Miku Rosen PRTD Complexity Intro

8/10/2019 Miku Rosen PRTD Complexity Intro

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Miku Rosen Complexity Intro October 10, 2014 Page 1 of 13

Robert Rosen Intro

ROSEN IN CYBERSPACE:

A HYPERTEXT INTRODUCTION TO

THE WORK OF ROBERT ROSEN AND

THE NEW SCIENCE OF COMPLEXITY

Bob Rosen

Don Mikulecky

Professor of Physiology

Organizer, Complexity Research Group

Medical College of Virginia Commonwealth University

PREAMBLE:

This is a hypertext document. The blue words or phrases are links to background material for those who wish to pursue it. Rosen wrote in Life Itself :

"This book represents part of the outcome and present status of about thirty years' work on theproblem "What is life?"...writing this text is the hardest thing I have ever tried to do, much harder

than doing the research it embodies. The problem was to compress a lot of interlocking ideas, drawnfrom many sources, which coexist happily in my head, into a form compressible into a linear script."

It is this non-linear collage of interrelated thoughts that will be handled by the use of hypertextlinks. As it progresses, it will begin to take on a new character as Don Mikulecky's interpretationand applications become more prevalent.

TABLE OF CONTENTS

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http://www.people.vcu.edu/~mikuleck/rosen.htm



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Definition of complexity

The modeling relation

Analytic and synthetic models

Some background: causality

Some background: Measurement

The complexity of nature

The Ontology of complexity

Emergence and Complexity

DEFINITION OF COMPLEXITY

D. C. Mikulecky



http://views.vcu.edu/~mikuleck/

1. Why is "What is complexity" a question not so easily answered?

For some time we have been being told that there is a "new science" called complexity.Universities and other research institutions have programs in "complexity research" and journals

carry this word in their title. What is complexity? What does it mean to be "complex"? The

dictionary does not help us here. There is more to the idea than what a dictionary definitionsuggests.

If we turn to science where words are carefully defined and have more precise meanings we findthat, in this case, things are not much better and may even be worse! It is here where we need to

look, nevertheless, since it is here where the answer does lie. One person who was quick to

exploit the failure of the scientific community to get together on this concept was John Horgan.

In his essay in his June 1995 Scientific American editorial entitled "From complexity to perplexity", he mentions 31 definitions of complexity and associates the concept with:

Too high a mouth to brain ratio

Tremendous hype Computer "hacking"

Too much journalism

He also points out the lack of a "unified theory" of complexity.

It is also worth noting that nowhere in his essay does he mention the definition which will be

given here and which, to my satisfaction, completely clears up the confusion.

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http://www.people.vcu.edu/~mikuleck/modrelisss.html


http://www.people.vcu.edu/~mikuleck/courses/rosmes/


http://www.people.vcu.edu/~mikuleck/cmpxnat.html


http://www.people.vcu.edu/~mikuleck/ONTCMPX.html


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Later, in his book, The End of Science, he adds some more fuel to the fire. There he develops a

stance which places all discussion which does not fit the mold we shall refer to as the Newtonian

Paradigm into a category called "ironic science" about which he says: "At its best, ironicscience, like great art or philosophy, or, yes, literary criticism, induces wonder in us; it keeps us

in awe before the mystery of the universe. But it can not achieve its goal of transcending the

truth we already have. And it certainly cannot give us-in fact protects us from- The Answer, atruth so potent that it quenches our curiosity for all time. After all, science itself decrees that wehumans must always be content with partial truths."

Horgan doesn't know it but he did a good job of giving validity to the concept called

"complexity" here. In fact he also doesn't know that the very definition furnished explains most

of what he is concerned about and clears it up. I can be sure that he doesn't know it because the

only place he ever refers to Robert Rosen is in his book where he says: "…and Robert Rosen, aCanadian biologist who was at the workshop…" It seems clear he has little knowledge of Rosen's

work if this is all he has to say about it.

2. A definition that works: and also explains the difficulty.

This may seem silly, but the entire real world is complex! That's right! So why the problem? Theanswer lies in the nature of science. This is what Horgan was struggling with in his book.

