Re: f:A -> B

Hey Tim,

Please don't worry one bit about the delay. The response that you have given me strikes me as well worth the wait. I don't know a great deal of mathematics, but I sometimes know when something has "the feel" and your response does.

I'll definitely need some time to chew on it. I sometimes feel as if Robert might be Morpheus asking me to choose between the red pill or the blue. How far down the rabbit hole do I want to go?

You have both confirmed some stuff and raised my awareness of how little I really know of mathematics. I wish that I could converse with you about it from a more experienced stance. Perhaps after a little more research into it I can come back to this subject with some more substantive questions. But you have given me some direction, thank you.

David

----- Original Message -----

From: Tim Gwinn

To: ***

Sent: Tuesday, August 30, 2005 9:04 PM

Subject: Re: f:A -> B

David,

Sorry for the delay. You wrote:

How many ways do you (or whoever feels compelled to respond) think that f:A--->B "metabolism" can be interpreted? Surely a great many and not all of them need be mathematical interpretations, right? My intuition is generally not mathematical. Also the arrow gives the impression of time but why could it not be merely an association?

I would imagine there are an infinite number of ways that the formal statement "f:A -> B" could be interpreted; that is, I would imagine that there are an infinite number of formal systems of which that statement could be a model, as well as a large, if not infinite, number of natural systems of which that statement could be a model.

'Metabolism' in the general (M,R)-system model is a network, which could be very complicated indeed. Abstracting that to "f:A -> B" does no harm for the purpose for which the more abstract description serves. Unfortunately, the ability for this to be an abstraction of so many different things can lead to confusion. The main criticism in the Landauer-Bellman paper relied on an assumption that this kind of abstract mapping must be an abstraction of an analytic equation (what they called the "equational distinction"), rather than an algebraic relation.

As you suggest, the statement does describe an algebraic relation. And while any analytic equation can be abstracted into an algebraic description, not all algebraic relations can be converted into analytic ones. In this form of algebraic relation, I consider that time is abstracted out as an explicit quality, and the arrow indicates a type of relation, just as the colon indicates a type of relation.

Regards,

Tim

-----Original Message-----
From: ROSEN Forum [mailto:***On Behalf Of David Macy
Sent: Sunday, August 28, 2005 11:08 AM
To: ***
Subject: Re: New JTB paper on (M,R)-systems

Hey Tim and all,

I'm relentless. I actually had the pleasure of hearing Juan-Carlos Letelier speak at a conference in Boston last September. He had many good things to say about Robert. He said Robert was a lone wolf and showed a slide of a magnificent specimen of same said. He also showed a slide picture of Robert which was the first picture that I had seen of him. I think Robert was a well spoken lion. At one point Juan-Carlos said that Robert was crazy (loco) and that he meant that in the best possible way!

I just received a copy of Fundamentals of Measurement and Representation of Natural Systems from Judith. She (quite unbeknownst to me) conspired with my folks to get me a copy for my birthday! Fantastic! (Thank you again Judith.) Judith can be sneaky y'all. Watch out. So I now have my compliment of the "big four".

Tim, I say all that because the question I'm about to ask you might be in there (FM), but sadly I have not yet had the chance to peruse it. Juan-Carlos and you clearly seem to have a mathematical bent and ability. I only dabble. I'm a mathematical tourist.

How many ways do you (or whoever feels compelled to respond) think that f:A--->B "metabolism" can be interpreted? Surely a great many and not all of them need be mathematical interpretations, right? My intuition is generally not mathematical. Also the arrow gives the impression of time but why could it not be merely an association?

I'll probably spend the rest of the day reading through FM. Thanks guys.

David