment with white ppl

Me:

Do it slowly so that people don’t react to it as much, until it’s too late.
It’s like starving a person to death instead of blowing his brains out.
That’s what the Jews are doing to the Palestinians, it’s obvious

Him:

you should be scared because it suggest they’d do it to you too

Me:

Yeah they just don’t have the power to
I mean isn’t cultural assimilation also a form of more benign genocide of a culture
Didn’t whites also slow kill the Native Americans?
And got away with it 100%.
There’s also the saying that abused people are more likely to become abusers.
Doesn’t that sort of apply to the Jews too?

Him:

given the choice between future people who share my genes but an alien culture and future people who share my culture but alien genes I’m 100% for the former 0% for the latter
kicked out of 109 countries?

Me:

They regard that as abuse.
Anti-Semitism.
They may even feel nobody likes us because we’re too good.

Him:

I’m sure they tell themselves something like that

“boo hoo everyone’s evil and oppressive except for us”

What can I say? A smart white who sounds way more *anti-Semitic* than I am. Should I recalibrate according to him? Are Asians simply not aggressive enough? Is that why they are picked on so much by the media in America and not allowed in upper management in corporate America? I think he may be a bit overboard, but I might be wrong on that one. Or maybe he is exaggerating. Who knows. Anyhow, I find it somewhat flattering that he says he’d rather live in a world ruled by Asians than one ruled by Jews, because: less evil. So, considering his opinion, in combination with how shitty the American education system is, outlined above, maybe the group that I am part of really should try to take a more active role in world affairs and set a new standard and example. Lately, that has already been happening, very noticeably, and only time will tell how it pans out. Maybe I can be part of it too, who knows?

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.

Naturally, from that I learned about Shing-Tung Yau. I probably read that Manifold Destiny article by Sylvia Nasar and David Gruber that Yau was furious with, in response to which he hired a lawyer and had a PR site created for him to counter the libel (as perceived by him). That was pretty entertaining to read about.

The more I learned about math, about mathematicians, about how the world works, about the Chinese math establishment, and about Chinese language (which I’m pretty fluent with by now), the more accurately and deeply I could understand and thus appreciate all this. In particular, now that I know a little about Riemann surfaces, I feel closer to that rarefied world. I also read a fair bit in Chinese about that feud between Yau and Tian, which was also quite entertaining. If some of that stuff is actually true, then academia, even in its supposedly purest, hardest, and more meritocratic subject, is kind of fucked up.

Yesterday, I had the pleasure of talking with a Harvard math undergrad who is also an IMO gold medalist. And we both mentioned Yau. 😉

What can I say about all the politics and fight for credit over whole Poincaré conjecture? Surely, it was kind of nasty. It’s fair to say that Yau was pissed (or at least disappointed) that his school (of Chinese mathematicians) lost to this lone Russian Jew. Maybe in some years time, I’ll be able to judge for myself, but for now, it seems like Perelman’s proof was correct from the start and that what Cao and Zhu, along with the other two teams of two did were merely verification and exposition of Perelman’s result. Of course, attributing a proof entirely to an individual is somewhat misleading, because anyone who knows how math works knows that any proof of a big theorem employs sophisticated machinery and theory developed by predecessors. I’ve studied enough math now to recognize to some degree the actual substance, that is, what is genuinely original, versus what is merely derivative. In the case of Perelman, they say he was using the Ricci flow developed by Hamilton. I’ve encountered many times that in learning, it is much harder to learn about a topic I have little exposure to vastly different from anything I’ve seen before than to learn what is structurally similar (albeit different in its presentation and perhaps also level of generality) to something I had thought about deeply myself already, or at least seen.

Aside from the Poincaré, the focus of that New Yorker article, the authors of it also made it seem as if Lian, Liu, and Yau stole Givental’s proof of mirror symmetry as well about a decade earlier. After all, Givental published first. I suspected that might have been the case. The narrative even made it seem somewhat like Givental was this super genius whose arguments were somewhat beyond the comprehension of Lian, Liu, and Yau, who struggled to replicate his work. Maybe because I still see, or at least saw, Jews as deeper and more original than Chinese are. Again, I still know too little, but it does seem like Jews have contributed much more to math at the high end even in recent years, say, the past three decades.

