Loved this. I’m curious why you think most people don’t think this way? Do you think it’s something learnable and if so, how do you think they can learn it? How did you learn to think this way?
My best guess for the reason it isn't taught this way is simply that our educational practices overall are extremely far from optimal! It might be that things really were taught this way in the past, but there's a kind of "drift" where what's taught now is a copy of a copy of a copy...
In my brief interactions with old school physics professors in the past they seemed to love this approach. They'd make you do it for rockets (easy) or bicycles (hard) to check you were good enough at mechanics (I wasn't)
This could is anecdotal but I've noticed that Physicists and Chemical Engineers often embrace this way of thinking much more than other backgrounds... reading this post I wonder if it's because they have to deal with calculations & unit conversion more than others? In other words, to deal with those topics you have to practice a lot of "arithmetic & unit conversion" as you frequently move between concepts (e.g., energy to mass to volume to sound, etc). One person that does this a lot is Randall Munroe (XKCD) and I just looked up that indeed he has a background in Physics... maybe there's something to this...
YES! I think part of the reason no one's done this is that it takes a consistent vision over quite a lot of years to cultivate this skill, and (after Montessori) few folk have been trying to build multi-year curriculums. BUT, we're actually building this into the K–12 curriculum that I'm helping create — you can see the progression of patterns we have, beginning in kindergarten, here: https://losttools.substack.com/i/140665036/math
The tl;dr — first teach abacus, then teach finger math, then teach the soroban, then teach mental math, then get kids to become comfortable w/ big numbers and guesstimates (i.e. to intuit when there's a trillion of something rather than just a billion), then to teach unit metaphors (e.g. a meter is a lightsaber, a gram is a chocolate chip), and THEN to teach Fermi estimates.
Another way of saying this is that the people who get excited about teaching Fermi estimates try to cram a lot of skills in all at once; that'll work for some math-minded people, but what's needed to make this widespread is to cultivate these from the earliest years.
Because then, my GOODNESS, you can have lots of people who experience the world quantitatively, not just qualitatively. A transformation of worldview, correlated to all sorts of other things we want to inculcate in education.
I definitely think it's weird in my professional life how many people don't know about units canceling and how many complex problems you can break down just by keeping track of units. IIRC it never came up in college either, I think I learned it from a clever high school chemistry teacher I had who taught in a really memorable way using the Mystical Island of Mole (situated precariously in the vast Sea of Ignorance).
Always adding salt increases all-cause mortality by 28%. Plugging that into an actuarial table, for a 40-year-old man, that would reduce his lifespan by 2.7 years. Not great, but exercise, food, or habits could offset it. Find your offsets here: https://www.unaging.com/determine-your-age/
Loved this. I’m curious why you think most people don’t think this way? Do you think it’s something learnable and if so, how do you think they can learn it? How did you learn to think this way?
My best guess for the reason it isn't taught this way is simply that our educational practices overall are extremely far from optimal! It might be that things really were taught this way in the past, but there's a kind of "drift" where what's taught now is a copy of a copy of a copy...
In my brief interactions with old school physics professors in the past they seemed to love this approach. They'd make you do it for rockets (easy) or bicycles (hard) to check you were good enough at mechanics (I wasn't)
This could is anecdotal but I've noticed that Physicists and Chemical Engineers often embrace this way of thinking much more than other backgrounds... reading this post I wonder if it's because they have to deal with calculations & unit conversion more than others? In other words, to deal with those topics you have to practice a lot of "arithmetic & unit conversion" as you frequently move between concepts (e.g., energy to mass to volume to sound, etc). One person that does this a lot is Randall Munroe (XKCD) and I just looked up that indeed he has a background in Physics... maybe there's something to this...
YES! I think part of the reason no one's done this is that it takes a consistent vision over quite a lot of years to cultivate this skill, and (after Montessori) few folk have been trying to build multi-year curriculums. BUT, we're actually building this into the K–12 curriculum that I'm helping create — you can see the progression of patterns we have, beginning in kindergarten, here: https://losttools.substack.com/i/140665036/math
The tl;dr — first teach abacus, then teach finger math, then teach the soroban, then teach mental math, then get kids to become comfortable w/ big numbers and guesstimates (i.e. to intuit when there's a trillion of something rather than just a billion), then to teach unit metaphors (e.g. a meter is a lightsaber, a gram is a chocolate chip), and THEN to teach Fermi estimates.
Another way of saying this is that the people who get excited about teaching Fermi estimates try to cram a lot of skills in all at once; that'll work for some math-minded people, but what's needed to make this widespread is to cultivate these from the earliest years.
Because then, my GOODNESS, you can have lots of people who experience the world quantitatively, not just qualitatively. A transformation of worldview, correlated to all sorts of other things we want to inculcate in education.
Thanks for this piece.
This book takes the same approach to all sorts of energy production and consumption, strongly recommended: https://www.withouthotair.com/
I definitely think it's weird in my professional life how many people don't know about units canceling and how many complex problems you can break down just by keeping track of units. IIRC it never came up in college either, I think I learned it from a clever high school chemistry teacher I had who taught in a really memorable way using the Mystical Island of Mole (situated precariously in the vast Sea of Ignorance).
Always adding salt increases all-cause mortality by 28%. Plugging that into an actuarial table, for a 40-year-old man, that would reduce his lifespan by 2.7 years. Not great, but exercise, food, or habits could offset it. Find your offsets here: https://www.unaging.com/determine-your-age/