Quotulatiousness

October 13, 2024

The Soviet Union’s surplus of math nerds

Filed under: History, Russia, Science — Tags: , , , , — Nicholas @ 05:00

The most recent review from Mr. and Mrs. Psmith’s Bookshelf is John Psmith’s musings on Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers by Alexander Zvonkin, and he starts by talking about something the Soviets did better than the west:

To me, one of the greatest historical puzzles is why the Cold War was even a contest. Consider it a mirror image of the Needham Question: Joseph Needham famously wondered why it was that, despite having a vastly larger population and GDP, Imperial China nevertheless lost out scientifically to the West. (I examined this question at some length in this review.) Well, with the Soviets it all went in the opposite direction: they had a smaller population, a worse starting industrial base, a lower GDP, and a vastly less efficient economic system. How, then, did they maintain military and technological parity1 with the United States for so long?

The puzzle was partly solved for me, but partly deepened, when those of us who grew up in the ‘90s and ‘00s encountered the vast wave of former Soviet émigrés that washed up in the United States after the fall of communism. Anybody who played competitive chess back then, or who participated in math competitions, knows what I’m talking about: the sinking feeling you got upon seeing that your opponent had a Russian name. These days, the same scenes are dominated by Chinese and Indian kids. But China and India have large populations — the Russians were punching way above their weight, demographically speaking. Today, those same Russians are all over Wall Street and Silicon Valley and Ivy League math departments, still overrepresented in technical fields. What explains it? Are Russians just naturally better at math and physics?

When I related these questions to an Ashkenazi-supremacist friend of mine, he immediately suggested that “maybe it’s because they’re all Jewish”. (I’ve noticed that the most philosemitic people and the most antisemitic people sometimes have curiously similar models of the world, they just disagree on whether it’s a good thing.) My friend’s question wasn’t crazy, since there are definitely times when asking “were they all Jewish?” yields an affirmative answer. But in this case I had to disappoint him with the knowledge that many of these Russian math and chess superstars were gentiles.2 What’s more, by the ’60s and ’70s the Soviets had an entire discriminatory apparatus dedicated to keeping Jews out of the scientific establishment, so it would be impressive indeed if they were the foundation of its success.

Another possible explanation actually hinges on the relative poverty of the Soviet Union. Assume there are a lot of people out there with natural mathematical talent, but who given their druthers would major in underwater basket-weaving instead. The United States, because it’s so wealthy, can afford to “waste” a huge proportion of our talented population on humanities, arts, and other stuff that doesn’t involve you sitting in the school library until 3am. In other words, not going into a technical field is a form of luxury, which America can afford to consume. The Soviets, rather like the Chinese today, were forced by their underdog status to allocate human capital more efficiently (and had the authoritarian means to do so by force if necessary). This theory is related to the curious fact that, on average, the more feminist your society, the fewer women there are in math and science — which makes total sense if you assume that on average women are good at math but uninterested in it.

The thing is, the émigré superstars I encountered didn’t seem at all grudging or resentful about their studies. If anything it was the opposite. I’ve previously complained about how much I hate Russian mathematician Edward Frenkel’s3 book, but one thing it gets across well is just how important passion is to being a great mathematician, and passion was the thing the émigrés seemed to have a surfeit of. In college, the joke was that seminars by American professors would last an hour, whereas seminars by Russian professors would turn into boisterous debates lasting all night. People have been writing for centuries about Russians having a tendency towards “maximalism” — whether aesthetic or ideological or anything else. Maybe a culture-wide commitment to not doing anything by half-measures explains it?


    1. There are scientific sub-disciplines where even at the end the Soviets had a clear lead, including several fields of math. Even crazier, there are sub-disciplines where we have not yet gotten back to where the Soviets were (for instance phage therapy).

    2. Undeterred, my friend pointed out that many modern Russian gentiles have significant Jewish ancestry. The Soviets actively promoted mixed marriages, to the point where in some cities the average urban gentile Russian is as much as 25% Jewish. I still don’t think this explains Soviet scientific prowess, but it’s an interesting data point because the most highly urbanized areas are the ones where most of the mathematicians (and most of the émigrés) came from.

    3. Before you ask, I looked it up and Frenkel is half Jewish, half gentile. I will leave it to you whether you count that as evidence for or against my friend’s theory.

April 18, 2024

“… the scary part of town, the place where the true freaks and degenerates hang out, is general topology

Filed under: Books, Science — Tags: , , — Nicholas @ 03:00

John Psmith does his level best to make mathematics interesting to layfolk like you’n’me:

In our end of year post I threatened to write more math reviews, and multiple people in the comments egged me on. So now, with Jane laid up in the final stages of pregnancy, I have seized control of the Substack for a very special lightning round of math textbooks I recently enjoyed. No, wait! Don’t close the tab! I promise that some of these will be fun for non-mathematicians as well.


  • Counterexamples in Topology, by Lynn Arthur Steen and J. Arthur Seebach Jr.

The mathematicians I have known included some eccentric characters. In fact when one considers research mathematicians as a class, it’s usually the normal people who are the exception. But there are degrees of weirdness. One of the most delightful things about the world is how fractal it is, and this extends to human hierarchies. Take any unusual group of people — frequent-flyers, monastics, the ultra-wealthy, members of genealogical societies — and zoom in on them, and it turns out there are even stranger or more elite subgroups buried within. This is true of mathematicians too, each subfield has its reputation, some of them regarded with awe, others with disdain. But ask any mathematician, “Who are the real weirdos? Who are the ones who are truly cracked?” The answer will be unanimous: it’s the topologists.

