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 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 minds 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.

Various thoughts, here and there

Another exhausting week of work is past, and I am presented with another chance to wind down. Last night, through various casual reading, I was reminded of the concept of “effeminacy.” In many contexts, if you’re a man, the worst you can be seen as is “effeminate.” And of course, American culture stereotypes Asian men (specifically East Asian men) as effeminate. On this, there is this and this, among many other similar articles, especially the notorious this, which I stumbled on several years ago. I’ll say that there is as far as I can tell some truth to this from an objective biological point of view, in the likes of higher and softer voices and lower testosterone levels in East Asian men relative to white men, and also in white men relative to black men. On this note, I was also reminded of some comment of Michael O Church on reddit (which I cannot easily find anymore) that used “high IQ androgyny” as a factor to illustrate how super smart people (like +3.5 even +4 sigma g) get smashed in the corporate world, politically. It brought me to wonder if far tail g men really are more effeminate, which is likely to be the case, as there has got to be some biological tradeoff for the substantially larger brain that is the material source of such extreme cognitive ability. The light, nasal (or whatever you call it, for lack of better word I can think of) of voices of various mathematicians echoed back to me one after another, in contrast to the deeper and superficially more assertive and aggressive (and masculine) voices of those dumber business guys (mostly WASPs) in positions of power in the corporate world. Speaking of WASP, I could see also how Jews are perhaps more effeminate as well; I’d seen and heard enough that I feel I could intuitively recognize a Jewish voice as well, with of course there being the style of language in combination with the vocal mannerisms that sounds it more distinctively Jewish. I’ve long noticed that though East Asians reared in US mostly speak without an accent, it is still often easy to tell that it is an East Asian voice; such just goes to show how real race is, how rearing in an alien land and culture changes not the deeply engrained racial characteristics which go beyond physical appearance. It is quite a marvel indeed and a beautiful product of human evolution, a panorama of human biodiversity, that of course varies significantly more among individuals of groups than among the group averages. East Asians may be effeminate in the sense aforementioned, but interestingly, there is this “mad Asian guy” on Steve Hsu’s blog who in comments has written of the East Asian cognitive profile relative to the white one as akin to the male one vis-a-vis the female one, which is the undebatable truth born out by the result of testing that has across generations revealed East Asians to be higher by about if not at least two-thirds standard deviation in math and visual spatial, thereby making white people more effeminate in another sense.

Human (biological) development is quite fascinating, especially those of outliers, of which I am one to quite a degree, though probably not enough to make me genuinely distinguished (as in 1 in 100,000 or even 1,000,000 in terms of rarity of ability and accomplishment) in any way ever. We all know that top athletes in legit sports like Shaq are physical freaks of nature who deviate dramatically from the norm in their physical development but in one still constrained by the bell curve, physically speaking, but more consequentially, there are geniuses of mind the brains of which are extremely unusual in such a way that concrete output, in terms of quality and profundity, and to a lesser extent quantity is exponentially increasing as one goes further along the tail in our artificially created bell curve. These people, by virtue of their unusual brain structure, are able to perceive the world, engage in a form of consciousness, far beyond, and more objectively correct than, what the normal human experiences. One can only put oneself in another mind rationally; it is impossible to do so for real. As an example to illustrate, it is impossible to feel the way a mentally sick person does when one is healthy and that does not change for one who has recovered from a depressive episode with respect to oneself. Saying this brings to my mind the following quote of Huxley:

Perhaps men of genius are the only true men. In all the history of the race there have been only a few thousand real men. And the rest of us–what are we? Teachable animals. Without the help of the real man, we should have found out almost nothing at all. Almost all the ideas with which we are familiar could never have occurred to minds like ours.

This quote obviously has eugenicist overtones. It hints at a need of measure to protect against degeneration of a human species that for all its wonder and power, relative to real animals, is still mostly degenerate. It also evokes fear, especially in this day and age when genomic prediction and selection is imminent, that some elite will use it to rule an ignorant, subservient masses. We are and already have been in such a world for ages, with the heritability of ability coupled with transmission of money and power in a feudalistic manner, just now in disguise, with additional channels for mobility now for those of ability from lower background. The elite still rules and exploits the masses, just in a way more benign than ages ago with slavery and priestly spiritual opium abound. There is all the evidence that the best we can create as a society is to provide for everyone an environment and position and work appropriate for his ability and temperament taking into account of course the needs of society. There is also the observation that in general, those of higher ability have higher expectations in terms of what they do and also in terms of their material life, just as kids expect less than adults, in terms of their lifestyle. While there are significant differences in ability, and it probably wouldn’t hurt to make people a bit smarter, I would not say there is anything terribly particular one should be, and that everyone should try to find and bring out what is suitable for one’s ability and one’s circumstances, and hopefully something that is never seen before. I’ve lived long enough to be aware that every stage there is a unique personal challenge, and that one’s position relative to others does not necessarily affect one’s happiness much.

