From: "Noam Chomsky" To: "Jeffrey E." <jeevacation®gmail.com> Subject: RE: Re: Date: Tue, 09 Jun 2015 01:32:26 +0000 Don't follow. Matrices are mathematical objects, and sets of matrices are sometimes very interesting mathematical objects, will studied in math and physics. They very definite mathematical meaning within the axiom systems of matrix algebra, etc. Apart from such systems, no mathematical objects have mathematical meaning. I presume I'm missing your point. What mathematicians do you have in mind? Noam From: jeffrey E. [mailto:[email protected]] Sent: Monday, June 08, 2015 5:16 AM To: Noam Chomsky Subject: Re: Re: I'd look at it somewhat differently. Mathematics, as I understand it, includes all of the formal apparatuses. Anything formalizable falls within mathematics — sometimes, rarely, interesting from a mathematical point of view, but that's a separate matter. Exactly, I had the same mistaken strong view . Now the best mathematicians all agree that both of us were incorrect. take for ex a Matrix - it is not a mathematical object. it has no mathematical meaning. it is a notation that allows a calculation on the blackboard . On Mon, Jun 8, 2015 at 1:17 AM, Noam Chomsky > wrote: From: jeffrey E. [mailto:[email protected] Sent: Sunday, June 07, 2015 2:07 PM To: Noam Chomsky Subject: Re: Re: 1. first deficiency - .input output modules in general ignore the membrane .. The membrane is its own complex system . (membrane computing alone is a brand new subject.) That might turn out to be a problem in the neurological analysis of input-output-central modules, one of many. Fundamental problems are those that I mentioned to you in connection with Randy Gallistel's critique: the inability of neural net models to capture the core component of any computational system, as we've known since Turing. But at the level of this discussion, the questions don't arise. Whatever the mechanisms may be, they will have to deal with the gene