"Comp is false". Let's see where *that* leads. I'm erecting
this as a signpost to indicate a direction, and I would beg the
list's indulgence in helping me to look in this direction, rather
than confining its comments to the ramshackle construction of the
signpost itself. My hope is that you will help me to expose whatever is
untrue or confused about what follows (I'm sure you will!). But I
hope you will also 'catch my drift'.
1) The bit-stream
Comp deals with a bit-stream representation of appearance. The theorems
of comp process this bit-stream in terms of a formal system, creating a
framework within which 'true or 'false' theorems may be
evaluated. This system is by its nature closed, or tautological. The
statements that can be made, their 'truth' or 'falsehood', are
inherent in the axiomatic and operational characteristics of the formal
system as applied to the bit-stream.
2) The instantiation
In order to implement the comp approach, an instantiation is required
that will represent the bit-stream and enact the formal operations. The
Turing machine is an idealised version of such an instantiation. A
digital computer is a physical version of a TM. Consequently comp may
be instantiated in a digital computer, and copied in innumerable media
that suitably preserve its informational structure.
3) Dimensionality
The bit-stream is 'pure' information and as such is 0-dimensional.
Multi-dimensionality emerges only at the level of the active
instantiation of the bit-stream. Consequently what is Turing-emulable
is the bit-stream (which includes a statement of the required formal
operations - i.e. the program) and because this emulation is
0-dimensional, it is indifferent to form ('substrate-independent').
Also because it is 0-dimensional, it is inherently powerless to
interact directly with multi-dimensional reality. All such interaction
takes place because what is implicit in the bit-stream is rendered
explicit by its multi-dimensional instantiation. Although we may speak
metaphorically (i.e. 'as if' projecting 'form' on to it) of the
bit-stream as 'representational' in a virtual 0-dimensional sense,
this is powerless as such to cause any interaction with the
multi-dimensional environment. To do this requires that additional
information, merely implicit in the bit-stream, is rendered explicit by
the instantiation.
If we consider an 'intelligent program' instantiated in a digital
computer, 'explicit form' - multi-dimensionality - is 'added
back' at the interfaces where the machine interacts with the external
environment. For example, a display device transforms the bit-stream
into pixels in a 2-dimensional arrangement. At the next 'layer' up,
a user decides whether to interpret the 2-dimensional arrangements
semantically (i.e. 'these are symbols') or graphically (i.e.
'this is a quasi-3-dimensional scene'). Up another layer, and the
user transforms these judgements into direct interaction with a
multi-dimensional environment.
All pure bit-stream representations rely on implicit environmental
assumptions in order to 'execute' as intended. DNA, for example,
relies for its expression both on its multi-dimensional orientation in
space, and the materials present in the local environment. This
information is not present, though implicit, in the codons, but is
*made explicit* by the environment that instantiates them.
4) Form
The 'physical' description of the world, as I was rightly reminded
by Peter, has no significant layering (well, perhaps it does, but more
later). Appearance, however, displays complex layering, and as we have
seen, this also 'appears' to extend to the intelligibility of the
world in which we 'appear' to participate. 'Form' and
'layering' somehow emerge from whatever the physical model
describes as a bit-stream. When we experience and interact with the
world, we do so in a way that is inherently multi-dimensional. What is
represented in this way is directly 'grasped' or 'enacted'
(i.e. represented, structured) in multi-dimensional 'form' and
unfolded by multi-dimensional 'motor units' into action in a
multi-dimensional world. This is both what makes it non-invariant to
Turing-emulation, and gives it its direct multi-dimensional linkage to
enaction in multi-dimensional environments. Certainly, 0-dimensional
bit-stream representations and pathways are entailed in such processes,
but they serve to store and transmit information, not to enact its
meaning or its consequences in the world - i.e. its intentionality
as information-put-into-action.
