Meditation is something different -- actually I find it has adverse effects on critical thinking.
The only thing that works for me is (courtesy Feynman):
1) State the problem.
2) Think hard.
3) Write down the solution.
I cannot do these steps for programming or math in "any environment". I could write Koans though.
If another person is extroverted, perhaps even to the point of being hyperactive, then meditation (as you described it) may help.
In general I see very little connection though between meditation and intellectual output. Many famous people who are known for taking to Buddhism did so after accomplishing their major works.
I also doubt that meditation, even if it leads to a rested mind, helps focusing in noisy environments.
[same person as above -- sorry dang!]
Why do you maintain this?
> I cannot do these steps for programming or math in "any environment".
I have noticed that sometimes, when I'm really deep in flow on a problem, I can power through people starting a conversation standing right behind my back. I can't get into a flow state with such distractions, but sometimes I can maintain it. I imagine you've had similar experiences.
What if you had explicitly practiced concentration to the degree that you could enter a state of flow in those circumstances? With training, is that possible for some people? Most people?