From: "Noam Chomsky" To: "Jeffrey E." <[email protected]> Subject: RE: Date: Wed, 10 Jun 2015 16:45:35 +0000 It's not hard to add probability and other factors to automata and recursive function theory. Sometimes it's done, e.g., Shannon's studies of provability with probabilistic automata. It's very rarely done because of irrelevance. The deep problems are not advanced in any way that's known by bringing in these considerations. Just as one doesn't bring in energy or time in studying number theory. Back to the origins of modern science there's been controversy about studying ideal systems vs real world interactions. Galileo had a devilish time convincing the funders (aristocrats) that it made sense to study balls rolling down non-existent frictionless planes when it is so much more interesting to watch flowers grow and figure out how they do it. The modern sciences finally developed as it became clearer that if you ever want to study "real world interactions" in a revealing way, you'd better base the inquiry on what can be learned from "ideal forms of relationships" and by exploring the limits of current understanding. True across the board, including vision and language. With current Big Data options there are widespread beliefs that something serious can be learned by virtually brute force methods. Very common now, and I doubt that much will come of it. Rather like trying to find the laws of motion not as science did from Galileo on but by taking a huge number of videotapes of what's happening outside the window, storing them in an immense data bank, and using statistical analysis. From: jeffrey E. [[email protected]] Sent: Tuesday, June 09, 2015 10:38 AM To: Noam Chomsky Subject: I have lot of work to do. but it appear obvious to me that both automaton and recursive theory, totally ignore . time entropy and energy, ( probabiltiy ?) so while they might describe in mathmatically mastabatory terms some ideal forms of relationsh