Gavin Kistner
10/27/2006 4:53:00 PM
From: ara.t.howard@noaa.gov [mailto:ara.t.howard@noaa.gov]
> right. i understood that. but this is where i see the
> contradiction: from
> the viewpoint of the __observer__ a clock which remains
> static for 20 minutes
> cannot also simoutaneously vary a mere 5 minutes from reality. ;-)
I suppose my perception is that it's OK because:
a) It's not 'static', given the implied variable ambiguity implied by
the '~'. (Maybe each call to the clock should use sequential characters
from '|/-\' instead of '~' to show it spinning and changing. :)
b) The observer is relying on the clock to know how much time has
passed. With access to no other timepieces, the observer has no idea
that it has stayed static for 20 minutes, just that it has stayed static
for...what feels like a long time. :)
> yes, i see that. still, it seems flawed. think about it on
> a number line,
> which does not wrap as times do.
[snip]
I think I see what you're saying here. It feels to me like you're saying
that because the short term variation cannot be truly brownian (being
both clamped and having a unidirectional filter on it), that the overall
statistical variation is flawed. I'm not enough of a statistician to
know if this is the case or not, but it feels true: given a random
chance of overshooting or undershooting, the time will probably
overshoot on the average since it has less chances to come back towards
the middle.
Ensuring an even distribution of over/undershoot is desirable, and
probably achievable with differently weighted probabilities for
over/undershooting. That seemed enough like hard work to me to put that
as the fifth Extra Credit item in the original. :)
> great quiz btw!
I hope so. It seems like such a simple problem (and I don't think
because it's under- or ill-specified), but I've yet to have the "Ah-HA!"
moment in the shower that gives me an elegant way to accomplish it. I'm
looking forward to trying to solve it this weekend, and very much
looking forward to see what other people come up with.