Identical yet Distinct
Tue, 16 Nov 1999 07:24:12 +0100 (MET)

In article <>,
Veronica Parsons <> wrote:
> silvio wrote:
> > Is there such a thing as an intelligent system? Or are
> > these computers just other calculators?
> Perhaps you would like to define your terms of reference. Try defining
> 'thing', 'intelligent' and 'system' for a start.

An attempt from first principles:

Distinct yet Identical

Mathematically "equivalence" can be defined as usual as in the case I.

Physically though we can define "equivalence" in terms of quantum
mechanic's (QM) notion of identical particles as in case II.
(QM includes case III. in terms of "entanglements" etc.)

The notion of distinct yet identical particles is more difficult
understand conceptually as is shown in case III.

We can use the terms 'metaphor' or 'analog' to define this notion
of 'equivalence' and we can employ metaphor to show an example of
this definition of "equivalance". For instance:

"an individual in society is considered distinct,
and yet under the law they are (ideally speaking)

And this metaphor between the distinct yet identical particles
and the individual in society, I will call a 'strong metaphor'
or a 'literal metaphor', because at the fundamental level there
is no distinction between the assignment of:

A <- distinct yet identical particles
B <- distinct yet equal citizens

and saying that these are 'equivalent' in the sense of case III.
That A is distinct from B is obvious, and yet they are related by
'metaphor'. Or we can also say they are 'correlated'.

How does the relationship by metaphor affect our definition of
distinctness ? If the metaphor is very very strong, the
case III. interpretation degenerates into the case I. interpretation,
and if the metaphor is very very weak the case III. interpretation
degenerates into the case II. interpretation of 'equivalence'.

It is essential that the case III. interpretation be considered
carefully in the context of degrees of orthogonality, interference,
and aliasing. All of these are related effects based on levels
of resolution, dispersion, distinguishment,fuzzy theory ... etc.

Logic makes connections between causually dependant variables,
and analogic makes connections between non-causually dependant
(independant) variables.

When we employ logic, it is wholely contained within some causual
system. That system may be analogous to another system. So we may
employ analogy and say:

"If 'A' is analogous to 'B', then perhaps if I know how
'A' works I can use that information to understand better
how 'B' works."

Logic is employed subsequent to this theoretical step of making
an analogy. The logic is used within 'A' or within 'B' to make
the causual connection and analogic is used between 'A' and 'B'
to make non-causual relations or 'functional relations'.

In the same manner we can say if two statistical distributions
are the same for two systems 'A' and 'B', there may not be a
causual connection between these systems but any understanding
of what leads to that distribution in 'A' may be useful in
understanding how the same distribution is generated by 'B'
from it's dependant subsystems.

Theory, employs analogical thinking more than empircism, which
employs logical thinking and the relationship of these two
modes of thinking combined form the basis of rational thinking.

(one may look into Vaughan Pratt's [Knuth TAOCP] work on Chu spaces
or contact Stephan Paul King. I find it difficult to understand
what these people are doing but I sense they are in general
addressing these ideas in a more conventional manner. There
are links to them on my home page.)

Now, it may be noted that the above description of the 'rational
process' can be subverted from its usual implementation in the
pursuit of knowledge.

Suppose for instance, that we have someone who is engaged in
some field of study 'A' who realizes that another person's work
in a totally different field 'B', is analogous to what he is doing.

Suppose further that the person in the field 'B' has made a
significant contribution to her field and proven some logical
(causual) connectives between many subsystems in the field 'B'
and received significant awards for doing so.

The person studying in field 'A' may, through the recognition of
analogs, be able to replicate all the work of the person studying
in the field 'B' by establishing the same logical connections in
the subsystem of 'A' as have analogs in the subsystems of 'B'
(to the extent this is possible).

The person studying in field 'A' may then "burn the analogical bridge"
and take full credit for his discovery in the context of 'A'
without making any reference to the work done by the other person
in 'B'. The 'A' person may then reap significant awards in his field
as we they are analogous awards to the 'B' person's awards.

This is essentially a holistic plagiarism and it is very likely that
many of our so called "greatest thinkers" in past history commited
this act either consciously or unconsciously.

It would take a holistic detective[1] to peer backwards through
history and try to determine who commited such acts. The process
by which such trangressions were uncovered would not be mearly
useful for judicial purposes but would be very instructive as well
in the analysis of information in quantum physics.

It should be noted that many skilled logicians satired their logic--
in life and in fictions. Doyle[2] became a "spiritualist" in later
life and Carroll's[3] works in fiction, are far better known than
his books on logic. And Houdini was indeed a master at hiding
causual connections.

[1] Dirk Gently's Holistic Detective Agency, Douglas Adams
[2] The Edge of the Unknown, Sir Arthur Conan Doyle
[3] Lewis Carroll


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