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
>The self is directly related to the Dx = "xx" trick, for me.
of the self/other distinction needn't replicate (eg certain robots).
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
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 point
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!"
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 computation.
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"?
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
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