Neither, go for a walk. We think best on our feet, with our hearts working a little bit, in a fresh environment. Just like our ancestors did.
I like to think while running too, but it might be tricky to do calculus level thinking in your head.
Jess H. Brewer
Alan is right. Go for a long walk! (Or a run, if you’re up to it. I’ve worked out many Physics research problems in my head while jogging.)
Among other famous thinkers, Henry David Thoreau claimed that long walks (preferably in the wilderness) were essential to his deepest thoughts.
(DO NOT take your cell phone along! :-)
That will depend on the person. Some people get their brightest ideas sitting in traffic, standing in the shower, talking about something else when sheer inspiration strikes. The more really is to relax the mind, get it off-topic and in more of a state of rest so that it changes modes from data output to data input. And that can be standing, sitting, walking, racing or lying on the bed unable to sleep.
Thomas Edison use to sit with two large ball bearings in his hand. As he would fall asleep the Ball bearings would fall to the floor and wake him up. He said the state of mind as he woke is the few seconds of complete clarity were his best solutions came to him.
Shower. Unless you’re in California.
I think seated.
And that too on a toilet seat while you defecate.
My most inspiring thoughts have taken birth in the latrine!
A tried and tested method is laying down, thinking deeply about the problem you are stuck with and eventually falling asleep. There is a fair chance that you will have a solution when you are up again. It’s like having a dream in which you or someone else solves the problem and when you wake up, you remember the dream along with the solution. I have done it many a time.
Sleeping is the best form of rest for the body. Sitting is better than standing if one wants some rest. If while sleeping one can solve the most difficult problems, as it is the case with me, then by that analogy, sitting is more productive than standing for thinking deeply and solving great problems for the people like me. Or I am just lazy.