On 17 Oct 2012, at 23:09, Stephen P. King wrote:
On 10/17/2012 1:29 PM, Bruno Marchal wrote:
On 17 Oct 2012, at 08:52, Stephen P. King wrote:
On 10/17/2012 2:07 AM, Russell Standish wrote:
The Dx=xx trick is about self-replication. Of course entities
with a sense
of the self/other distinction needn't replicate (eg certain
>The self is directly related to the Dx = "xx" trick, for me.
I have some papers and list posts from Lou Kauffman that backs
up Bruno's claim on the Dx = xx stuff. I'll try to dig it up and
post on it.
Very nice! Thanks.
Here is a relevant sampling from Lou Kauffman resent posts:
"...to determine the level of granularity we need a yet finer mesh
of discrimination. This leads to an infinite regress.
Conscious awareness is where the buck stops. I used to think that as
in <<<<<...>>>>> = J ----> J = <J> awareness
was the limit of an infinite process."
"Another way out (of infinite regress) is the Church-Curry fixed
We begin in what I like to call a Reflexive Domain D where every
element d of D is also an operator on D taking x in D to dx in D.
(This means the same as saying that there is a two place binary
operation on D X D and Gavin will have it all in a Cartesian closed
category but I digress.)
I also assume that for every algebraic transformation of D,
there is an element of D that accomplishes this transformation.
Thus if we have the operation x -----> (ax)(xb) ON D then there is
an element c IN D such that Cx = (ax)(xb) for all x in D.
In a reflexive domain there is no difference between object and
process. Processes are objects and objects are processes.
To say that one is in a reflexive domain is to say that one is
already 'at the limit' and things like self-reference and fixed points
are just part of the territory. For example Let Gx = <xx>. Where G
is an element of D that realizes this boxing operation.
Then Gx = <xx> implies that GG = <GG>. And so we can take J = GG and
then J = <J> and there was no excursion to
infinity because we had already arrived there!"
Yes. It is the way we can handle self-reference, either in lambda
calculus, or in such reflexive domain.
I already appreciate a lot Louis Kauffman's book "Knot and
physics", and from it I got some speculation of how space arise
from the Bp & Dt (& p) "hypostases" (points of view in arithmetic).
I am currently reading the chaper that Lou wrote (with S. J.
Lomonaco Jr.) in Entanglement and Decoherence: Foundations and
Modern Trends (Lecture Notes in Physics) that discusses the
connections between knot, braid and link groups and quantum
I found also an incredible way to dispose rope generating the
finite ordinals, but all such stuff needs drawing facility.
"Rope"? Do you mean "braid"?
you can "simulate" braid with rope, but rope can simulate other
structure, like knots, or tangles. But plausibly the ordinals
represent here an infinite braiding.
Mailing math without a pen is a form of torture.
I feel your pain, most of my ideas don't make much sense in
discussions unless I can point to a series of diagrams to illustrate
the idea... I try to make up for this by using extensive
biographical notes with hyperlinks in my postings here, but I
understand that this can be confusing...
Oh! I am glad you are aware :)
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