Re: General formula

[Ed Gerck <egerck@xxxxxxxxxx>]

Bob Blakley wrote:

> Ed,
>
> >Wait -- this is NOT the issue here. Bob Blakley wrote that equal lifetimes
> >would indicate a "property" -- that the corresponding attributes would
> >actually be dependent or at least have a tendency to be dependent. I replied
> >negatively -- such property or tendency does NOT exist. Lifetime distance
> >does not correlate with attribute independency -- much in the same way that
> >a pointer's value (lifetime) does not correlate with a pointer's address
> >(attribute).
> >They are two entirely different concepts, not only different values. Thus,
> >the fact that the lifetimes are equal or even similar for two attributes does not
> >authorize me to say anything about the attributes' dependencies.
>
> This may be the source of our apparent disagreement -- I say apparent because
> it does not now and has not yet appeared to me that we actually disagree
> on anything of substance.

Yes, I believe we are in substantial agreement  -- but certainly not on this
subject. And, IMO, this is a simple confusion which is hiding the forest --
but, only because of some trees so, let me help chop them down.

> I did NOT write that equal lifetimes indicate a property.  What I *did* write
> is that there are many real-world cases where there is *either* exact equivalence of
> lifetimes because of dependence, or dependence without exact equivalence
> of lifetimes.  I gave an example of the former.

IMO, the problem is a simple confusion. You said in your former e-mail
that you are using the word "lifetime" to designate the origin of a period in
time, but such use is not warranted as I extensively commented and
exemplified in my e-mail right before this reply. The lifetime of an object
designates "the duration of the existence of the object" -- "attribute lifetime",
"star lifetime", "certificate lifetime", "battery lifetime".  All, the same concept.
In Engineering and Physics, it is usually a stochastic variable that represents
the expected duration of an object's existence -- quite in accordance with
the linguistic use.

So, there are NO "real-world cases where there is *either* "exact equivalence
of lifetimes because of dependence", or "dependence without exact equivalence
of lifetimes", as you wrote above.  Your example does not apply. As I wrote
above, "Lifetime distance does not correlate with attribute independency" --
so "lifetime equivalence" (ie, equivalent values) has nothing to do with "lifetime
dependence". The numerical values of a set of lifetimes CANNOT be used
to infer anything about their dependencies, or lack of.

> I noted that your formula does not *and is not intended* to cover these cases
> if you treat the dependent attributes as separate and plug their lifetimes into
> the formula as if they were independent.

The equation I derived neither makes nor depends on such assumptions. The
equation does not depend on the attributes being independent. Please see
my example in reply to Tony -- the one where he used his own name to
exemplify strong dependency.

> In this sense, the formula is not "general" in the sense that gravitation is
> "universal".

I never [yet ;-)] said that the equation I derived is "universal". But,
that it is based on assumptions which are generally valid for PKIX
certificates. In fact, I know no counter-examples.

And, one of the predictions of the equation I derived is that "the
lifetime of a certificate is inversely proportional to the number of
its attributes".

Which means "good news" when compared with what was
previously believed (though without proof) and which you first
questioned on the list -- providing both a reason and an excuse
for my posting with that equation. As I wrote last week,  my
posting was  excerpted from a paper which I expect to be
ready from review this week. I hope the paper will provide
(at the expense of reading time) for a more comprehensive
context.

Cheers,

Ed Gerck