A Reply to Someone Who's Fascinated by Mathematical Questions

Another question about math is whether it is something intrinsic to nature which people have discovered, or a very useful tool which we have invented, and which we impose upon nature. I've always seen it as the latter, which diminishes, at least for me, the intrinsic interest of those other questions you mention.

Of course, I may have been entirely wrong this entire time. I have the impression that most contemporary mathematicians and physicians and zoologists and botanists would say that I'm wrong.

Nietzsche believed we invented math. See Menschliches Allzumenschliches, vol 1, section 1, "Von den ersten und letzten Dingen," paragraph 19, "Die Zahl." Mathematicians and physicists might find this passage interesting, among other reasons for the grasp of atomic theory which Nietzsche demonstrates in something he published in the late 1870's.

But many years after I first read that, it suddenly struck me, like a hammer striking a gong, that everyone knows exactly what a circle is, although none of us has ever seen a perfect circle. This very simple fact, available to anyone who thinks about it for as long as a moment, seems to me to be a very strong argument in favor of Plato's forms, and in favor in math being something we discover as opposed to something we invent.

Nietzsche despised Plato more intensely than he did any other single human being. I went through a period of very intense admiration for Nietzsche (except for his sexism and enthusiasm for war, which I always rejected), and I adopted his contempt of Plato. But my gong-moment, my insight about circles, has forced me to reconsider Plato. And when you reconsider something as influential as Platonic philosophy, you necessarily re-consider many other things.

Dream Log: Fun with Physicists

Before going to bed last night I browsed through a two-volume work: Electromagnetic Theory: A Critical Examination of Fundamentals by Alfred O'Rahilly (1884-1969), who wrote mostly in the genre of theology. Published in 1938, O'Rahilly's work on electromagnetics rejected major aspects of Maxwell's electromagnetic theory, and, as a consequence, also much of the mainstream physics which followed Maxwell, including Einstein's theory of relativity. Whether O'Rahilly altered his views on physics after 1945, when two rather large ka-booms had offered striking practical demonstration of the soundness of Einstein's formula E=mc2, I have not yet been able to determine.

So anyway, that's what I was reading before I went to sleep last night. And then I dreamed that I was hanging out in someone's living room with some contemporary physicists -- conventional ones, a dozen or so, both genders and a wide range of ages. The subject of O'Rahilly never came up. Neither did the subject of COVID-19. We did, however, talk about Newton, Maxwell, Faraday, Lorentz, Planck, Einstein, Bohr, Heisenberg, Susskind and others. To be more precise: the physicists mostly talked and I listened.

One of the physicists, a thin, grey-haired man in a worn-out sweater, was also an amateur sculptor. He had made pieces each of which was intended to combine with one of us as a temporary, partly-living sculpture. The sculptures were plastic or metal or both, some looked somewhat like molecules, others looked somewhat like abstract animals. The art show was just for us. It was great. We would each stand next to the sculpture made for us, positioned according to the physicist-sculptor's instructions, as we quoted a famous physicist of the past. I quoted Bohr. There's no way I could quote a word of Bohr from memory right now. Nor could I explain any of his ideas to you. I was not mistaken in the dream for a physicist, and every other person in the dream was quite an advanced physicist. But everyone was very friendly, and they all seemed more than glad to explain any point of physics which was unclear to me. 

After the art show, we put on coats and headed out into a wintry, snowy afternoon. There was a woods nearby, and today was supposed to be especially good for bird watching in that woods, and sure enough, we saw woodpeckers and finches and cardinals and an owl. We kept walking through the woods until we got to a university campus where a conference was underway in which some of our group were scheduled to speak.

On the other side of the woods, we had to walk across a two-lane road, and then we would be on the campus. A new car with the windows rolled down, full of young men, probably rich kids and students at this college, and probably not straight-A students, roared past while the young men inside yelled obscenities in our general direction and one of them hurled some litter at us. He missed. A young woman in our group mumbled something which I didn't hear, but everyone else in the group laughed quite heartily, so I was going to ask her to repeat it, but I woke up.

