# Re: Idempotence and "Replication Insensitivity" are equivalent ?

From: vc <boston103_at_hotmail.com>
Date: 25 Sep 2006 09:39:23 -0700

Marshall wrote:
> vc wrote:
> > Marshall wrote:
> > [...]
> > > Furthermore, you seem to have
> > > completely misinterpreted Phil's point, which as I understand
> > > it was that the minimizing property does not indentify a unique
> > > value, but in some cases a range of values. Your complaint
> > > about Phil's point seems to be that the minimizing property
> > > does not identify a unique value. Since that was Phil's point
> > > in the first place, it is altogether unpersuasive in refuting him.
> > >
> >
> >
> > " I'm saying that the property does not always
> > uniquely define a median ("*the* value", emphasis mine), and therefore
> > cannot be used as the definition therefor"
> >
> > Apparently the implication was that some other definition would allow
> > to compute the median uniquely.
>

OK, let's go to the source:

<quote>
> Phil Carmody wrote:
> > pamelaflue..._at_libero.it writes:
> > > the Median is the value which minimize the sum of absolute differences

> > > ie. sum | xi - c | is minimum for c = MEDIAN()

> > If I were Bob Silverman, you'd get one heck of a flaming for
> > posting something so obviously somewhere in between unintelligible
> > and meaningless (including both endpoints) to sci.math.
<quote>

In your opinion, what's unintelligible and meaningless re. the minimizing property to deserve the accusations ?

And further:

<quote>
[PC]
I'm saying that the property does not always uniquely define a median ("*the* value", emphasis mine), and therefore cannot be used as the definition therefor. </quote>

According to you, what was the passage above supposed to accomplish ? Buttress the "Bob Silverman" type of "argument" ? If not, what was the purpose of the statement ?

Further, "therefore" implies that since the minimizing property cannot uniquely define the median, some other definition can. Obviously there is no such definition except for the arbitrary convention (that does not always work) in the case of real valued random vars.

>
>
> > If that was not the implication, why
> > jump at the OP and try to ridicule her for using the mentioning
> > property ?
>
> Because the way she used it indicated that it produced
> a unique value, which it doesn't, and that it was the
> definition of the term, which it isn't.

Why is it not a definition ? Because of non-uniqueness (" therefore cannot be used as the definition therefor") ? If so, then no definition is useful because none yields a unique result (except for the arbitrary convention, see above).

>
>
> > My point sumply was that neither the minimizing property, nor any
> > other median definition defines the median uniquely in certain cases.
>
> That seems in complete agreement with what Phil was saying.

How so ? Are you choosing to ignore the " therefore cannot be used as the definition therefor" part ? Are not you also contradicting yourself : on one hand you seem to agree that there is no alternative defintion that would yield a unique result, on the other you state "and that it was the definition of the term, which it isn't." ?

>
> Marshall
Received on Mon Sep 25 2006 - 18:39:23 CEST

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