Here is out-lined the sketch of a strategy for attacking the puzzles
of reflectivity and consciousness.  Reflectivity is the puzzle how a
cognitive system can effectively reason about its own internel
processes - reasoning about reasoning.  Consciousness is here used in
the sense of subjective experience, including sensations and

The strategy considers Reflectivity not to be a part of decision
making, but rather as a system of internal communciation.
Consciousness is considered as a mathematical proccess strongly
associated with knowledge representation.  It is argued that
consciousness and reflectivity are one and the same one.


A long standing puzzle in decision theory is how decision theory could
be applied to itself - that is, how could the cognitive provesses of
decision making be applied to reason about these very proccesses
(reflection).  The reason there is not yet any 'Reflective Decision
Theory' is likely to be that the very concept itself is ill-
conceived.  That is, there is no 'Reflective Decision Theory'.

Concepts of 'Utility', goals and decisions about how to most
effectively achieve these goals are the domain of a cognitive
'decision making' system.  And 'Decision Theory' is the science of
such systems.

But the concepts can only be applied to 'external goals' (i.e goals in
the external world).  To attempt to solve 'Reflectivity' by trying to
deploy the same concepts of decision theory to the internal workings
of the cognitive system is simply an invalid use of these concepts.

The first step to solving reflectivity then, involves attempting to
ascertain the true nature of 'Reflection'.  For 'Reflectivity' is
*not* in fact, in the decision making business.  The true role of
'Reflection' it seems is *Communciation*.  That is to say, it appears
that 'Reflectivity' should be thought of, not as part of *Decision
Theory*, but instead as part of *Communication Theory*.

This is because any cognitive system of sufficient complexity to
achieve genuine intelligence appears to require the division of the
system into seperate modular 'sub-agents' which interact with each
other to achieve desirable results.  Marvin Minsky wrote  a famous
book 'The Society of Mind' emphasizing this soup of many interacting
agents.  It's not enough for a cognitive so composed to merely have an
effective system of decision making.  There must also be an effective
*Communication System* to integrate and co-ordinate the behaviour of
the all the sub-agents into an effective whole.  And this is the
aspect of AI research that has been neglected.  Further, the
connection between 'Communication' and "Reflectivity' has appeared to
elude the minds of the best and brightest.  But it is here being
established that an effective communication system *is precisely the
solution to reflectivity*.  The two problems are one and the same.

If the hypothesis is correct, new strategies for atatcking the
reflectivity puzzle can be formulated.  For one thing, there is a wide
body of pre-existing knowledge on Communications Theory which can
start to brought to bear on the reflectivity puzzles.  For another,
analogies from the field of computer networking can be ported over to
the reflectivity problem.

For instance: Consider sub-agents as nodes, the combined actions of
the sub-agents as networks and the interactions of the sub-agents as
data transfers.

But what justification is there for thinking that this hypothesis is
applicable to reflectivity?  To see the reasons, let us consider that
other great puzzle, subjective consciousness, or subjective
experience.  What is consciousness.  For all the huge volume of past
words expended in this debate, there emerge three key points:

The first point is that consciousness is not a *thing*.  It is a
*process*.  The second point is that consciousness is not something
concrete.  It is not for instance, a process similar to digestion.
The process instead appears to involve *asbtract patterns*
(functionalism).  Patterns are abstractions which are the essence of
mathematics.  Thus we can say that consciousness is a *mathematical
process*.  And the third point is that consciousness appears to
involve a cognitive system examining aspects of its own internal

All three points should immediately lead us to suspect that
consciousness is connected to 'Reflectivity'.  On the first point,
conscious as a proccess ; a working reflection system is also a
process.  On the second point, consciousness as patterns (mathematical
abstractions) ; a working reflection system involves reasoning about
reasoning ; reasoning uses predicate logic and probabilities - fields
of mathematics.  Further, patterns are both the essence of mathematics
and representations of knowledge itself.  So a series of reasoning
steps (an algorithm) is really a mathematical construction.  Finally
on the thrid point, a cognitive system examining its own internal
working smacks of reflection immediately.  Thus a reasonable a priori
suspicion is that consciousness and 'Reflectivity' are in fact one and
the same.

Let us now apply a unique new perspective on mathematics - we shall
now attempt to view mathematics through the lens of the object
oriented framework.  That is to say, consider mathematics as we would
try to model it using object oriented programming - what the classes,
methods and objects of math?  This is a rather un-usual way of looking
at math.  Mathematical entities, if they are considered in this way at
all, are not regarded as 'Objects' (things with state, identity and
behaviours) but merely as static class properties.  For instance the
math classes in the Java libraries consist of static (class) variables
and class methods.

But consider instead that there could be mathematical 'objects' (in
the sense of entites with states, identities and behaviours).  What
could these mathematical 'objects' look like?  if there are
mathematical objects they have to be dynamic.  This conflicts with
standard platonic pictures of math as entities which are eternal and
static.  What could these 'dynamical mathematical objects' be?

The obvious answer, based on the previous points made, is that
*algorithms* (reasoning procedures) are identical to *mathematical
objects*.  The implementation of the algorithm (ie running the
program) would be equivalent to the state changes in the mathematical

The advantage of this perspective on math is that it points to a way
to unify the mathematical sciences with the computational sciences.
Once we are clear about the equivalence of computation with dynamical
mathematical objects, we can begin to see why reflectivity might be
identical to consciousness.

What is the fucntion of consciousness?  The perspective discussed
suggests an answer.  It's got to have something to do with *knowledge*
(because a mathematical process - a 'dynamical mathematical object'
is equiavlent an algorithm, and astract mathematics - the language of
math -are also the language of logic) .

Now return to the discussion about the sub-agents in an intelligent
cognitive system and the need for all these sub-agents to communciate
effectively.  Rather than a reasoning system consisting of a single
big algorithm then, we should think of the system as composed of many
small algorithms which interact together to produce intelligent
behaviour.  From what we said above, all of these sub-algorithms
should be considered to be 'dynamical mathematical objects'.  Thus,
the picture we obtain is analogous to a network - the mathematical
objects are the nodes, the system is the network, the co-ordination
and interaction of the sub-agents is the data communication.  Consider
that each mathematical node represent a 'node of knowledge'.  Then we
see that the function of consciousness must invovle 'knoweldge
integration' (nodes working together to achieve a co-ordinated
whole).  And we can push this hypothesis further and conjecture that:


This, in bold-type, is the first 'Key Hypothesis' of this peice.

If in fact we have nailed the purpose of consciousness and the
perspective offered is roughly correct, a second key hypothesis
presents itself by pushing the first hypothesis furtehr and
considering again the perspective offered.  If the function of
consciousness is as an internal communication system of the mind, why
not say that consciousness itself is a 'DP Modelling Language' (Data
Process Modelling language)?  This is strongly suggested by the
picture of the equiavlence between 'mathematical nodes of knowledge'
communicating and consciousness enacted as an algorithm.  Knowledge is
communciated by a data process modelling language.  This second 'big
idea' can be summarized thusly:


(End of part 1)

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