(*JK*)

Arithmetic is the science of specific amounts. Algebra is the science of general amounts. Calculus is the science of changing amounts.

I flunked Calculus I, took it again and passed it with a C. After I came back from the Navy I took it a third time for a refresher and the best I could do was a B. I took 4 calculus courses and never aced one of them. But when I finally put Dr Goodman’s book away, I felt a greater sense of accomplishment than when I earned my degree.

But the book of nature is written in Differential Equations. In DE you use calculus like you used algebra when you were doing calculus, and arithmetic when you were doing algebra.

One of the proudest moments in my life was when my wife finished her Calculus IV course at DeAnza (she had never graduated from high school when I married her).

Computers can certainly solve calculus problems, but doing calculus “on paper” can actually create new problems, new equations.
Most physical laws are expressed as differential equations. Bear with me for a moment here…

Newton defined a force as the derivative of momentum. Momentum p
is mass m times velocity v. That’s human genius; here, calculus takes over

So F = dp/dt = d(mv)/dt

and by the chain rule

= m(dv/dt) + v(dm/dt)

dv/dt, the derivative of velocity,
is just the acceleration, so the first term is just F = ma, Force = mass times acceleration.. The second term drops out because the derivative of the mass is 0. Mass does not change. At least, not until Einstein came along. There are no numbers there at all, just abstract quantities, but not only does it show us how to calculate the force on a rocket (where the mass changes as propellant is consumed) but it even hints at the relativistic case where the moving mass itself DOES change.

The point is calculus just doesn’t solve problems, it gives us a way to think about problems, and rephrase them, and even suggest answers. When I first realized that I freaked. That is POWER.

When I got to college I struggled with math. Although I had a great intuition for physical science, that will only take you so far. Without the math you really can’t get any creative work done. But I stuck with it, and by the time I finished my astronomy degree
I was 3 undergraduate courses short of a degree in math, so I took them, passed with C’s and got the second Bachelors. It damned near killed me, though. I’d never studied so hard.

My undergraduate grades were above average, but not superior. I was a B student. (This was before grade inflation!) The highest level math I was exposed to was partial differential equations and some complex analysis.

It wasn’t until my second term in astronomy graduate school that I realized I was out of my depth. I hit a wall. I realized I might kill myself and eventually get a Master’s in Astronomy, but I would never get any higher, never do any really creative work in research. I was destined to play Piano Bar at some community college, not Bach at Carnegie Hall. I quit and went to work overseas to get my head sorted out.

Math is like music, or foreign languages. Anyone can do it, if you work hard enough. But some people have a real talent for it, and they are the ones who get to do the really neat things. I envy them. They are very lucky people.

I’ve pretty much forgotten most of my calculus and DE, and my linear algebra and set theory–I haven’t used them since I left school. I’m still pretty conversant with my trigonometry and algebra, because I use it in navigation a lot. So I have managed to retain pretty much what I had when I left high school.

Anyway, it wasn’t a matter of overcoming a disorder, it was a matter of attaining (and retaining) the required skills.

Anyone who doesn’t either work or play with numbers will get rusty with them after a while. Hence figuring a tip or proper change may become something of a challenge. It doesn’t help that those people may also cramp up a bit further with math-phobia.

I’m a firm beleiver in the notion that anyone can become, and remain, fluent and relaxed with numbers if they simply exercise their numerical abilities once in a while.

I’d have to do each subtraction in my head one at a time. And yes, my fingers sometimes start moving when I’m dealing with thirteens and fourteens, or figuring a tip.

This popped out to my cynical eye:

Dyscalculia researchers have speculated that the disorder gets less attention than dyslexia and other reading disorders for the same reason – it’s not seen an urgent crisis like illiteracy. Research dollars bear this out. According to Butterworth’s paper, the National Institute of Health has spent almost 50 times more money on dyslexia than dyscalculia since 2000 ($107.2 million vs. $2.3 million).

Follow the money?