我们在群里所讨论的好多与种族，文化，智商，和学科相关，还记得我曾经对数学尖子开玩笑，美国IMO选手，非亚裔，必犹裔，而他似乎未感到我的玩笑口气，回说他那界有一两位非犹太白人。他还强调自己很美国人，不是那种在以色列待过的。高中时，他选了中文为他的外语，以童话为他爱听的一首中文歌。学术上，给的感觉是专注，单一的纯数学本科生，非常肯定他会走学术道路。他的具体数学兴趣及倾向为组合数学和理论计算机和解析数论。那天晚上，问他知道那几个二次互反律(law of quadratic reciprocity)的证明，他回答一个引用Zolotarev’s lemma的，并且发了个链接。当时，我只知道高斯和(Gauss sum)的那个，而细节已经记不清楚了。我花了一小时细读那个证明，领悟后感觉漂亮无比，引用的工具极其简单。从来没有想到可以将这数论皇后的定理视为，表达为置换的奇偶的积，毕竟Legendre symbol给的是1或-1，与sgn一样，好妙啊。回顾透明Legendre symbol给的基本是在给循环阿贝尔群的元素奇偶，二次剩余和偶置换在他们对应母群都是指数为2的子群。这又让我想到高斯对于正十七边形可作图的证明也是引用指数2的子群，其由Galois theory对应于度数为2的域扩张。过两天，我又学到了Gauss lemma，就是, 为大于的元素的数量。证明思路很直接，将的大于的元素负掉，可和其他元素从新凑成. Eisenstein对该定理的证明，我以前知道其存在但没看懂的，引用类似于Gauss lemma的引理，思路及证明策略抓住，这次却清晰了然。二次互反律的美妙我之前无法欣赏，记得对此定理有过一种稀奇古怪，难以思议之感，是没有抓住并且悟觉它的美妙的对称结构。想起在Eisenstein的证明中，画了一个乘的格子，将-1的次数示为格子的下左象限所有的点数，此为的来源。
I noticed that
In the difference on the RHS, it is apparent that terms without or will vanish. Thus, all the negative terms which are not cancelled out have a and all such positive terms have a . Combinatorially, all terms of degree with can be generated by multiplying on all terms of degree . Analogous holds for the positive terms. The terms with only and are cancelled out with the exception of the that remains.
This recurrence appears in calculation of the determinant of the Vandermonde matrix.
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…
Readers of my blog might recall my post titled The Chosen People. I’ve had the privilege to have had some fruitful and stimulating discussions with a friend of mine who was raised Christian on this matter. Such reminds me of Bobby Fischer, and I had just found my way to this, which has a transcript of some of Fischer’s antisemitic remarks. I was also reminded of sayings of a CCTV reporter along the same lines. When I was a child, I enjoyed watching the kids show Arthur. Particularly memorable was this rich girl Muffy Crosswire. I remember particularly vividly this clip, where when that girl’s psychopath auto CEO daddy turned on the speaker that exposed the dealings within the “strategy room,” it was like: so what if the engine falls out, once they’re off the lot, it’s their problem! Hmm, maybe that’s why American cars couldn’t compete with Japanese ones, because there were such people in executive management at Ford and General Motors? Also, there was the special Christmas episode of Authur, from which I learned that Muffy is the Gentile while her bestie Francine, the poor daughter of garbage man, is the Jew. Given how so a high percentage of the Russian oligarch robber barons are Jewish as are so many of the financiers and media moguls in America, aren’t the roles a bit reversed? Now, given that, would Marc Brown have had difficulties in his career had the portrayal been more in phase with the statistical reality? On this group that is the subject matter of the blog post, I have also heard people say in private things in the likes of: it’s always they win others lose, that’s why nobody likes them. And they’re basically doing to the Palestinians what the Nazis did to them!