History has witnessed clashes, often in the form of war, between races, cultures, beliefs, systems. Groups have, in contempt or hatred of another, sought the other’s destruction, the other’s subjugation, the other’s cultural conversion, particularly in the religious sphere. It is human nature and also human weakness. There is a human inability to respect another far different from oneself for what the other is and a tendency in such cases to be imposing, with this’s being particularly prominent in certain religious cultures. I have had such myself, but they are as far as I can tell largely cleansed away, upon my realization of the differences in humans inherent and not permanently malleable, as evidence by significant changed in people once removed from parental pressure, once they are more free to do as they choose. In this regard, I take a more liberal attitude and come to cherish the diversity in culture, the diversity in styles of thinking, the diversity in talents across the world and across professions. I’ve come to realize over time that to feel contempt for another for his beliefs and tastes is futile, a waste of energy, and in such cases, parting ways, and viewing the difference as a mere reality, one observed and chuckled at, is the best way to go. Moreover, contempt can even metamorphize into some form of appreciation for the richness of our world in the variety it offers, in which one is but one constituent.

 

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, when 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 pth 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.

一说起偏微分方程,想到此行有不少杰出的浙江裔学者,最典型的可以说是谷超豪。想起,华盛顿大学一位做非交换代数几何的教授,浙江裔也,的儿子,曾经说起他们回国时谷超豪,复旦的,如他父亲一样,逝世了,又半开玩笑言:“据说谷超豪被选为院士,是因为他曾经当过地下党。”记得看到杨振宁对谷超豪有极高的评价,大大出于谷超豪在杨七十年代访问复旦的促动下解决了一系列有关于杨-米尔斯理论的数学问题。之外,还有林芳华,陈贵强,都是非常有名气的这套数学的教授,也都是浙江人。我们都知道浙江人是中国的犹太人,昨天Brian Bi还在说”there are four times more Zhejiangnese than Jews.” 可惜我不是浙江人,所以成为数学家可能希望不大了。:(

一周终过

新工作首周刚完,经过了繁忙紧张漫长的五天,对新环境,新代码,新系统的适应,以及新领域知识的吸收,周末终于来临,可趁机缓冲一下。这周收获相当大,感到对新工作所做的事情已得以大致的了解,足以下周完成更细节式的工作。加上,跟其他人也有一定融合之感。工作之余,比如在坐车时,也稍微想了想,学了学数学,有点增加。

昨晚,我跟那位犹裔美国IMO金牌在脸书上讨论犹太人与中国人在最高智力层次相比的问题,想起有两位我所认识的以基督教传统长大的学习理论科学的美国人所我当时难以思议的东亚人智力上强于犹太人的观点。怎么说那,虽然在这前五十年,日本人和华人在理论科学上做出了的不少伟大的贡献,占有美国好研究大学不少教职,加上我这一代的华人在竞赛中出色的表现,可是还是感觉在科学里的绝顶,犹太人更多,以犹太人更具有一定的高瞻远瞩,可促以颠覆性的跨越,苏联那批犹裔数学大师为典型例子。同时,这个人,作为组合数学为学习及研究方向的高材生,又提醒我犹太人在理论计算机以及匈牙利式组合数学所有的牛耳。他说世界上最聪明的人是亚洲人,他的名字是Terry Tao,可是前一百犹太人综合强于前一百亚洲人的综合。对此,我问他:你了解任何Tao所做的工作吗,可肯定他是世界上最聪明的人?他回:我读过Green-Tao定理的证明。我没啥好说的,只言那还算比较前沿的东西,又跟他说我在对一些华罗庚撰的数论引导,虽引导,可以包含一些我现在认为相当深的数论,如Selberg所做的一些。Tao是个神,可是我也有朋友说:我有事想是否Tao未有过以自己不如von Neumann聪明而心里不安,加上数学那么难,连Tao都差点没有通过博士生资格考试。加上,von Neumann精通数门外语,具有即兴无迟钝翻译之能,以及过目不忘的记忆力,而我都看到过有些中国人在网上以将自己视为”primarily an Australian”的Tao对中国文化一无认同和他对中文一无所知表示反感。我在此博客上前所提到那位犹裔数学博士,念到深到Goro Shimura所做的工作,也觉得Tao有点overrated,觉得他的工作没有例如陈省身所做的深远及原创,说Tao至今还没有创造新的领域。关于犹亚之比,我想到的还有环境的因素,在这一点华人还是比较吃亏,由于经济原因,也由于名字及文化陌生原因,老一辈的华人还在为了自己及国家的生存挣扎,没有那么多经历投入科学研究。或许现在歧视对华人,即使在理论科学界,还是相当严重,虽理论科学少有集体性及宣传及政治因素,与比如生物或软件开发不同,可是人都是有偏见的,这包括评审委员会,如我听到的诺贝尔委员会对苏联科学家的工作的贬值。我这一代,华人在那些完全公平没有任何主观因素的竞赛里已经遥遥胜于犹太人,而那些是最好的对纯粹智力顶级的测试。我有时候想:中国人现在最缺的不是科学技术人才,而是反抗歧视,争取话语权的人才。在外国人眼中,中国人经常有性格被动的刻板印象,的确有这一点,但是好多也是不太客观的媒体所造成的。加上,中国人在美国也是少数,又有语言文化障碍,这又是一个视为寻常的Asian penalty.

