This is the question that the industrial psychologist Paul Fitz wrestled with
in the 1950's.
This was an era of factory automation, and Fitz was interested in understanding,
say for example a machinist in a factory is grabbing parts out of different bins.
How long is that gonna take?
He distilled this down to a laboratory task and
he had people tap alternatively between two different strips of metal,
and what he did is he had people go back and forth as fast as they possibly could.
And the limit of that speed was the time that was purely a function of
the motor ability, as opposed to how long it took you to think and plan and
all of that stuff.
And what he found, this was also an era when information theory was on the rise,
is what he found is that in essence, the motor motion could be
modeled as if it were like an initial ballistic trajectory.
You start throwing your arm over towards the target, and
then you update in real time, and so in essence, you're adding bits to
the signal as you try and land in the particular location that you wanna hit.
And so, the amount of time that it takes is
a function of, so we can take our time here,
is gonna be a function of the distance is clearly involved.
The other thing that matters is the width of the target.
Fitz's initial study was in one dimension, it later got generalized to two.
So if you have a really narrow target, it's gonna take a long time.
If you have a big fat target, that's gonna go faster.
It turned out the ratio between the distance and the width matters a lot,