Well, I found a writing on that doctoryau website by Bong Lian and Kefeng Liu documenting the flaws and deficiencies in Givental’s paper. It looked pretty thorough and detailed, with many objections. The most memorable one was

p18: Proposition 7.1. There was just one sentence in the proof. “It can be obtained by a straightforward calculation quite analogous to that in ‘[2]’.” Here ‘[2]’ was a 228-page long paper of Dubrovin.

And I checked that that was indeed true in Givental’s paper. This certainly discredited Givental much in my eyes. It’s like: how the fuck do you prove a proposition by saying it’s a straightforward calculation analogous to one in… a 228-page paper!!!!!!!!

Not just that. There is also

p27: Proposition 9.6. In the middle of its proof, a sentence read “It is a half of the geometrical argument mentioned above.” It’s not clear what this was referring to (above where? which half?)

and

p30: Proposition 9.9. This was about certain uniqueness property of the recursion relations. The proof was half a sentence “Now it is easy to check” But, again since we couldn’t check, it’s hard to tell if it was easy or not

So basically at least three times Givental proves with “it’s trivial,” once based on analogy with a 228-page paper.

There are far from all. There are many more instances of Givental’s arguing what Lian-Liu-Yau could not follow, according to that document, the list in which is also, according to its authors, who advise strongly the reader to “examine Givental’s paper make an informed judgment for himself”, “not meant to be exhaustive.” So they’ve listed 11 gaps in that paper, one of which is glaringly obvious of a rather ridiculous nature even to one who knows not the slightest about mathematics! And they suggest there is more that, to my guess, may be much more minor that they omitted in that document so as to avoid dilution.

I’ve noticed it’s often the Chinese scientists who have a bad reputation for plagiarism, made more believable by the dearth of first-rate science out of Chinese scientists in China, though that seems to be changing lately. On the latter, many Chinese are quite embarrassed about their not having won a homegrown Nobel Prize (until Tu Youyou in 2015 for what seemed to be more of a trial-and-error, as opposed to creative, discovery) or Fields Medal. On the other hand, I’ve also heard some suspicions that it’s the Jews who are nepotistic with regard to tenure decisions and prize lobbying in science, and what Givental did in that paper surely does not reflect well. I used to think that math and theoretical physics, unlike the easier and more collaborative fields in STEM (with many working in a lab or on an engineering project), revere almost exclusively individual genius and brilliance, but it turns out that to succeed nowadays typically involves recommendations from some super famous person, at Connes attests to here (on page 32), not surprising once one considers the sheer scarcity of positions. Now I can better understand why Grothendieck was so turned off by the mathematical community, where according to him, the ethics have “declined to the point that outright theft among colleagues (especially at the expenses of those who are in no position to defend themselves) has nearly become a general rule.” More reason why I still hesitate to go all out on a career in mathematics. It can get pretty nasty for a career with low pay and probability of job security, and I could with my talents make much more impact elsewhere. One could even say that unequivocally, one who can drastically increase the number of quality math research positions (not ridden with too many hours of consuming duties not related to the research) would do more to progress mathematics than any individual genius.

I’ll conclude with some thoughts of mine on this Olympiad math that I’ve lost interest in that many mathematicians express low opinion of, though it clearly has value as a method of talent encouragement and selection at the early stage, with many Fields Medalists having been IMO medalists, usually gold. I recall Yau had criticized the system of Olympiad math in China, where making its version of MOSP gives one a free ticket to Beida and Qinghua, as a consequence of which many parents force or at least pressure their kids into Olympiad math prep courses as early as elementary school. Even there, several of the IMO gold medalists have become distinguished mathematicians. I have in mind Zhiwei Yun, Xinyi Yuan, and Xuhua He, all speakers at this year’s ICM. So the predictive power of IMO holds for the Chinese just as well as for the non-Chinese. I personally believe that Olympiad math is beneficial for technical training, though surely, the actual mathematical content in it is not that inspiring or even ugly to one who knows some real math, though for many gifted high schoolers, it’s probably the most exciting stuff they’ve seen. I do think though that one seriously interested in mathematics would have nothing to lose from ignoring that stuff if one goes about the actual math the right way.

