Harnessing Complexity 58
| Harnessing Complexity | |
| author | Robert Axelrod & Michael D. Cohen |
| pages | 184 |
| publisher | The Free Press |
| rating | 9.5 |
| reviewer | Cliff Lampe |
| ISBN | 0684867176 |
| summary | Become a professional Complexity Rassler! |
The Scenario
Complexity science has grown increasingly popular in the past few years, with increased tools available for modeling, and increased examples of successful interventins in complex systems. Unfortunately, books on complexity have remained mostly crap, until now. In this slim book is a framework for not only understanding complex systems, but for doing something besides standing at the sideline and watching them unfold.
Axelrod and Cohen are founding members of the BACH group, which has been very influential in complexity research. They have been long standing members at either the Santa Fe Institute, which is the premiere complexity research facility in the world, or the University of Michigan's Study for Complex Systems, which has also had a large effect on the science. In other words, these are two cats who know their bidness. Now here's the good part. Axelrod and Cohen are solidly academic, but this book is not. The weakness of books on complexity is that they have either been written for other complexity theorists, making them inacessible, or for the general population, making them insipid. Even though both researchers have been studying this field for decades, and could have written something brillant yet obtuse, but instead they wrote something brilliant and useful.
The authors describe the characteristics of Complex Adaptive Systems in terms of the three main elements of those systems: variation, interaction and selection. The book is divided into roughly three parts, each dealing with one of these aspects. The systems described have many different components, and one of the contributions of this book is to provide a common vocabulary for these elements. Here's a sample bit of text that the authors claim would give you a rough summation of the book:
"Agents, of a variety of types, use their strategies, in patterned interaction, with each other and with artifacts. Performance measures on the resulting events drive the selection of agents and/or strategies through processes of error-prone copying and recombination, thus changing the frequencies of the types within the system."
There are many examples of complex systems that the authors use to bolster their explanations of complexity theory. How a disease spreads, how the military makes far reaching changes in philosophy, and of course evolution all drive home concisely crafted observations about complex adaptive systems. There's even a little gem that talks about the development of an open source project, specifically Linux. The authors discuss some conditions under which an open source development model might thrive, or at least make sense. As a favor to the authors, we'll make you read the book to find out what those are.
Complexity theory is not the same as chaos. Complex systems are not chaotic, though they do depend on variation in order to adapt, or change the equilibrium point. The important message here is that complex systems are not beyond our understanding, though it may be tough. Also, because complex systems depend on churn, if we can arrange ourselves at that point of churn, and try to direct we can affect systems that have been previously thought unalterable.
What's Good?
The tone of this book is killer. Combining lucid explanations with meaningful descriptions makes this very readable without diminishing the topic at all. The final chapter even outlines the rest of the book for you, boiling it down to the bare bones points that you should really take from the text. It might be helpful to read it first, and then go through and read the rest of the book.
The other strength of the book is how the authors manage to follow a strong academic tradition of supporting points with evidence without succumbing to making the book sound like the usual academic crap. All of the points made are supported not only with the great examples, but with evidence from a large body of research, mostly academic. The bibliography for this book would be a great place to start for any person or group interested in delving deeper into issues surounding complexity theory.
This assertion that we can understand complex systems, and exert influence over them is an important concept for a new paradigm for thinking. The systems being developed, computer or otherwise, are mostly examples of complexity in action. Whether it is an open source project being created or a new design team you are putting together, they are rarely systems that can be boiled down to simple cause and effects. The Newtonian view of a mechanical universe has polluted the very way in which we think about systems, the way in which we understand the universe. The people researching complex adaptive systems are working against that, and this book is a definitely volley in the right direction.
What's Bad?
This question is a matter of audience in the case of this book. It is definitely written for laymen, so if you are into the math of complexity research, or the modeling, then seek on crazy diamond. The intended audience here is the person who has to deal with complex, adaptive systems, but is not an expert in math. This book is intentionally short and brief, designed for those without a lot of leisure reading time. If you're after the uber compendium of complexity theory, this is not your book either.
While it is a minor point, the title of the book is annoying. It is understandable for marketing reasons, but it could turn off some smart people to reading the book, fearing it might be of the "Business Guru" shallow variety. Do not listen to these fear, buy this book.
