Rosen, functional entailments
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Roseneers,
If anybody is still willing to help out in understanding chapter five, of LIFE ITSELF I have posted a queston at http://www.sfcomplex.org/mw/index.php?title=Talk:RosenNoodles#More_struggles_with_chapter_five
Let me know, if you cant get in.
One of you wrote me a kindly note asking after my mental health , given my obsessive pursuit of this quest. It's ok. I guess. Like all obsessives, I don't see that I have much choice: I cannot see how one could possibly understand a text so complex WITHOUT engaging in the sort of obsessive collaborative head-bashing that goes on in graduate seminars. And I cant see how I could have the gall to have opinions on Rosen, or on category theory, unless I understood the text. And I dont see any seminars on Rosen within easy reach. So..... onward!
Thanks for the help given so far.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([hidden email])
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
Re: Rosen, functional entailments
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Your question on what F(f,g) is: I think it is ordinary function
composition, usually denoted fog (where the o is actually a small circle, not the letter "o"). ie (fog)(x) = f(g(x)). I'm not entirely sure why the use of "inner" and "outer" entailment refers to this, though. Inner and outer normally refer to products. but I don't see an obvious generalisation from the product concepts to If we specialise functional notation to linear algebra with linear functions f: R^n -> R and g: R -> R^n then f(x) is an inner product when f is represented by a row vector and gof is an outer product when f is as above and g is a column vector Perhaps that's the generalisation being talked about. On Fri, Aug 15, 2008 at 12:02:43AM -0600, Nicholas Thompson wrote: > Roseneers, > > If anybody is still willing to help out in understanding chapter five, of LIFE ITSELF I have posted a queston at http://www.sfcomplex.org/mw/index.php?title=Talk:RosenNoodles#More_struggles_with_chapter_five > > Let me know, if you cant get in. > > One of you wrote me a kindly note asking after my mental health , given my obsessive pursuit of this quest. It's ok. I guess. Like all obsessives, I don't see that I have much choice: I cannot see how one could possibly understand a text so complex WITHOUT engaging in the sort of obsessive collaborative head-bashing that goes on in graduate seminars. And I cant see how I could have the gall to have opinions on Rosen, or on category theory, unless I understood the text. And I dont see any seminars on Rosen within easy reach. So..... onward! > > Thanks for the help given so far. > > Nick > > > Nicholas S. Thompson > Emeritus Professor of Psychology and Ethology, > Clark University ([hidden email]) > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org -- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [hidden email] Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
Re: Rosen, functional entailments
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In reply to this post by Nick Thompson
Nick,
The capital F represents the functor (functional object) in
Category Theory. The small f is a function. A functor serves as
a relationship operation between categories. I think it might help if you
looked at several examples of functors to see 1) what they do, and 2) how they
are related to, but different than functions.
Ken
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
Re: Rosen, functional entailments
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In reply to this post by Nick Thompson
Thanks, Russell.
Is your comment differ with Ken's or is it Ken's in another language. For a former english major, the LANGUAGE is everything. Nick Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, Clark University ([hidden email]) > [Original Message] > From: Russell Standish <[hidden email]> > To: <[hidden email]>; The Friday Morning Applied Complexity Coffee Group <[hidden email]> > Date: 8/15/2008 10:09:06 PM > Subject: Re: [FRIAM] Rosen, functional entailments > > Your question on what F(f,g) is: I think it is ordinary function > composition, usually denoted fog (where the o is actually a small > circle, not the letter "o"). ie > > (fog)(x) = f(g(x)). > > I'm not entirely sure why the use of "inner" and "outer" entailment > refers to this, though. Inner and outer normally refer to products. > but I don't see an obvious generalisation from the product concepts to > > If we specialise functional notation to linear algebra with linear > f: R^n -> R and g: R -> R^n > > then > f(x) is an inner product when f is represented by a row vector > > and > > gof is an outer product when f is as above and g is a column vector > > Perhaps that's the generalisation being talked about. > > On Fri, Aug 15, 2008 at 12:02:43AM -0600, Nicholas Thompson wrote: > > Roseneers, > > > > If anybody is still willing to help out in understanding chapter five, http://www.sfcomplex.org/mw/index.php?title=Talk:RosenNoodles#More_struggles _with_chapter_five > > > > Let me know, if you cant get in. > > > > One of you wrote me a kindly note asking after my mental health , given my obsessive pursuit of this quest. It's ok. I guess. Like all obsessives, I don't see that I have much choice: I cannot see how one could possibly