I can tell I’ve been working on something too long when I start arguing with the mathematical we. You may be wondering, “What (or who) exactly is the mathematical we?” Consider the following for illustrative examples:
Hence, from Equation (4.4) we see that P ~ 1/?n
It is quite intuitive that the limiting probabilities for this Markov chain should just be p,q, and r. To verify this we must show that they satisfy Equation (4.7)
(Another sign I’ve been working too long – writing things like “Consider the following for illustrative examples” with a straight face.)
These mathematicians are clearly trying to make me feel more included. And in the beginning, perhaps I do join them in the slog from equation 4.4 to 4.7. But after awhile, every time I see a we, I begin an imaginary argument, like
Mathematician: We see that…
Me: No, we don’t. You’re not making any sense. Don’t try to sneak that combinatorial identity by me like it’s nothing.
Mathematician: Let’s assume there are n blue balls…
Me: Do you even hear yourself? I’m not assuming anything about blue balls. Can we use some other color that leads to less snickering? Honestly, I’m pretty sick of talking about balls in general. Can we switch to marbles or skittles or kittens?
Mathematician: So let us consider state 0 and attempt to determine if P is finite or infinite
Me: What? All we ever talk about is state 0. Can’t we branch out a little and start at 1?