数学上,我闻到了在\mathbb{F}_p域下的次数整除n的不可约首一多项式的积等于非常干净的x^{p^n} - x。此多项式很容易看到没有平方因式,用典型的此与此导数非共有因子去证。同时,取任意次数dd | n的不可约首一多项式\phi,则\mathbb{F}_p[x] / (\phi)是个p^d元素的域,则所有元素是x^{p^d} - x的根(x也是此域一元),从此可以得到任意多项式(这包括x)代到x^{p^d} - xx里都在模\phi等于零,也就是说他会是\phi的倍数。因d | nx^{p^d} - x | x^{p^n} - x,则\phi | x^{p^n} - x。不难证明\mathrm{gcd}(x^{p^n} - x, x^{p^d} - x) = x^{p^{\mathrm{gcd}(n, d)}} - x. 若d \nmid n,次数d的多项式若要整除x^{p^n} - x,必整除x^{p^{\mathrm{gcd}(n, d)}} - x,可以用归纳法证明此不可能,在\mathrm{gcd}(n, d)< d的情况下。从此,可以得到x^{p^n} - x没有因子次数非整除n。证闭。

 

Humanities

I’ve been very distracted by humanities lately and I am even contemplating making a career in it, which would have been farthest from my mind in high school or college. In high school, I struggled greatly with English class when in the novels I was forced to read, I couldn’t understand what was going on half of the time, due to misunderstanding of definitions of words or lack of requisite familiarity with the cultural context. There is also that I only started learning English at age 6, without being exposed to it much at home, which means I don’t know the English names of certain household items. Literature made little sense to me, but history I rather liked, though I disliked the American rendition of history.

I started reading Chinese online in high school. It was very difficult for me at that time, but gradually I was able to make sense of things. For language at school, I took Spanish and I was horrendous at it. I’ve forgotten most of it by now, but I could easily relearn it with my much enhanced level of verbal maturity. I’m not very motivated to learn Spanish anymore because there isn’t very much high culture in it (pardon my snobbery).

I hardly took humanities courses in college, but I did take a few that were required. I remember vividly how in the writing class I took most of the students couldn’t write coherently at all. I did starting in my third year of college develop an interest in Chinese poetry. I remember spending quite a while to memorize 蜀道难, without understanding what it was really saying as it was full of type of Chinese language literary that I had no exposure to at that time. I started reading Baidu Baike without feeling like it was too overwhelming.

In high school and even in college, it never occurred to me to take humanities seriously. There are no jobs in that. And students who major in it, at least not in the very top schools, are pretty fucking dumb. Additionally, I always considered language my weak point. In high school, I remember calculus being super easy for me while English class being almost torture. I had to really force myself to write those literary analyses and memorize the details of what happened in the each chapter of Dubliners by James Joyce so that I could actually ace the quizzes. Honestly, how do you fucking expect high school students to really understand what’s going on in that.

