Who Should be Doing Mathematics?

Let me begin with the following declaration: “Not anyone can do mathematics” or “Mathematics is not for everybody.” Who should be doing mathematics then? Some people might say smart people. Being smart is certainly helpful to do mathematics. Someone being smart is a necessary condition to be a mathematician but not a sufficient condition. In other words, being smart does not necessarily mean that one can be a mathematician. As seen from math’s many difficult problems that have haunted the smartest mathematicians, one can’t be too smart in the world of mathematics. The awe-striking depth and difficulty of mathematics make any smart person who studies it humble. But then such depth and difficulty are also the reasons that make mathematics so attractive to people who love doing mathematics. Yes, to love doing mathematics is the first and the foremost qualification to be a mathematician. You may not be so smart but you can still be a mathematician as long as you love doing mathematics. You may be slower than some of others but you can eventually encounter a glimpse of the true beauty of Mother Nature if you are patient and persistent. Being a mathematician is comparable to being an artist. Being a mathematician means that you are just fascinated with the beauty of Mother Nature, even a glimpse of it, and you have insatiable desire to quest after the hidden beautiful structures of Mother Nature.

If you wonder what mathematics is useful for, what the purpose of doing mathematics is, or why one must do mathematics, while they are quite legitimate questions by laypeople, you are already disqualified to be a mathematician. Mathematics is really for people who love doing it not because it is useful but because it is beautiful.

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Lenny Susskind’s Humour

I stumbled upon one of Lenny Susskind’s old arXiv papers titled “Rebuttal to a Paper on Wormholes“. In the abstract, he wrote a pretty harsh criticism on another arXiv paper by saying “the author of that paper demonstrated that he didn’t know what he was talking about. In this paper I correct the author’s naive erroneous misconceptions.” I was thinking whoever wrote the other paper must have been stunned and discouraged a lot considering Susskind being a pretty big guy in physics community. It turns out that the author of the other paper is Susskind himself! So after all, it was a harsh self-criticism:). In the other paper, he argued that time travel using a traversable wormhole is not likely possible because (he thought) it would violate two fundamental principles of physics. Apparently, he changed his mind in his rebuttal to himself. It’s funny.

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One cannot fight physics and math

The other day I was reading a blog article by Andrei Martyanov and he said in there: “One cannot fight physics and math, it’s impossible.” The article was not about math or physics and he is neither a mathematician nor a physicist, but what he said rings so true to me. I think it should be a guiding principle for mathematicians and physicists. I would add one more to that though: Occam’s razor. When stumble upon a seemingly improbable or inexplicable phenomenon, even some serious scientists often accept a possibility of answers, such as God, outside the realm of science. Pythagoras did it with the existence of irrational numbers. While examining his famous so-called Pythagoras theorem regarding right triangles, he evidently discovered the number $\sqrt{2}$ which is the hypotenuse of the right triangle with both the lengths of base and height equal to 1. (At that time Greeks believed that there are only rational numbers because they are beautiful as rightful creation of God.) After failing many attempts to write the weird (no not really) number as a rational number, Pythagoras finally has given it up and told his pupils that God made a mistake and ordered them not to reveal this to anyone outside of his school. (Anyone who disobey this would’ve been killed.) It turns out God (metaphorically speaking) created way more irrational numbers than rational numbers. Apparently, the notion of beauty for God was different from that for Greeks. Newton did it also with precession of the perihelion of Mercury. When Newton realized that the precession of Mercury’s orbit could not be explained by his law of universal gravitation, he concluded that it is God’s domain. But he was wrong. It had nothing to do with God. Humanity just had to wait until another theory of Gravitation, Einstein’s general theory of relativity came along, which finally could nicely explain the precession of Mercury’s orbit. If Nature obeys the laws of mathematics and physics, so should any phenomenon that occurs in it. In the Chinese TV series Three-Body (adapted from the novel The Three-Body Problem by Liu Cixin), some of the elite theoretical physicists committed suicides because they were in despair over the thought that physics doesn’t exist anymore after stumbling upon improbable/inexplicable phenomena that defy the laws of physics. Those phenomena, however, turned out to have been created by a highly advanced alien civilization to dismantle Earth’s scientific community because it could pause a threat to their plan of invading Earth. (Sorry for the spoiler.) Under the pretense of this having happened in real life, if those unfortunate theoretical physicists were to stick to the guiding principle that one cannot fight physics and math, they would’ve been still alive.

