[FRIAM] Fwd: ABM (Object-Oriented)

[Marko A. Rodriguez]

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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