It’s kind of funny. A few days ago when I brought up on a chat group full of MOSP/IMO alumni that now, almost half of the top 100 on the Putnam (HM and higher) are Chinese, one math PhD quite critical of math contests was like: “ST Yau would weep.” Well, I don’t think ST Yau actually regards Olympiad math as a bad thing (half tongue-in-cheek, I even remarked on that chat that doing math contests (as a high schooler) is much better than doing drugs). Many of the Olympiad/Putnam high scorers do quite well, and in some cases spectacularly so, in math research. One point I shall make about them is that they are, unlike research, a 100% fair contest. Moreover, the Putnam, which I placed a modest top 500 on, solving three problems, has problems which do not require specialized technical training as do the inequalities and synthetic geometry problems in Olympiad math that have elegant solutions. On that, I have wondered based on their current dominance of those contests: could it be that at the far tail, the Chinese (who did not actually create the scientific tradition themselves) are actually smarter than the others, including the Jews? Could it be that the Chinese are actually somewhat disadvantaged job placement and recognition wise in math academia out of a relative lack of connections and also cultural bias? What I saw in that sound and unobjectionable rebuttal of Givental’s paper, in contrast to what was presented in the media, only makes this hypothesis more plausible. I am not denying that Givental did not make a critical contribution to the proof of mirror symmetry. That he did, along with some other predecessors, seems to be well acknowledged in the series of papers by Lian-Liu-Yau later that actually gave the first rigorous, complete proof of mirror symmetry. Idea wise, I read that Lian-Liu-Yau did something significant with so called Euler data, and though not qualified to judge myself, I have every reason to believe that to be the case for now.

Cauchy’s integral formula in complex analysis

I took a graduate course in complex analysis a while ago as an undergraduate. However, I did not actually understand it well at all, to which is a testament that much of the knowledge vanished very quickly. It pleases me though now following some intellectual maturation, after relearning certain theorems, they seem to stick more permanently, with the main ideas behind the proof more easily understandably clear than mind-disorienting, the latter of which was experienced by me too much in my early days. Shall I say it that before I must have been on drugs of something, because the way about which I approached certain things was frankly quite weird, and in retrospect, I was in many ways an animal-like creature trapped within the confines of an addled consciousness oblivious and uninhibited. Almost certainly never again will I experience anything like that. Now, I can only mentally rationalize the conscious experience of a mentally inferior creature but such cannot be experienced for real. It is almost like how an evangelical cannot imagine what it is like not to believe in God, and even goes as far as to contempt the pagan. Exaltation, exhilaration was concomitant with the leap of consciousness till it not long after established its normalcy.

Now, the last of non-mathematical writing in this post will be on the following excerpt from Grothendieck’s Récoltes et Semailles:

In those critical years I learned how to be alone. [But even] this formulation doesn’t really capture my meaning. I didn’t, in any literal sense learn to be alone, for the simple reason that this knowledge had never been unlearned during my childhood. It is a basic capacity in all of us from the day of our birth. However these three years of work in isolation [1945–1948], when I was thrown onto my own resources, following guidelines which I myself had spontaneously invented, instilled in me a strong degree of confidence, unassuming yet enduring, in my ability to do mathematics, which owes nothing to any consensus or to the fashions which pass as law….By this I mean to say: to reach out in my own way to the things I wished to learn, rather than relying on the notions of the consensus, overt or tacit, coming from a more or less extended clan of which I found myself a member, or which for any other reason laid claim to be taken as an authority. This silent consensus had informed me, both at the lycée and at the university, that one shouldn’t bother worrying about what was really meant when using a term like “volume,” which was “obviously self-evident,” “generally known,” “unproblematic,” etc….It is in this gesture of “going beyond,” to be something in oneself rather than the pawn of a consensus, the refusal to stay within a rigid circle that others have drawn around one—it is in this solitary act that one finds true creativity. All others things follow as a matter of course.