Early in my fourth year of undergraduate, I started learning Russian out of a desire to understand the lyrics of some beautiful Russian songs. Also, the grammar of the language, being highly inflectional, was quite fascinating. Also, the Soviet Union, which shaped the course of 20th century history so substantially, was viewed by me as an entity to be understood to a reasonable level.

I know American education really emphasizes liberal education where in undergraduate you study very generally. It is in contrast to many other systems, where students focus mostly on their major in college. In China, the education system of which was influenced by the Soviet Union in the 50s, has very specific majors, where say you major and engineering and by the time you graduate you are already sort of an expert in a very narrow part of engineering, such as automobile engines. So because of that, I didn’t actually learn a ton of math or computer science despite majoring in them, although it also had to do with my having been quite dysfunctional back then.

On humanities, I’ve also seen people who major in them as rather spoiled. “English literature” was cited by a Chinese immigrant engineer I worked with as something for rich people who don’t have to worry about making a living. Yes, there are actually parents who pay for their kids’ tuition at a non-state school which is like $50k / year now for them to study a useless subject with no employment prospects, and I’ve even seen cases of parents paying them for continual study. To be fair, just being able to study is already privilege. After all, most people in this world not by choice are engaged in menial labor that is often also dangerous and bad for health. It’s especially egregious when these useless humanities students (many of whom aren’t even any good at humanities or language) also support very unprogressive and even vile politics. There are probably many of those at many of America’s Ivies (I’ve been told that at Yale the major for kids who party too much to graduate is American Studies). On that other hand, there are obvious advantages of entitlement, which I won’t go into.

I grew up in very ordinary middle class American neighborhoods, surrounded by very ordinary people. I wasn’t like the other kids at all, though the environment made me fit in artificially. That there are parents who spend over $50k / year on enrichment for their (often idiot) children was so foreign to me at that time. I believed firmly in, by virtue of upbringing, meritocracy, and the gradual realization of the world’s so not being that way was rather disillusioning. Why play it fair when you don’t have to? Instead of feeling of disgust at such, I have evolved to view it as very normal and inherent to human nature.

As for humanities, I haven’t been reading novels in their entirety, which I don’t really have the patience for, but I have learned countless words in Chinese, English, and Russian, which I have a much better memory for now. The humanities culture in China, a rich civilization and culture of millennia, which I have indirect access to via my internet connection, has deeply impressed me. I read classic poetry in it and imagine how anybody could have possibly written this. It is evident that I am still quite a ways away from the big brains in anything, and it is possible that I am simply not naturally talented enough. I will say though that most kids in my current generation, especially in America, are as dumb and ignorant as rocks. Is this due to genetic deterioration or due to the degenerate culture that pervades my generation? I feel like much is the inability of many to recognize that latter and the mental courage to counter it at the expense of some degree of social isolation. We are in an era of civilizational decline, and when I say this, I echo the private exchanges among many highly gifted and aesthetically discerning people who must hide to some degree in the suffocating atmosphere of this country, especially in the corporate world.

Most of my friends are in STEM, in fields like math or software engineering, so the types within my milieu constitute a rather lopsided group. I have little contact with any in the world of humanities and social science in America and I am curious as to what kind of people they are. Well, Steve Hsu says many of them are high V lower M types, confused, in the likes of Stephen Gould. My temporary loss of interest in mathy material is worrisome. Am I degenerating into those I looked down on as saying nothing of substance. (In case you haven’t noticed, I am saying absolutely nothing of substance right now, but perhaps it needs to be said for social and political reasons, as part of an cultural/ideological war in some sense?) Perhaps this is an artifact towards my intelligence shifting more towards the verbal end of things? Could it possibly be that now with some more years of organic cognitive maturation I am now metamorphosing towards the reverse direction of lopsidedness?

When I talk with people in the software profession, it is apparent that they are types for whom learning natural language is unintuitive, despite programming being a very languagy pursuit, with many programmers conspicuously bad at math, as the work is of a very qualitative nature. There had been to me many parallels to writing in software engineering to my blind intuition but such is clearly not the case empirically.

There are many people, especially certain parents, who will say that once you’re an age, you can’t just study and that you have to go out and earn money and do something that’s directly useful to others, that makes some tangible contribution to society. That can be writing software or building houses or scrubbing toilets. But it can’t be hiding in academia, especially in a subject like pure math or comparative literature. There are all these stereotypes of about those in pursuit of or already in possession of Permanent Head Damage as kids who don’t want to grow up many of whom also lack common sense or have no practical skills, who manage to put spoons and forks flat on the dishwasher. There are also stereotypes in virtually all societies that those people only know books and are often too uppity to engage in forms of labor regarded as more menial.