The Jews are a very unique group. They seem to take almost exclusively jobs in the intellectual class. You see very few in the low end menial jobs. Now that is a natural consequence of their high average IQ over 115ish. This naturally breeds resentment. People love to say how now Asians are the new Jews, but keep in mind there most Chinese do menial labor for living, especially in China. Even in the US, many of them work at restaurants and laundromats and such and they are very socially disjoint with the Chinese intellectual class, the ones who work for Microsoft or profess at universities. Also, there are almost no Chinese in positions of power in the US right now. We all know that ruling classes of virtually all cultures are scumbags in one way or another. However, I would say that some are more benign than others. Remember that during the Cultural Revolution in China, children of the communist elite were actually forced to go work in the countryside to get a taste of what the majority of working class people go through on a daily basis, and many of the current leaders of China are in that category. Steve Hsu has pointed out a possible lower prevalence of psychopaths among those of East Asian descent as a partial explanation to the dearth of East Asians in “leadership” positions in America. There is also the (very politically incorrect theory) that the Holocaust wiped out the weaker and nicer portion of the Jewish population that further contributes to the phenomenon here described. Now we all know that people who are too smart for their own good are a root of resentment but those people are quite benign and contribute much to our culture and are responsible for the radical scientific and technological advances which enrich (hopefully) people’s lives. However, there is more cause for hate when you have a group of parasites who do no menial labor and hoard the wealth created by the blood and sweat of working masses for themselves and even feel entitled to do so.
I have not much more to say at this moment on this matter. You, the reader, be the judge.
A friend of mine (white American, not Jewish) sent me this photo:
I never would have expected anything like this. A compilation of the rulers of the major media outlets in America, with a classification of their background, with Jewish as one of them. We all know that Jews in many racial classifications are not in their separate group, as they are considered white.
It reminds me of a guy who worked for Xinhua News Agency who switched to a technical field when he came to America, in particular a remark of him. Remember back a few years, the whole Jimmy Kimmel kill all Chinese episode? On that, he commented: in America, a TV host says “kill all Chinese,” and it’s like a joke. Just imagine if someone said that about the Jews. Of course, that would never happen because Jews control the media outlets in America. Now this is something that many people know is 100% true, but which our suffocating atmosphere of PC prevents us from talking about.
Now my question is how Jews managed to politic their way to such a position. Yes, we all know that they are very verbally and culturally gifted (they dominate film as well), but that can’t explain it all. There must be other major factors in play here.
Green in that diagram is for “goy”. With the murky resolution, I initially saw that as “gay”. Now that’s another minority group known to have been shunned, persecuted, historically that produces many a creative genius. Kolmogorov? Alan Turing? Robert MacPherson? But no, it refers to the complement of Semite minus non-white in this diagram, in other words, the white and non-Jewish. Check out this.
What I am bringing up here could not be more consequential. What people do is a function of what resides in one’s mind, which is influenced or even controlled in some cases by the cultural environment, by the information one accesses. Now, most people aren’t like me. Most people don’t have the awareness of their possibly being brainwashed that I do that leads them to learn foreign languages and contact alternative perspectives on matters. Most people don’t have the rigorous, critical mindset that brings them to question conventional modes of thought and taboos imposed by social and cultural norms. Most people don’t realize that information is often fed out of narrow self-interest of those who control it so that the people they rule can be controlled, so that they can worry less about the risk of being overthrown.
The US brought down the Soviet Union with ideas. It could not through military means. With economics, it is also tough. But it could by penetrating and influencing the elites and the masses with dangerous liberal ideology, or whatever one phrases it as, so that idiots like Gorbachev and Yeltsin may come to power there. That’s how powerful propaganda is. War is largely cultural. You win by winning someone’s heart.
Now, I’ve seen a girl born in Russia but raised in the US who actually believes that it was America who defeated Nazi Germany. That’s how successful America has been at brainwashing. As brilliant as Russians are technically, a bulk of the best of them are now in America working for the profit of American capitalists who are fundamentally at odds with them. This just goes to show how important cultural preservation and political organization are.
Kong Qingdong has noted that the West still controls international debate, and on that, perhaps the GFC is a form of self-protectionism? 扬长避短 (play up one’s strengths and down one’s weaknesses), as the Chinese would say. The Chinese communists did that in combat to great success. In China, I have seen many emphasize the importance of winning China’s international voice, as Chinese culture is still grossly misunderstood and misrepresented outside China, to the extent that even most Chinese kids reared in America learn a pseudo version of it. It should be obvious that there is another world on the other side of the curtain that one needs to learn a notoriously difficult foreign language in order to access. The gap here is no longer physical, with the internet. It is mental.
