Tag: math

Matt Parker on the Greatest Maths Mistakes

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In Praise of 3Blue1Brown

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I’ve been talking about bloggers I admire this past week, in one way or the other. But when it comes to consuming audio and video content, I’m at a comparative disadvantage. I much prefer reading to listening or viewing – partly because I read much faster. The other reason, of course, is that my preference for reading very quickly becomes a vicious cycle. Because I’m better at reading than at listening or viewing, I read more, and as a consequence, I get even better at reading. And so on.

But that’s just me, of course. Other folks might have (and do have) different preferences. In fact, I’ve often been told that I really should be creating videos in addition to writing this blog. And I don’t disagree, not even one little bit, and for the following reasons:

  1. If my purpose behind writing on this blog is to help people learn better (and that very much is the case), I’m not doing a very good job if I’m not optimizing for the medium that people prefer
  2. Creating YouTube videos really forces you to hone in on the exact message. Writing blogs allows me to be lazy while writing, and I needn’t worry about length and conciseness. I know this is a bad habit, and one of my to-do’s is to get better at writing bogposts.
  3. Creating videos allows you to be much, much more creative.

But that last point is precisely why I haven’t gotten around to creating videos just yet. Well, that last reason combined with my talent for procrastination, but let’s not go down that road. Let us, instead, go down that first road, the non-procrastination one.

It comes down to (surprise, surprise) an economic concept. Specifically, complements and substitutes. It would be the easiest thing in the world to set up a camera in a class in which I am already teaching something, and put up that video on YouTube. And folks who might watch this recording are simply substituting physically attending my class for virtually attending it. Which is great, of course, and I’ve have enjoyed watching videos that use this technique created by other folks.

But there are other videos on YouTube that don’t just substitute for the real world. The creator treats the format (video) as a complement to his content. The video is not a substitute for the physical classroom, it is a complement to what the creator is saying. And if you want to understand what that really means, try the following. Pick a math textbook of your choice, and try to understand linear algebra. Then watch Grant Sanderson weave his magic on the same subject.

And sure, maybe I was taught the subject badly in college. But even with a really good teacher and/or a really good math textbook in college, I cannot imagine not falling in love with the way Grant teaches us linear algebra. If you’ve watched even one of the videos in that series (and I really do hope you will watch all of them), I think you’ll agree that he comfortably ticks all of the boxes in my little list above.

And there’s so much to admire with all of his videos. The little “pi’s”, the music, his voice (an underrated part of what makes him such a good teacher. His pauses, his inflections and modulations, the pace at which he talks, all are always perfect), and the animations all end up making his videos so much better. And the content itself, and the insane amount of both coding and thinking that must go into each of them, is a whole other story.

My personal favorites from the channel are the Linear Algebra series, and the series on calculus. And as someone who teaches statistics, his video on Bayes Theorem is also fantastic. But let me be clear, these are simply the ones that resonated the most strongly with me. All of 3Blue1Brown’s videos that I have seen are fantastic. All. Every single one of them.

And if you left school/college with a slight dislike for mathematics (as I did), you couldn’t do yourself a better favor then spending a little bit of time everyday watching 3Blue1Brown’s videos. And if you are in love with mathematics (as I now am), you don’t need me to tell you to go watch his videos, now do you?

Grant, thank you very much for your work!

Veritasium on FFT’s and Nuclear Testing

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Bertrand’s Paradox, Explained By Numberphile and 3Blue1Brown

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… which, by definition, makes this self-recommending!

Tech: Links for 16th July, 2019

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  1. “On July 3, I challenged readers of my Big Internet Math-Off pitch to try to find the way to divide 24 muffins among 25 people that makes the smallest piece as large as possible. ”
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    Click on this link to get a sense of a truly interesting math problem, and how to think about them.
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  2. “Sitting in a hotel lobby in Tangier, Morocco, Charity Wayua laughs as she recounts her journey to the city for a conference on technology and innovation. After starting her trip in Nairobi, Kenya, where she leads one of IBM’s two research centers in Africa, she had to fly past her destination for a layover in Dubai, double back to Casablanca, and then take a three-and-a-half-hour drive to Tangier. What would have been a seven- to eight-hour direct flight was instead a nearly 24-hour odyssey. This is not unusual, she says.”
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    An interesting set of links contained in this link, which speaks about how AI is being used in Africa – and you also get a sense about the opportunities and limitations in Africa.
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  3. “Then there’s Matthew Porter. He requires only a camera, model cars, and a bit of Photoshop to send muscle cars flying in his new book, The Heights. It’s a resourceful, low-tech homage to some of the most iconic, memorable stunts in the car-chase genre. “There’s just nothing more visceral than a car in the air,” he says. “It’s aspirational and romantic.””
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    These kind of tech articles are the most fun to read. Tinkering around can yield surprisingly good (and fun!) results.
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  4. “Obviously, then, what is needed is not only people with a good background in a particular field, but also people capable of making a connection between item 1 and item 2 which might not ordinarily seem connected.”
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    That is from a lovely essay by Isaac Asimov on creativity.
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  5. “A group of researchers have now used this technique to munch through 3.3 million scientific abstracts published between 1922 and 2018 in journals that would likely contain materials science research. The resulting word relationships captured fundamental knowledge within the field, including the structure of the periodic table and the way chemicals’ structures relate to their properties. The paper was published in Nature last week.”
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    A very short, but no less delightful read on some of the more mind boggling applications of AI.

