Subject: Madonna

From: Henry Story <[email-masked]>
Date: Wed, 9 Feb 2005 10:42:03 +0100

Just a point of clarification about identity. (I thought the example
is fun enough that it may be of interest)

As we all know Madonna is a material girl, and she lives in a material
world [1].

Madonna is a US citizen also. Let us imagine the day she received her
social security card through the post. That day Madonna, the material
girl, had a very specific material constitution. Let us call the set
of cells, organic and inorganic material that composed Madonna that
moment M1.

Now let us stipulate that two material things are equal if they are
made of exactly the same matter.

That afternoon Madonna goes to the beauty salon where she gets her hair
cut and fingernails and toe nails clipped. The resulting material girl
call her M2 is no longer the same as M1, as M2 is M1 less some hair
and nail material. M2 may also contain a little more water (she was
drinking some beauty drink during the process). So M1 is not the same
material thing as M2.

Both M1 and M2 are also girls, and have a functional relation to a
social security number. Ie M1 and M2 each only have 1 social security
number. There are in fact a very large number of such material Madonnas
Mx that have a functional relation to that same social security number.
So clearly the inverse relation (from social security to temporal 
Material Madonnas) is not functional.

Now let us think of the mereological fusion [2] of all of these
Material Madonnas, and let us call that MM. MM also has a functional
relation to the social security number. But it is also clear that
there is an inverse functional relation from social security number
to MM.

So the social security number identifies madonna in two ways.

1. via a functional relation
     temporalId:  temporal material madonnas --> social security number
2. via an inverse functional relation
     fusionId: MM --> social security number

Given a social security number we can via the fusionId relation
get a hold of the mereological fusion of that person, and from
the mereological fusion we can find the individual temporal parts,
each of which of course have a temporalId relation to the same social
security number.

The above can probably be also put in terms of set theory, and
so in terms of rdf graphs. In which case it clearly shows how
rdf can speak about temporal and non temporal identity.

Henry Story

[1] http://www.lyricsfreak.com/m/madonna/86925.html
     audio clip: http://tinyurl.com/5k9et
[2] http://plato.stanford.edu/entries/mereology/

---

From: Henry Story <[email-masked]>
Date: Wed, 16 Feb 2005 09:09:57 +0100

Now I would like to show how the Madonna example is relevant to Atom.
In a mail recently Roy Fielding pointed to the following passage of the
the RDF Semantics document:

[[
  It assumes, implicitly, that URI references have the  same meaning
whenever they occur. To provide an adequate  semantics which would be
sensitive to temporal changes is a  research problem which is beyond
the scope of this document.
]]

To make a point as to how apparently graph theory is not powerful enough
to make temporal based statements.

In fact the above says nothing of the sort.

It is exactly what first order logic does. And people like David Lewis,
and many other great logicians have shown that this is entirely 
sufficient
not only for basing temporal reasoning on, but the often even less well
understood counterfactual reasoning. [1].

My guess is that the temporal reasoning problems people discover
are not so much related to RDF, as to the novelty of these tools
and the lack of experience people have with them. I would like to
note also that quoted passage does not says temporal reasoning
is impossible, only that it is beyond the research scope of the 
document.

The problem as I understand it lies just in the simplicity of that
claim, that a URI denotes some thing that does not change. People then
look at URIs such as <http://www.worldtimeserver.com/> and notice that
it changes, and so the conclusion is easily made that rdf does not model
the web correctly. But what we know when we fetch the above web
page is that we are getting a description of that resource. Since we
can get the resource over time, the problem is exactly the same as the
one I described with my Madonna post. Each of these returned
descriptions are descriptions of that resource returned at different
times, but the whole resource itself is described only by the whole set
of those description.

The parallel with Madonna, the material girl, is instructive.
When the government assigns a social security number to her, they
are naming one resource that does not change. But let us look how
modern skeptics following the ancients could use this to their
advantage to argue that the social security numbering system is broken.
At age 18 Madonna goes to get her drivers license. The clerk could
write down the following:

<urn:ss:123456789>
   |---name------> "Madonna"
   |---size------> 170cm
   |---sex-------> <female>

  Then at age 25 she may get stopped by the police who write
down the following

<urn:ss:123456789>
   |---name------> "Madonna"
   |---size------> 175cm
   |---sex-------> <female>

An ancient skeptic would have used this to show the inherent
contradiction in the whole social security system.

Of course the answer is that the social security number
only identifies the mereological fusion of all temporal
Madonna parts. If you wish to speak of one temporal instance
of Madonna, you need to introduce a blank node.

:M1
  |---ssn---> <urn:ss:123456789>
  |---name------> "Madonna"
  |---size------> 170cm
  |---sex-------> <female>
  |---age-------> "16 years"

ssn is a functional property of the temporal madonna part M1. It
is not an equivalence property, and neither is it inverse functional.
It is therefore possible to have numerous Madonna parts each with
different descriptions.

No problem really.

Notice the incredible similarity with my arguments concerning
the Atom feeds. An Atom feed describes various resources, Entries,
that can change over time.

If you insist on describing the resource directly with a URI
you will either force the URI to be the URIs of a time slice, going
against the syntax of http urls especially (since they can be used
over time), or you will say something false.

<http://www.worldtimeserver.com/>
    |----content----> "the time is 9:24am in Cuba"
    |----date-------> "14:24 French time"

<http://www.worldtimeserver.com/>
    |----content----> "the time is 10:00am in Cuba"
    |----date-------> "15:00 French time"

That of course is again a contradiction, and your ancient
skeptic would have used that to prove that time does not
exist.

Of course we can identify via a blank node a time slice
of the resource

:T1
  |----content----> "the time is 9:24am in Cuba"
  |----date-------> "14:24 French time"
  |---funcId------> <http://www.worldtimeserver.com/>

And with another blank node identify another time slice
of the resource

:T2
  |----content----> "the time is 10:00am in Cuba"
  |----date-------> "15:00 French time"
  |---funcId------> <http://www.worldtimeserver.com/>

There you go. We have it down to a T. There is no
contradiction here. Not within a document and not across
documents.

And therefore having multiple entries with the same id in
a feed is perfectly alright, according to rdf, according
to simple first order logic.

But perhaps some people in this group have stepped beyond logic,
have seen  further than the greatest thinkers of the 20th century.
Please do enlighten us.

Henry Story

[1] http://www.amazon.com/exec/obidos/tg/detail/-/0631224254/

---

From: "Roy T. Fielding" <[email-masked]>
Date: Wed, 16 Feb 2005 17:17:11 -0800

> the RDF Semantics document:

No, you pointed to that passage.  I pointed to the RDF semantics
intro.  Moreover, just prior to stupidly answering your question,
I wrote:

   "Okay, but only if you promise not to extend this discussion
    on the atom list ..."

and since you chose to ignore that, I cannot sensibly continue
this discussion other than to say I was talking about RDF, not
graph theory in general (obviously).

....Roy