The Science-Humanities Split

Perhaps you've heard: STEM -- Science, Technology, Engineering and Mathematics -- and the humanities -- art, literature, history, music, etc -- have split apart from one another.

Perhaps you've just read the previous sentence, and asked: Whaddya talkin' about, Steve? Was there some time when science and art actually got along?

Oh yes. The time was up until the eighteenth century, and can perhaps be seen most dramatically in Western civilization -- I really don't have much of a clue about non-Western civilizations, but I'm trying to catch up -- in the example of philosophy, and of individual philosophers. Up until a few centuries ago, the leading philosophers were also the leading mathematicians and scientists, and people generally took for granted that this was so. Descartes, Spinoza, Leibniz were the leading philosophers and the leading mathematicians of their time. Newton was a leading scientist and mathematician, but he left scarcely a mark in what today is generally considered to be philosophy. The split seems to be beginning already in Newton's time. Kant, Schopenahuer, Marx, Nietzsche and the other most prominent 19th-century philosophers are not, to my knowledge, enthusiastically read today by most scientists. Bertrand Russell and Alfred North Whitehead were prominent 20th-century mathematicians and philosophers, but they were very unusual in being both at the same time. In the 21st century, Stephen Hawking and Neil deGrasse and Lawrence Krauss Tyson have said that philosophy is worthless, without causing much of an uproar among their fellow scientists, which shows you how little you can know about philosophy today and still be a brilliant scientist.

My brother, an engineer, goes probably even farther than Hawking and deGrasse Tyson and Krauss in his ignorant dismissal of philosophy -- and that's all this is: ignorance. If Hawking or deGrasse Tyson or Krauss or my brother knew very much at all about philosophy, they wouldn't say such things.

This unfortunate split, this destructive antagonism between two vital types of human endeavor is not, of course, all the fault of the scientists. Those who have objected to the dismissal philosophy by prominent scientists have included other prominent scientists. And it's certainly not as if all philosopher, artists, musicians, poets etc, have a decent appreciation of STEM. There is plenty of fault on both sides of the split.

I've tried to bring the sciences and the humanities back together, but I could've done much more. I stopped studying math in school just as soon as I was allowed to stop studying it, after completing 10th-grade geometry. I usually had the best math grades in my class -- the only exception I can remember was in 9th-grade algebra. The teacher posted a constantly-updated list of the members of the class by our current grade. I don't remember whether A was 90% and up, or 94% and up, or what exactly. I do remember that it was possible to score above 100% with extra-credit work, and that the 2 of us at the top of the list were over 100%, and that I wasn't on top. That felt very strange, not being the best math student in sight.

That 9th-grade algebra teacher, and some other math teachers I had, talked to me very excitedly about how far I would be able to go in math. They didn't realize that I didn't enjoy math at all. It was my undiagnosed autism which allowed me to make those grades without trying and without being interested.

The 9th grade was 45 years ago. Since then I've made a few feeble attempts to make more progress in math, which, it seems to me, would amount to developing an interest in and enjoyment of math. I was talking to a math teacher the other day, and he said, You have to enjoy math to go far in it.

My brother was valedictorian in high school and got 2 degrees from MIT. He enjoys math. During one of those periods when I was trying to develop an enjoyment, my brother gave me his copy of the 5th edition of Calculus and Analytic Geometry by Thomas and Finney, one of his former MIT textbooks. He's a good brother, even though he is an appalling philistine when it comes to the arts.

Pages 355 through 362 of this book are missing. Did my brother remove these pages before giving me the book? Are there things on pages 355 to 362 which, my brother decided, must remain hidden from librul artistic types such as me?

I still haven't made that big breakthrough, to where I enjoy math. Although, in the past year or so, chess, mildly interesting to me already for decades, has become much more interesting, and a large part of chess, or maybe all of it, is math. (Well, no, not all of it. There's also psychology in sizing up one's opponent.)