I’ll conclude by encouraging my readers to be more reflective and cognizant of the grasp one’s cultural environment has on oneself. You are not liberated until you tear its fetters away!
想起，我有一次观大美国数学家Robert MacPherson的采访，在此，他说在五十年代末六十年代初时，美国主流的教育哲学认为学（比如微积分）过早不良由此必导后正式学闲无聊，及他父母也如此认为。当然，他将此形容为”terrible educational theory”。其与苏联的恰恰相反，在苏联他们是鼓励在各种方面有超常天分的人从小纯粹追求卓越的发挥发展自己，并且政府公家会给这些人提供更多的教育及培养资源。想更细的了解他们怎么做的，可以看看Masha Gessen写的Perfect Rigor，是讲解决庞家来猜想的怪才Perelman，里面可预料有描述当时苏联高中数学尖子之圈的组织及文化。回到美国，真难以想象美国在冷战时期尽然有如此之愚昧的无科学根据的教育思想嵌入主流。
我自己是承受了十二年美国的垃圾公立教育，在一个普通的美国学校，与一些普通的美国孩子。老师实在太差，学生也笨得要命，我也是，只不过在某些地方没有像其他人那么差。美国老愿意指责某些别的国家没有言论自由，竟是政府的propaganda，但是在我眼里在教育洗脑，很难比美国做得更严重，美国教政治教历史是极端的不客观，忽略一切不符合美国统治阶级意识形态的，是建立在无知的基础之上。老师将荒唐讹谬熏陶在无辜单纯的孩子上，所以美国人长大了好多却认为希特勒是美国打败的。在数理化，美国学校不要求学生做证明题，所以美国人的严谨思维能力那么差，我都看到在美国技术公司当官的美国人愚昧到不记圆的面积公式，何况对诸如此类有任何理解。好多老师讲的这些我还都相信了，比如我的四年级老师说三角形内角度之和为一百八十，因为数学家每次以量角器测量所画的“稍有特殊的”三角依然会得一百八十。九年级，我们在历史和英语课，读的都是像Ayn Rand和Solzhenitsyn这样的人的作品，有明显的政治偏见。在这种环境之下，基本百分之百的中国孩子会对中国文化有极其稀奇古怪的眼观。孔庆东说过，现在主要战场是文化战场而在此，中国一大片土地都已经被占领了！因为我这个人智商比较高，不太受制于环境及社会压力的影响，所以我慢慢悟觉到，通过阅读网上的许多中文资料及客观的非畅销的英文资料，才晓得美国是如此之大的一个骗局。我这种人是不那么容易上当的，可惜，如我一般的人过少。我想强调，中国有墙，是，美国也有，它的墙是教育及文化自然导致的对外的不接受加上复杂的政治正确文化，达到人曰男女在理工科能力不平等都会遭到冲击，看看Larry Summers就知道了。对于某些体制，美国主流媒体也是扯淡回避，所以他们对中国的预测基本上都是错的。
I have always had a fascination with Jews as a group. They are after all this super high achieving, creative ultra minority group that accounts for like 25% of the people at the top of various disciplines. Most notable are mathematics and physics. In math, you have von Neumann, Grothendieck, Paul Cohen, etc. In physics, the list is even longer: Einstein, Feynman, Gellman, Landau, Teller, too many to name. And these are the brainiest fields. But also, Jews excel at the highest levels in literature and music and in softer sciences. Marx, Freud, Chomsky, etc. They also excel in finance, law, and entrepreneurship. Look at the founders of some of the important SV firms and the top Wall Street hedge funds. This is rather universal. Even in the Soviet Union, some of the most prominent musicians and film producers were Jewish. Sergei Eisenstein, Iosif Kobzon. And many of the most infamous Russian oligarchs are Jewish too. In that realm, comes to mind Roman Abramovich, that guy who, in addition to marrying a trophy wife, bought the world’s best soccer team!
