Wednesday, June 23, 2021 ... //

Tetrahedron instantons, Magnificent Four, and the mother of all random partition models

The most interesting new hep-th arXiv paper today is the DESY-Rutgers-Beijing work

Tetrahedron Instantons
by Elli Pomoni, Yan, and Zhang. Instantons are localized configurations in the Euclidean spacetime (they are also localized in the Euclidean time, in this sense they live at an "instant", and that explains their names) and as local extrema of the path integral, they contribute to the transition amplitudes in Feynman's approach to quantum mechanics. The contribution is typically nonperturbative at small $$g$$, scaling like $$\exp(-C/g^2)$$ at least in the simplest cases.

In gauge theory, we have the simplest or "real" instantons in which the field strength is self-dual but arranged in a topologically nontrivial configuration that makes its magnitude decrease away from the center of the instanton. In string theory, there are other instantons that may be made of strings and branes, not just fields (gauge fields).

Tuesday, June 22, 2021 ... //

The Bitcoin trades around $29,000-$31,000 again (and the price dipped below $29,000 an hour ago); the Chinese ban on miners (plus the death cross) have helped a bit to drive the Bitcoin price closer towards the fair price (known as zero). It seems like a good time for some explanations why I consider the builders of the Bitcoin bubble to be a left-wing spiritual organization, not just a generic group of morons. Here are the main eight reasons. 1. Hatred for commercial banks, loans, shortsellers, diverse capitalist activities The members of the Bitcoin cult are often very open about the fact that they hate banks – commercial banks, central banks, and the activities that these vital institutions are doing. The Bitcoin cultists are standard anti-capitalist leftists who think that the banks are evil, capital is evil, lending, borrowing, and interests are evil, and shortselling is even more evil. They don't understand that all these things have played and still play an existential role in the economic progress of mankind. Their idealized Bitcoin society is just a version of the communist society where things like banks have been eliminated and banned. Monday, June 21, 2021 ... // Calculation of $$\zeta(2)$$ This post is just an irrelevant pure fun celebrating the release of MathJax 3.2.0 which replaces the version 3.1.4. The most visible improvement of the new version (which is used to make $$\rm\LaTeX$$ nice on this website) is the "lazy typesetting" which guarantees that your device doesn't waste time with printing the equations that aren't seen right now. Consequently, the typesetting becomes an order of magnitude faster; check the blog post about the Euler characteristic as an example. And it has already been fast for quite some time. Let us pick some "elementary but not quite elementary" calculation in the parts of mathematics that are important enough for a physicist. Among the few hundreds that a theoretical physicist should be able to produce when he is woke up at 3 am, let us pick the calculation of $$\zeta(2)$$ (the Greek letter is called zeta, the function is the Riemann zeta function). OK, $\zeta(2) = 1 + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \dots$ Is there a closed expression for this sum? Numerically, you may find out it is close to $$1.6449$$. Yes, most of you know that it equals $$\pi^2/6$$, pi squared over six. The very fact that the sum may be expressed in terms of the most famous transcendental number, the ratio of the circumference and the diameter of a circle, may be considered impressive by itself. But once you know a proof, or at least a proof of similar identities, you realize that $$\pi$$ is obliged to reappear and mathematical problems such as one above are solvable, integrable, or "trivial" in some sense, so a solution in terms of well-known constants has to exist. Friday, June 18, 2021 ... // Delta variant of Covid-19 strictly IS a common cold virus Since the beginning of the Covid-19 era, there has been a battle on "whether it is right to compare Covid-19 to the flu". Of course it is. It is a totally analogous disease. Because Covid-19 was really new and the world population really lacked immunity, the virus could have spread to a much higher fraction of the world population and the case fatality rate was correspondingly higher because the individuals had no defense at all. So 0.05% of mankind has died (4 million) which is still a tiny fraction. After a great majority of many nations have obtained (or are obtaining) either the natural immunity or the immunity from a vaccine, the virus is either destined to go extinct, or to mutate, establish some co-existence with the people who are (partly?) immune, and become a strict