That mean my vision is free to concentrate at the screen. That means that my short-term memory don't have to memorize what I am currently seeing at the screen. This means I have more precious short-term memory to do whatever important task I am doing, like, programming.
Subjectively, touch typing is surprisingly comfortable. So even if I'm completely wrong about the above, I still feel better, and that alone is worth the investment.
http://sites.google.com/site/steveyegge2/practicing-programm...
Now, does doubling your typing speed also double your productivity? No, of course not, you spend time thinking, looking through code, reading specs, searching for solutions, compiling, etc. But I don't see how improving your typing speed would not result in at least some productivity gains.