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 self is directly related to the Dx = "xx" trick, for me.
The Dx=xx trick is about self-replication. Of course entities with a sense
of the self/other distinction needn't replicate (eg certain robots).

Hi,

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.

Dear Bruno,

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 operation. 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 confusing...


Bruno


http://iridia.ulb.ac.be/~marchal/





--
Onward!

Stephen

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