2.1 The Newtonian Paradigm is built on Cartesian Reductionism: Hard Science.

What Horgan defends, as "strong science" is essentially what we will call "hard science". Byhard science we mean the model for all science that is the embodiment of the so-called " scientific

method". Since everyone probably thinks they know what this is, it is worth spelling it out in

some detail, just so we know what I am really talking about.

2.1.1 Cartesian Reductionism and the Machine Metaphor.

Descartes is attributed with the popularization of the machine metaphor and he did it in a very

interesting way. He saw the body as a biological machine and the mind as something apart from

the body. This is called Cartesian Dualism and survives to this day as one approach to the so-called mind/body problem. What the machine metaphor did was to set the tone for modern

science. It has lasted since that time. Descartes really did not know what a machine is, or if he

did, he never told anyone. Ironically, not only do we not have a good definition of complexity,

but we also lack one for a machine. The importance of this metaphor is in the intuitive concept ofmachine that almost everyone shares. A machine is built up from distinct parts and can be

reduced to those parts without losing its machine-like character. We call this idea "Cartesian

reductionism". We will see that this is not true for complex (real) systems except under very

special circumstances. Cartesian reductionism does not work for complex systems; it onlyreduces them to simple mechanisms.

2.1.2 `The Newtonian paradigm.




Newton gave us three laws of motion, which were intended to describe the motion of the planets.

It turned out that these laws could be applied in a seemingly perfectly general way. This broader

application has been the foundation of the modern scientific method and will be referred to hereas the Newtonian Paradigm.

In the center of this paradigm is dynamics. Dynamics is the way the laws of motion get applied.The local description of the motion is formulated as a differential equation called an equation of

motion. The equation of motion is manipulated by using the calculus (integrated) and results in a

trajectory, which is an algebraic equation for calculating a particle's position as a function oftime. Later, this was made somewhat more complicated by quantum mechanics, but the central

philosophy was never changed.

The paradigm has been generalized from particle motion to all systems if we recognize that

quantum mechanics is part of that generalization. When we look carefully at the subject matter of

physics, we see that it is the application of the Newtonian Paradigm to the universe. This

application then makes the world into simple mechanisms. That is to say that the subject matter

of physics is the study of simple mechanisms. Note that in this context, "simple" means theopposite of complex, not the opposite of complicated.

3.0 Complexity is the result of the failure of the Newtonian Paradigm to be generic.

The success of the Newtonian Paradigm cannot be ignored. Most of modern science andtechnology is the result of it. For that reason alone it is difficult to suggest that it has limits and to

then make that suggestion stick. Not only does the paradigm have limits, but also those limits are

what gave rise to a concept like complexity.

3.1 Complex systems and simple systems are disjoint categories that encompass all of nature.

The world therefore divides naturally into those things that are simple and those things that are

complex. The real world is made up of complex things. Therefore the world of simplemechanisms is a fictitious world created by science or, more specifically, by physics as the hard

version of science. This is the world of the reductionist. It is modeled by the Newtonian

Paradigm and simply needs sufficient experimentation to make it known to us. Those

experiments involve reducing the system to its parts and then studying those parts in a contextformulated according to dynamics.

The paragraph above is one of the most controversial things one can say about modern science. Itflies in the face of all that everyone is taught. Yet, it really does no harm to those teachings. It

simply puts them into perspective. What is needed is to see that is the picture of how science is

done.

3.2 The way science is done: The modeling relation. [see article by Dress as well]

How is science done? It is a combination of using our senses to observe the world around us and

then to use some mental activity to make sense out of that sensory information. The process is

what we will call the modeling relation. If we call the world we are observing and/or trying to

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understand the Natural System and the events that make it change as we observe causality, then

that represents our object of study. What we do in our minds is to encode the natural system into

another system that is of our making or choosing which we can call a formal system. Once wehave chosen a formal system, we can manipulate it in various ways with the objective of

mimicking the causal change in the natural system. These manipulative changes in the formal

system we will call implication. Finally, once we think we have an appropriate formal systemand have found an implication that corresponds to the causal event in nature, we must decode from the formal system in order to check its success or failure in representing the causal event.

