Re: Summary, was Re: Every time ..., was Re: General formula

[Tony Bartoletti <azb@xxxxxxxx>]

Ed,

Apologies for being somewhat imprecise (and perhaps a little dense)
but I still fail to see how T can approach To.

I know that terms like "almost perfectly redundant or dependent"
are vague, so let me try to define "X almost redundant to Y" to
mean that the probability that X changes (becomes invalid) while
Y does not change can be considered very small.  Indeed, smaller
by orders of magnitude when compared to the size of the set of
variables to which the phrase "almost redundant" applies to every
pair.

Now if I consider 100 such variables, and independently assess
each to have an expected lifetime of 1 year, then I get

   To = T1 = T2 = ... = T99 = 1 (year)
and
   1/T = 1/To + 1/T1 + ... + 1/T99
so
   1/T = 100, T = 1/100  (not at all close to To = 1)

But perhaps the problem is that I cannot find REAL variables that
behave this way.  As hard as I tried, I could only come up with
examples that support your formula.  To wit:

   Consider a very old stick of dynamite, so unstable that it
   may self-detonate at any time, with an expected life of 1 year.

   Now consider a box of 100 such sticks.  IN ISOLATION, each
   stick has expected lifetime 1 year.  But given 100 such sticks,
   the likelyhood that at least one stick will detonate within a
   weeks time is rather large.  So, packaged together in the box,
   the collection of dynamite sticks will likely not last a week.
   (When one of them goes boom, it is almost a certainty that the
   others will follow!)

But this is a strange kind of "strong dependency", and not the kind
I intend by "almost redundant".  In the dynamite example, the
"linkage" of lifetimes is one of causality.  If one stick goes,
then the others follow as an effect.  And if, at time t, one of the
sticks is still intact, it is almost certainly because none of the
other sticks have detonated.

Perhaps what I intend by "almost redundant" is not a reality?
Informationally, a bit is either redundant, or not (boolean).

Comments?

___tony___


Tony Bartoletti                                             LL
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