From: "Noam Chomsky" To: "Jeffrey E." <jeevacation®gmail.com> Subject: RE: Re: Date: Tue, 09 Jun 2015 01:58:41 +0000 1. I haven't studied the hyperbolic groups that Gromov devised, and have only limited familiarity with the hyperbolic geometry developed in the 19th century. But I don't see what it says about matrices not being mathematical objects, and don't even know what that would mean. All of this is mathematics. 2. It's not that boundaries are the result of mechanisms. Rather, boundaries of the kind you mention gain significance when we are studying mechanisms. I don't see how they bear on the general architectural issues of input-output-central, though the might be suggestive analogues for the inquiry into rule systems inaccessible to consciousness. Seems to me a Marr-type distinction between computational, algorithmic, and mechanical level. 3. True enough, but I don't see how it bears on the subsystems of recursive function theory under investigation here, though would be glad to learn how I think I may have mentioned to you Massimo Piattelli's work on language jointly with several quantum physicists at U Arizona. Something you might want to look into. Noam From: Jeffrey E. [[email protected]] Sent: Monday, June 08, 2015 9:46 PM To: Noam Chomsky Subject: Re: Re: Mikhail Leonidovich Gromov , a good example. , definitive on matrix not being a mathematical object . probably the best thinker in the math field. like you he created a new field of study . - hyperbolic geometry, 2. no-! boundarys are not as a result of mechanisms. it defines a limit to the "what " , and everything else.. 3. quantum probablility distributions can be described as a shape that appears to have a restoring force. pushing things towards the mean. a similar human created pseudo force like centripetal force. wholly dependent on ones reference frame. On Mon, Jun 8, 2015 at 9:32 PM, Noam Chomsky < > wrote: Don't follow. Matrices are mathematical object