Programming is quite a remarkable activity:
- It has an extremely low barrier to entry
- You don't need expensive equipment
- You don't need to be in a particular location
- You don't need special credentials
- You can finding information / resources just by opening the internet
- You can learn it / do it independently
- It gives you rapid feedback (which can lead to rapid growth)
- It gives you frequent rewards (which gives a huge boost in motivation)
- It's objective and unforgiving (this is a good thing, because it teaches you how to confront reality)
- It's intellectually stimulating
- It's useful in the real world
- Corollary: you can make money or even build a career out of it
- It's badass (or are you telling me that Hackers WASN'T your favorite movie of all time?)
- Electronics (but this is basically still programming)
- Math (lacks "rapid feedback" and "frequent rewards"; "useful in the real world" is also questionable)
- Go, poker, video games (usually lacks "useful in the real world", sometimes lacks "badass")
- Juggling, poi (lacks "intellectually stimulating" and "useful in the real world")
That's a fact, eh?
So, when a mathematician is approximating solutions to differential equations, their brain is functioning the same as if they were catching a ball?
To catch a ball in midair, requires the same hand eye coordination as moving a drumstick to hit a drum at the right time.
But what I'm talking about, is not how the hand moves to catch the ball or hit the drum or find the right fret.
To catch a ball, the hand moves to catch a ball. The ball is the input, the catch the result.
What I'm talking about happens before hand-eye coordination ever begins.
To play music, you are mentally throwing multiple balls all the time, and then catching them at the right time. The part of music that engages in the brain is not catching the ball, it is mentally placing the ball on a discrete grid.
Again, if you disagree, I'll take your word for it.