Topology is the study of spaces in the most abstract sense, so abstract that they may not even support a well-defined notion of distance (if your spaces are guaranteed to have distances, then you are now doing geometry rather than topology). Topology takes a coarser view of space: forget about curvature, distance, or really anything involving numbers at all. To a topologist, two points can be “near” each other or not, “connected” or not, and beyond that it doesn’t matter. This is the source of all the jokes about topologists mistaking donuts for coffee cups,1 but the kind of topology that studies multi-holed donuts, algebraic topology, is actually comparatively tame and normal. Also relatively normal is differential topology, which is the next neighborhood over from differential geometry, and which produces cool videos like this.

No, the scary part of town, the place where the true freaks and degenerates hang out, is general topology. General topology is where we go to figure out the basic definitions and frameworks that underlie the rest of topology. It’s about exploring what nearness and connectedness even are, and when mathematicians are trying to figure out what things are, that usually means probing the outer limits of what they can be. So general topology turns into the study of the most bizarre and deformed and disturbing spaces accessible to human cognition. No wonder its practitioners are a little weird.

Which brings me to this book, whose perversity is laid out right there in the title. It’s a big book of counterexamples to statements which seem obviously, intuitively correct. In general topology, things that seem intuitively correct are usually wrong:2 the field is notorious for proofs that almost work but twist out of your grasp at the last moment. A big book of counterexamples is exactly what you want for understanding why your proof that “all Xs are Ys and all Ys are Xs” falls flat. Seeing the logic fail is one thing, but seeing a concrete example of an X that is not a Y (or vice versa) brings it home with a satisfying finality.

But the real reason I love this book is the names, oh, the names. Let me flip through the table of contents with you: are “the Infinite Cage” and “the Wheel Without Its Hub” examples of topological spaces, or planes of the underworld? Are “Cantor’s Leaky Tent” and “Tychonoff’s Corkscrew” important counterexamples, or Level 2 wizard spells? I could spend hours idly leafing through this book, pondering these twisted and prosperous spaces, imagining them as worlds in themselves, imagining the bizarre sorts of creatures that might live there. Is this a math textbook or an RPG sourcebook? Trick question, they’re the same thing.


    1. One of the proudest moments of my mathematical career was when I attended a faculty tea and a distinguished topologist asked me for a donut and I handed him a cup of coffee instead. Everybody lost it. Alas, I turned out to be much worse at math than I am at improvisational comedy, and my mathematical career ended shortly afterwards.

    2. This is why we have the “separation axioms“. Every rung on that latter is the “well, actually …” to something that seems self-evident but isn’t.

February 6, 2024

Greek History and Civilisation, Part 1 – What Makes the Greeks Special?

Filed under: Greece, History — Tags: , , , , , , , , , — Nicholas @ 04:00

seangabb
Published Feb 1, 2024

This first lecture in the course makes a case for the Greeks as the exceptional people of the Ancient World. They were not saints: they were at least as willing as anyone else to engage in aggressive wars, enslavement, and sometimes human sacrifice. At the same time, working without any strong outside inspiration, they provided at least the foundations for the science, mathematics, philosophy, art and secular literature of later peoples.
(more…)

December 22, 2023

QotD: Mathematically inclined people

Filed under: Humour, Quotations — Tags: , — Nicholas @ 01:00

I’ve often said that mathematically inclined people generally get that way because God takes everything in their skulls and pushes it over to the left. Tensor calculus? No problem. Understanding that it’s disturbing for a grown man to speak Klingon? Sorry, the part of the brain that ordinarily handles that is busy thinking about the Pauli Exclusion Principle.

Steve H., Star Wars Still Sucks: ‘Quick, Someone Put More Minwax on Natalie'”, Hog on Ice, 2005-05-26.

July 3, 2023

Schools fail their students when they try to teach things the students have no interest in learning

Filed under: Education, Gaming — Tags: , , — Nicholas @ 03:00

David Friedman has several examples of success in learning when the learner suddenly wants to learn the material:

One of the problems with our educational system is that it tries to teach people things that they have no interest in learning. There is a better way.

What started me thinking about the issue and persuaded me to write this post was an online essay, by a woman I know, describing how she used D&D to cure her math phobia.

How to Cure Mathphobia

    I was failed by the education system, fell behind, never caught up, and was left with a panic response to the thought of interacting with any expression that has numbers and letters where I couldn’t immediately see what all of the numbers and letters were doing. The first time I took algebra one, I developed such a strong panic response that it wrapped around to the immediate need to go to sleep, like my brain had come up with a brilliant defense mechanism that left me with something akin to situational narcolepsy. (I did, actually, fall asleep in class several times, which had never happened to me before.) I retook the class the next year. I spent a lot of that year in tears, with a teacher who specifically refused to answer questions that weren’t more specific than “I don’t get it” or “I have no idea what any of those symbols mean or what we’re doing with them”.