The following diagram represents the modeling relation we have just described.

If all the parts of the diagram are in harmony, in other words if 1 = 2 + 3 + 4, we say that the

diagram commutes and we have a model. A model of the world is the outcome of a successfulapplication of the scientific method, but it can also arise in other, less formal ways. Whenever

someone tries to make sense out of the world, they are trying to construct a successful modeling

relation, or a model.

Now the definition of complexity is complete. The world, from which we single out some

smaller part, the natural system, is converted into a formal system that our mind can manipulate

and we have a model. The world is complex. The formal system we chose to try to capture it canonly be partially successful. For years we were satisfied with the Newtonian Paradigm as the

formal system, forgot about there even being and encoding and decoding, and gradually began tochange the ontology so that the Newtonian Paradigm actually replaced or became the real world(at least as seen through the eyes of science). As we began to look more deeply into the world we

came up with aspects that the Newtonian Paradigm failed to capture. Then we needed an

explanation. Complexity was born! This easily can be formalized. It has very profound meaning.

Complexi ty is the property of a real wor ld system that i s mani fest in the inabil ity of any one

formal ism being adequate to captur e all its propert ies. I t requi res that we find distinctly

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dif ferent ways of in teracting wi th systems. Di stinctly dif ferent i n the sense that when we make

successful models, the formal systems needed to describe each distinct aspect are NOT

der ivable fr om each other.

Now we have it! Rosen spent his life refining this idea. There is far, far more to it. We will spell

all that out very carefully.

THE COMPLEXITY OF NATURE

D. C. Mikulecky




Complexi ty is the property of a real wor ld system that i s mani fest in the inabil ity of any one

formal ism being adequate to captur e all its propert ies. I t requires that we find distinctl y

dif ferent ways of in teracting wi th systems. Di stinctly dif ferent i n the sense that when we make

successful models, the formal systems needed to describe each distinct aspect are NOT

der ivable fr om each other.

This is the basic definition of complexity that I suggest everyone adopt. I will now show that iteither leads to or is consistent with all the following attributes/properties/definitions of a

complex system.

o It is non-fragmentable. If a complex system were fragmentable it would be a

machine. We require the distinction to be dichotomous. Therefore complex

systems are not fragmentable. That is not to say that they are incapable of beingreduced to parts, but such reduction destroys important system characteristics

irreversibly.

o Consists of real components that are distinct from its parts. At least one set of

these components is defined by its functions. These functional components are notsimply collections of parts. If they were the system would be fragmentable in theabove sense. These functional components are therefore defined by the system

and have their ontology dependent on the context of the system. Outside the

system they have no meaning. Further, if they are "removed" from the system in

any way the system looses its original identity as a whole system.







o Real (complex) systems have models as in the modeling relation. These models

may be analytic or synthetic models. The analytic models differ from the

synthetic. This must be so for consistency with the requirement for non-fragmentability. When synthetic models can replace analytic models, the system

is fragmentable and is therefore a machine.

o There can be no "largest model". If there were a largest model, all other models

could be derived from it and fragmentability would result.

o The system falls outside the Newtonian paradigm in some important ways. If it

could be described by the Newtonian Paradigm it would have a largest model

from which all others could be derived.

o Causalities in the system are mixed when distributed over the parts. There is final

cause in the sense that functional components have their own ontology. Thesecomponents are defined by their function. For this reason, the system can be

"anticipatory". That is to say, it can have causal relations which arise out of somefuture event if these future events are contained tentatively in a model the system

has of its environment (in the broadest sense, i.e., the system is included in itsenvironment.)

o The nature of causality and, especially the definition of functional components,requires that there be closed loops of causality of a nature forbidden, or at least

excluded, by the Newtonian Paradigm.

o The result of these traits is that much of the system's important attributes are

beyond algorithmic definition or realization by algorithms and therefore non-

computable in the usual sense. In that sense they refute Church's thesis.

THE ONTOLOGY OF COMPLEXITY

D. C. Mikulecky




Why are complex systems different from simple mechanisms?