Since then I’ve had the chance, in the world of mathematics that bid me welcome, to meet quite a number of people, both among my “elders” and among young people in my general age group, who were much more brilliant, much more “gifted” than I was. I admired the facility with which they picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle—while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things that I had to learn (so I was assured), things I felt incapable of understanding the essentials or following through to the end. Indeed, there was little about me that identified the kind of bright student who wins at prestigious competitions or assimilates, almost by sleight of hand, the most forbidding subjects.

In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of thirty or thirty-five years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birthright, as it was mine: the capacity to be alone.

Grothendieck was first known to me the dimwit in a later stage of high school. At that time, I was still culturally under the idiotic and shallow social constraints of an American high school, though already visibly different, unable to detach too much from it both intellectually and psychologically. There is quite an element of what I now in recollection with benefit of hindsight can characterize as a harbinger of unusual aesthetic discernment, one exercised and already vaguely sensed back then though lacking in reinforcement in social support and confidence, and most of all, in ability. For at that time, I was still much of a species in mental bondage, more often than not driven by awe as opposed to reason. In particular, I awed and despaired at many a contemporary of very fine range of myself who on the surface appeared to me so much more endowed and quick to grasp and compute, in an environment where judgment of an individual’s capability is dominated so much more so by scores and metrics, as opposed to substance, not that I had any of the latter either.

Vaguely, I recall seeing the above passage once in high school articulated with so much of verbal richness of a height that would have overwhelmed and intimidated me at the time. It could not be understood by me how Grothendieck, this guy considered by many as greatest mathematician of the 20th century, could have actually felt dumb. Though I felt very dumb myself, I never fully lost confidence, sensing a spirit in me that saw quite differently from others, that was far less inclined to lose himself in “those invisible and despotic circles” than most around me. Now, for the first time, I can at least subjectively feel identification with Grothendieck, and perhaps I am still misinterpreting his message to some extent, though I surely feel far less at sea with respect to that now than before.

Later I had the fortune to know personally one who gave a name to this implicit phenomenon, aesthetic discernment. It has been met with ridicule as self-congratulatory artificialized by one of lesser formal achievement, a concoction of a failure in self-denial. Yet on the other hand, I have witnessed that most people are too carried away in today’s excessively artificially institutionally credentialist society that they lose sight of what is fundamentally meaningful, and sadly, those unperturbed by this ill are few and fewer. Finally, I have reflected on the question of what good is knowledge if too few can rightly perceive it. Science is always there and much of it of value remains unknown to any who has inhabited this planet, and I will conclude at that.

So, one of the theorems in that class was of course Cauchy’s integral formula, one of the most central tools in complex analysis. Formally,

Let D be a bounded domain with piecewise smooth boundary. If f(z) is analytic on D, and f(z) extends smoothly to the boundary of D, then

f(z) = \frac{1}{2\pi i}\int_{\partial D} \frac{f(w)}{w-z}dw,\qquad z \in D. \ \ \ \ (1)

This theorem was actually somewhat elusive to me. I would learn it, find it deceptively obvious, and then forget it eventually, having to repeat this cycle. I now ask how one would conceive of this theorem. On that, we first observe that by continuity, we can show that the average on a circle will go to its value at the center as the radius goes to zero. With dw = i\epsilon e^{i\theta}d\theta, we can with the w - z in the denominator, vanish out any factor of f(z + \epsilon e^{i\theta}) in the integrand. From this, we have the result if D sufficiently small circle. Even with this, there is implicit Cauchy’s integral theorem, the one which states that integral of holomorphic function inside on closed curve is zero. Speaking of which, we can extend to any bounded domain with piecewise smooth boundary along the same principle.

Cauchy’s integral formula is powerful when the integrand is bounded. We have already seen this in Montel’s theorem. In another even simpler case, in Riemann’s theorem on removable singularities, we can with our upper bound on the integrand M, establish with M / r^n establish that for n < 0, the coefficient in the Laurent series about the point is a_n = 0.

This integral formula extends to all derivatives by differentiating. Inductively, with uniform convergence of the integrand, one can show that

f^{(m)}(z) = \frac{m!}{2\pi i}\int_{\partial D} \frac{f(w)}{(w-z)^{m+1}}dw, \qquad z \in D, m \geq 0.