Until she had a use for it:

    The first time I played D&D, I was a high school student. My party was, incidentally, all female, apart from one girl’s boyfriend and the GM, who was the father of three of the players. We actually started out playing first edition AD&D, which I am almost tempted to recommend to beginners, just on the grounds that if you start there you will appreciate virtually every other edition of D&D you end up playing by comparison. I might have given up myself before I started, except that one of the players in the first game I ever spectated was a seven-year-old girl, and I was not about to claim that I couldn’t do something that a seven-year-old was handling just fine.

    One of my most vivid memories of this group is the time we were on a massive zigzagging staircase — like one of those paths they have at the Grand Canyon, that zigzag back and forth down the cliff face so that anyone can reach the bottom without advanced rock-climbing. We saw a bunch of monsters coming for us from the ground below, and we weren’t sure whether they had climb speeds, but we didn’t super want to wait to find out. The ranger pulled out her bow to attack them before they could get to us.

    “Now, wait a moment,” says the GM. “Can your arrows actually reach that far?”

    “Well, they’re only, like, sixty feet away.”

    “No, it’s more than that, because you have to think about height in addition to horizontal distance.”

    “Yeah, but that’s, like, complicated?”

    “Is it? Most of you are taking geometry right now, don’t you know how to find the hypotenuse of a right triangle?”

    There were some groans. Math was hard. But we did know how to find the hypotenuse of a right triangle. We got out some scrap paper and puzzled over it for a couple minutes, volunteering the height of the cliff and the distance of the monsters and deciding that we could ignore the slight slope caused by the zigzagging stairways. We got a number back and compared it to the bow’s range per the rules. We determined that we could hit the monsters without a range penalty.

    We killed the monsters. This wasn’t the real victory that day.

April 28, 2023

Use and misuse of the term “regression to the mean”

Filed under: Books, Business, Football, Sports, USA — Tags: , , , — Nicholas @ 03:00

I still follow my favourite pro football team, the Minnesota Vikings, and last year they hired a new General Manager who was unlike the previous GM in that not only was he a big believer in analytics, he actually had worked in the analytics area for years before moving into an executive position. The first NFL draft under the new GM and head coach was much more in line with what the public analytics fans wanted — although the result on the field is still undetermined as only one player in that draft class got significant playing time. Freddie deBoer is a fan of analytics, but he wants to help people understand what the frequently misunderstood term “regression to the mean” actually … means:

Kwesi Adofo-Mensah, General Manager of the Minnesota Vikings. Adofo-Mensah was hired in 2022 to replace Rick Spielman.
Photo from the team website – https://www.vikings.com/team/front-office-roster/kwesi-adofo-mensah

The sports analytics movement has proven time and again to help teams win games, across sports and leagues, and so unsurprisingly essentially every team in every major sport employs an analytics department. I in fact find it very annoying that there are still statheads that act like they’re David and not Goliath for this reason. I also think that the impact of analytics on baseball has been a disaster from an entertainment standpoint. There’s a whole lot one could say about the general topic. (I frequently think about the fact that Moneyball helped advance the course of analytics, and analytics is fundamentally correct in its claims, and yet the fundamental narrative of the book was wrong.*) But while the predictive claims of analytics continue to evolve, they’ve been wildly successful.

I want to address one particular bugaboo I have with the way analytical concepts are discussed. It was inevitable that popularizing these concepts was going to lead to some distortion. One topic that I see misused all the time is regression/reversion to the mean, or the tendency of outlier performances to be followed up by performances that are closer to the average (mean) performance for that player or league. (I may use reversion and regression interchangeably here, mostly because I’m too forgetful to keep one in my head at a time.) A guy plays pro baseball for five years, he hits around 10 or 12 homeruns a year, then he has a year where he hits 30, then he goes back to hitting in the low 10s again in following seasons – that’s an example of regression to the mean. After deviation from trends we tend (tend) to see returns to trend. Similarly, if the NFL has a league average of about 4.3 yards per carry for a decade, and then the next year the league average is 4.8 without a rule change or other obvious candidate for differences in underlying conditions, that’s a good candidate for regression to the mean the next year, trending back towards that lower average. It certainly doesn’t have to happen, but it’s likely to happen for reasons we’ll talk about.

Intuitively, the actual tendency isn’t hard to understand. But I find that people talk about it in a way that suggests a misunderstanding of why regression to the mean happens, and I want to work through that here.

So. We have a system, like “major league baseball” or “K-12 public education in Baltimore” or “the world”. Within those systems we have quantitative phenomena (like on-base percentage, test scores, or the price of oil) that are explainable by multiple variables, AKA the conditions in which the observed phenomena occur. Over time, we observe trends in those phenomena, which can be in the system as a whole (leaguewide batting average), in subgroups (team batting average), or individuals (a player’s batting average). Those trends are the result of underlying variables/conditions, which include internal factors like an athlete’s level of ability, as well as elements of chance and unaccounted-for variability. (We could go into a big thing about what “chance” really refers to in a complex system, but … let’s not.) The more time goes on, and the more data is collected, the more confidently we can say that a trend is an accurate representation of some underlying reality, again like an athlete’s level of ability. When we say a baseball player is a good hitter, it’s because we’ve observed over time that he has produced good statistics in hitting, and we feel confident that this consistency is the product of his skill and attributes rather than exogenous factors.