5) Correlation
How is the above to be correlated with the physical or bit-stream
representation? Through appropriate forms. We already know this from
the fertility of 'laws of form' that are intrinsic to science as
practised - whether physical, chemical, biological, physiological,
psychological, sociological, and so on up the 'levels'. At each
level, 'laws of form' are abstracted that render this world-view
intelligible, although they are not directly implied at the level below
- hence Peter's comment about the 'lack of layering'. So,
consider the brain. We can approach this through the lens of a variety
of forms - squidgy grey mass, neural network, bio-electrical
circuitry, neuro-chemical pathways, etc. - even 'digital
computer'. None of these has yet succeeded in capturing a 'formal
decomposition' that yields appearance, or even a mechanism that seems
capable of enacting the construction of multi-dimensional
representation as experienced.
However, as the above analogies indicate, this is not a fruitless task,
but an empirical one. There have been, and still are, innumerable
'formal decompositions' of the world that have served only to
multiply mystery. The world, as we know, stands on the backs of an
infinite stack of turtles, and motion is accomplished through the
efforts of an innumerable insensible angelic host. ????? .......... We
should be looking for a 'formal decomposition' of the brain that
embraces both isomorphic representation of, and direct
multi-dimensional interaction with, the external environment of the
body, and beyond it the world. We should expect these forms to
'construct boundaries', the 'lines of cleavage' that do not
exist in the 0-dimensional physical description. We should ask - from
either side of this cleavage - 'who is looking, listening, tasting
what lies on the other side?' The 'side' that is able to answer
these questions intelligibly by enacting its responses in the world is
the 'perceiver'. The other is the 'perceptual model'.
The explicit multi-dimensional 'grasp' of form is what I contend
makes all this non-invariant to Turing emulation. Note that I've not
said 'non-Turing emulable', since anything that can be represented
as a bit-stream may be Turing-emulated, but the issue here is whether
multi-dimensional experience and enaction is invariant to such
emulation. My claim is that it can't be, because it requires the
instantiation to explicitly 'add back' the missing information that
is only implicit in the 0-dimensional emulated bit-stream. It is this
that makes multi-dimensional environments 'non-invariant to
computation', as opposed to 'non-computable'. This is IMO the
'understanding' - the multi-dimensional enaction of
multi-dimensionally-represented information - to which, for example,
Penrose appeals as the source of mathematical intuition. It isn't
Platonic reality to which the mathematician, or any of us, has direct
access, but rather the multi-dimensional forms from which these
'perfect' concepts are abstracted.
6) Indexical existence
Missing information? Surely this isn't the dreaded 'hidden
variables'? I don't think it is. The missing information is what
(some of us) are trying to express by 'I assert my indexical
existence as a necessary fact'. This 'information' is entirely
absent from the physical or other formal (virtual, or what we've
sometimes rather unfortunately called 3rd-person) accounts of
appearance/ reality. It expresses itself self-referentially, and this
expression has 'qualities' (again what we perhaps unfortunately
call 'qualia', but let it serve). I contend that qualia carry the
meaning *like this!*, or more simply *this!*. From such 'codons'
worlds of 'thisness' emerge. Since 'thisness' is at the same
time the instantiation of the multi-dimensional environment, the
'thisness' of experience' can transform directly to the
'thisness' of enaction in the world. This is what we call meaning
and intentionality. The project of mapping and correlating our accounts
of the world-as-appearance-and-meaning and the world-as-structure has
been well-termed 'Dual-aspect Science'. Let's get on with it.
7) Mass, space, gravity
If the foregoing is speculative, what follows is ruminative. Having
dismissed 'form' as significant in a physical decomposition of
reality, does this perhaps force a re-appearance at the point where QM
collides with General Relativity - i.e. where the bit-stream hits the
instantiation? Curved space, gravitational interaction - these seem
intrinsically geometrical/ topological/ 'shaped' ideas. Is there
any analogy here to the relationship of formal description to
instantiation? I wonder.....
David
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Received on Thu Aug 17 2006 - 09:43:58 PDT