Well and honestly most of War and Peace is pretty easy and pleasant to read as well (I'm setting aside the philosophy-of-history stuff) -- there's just so much of it.
What is a "large company" in this context? My employer is on track to run about $5m through Stripe this year, which will be our fourth full year using Stripe. Our first year we did about $2.75m. This year I've been getting occasional emails from a Stripe sales rep for the first time, which suggests that we've crossed some sort of threshold...
Maybe "asking 'why'" isn't the right way to express it. Perhaps what the OP was really after here was a concrete illustration of the formula, rather than a rigorous derivation of the formula from first principles.
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.
This goes to the question of why anything other than basic arithmetic is compulsory. The famous 10th-grader's whine "what are we going to use this for", which infuriated my own 10th-grade Algebra 2 teacher, and even made me roll my eyes at the time, is actually a fair question when algebra is taught as abstractly as it typically is.
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.
Fair enough. Maybe I should have just said that it's possible to give concrete illustrations of basic algebraic concepts, and that doing this would probably help some students learn algebra, and might help others retain it.
But for whatever reason this is generally skipped in middle/high-school algebra.
> there ARE points in a student's academic path where they HAVE TO memorize stuff and do rote operations like the multiplication tables.
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.
I suspect most of us have a serious imbalance in our lives between productive work, leisure, and recreation. See Louis Kelso and Mortimer Adler's book "The Capitalist Manifesto" for a rich discussion of these topics. They define 'leisure' somewhat counter-intuitively as work, but the sort of work that elevates the mind or advances the common good -- as opposed to the productive work one is required to do in order to earn a living.
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.
Similarly I would doubt that anyone actually thinks that the past was good simply because it came before the present. The desire to return to "the way things were" is born of a critique of specific aspects of "the way things are", combined with a sense that tradition is likely to embody hard-earned wisdom that may not be immediately apparent or perfectly defensible by abstract argument.
This is an interesting take on conservatism. I suppose it must be a fairly common take among people who consider themselves progressive, and helps makes sense of some things I've observed recently.
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.
>In the early seventeenth century, for example, the French Jesuit missionary Pierre Biard complained that the Wabanaki did not have to work hard enough to feed themselves ... “Had he ever gone fishing…? Gathered nuts, or berries deep in thorns and mosquitoes? Ever tracked a deer through snow, skinned a rabbit…?”
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]
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.
Interesting take, I would have thought that the early moderns were not too interested in vindicating monasticism. Do you have particular thinkers in mind here?
Yeah I think Miller was using the nuclear holocaust as a vehicle to reflect on original sin (i.e., the inevitable tendency of human beings to engage in self-destructive behavior) and the antidote to it offered by the Catholic Church. If he had written the novel today it probably would have been something other than MAD that nearly wiped out civilization twice.
Reminds me of Jakob Nielsen's rule for writing a good "About" page. If you can insert a "not" into a sentence and get something that no other company would ever put on their own About page, the sentence is worthless.