However, we know that good hitters have bad games, just as bad hitters have good games. We know that good hitters have slumps where they have bad three or five or ten etc game stretches. We even acknowledge that someone can be a good hitter and have a bad season, or at least a season that’s below their usual standards. However, if a hitter has two or three bad seasons, we’re likely to stop seeing poor performance as an outlier and change our overall perception of the player. The outlier becomes the trend. There is no certain or objective place where that transition happens.

Here’s the really essential point I want to make: outliers tend to revert to the mean because the initial outlier performance was statistically unlikely; a repeat of that outlier performance is statistically unlikely for the same reasons, but not because of the previous outlier. For ease of understanding let’s pretend underlying conditions stay exactly the same, which of course will never happen in a real-world scenario. If that’s true, then the chance of having an equally unlikely outcome is exactly as likely as the first time; repetition of outliers is not made any less likely by the fact that the initial outlier happened. That is, there’s no inherent reason why a repetition of the outlier becomes more unlikely, given consistent underlying conditions. I think it’s really important to avoid the Gambler’s Fallacy here, thinking that a roulette wheel is somehow more likely to come up red because it’s come up black a hundred times in a row. Statistically unlikely outcomes in the past don’t make statistically unlikely outcomes any less likely in the future. The universe doesn’t “remember” that there’s been an outlier before. Reversion to the mean is not a force in the universe. It’s not a matter of results being bent back into the previous trend by the gods. Rather, if underlying conditions are similar (if a player is about as good as he was the previous year and the role of variability and chance remains the same), and he had an unlikely level of success/failure the prior year, he’s unlikely to repeat that performance because reaching that level of performance was unlikely in the first place.


    * – the A’s not only were not a uniquely bad franchise, they had won the most games of any team in major league baseball in the ten years prior to the Moneyball season
    – major league baseball had entered an era of unusual parity at that time, belying Michael Lewis’s implication that it was a game of haves and have-nots
    – readers come away from the book convinced that the A’s won so many games because of Scott Hatteberg and Chad Bradford, the players that epitomize the
    Moneyball ethos, but the numbers tell us they were so successful because of a remarkably effective rotation in Tim Hudson, Barry Zito, and Mark Mulder, and the offensive skill of shortstop Miguel Tejada – all of whom were very highly regarded players according to the old-school scouting approach that the book has such disdain for.
    – Art Howe was not an obstructionist asshole.

July 18, 2022

John von Neumann, The Man From The Future

Filed under: Books, History, Science — Tags: , , , , , — Nicholas @ 05:00

One of the readers of Scott Alexander’s Astral Codex Ten has contributed a review of The Man From The Future: The Visionary Life of John von Neumann by Ananyo Bhattacharya. This is one of perhaps a dozen or so anonymous reviews that Scott publishes every year with the readers voting for the best review and the names of the contributors withheld until after the voting is finished:

John von Neumann invented the digital computer. The fields of game theory and cellular automata. Important pieces of modern economics, set theory, and particle physics. A substantial part of the technology behind the atom and hydrogen bombs. Several whole fields of mathematics I hadn’t previously heard of, like “operator algebras”, “continuous geometry”, and “ergodic theory”.

The Man From The Future, by Ananyo Bhattacharya, touches on all these things. But you don’t read a von Neumann biography to learn more about the invention of ergodic theory. You read it to gawk at an extreme human specimen, maybe the smartest man who ever lived.

By age 6, he could multiply eight-digit numbers in his head. At the same age, he spoke conversational ancient Greek; later, he would add Latin, French, German, English, and Yiddish (sometimes joked about also speaking Spanish, but he would just put “el” before English words and add -o to the end). Rumor had it he memorized everything he ever read. A fellow mathematician once tried to test this by asking him to recite Tale Of Two Cities, and reported that “he immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes”.

A group of scientists encountered a problem that the computers of the day couldn’t handle, and asked von Neumann for advice on designing a new generation of computers that was up to the task. But:

    When the presentation was completed, he scribbled on a pad, stared so blankly that a RAND scientist later said he looked as if “his mind had slipped his face out of gear”, then said “Gentlemen, you do not need the computer. I have the answer.” While the scientists sat in stunned silence, Von Neumann reeled off the various steps which would provide the solution to the problem.

Do these sound a little too much like urban legends? The Tale Of Two Cities story comes straight from the mathematician involved — von Neumann’s friend Herman Goldstine, writing about his experience in The Computer From Pascal to von Neumann. The computer anecdote is of less certain provenance, quoted without attribution in a 1957 obituary in Life. But this is part of the fun of reading von Neumann biographies: figuring out what one can or can’t believe about a figure of such mythic proportions.

This is not really what Bhattacharya is here for. He does not entirely resist gawking. But he is at least as interested in giving us a tour of early 20th century mathematics, framed by the life of its most brilliant practitioner. The book devotes more pages to set theory than to von Neumann’s childhood, and spends more time on von Neumann’s formalization of quantum mechanics than on his first marriage (to be fair, so did von Neumann — hence the divorce).

Still, for those of us who never made their high school math tutors cry with joy at ever having met them (another von Neumann story, this one well-attested), the man himself is more of a draw than his ergodic theory. And there’s enough in The Man From The Future — and in some of the few hundred references it cites — to start to get a coherent picture.