And when people like Melvin Schwarz -- co-recipient of the 1988 Nobel Prize in Physics -- are writing about things like vectors, I actually understand part of it. So, hey, lookit that, I actually have learned some calculus! Schwarz also writes things like: "Electromagnetic theory is beautiful!" And I believe him even thought I still don't understand it.


And I still want to understand. So that I can enjoy math at last, and for many other reasons.

Who knows: maybe, if I understand things like advanced physics, I'll become much better at helping people like Neil deGrasse Tyson appreciate things like existentialism.

Dream Log: Physics and Disapproval

I dreamed that my brother was living with some fanatical Christians. They may have been his father- and mother-in-law, but I don't remember meeting his bride. Their home, a large apartment on a high floor of a drab brick building among high drab brick buildings, had the look of guilty religious conformity. Even the benches on either side of one long narrow table looked like church pews.

I had brought with me an armload of books, mostly books on topics of physics and math published by Dover, such as this one:

My brother had some Dover books on related topics, and he seemed to deliberately be mixing up his Dover books with mine. I kept trying to separate them again, and I asked myself in vain why I had brought so many books with me to begin with. It wasn't as if I was going to teach my brother anything about such things. He's an accomplished mechanical engineer, his knowledge of physics and advanced math is far ahead of mine. And I also wasn't intending to give him any of the books or loan any of them to him. And I felt sure that my brother knew all of this. I wondered whether he was teasing me by mixing up his books with mine.

I scrambled around, trying to make sure that I had all of my books and none of my brother's, getting ready to flee this place. I asked myself why I hadn't carried the books in a backpack, or at least in a box: there were too many of them to comfortably carry in my arms.

My brother's mother-in-law (I presumed) was darting around and loudly disapproving of me and my scientific outlook. Then she spotted, among my books, this one --

-- which may well have been the only book ever written by a communist, small- or capital-c, whose title or author she would've recognized -- and she became louder and more agitated still, screeching, "He's communistic! He's communistic!"

For a moment I thought of correcting her, telling her that the correct adjective was "communist," or, even better, she could use the noun form and say that I was a communist. But immediately I asked myself what good that could do. It was about then that I woke up.

Am I Finally Developing An Interest In Math?

I've always been freakishly good at doing arithmetic in my head. Not quite as good as Rain Man, but definitely unusual. However, I've never found mathematics to be interesting. I wonder whether that's an unusual combination of aptitude and disinterest. I stopped taking math classes in high school as soon as I was allowed to, at the end of 10th grade, when the algebra and geometry courses I had completed met the minimum requirements for graduation.

My younger brother took more advanced math courses. Much more advanced. My brother is literally a rocket scientist. He's got a Bachelor's and Master's of Science from MIT. As an undergrad he had a summer internship working for Martin Marietta and NASA on the Space Shuttle. Then between the Bachelor's and the Master's he took two years off from school and worked for a private company which has sent all sorts of things into orbit. A genuine rocket scientist. We're very proud of the little genius.

Every couple of years, I get an urge to study some more advanced math, and engineering and physics. The urge usually passes very quickly, but then again, it keeps coming back. About 30 years ago I had the urge, and my brother gave me this:

It's the 5th edition of Calculus and Analytic Geometry by George B Thomas and Ross L Finney, both professors at MIT when the 5th edition was published in 1979. It was a worn-out copy, my brother was done with it. I don't know whether he had studied this book in high school in preparation for MIT, or if it was the textbook for a freshman class he took at MIT, or maybe both.

I still have that old worn copy of the Thomas/Finney that my brother gave me. But I still haven't looked at it much. I'm currently having another one of those urges to make myself interested in math. But that's just the problem: math remains excruciatingly boring to me. But now I've been looking at that textbook, paging through it. And also looking at other books such as Blatt and Weisskopf's Theoretical Nuclear Physics, Rojensky's Electromagnetic Fields and Waves and Tolstov's Fourier Series. Looking for something which I can honestly say that I find interesting.

