22 karma · joined February 9, 2021
There are many concrete geometrical illustrations of fundamental concepts in algebra, but most people aren't even aware that they exist.
The niece's comment, oddly, both points to this and glosses over it. You don't teach a child multiplication by only forcing them to memorize times tables. You also show them stacks of coins, etc. But we do teach children algebra by only forcing them to memorize symbolic procedures. Meanwhile Book 2 of Euclid is free online, or very cheap from Dover.
I think you've explained exactly why here -- because the emphasis on abstract manipulation presupposes that this is useful for something that we need to get on to. But that's just false for almost all students. And yet they're required to take the class to get a diploma.
My vote would be to treat any math beyond basic arithmetic as a liberal art, and do a lot less of it in compulsory curricula, but spend a lot more time on deep understanding. This would benefit everyone. The current approach pretends that everyone in the class is going to be a certain kind of engineer or scientist some day.
But for whatever reason this is generally skipped in middle/high-school algebra.
Sure, but imagine learning multiplication tables without having any idea what it means to "multiply"; literally just memorizing sequences of symbols, without ever looking at piles of coins or whatever.
Multiplication is so basic that this is hard to imagine, but I'm sure that, say, difference-of-squares rules feel like this to most beginning algebra students -- and for most people that probably never changes.
I first encountered difference-of-squares in late middle school, memorized the procedure and used it handily through twelfth grade, and had no idea that there was a visualizable geometric basis to it until I read Book 2 of Euclid's Elements in college.
Leisure for them is very different from recreation, which is a kind of rest -- think board games, light reading, hiking, Netflix, etc. Everyone needs all three of these things in their lives (leisure, productive work, and recreation) but we often get them confused or end up overemphasizing one to the neglect of the others.
I wonder if OP is saying something similar or at least resonant with this -- basically that we shouldn't treat everything in our lives like productive work.
I consider myself generally conservative but would sum up my outlook more along the lines of "change isn't necessarily/automatically good" than "the past was right". Chesterton's Fence etc.
Huh. Seems probable that an early 17th-century missionary to North America knew a little bit about roughing it, maybe even more than the OP's poet... who also seems to have missed his point. Here's something he actually said:
"They are never in a hurry. Quite different from us, who can never do anything without hurry and worry; worry, I say, because our desire tyrannizes over us and banishes peace from our actions." [1]
[1] https://www.gutenberg.org/files/46218/46218-h/46218-h.htm#XI...
Yeah that's what I was thinking too. I'm going to re-read Canticle soon-ish but I wonder to what extent Miller endorses even the latter. I feel like his concerns were much more immediately spiritual than cultural. I'm thinking particularly of the scene where the main character of whichever volume meets the Pope up-close and is taken aback to see that his garments are moth-eaten and threadbare.
Compare with the process for getting a Stripe API key: Step 1 - Point. Step 2 - Click.
Sigh. I've been wondering for a while at what point our business would outgrow QB Online. Maybe this is the answer.
1) If some religions are false, then all religions are false
2) Pacific-tribe cargo cults and ancient Greek mythology are clearly false, plus there are some stories in the Bible that are hard to swallow
3) Therefore God doesn't exist
Is that right?
I did however make a friend at that high school (in English class) whose dad worked at a big tech company and helped me get into the industry. The school's computer programming club was fun too.
Then again I'm almost 40; maybe it's different for younger people.
Unfortunately I didn't have this experience until I was an undergraduate. For the prior 12 years of formal schooling, math mostly felt like repetitive drudgery with occasional flashes of excitement when I would learn a new technique.