I thought that maybe I could go into history or political science or language. Maybe I could even make a career in that. It’s not impossible. Or maybe even go into the legal profession?

I’m at a loss on where to take my life as software, which I’m not bad at, does seem not to marry my personality. Most software engineers will see me as too weird for say learning Russian on my own. Now am I one of those dysfunctional weirdos who can only survive in academia, which we already know has no jobs? Also, at this point, I am mostly a consumer, rather than a producer, of knowledge, a state of intellectual incapacity that will hopefully alter itself. There have been times when I could not help but see myself as good for nothing, though surely my standards on that are quite high. Hopefully, I can find something in which I can truly excel and even make a name for myself. Let’s see if that happens.

Metacognitive musings

It feels like ages since I last posted here, though a month ago is short in the time frame of great minds, who endeavor on projects for years and even decades. Since then, much has passed through my mind philosophically and meta-cognitively that I have not kept record of out of a belief in their triviality and lack of detail as well as the lack of natural inclination to write them out, compared to before. Though I share my thoughts with close friends through private (or not so, as nothing is private nowadays, electronically) channels, my past month has been loaded more on the intake end as far as text is concerned, with much of it being in Russian, and to my great pleasure, I now converse in it regularly with a number of people non-orally, including a charming, talented girl who won a worldwide chess championship for those under a specified age group.

Now to propagate my bull shit mental signals to eternity. I recall in some math circle, the motto was “existence is a state of mind.” I identify with this quite deeply. One cognitively mature to a sufficient degree can appreciate that what one experiences consciously, the extent to which it can be precisely characterized in qualitative terms, is a function of brain structure. Steve Hsu has proposed on his blog a toy model where there are n genes, each with some (finite) number of variants. This can be represented as a (bounded) lattice on an n-dimensional space, on which some metric can be defined, that correlates with reasonable metrics for outward behavior and cognitive manifestations. This space has been far from exhausted by all organisms which have lived on this planet. In particular, the theoretical extreme relative to the realized one is almost certainly Mount Everest relative to molehills which occur at several orders of magnitude higher of frequency. To go back to the motto, we must clarify that the “existence” here by the very context in which it resides is what can be perceived mentally by the human brain, which is very likely a minuscule subset of the theoretical maximum of biological perception of the world.

Growing up is a process of realizing successively how broken one’s former brain was. Eventually, provided that one is above some threshold in IQ, it will dawn on one that there are people capable to perceiving the world much more clearly and correctly than you can, and that there is a much higher world that one is incapable of experiencing. One sees the great extent to which what one becomes is determined at conception.

Different people think very differently, much of it owing to nature. People have different upbringings, which accounts for much of the variance in what one is exposed to, but when one is an adult and settles independently, one is more able to choose what to expose oneself in a free manner, free of cultural constraints, especially with the near ubiquitous access to information nowadays. To illustrate, a good example would be the countless I’ve seen go from evangelical to atheist and the reverse. This is especially so, in my opinion, for those higher on the bell curve, who are harder to control mentally.

I myself am a materialist, as is obvious from the thesis of this post. God to me is Mother Nature. I will not say I am an atheist as such cannot be definitely proven or witnessed before afterlife but I will shy away perhaps with partiality in the other direction. It is a misfortune maybe that God has produced me to be incapable of being penetrated by him and I have wondered what it would feel like to be the complement of what I am, though such is of course futile assuming non-existence of brain transplants. On this note, religiosity is, according to my reading online, rather heritable (surprise surprise), and it has occurred to me that perhaps those of East Asian descent due to a divergent branch of evolution are less prone to religiosity, especially with my seeing that Japan, in addition to the heathen middle kingdom, now directed by a Marxist-Leninist (or maybe only in name) party, is also high in its degree of secularity. The aggression within missionary men has both amazed and perplexed me. What is it, after all, that enables the conviction that those conquered, enslaved, culturally teared apart, are in fact being saved in the name of God or to be less extreme that there is such a holy duty to proliferate this conception of the human mind, a product of God itself, (or not) that fuels such intrusive and unceasing behavior, often targeted towards the young, impressionable, and often impoverished? I do not see behavior anywhere near in degree of magnitude exhibited within those on the reverse end of the religious/ideological spectrum, as an expected value. One’s religious faith, as far as I see, ought to be a private affair that is respected regardless of differences, barring cases of excessive and grotesque infringement. Moreover, the Christian culture, the Abrahamic tradition, is one I seek to know more about on a factual basis, as it is an integral and indispensable part of the Western culture that is dominant globally today owing to the exponential leap in penetration of thought and sophistication of production sprung forth by an explosive awakening of the slumbered Greek and Roman, tearing fetters and opening grand vistas the last half millennium.