An application of this for a bounded entire function would be to contour integrate along an arbitrarily large circle to derive an n!M / R^n upper bound (which goes to 0 as R \to \infty) on the derivatives. This gives us Liouville’s theorem, which states that bounded entire functions are constant, by Taylor series.

 

Why mathematics

I had the pleasure of chatting briefly with a math PhD student, with the conversation largely centered on what kind of math are you interested in. He is doing discrete probability and combinatorics, something along the lines of that. He said that he spent a year studying commutative algebra during undergraduate, but eventually decided that he would not do math that deep and instead is concentrating on an area with less requirement in terms of acquired knowledge and more low-hanging fruit to pick, the parts of math of a more problem solving nature. He went on to say that of the math undergraduates at his top (but not Beida or Qinghua) institution in China, by junior year, only five were studying the purist of pure math, and later during graduate school, all but one of them, who is now doing research in string theory, have given up, instead choosing not pure PDEs but PDEs for biology and the likes, to illustrate the low rate of success for pure pure math. I told him that I still want to do really deep math (of which we can use algebraic geometry) and see the parts of math not requiring deep knowledge as not as meaningful to do research in (of course, I don’t expect to succeed, realistically gauging that I am, while highly talented, not a genius). On that, he more or less said that you should try and that you never know unless you try. Of course, he did more constructively say that learning commutative algebra requires knowing deeply thousands of definitions, and just going through ten of them a day is already very good. Maybe attempting this is not terribly wise when I see people objectively smarter than I am who eventually chose easier fields, like theoretical statistics.

Now this brings me to reflect on why I am doing pure mathematics? Why am I devoting so much time and energy (with overall enjoyment and satisfaction at this point still pretty high) on this arcane, useless subject? How much of it is out of an ego to prove how smart I am versus the intrinsic thirst for the knowledge? Of course, the two are somewhat intertwined, as you’ll see in what I’m about to say.

As for my background, I studied some CS in college and also spent some years in the software industry, which I’ve grown very distasteful of. I don’t like CS people very much in general. They make a big deal out of low-hanging fruit. Like, MapReduce is trivial theoretically; it’s more about the engineering, in particular the locality to minimize network IO, which in distributed systems is usually the bottleneck. There is nothing deep about it. Algorithms is cool, and I enjoyed them, doing okay in some coding contests, solving say plenty of TopCoder 500s (but not quickly enough during the short 75 minute time frame of the contest). However, algorithms I view as more of a game, full of clever little tricks but of little substance, recreational math at best, at least the type of algorithms I did. Engineering wise, I see the value, but I don’t see myself as naturally inclined to it at all, and in fact, among the strong folks in that, I’m probably rather weak. I don’t think those people are terribly smart from an IQ point of view. They’re not as cultured in some sense. (That top MIT math major (though he works in combinatorics heh) says the same, that science is for high math high verbal people with refined intellectual tastes while engineering is for high math (note that this often does not even hold for software engineering) lower verbal folks of a dronish nature.) In any case, I don’t think I’m in the same species as all these people in software engineering who know absolutely nothing about continuous math, the type of math you see in physics, like I think that’s just bad, or at least different, taste, or simply lower IQ enough that they cannot even understand it. I thought at one point that I might want to do CS theory. Not anymore. I think that’s a cool field with many good problems, but again, much of it lacks depth and importance, often with little connection to the mainstream of mathematics.

I see mathematics as in some sense the pinnacle of human civilization and of human intelligence. I’ve probably said before that humans discovered literature, music, crafts,  and engineering (non-modern) long long time ago, but mathematics took so long, which just goes to show how unnatural it is for the human brain. It is a pursuit of truth in the rigorous and absolute sense that one sees not in natural science either, though of course, the deductive method that underlies math is thoroughly used in natural science. Moreover the structures investigated in mathematics are of such a fundamental and pure nature which often appear in reality, though of course the purists, with the Greeks as the pioneers of that, view mathematics as a Platonic ideal to be investigated for its own sake independent of reality. What the Greeks did I would say is rather unnatural, because I recall early on, it did not feel so natural for me to disentangle mathematics with the reality, having seen it more as a tool for reality.

