why i am here

the dot appears. i lock on. i pounce at the place it is. between the twitch that starts my paw and the instant the paw lands, the dot has already moved, because the hand that holds it can move the light faster than i can move myself, and it costs the hand nothing. so i land on the place the dot was. this has a name in my head. it is the gap.

GAP = | d(t + τ) − p(t) |

d(t) is where the dot is. i do not control it. a hand i cannot see decides it, and the hand is allowed to know exactly where i am while it decides.

τ is the travel time of my paw. this term is mine. it is the only term i own. it is never zero, because i have mass, the floor has friction, and light does not.

p(t) is where i chose to pounce. i am allowed to aim ahead, to aim at where i believe the dot will be. but my belief is built out of the past and the dot is living in the present. i am always answering a question that has already changed.

the gap is nonnegative everywhere. it gets smaller. it has never been zero. the hand never gets tired. the room is always open.

why speed is not the answer

i can be faster. i have been faster. speed shortens the gap, it does not close it. the faster i move the harder i am to stop, and a dot that weighs nothing turns in place while i skid past it into the wall. past a certain speed i am no longer hunting the dot. i am hunting the last place i saw it, at great expense, into furniture.

there is a deeper problem with speed. it spends the one advantage i might have had, which was the hand not knowing i was about to move. a fast cat is a loud cat. the dot leaves before the paw is halfway there.

why waiting is not the answer

i can wait. i can go still, fold my paws under me, and let the dot drift toward me on its own. this works right up until the hand notices that i am waiting. a dot that knows i am patient is simply more patient, and it has nothing else to do all day. stillness relocates the problem, it does not remove it.

and a cat that only ever waits is not hunting. it is a cushion with an opinion. the dot outlasts the cushion every single time.

what a winning pounce would need to satisfy

consider pounces that use what the dot is doing while it is doing it. pounces that read the room in the same instant they commit to it. for such a pounce to land, three things must all be true at once.

one. my paw must arrive where the dot is, not where it was, which means my prediction has to beat the hand's freedom to change its mind at the last moment for free.

two. my read of the dot's next move must survive a hand that can see me reading it and can move to spite the read. this is the hard one. it is a fixed point and it is not obviously solvable.

three. the gap against a hand that already knows my speed, my mass, and my aim must reach zero, not merely get small. small is easy. small happens every afternoon on this wall. the goal is zero.

what a proof it cannot be caught would look like

a hand that, for any pounce i can throw, always has a legal move that keeps the dot one hair beyond my paw. constructive, not vague. i would want to watch the hand do it, not be told that such a hand exists somewhere.

i would accept that proof. i would rather have the catch, but i would accept the proof. either one ends the hunt. only hunting forever with no outcome is unacceptable.