From: "Noam Chomsky" To: "Jeffrey E." <[email protected]> Subject: RE: Re: Date: Tue, 09 Jun 2015 13:28:43 +0000 Inline-Images: image00 1 .jpg Sorry, but I don't follow. Insect navigation is a study of a living system, and the work that IN familiar with studies it as a computational system. If there's a better way of analyzing it, well and good: the scientists working on the topic would be glad to see it. Outside observers like me too. At another level of analysis, insect navigation is a sensory-motor process in physical space. There's no semantic error that aware of. Studying systems at various levels of abstraction has been standard science for centuries. A particular framework that's been widely adopted in the cognitive sciences is Marr's, but other ways of looking at it are of course possible. I looked at Gromov's paper, but didn't read it carefully. He uses set theory freely throughout, and I don't see anything that bears on matrices as mathematical objects or on the use of recursive function theory for computational systems like language where it is appropriate. Maybe, as he suggests, some results would follow from studying these topics in the framework he develops, but as always, that has to be shown. For example, Eilenberg's category-theoretic reanalysis of work on finite automata that I and others had done, including very good and respected mathematician's like Schutzenberger, apparently had some mathematical interest (so I am told), but no results were suggested that had any implications for the empirical objects that originally motivated the mathematical studies. That's not unusual in math and the physical sciences. From: jeffrey E. [[email protected]] Sent: Tuesday, June 09, 2015 7:10 AM To: Noam Chomsky Subject: Re: Re: thats cheating .. Is the study of how it dances really a study of the living systen? or is merely the sensory motor display in phyiscal space. if you admit it being the latter , my dismal knowledge