How to see heaven and earth in the eyes of a demigod? How to transcend mankind? How to control the own evolution of man? The very essence of our existence, the cognitive of it, to be unveiled the years soon to come!

共产主义何能实现(how to realize communism)

我突然想起在DNA Dreams (中文粗翻译为《DNA梦想》),徐道辉(Stephen Hsu),大概为:if we could shift the mean IQ of a society in one direction, we could bring forth one that would be very qualitatively different in a way that would be unrealistic in the society prior to the shift.

This reminds of communism, communism as in from each according to his ability, to each according to his need. I’ll first say that even capitalist societies are already very much like that. People generally go into professions that they’re talented in. If one has multiple things one can do, one has to make a pick in favor of one, as one has only 24 hours in a day. There are economic incentives now for this, say for one to pick say computer science over physics, which has no jobs and pays below what a schoolteacher or police officer is paid. Another example would be choosing NFL/NBA (where the big bucks are) over track and field.

I have always perceived money as very artificial. I don’t think my life would change that much if I become super rich. How you feel is more determined by what you know and how your brain is wired, and what you actually do, than how much money you have. I also have doubts on the use of money to motivate people to do better work, especially on the creative end. It works and it doesn’t. In fact, I would say in that in an ideal society people, or at least the ones with the ability and spirit, should be able to do creative work without having to worry too much about money, which is far from the case nowadays. Our society is being so money obsessed (or compelled) due to the so called Satanic Trinity (education, health care, housing). People are scared of falling behind on that game that the system forces people to play.

In my silly K-12 social studies class, we were told that communism doesn’t work because people don’t have an incentive. X could be doing all this work and Y could be doing nothing and at the end they’d get the same. This is such a gross oversimplification of a very complex matter, looking at human nature in a binary way essentially. People edit Wikipedia for free. People volunteer for the homeless and disadvantaged, for free. People go into science for almost nothing. In companies, you’ll find that the stars contribute like 10 times or more, or in some cases, infinity times more by solving a problem nobody else can than the median. Those people are generally higher ranked too on the ladder, but their salary is not matched by difference in magnitude of their contribution. The people who do make 10x more, or even 100x, are largely people planted in positions of parasitism by having the right social connections, playing the politics right, etc. That’s just how broken the current system is, and we all have to live with it, or not.

Again, in those social studies classes, we debated why America is the most innovative and the most successful country in the world. People will say freedom. Freedom to do your own thing, to start your own company, to be a non-conformist. While there is an element of that, it’s rather overblown in my opinion. There are other, more influential factors omitted here: such as the exploitation of labor (remember that America is a nation founded on dispossession and slavery), vast natural resources per capita (and also a geographic position that immunes America from war, barring civil war), and import of foreign talent. With such advantages, it’s almost impossible for America not to be number one. Especially, after WWII, when so many of the best and brightest from Europe came to America. Many of the top Manhattan Project scientists were foreigners, many of them Jewish. Many of the top scientists and engineers (like von Braun) of the space program were captured Nazis. In the 90s, America got a huge chunk of the best and brightest of the former USSR and its satellite states. From the 80s on, many of the smartest young people from mainland China came to the US as well. Those people could hypothetically be making China or the USSR/Russia better instead of making America better.

I remember Nassim Taleb has a high opinion of the America system’s tolerance and encouragement of ad hoc tinkering and experimentation. He cites these Europeans who criticize Americans for being uncultured or lacking knowledge or whatever, and it’s like: you guys writing this silly criticism in Microsoft Word, while looking up stuff on Google, on your iPhone, and all of that was created in America! He does have a very good point. Why do Europeans not create and use their own? Is it because their system is too egalitarian and discourages entrepreneurship? I’m not the most qualified to answer this, but I’ll say that Europe is more or less subordinate to America. There’s NATO and the EU and all that. Also, those technologies listed are very marketing, business driven products. For instance, Microsoft won in the reasonable judgment of many mostly due to its business and legal tactics. Also, Taleb has done some cherrypicking. Linux, an arguably better from a technical point of view operating system, was created by a Finnish genius in his early 20s. American cars lost to Japanese cars and they’re nowhere near able to compete with German cars, because they were objectively worse. I know almost nothing about cars, but I know Japanese cars are more fuel efficient and last longer. America as far as I see it is a society very into marketing and superficial things. It does not revere and respect people who do hard science and technology, real things, enough.

