a weekly roundup of cartoons, links, and things to make your eardrums bleed
This cartoon draws inspiration from the tireless work of Julia Galef, the patron saint of being patient in internet arguments. Recently, she has been compiling lists of “unpopular ideas” (about political systems, social norms, and criminal justice).
Even better, she offers this list of reasons to engage in internet arguments, even when you know that neither of you is likely to change your mind:
Also, a confession: I cribbed the Zeno joke from a comment by my stepbrother Justin on Facebook. Speaking of which, go “like” Math with Bad Drawings on Facebook!
This summer, Brilliant.org put together a lovely sequence of daily problems, aimed at combating the summer slump. A typical example:
At this point, it’s probably too late to prevent the deflation. But it’s not too late to breathe in some mathematical helium and enjoy that high-voiced feeling.
What I’m saying is that the problems are still available and you should go check ’em out!
What’s that? You’d like me to direct your towards my favorite math-related songs? Well, you’ve come to the right poorly illustrated place.
First, there’s the incomparable Jonathan Coulton, paying homage to Mandelbrot:
Second, there’s the shockingly elaborate Will Smith parody “Gettin’ Triggy Wit It,” which appears to have consumed the efforts of an entire high school for months on end:
And finally, there’s this gem, widely considered* the greatest love song of all time:
I close with a lovely piece of writing from math historian Viktor Blåsjö, on the power of intuition and the dismal fact that intellectual fashions in math run against it:
5 thoughts on “A Symphony with an Irrational Time Signature”
I would argue (discuss) that interaction helps me clarify my own thinking and deepen thought. I choose not to use the word “argument,” because it implies a back-and-forth without additional data. “Discussion,” on the other hand, opens the field for new information that may influence all participants, who then reach new levels of understanding.
It is, indeed, far better to engage with a discussion and interact with other folk, than to argue.
I did the Brilliant.org 100 day challenge.
There is a test (actually a bunch of them) that you have to take if you want to teach math in the state where I live. I failed the “are you good enough at math to teach math?” test the first time through and the re-test was in August. So I did the challenge to be in good form for the test.
Passed it this time.
The problem the first time was that I tried to actually DO the math, and ran out of time. The second time, most of my answers were first guesses without actually doing the work. There was just barely time for that. But I passed, with a score considerably higher than the minimum.
Apart from the (as always) wonderful stories and drawings, thank you also for the songs! They remind me of the “Hauptsatzkantate” from Friedrich Wille, a Cantata of the Fundamental Theorem of Calculus, which we performed at a ball when I studied mathematics. Unfortunately, it’s in German but some performances can be found online. This one is nicely illustrated and I hope you can enjoy it: https://www.youtube.com/watch?v=4n6aB4aasyg
Among Julia Galef’s reasons to engage in internet dialogues, you mention: “To give relief and comfort to onlookers”. This is indeed important – and it has a dual: to undermine any relief and comfort, that others might be drawing from whatever you are opposing (be it overt or otherwise). This is particularly important when you are opposing a toxic view. For example, those who tell sexist “jokes” give relief and comfort (even though they typically haven’t thought about it as such) to rapists and others with the worst kinds of sexist attitudes (who most likely imagine that “other guys are just ‘like me’, aside from not having the balls to *do it*”; any context, in which such sexist “jokes” go unchallenged and are laughed along to, tells them that they are “normal”; which they desperately crave (because our culture says anything that’s “normal” is OK). At the same time, those “jokes” tend to alienate women (among others) from any social context in which they are told (and not objected to). (Also, articulating this point to those who tell sexist “jokes” is quite a good way to undermine their tendency to rebuff any objection as “killjoy”. I’m not killing “joy”: I’m challenging you to chose whether you want your social contexts to make women feel uncomfortable and rapists feel included, or the other way round.) So, as well as giving relief and comfort to (like-minded) onlookers, engaging in a discussion is a way to reassure (like-minded) onlookers that they are not the oppressable minority that those you oppose are making them out to deserve to be. Standing up for your views encourages others to believe that they can do the same.
On intuition: furthermore, the fashions of those long-gone times have given us some jargon to describe schools of mathematicians: the “intuitionists” take the axiom of trans-finite choice and the law of the excluded middle as “intuitive”, while the “constructivists” are, allegedly, not intuitive – despite taking care to avoid the logical premises that inevitably lead to wildly intuition-scrambling conclusions such as (not only Cantor’s mostly-tolerable “some infinities are bigger than others” but also): the Banach-Tarski anti-intuition that volume has no respect for sets; and “almost everything” (in an entirely technical, but very reasonable, sense) is unrepresentable. Just in case anyone is unclear on what that last means: the stuff “intuitionists” are capable of describing is a negligible part of the domain they thought they were trying to describe. The constructivists chose to describe a domain in which everything they talk about lies within the domain they *can* describe. (Knowing that there “exists” a better place to eat, in the town I’m visiting, is of negligible use; while I shall always treasure instructions that have enabled me to find, in an unfamiliar town, a place in which to eat a meal with which I have been entirely satisfied.)
As it happens, computer science likes algorithms that tell how to construct a thing with desired properties from the ingredients (likewise constructibly) available. Knowing that a value satisfying certain constraints “does exist” is seldom of any use in practice: what typically matters is the ability to construct a value that satisfies those constraints (so as to use it in some way that makes use of the fact that it *does* satisfy those constraints).