Hi Robert (and HPCoder)
In a semantic network, you need not destroy an object's present
manifestation through a transformation. You can maintain a "snapshot"
of the object by using some sort of provenance and thus, forever
express its "Platonic" realization at some particular moment in time.
Reification and named graphs are good for this. Furthermore, in terms
of Platonic concepts, a semantic web does not transform values, it
merely redirects edges. When you add x + 1 to get 7 from 6, you did
not "destroy" the 6. That URI still exists. What you did is you
redirected the x URI to the 7 URI. You didn't change vertices, you
changed edges. I believe this representation is more in line with
mathematics than with computer science where a register value is
dynamic.
I don't know the notation convention (I think its called denotational
semantics or something along those lines), but its in my book on
Formal Semantics of Programming Languages where when there is an
operation on a value, they represent the state of the machine for
when that operation took place. In this sense, the concept of time in
the mathematic sense and the concept of state in the computer science
sense, preserve the notion of a mapping (not a disfiguring
transformation).
I don't think there are any contradictions between the two systems.
However, in the computer sciences, where practical applications tend
to be the end goal and memory is bounded, its preferable not to map
the present to the future, but to transform the present into the future.
Take care,
Marko A. Rodriguez
Los Alamos National Laboratory (P362-proto)
Los Alamos, NM 87545
Phone +1 505 606 1691
http://www.soe.ucsc.edu/~okram
On Jun 3, 2007, at 4:35 PM, Robert Howard wrote:
Marko (and Russell Standish),
In Graph Theory, you have circles and lines (i.e. nodes and edges,
or vertices and connections).
It is possible to have circles and no lines, but not the converse.
This is because every line presupposes two circles—one on each end
of the line. The two circles can be the same circle (i.e. a
reflexive line) but in this case, that circle is playing two roles:
FROM and TO (or source and sink).
PROOF: If you look at the definition of a graph in the PDF you sent
or on Wiki, it says V is a set of vertices, and E ⊆ V X V is a set
of edges. Well, every subset presupposes a superset. QED.
As mentioned previously, and for the same causal relationship,
dynamics presuppose statics. If your goal is to model the dynamics
(you used the term “procedural aspects”), then first model the
statics (you used the term “structural aspects”).
When I try to fit the definition and uses of “objects” as per
the semantic web into my own paradigm, I get contradictions. As I
define:
An object is two parts: a static part and a dynamic part.
Although mathematics is the first object-oriented language
(practically perfected at inception), the computer industry has
really convoluted the definitions to the point where nobody know
what anyone is talking about these days.
Computers bestow the concept of “lifetime” to objects. Computers
create objects in memory, and then dispose of them when no longer
needed only to create different objects later at the same identity.
We almost take this for granted!
Mathematics does not have this concept of lifetime. In fact, the
Platonic philosophy imagines the number “7” as something that
just exists out there timeless, immutable, and consistent, where
its identity equals its class and state. Its identifier maps
bijectively to its identity. Its name is its value. However,
computer objects pop into existence during the execution of some
system and pop right back out. I can’t help but think about
virtual particles (or for that matter, universe bubbles) popping in
and out of the space of all things possible. When the program ends,
the universe ends too.
Mathematicians are “inside” the world of mathematics whereas
computer programmers are “outside” the world of computers. It
should be no wonder that historically, the best theories of
physics: Newtonian, Relativity, Quantum, come when we move our
godlike egos from outside to inside. Perhaps computer programmers
are the last bastion fighting the wave of humility. Bekenstein’s
Theory of Information suggests that they are starting to come inside.
I just bought Russell Standish’s book “The Theory of Nothing”
after reading the cover. I’m always looking (mostly in vain) for
someone else’s perspective on what I think I understand but cannot
express: that our multiverse is the superposition of all consistent
solutions (or family of curves) that sum to zero. That’s how you
get something from nothing. I have high hopes with this book. Still
waiting for it to come!
Anyway, the physical limitations of finite computers force us to
partition the static part of an object into two parts: its class
and its identity. The dynamic part of an object is still called its
state.
In the world of computers, an object’s class is the static set of
immutable rules that the object always conforms to – even before
the object was created and long after it’s destroyed. This set of
rules, called a category in mathematics, acts as a set generator
for other objects—a method to instantiate different objects from
the same class. An object’s identity is the static part that is
created at the same time the object is created and remains
immutable during the lifetime of that object. The number one source
of bugs in any data system occurs when an object’s identity
changes during its lifetime. Think of links to a web page that
changes its content, or moves. 404 Error – File Not Found!
The dynamics of a computer object are the methods (i.e. contained
functions) that transform its internal values from one state to
another while keeping its class and identity intact (sort of like
eigenvectors are to a mathematical matrix operator).
Again, this concept does not exist in mathematics. Given F(X) =
3*X, then F(7) = 21. Yes, we call F a function or a transform, but
it did not “turn” a 7 in 21. It functionally mapped a 7 to a 21.
The 7 never changed and didn’t notice anything. Where our space of
focus once contained only a 7, applying F added a 21 to our space—
not changed a 7 into a 21.
Good luck trying to model dynamics in the semantic web.
Unfortunately, in the semantic web, an object’s identity is subtly
destroyed when transformed – it’s overwritten. There is no
symmetry between an object’s identity and its state in the
semantic web.
Robert Howard
Phoenix, Arizona
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