I’ll also say that America is very much a nation of taking advantage of and breeding the ignorant, for the benefit of people with capital. If people were smarter, it would be harder for banks to get people to not pay their credit cards or take on shitty deals. It would be harder for universities for fool people into paying so much for such a shitty education that gets most people nowhere. America also de-emphasizes discipline and self-control. Hey, even Einstein said that imagination is more important than knowledge. Also, isn’t discipline and self-control counter to creativity, to the freedom that makes America so successful? This might seem the case intuitively to a naive one, but creative people will tell you that’s so not the case. With everything, there’s a right, systematic way of doing things that is required to be creative. I’m somewhat of an iconoclast I suppose, but I have a high opinion of discipline and self-control. In any case, these words are so vague, mean so little, that it’s rather pointless to use them. You need to be more specific.

I have asked a friend of mine in his 30s, who’s seen much more of the world than I have, if we’ll ever reach the point where education and health care are more or less free, where people don’t have to worry about money much. He, very optimistically in my view, said probably in 30 years or so. I sure hope so, because the current system is very obsolete with respect to the level of technology and production we have available. Self driving cars, AI, will only put more people out of job, and we need to find a place for them.

I recall that in the 50s and 60s, it was widely believed, especially in the socialist camp, that there would be a world revolution and that we would eventually attain communism. This had arguably reached its height in the mid 50s. In the early 50s, America was in a rather passive position ideologically, especially when it was not successful in the Korean War. McCarthyism did not happen for no reason. As a law of nature, any entity whose survival at risk will go to extremes. The denunciation of Stalin by Khrushchev in fact weakened the prestige of the Soviet Union tremendously. Many pro-left people in the West lost hope from that. There was a great ideological rift between the USSR and China following that. The Chinese believed that the Soviets were being revisionists and that their party leadership was being gradually infected by ones who secretly wanted to restore capitalism, or whatever you call it. It was widely believed, according to the writings of Chinese party leaders, that the transition from capitalism to socialism to communism was to be this great social transformation that would span decades or even centuries, with importance, scale, and qualitative difference equal to that of the transformation from feudalism to capitalism in Europe, and that the process would need much consolidation over a long period of time. To them, without that, there could easily be a relapse, and there was, as evidenced by the disastrous (you can look up the increased death rates in Russia that was coupled with prolonged economic depression) disintegration of the USSR and to a lesser extent by the Chinese economic reform. On the opposite view, such was viewed by liberals in the West as the “end of history,” as termed by Fukuyama.

This end of history theory is becoming increasingly discredited more with China’s success and rise. In the 90s, however, it was quite mainstream. In this talk, Kong Qingdong characterized himself as having become political out of what he perceived as the need for him to do so, referring to how in the 90s, the atmosphere in China was so dangerously liberal and pro-West, which is not surprising as the failure of the USSR made everyone suspicious of the whole system and ideology that it had promulgated. If not that, he said he, as a very well-behaved kid, would have become purely a scholar, an academic in a more or less apolitical way. He spoke of how in the 90s, writings in China which criticized America or imperialism had difficulty being published, and in addition to that, he mentioned the laying off of millions of workers from the privatization of many state owned enterprises that enriched many with party connections. The 90s was in some sense a low point, akin to China from the 1927 through the 30s or the Bolsheviks following the failed 1905 Russian Revolution.

