Well father...moving right along with my bedtime story....
===================================================
STEP 4: Axioms= primitive signs = fluctuations.
( )
You can either think of EC as having no numbers at all. You can also
imagine the same calculus implemented in number, but this would be an
emulation of EC, not EC. It is one of the goals here to investigate what
properties of EC may be lost by re-representing it in a number 'as-if'
form.
NOTES:
1) ( ) is the one and only necessary symbol in EC. It is the 1 type of
axiom: The 'fluctuation'.
2) This means that EC is made of change. Or better: whatever is made of EC
is persistent structure exhibited by a collection of EC primitives. 3) In
lambda calculus there are functions f(.)
4) Mathematically functions can be of one or more variables. I think Bruno
proves someplace that you can reduced all functions of many variables to
a collection of functions of one variable. This is a top-down way to the
EC 'function' ( ).
5) In 'number' versions of calculus like COMP we have a mapping from
integers to integers. f(N). In EC all that ever happenes is a mapping of
'fluctuation to fluctuation). The behaviour of ( ) is all there is. 3) We
have a label f which we do not really need in EC. As I am making this up
as I go along I need to pre-warn of a complication. There is, in effect,
one 'parameter' which can be thought of as built into ( )
(intrinsic to parallelism) which I'll cover more later.
4) At this stage there is no concept of spatial extent. 'dimensionality'
is constructed as the structure of EC evolves from the initial conditions.
Space is actually constructed of EC fluctuations and the remnants of the
process are all the EC stuff left over in the process. At least space it
what it looks like when you're made of EC like us.
=============================================
I Think I'll just post this bit for now and let it sink in. Next will be
syntax (rules of formation) and then grammar (rules of transformation).
These are also intrinsic... and the 'rolling proof' and the
'mathematicians' that drive the whole thing. Here is a tiny chunk of EC
(((((()())()()())()))())
^^^^^^
To 'be' inside EC is, for example, to be the marked ^^^^^^ structure and
inherit the intrinsic view of the rest of EC. There is only 1 proof in EC.
One 'theorem'. I suspect that the number of axioms in EC is 10^(a 3 digit
number). That is how many ()s there are in this one string that is EC.
'nacht
Colin Hales
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Received on Sun Oct 22 2006 - 17:25:03 PDT