People use IQ as an explanation. Jews as a group, as we all know, have a very high median IQ (with extra advantage at verbal), and we all know what effect such has on the far tail (assuming same sigma (even there, Jews may be higher)). But could IQ alone account for most of such disproportionate achievement? A highly talented math PhD of Jewish origin has hypothesized (and communicated such directly to me) that Jews, aside from cultural and socioeconomic advantages, have higher aesthetic discernment, which enables them to be more creative. We all know that in science and the arts, horsepower is important, but there is also the taste and vision aspect.
I know some Jews, some of whom have lived in Israel, and I enjoy talking with them enormously. One of them I consider far smarter than I am. On the other hand, one of them, who is quite deficient academically and spouts a lot of nonsense, I have a rather low opinion of. He once sent me photos of military hardware that China bought and cloned from Israel to express to me how uncreative Chinese people are. I had already know, from talking with people in China, that China imported some cutting edge military technology from Israel, especially in the 80s. Earlier today, I glanced through the page on the Six Day War, the one in which Israel decisively defeated Arab countries that the Soviet Union had supported during the Cold War. It further reinforced my impression of how formidable the Israeli military is. I know that they have nuclear weapons, and are widely believed to possess thermonuclear ones as well, which they are very confident work despite not having tested them. A guy I talk to, who is doing a PhD in string theory at a top school, of very neutral Indian origin, however, says that they didn’t develop them on their own. (In contrast, it is almost universally accepted that China developed those independently in the 60s after the Soviet experts left.) To my great surprise, Gwydion Madawc Williams, who is highly knowledgeable about history and politics in an objective way, has publicized his doubts as to whether Israel would even survive in the long run. That seems to me quite far-fetched. Even though the demographics, and perhaps even public opinion, is against them, they are too competent and powerful (with weapons of mass destruction) not to survive. I may be wrong though in that judgement, with my near total lack of knowledge at the detailed level.
Yes, I know almost nothing about Jewish culture or even about Israel. I recall learning about it in my bull shit history class senior year of high school, which had the Israeli-Palestinian conflict as one of its major units. I know who Herzl was, what the Balfour Declaration was, and other such commonly known facts. However, how could a 17 year old possibly understand something like that in any deep, non-trivial way? Maybe in my spare time, I can actually accumulate all that requisite knowledge of biblical history as well as of the modern one. And learn some Hebrew too. If only I had the intellectual horsepower to devour that alongside Chinese language and history, which is already boundless enough. In spite of the great degree of my lack of JvN, I’ll do what I can. I could at least do better than all those Jews I’ve talked to who’ve said completely ridiculous things about Chinese culture and history to me. Jewish culture is little known and misunderstood outside those who practice it, but Chinese culture is far more so, with China having been traditionally isolated from and developed almost entirely independently of the West, alongside the freeze in relations with America following the Korean War that lasted for 20 years, the legacy of which is still ubiquitous today in America, around which global culture revolves. Though I grew up almost entirely in America, someone as intelligent as I am inevitably realized over time that the American or Western portrayal of Chinese culture, both the traditional one, and the PRC one, is more or less nonsense, and factually inaccurate in many ways. To de-brainwash myself on that one, I did what any reasonable person would do: read a ton of Chinese online, learning it in the process.
I’ll conclude by writing that as far as I see it, Jewish intellectual supremacy is hard to deny. As a group, Jews really do seem to produce a lion’s share of the geniuses, and by genius, I mean one who radically changes a field, who produces revolutionary work, as opposed to one who merely becomes professor at first rate university. It won’t be a surprise if this persists for quite a while, perhaps through the 21st century. People love to talk about now how in the young generation, it is the East Asian students who are outperforming, with their domination now of the IMO and Putnam contests, and other olympiads, as well as their increasing population in hard STEM departments in universities. There is still however some doubt on their ability to create new fields, to alter the face of science, as there is the widespread belief that East Asians are not as creative. Though I definitely cannot say with confidence, at this point, that Jewish ultra intellectual elite can be matched, I do think the aforementioned hypothesis regarding East Asians is rather overblown. I’ll explain why in the next paragraph.
