There may be a constant of undetermined value in there as well to reflect the efficiency of one's idea generation mechanism. This would vary from blogger to blogger and might be time-variable as well. I'd add it, but I already made the figures, and well, I don't have time. Hence...
This is it - 1/70, to be prcise, assuming t in years.
My final post. Lacking any insight or creativity
A few muddled clarifications.
I meant z to have units of years. Thus a nine-month old results in K to the 4/3 power.
Oddly enough, my eta is 4/3 at the moment. This suggests that there is definitely a constant missing - maybe a multiplier, maybe an exponential - but calibration is needed. I might also need to adjust the Beta factor. I just realized that if you have one student working for you, Beta is always 1 regardless of the number of projects you are involved with. Doesn't seem quite fair. But I'm not sure how to represent the math. I wanted to capture that research is easier when you have students, but that managing the students can become a chore in and of itself.
Any other suggested revisions?
I'm concerned that because x=0 for a class you are teaching for the first time, there is an undefinable term in the equation. Then again, maybe that's intended for that first-time class...
Brad: I like your interpretation, but I think I got my math wrong (again!)...I meant to define x = the xth time you've taught the class
Geesh. I think I should stop writing math in a hurry. I may take this down and revise it this weekend. Hopefully my paper revisions are making more sense.
This is a new idea to me. Expressing my life in terms of math?!? I should try that some time.
There is definitely a variable lacking here, or more precisely,another principle which has not been factored in.
That principle is the rule stating that time posting blogs tends to interfere with and utilize time which should be used for other, probably more disagreeable, endeavors. This is why major corporations monitor every office peon's internet use.
Of course, I'll grant that certain factors, such as young children, tend to steal back some of this available time. One doesn't mess around when a child utilizes unconventional means, such as a big rock, to open a "child-proof" bottle.
It is, however, quite easy to delegate taking roll in a classroom, or to delay a project a few minutes. Perhaps an equation reflecting these time theft factors could be developed, and utilized in conjunction with the existing formula. I'd offer to help, but I've hated math since I learned that pi goes on forever, and life doesn't.