[jessenichols]

Because most school is forced knowledge work on problems that don't fit the person's problem situation.

When people are free, they learn the math they need for the problems they are trying to solve.

Traditional, compulsory school forces children to solve problems they don't have. See Karl Popper's idea of the bucket theory of mind, or David Deutsch and Taking Children Seriously.

[bjarneh]

> most school is forced knowledge work on problems that don't fit the person's problem situation.

Have you never been in a situation where you are about to take train going at 80 mph; wondering when you'll meet up with your friends going in the opposite direction at 90 mph?

[mulmen]

I recently saw a great photo [1] by Ben Cooper of a Falcon 9 on ascent crossing the Moon from the photographer’s perspective. I wonder how much math went into finding that vantage point.

[1]: http://www.launchphotography.com/Starlink_4-6.html

[dekhn]

It's not really that hard. I set up several systems to do this for the previous total solar eclipse. The ephemerides for the moon are easy to download and calculate the position in the sky (IE, altitude and azimuth at time t) with a python script.

I believe also the launch vehicle has a launch window (the moon moves 15 degrees per hour) and launch trajectory. I'm lazy so I'd compute the extends of the launch vehicle's motion in the sky (from earliest possible launch to latest possible launch), and then intersect that geometry with the moon position geometry without explictly trying to solve the equations simultaneously. That should back-project to shapes on the ground at which point you could reasonably expect to be able to get a good shot, and then you'd do some adjustment in your pointing in real time.

A smart college senior could do it directly (IE, not lazily compute a bunch of points and manually intersect them on a screen).

[jimmygrapes]

Having done a lot of long road trips, I have often entertained my tired brain by trying to calculate how long it will take me to get to mile marker x, or city y (SPRINGFIELD 400 says the sign) based on how fast I'm going, then how long it would take if I was going 1mph faster or slower, or 5mph, etc. It's relatively simple but to do so entirely mentally seems to take a lot longer for me than I if I could just jot a few notes down. It gets more fun if you try to account for how long it takes for you to slow down for an exit, take a piss and get a snack, then get back up to speed.

I didn't know, for the longest time, what a derivative was. I still don't, not really, though I can bluff my way to a reasonably correct answer using the above analogy and going from dry "rate of rate of change" sort of language into more practical concepts.

[kleer001]

> When people are free, they learn the math they need for the problems they are trying to solve.

Citation needed.

[the_only_law]

Yeah really, when I finally found a reason to get interested in higher level math, I then realized it built on much knowledge from my 12 years of school that I neglected to care about to learn, all further down the chain of abstraction and further away from my problem to the point where it’s no longer interesting again.