December 30, 2021

QotD: Richard Feynman discovers (to his shock) that females can understand analytic geometry

Filed under: Education, Humour, Quotations, Science — Tags: , , , , — Nicholas @ 01:00

I would like to report other evidence that mathematics is only patterns. When I was at Cornell, I was rather fascinated by the student body, which seems to me was a dilute mixture of some sensible people in a big mass of dumb people studying home economics, etc. including lots of girls. I used to sit in the cafeteria with the students and eat and try to overhear their conversations and see if there was one intelligent word coming out. You can imagine my surprise when I discovered a tremendous thing, it seemed to me.

I listened to a conversation between two girls, and one was explaining that if you want to make a straight line, you see, you go over a certain number to the right for each row you go up – that is, if you go over each time the same amount when you go up a row, you make a straight line – a deep principle of analytic geometry! It went on. I was rather amazed. I didn’t realize the female mind was capable of understanding analytic geometry.

She went on and said, “Suppose you have another line coming in from the other side, and you want to figure out where they are going to intersect. Suppose on one line you go over two to the right for every one you go up, and the other line goes over three to the right for every one that it goes up, and they start twenty steps apart,” etc. – I was flabbergasted. She figured out where the intersection was. It turned out that one girl was explaining to the other how to knit argyle socks. I, therefore, did learn a lesson: The female mind is capable of understanding analytic geometry. Those people who have for years been insisting (in the face of all obvious evidence to the contrary) that the male and female are equally capable of rational thought may have something. The difficulty may just be that we have never yet discovered a way to communicate with the female mind. If it is done in the right way, you may be able to get something out of it.

Richard Feynman, “What is Science?”, Richard Feynman [presented at the fifteenth annual meeting of the National Science Teachers Association, 1966 in New York City, and reprinted from The Physics Teacher Vol. 7, issue 6, 1969].

November 20, 2021

DicKtionary – M is for Mathematics – Newton and Hooke

Filed under: Britain, History, Science — Tags: , , , , — Nicholas @ 04:00

TimeGhost History
Published 19 Nov 2021

Today we turn away from killers and sociopathic rulers and look at two men from the world of science. Isaac Newton and Robert Hooke were certainly very intelligent and creative, but were they dicks as well?
(more…)

June 28, 2021

Pounds, shillings, and pence: a history of English coinage

Filed under: Britain, Economics, History — Tags: , , , , , , — Nicholas @ 04:00

Lindybeige
Published 18 Dec 2020

I talk for a bit the history of English coinage, and the problems of maintaining a good currency. Once or twice I might stray off topic, but I end with an explanation of why the system worked so well.

Picture credits:
40 librae weight
Martinvl, CC BY-SA 3.0 https://creativecommons.org/licenses/…, via Wikimedia Commons

Sceat K series, and others
By Classical Numismatic Group, Inc. http://www.cngcoins.com, CC BY-SA 3.0, https://commons.wikimedia.org/w/index…

William I penny, and Charles II crown
The Portable Antiquities Scheme/ The Trustees of the British Museum, CC BY-SA 2.0 https://creativecommons.org/licenses/…, via Wikimedia Commons

Bust of Charlemagne
By Beckstet – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index…

Edward VI crown
By CNG – http://www.cngcoins.com/Coin.aspx?Coi…, CC BY-SA 3.0, https://commons.wikimedia.org/w/index…

Charles II guinea
Gregory Edmund, CC BY-SA 4.0 https://creativecommons.org/licenses/…, via Wikimedia Commons

Support me on Patreon: https://www.patreon.com/Lindybeige

Buy the music – the music played at the end of my videos is now available here: https://lindybeige.bandcamp.com/track…

Buy tat (merch):
https://outloudmerch.com/collections/…

Lindybeige: a channel of archaeology, ancient and medieval warfare, rants, swing dance, travelogues, evolution, and whatever else occurs to me to make.

▼ Follow me…

Twitter: https://twitter.com/Lindybeige I may have some drivel to contribute to the Twittersphere, plus you get notice of uploads.

My website:
http://www.LloydianAspects.co.uk

April 8, 2021

QotD: Thomas Hobbes and his “state of nature”

Filed under: History, Liberty, Quotations — Tags: , , , — Nicholas @ 01:00

One reason I had such a hard time teaching this stuff to undergraduates back in my ivory tower days was that, ironically, we can imagine a much more “realistic” State of Nature than Hobbes could. We even had a TV show about it: Lost (in which, I’m told, one of the characters was actually named “John Locke”). A large group of strangers, unrelated by blood or affinity, would never be shipwrecked on a deserted island in Hobbes’s day, but we Postmoderns have no problem imagining a large international flight going down. Assume everyone survives the crash, and there’s your State of Nature – a much better one than Hobbes’s.

Under those very specific conditions, something like what Hobbes says might come to pass. In reality, of course, we seem to be much likelier to pull together in a disaster than to immediately go full retard, but let’s envision the most apocalyptic scenario, in which every guy who can bench press his body weight (assuming such still exist on international flights) immediately tries to lord it over everyone else on the island. There, and only there, the stuff Hobbes says about equality is true – the strong guy can beat up the weak guy, and enslave him, but the strong guy has to sleep sometime …

… so pretty soon there are no more strong guys, only various flavors of weak, clever guys, and now they have to band together, because you need three or four of them to accomplish the physical labor that one strong guy could’ve before they murdered him in his bed. And so on, you get the point, eventually everyone grudgingly lays down his arms and starts working together for mutual survival.