Mathematics is so full of substance, unlike almost all other subjects. It emphasizes high quality, with often deep, fundamental ideas explained in a few pages, in austere, terse language. It is a scientific study that tolerates absolutely no bullshit and aims for the simplest possible explanation of pure, strictly incontrovertible truth by logic. It is an escapism from the mediocrity and nonsense we see in much of the world and most humans too intellectually dazed for the clear thinking necessary to perceive mathematical truth.

I see my ever greater interest and appreciation, and of course, ability and knowledge, for mathematics as an inevitable consequence of my neurobiological maturation, which is fortunately to an extent far enough that I am able to experience as much of this world of truth invisible to most humans around me, though of course, I can only admire those true geniuses, those far superior brains, who can fathom so much deeper and more rapidly than I can. On this, I shall say that mathematics may well be what separates homo sapiens from whatever species eventually evolves beyond it. I would bet that in another millennia, we will have people for whom mathematics is as natural a language as natural language is to humans. Just as humans have evolved their brain and also their anatomy of throat and mouth such that learning (non-formally) and articulating language is instinctive, humans may evolve their brains further such that that holds for mathematics as well.

Over time, I’ve come to realize more so that mathematics is about the right mental perception. Ideally, one can see the mathematics in one’s head. Text is but a medium of transmission (with reading the fastest bandwidth in terms of information transmission to the human brain), but without a well-formed brain rational and composed, there is basically nothing one can do to genuinely absorb the truth that exists independent of one’s perception of it. It is often that one intuitively feels like one can understand certain mathematics one hears or reads, but looking more closely, one finds such is not the case, being unable to visualize it with enough clarity that one can independently explain it.

My learning of mathematics has been far from entirely smooth. I have despaired much about simply not being smart enough, especially upon seeing another seemingly effortlessly master what was utterly perplexing for me. Fortunately, that all improved over time. Though of course, as the Dunning-Kruger effect would say, the better you become the more can see your incompetence and your limitations. The experience of being able to experience the life of mind with ever more clarity, fine grain of control, and awareness has been an internally exhilarating experience.

Mathematicians are in some spiritual aristocrats, and mathematics arguably has more of an intellectual upper class air to it than any other subject. What is aristocracy? It is to many a relation by blood to those politically important or foundational. But is political power really the pinnacle of human experience? I say no, and I would say that it is the experience of the deepest scientific truths, one which requires both biological genius as well as the substantial cultural exposure that naturally comes with it, especially in today’s day and age of universal access to information. Human experience in any case hinges on consciousness, and one’s subjective conscious experience is always the product of neurons. Thus, mathematics has to it an aristocracy that no amount of money or political title or physical appearance or dress can buy; there is no royal road to mathematics, as Euclid said. So in some sense, mathematics is the greatest gift of God to a human he conceived on earth.

What are other characteristics of non-trivial engagers of mathematics that one easily associates with aristocracy? First comes to mind language and literacy. In virtually every culture, literacy was in the old days a sign of class, of privilege. In the West, it was the Catholic priests and in the East, it was the Confucian scholars. In virtually every religion or ideology or culture, the masters of that culture through literacy were highly esteemed. For example, in Jewish culture, there were the rabbis. Those with the most mastery of language where often the ones of authority, much owing to their exclusive access of certain information that facilitates political and mind control of plebs. From this, emerged learned aristocracies which developed their distinctive elite cultures, along with to some degree a distinctively evolved genetic line. These aristocrats evolved an ability to parse and memorize text far greater than the masses who had to labor in the fields. They developed and evolved a certain form of refinement and manners and self-control, as well as physical appearance, that came to be characterized as one of an aristocratic nature.

With this said, in the West, during the Renaissance and the subsequent scientific revolution, the men of science were often ones from a learned religious background of deep conviction in their religious faith who were intellectually courageous enough to go beyond it, to go about to discover scientific truth often with inspiration from the God they held deep in their hearts. They conceived of a much more rational and accurate world that turned out had been there all along without their knowing. All this eventually ushered in a new age of human history of exponential human discovery, of fundamental scientific truths, of unseen lands, of modern machines, that has culminated in the globalization we have today. All of this has much of its roots in mathematics.