First of all, I’ve come to realize that Japan has been producing ceiling creative people at a very high rate since they’ve been a developed country. This is true for mathematics, for physics, for engineering, for video games, for anime. That Jewish math PhD cited earlier in this post feels the same. Their high performance in science is evident from the plethora of Japanese names at the apex of various scientific fields who created their own directions which turned out to be extremely important and fundamental. In theoretical fields, Yoichiro Nambu, Hideki Yukawa, Goro Shimura, Kiyoshi Ito, Kenkichi Iwasawa, too many to name. Japanese have won a lion’s share of Nobel Prizes in the 21st century. Given such, it’s ironic that Satoshi Kanazawa wrote that Asians can’t think. People then will point to China and its underperformance. For that, one needs to keep in mind that China did not begin rapid modernization until the 1950s, whereas Japan was already more or less an advanced country during WWII. The high level of poverty, the great need for applied work, which diverted many of the smartest people away from pure science, and political movements such as the Cultural Revolution that substantially disrupted pure research all contributed to this. China following the reforms had many of its best and brightest go to American PhD programs, with most of them not returning, many of them eventually becoming professors in good or top American universities. It seems like that that cohort of mainland Chinese in America did exceedingly well, many becoming quite distinguished. As for conformism, if one knows the slightest about 20th century Chinese revolutionary culture and history, it will be apparent that Chinese are plenty non-conformist. That way smarter than me guy with Jewish blood, who I talk to regularly, once said that Jews produce the greatest extremes in virtually every direction, from Benjamin Netanyahu to Norman Finkelstein, from Garry Kasparov to Bobby Fischer, which I could not disagree with. As I learned more about 20th century Chinese history and culture though, I feel like Chinese are plenty crazy too. Politically, there is the very original culture and political system created by the Chinese communists, and on the other direction, you have liberal anti-communists like Fang Lizhi as well as Liu Xiaobo and other Tiananmen Square liberals who are now saying crazy things in America in the likes of Kasparov and Fischer. The Chinese communists developed one of a kind methods of warfare that proved to be highly successful, that enabled them ultimately to fight successfully against the most powerful country in the world, proving Chinese military ability in the modern era for the first time. However, due to cultural and linguistic isolation, coupled with political bias from the West, this is little known by the rest of world.
I’ll conclude by saying that all of this, on Jews, on East Asians, is rather consistent with theories derived from psychometrics. Psychometrics would predict, based on their higher base IQs, that those two groups would be vastly overrepresented within the intellectual elite, as they are. And it also seems to me that higher IQ really does make people more likely to be non-conformist and extreme, not only intellectually but also politically. Genius and madness go together.
I will say pretty bluntly that I am the type of person who reveres most genius, theoretical genius in the brainiest disciplines, like math and theoretical physics and the likes. They are much more worth idolizing than people who obtain great success in other ways, such as through entrepreneurship. After all, mathematics represents in some sense the pinnacle of human civilization, the peak of human intelligence. Every civilization worth talking about developed seemingly effortlessly crafts, music, literature, engineering (of the non-modern kind), but it took so long for us humans to discover those fundamental theoretical truths. The pioneering of the axiomatic method, which planted the seed for modern science, of the Greeks, is in many ways as significant and as epoch-making in the long run of history as the controlled use of fire or invention of written language. This was something other great civilizations did not develop. The Chinese, for instance, as remarkable as they were in the practical arena, did not develop mathematics of that nature, and scholars in the area are more or less in consensus that such was why modern science could not spring in China as it had done in the West. It is worth noting that Euclid’s Elements was translated to Chinese jointly by Jesuit Matteo Ricci and Chinese scholar Xu Guangqi in the early 17th century, but it did not have the impact on Chinese thinkers and scholars that it should have had.
In virtually every nation, students who study math and theoretical physics are commonly seen as the smartest. Those are the fields that are widely seen as only for the geniuses. They are abstract in a way that many if not most people who excel in more practical, concrete disciplines, such as engineering, cannot handle. For instance, I’ve seen many computer science students struggle with the delta epsilon definition of limit, despite trying very hard and having had it explained to them by people who understand the subject matter well. From this, one can only hypothesize the high cognitive threshold associated. There must be something about their brain structure that renders it impossible or at least very difficult for those people to form the mental process for accurately understanding that abstract definition.