At this point, I need to point out something fundamental about Thomas Hobbes, that y’all probably don’t know. Hobbes always considered himself first and foremost a mathematician. But he wasn’t a very good mathematician. He’d thought he’d discovered a way to “square the circle,” for instance, and that’s not a metaphor – that was really a thing back then, and Hobbes’s attempt got ripped to shreds by real mathematicians, who thought they were thereby discrediting his metaphysics and, by implication, his political philosophy …

… fun stuff, but irrelevant, the point is, Hobbes was a bad mathematician. So bad, in fact, that even I, a former History professor who needs to pull off a sock every time I have to count past ten, can see the glaring flaw in his “geometrical” political theory: IF it’s based on “the State of Nature,” and we legitimize the Leviathan because that’s what gets us out of the State of Nature, then once we are free of the State of Nature, what’s the point of the Leviathan?

Hobbes didn’t see it that way, of course. He thought that we really did revert to “the war of all against all” the minute the social contract was broken, and in his context – the English Civil Wars, recall – that’s not unreasonable. But what about all the periods of “normal” government? You know, those periods of peace we created the Leviathan specifically to secure? If we get those – and there’s no point to the exercise otherwise – then we seem to have created an all-powerful government that, while it CAN do everything, really shouldn’t do anything.

Severian, “Hobbes (II)”, Founding Questions, 2020-12-11.

March 20, 2021

Iron cannon, improved celestial navigation techniques, and “race-built” galleons

In the latest Age of Invention newsletter, Anton Howes considers some of the technological innovations which helped English sailors to overcome powerful adversaries of the Spanish and Portuguese navies in the late 1500s and early 1600s:

Stern view of a model of the Revenge as an example of a race-built galleon, 1577.
Image from modellmarine.de

Apart from the adoption and refinement of celestial navigation techniques, however, English seafaring capabilities also benefited from some more obvious, physical changes. In 1588, for example, on the eve of the Spanish Armada, a senior Spanish officer believed that the English had “many more long-range guns”. By the 1540s, medieval ironmaking techniques involving the blast furnace had gradually spread from Germany, to Normandy, and thence to the Weald of Sussex and Kent. Whereas in the first half of the sixteenth century England had typically imported three quarters of its iron from Spain, by 1590 it had not only quintupled its consumption of iron but was also almost entirely self-sufficient. And by allowing England to exploit its plentiful domestic deposits of iron, the blast furnace resulted in it producing many more cheap cannon.

Iron guns were in many ways worse for ships than those of bronze. They were heavier, prone to corrosion, and more likely to explode without warning. Bronze guns, by contrast, would first bulge and then split, but in any case tended to last. When the British captured Gorée off the coast of Senegal in 1758, they found a working English-made bronze cannon that dated from 1582. Yet iron was only 10-20% the price of bronze. Although the Royal Navy for decades continued to prefer bronze, cheap, medium-sized cannon of iron proliferated, becoming affordable to merchants, pirates, and privateers — a situation that was unique to England.

English ships were thus especially well-armed, allowing them to access new markets even when they sailed into hostile waters. They were soon some of the only merchants able to hold their own against the latest Mediterranean apex predator, whether it be the Spanish navy, Algeria-based corsairs, or Ottoman galleys. And they were able to insert themselves, sometimes violently, into the inter-oceanic trades — all despite the armed resistance of the Spanish and Portuguese, who had long monopolised those routes. In the 1560s, John Hawkins tried a few times to muscle in on the transatlantic Portuguese and Spanish trade in slaves. With backing from the monarch and her ministers, he captured Portuguese slave ships, raided and traded along the African coastline himself, and then sold slaves in the Spanish colonies of the Americas, sometimes having to attack those colonies before the local governor would allow them to trade. (The attempt was ultimately unsuccessful, as Hawkins’s privateering fleet was all but destroyed in 1568 and the English were not involved in the slave trade again for almost a century.)

The English hold over the hostile markets was only threatened during times of peace on the continent, when their ships’ defensiveness no longer gave them a special advantage. The Dutch usurped English dominance of the trade with Iberia and the Mediterranean, for example, during the Dutch Republic’s truce with Spain 1609-21. Their more efficient ships, especially for bulk commodities — the fluyt invented at Hoorn in the late 1580s — were cheaper to build, required fewer sailors, and were easier to handle. But these advantages only made them competitive when the risk of attack was low, as they were hardly armed. When wars resumed, the English had a chance to regain their position.

Finally, the English acquired a few further advantages when it came to ship design. Thanks to the shipwright Matthew Baker, who had been on the trial voyage Cabot dispatched to the Mediterranean, England experienced a revolution in using mathematics to design ships. Baker’s methods, seemingly developed in the 1560s, allowed him to more cheaply experiment with new forms, and by the 1570s these began to bear fruit. The old ocean-going carracks and galleons, with their high forecastles and aftercastles, became substantially sleeker. Taking inspiration from nature, Baker designed a streamlined, elongated hull modelled below the waterline upon a cod’s head with a mackerel tail. Above the waterline, too, he lowered the forecastle and set it further back, as well as flattening the aftercastle.

