=============================================
STEP 5:  The rolling proof

NOTES:
1) There is only 1 proof in EC. (Symbolically it has been designated U(.)
above)
2) It consists of 1 collection of basic EC primitives (axioms)
3) The current state of the proof is 'now' the thin slice of the present.
4) The documentation of all the outpouring prior states (configuration of
the entire set of axioms) is what would be regarded as a standard proof - 
A theorem evolving under the guiding hand of the mathematician. It's just
that there is 1 mathematician per axiom in EC.
5) In effect, all that every happens in EC is rearrangement of axioms into
a new configuration, which then becomes a new configuration of axioms.
6) The 'theorem' proof never ends.
7) This process, when viewed from the perspective of being part of EC
looks like time. Local regularity in the state transition processes would
mean that local representations of behaviour could have a t parameter in
them.
8) Each fluctuation can be regarded as a 'mathematician'. This makes EC a
single gigantic parallel theorem proving exercise where at each 'state',
each mathematician co--operates with a local subset of other
mathematicians and where possible they merge their work and then form a
'team' which then works with other local mathematicians.
7) The local options for a mathematician are totally state dependent i.e.
depending in what other mathematicians (or teams of merged mathematicians)
are available to merge with.
8) The rules for cooperation between mathematicians will look like the 2nd
law of thermodynamics from within EC. Those rules will emerge later.
===============================================

Well I hope they will!.....

NEXT: some of the rules. Remember we are headed towards analysing the
nature of the structure of the EC proof and at the mechanism of 1-person.
In terms of EC, if local structure in EC is a part of the single EC proof,
then it is a 'sub-proof' in EC. At the outermost structural levels the
proof literally is 'matter'. The 1-person is a virtual-proof performed by
matter. Virtual matter. It's done under the same rules. Nothing special.
Everything is the same in EC. We can then look at what COMP would do to
it.

cheers,

colin hales




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