I submit that in the answer to this question is the essence of what we mean by complexity. The

complex system possesses something that the machine or the simple mechanism does not. It is

the truth or falseness of that assertion which is at the heart of complexity. If there is no"something" complexity becomes a synonym for complicated and we have nothing more to say.

On the other hand, it seems clear that the existence of that something is obvious. There is anontology associated with the term "complexity".

If this is so, then there is a problem. One major response to these writings has been that the word"complexity" as used here, does not correspond to others usage of the word. That is the very

point of all this! If this usage of the word is not what others mean by complexity, then what is the

ontology behind the other meanings and how does this one differ?

The essence of the ontology of complexity is in the existence of something that is lost as the

system is reduced to its parts. Otherwise, the whole is merely the sum of its parts, but the wholemay be a more complicated arrangement of the parts. The idea complexity connotes is that when

the whole exists; it is now the parts arranged in a more complicated way and this newarrangement gives rise to something real that the whole possesses.

I also assert that this can be formalized. Call this set of properties that arise out of the

complicated arrangement functional components. These functional components only havemeaning in the context of the whole system. Once they are "removed" from that context, theylose their meaning. In this sense, the functional components are a kind of semantics arising out of

the syntax provided by the parts of the system. In this sense we have a nice analogy with

language as a complex system.

This poses a challenge for anyone who wishes to say that complexity is something else. They

would seem to need to establish a separate ontology and distinguish between what is beingformalized here and their alternative. So far, none of the other notions of complexity have dealt

with this. Until the "something" can be identified, I would wonder if they were not merely new

forms of reductionist mechanisms that are so complicated that they need to be singled out. If thatis what they are, why not call them complicated machines? If that is not what they are, then they

must fall into the same category as what we are calling complex.

COMPLEXITY AND EMERGENCE

D. C. Mikulecky




1. Emergence results from the complexity of nature and the limits of the machine metaphor







We have observed that the concept of complexity had to arise when the dominant formalism, the

Newtonian Paradigm, began to be pushed to its limits. What happened was a series of surprises,

all of which led to a need for the concept of complexity in order to explain what was happening.This process was repeated many times in many independent settings. Gradually, as different

people experienced it, the field of complexity research was born. The appearance of seemingly

new attributes of systems that were recognized as complex often was called emergence. Thus, inone sense, emergence is a result of the limits of a dominant formalism, and might even beassociated with error of a certain kind. There is a value in seeing this since we can then

distinguish between truly differing forms of emergence.

1.1 Emergence and complexity as new developments within the dominant formalism: chaotics

The Newtonian Paradigm centers on dynamics. Because of the way the mathematical basis for

the formalism developed, it was dominated by linear dynamics, first in particle kinematics then

in linear systems theory. As the mathematics of non-linearity was developed in the context of

dynamics, new results were obtained that significantly altered our view of the world. The

culmination of these was the discovery of chaotic dynamics. It was easy to see how thesediscoveries in the mathematical structure underlying the Newtonian Paradigm, which really were

forerunners to the concepts of complexity and emergence, became central examples of thoseconcepts. Once the identification was made, it had the added reinforcement of novelty, public

awe, and widespread applications. Suddenly chaos appeared everywhere one looked and

butterflies were making weather happen. As novel and exciting chaos is, it is neither an example

of complexity nor of the strongest kind of systems emergence. It did give rise to another concept,the idea that emergence is aided or even stimulated as systems leave some stable domain and

approach chaos. The "edge of chaos" became associated with novel behavior and emergence of

new phenomena. Thus, the Newtonian Paradigm, for a moment, seemed to regain its claim to being generic and seemed to exhibit all that was necessary to absorb the newly recognized realm

of complexity and emergence. This did not last long and soon chaotics was seen, by at least

some, as a diversion. The reason is clear in the context of this discussion. Nothing chaotics

revealed was outside the Newtonian Paradigm. It merely explored the limits of the non-lineardynamics that lies at the heart of the formalism. Complexity defies this formalism, for by its very

nature, it can not be seen from within formalism. It requires that one view from outside! This

brings us right back to our definition, and once more things are consistent. That leads us to thenext form of emergence that arises from our surprise when the dominant formalism fails us.