Starting in 1570 with his prototype the Foresight, and more fully developed in 1575-77 with the Revenge, these razed or “race-built” galleons gave the English some significant advantages. Drake even chose the Revenge as his flagship to battle the Spanish Armada in 1588, and to lead an ill-fated reprisal invasion of Portugal the following year. The higher castles of carracks and old-style galleons were suited to clearing an enemy’s decks with arrows and gunfire, as well as to defend against boarders. They were designed for combat at close quarters, in which height was an advantage. They were floating fortresses, their imposing height known to inspire terror. The race-built galleons, by contrast, by making the ship less top-heavy, could have longer and lower gundecks, with more of the ship’s displacement devoted to ordnance — especially useful when taking advantage of the cheaper but heavier cannon made of iron. Rather than killing an enemy ship’s sailors and soldiers, the race-built galleons were optimised for blasting through its hull. What they lost in “majesty and terror”, they made up for with overwhelming firepower. They aimed to sink.

March 5, 2021

Schools told they need to “identify and challenge the ways that math is used to uphold capitalist, imperialist, and racist views”

Filed under: Education, Politics, USA — Tags: , , , , — Nicholas @ 09:15

No wonder I had trouble with math back in grade school: Math is a racist tool of White Supremacists!

“Math Class” by attercop311 is licensed under CC BY 2.0

Mandatory teaching standards that focus on critical theory and identity politics to the detriment of liberalism and individualism are already working their way through state legislatures.

Now, math education itself has been deemed “racist.” A group of educators just released a document calling for a transformation of math education that focuses on “dismantling white supremacy in math classrooms by visibilizing the toxic characteristics of white supremacy culture with respect to math.”

Among the educators’ recommendations, which officials in some states are promoting, are calls to “identify and challenge the ways that math is used to uphold capitalist, imperialist, and racist views,” “provide learning opportunities that use math as resistance,” and “encourage them to disrupt the disproportionate push-out of people of color in [STEM] fields.”

Beyond activism, these recommendations also argue that traditional approaches to math education promote racism and white supremacy, such as requiring students to show their work or prioritizing correct answers to math problems. The document claims that current math teaching is problematic because it focuses on “reinforcing objectivity and the idea that there is only one right way” while it “also reinforces paternalism.”

October 30, 2020

Halloween Special: H. P. Lovecraft

Overly Sarcastic Productions
Published 31 Oct 2018

HAPPY HALLOWEEN IT’S TIME TO GET SPOOKY WITH HISTORY’S MOST PROBLEMATIC HORROR WRITER LET’S GOOOOO

While there’s something to be said for separating the art from the artist, I think there’s a lot of merit in CONTEXTUALIZING the art WITH the artist. Did Lovecraft write some pretty incredible horror? Sure! Was he also a raging xenophobe? Absolutely! Are his perspectives on life connected with the stories he felt compelled to tell? Duh! If you look at Lovecraft’s writing through the lens of his life, clear patterns emerge that allow us to pin down what exactly he built his horror cosmology out of. It’s an invaluable analytical tool that allows us to take apart his writings by getting inside his head. So before you yell at me for Not Separating The Artist From The Art, know that it was completely intentional and I’m not sorry.

3:20 – THE CALL OF CTHULHU
8:40 – COOL AIR
10:36 – THE COLOR OUT OF SPACE
14:38 – THE DUNWICH HORROR
19:32 – THE SHADOW OVER INNSMOUTH

PATREON: www.patreon.com/user?u=4664797

MERCH LINKS:
Shirts – https://overlysarcasticproducts.threa…
All the other stuff – http://www.cafepress.com/OverlySarcas…

From the comments:

Overly Sarcastic Productions
1 year ago
Hey gang! Can’t help but notice the comment section is a little bit on fire. That’s all good with me, but one recurring complaint I’ve noticed has started to get under my skin – namely that my explanation of non-euclidean geometry was insufficient, or even – dare I say – inaccurate. Now this is a fair complaint, because after a lifetime of experience finding that people’s eyes glaze over when I talk math at them, I concluded that interrupting a half-hour horror video with a long-winded explanation of a mathematical concept wouldn’t go over too well. I put it in layman’s terms and used a simple example to illustrate the point. However, since some of the more mathematically-inclined of you took offense, I now present in full a short (but comprehensive) explanation of what exactly non-euclidean geometry is.

First, we axiomatically establish euclidean geometry. Euclidean geometry has five axioms:
1. We can draw a straight line between any two points.
2. We can infinitely extend a finite straight line.
3. We can draw a circle with any center and radius.
4. All right angles are equal to one another.
5. If two lines intersect with a third line, and the sum of the inner angles of those intersections is less than 180º, then those two lines must intersect if extended far enough.

Axiom #5 is known as the PARALLEL POSTULATE. It has many equivalent statements, including the Triangle Postulate (“the sum of the angles in every triangle is 180º”) and Playfair’s Axiom (“given a line and a point not on that line, there exists ONE line parallel to the given line that intersects the given point”).

Euclidean geometry is, broadly, how geometry works on a flat plane.

However, there are geometries where the parallel postulate DOES NOT hold. These geometries are called “non-euclidean geometries”. There are, in fact, an infinite number of these geometries, and because the only defining characteristic is “the parallel postulate does not hold”, they can be all kinds of crazy shapes. (As you can see, my explanation of “this is just how geometry works on a curved surface” is quite reductive, but at the same time serves to get the general impression across without going into too much detail.)

