From: "Noam Chomsky" To: "Jeffrey E." <[email protected]> Subject: RE: Re: Date: Mon, 22 Jun 2015 03:13:20 +0000 I follow up to the point where you write "the organizing principle of the shape is language..." No doubt it can (partially) be described in language, but that's not what you mean. Zipf's law is a rank-frequency distribution. And also meaningless, as Mandelbrot showed 60 years ago. I hope Yang is clear about this. He surely knows. Noam From: jeffrey E. [[email protected]] Sent: Sunday, June 21, 2015 2:48 PM To: Noam Chomsky Subject: Re: Re: it is my failing not yours. the old math requires numbers . too limiting. ( we can put a metric overlay on later in the chain) imagine a shape in real space. it is readily apparent if a line either fits on the shape or not . how do you know. ? you compare the line with the shape. your visual system allows the mental shape to either map onto or not onto the shape in a coherent manner. the shape is not an input device ,it is an object . the organizing principle of the shape is language, the shape is a collection of grammars. lines on the shape are either coherent or not. coherent ones are legitimate sentences . yang is flexible in his use of the term probability.. for example he in a number of papers refers to zipf as a probabiltiy distribution. i have checked a number of his papers after your last remark, I think it is a mistake. he means that after empirical measurement . for ex word frequency, . if ten times out of 100 the corpus has the word x. then he describes the probablility of finding the word as 10 percent . this is not correct. it is only the probablity of finding the word in the frequency list . but he is very accomplished at mathematical models. On Sun, Jun 21, 2015 at 1:03 PM, Noam Chomsky < Interesting image, but I don't see what it tells us about language. The problem looks to me like this, roughly. > wrote: Take, say, the human visual system. There's a genetic com