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Pair of huge plasma jets spotted blasting out of gigantic black hole

The above title is the verbatim from a Guardian news article that a colleague in chemistry shared. I don’t usually read the Guardian and it is not a reliable source of science news. The article is not well-written and it is missing basic important information such as where the huge plasma jets originated from, i.e. which supermassive black hole and host galaxy. According to the article, the plasma jets are the most powerful ever observed whose streams are measured to be 23 million light years from end to end. The jets were named Porphyrion after a giant in Greek mythology.

This is not a newly observed phenomenon in the universe. Such powerful jets from the center of a galaxy have been observed for a long time and they are called quasar jets, or quasars in short. Quasars are not rare. More than a million quasars have been identified. The known closest one to Earth is a Type-1 Seyfert galaxy Markarian 231 (UGC 8085) which is located about 581 million light years away from Earth in the constellation of Ursa Major. The farthest known quasar from Earth, of course, keeps being updated as observation is being improved. For now, it is QSO J0313-1806 with oldest known supermassive black hole at $(1.6\pm 0.4)\times 10^9$ solar masses, which is in the constellation of Eridanus. So how far is it? When we talk about the distance to a really distant part of the universe, there are two different ways to measure it: one is called light travel distance and the other is called proper distance. Why is that so? That is because the universe is not static but is expanding. The light travel distance to QSO J0313-1806 from Earth is 13 billion light years. What this means is that the light from QSO J0313-1806 we see on Earth was emitted 13 billion years ago. Due to the expanding of the universe, the proper distance, i.e. the distance measured by the cosmic scale ruler (figuratively speaking) is 30 billion light years away from Earth.

The source of a quasar is not necessarily a black hole but in theory it could be a white hole (A hypothetical celestial object that spits out matters.  It is the counterpart of a black hole which sucks up whatever comes nearby, even light). Although many physicists doubt the existence of a white hole (It’s only a mathematical solution of Einstein’s field equations and there is no known physical reason or mechanism for its possible existence. Besides, even if a white hole is created, it would be very unstable and would quickly become a black hole), some physicists proposed that we may be able to observe one if there is any by searching for quasars.

Some observations indicated that the speed of a quasar jet appears to exceed the speed of light. Of course, if confirmed, it would shake up the foundation of Einstein’s special theory of relativity. So far, it is inconclusive so relativity is still safe. I bet my dime on the (inconclusive) findings being due to a measurement error or a statistical fluke like OPERA faster-than-light neutrino anomaly back in 2011 (it later was found to be a result of an equipment failure).

I recently wrote a paper which proposes a possibility of the non-existence of the faster-than-light under the assumption that the Big Bang created not just one universe but its twin brother with a different orientation. It is a preprint and I am still working on a revision requested by the reviewer. By the way, Einstein’s special theory of relativity does not actually prohibits the existence of the faster-than-light. For such as the hypothetical particles, tachyons, as long as particles are born with the initial velocity already exceeding the speed of light, their existence won’t contradict the relativity.

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Doctor Who: Terror of Autons

I was born and grew up in South Korea, and back in 1970’s not many people owned a TV. I was living in a rural area and my family was luckily one of very few families that owned a TV in that area. Our TV was an American one with brand name Zenith (which no longer exists). There were only two TV channels available, and not many programs for kids to watch. So when something like Doctor Who was aired on TV, it became one of the most exciting moments for me. I remember watching only one particular season of Doctor Who, though I am not sure if it was the only season that was aired on TV.

Recently, I found out that my cancer relapsed and I have been undergoing cancer treatments. As a typical side effect of chemotherapy, I have been struggling a lot with the so called chemo brain or brain fog, especially I am having trouble with my memory. But one day, I just remembered about that particular season of Doctor Who for no reason. Perhaps nostalgia for the old time, I decided to search for the season. The only things I remembered were Autons (back then I was pretty terrified by them), a carnival (circus), and plastic daffodils. With help of the internet, those were enough clues for me to find out the season. It was the eighth season (1971) Terror of the Autons. To my pleasant surprise, an internet search turned up free online streaming of the eighth season (all 4 parts), so I was happy to be able to watch them again. You can watch them at Dailymotion:

Doctor Who Terror of autons (1)

Doctor Who Terror of autons (2)

Doctor Who Terror of autons (3)

Doctor Who Terror of autons (4)

or at the Internet Archive.

Enjoy if you will.

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