Ok David,
Let's start afresh and do this. At least give it a go. This is to be FUN.
Not work.

I know enough about EC. You know enough about COMP. The goal is to get to
a more concrete formal understanding of the difference between reality and
computation, physics, logic, maths and 'being' through contrasting Entropy
Calculus (EC) as the actual logic of the noumenon (reality as a
mathematics, which becomes a physics when you are IN it, made of it,
trying to understand it) with COMP, as a 'master abstractor' of

We can jointly address epistemological and ontological issues along the
way. We can do this incrementally, one posting at a time. Nice and slowly
so we can follow it and point to where we fly off into
respective weeds. I can pose symbols and relata. You can tear it to bits
and interpose COMP interpretations.
STEP 1:    The noumenon that is EC

In EC I would write U(.) (for universe)

1) U(.) is our singular reality. It. The only one we truly know.
2) U(.) is not an abstracted computation.
3) U(.) is not a mathematical abstraction of reality.
4) U(.) is treated as a function for reasons of the later logic
5) U(.) is merely a symbol which 'points' to reality as a computation.
U(.) is an interpretive tool, not a generative tool.
6) U(.) is made of EC/recursive logic of a class as not yet defined.
7) U(.) is literally made of a relationship between the original axiomatic
8) U(.) has no 'appearance', is not an 'observation' of anything.
9) A side issue: U(.) can be regarded as a 'free-form' cellular automata
which manufactures its own cells and the cells and their relationships
emerge as collaborations of cells within cells. eg. At one level an 'atom'
is a cell. Also, if you collected all wolframs 'cellular automata
drawings' and condensed them into single cell in a new collective CA,
making whole CAs relate to each other ...and so on... to an arbitrary
depth, you can get an idea of where I'm headed.

STEP 2:  Ontological demarcation (notional virtual cells)

In EC, if there is a chunk of noumenon that I would wish to depict I can
draw a completely fictional CLOSED boundary around any subset of U(.), say
X(.) and define its relationship to U(.) thus:

U(.) = X(.) |+| NOTX(.)                      (1)

1) |+| must be regarded as messy/complex.
2) |+| must be regarded not as addition, but SURGICAL RESECTION or JOINING
3) |+| includes all entropy in and out of X(.).
4) |+| is to be thought of as a 2 way interchange over a notional
5) INPUTS to X(.) are OUTPUTS from NOTX(.). If X(.) was a human then |+|
includes inputs (food/water/photons/heat/potential/kinetic energy,
impacting nuetrinos, cosmic rays, everything)
6) OUTPUTS from X(.) are INPUTS to NOTX(.) waste material, heat energy,
phonons, kinetic energy dissapation, potnetial energy reliquishment and so
7) |+|, despite all the above complexity, mentally can be conceptualised
as addition. Just a very very messy addition.
8) X(.) and NOTX(.), like U(.) are NOT abstractions. They are pointers to
real EC entities just like U(.)
9) boundary CLOSURE makes the whole system lossless in an entropy sense.
This means that |+|, as a 'joining' of X(.) and NOTX(.)

10) The reality of EC is such that the |+| is NOT POSSIBLE! In other words:
 X(.) cannot exist without NOTX(.). There is no real boundary. No real
separation. At the same time U(.) is not a continuum in the
spatial/mathematical abstraction sense, although for practical empirical
purposes, because of the sheer deth of the structure, it can be regarded
as a continuum at certain scales.

11) 'fundamental building blocks are IMPOSSIBLE in EC. Fundamental
building blocks means that there exists X(.) and NOTX(.) for which no |+|
exists. This assumption is the 'biggee' about which science is curently

12) Having said (11) the 'axioms' are in fact 'fundamental'... but "the
ways of the turtles" offers a way out of this - which will become apparent
later (I hope!)

I am going at this TOP-DOWN. When that is done the 'bottom up' axiomatic
beginnings will emerge. I hope. On route towards an empirically testable
outcome we'll look at what happens when X(.) is considered to be a human
and how to depict a human including all the layers of nested hierarchy
that we see as brain material. I'll also introduce a 'being' operator.

We can later look at COMP equivalence at any level of what I have called
in the past 'Turing Granularity'. A bit like what Chalmers did in his
'silicon replacement' zombie thought experiments....Except at multiple
scales. At some point consciousness will be effected/affected. This will
be COMP replacement instead of silicon. Bruno(COMP)-granularity? :-)

Over to you. On with the fun.

Colin Hales

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