So, agreed with this all being an excellent world modeling technology and it would be great if more humans felt comfortable using it. And I agree that most humans are not comfortable using arithmetic.
However, I don’t think units are part of arithmetic. I think they’re part of algebra. They’re like variables that you know never equal zero.
Now, if you know arithmetic, there’s really only a couple of things algebra tells you you’re allowed to do, and most people probably never internalize them: you can always add zero or multiply by one for any quantity, and you can multiply by or add a constant to both sides of an equation. That’s basically it. Using units is all about creative ways to multiply by one.
Also: A significant part of my professional life gets called “modeling” but is really just things like this, in the form of building spreadsheets of constants and assumptions to make rough estimates of quantities we can’t measure, then sanity checking them. It’s the kind of thing even many professional scientists and engineers and investors don’t feel comfortable doing outside their own specialties.
Edit to add: in college my first physics class assignment was just random Fermi problems to be answered without looking anything up using top-of-mind round-number assumptions (1, 2, or 5 x 10^n). Things like “How many feathers does a chicken have?” or “How many letters are there in every book in the main campus library?” Second favorite homework assignment I’ve ever been given.
Most people never realize how much the things they know imply about the things they don’t.
May I throw geometry’s hat into the ring? If you consider things like complex numbers and quarternions, or even vectors, what we have are two-or-more dimensional numbers.
I propose that units are a generalization of dimension beyond spatial dimensions, and therefore geometry is their progenitor.
So, agreed with this all being an excellent world modeling technology and it would be great if more humans felt comfortable using it. And I agree that most humans are not comfortable using arithmetic.
However, I don’t think units are part of arithmetic. I think they’re part of algebra. They’re like variables that you know never equal zero.
Now, if you know arithmetic, there’s really only a couple of things algebra tells you you’re allowed to do, and most people probably never internalize them: you can always add zero or multiply by one for any quantity, and you can multiply by or add a constant to both sides of an equation. That’s basically it. Using units is all about creative ways to multiply by one.
Also: A significant part of my professional life gets called “modeling” but is really just things like this, in the form of building spreadsheets of constants and assumptions to make rough estimates of quantities we can’t measure, then sanity checking them. It’s the kind of thing even many professional scientists and engineers and investors don’t feel comfortable doing outside their own specialties.
Edit to add: in college my first physics class assignment was just random Fermi problems to be answered without looking anything up using top-of-mind round-number assumptions (1, 2, or 5 x 10^n). Things like “How many feathers does a chicken have?” or “How many letters are there in every book in the main campus library?” Second favorite homework assignment I’ve ever been given.
Most people never realize how much the things they know imply about the things they don’t.
What was your first favorite?
It was a 2 sentence problem set from my sophomore year wave mechanics class. Really got the whole class working together.
1) Derive rainbows.
2) What angle does the wake of a boat make with the boat?
May I throw geometry’s hat into the ring? If you consider things like complex numbers and quarternions, or even vectors, what we have are two-or-more dimensional numbers.
I propose that units are a generalization of dimension beyond spatial dimensions, and therefore geometry is their progenitor.
It’s a mathematical Maury Povich situation.