It seems though now that China may well surpass America, with its only being a matter of time, a proposition that would have been beyond the pale in the 90s. Back then, people had serious doubts on China’s ability to innovate with its system, coupled with aspects of traditional Chinese culture viewed as not conducive to non-derivative R&D. People cited how the successful countries were all democracies, and the Chinese dissident Fang Lizhi, who produced some first rate work in astrophysics, had openly said that in order for China to become developed, it would need to adopt the parliamentary democratic system. The financial crisis in 2008-9 ruined America’s credibility enormously, especially given that China in many ways appeared virtually unscathed by it. Since then, China has made enormous progress technologically as well. Representative examples are its high speed trains as well as the development of its passenger aircraft. China has also developed an indigenous CPU, Loongson, which is already proliferating across government and military organizations in China. It is their goal to create a whole software ecosystem around their hardware, as has been done for Intel’s. Of course, there is all this military technology too, the details of which are highly classified. A guy from China once said to me that the system there, with its network of state owned enterprises, can complete projects with little delay. Some might say that none of that is very creative, as it is all large scale engineering. As for that, there is basic science, and while China is quite a ways away there, they seem to be improving rapidly. In that respect, Chinese have done exceedingly well in America. Now with more money, many of the best scientists abroad can be lured back and a higher percentage of the best of the younger generation will stay in China to conduct their research. The career prospects in America for scientists are quite dismal, and China I would say has a chance of competing there. As a consequence, a much higher percentage of people in China will be able to enjoy the luxury of doing basic science research. Rather beside the point, but I’d like to note that Fields Medallist Alain Connes has written that the European system is better for breeding truly original thinkers in math who open up new fields, with its having less pressure for grants and for results produced on a shorter time frame than the American tenure system. He expressed his belief that the Soviet mathematicians would have done better had they stayed in the old Soviet system, where the job was just to talk about science. We can see how Perelman solved the Poincare back in Steklov Institute in Russia after America offered him no tenured position and how Yitang Zhang was failed by the American system, where you need to play it safe to secure your next position.

There is even a camp of scholars who believe with confidence that the future will be China’s, that of the IQ proponents, representative figures of which include Philippe Rushton and Richard Lynn. Richard Lynn has written here that China will win after discovering the genes for IQ. It is definitely not impossible, and Steve Hsu has already worked with BGI on that. This goes back to Steve Hsu’s remark on that hypothetical society that can function in a way that the current one cannot because its constituents, its ones in positions of power especially, are too unintelligent. On this, I see a parallel between two highly politically sensitive words in America, which are communism and IQ. I’ll say, judging from their writings, that many of the leaders and scholars of and associated with the Chinese Communist Party in the 20s were highly intelligent, as were Marx, Lenin, Stalin, and Mao, all of whom were philosophers very profound and one could say, attaching a somewhat subjective judgment, visionary in their thinking. Mao wrote some of the most beautiful and high quality Chinese poetry, from a literary point of view. It seems that the Chinese with extraordinary literary or verbal gifts are more Maoist leaning, with on the other hand, Deng Xiaoping’s, dubbed by many on the left in China as the father of its corruption, for having promoted short-sighted people like Zhao Ziyang and Hu Yaobang who contributed to negative outcomes of the Tiananmen Square protests, being noted for having a dumb mouth and a dumb pen. Examples include Kong Qingdong, Li Ao, and Lang Xianping. I see the possibility of what many would perceive as too far-fetched: China’s becoming more communist as it closes in on the mystery of human intelligence.

When I was a kid, I thought over-simplistically, not having the intellectual capacity to reason rationally and rigorously. I could not imagine all those people who did crazy things, from geniuses to suicide bombers. I believed that what was easy/difficult for me would be the same for others and that people who struggled were not working hard enough. As I grew cognitively, I became increasingly aware that free will was bunk, that people are not in control of the way they are in a strict sense of the word. The way they are wired biologically correlates with what they become in a statistically predictable way. Science and the American Dream are in opposition to each other. We have in theory the resources for the most part to provide people with what is appropriate for them. This does not happen though in many places due to special interest groups, the hoarding of wealth, and deficiencies in resources affordably accessible to the public at large, based on needs of individuals. America, as unequal as it is, has an irrationally egalitarian education system that comes with stuff like No Child Left Behind. In America, the school one attends is based finely on where one lives, a proxy for parental socioeconomic status, or one of those fancy shmancy prep schools for kids whose parents can afford it, whereas in many other countries, like Germany, it is determined by what is most suitable for the kid given his performance and ability. In America, many employers now require a bachelors for jobs with nothing to do with academic learning, and colleges see this as a way to inflate their tuition, further oppressing the majority of people. There is also the medical system, which I will not go into. America will only further discredit itself by doing this; its facade cannot go on forever.

Let’s see what happens in the 21st century. Humanity may well undergo arguably its most revolutionary transformation ever yet, the ability to predict and control the types of people being born and from doing so realize a resemblance of the ideal society envisioned by Marx.