Posts

38. Math Isn’t About Working Hard, It’s About Being Cleverly Lazy

(Epistemic status: a time-worn explanation I used to give my undergrads, fancied up a little.) Math isn't about working hard to get the right answer. It's about being cleverly lazy. Let me explain. For most of your life, you've probably been afraid of math, or burned out by it, or intimidated. There's a single right answer, and everything you need to do to get that answer is hard and weird and abstract. Surely as you keep going in math, as you learn harder math and are asked to do more difficult things, you'll also need to keep putting in more and more effort? Surely you need to work yourself to the bone doing it "the right way" just to keep up? No! Absolutely not! If you try to pull that garbage you will end up doing a literally infinite amount of work! For a good example of this, consider something like the sum of negative powers of 2: 1, 1/2, 1/4, 1/8, and so on forever. You could spend a lifetime adding those up by hand and not get anywhere, and if you...

37. Seven-ish Emotions From My Culture

(Epistemic status: There sure do seem to be a lot of folks from other Everett branches who washed up in this one, aren't there?) It's not just words and sayings I bring from the culture and the [counterhistory] I surely wasn't actually drawn from, it's emotions as well. In particular, they're emotions which we would consider every bit as fundamental as irritation or delight or disdain are to American culture. Unfortunately, I don't have good terms for any of them, so I'll just have to describe them carefully. 1.  You know the thing about "do it scared, do it messy, but do it"? An emotion that corresponds passably well to that. Or for another much closer point of reference, the sort of thing Luigi Mario seems to be experiencing constantly in the Luigi's Mansion series - sobbing and terrified and still sucking up one ghost to wail on another one with. Driving forward progress driven by a terror of stopping, with a side of near-total [emotional-co...

36. On Removing Fishhooks From Your Heart

Other people have written about the necessity of grieving losses - everything from dead relatives to missed opportunities, from ruined years to sharply ended relationships. Here's a mental motion I have found to help keep the process moving when the grief might otherwise uselessly paralyze you. First, notice the feeling of grief as it arises, likely by chance - this is a technique best suited to those times when grief for the loss arises spontaneously, as it often does. (There is a model of grieving where there is a ball bouncing inside a box, and a button within it of shrinking size, and when the ball hits the button, you feel grief. This is a false but useful model: this technique is for when the ball hits the button.)  Locate where in your body you feel the grief. Maybe it's in your chest, or your heart - it sure is for me. Maybe it's in your neck, or your guts. Wherever it lives in you, feel the pain and loss sharply; concentrate on it. This will likely bring you to t...

35. Consumption Isn't a Hobby

I have a problem with the way many people seem to think about hobbies. In particular, it bothers me badly when people claim that they have a hobby of anything from "listening to music" to "traveling" to "eating tasty food". Even trying to frame it as a matter of aesthetic appreciation or skilled curation doesn't change that for me. As far as I'm concerned, a hobby can't consist primarily of consumption of things other people have made, nor mere appreciation of enjoyable surroundings - there must be an active, creative component to it. Reading is not a hobby, but writing, even be it fanfic or DIY guides, is; eating tasty food is not a hobby, but experimental cooking and wild foraging are; shopping in full generality is not, while making in full generality is. It's not clear to me where the mindset comes from; that mindset that considers watching films a hobby without ever seriously contemplating ever filming anything, that contents itself wi...

34. At Human Scale

There's a metaproperty - a property of properties of objects - that I've noticed that I've never read anyone remark on. That metaproperty is something like "being human-legible" or "being unsurprising for possibly ancestral-environment reasons" or just "being at human scale". It's a little hard to operationalize well, but one stab would be something like: we have a property of objects - density, say - that can have a number reasonably attached to it. The lower and upper extremes of the range of that property give an object or material surprising properties, because they don't act like anything found in nature, but only in human-built environments. If an object has this property at the extremes, it's not human-legible in this way; if it falls well within that range, by contrast, it's human-legible or at human scale. I'll give a few clarifying examples. As above, density is one of the best examples of this metaproperty: not f...

33. Your Heart Will Go On

When I talk about metaphorical hearts - or, if you like, in My Culture's Language and Idiom - what that means is not something necessarily about love, but something about desire or longing. (Love - affection and things akin to romantic love and limerence - lives in the liver, along with care and worry; sometimes also in the lungs, with action and expression and centeredness.) It's about what feels alive to you, what feels innately appealing, what strikes directly at your core, your sense of self, your motivation and drive. Crucially, the broader context of that idiom is visibility; think "wearing your heart on your sleeve", or prying your chest open. With that in mind, I'll define four attitudes or actions that extend that sense of "heart": showing your heart, hiding your heart, denying your heart, and trampling on your heart. To "show your heart" means to pursue your desires freely and openly, and to be frank about the things that you want - a...

32. What Do You Want That Definition For, Anyway?

I have lost track of the number of times I've been in a discussion, and it's already circling a drain called "arguments about definition". It's a terrifyingly powerful vortex to get stuck in, whether you're sailing alone or with a crew; many a bold mathematician has been sucked into it, never to return. It's the spiral of trying to figure out whether a hot dog counts as a sandwich, or whether a tree falling in the forest makes a sound, or whether abortion is murder, or whether 1 should be a prime number. My answer to all such questions these days is one and the same: "what do you want to know that for?" Any working mathematician or philosopher worth their salt will tell you that proofs and theorems are flashy and beautiful and nice and all, and that the choice of axioms backing them up is critical, but the most important thing of all is your choice of definitions. Those definitions, in turn, need to capture something important about some concept...