counterpart of the flu or the common cold that may regularly reappear. Taken from the article: "The fun is over. The genuine men's little cold IS a serious problem, a physician claims." Note that the "little cold of the genuine men" (chlapská rýmička) is often used by Czech women to mock men who are never seriously sick but who complain about minor diseases. However, a 2017 Canadian research showed that (similarly to Covid-19) men are more likely to have complications out of these mundane diseases. Nature discriminates against the men again. A few months ago, the Covid hysteria has mutated into a special form, the hysteria over Covid variants. Indeed, new variants have prolonged the disease and dying by two months or so (some variants were more contagious, others were partly circumventing the immunity created by older variants) but they haven't changed the big picture. What is happening now, especially in the U.K., is just amazing. And I don't mean any medical events, I mean the propaganda and policy events. Thursday, June 17, 2021 ... // Left-wing "virtue signalling" no longer consists of credible signals according to signalling theory It is us who is actually virtue signalling today! Some years ago, I have participated at and especially listened to numerous high-brow discussions about signalling theory. Several fellow Harvard Junior Fellows did this segment of general biology at the world class level so I couldn't have escaped. Richard Dawkins was among those who have participated in the discussion whether the signalling should be considered an attribute of individuals, groups, genes, or species, and many other "details". What am I talking about? Animals (and humans) communicate in various ways and they need to send the information to their prey, to predators, to potential or current sexual partners, and more. "I am great" is a very typical message that needs to be sent but some individuals may be incentivized to lie and cheat and send this "information" even when it is untrue. One of the core tenets of signaling theory is that the best and strongest (or most credible!) signals are the costliest ones. Tuesday, June 15, 2021 ... // Widespread defense of "1+1 isn't 2" means that the whole education system has collapsed Would-be fancy apologists for the woke insanity are wrong about everything Back in 2017, the following wonderful satirical minifilm was released: Danny, a boy who struggled with math, wrote that $$2+2=22$$ into a test. His old-fashioned teacher, an older woman, did everything she could to professionally teach him that $$2+2=4$$ but it was hard. Instead, the spoiled brat's wrong answer was increasingly violently defended by Danny's dumb parents, the teacher's dumb principal, activists on the street, and an Orwellian legal committee of the city hall. The plot ended with a happy end. When the teacher was fired, she got a compensation of$2 thousand for the last month plus $2 thousand for the present one. She could use the new standards to claim that the total is$22 thousand. ;-) She would be even richer with $20002000 dollars. Saturday, June 12, 2021 ... // Technical analysis only "works" as a self-fulfilling prophesy The Bitcoin price is apparently likely to exhibit the "death cross" within a week. It is a bearish sign that makes people expect a significant collapse of the Bitcoin price. If you click, you will learn that a death cross is the situation when the 50-day moving average is above the 200-day one but they are approaching one another and the "death cross" moment is when the short-term, 50-day moving average drops below the long-term, 200-day one. It tells you that "the recent prices are getting lower than the historical prices" so we're going down. The opposite situation is a "golden cross" which would be a bullish sign, a sign expected to induce an increase in the price. Is this rule correct? Does it follow from pure mathematics? From the pure laws of economics? From the laws of physics? Or is it a counterpart of astrology? Indeed, these methods are called "technical analysis" (and these astrologers – believing that you may predict the future of a graph just by seeing patterns in the past – are called "chartists") and the first paragraph of the Wikipedia page says that "many Academics consider technical analysis a pseudoscience". Well, of course, I largely endorse that group. But things are more subtle and I would be absolutely dissatisfied with a simple one-word judgement here. Friday, June 11, 2021 ... // There won't be any nontrivial Fall 2021 Covid wave in CZ, UK, most of Europe, US... I can guarantee it for you, insure you The numbers of new positive tests have been dropping in Czechia since early March and this time, it is obvious that this quasi-exponential decrease is the last one. Technically