understand a text so complex WITHOUT engaging in the sort of obsessive collaborative head-bashing that goes on in graduate seminars. And I cant see how I could have the gall to have opinions on Rosen, or on category theory, unless I understood the text. And I dont see any seminars on Rosen within easy reach. So..... onward! > > > > Thanks for the help given so far. > > > > Nick > > > > > > Nicholas S. Thompson > > Emeritus Professor of Psychology and Ethology, > > Clark University ([hidden email]) > > ============================================================ > > FRIAM Applied Complexity Group listserv > > Meets Fridays 9a-11:30 at cafe at St. John's College > > lectures, archives, unsubscribe, maps at http://www.friam.org > > -- > > > A/Prof Russell Standish Phone 0425 253119 (mobile) > Mathematics > UNSW SYDNEY 2052 [hidden email] > Australia http://www.hpcoders.com.au > ---------------------------------------------------------------------------- ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
Re: Rosen, functional entailments
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On Fri, Aug 15, 2008 at 8:57 AM, Nicholas Thompson <[hidden email]> wrote: Thanks, Russell. The operation of functional composition, taking f: A -> B and g: B -> C and composing them to get gf: A -> C, is qualitatively different from the inner entailments which only involve sets and mappings. The inner entailments were summarized as f => (a => f(a)) which reads that f is the efficient cause and a is the material cause of f(a). This gives us an element, f(a), as a consequence of a mapping and an element, f and a. The outer entailments speak to the causes of mappings and sets. So F => (f, g => F(f,g)) says that functional composition is the efficient cause and the functions f and g are the material cause of the function gf. And, the example left for the reader to work out, C => (a, b => C(a,b)) says that the cartesian product is the efficient cause and the elements a and b are the material cause of the element a x b. In the first case we get a mapping as a consequence of composition and two mappings, in the second case we get an element as a consequence of cartesian product and two elements. No functors were deployed in the construction of these paragraphs. At the end of section 5H (p 130) Rosen notes: We can formally do a great deal with the modes of inner and outer entailment inherent in any category. In particular we can concatenate them to form, and characterize, arbitrarily complicated abstract block diagrams from the sets and mappings in any particular category. In fact, the totality of abstract block diagrams that can be formed in this way constitutes a new category [ ... ] as a (free) monoid A~s stands to its set of A of generators [...]. Baez and Stay in "Physics, Topology, Logic and Computation: A Rosetta Stone" are essentially applying the same "arbitrarily complicated abstract block diagrams" formalized as various subclasses of "symmetric monoidal categories". By now there is an extensive network of interlocking analogies between physics, topology, logic and computer science. They suggest that research in the area of common overlap is actually trying to build a new science: a general science of systems and processes. So they agree that physics, logic, and computation are pretty much the same thing, that arbitrarily complex block diagrams are the key, and that a general science of systems and processes is the goal. -- rec -- ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
Re: Rosen, functional entailments
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Roger Critchlow wrote:
> No functors were deployed in the construction of these paragraphs. I agree that the "F" isn't a functor. But, it is at the same level of discourse as functors. It's part of the definition of a category, an axiom, which means it comes from _outside_ the formalism. I.e. it comes from somewhere other than the formalism itself. Functors, being morphisms between categories are also outside of the categories they relate. So "outer entailments" involve extra information not available within the context and "inner entailments" involve only information available within the context. I think this is why Rosen links it to a discussion of final (externally imposed) cause. The whole goal is to find a way to _close_, feed back, or turn these arrows back in on themselves. The claim is that an organism will not have any efficient outer entailments (though we expect material outer entailments). To go back to parsing the notation, how about this: f => ( a => f(a)) means "f dictates that ( a dictates that f(a) )" g => ( b => g(b)) means "g dictates that ( b dictates that g(b) )" g => ( f(a) => g(f(a)) ) means "g dictates that ( f(a) dictates that g(f(a)) )" i.e. "g is defined so that the things in its co-domain (e.g. f(a)) dictate the composition g(f(a))." F => ( (f,g) => gf) means "F is defined in order to clump two functions in its co-domain so that the clumping is identified as an operation, specifically, the composition operation". p.s. I use "dictates" as opposed to "entails" just for a linguistic parallax. One might also use "specifies", "requires", "imposes", etc. -- glen e. p. ropella, 971-219-3846, http://tempusdictum.com ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org |
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