Re: poly: Hurry paradox

>We get about 70 channels on our cable TV system. One of the channels
>is a cable guide, which shows what will be on each channel over the next
>90 minutes. It scrolls through all the channels at a painfully slow rate,
>so it takes about three minutes to go through the whole list and get back
>where you started. [...]
>
>On the one hand, hurrying doesn't make any sense. My actions are
>completely uncorrelated with the timing of the cable guide, and no matter
>when I switch to that channel the average amount of time I will have to
>wait to see my channel's listing is the same.

Yes, but the wait starts when you get the channel guide to appear.
Imagine you switched it on now...or six minutes from now. You would
definitely find your program at different times. Your actions are
correllated with *which* rolling-around of the given channel you see.

>But on the other hand, if I could get to that cable guide channel 10
>seconds earlier, I might be able to see my channel listing just as I get
>there, while if I had waited 10 seconds I would have just missed it and
>have to sit through the entire cycle before I see it again.

On average, if you get to the channel guide n seconds sooner, you'll
get to the program you want n seconds sooner. But the average delay
will be n + 90 (half of 3 minutes). So you can't affect the total by
a large proportion, but you can affect the absolute total. On average.

I think about things like that because my mind goes into a kind of
spasm of trying to think of the optimum way, especially when there's
an element of randomness like in Hal's problem.

For instance,I'm late--should I run to the subway stop, given that the
trains are spaced about 10 minutes apart but otherwise not predictable?
My pace slacks for a moment until I remember the argument above.

It's a curse--I'm sure
too much effort and stress put on silly optimizations is non-optimal.
Fortunately, arguments about how much difference a choice makes on
average work for me emotionally.

 --Steve

--
<sw@tiac.net> Steve Witham  The Pentium: Processaurus Rex