I may have found something. Thomas and Finney may have been rather sly when it came to education. There are a lot of word problems for the students to solve in their textbook, problems demonstrating some applications of calculus and analytic geometry, and one of those problems has actually caught my attention. That's right: something in a math book has begun to interest me.

I can't find that problem right now. I think it's somewhere in the first 50 pages or so of this textbook which runs to well over 900 pages. And it's a collage freshman textbook. Freshmen at MIT, which is certainly not the same thing as freshmen everywhere, but still. Early on in a freshman math textbook, there was a problem which I don't know how to solve.

Yes, it was arrogant of me, but I had wondered whether, in addition to boring me, this textbook would also teach me anything, or not. Arrogant, yes. But, for example, I was factoring 3-digit numbers in my head as a small child, years before a math teacher introduced me to the term "factor." Without finding it interesting. Just because it was there in my head.

But somewhere toward the front of Thomas/Finney 5th ed is a problem which, reconstructed from memory, goes something like this: a person of height X is walking at speed Y directly toward a streetlamp of height Z. Determine the rate at which the length of X's shadow decreases.

I can't do that. But apparently the first chapter or two of this textbook will show me how to do it. (Assuming I'm smart enough to understand what the book says.)

And that is interesting. That is definitely an example of something this textbook could teach me. And, apparently, that's just the beginning of introductory calculus. Just scratching the surface.

That's pretty cool.

So, you realize what this means, right? That's right: I'm going to be the first person to win a Nobel Prize in Literature and another one in Physics, plus a Fields Medal.

Thought-Experiment About Science, Technology, Engineering, Medicine And Hollywood

If Einstein, Planck, Bohr and other prominent physicists had make a concerted effort, around, say, 1920, to warn against the dangers of using radioactive materials in research, and had succeeded in keeping such research very small-scale and protective measures at a very high level, would they have succeeded in effectively banning nuclear power and weapons 20 years before they were developed, simply because things like radium and uranium and plutonium were consistently treated like exactly what they are: extremely dangerous things which should be kept as far from people as possible? At the very least, they might've lengthened Marie Curie's life a little bit, and who knows to how many beneficial scientific breakthroughs that alone might have led? And she's only the most famous of many physicists who killed themselves with radioactivity.

And if this had happened, would there have been fewer of those dopey movies made whose message, in a nutshell, is: Oh noes! Cutting-edge science and technology is leading directly to an apocalypse which will eradicate all of mankind, helphelphelp they're gonna kill us all?

You say you hadn't noticed such anti-STEM fearmongering in Hollywood? Well, sometimes it's hard to see the forest for the trees. Take a stroll with me through time: remember 1995? People were starting to get excited about the Internet. Remember the 1995 movie The Net, with Sandra Bullock and Dennis Miller? Sweet Sandra's life is threatened by one swarm of evil people after another -- all because she works on the (duh-duh-DUHHHHH!) Internet. Remember 2001's Swordfish, with convicted hacker Hugh Jackman forced by extremely-dangerous John Travolta and completely-topless Halle Berry, tempted by evil, evil cutting-edge equipment to participate in extreme violence via the (duh-duh-DUHHHHH!) Internet? Like many other movies, Swordfish is notable for unintentionally-hilarious depictions of how non-experts imagine that cutting-edge technology works. Movies about computers tend to age very badly.

Remember what genetic modification led to in The Fly and the Jurassic Park movies? Not to mention almost every single Frankenstein movie? Young Frankenstein ends pretty nicely. It's the only exception which occurs to me at the moment. Can you name one other Hollywood movie in which genetic engineering leads to anything other than pure horror? ("How could you have been so blind as not to see that playing God would end up killing us all?! Oh, damn you, damn you, you fool!")