speaking, it is right to say that Czechia has enjoyed the herd immunity (towards the latest, most contagious, variants) since early March (even though the daily casualties were huge and the fraction of infected surely counted as an epidemics) because the quasi-exponential decrease has been statistically guaranteed since that moment because $$R_0\lt 1$$ was true, even with relaxed restrictions. But only these days, the number of deaths has dropped to "roughly one or two" and the herd immunity has clearly done an overwhelming fraction of its hard work. Dr Zdeněk Hostomský, the director of the Institute of Organic Chemistry and Biochemistry of the Czech Academy of Sciences (and a former boss of cancer research at Pfizer!), became the latest competent Czech scientist who has communicated the vital scientific knowledge to the media. For months, he has emphasized that the lockdown didn't work and should have been terminated. In more recent interviews and essays, he says that lives may still be saved by vaccinating the people in the risk groups (my estimate is that we would have had 40,000 casualties instead of 30,000 if there had been no vaccines; but now, only dozens of lives will be saved by new vaccinations) and it's a good idea to spend energy by persuading them. Also, he says that in the summer, there will be almost no Covid virus in Czechia because we've achieved some sort of herd immunity that will show its muscles. Thursday, June 10, 2021 ... // Why some stopped hiring Ivy League alumni Russell Ronald (R.R.) Reno III, the editor-in-chief of First Things, an intellectual Christian magazine, wrote a nice essay for the Wall Street Journal, Why I Stopped Hiring Ivy League Graduates. A decade ago, he would still consider Princeton, Harvard, and similar graduates as top candidates for a job (of writers). But it has changed. These days, some are woke; some are self-important; but more importantly, most have been stripped of role models and trained to be silent when it matters. I couldn't agree more. Wednesday, June 09, 2021 ... // M-theory on $$G_2$$ manifolds, heterotic strings, oceans, climate, and carbon This unattractive Titanic-like building will become Czechia's tallest building (135 meters) and will be built just miles from the Prague Castle, in order to make us remember that the "architect" was impressed by the climate hysteria and willing to promote the lies about the climate. Among the new hep-th papers that were released today, five mention a "string" in the abstract. I think that the following paper is the most interesting one: Non-Perturbative Heterotic Duals of M-Theory on $$G_2$$ Orbifolds It's a nice paper that could have been written during the Duality Revolution in string theory of the mid 1990s but it waited up to 2021. It is a six-or-seven-dimensional or $$G_2$$ counterpart of the statement that the $$T^4/ \ZZ_2$$ orbifold is a special case of a $$K3$$ manifold; and that the $$K3$$ manifold may degenerate into two "half-$$K3$$" manifolds that are connected by a three-toroidal throat (times a line interval with irregular ends). Tuesday, June 08, 2021 ... // The FBI may very well possess most Bitcoin private keys, other passwords in the world The U.S. and China are among countries whose governments are planning to restrict the cryptocurrency activities. On the other hand, a confederacy of 25,000 gang members known as El Salvador claimed to adopt the Bitcoin as an official currency (these criminals have been using crypto for a long time so it's not really news). Another great friend of the U.S., Iran's mullah-in-chief, has also called for the legalization of the Bitcoin (Iran and North Korea have used Bitcoin to circumvent sanctions etc., too). Meanwhile, Donald Trump said that the Bitcoin seemed like a scam – and a thing that wanted to challenge the global dominance of his preferred currency (it has a name imported from the Czech language). Meanwhile, the FBI did something cool that drove the Bitcoin price below$32k again.

Hackers have hacked and encrypted files on the Colonial Pipeline servers. The breach was harmful, oil stopped flowing, and the company has actually paid some $4 million in Bitcoin in ransom. The files were decrypted (not all extortionists are this honest!) and the oil flows were resumed. That ransom came to dozens of wallets but... the FBI conquered$2.3 million, a majority of the ransom, because it acquired the private key – the longer gibberish sequence of digits that is needed to send funds (to "sign" the electronic confirmations that the owner wants to send something) – from the largest Bitcoin wallet. How is it possible? It should be impossible (in any realistic timeframe) to calculate the (longer) private key from the publicly known data – which seems to be just the public key.