There is hard science, where there are 100% objectively correct answers, and there are softer sciences, where there is a lot of bull shit and much subjective judgement involved, and lots of people things and politics involved. I’d put computer science unambiguously in the latter category, especially the software engineering side of it. Computer science, as far as I see it, is a very marketing driven field. It is not a hard engineering. It is not making a chemical plant or sending a satellite into space where there is essentially no human component involved. Needless to say, software is much easier to get right than hardware. Just about any country can make a decent search engine (if they buy the hardware), but very few nations can make a decent CPU. In this respect, America is far far ahead, with Intel, AMD, Nvidia. Making a CPU requires learning not only of the VLSI but also mastery of the fabrication process, which has some pretty cutting edge applied physics. (Okay, I know nothing about that, just saying what seems to be true to me.)
It is rather odd that people, or the mass media, associate “innovation” and “technology” so much with these soft engineering companies, those who make products for regular end users. Google, Microsoft, Facebook. I recall this guy with a PhD in solid mechanics, who later did compiler development’s saying that EE is so much harder than software engineering but pays less for economic reasons. In contrast, Facebook is just a website, but it makes so much money! It is quite obvious (or at least it should be) that most of the most cutting edge technology is firstly developed for or by the military, and military use generally precedes civilian use.
It does appear though that nowadays the smartest people are staying away from the hard technology and science because there’s no money in that. They’d rather do some bull shit work at a SV firm or work in finance because it pays. In hard STEM, there are so many high IQ immigrants from China, Eastern Europe, India, driving down wages. Some of those people are so brilliant and intellectually powerful and know it all that it’s hard to imagine competing with them. This I find to be quite a pity, because in the ideal society the smartest people should be working on the hardest problems.
People who are into real STEM are a very small minority. They ignore those in SV tech who don’t know a thing about real math and science for instance. Yes, there are people in software engineering or computer science who don’t know what an eigenvalue is or what divergence or curl are. Many of the people in that field are more interested in the latest app and the latest IPO than in actual science and technology. This is especially so in the US, where the math and science education is quite dismal, and where the society is very money driven. It didn’t take me that long to realize that the undergraduate requirements are quite a joke. Students, who come in with minimal knowledge of math, physics, chemistry, take general courses for two years and major courses for the final two years. In contrast, education in Eastern Europe is 5 years and the students there take general STEM their first few years and specialized courses after that, and when they graduate they’re already at a very high level. Of course, at the top US undergraduate programs, the students are much better, and some extremely good, but even there, many of them are ill-prepared.
I really dislike marketing and faking it, though I see the need for it. There are some things that are simply impossible to fake, and the more you try to do so, the more pathetic you will seem. Nassim Taleb once said that it’s easier to buy and sell than to fry an egg. Steve Hsu has also said, in response to a comment on charity and service to the community with regard to college admissions, that one can fake that by volunteering in soup kitchens but on the other hand, one can’t fake the SAT or fake math contests. Richard Feynman once said that nature cannot be fooled. I myself look down on those who insist on denying what is objectively true. When one does that, it’s impossible to argue with him, and one should just let history prove him wrong and make a farce out of him. In Chinese, one can say that 事实胜于雄辩, which means that [objective] reality triumphs over oratory.
Since truth cannot be indefinitely hidden, let us strive for a culture of honesty and openness. Let us create a society where such is the norm, where one can speak the truth without fear of repercussions. Only then will we have genuine free speech, not the pseudo one granted to us by the constitution.
A friend pinged me this on Facebook. I decided to look at it to exercise my technical chops. Well, the value of the denominator is given by the hint. In the sum of the first triangular numbers, is summed times, and the number of ways to split items in a line and pick one on each side of the split is the same as the number of ways to select items from , with the middle one representing the split point. Finally do a partial fractions to telescope. You’ll get .
The canonical definition of compactness of a topological space is every open cover has finite sub-cover. We can via contraposition translate this to every family of open sets with no finite subfamily that covers is not a cover. Not a cover via de Morgan’s laws can be characterized equivalently as has complements (which are all closed sets) which have finite intersection. The product is:
A topological space is compact iff for every family of closed sets with the finite intersection property, the intersection of that family is non-empty.