On China

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

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

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

On that, I was like:

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

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

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

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

On this, I’ll give some of my thoughts. Recall that I said in my chat with him: “when you’re down, it’s really hard to get back up.” This is in general, it applies to individuals as well, with unemployment and such. In the context of the chat, I was referring to the century from 1850 to 1950, when China kept being beaten and made little progress when the rest of the world was advancing rapidly, including China’s foe from the East, Japan. Back then, many intellectuals desperate believed China to be hopeless and on that, even advocated the abolishment of Chinese characters. I believe China was very fortunate to get out of that, as it could have easily been much worse. The international situation, in particular the world’s having been exhausted after WWII destruction, gave China the opportunity to win the civil war, ending a century of violent internal strife that had severely hampered development. The Korean War did much to help Chinese regain their confidence. It proved Chinese military ability for the first time in modern history, much needed at the time, and America blundered by letting China do so. The 1950s was a golden period for China, during which with Soviet aid, China modernized essentially, developing the industrial foundation that even after the Soviet Union withdrew its support for China, though it had a significant negative effect development, China was able to do okay. In the 60s, the international situation was very unfavorable for China, but by 1970, China was high up enough in terms of capability that America had no choice but to recognize it, seeing that there was no way the old regime in Taiwan could retake the mainland. At that time, China was still extremely poor standard of living wise, but there was already a fair degree of technological sophistication. China was also very lucky not to suffer the demise that the Soviet Union did that is literally impossible to recover from. Why that did not happen, why America did not succeed in 1989 in bringing China down, is a very complex question. The Chinese elite were not as foolish as the Soviet ones. Since then, China has made tremendous progress in terms of developing economics and standard of living and also STEM, and though of course, China is still behind in certain areas, it is only a matter of time as many believe before the gap closes. Throughout the last 50 years, these “experts” have doubted the PRC, but the PRC keeps proving them wrong. Maybe these “experts” should stop deluding themselves on many matters.

I’ll give my personal opinion. I believe that every individual, every nation, should develop in a way that’s most suitable for them. Copying someone very high up blindly usually leads to disaster, because that high up person is genuinely well equipped enough to do what you are realistically unable to presently do. Instead, try to find something that hasn’t been tried before without large risks that you have an argument might be successful for you. This was exactly what China did and is still doing, so far to great success. China was lucky to switch its system at about the right time compatible with its circumstances. In the 1950, China was emerging from a century of war and stagnation, and the odds seemed so against her. Many could not believe that the communists would win the civil war, as ill equipped as they war. They did so, according to many, by developing a unique way of combat. It shocked the world that with it, China, avoiding its weaknesses, was able to succeed against the most powerful country in the world at war. China had no air force or navy at that time, with the exception of what of that had just been provided to China by the Soviet Union. China also made the right choice of using the Stalinist style economy that had already been proven to be successful in the Soviet Union, which enabled her to modernized very rapidly in a decade. China, as far as I can tell, had no intention to go to war with America and no expectation that it would. If not for MacArthur’s foolish and miscalculated decision to invade North Korea, China probably would have established normalized relations sooner or later and would not have leaned so one-sidedly towards the Soviet Union, and would not have taken such extreme measures at home subsequently. Another major success was that China was able to establish relations with America before Mao’s death on relatively good terms, owing to the capability China possessed at that time in addition to that threat posed to China by the USSR brought about common interest between the two. China did not stick to the old planned economy, instead embarking on a mixed economy with gradual proliferation of private enterprise, seeing perhaps that it was past the stage when the Stalinist style economy was needed. At the same time, China did not fall for the market fundamentalism that America has, and simultaneously, China kept its faith in developing a political-economic system suitable for the stage that it was at amidst enormous pressure, especially after the death of the USSR brought about a tide of “the end of history” in international political thought. Now China seems to be doing quite well, with rapid development economically and also in science and technology, and about to become competitive at the forefront in arenas at which she had been seen as backward. As this happens, Chinese, with a deeply engrained inferiority complex, becoming more confident in themselves and in their system, which with political bias aside has many advantages, such as long term planning.