1.2 Emergence as the failure of the dominant formalism.

Nature is complex and therefore it is replete with examples of things that do not form models

when placed into a modeling relation with the Newtonian Paradigm. Here is another source ofemergence. This is a temporary class of emergent phenomenon, since the eventual expansion of

science beyond the Newtonian Paradigm will incorporate the explanation for these phenomena

into the dominant set of formalisms.

.1.3 Emergence in nature




There are a number of natural phenomena which include aspects which would seem to warrant

the description of being emergent. Two, in particular, are developmental biology and evolution.

In each case, a system is able to change profoundly and to generate new properties and structuresfrom existing ones. Neither of these is capable of being modeled by the Newtonian paradigm, so

they also fit that category of emergent property. Once again, the lasting aspect of the emergent

nature of these systems is in their own change, not in the need for new ways to describe them.

2.0 The claim for emergent properties in computer simulations

The use of genetic algorithms, Boolean networks, cellular automata, artificial neural networks,

and other related approaches is merely an implementation of the Newtonian Paradigm made

possible buy the huge increases in modern computing power. Some of these interesting andimpressive systems behave in ways that, in limited ways, seem life-like. In this limited context,

the systems do exhibit what might be called a form of emergence. This emergence is a

manifestation of a form of surprise when the Newtonian paradigm is taken to new limits of

complication. The confusion between complication and complexity is one which needs further

elaboration and that will be forthcoming. Another forthcoming topic requiring far moreelaboration is the difference between simulations and models.

The modeling relation: how we perceive

D. C. Mikulecky




1.0 How do we perceive our world?

The world around us is something we take for granted. We rely upon on our senses to bring

information about that world to us. The process results in something we call awareness. Scienceattempts to make the process as true to what is "out there" as possible. Hence, we developed the

scientific method which involves methods for keeping our senses under control and, often,

enhanceing them as well. The main process for this in the scientific method is measurement.

Measurement is a complicated process and has been analyzed in great detail (Robert Rosen, Fundamentals of Measurement and Representation of Natural Systems, 1978).

2.0 How can we understand perception? The modeling relation.

The modeling relation is based on the universally accepted belief that the world has some sort oforder associated with it; it is not a hodge-podge of seemingly random happenings. It depicts the

process of assigning interpretations to events in the world in a diagrammatic form. The best







treatment of the modeling relation appears in the book Anticipatory Systems (Rosen, 1985, pp

45-220). [see also the article by Dress]. Rosen introduces the modeling relation to focus thinking

on the process we carry out when we "do science". In its most detailed form, it is a mathematicalobject, but it will be presented in a less formal way here. It should be noted that the mathematics

involved is among the most sophisticated available to us. In its purest form, it is called "category

theory". Category theory is a stratified or hierarchical structure without limit, which makes itsuitable for modeling the process of modeling itself.

Figure 1. The modeling relation.

Figure 1 represents the modeling relation in a pictorial form. The figure shows two systems, a

natural system and a formal system related by a set of arrows depicting processes and/ormappings. The assumption is that when we are "correctly" perceiving our world, we are carrying

out a special set of processes that this diagram represents. The natural system representssomething that we wish to understand. We believe that information about the natural system is

brought to us by our senses. This is only partly a true picture of what goes on. Sensory

information may be the origin of what it is that we are aware, but the awareness has other, lesswell characterized components.

2.1 The percept is what we have in our awareness.

The percept is often the result of immediate sensory input, but need not be. Very often, the entire

modeling relation can be formulated in terms of memory or imagination furnished percepts.Once this is realized, a question should be brought to mind, namely, is the percept ever totallythe manifestation of sensory data alone? The answer has to be "no".

In particular, arrow 1 depicts causality in the natural world. On the right is some creation of our

mind or something our mind uses in order to try to deal with observations or experiences we

have . The arrow 3 is called "implication" and represents some way in which we manipulate theformal system to try to mimic causal events observed or hypothesized in the natural system on







the left. The arrow 2, is some way we have devised to encode the natural system or, more likely

select aspects of it (having performed a measurement as described above), into the formal

system. Finally, the arrow 4 is a way we have devised to decode the result of the implicationevent in the formal system to see if it represents the causal event's result in the natural system.

