I think the case here is also what got me into computers at a young age. What makes computers, and software specifically, so appealing is its accessibility and control.

To feel a sense of true accomplishment as an architect, physicist, or biologist you generally need something to happen that can be completely out of reach: erect a building or collide particles. Writing code had a profound effect on me when I was eight. I realized that me, sitting at home and banging away on my keyboard, I had potentially the same power as scientists and corporations with much, much larger resources than me. The fact that a few guys in their early twenties can compete with multi-billion dollar corporations is not to be taken lightly, and isn't exactly shared by many other vocations and industries. Not to mention the existence of an open community, willing to share methods and hacks.

Also, when someone codes a very cool tool or program, many can appreciate it; even if they don't understand it. It's hard to say the same about math or physics theorems.

Basically, the notion of an ivory tower is less evident in programming than in other fields.