Or artificial intelligence in 2001: A Space Odyssey, the Terminator movies, the Matrix movies, or, to take a more recent example which may or may not prove to be as memorable, Transcendence, released in 2014, starring Johnny Depp, Rebecca Hall, Cillian Murphy and Morgan Freeman, which has both the hilariously non-realistic computer stuff and the horrifying apocalypse as the inevitable result of AI? ("Oh, how could you have been so blind?! How could you not have seen that the attempt to make a computer brain could only lead to huge massacres?!" That's not a direct quote from the script of Transcendence but it's pretty damn close.) You beginning to see the trend I'm talking about?

You beginning to understand how vaccination could be so unpopular in Hollywood because so many people there don't understand STEM (that's Science, Technology, Engineering and Medicine) [PS, 1 July 2017: Actually, STEM stands for Science, Technology, Engineering, and Mathematics. Whoops!] and have an uninformed fear and loathing of it?

I agree, unreservedly, that nuclear energy and nuclear bombs are very, very bad things, and that it's only natural that they would lead to an association of STEM and disaster in many minds. But things could have been very different. Scientists themselves could have prevented that nuclear power plants and nuclear bombs ever came to be, and if they had acted early enough, that prevention could have been relatively easy. There's nothing intrinsic about physics which had to lead straight to nukes.

And the fact that those bombs and plants did come to be has had a tremendous effect on the way that people in STEM research work. But that's one of the things you don't know if you don't know very much about STEM besides what you see in movies.

History of the World, Condensed Version, Part I, Clearly Hampered By My Having Studied Mostly Just Western Civ.

About 15 billion years ago, something very small and heavy, containing everything in the universe of which we know, exploded and became very big and hot and gassy. Gravity occurred somehow, or had already been there, or is an aspect or manifestion of the universe being curved, I don't know. Anyhow, hot gas eventually settled into balls, and one of these hot gas balls is our sun, and the Earth was a gas ball orbiting the Sun, and it cooled to the point where it became partly solid, and the Moon started orbiting the earth by mistake, it seems, because generally moons are much smaller proportion to their planets. See Stephen Hawking, A Brief History of Time, and Brian Greene, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, or better yet, ask an actual scientist for tips for further reading.

Water appeared, then single-celled organisms. These eventually became more complex and differentiated into plants and animals. Richard Dawkins in The Ancestor's Tale: A Pilgrimage to the Dawn of Life tells us when certain species appeared, all of which are ancestors of us humans, hence the book's title. Did you know we're descended from lungfish? They were around 417 million years ago!

Yeah, I'm pretty clueless about such things. I refer you to Dawkins and Darwin, The Origin Of Species.

Darwin referred to the "struggle for existence. The geologist McCandles in William Gaddis' novel Carpenter's Gothic, presumably speaking for the author, complained about people having to struggle against the stupidity of other people, and speculated that it had been thus for quite a while: he imagined the brightest of out hominid ancestors two million years ago in Africa, banging away with rudimentary stone tools and trying to get something done despite the interference of idiots.

Art seems to have pre-dated urban life. Human life so far seems to have included at least 30,000 Years of Art; whether there actually were, by 10,000 B.C., huge stone temples and substantial towns such as those depicted in Roland Emmerich's film, I don't know. I'm picturing nothing much more than huts and cabins at that point, but what do I know?

I know that by 7,000 or 6,000 BC there were cities in Mesopotamia like Ur. (I don't know whether the name of the Mesopotamian city is only coincidentally the same as the German prefix or whether there's more to it than that.) Within a couple of thousand years after that, there were fairly complex civilizations with big towns in Mesopotamia and also in Egypt.

After 3,100 BC the record becomes much more detailed, because by then people had started writing. Probably in Mesopotamia first, in Sumeria, followed closely by Egypt. In both areas writing began as hieroglyphics, picture-writing, but in Mesopotamia it quickly became more abstract. Egypt became a very monolithic single state, Mesopotamia was filled with competing political entities, rising and falling over and over: among these were the Babylonians in the early second millenium BC, the Assyrians in the late second and early first millenia, and in the mid-first millenium, the neo-Babylonians and, pushing into Mesopotamia from the east where they held much more territory still, the Persians.

End of Part I of the Condensed Version