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)
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).
I wasn't taught dimensional analysis until first semester senior year doing engineering at a good college, which in retrospect is unbelievable. Should have been taught during high school physics at latest!
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/
If you've ever talked to a spreadsheet jockey — someone who does Excel for a living — it's all arithmetic. Companies are managed and run via arithmetic. The financial planning teams exist to do arithmetic. Microsoft Excel is a magical tool, still going strong 40 years after release, because it makes arithmetic easy to do and thus makes it easy to build lots and lots of simple models.
Spreadsheets are a missing part of the curriculum for junior high school, in my opinion. I'm planning to find a way to teach my daughter to use them around then.
I considered writing a calculator app that had connected nodes like Blender's geometry nodes, where you could set up calculations and changing inputs would propagate to its outbound connections.
I scrapped that idea when I realized it was just Excel.
Popular spreadsheets don't (as far as I know) really allow you to keep units around. So if your app could include them and do the kind of automatic conversions I'm talking about, maybe it would be great!
That would be pretty cool, though I would need a lot more knowledge of units to really make it work. Linux and alikes have a units command line tool that knows all sorts of obscure units, so I'd have a lot of work to do, plus letting users define their own, like "chimps per kWh" or something. Thankfully, in dimensional analysis, most of the units don't need to be physically realizable!
At one point in my career, I was very interested in getting into management consulting. That has various pros and cons, but it was very good for getting lots of practice at Fermi estimates and mental arithmetic. My dad was also an old-school structural engineer who had me check all of our restaurant receipts when I was a kid by adding the numbers in my head, more or less. Also pretty good practice.
We actually do use lots of elevated mass to store energy surplus. It's just that it's water, not steel. We can pump it up in small increments, obviating the need for massive mechanical advantage necessary to raise a steel cube, and the shape of the reservoir lets us control the pressure and this the force of the discharge.
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)
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).
I wasn't taught dimensional analysis until first semester senior year doing engineering at a good college, which in retrospect is unbelievable. Should have been taught during high school physics at latest!
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/
This assumes that everyone has the same salt sensitivity, which I believe isn't the case. https://www.nature.com/articles/s41371-020-00407-1
If you've ever talked to a spreadsheet jockey — someone who does Excel for a living — it's all arithmetic. Companies are managed and run via arithmetic. The financial planning teams exist to do arithmetic. Microsoft Excel is a magical tool, still going strong 40 years after release, because it makes arithmetic easy to do and thus makes it easy to build lots and lots of simple models.
Spreadsheets are a missing part of the curriculum for junior high school, in my opinion. I'm planning to find a way to teach my daughter to use them around then.
I considered writing a calculator app that had connected nodes like Blender's geometry nodes, where you could set up calculations and changing inputs would propagate to its outbound connections.
I scrapped that idea when I realized it was just Excel.
Popular spreadsheets don't (as far as I know) really allow you to keep units around. So if your app could include them and do the kind of automatic conversions I'm talking about, maybe it would be great!
That would be pretty cool, though I would need a lot more knowledge of units to really make it work. Linux and alikes have a units command line tool that knows all sorts of obscure units, so I'd have a lot of work to do, plus letting users define their own, like "chimps per kWh" or something. Thankfully, in dimensional analysis, most of the units don't need to be physically realizable!
At one point in my career, I was very interested in getting into management consulting. That has various pros and cons, but it was very good for getting lots of practice at Fermi estimates and mental arithmetic. My dad was also an old-school structural engineer who had me check all of our restaurant receipts when I was a kid by adding the numbers in my head, more or less. Also pretty good practice.
We actually do use lots of elevated mass to store energy surplus. It's just that it's water, not steel. We can pump it up in small increments, obviating the need for massive mechanical advantage necessary to raise a steel cube, and the shape of the reservoir lets us control the pressure and this the force of the discharge.