obrentharris 

I'm guilty on both counts!
The counting is completely mindless and I never notice it until I'm up to about eighty!
The songs usually come out of "nowhere," but If I think about them long enough I can usually figure out what triggered them, many times it's a word in the title: Classic example, I often find myself singing out loud "The Great Pretender" made famous by the platters whenever I am on a rapid, curvy descent. Then one day I caught myself singing "Yes, I'm the great descender, descending like you're still around..."

Often it's tunes I've recently learned: I play old timey music with a bunch of friends every week and a couple of these friends have been playing for decades longer than I have so they are always bringing new tunes that I've never before heard. I guess my mind has decided that bike rides are a good time to try to commit those tunes to memory. But I've never composed a tune while riding; somehow the fingers need to take the lead in that process.

I compose a lot of dialog while I'm riding, things I think I will say in some upcoming conversation, puns, and things I should have said in past conversations if only I had a quicker wit.

I do still spend about an hour of each ride doing what @plonz describes: If you can think coherently you aren't working hard enough so crank it up a notch. As I get older (I'm in my sixties) I can't keep that up for hours on end like I did when I was a young whippersnapper of 50. I spend more time smelling the roses and enjoying the great scenery in most of the places that I am luck enough to ride. After a couple of hours on the bike I can get into a meditative state in which I'm mainly just watching the world go by.

Thanks for bringing up the subject Jim.

Brent