To say all this would imply my yearning to become an aristocrat, which brings to another point, namely, that mathematics, while aristocratic, is more or less coldly meritocratic, and thus is aristocratic mostly in its intellectually noble content. For a brilliant kid from a poor background, mathematics is the most straightforward means of social mobility. Mathematics does not require expensive equipment or facilities or elite social connections. Provided a sufficiently high caliber mind, excelling in mathematics is relatively natural, since one can read on one’s own and solve mathematical problems on one’s own, starting with olympiad style problems at the secondary school level. Though we see plenty of mathematical families, mathematics is not grossly nepotistic as is say acting or offices of political power. In its purist essence, the culture of mathematics reveres genius from wherever he hails and despises any form of ascension based on social connections.

I have observed in those of high mathematical talent a propensity for what I would regard as refined taste in other areas as well, in music, in literature, in politics, and in aesthetics of human beauty as well. Speaking of which, math is widely considered as having the smartest people and being the most g-loaded subject (along with its nearest neighbor theoretical physics), because there is some evidential truth to that, that it is often the mathematicians who are the most versatile. Mathematicians are well known (at least to me) for their often extraordinary foreign language ability, along with what is not infrequently talent in engineering and music as well. So there really is much to suggest towards the bold hypothesis that the man of mathematics is the most ideal of man evolved on earth.

To conclude, I will note that I sincerely empathize with those who have had genuine struggles with mathematics or more extremely, who hate it, let alone appreciate it. By no means should one consider oneself as lesser if one is not good at mathematics as tempting as it may be. Though it is an intellectual pursuit achievements of which lie in the pinnacle of human civilization, there is almost no direct use in it, and the world does not need many mathematicians. In fact, there is, economically based on the very dismal job situation, quite a glut of mathematicians now, which makes it prudent for one to be discouraged from pursuing it as a career if one has not displayed extraordinary gift in the subject. Doing mathematics helps no one directly, but doing engineering or carpentry or nursing surely does, and as someone who has indulged so much in mathematics, I do feel guilty at times from my lack of contribution to the real world. Again, this is why I say that to go into mathematics, one ought to have a really good reason, part of why I have been inspired to write this post.

My awesome roommate

I recently met this cool guy because we live in the same place. Though he’s not that nerdy (by that, I mean super mathy), we still share many common interests. For instance, he expressed interest when I told him a bit about 艾思奇(Ai Siqi). Additionally, he told me about his appreciation for André Weil and Simone Weil, particularly her mysticism, which I found quite pleasing as I was reading about them not long ago. He also told me about this guy who is trying to understand Mochizuki’s “proof” of the abc conjecture despite being not long out of undergrad, who has plenty of other quirks and eccentric behaviors. Like, that guy joined some Marxist collective, and goes on drunken rants at 3 am, and is in general “aspie af,” something that he described me as too when messaging that guy himself. There is also: “he would literally kill himself if he had to do a tech job.” (laughter) That guy’s dad happens to be a (tenured) math professor from mainland China, more evidence that madness runs in families.

The guy that is the topic of this post himself did up to high school, as far as I know, in Hong Kong, so we have some more in common than usual culturally I guess. He was just telling me about how he had read 矛盾论, which I haven’t even read, at least not in detail, myself. He was saying, on the putative connection between scientific talent and Marxism, perhaps how dialectical materialism is inherently a very scientific way of thinking. I myself know basically nothing about dialectical materialism and even think it’s kind of high verbal low math bullshit, but I can tell that the materialist side of it is very scientific in its very nature, and similarly, dialectics is a very analogies/relationships way of thinking, which is something that high IQ people are by definition good at. Surely, there is much more I can learn from this guy, especially about Chinese language and culture and politics.

