Re: Von Neumann vs. Robert Rosen

["glen e. p. ropella" <***>]

Judith Rosen wrote:
> I can't speak for anyone else, but in my view honest questions are 
> never "too pedestrian". (I have a question of my own.... What does 
> "RTFM" mean? I can come up with a number of possibilities that fit the 
> initials, but there's no way to know which, if any, are the words you 
> mean!)

It means "Read The Freaking Manual"... which on this list might mean, go 
read more of what Rosen actually wrote.  I've only read 2 of his books 
closely.  So, it's a valid response to me. [grin]

Let me paraphrase you to be sure I understand.  There are alot of side 
issues you bring up in your prose; but, I'm not going to address those, 
yet (like the idea that complexity is binary, the difference between 
complicatedness and complexity, and the existence/usefulness of the 
concept of "state").

You mean to say that von Neumann suggested that living systems could be 
linear and _not_ self-referential and that complexity is achieved 
through concreteness (i.e. moving from abstract to the detailed 
concrete).  And that RRosen's work suggests that a living system must be 
non-linear, self-referential and complexity is coincident with 
self-referentiality and closure under iteration.

Am I close?

_If_ that's the argument you're making, I disagree.  I think von Neumann 
handled non-linearity, self-referentiality, and closure under iteration 
explicitly by building a full _ontology_ in which the evolution of the 
machine would occur.  In this regard, it seems like von Neumann and 
RRosen would be in full agreement.

Further, I don't think vN would suggest that complexity is solely 
achieved through added detail... if that were the case, then why would 
he go to so much trouble to try to build a machine that was as ideal as 
his machine?  He would have been better served doing more engineering 
work with concrete materials (like our current gene-o-philes ;-).  It 
wasn't concreteness or detail that gave him his growth and evolution of 
complexity. It was the structure and dynamics (organization) of the 
machine that presents the meat of his work in that area.  (at least from 
what I know of it)

The point I was making to Tim and Dan, however, _is_ related to added 
detail.  My claim is that _no_ formalism can completely describe an 
extant system without getting into a high degree of complexity.  And by 
complexity here, I mean, self-referential, causally looped, iterative, 
nonlinear properties.  For example, the gasoline engine, when modeled in 
all it's gory detail, would present intra-formalism problems like 
turbulence.  The real engine decays, rusts, blows gaskets, explodes, 
etc.  These are phenomena that aren't easily captured in formalisms. 
Any model of the formalism that captured them would not be "computable".

Indeed, it may well take an infinite number of models to successfully 
capture all the gory detail of a combustion engine.

So, in making this statement, I'm trying to get at the practical 
usefulness of calling one thing a machine and another thing an organism. 
 What do we achieve by making this distinction?  If we were really good 
at it (and most others were really bad at it), could we get rich doing 
it? [grin]  Sorry to be banal.

> My paraphrase of my father's argument goes like this: Von Neumann 
> described a complex system as a system that has "more" of something, 
> which he called complexity, than a non-complex system. He described a 
> complexity threshold that a system could (theoretically) cross, which 
> was the demarcation point between complex systems and non-complex 
> systems. In this worldview, complexity is equivalent to a high level 
> of detail and/or intricacy, which we can achieve in a non-complex 
> system by adding more detail and intricacy to it. This definition of 
> complexity differs markedly from the Rosennean one. If Von Neumann's 
> definition were true (meaning, if it commuted with reality), then life 
> is computable, all systems really are just like machines, and we will 
> be able to create a self-reproducing machine which would be a living 
> organism. Von Neumann's idea of a self-reproducing machine was a 
> theoretical idea, based on a particular conceptualization of what 
> complexity might be, and it's never been officially tested (unless we 
> consider the past several decades of science trying like hell to 
> achieve it "a test").
>
> Robert Rosen said that this definition cannot be the case: complexity 
> cannot be the same as "complicatedness" because if it were, we 
> wouldn't have the problems we are having in science when dealing with 
> complex systems-- where we can compute planetary trajectories on a 
> galactic scale, and have our computations commute when predictions are 
> compared with behavior of the actual system-- and yet we cannot 
> account for the systemic behaviors of a single-celled organism. If Von 
> Neumann were correct, there would be no such thing as a system being 
> "more than the sum"... etc. Size would matter, in a sense. So, RR 
> followed the problem: If complexity is some property or quality which 
> is innately different from complicatedness, then what is it? His 
> answer ended up being that complexity was an organizational issue. The 
> relations, as specified/created/maintained by the system organization, 
> are the source of the added value in a complex system. The nature of 
> the relations is key, therefore the way some system is organized is 
> what determines complexity or non-complexity (simplicity) of that 
> system.
>
> In this definition, complexity is something which is true of the 
> system organization from the outset. In other words, it isn't 
> something which can be achieved by adding detail to the existing 
> organization of a non-complex system.  No one knows how complex 
> systems spontaneously self-organize in this universe, but, however it 
> happens, complex systems are that way from inception. Therefore, it is 
> not a matter of arithmetic.  The only way to make a simple system into 
> a complex system, in the Rosennean sense, is to reorganize it. Thus, 
> complex systems are innately different from simple systems, and cannot 
> be productively analyzed by reductive means the way simple systems 
> can. All the "added value" disappears as soon as the system is 
> fractionated and we are left with "the sum of the parts". There is no 
> way to figure out what's missing and add it back in. Do you see?
>
> My father often used mathematical arguments to illustrate things like 
> this; for example, pointing out that it is not possible to reach 
> infinity by addition. In order for some system to be infinite, it has 
> to include a circularity or what he described as an "impredicativity," 
> in its organization. If you try to straighten the circularity out into 
> linear form, you lose the system. My way of describing this concept is 
> to say that, in a complex system, time itself is incorporated-- as an 
> ingredient-- into the system's organization. With a system like this, 
> there is no such thing as a "state", even in a theoretical sense. 
> (Frankly, it seems to me that there is no such thing as a "state" in 
> this universe, period. It is a condition devoid of time which can only 
> be approximated experimentally and only exists in human theoretical 
> models.) The models based on notions of state, then, are inapplicable 
> to complex systems except in very limited ways. And this is what the 
> difference between Von Neumann and Robert Rosen leads to. Nothing at 
> the foundations of science can remain the same.
>
> There are several "tests" or conditions by which complex organization 
> will reveal itself. One is reduction to syntax: If you can do that to 
> a system and not lose the system in the process, it's a simple system. 
> In order for a system to be computable, it must be reduced to syntax, 
> so we can extrapolate from that: complex systems are not computable. 
> Fractionation is another test: if you can take the system apart and 
> not lose information (which means you can also put it back together 
> again, using the information learned purely from studying the parts), 
> then it's a simple system. If fractionation destroys the system, 
> irrevocably, then... it was complex.
>
> By this measure, atoms are complex systems. Can you see what the 
> consequences of that realization are?


--
glen e. p. ropella              =><=                Hail Eris!
H: 503-630-4505                       http://ropella.net/~gepr
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