An example of a non-euclidean geometry is “Elliptic geometry”, geometry on n-dimensional ellipses, which includes “Spherical geometry” as a subset. Spherical geometry is, predictably enough, how geometry works on the two-dimensional surface of a three-dimensional sphere.

In spherical geometry, “points” are defined the same as in euclidean geometry, but “line” is redefined to be “the shortest distance between two points over the surface of the sphere”, since there is no such thing as a “straight line” on a curved surface. All “lines” in spherical geometry are segments of “great circles” (which is defined as the set of points that exist at the intersection between the sphere and a plane passing through the center of that sphere).

The axiom that separates spherical geometry from euclidean geometry and replaces the parallel postulate is “5. There are NO parallel lines”. In spherical geometry, every line is a segment of a great circle, and any two great circles intersect at exactly two points. If two lines intersect when extended, they cannot be parallel, and thus there are no parallel lines in spherical geometry.

Since the Parallel Postulate is equivalent to Playfair’s Axiom, the fact that no parallel lines exist in spherical geometry negates Playfair’s Axiom, which thus negates the Parallel Postulate and defines spherical geometry as a non-euclidean geometry. Also, since the Triangle Postulate is another equivalent property to the Parallel Postulate, it is thus negated in spherical geometry. Hence, my use in-video of an example of a triangle drawn on the surface of a sphere whose inner angles sum greater than 180º.

Hope that cleared things up (and helped explain why I didn’t want to say “see, non-euclidean geometry is just a geometry where Euclid’s Parallel Postulate doesn’t hold – hold on, let me get the chalkboard to explain what THAT is-” in the video)

Peace!

-R ✌️

May 27, 2020

The Battle to Crack Enigma – The real story of ‘The Imitation Game’ – WW2 Special

World War Two
Published 26 May 2020

For the British, breaking the Germans’ seemingly unbreakable codes is one of the most vital battles of the war. If they fail, there is litte to stop the German U-Boats hunting down Allied shipping in the Atlantic.

Join us on Patreon: https://www.patreon.com/TimeGhostHistory
Or join The TimeGhost Army directly at: https://timeghost.tv

Follow WW2 day by day on Instagram @World_war_two_realtime https://www.instagram.com/world_war_t…
Between 2 Wars: https://www.youtube.com/playlist?list…
Source list: http://bit.ly/WW2sources

Hosted by: Indy Neidell
Written by: Francis van Berkel
Director: Astrid Deinhard
Producers: Astrid Deinhard and Spartacus Olsson
Executive Producers: Astrid Deinhard, Indy Neidell, Spartacus Olsson, Bodo Rittenauer
Creative Producer: Joram Appel
Post-Production Director: Wieke Kapteijns
Research by: Francis van Berkel
Edited by: Mikołaj Cackowski
Sound design: Marek Kamiński
Map animations: Eastory (https://www.youtube.com/c/eastory)

Colorizations by:
Jaris Almazani (Artistic Man), https://instagram.com/artistic.man?ig…
Norman Stewart, https://oldtimesincolor.blogspot.com/
Carlos Ortega Pereira, BlauColorizations, https://www.instagram.com/blaucoloriz…

Sources:
Bundesarchiv
Narodowe Archiwum Cyfrowe
IWM D 23310, A 13709, A 23513
Picture of Enigma G model, courtesy Austin Mills https://flic.kr/p/2bQ9Q
reconstructed bombe machine at Bletchley Park, courtesy Gerald Massey
Picture of Enigma M4 model displayed at Bletchley Park, courtesy Magnus Manske
Picture of John Herivel, courtesy GCHQ
From the Noun Project: Letter by Mochammad Kafi, Desk by monkik, Phone by libertetstudio, person by Adrien Coquet, Letter by Bonegolem, Table by Creative Stall, documents by Johannes Hirsekorn, sitting at desk by IYIKON, Paper by James Kopina

Soundtracks from the Epidemic Sound:
Reynard Seidel – “Deflection”
Johannes Bornlof – “The Inspector 4”
Phoenix Tail – “At the Front”
Johannes Bornlof – “Deviation In Time”
Gunnar Johnsen – “Not Safe Yet”
Hakan Eriksson – “Epic Adventure Theme 3”
Howard Harper-Barnes – “London”

Archive by Screenocean/Reuters https://www.screenocean.com.

A TimeGhost chronological documentary produced by OnLion Entertainment GmbH.

From the comments:

World War Two
4 hours ago (edited)
Hopefully you’re all staying safe in these difficult times. We’re still marching on so that we can keep all of you entertained when you’re stuck at home. But we can only continue doing so thanks to your ongoing support. Ad revenue has dropped significantly because of COVID, and we rely on your support now more than ever. If you can, please support us on www.patreon.com/timeghosthistory or https://timeghost.tv.

Please let us know what other specials you’d like to see. And if you would like to know something about a smaller topic, make sure to submit that as a question for our Q&A series, Out of the Foxholes. You can do that right here: https://community.timeghost.tv/c/Out-of-the-Foxholes-Qs.

Cheers,
Francis

Older Posts »

Powered by WordPress