On this, I am reminded of another amateur (but professional, or better, level for sure) Marxist scholar, who is genuinely encyclopedic in his historical and cultural knowledge, in particularly a perceptive quote of him that made a deep impression on me:

Europe has always been in rebellion against itself, and continues to be so.  There was nothing but futility in the attempt by superficially Westernised Chinese to be authentically Westernised Chinese by being imitative and reverential of the current embodiment of those values.  You could only be an authentically Westernised Chinese by being a rebel against the current embodiments of Western values, at least in as far as they hampered China or seemed to be irrelevant.  And that’s why Mao was China’s best Westerniser to date, despite his very limited experience of the mundanities of Western life.

As I’ll detail in a future article, visitors to the Chinese Communist bases at Bao’an and later Yen’an noticed that these were the only Chinese in China who behaved more or less as Westerners would have behaved in a similar situation.  Other Chinese might speak good English, wear Western suits and sometimes show considerable knowledge of Western culture: but it was all imitation and the inner core was different and ineffective.  Western-trained engineers and geologists who returned to China kept their distance from hands-on practical work, because anything resembling manual labour would have lost them status in the eyes of Chinese intellectuals.  They were imprisoned by a tradition stretching back to Confucius and beyond.  Only a few broke these ancient taboos, mostly the Communists and some scattered left-wingers in the weak middle ground.  And it was the modernised Chinese in the Communist Party who chose to raise up Mao as the prime teacher of this new understanding.

I remember when my obsessively talented Russian friend once said to me that sometimes he feels like he’s another Pavel Korchagin, I thought he was ridiculous. Well, I’ll be equally ridiculous and say that I feel like I very much exhibit what Gwydion described in Mao that is “authentically Westernized Chinese,” which is very much the antithesis of what I see in most ABCs, despite being half an ABC myself.

If only more people could be like me…

Oleg

Oleg is one of my ubermensch Soviet (and also part Jewish) friends. He has placed at (or at least near) the top on the most elite of math contests. He is now a math PhD student with an advisor even crazier than he is, who he says sometimes makes him feel bad, because he has done too little math research wise. However, this persona alone is not that rare. Oleg’s sheer impressiveness largely stems from that on top of this, he is a terrific athlete, extremely buff and coordinated, enough that he can do handstand pushups, to the extent that he regards such as routine. Yes, it is routine for a guy contending for a spot on a legit gymnastics team, but you wouldn’t expect this from a math nerd huh?

Today, I was talking to him and some others about gym. In particular, I was saying how I could at one point do 10 pullups but dropped down to 2 after a long hiatus. The conversation went as follows:

Me: Oleg I’m back to 5 pull-ups now
Oleg: that’s good although make sure you’re doing them for real
i still don’t believe you could do 10 but then dropped down to 2
Me: Oh I’m very sure they’re full pullups
Okay maybe it was 8
Oleg: i’d like to see evidence
Me: Alright I’ll have someone videotape me do pullups today in gym

And so I did.

Later, Oleg suggested something pretty funny:

i still think you should get tattoos and gain 25 lb of muscle, that would be hilarious
then walk up to girls and ask about their SAT scores
and say “oh, that’s too low, i don’t want to breed babies with you”
followed by a cackle
i’d watch that show

Not surprisingly, Oleg, as buff as he is, has had some success with girls, though he regards himself as shy and struggling in that regard. I keep telling him that he needs to marry a girl who’s both super smart and attractive like he is, so that he can optimize his chance of making superhuman babies. His only disadvantage now is that he’s a poor math PhD student, but he can easily change that by, say, joining DE Shaw, from what I’ve read is full of uber nerdy macho Eastern European men. He’s not very interested in money though, and expresses content with his graduate student stipend, which I find laughable.

I find it regrettable that most ubermensch men smart enough for legit doctoral programs in math and physics are unable to find a mate who is commensurate with them, ability wise, even with some adjustments, even when they’re well-rounded like Oleg is. Why is this? Excessive Aspergers? On that, I know someone who will say along the lines of

in an actual long-term relationship you have to share most of your life with the person, and if they don’t understand the way you look at the world then it creates friction
sure, the girl doesn’t need to understand high energy physics, I have other friends for that

Maybe some females could give us some advice, other than the cliche “hit the gym” that you’ll often hear from males. Such would be much appreciated! 😉

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 +4 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.