Clearly, this is a delicate process and has many potential points of failure. When we are fortunate

to have avoided these failures, we actually have succeeded in having the following relationship be true:

1 = 2 + 3 + 4.

When this is true, we say that the diagram commutes and that we have produced a model of our

world.

Please note that the encoding and decoding mappings are independent of the formal and/or

natural systems. In other words, there is no way to arrive at them from within the formal systemor natural system. This makes modeling as much an art as it is a part of science. Unfortunately,

this is probably one of the least well appreciated aspects of the manner in which science isactually practiced and, therefore, one which is often actively denied. It is this fact, among others,

which makes the notion of objectivity as defined above have a very shaky foundation. Howcould such a notion become so widely accepted?

2.1.1 The Newtonian Paradigm and the modeling relation

Traditional science as described above is the result of many efforts, yet it has a core set of beliefsunderlying it which Rosen refers to as The Newtonian Paradigm. There is no strict definition of

what this is, but it is the entire attitude and approach that arises after Newton introduced his

mechanics , especially, his mathematical approach. It certainly embodies the ideas of Descartes

and the heliocentrists, for example. It also embodies all of the changes brought about by quantummechanics. It is so much what modern science is that it could almost be used as a synonym. For

these reasons, it has had a profound effect on our perception. It is so powerful a thought pattern

that it has seemed to make the modeling relation superfluous. For The Newtonian Paradigm, all of nature encodes into this formal system and then can be decoded. All our models come from

this one largest model of nature. In the modeling relation, the formal system lies over the natural

system and the encoding and decoding are masked so that the formal system is the real world .The fact that this is not the case is far from obvious to most. The task then, is to understand why.

2.1.2 Putting it all together: the modeling relation is the key

Rosen calls the results of our sensory experiences as they manifest themselves in our awareness

percepts. If all we did were to use measurement to objectively become aware of what our senses

pick up, the situation would be simple. We would be like a piece of magnetic tape or computermemory filing away this information as it comes in. The key word in the definition of percept is

awareness. There is more to that awareness than a mere entering into memory. The first thing we

would have to do, even to merely file the information correctly is to discriminate and classify. Inshort, we form relations between percepts. What is fascinating about this is the fact that these

relationships between percepts can be matched by relationships between objects used in the




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formal system. Here is the place where semiotics and other aspects of our thought process get

mixed into the process in an irreducible way (Dress, 1999, a and b).

The confusion that arises from the failure to recognize this process at work is immense. Rosen's

whole concept of the modeling relation is the explanation for why words like complexity and

emergence have become so popular. The suppression of awareness of the process by the Newtonian Paradigm resulted in some real problems, surprises and errors. It was not until there

was widespread recognition, consciously or unconsciously, that this paradigm was inadequate

that these words became widely talked about. The world as modeled by the Newtonian Paradigmwas but one possible picture of the world. Rosen named this world the world of simple systems

or mechanisms.

There is another world, namely the one containing the natural systems we seek to understand,

which can not be totally captured by the Newtonian model. This world, in fact, can not be

captured by any number of formal systems except in the limit of all such systems. The name of

this world is the world of the complex. Emergence then is the phenomenon of being surprised

when the real world doesn't conform to the simple model, in other words, the discovery of itscomplexity. Since the entire real world is complex, discussions of degrees of complexity refer to

the nature and number of formal systems being used to create models within the modelingrelation. Unless this is realized, the amount of confusion generated trying to classify things by

their complexity can be immense. There are many other definitions of complexity (Horgan, 1996

) that exemplify this confusion.

Given the modeling relation and the detailed structural correspondence between our percepts and

the formal systems into which we encode them, it is possible to make a dichotomous

classification between various models of the real world. These models are either simplemechanisms or complex systems. It then becomes possible to formulate the "what is life"

question in an entirely new way, one which leads immediately to an answer.

Documents

Miku Rosen PRTD Complexity Intro