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 asenseof the self/other distinction needn't replicate (eg certain robots).Hi,I have some papers and list posts from Lou Kauffman that backs upBruno's claim on the Dx = xx stuff. I'll try to dig it up and post onit.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 finiteordinals, 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/

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