Etc: Links for 5th July, 2019

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  1. “…in the series, Valery Legasov (Jared Harris), a member of the Academy of Sciences, lives in nearly the same kind of squalor as a fireman in the Ukrainian town of Pripyat. In fact, Legasov would have lived in an entirely different kind of squalor than the fireman did.”
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    This is one of many, of course, but that line above was particularly illuminating. A review of the excellent series, Chernobyl.
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  2. “The productivity equation is a non-linear one, in other words. This accounts for why I am a bad correspondent and why I very rarely accept speaking engagements. If I organize my life in such a way that I get lots of long, consecutive, uninterrupted time-chunks, I can write novels. But as those chunks get separated and fragmented, my productivity as a novelist drops spectacularly. What replaces it? Instead of a novel that will be around for a long time, and that will, with luck, be read by many people, there is a bunch of e-mail messages that I have sent out to individual persons, and a few speeches given at various conferences.”
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    Neal Stephenson (whose books are excellent, and uniformly so) on productivity.
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  3. “Thanos, observing that there were too many people, decided to kill half of them. But this is curiously short-sighted for a man regarded by many as a policy prophet. Any exponential population growth process will soon replace the lost people: that is why exponential growth is such a headache in the first place. For example, if an economy’s resource footprint grows exponentially at a rate of 7 per cent, it doubles in just ten years — meaning that in less time than has elapsed since the first Iron Man movie, we could be back where we started.The only lasting solution is an economy that uses resources at a sustainable rate. Malthus’s qualms notwithstanding, contraception has been a very good start. The world population growth rate is steadily approaching a very sustainable-sounding zero.”
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    Tim Harford analyzes Thanos like only an economist can.
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  4. “Imagine you’re cooking a roast dinner for your family of four. You opt for beef with all the trimmings, safe in the knowledge that it’s a firm family favourite. But just as you’re about to serve up, your daughter announces she’s vegetarian, your partner texts to say they’re running late, and your son tells you he’s invited “a few” friends over for dinner too. Then, your dog runs off with the joint of beef while you’re desperately trying to work out how you are going to meet the needs of all these (quite frankly) very demanding and unruly individuals.”
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    The BBC on the problem of dynamic resource allocation. The excerpt, by the way, has nothing to do with the rest of the article.
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  5. “Because at the end of their pilgrimage, the weary are rewarded with two things: a footbath and a bowl of steaming noodles. The footbath is just a footbath, but the noodles are extraordinary. Su filindeu is—quasi-official designation here—the rarest pasta on the planet. The dish is made specifically for this occasion; its very existence revolves around this trek. So specialized and obscure and mind-bendingly intricate is it that only a few souls can make it. And only those who reach Lula will ever try it.”
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    The rarest pasta on earth. Why wouldn’t you want to read!

Tweets for 28th June, 2019

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Links for 3rd April, 2019

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  1. “There is something touchingly human in the dispersal of these games—in the vision it evokes of travelers packing for long, hard journeys and remembering to take with them something to kill time, something to satisfy their impulse to play. Anthropologists often regard these old games as novelties, Crist told me, but they can narrate plenty about their era. “Games function socially as a way for people to interact with one another,” he said. “People will play games when they vaguely know each other, to get to know one another.”
    Samanth Subramanian on the oldest board game known to us – dates back to around four thousand years ago. Games were, and are, a way to connect socially with people.
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  2. “But even with increasingly powerful computers and more efficient algorithms thrown at the problem, some whole numbers have stubbornly refused to yield any winning tickets. And 33 was an especially stubborn case: Until Booker found his solution, it was one of only two integers left below 100 (excluding the ones for which solutions definitely don’t exist) that still couldn’t be expressed as a sum of three cubes. With 33 out of the way, the only one left is 42.”
    The rest of the article, fascinating in its own rights, contains many more excerpt-able quotes. But if you are a fan, as I am, it had to be an excerpt that ended with that sentence!
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  3. “Nine years after giving grants for youth in Uganda to start businesses, those who didn’t receive grants had caught up on income! Nevertheless, “grants had lasting impacts on assets, skilled work, and possibly child health, but had little effect on mortality, fertility, health or education.”
    Honestly, there’s no particular reason why I chose to go with this quote in particular. David Evans has done yeoman service in putting together extremely brief summaries of I don’t know how many papers presented at the annual Center for the Study of African Economics (CSAE) conference.
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  4. “Take the example of San Francisco; with nicer streets, even more people might want to move there. That would push up rents by an amount roughly equal to the value created — putting the gains from the higher quality of life into the pockets of landowners. In a normal market economy, those higher rents would then induce more construction and, eventually, a corresponding decline in rents. But San Francisco is a “not in my backyard” locale where the amount of new construction just isn’t that high, for legal and regulatory reasons. Again, as both Ricardo and George realized, the incidence of the benefit falls upon the very scarce factor, namely land.”
    What happens when you apply the Ricardian theory of rent to San Francisco? Tyler Cowen provides the answer. Also think about where else, besides land, this argument might apply. Cough *education* cough.
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  5. “As AnsĂłn puts it: “In principle, because of how it started, a tapa is something that you eat with one hand, a cocktail stick, a fork, or a spoon, allowing you to hold a drink in the other. This style of eating creates a kind of harmony between solid and liquid.”
    This will, if you are as big a fan of food as I am, take up a lot of your time – but also, it will be worth it. Also, if you are anything like me, it will make you want to go to Spain! A lovely, interactive website about Spanish gastronomy.