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

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

Math sunday

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

I also find the proof of the first Sylow theorem much easier to understand now, the inspiration of it. I had always remembered that the Sylow p-group we are looking for can be the stabilizer subgroup of some set of p^k elements of the group where p^k divides the order of the group. By the pigeonhole principle, there can be no more than p^k elements in it. The part to prove that kept boggling my mind was the reverse inequality via orbits. It turns out that that can be viewed in a way that makes its logic feel much more natural than it did before, 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。:(









这几月,我在学习俄语,网上找到了毛泽东十八首诗的俄文翻译, 此中有《长沙》的。


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













我们细细想想资本家握有一切的工具——无线电、报纸、杂志、电影,他说一句话的力量当然不是我们一句话所可以比拟的;等于在人家锣鼓喧天的场合下,我们在古琴独奏。固然我们都有“自由”,但我敢断言,在手酸弦断之下,人家再也不会听到你古琴的妙音。在经济不平等的情况下,谈“民主”是自欺欺人;谈“自由” 是自找枷锁。人类的真自由、真民主,仅可能在真平等中得之;没有平等的社会的所谓“自由”、“民主”,仅仅是统治阶级的工具。


现在再让我们看看新生的祖国,怎样在伟大胜利基础上继续迈进!今年元旦新华社的《新年献词》告诉我们说:一九四九年,是中国人民解放战争获得伟大胜利和中华人民共和国宣告诞生的一年。这一年,我们击破了中外反动派 的和平攻势,扫清了中国大陆上的国民党匪帮……,解放了全国百分之九十以上的人口,赢得了战争的基本胜利。这一年,全国民主力量的代表人物举行了人民政治协商会议,通过了国家根本大法共同纲领,成立了中央人民政府。















想起我是八年级左右首次得知文革,那时的我中文不明,毕竟小学就一直在美国上的,所以看的都是英文的那些反共的扯淡。过一年,历史课有讲中国那时,美国老师不用说是讲的完全不符合事实,有夸张,有偏见,以“将农民当rocket scientist“以及类似之之非正当之语形容。反正给的印象就是文革彻底毁灭了中国,是共产党最大的罪之一,是破坏中国文化的。






一位哈弗毕业的,发表超弦的,科学通才的,也是无出于意料,犹裔的(现已归以),在脸书上有过几次闲聊。此中,他有提到他的在文化上科学与马克思相连的观点。当然,这不是绝对的且远之。好多伟大的科学家,如Edward Teller,都是坚决反共的。他也说过美国在二战前没有什么科学,加上美国文化好的一面都是从欧洲带来的。他也在网上多次提到过西方物理学家剽窃苏联的行为,尤其在七十年代,此例子众多,这我没法评价,鄙人莫谙物理,基本此盲也,可是我相信是这样的,凭受制于某某利益集团之美国媒体及教育的极其偏见及歪曲现实。我个人也有类似的感觉,虽然马克思的著作我从未认真读过,目前难以解之,仅感觉而已,也许因为我对于美国教育及体制及文化某些地方的叛逆,也许因为在美国的好多科学家工程师,包括拔尖的,都非美美国人。此人也说过,美国是建立于使对方失地,白人优越主义的新国家,未有不已之外入,则一切良素成烟。有一定道理,这样的国家,何可文化不稍偏夷焉!





这让我回想起我上小学中学,好几次有美国同学争论is Taiwan part of China,一般最终得到结论都是不是。不用说,他们所想的,无论如何,都不会改变事实,所以这种争论是毫无意义的,尤其在他们和当时的我对与历史客观具体事实的无知的情况下。基本在那儿,小学中学的历史课都是垃圾,尤其是在美国,因为老师水平一般不会太高,经常还会很差,比如在美国,好多历史老师会自以为是地将自己的主观偏见施加在学生上。孩子们都想得很简单,什么东西都用好与坏衡量,我也是。现在长大了,就知道好坏正邪非客观存在,但赢者输者是有的,无庸隐讳,败到台湾的蒋介石国民党就是极度的输者。







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




如何解释之?我想是大科学家,按照在Steve Hsu的博客上在关于g的讨论中用的语言,V都很高与中国老的科举的那一套结合所产生的自然结果。