So What's In It For Me?
If you've been interested in complexity theory, or need to work with complex adaptive systems (which everyone must) then this book has quite a bit to offer to you. Practical advice on how to exert influence in a complex environment could be invaluable to the reader. Besides the practical good it can do the reader, this book also has something to teach you about how you think about the world in general. Being aware of the complex systems around you, and thinking more deeply than black and white, or even gray, about these systems has benefits that far exceed your current job or project.
This book could also become valuable for the open source movement in general. Understanding complex, adaptive systems will also increase the chances for success of a number of possible open source projects as well as how to position them in software markets, which are themselves great examples of complex systems. It would be great if people involved with open source could champion this method of worldview both for its intrinsic and extrinsic benefits.
Purchase this book at ThinkGeek.
Isn't this topic usually beyond most? (Score:1)
Re:Isn't this topic usually beyond most? (Score:1)
harrumph (Score:1)
Complexity theory solutions fall into two types:Ones where you can't understand the underlying process, in which case you can't trust the complexity theory result.
It's a pile of charlatanry. I say don't spend another tax dollar on it.
Order in Chaos. (Score:1)
So the next time you go past that desk at work that looks like the desk from "Shoe", just leave it. Chances are that that desk jockey has everything straightened out in some kind of system.
After reading the book... (Score:1)
Because there isn't one (Score:1)
Re:Isn't this topic usually beyond most? (Score:1)
Re:The purpose of book reviews (Score:1)
The book review was to alert
It's the lack of proper coverage (Score:1)
In the practical world most people even in science and engineering usually only use up through some basic level of differential equations.
The rest is pure theory that dosn't work in the physical universe.
Complexity theory IS Chaos Theory? (Score:1)
Assimilate the contents of the book and make it (Score:1)
Re:Order in Chaos. (Score:2)
Re:I'm going for redemption. (Score:1)
To clarify (Score:1)
Next time you want to critize sigs please look at some of the rather banal, smug ones that you see on other's and give them a whirl.
If english isn't your first language then ask what it means first.
Dreams of Reason by Heinz Pagels (Score:1)
by Heinz R Pagels, ISBN 0553347101
Not so new (Score:3)
Look at children. They learn to master extremely difficult complex systems like locomotion, language and exploration - all by the time they are five years old. How is most of this accomplished? Through imitation and experimentation. Children imitate what they see but they also explore their world. It's how many things are accomplished. Flight was mastered by looking at how birds fly and experimenting. So was medicine, math and every other complex system.
We may develop new terminology or methodology, but it all boils down to the same concepts.
Complexity Science?!? (Score:1)
[rough summation of the book]: "Agents, of a variety of types, use their strategies, in patterned interaction, with each other and with artifacts. Performance measures on the resulting events drive the selection of agents and/or strategies through processes of error-prone copying and recombination, thus changing the frequencies of the types within the system."
They did say this is written for a layman, right?
Anyway, this basically describes "genetic algorithms", an optimization technique. Nothing particularly innovative and there are better books about it. Certainly, the complexity study field is much wider than this.
Complexity theory is not the same as chaos.
Well, a theory is not the same as chaos. That's reassuring to know.
Complex systems are not chaotic, though they do depend on variation in order to adapt, or change the equilibrium point.
Err... "complex systems" is a very very wide term (usually meaning "I can't understand how it works and I've been looking at it for five minutes already!") and generally chaotic systems are treated as a subset of complex systesm. Not that the quoted sentence makes much sense, anyway. "Depend on variation in order to adapt"? Ahem, and how else could one adapt except by changing something?
The important message here is that complex systems are not beyond our understanding, though it may be tough.
No kidding! That is the important message of the book? Wow! That's really, really useful to know.
[flame] It sure looks tough, for complex systems are clearly beyond the understanding of the reviewer. Hint: before reviewing a book on Slashdot it's useful to know at least something about the field. [/flame]
Kaa
Re:Order in Chaos. (Score:1)
Lucid? (Score:2)
If this is the article author's idea of "accessible" and "lucid," I'd hate to see what he'd consider obtuse.
The author's right about the prose not being either academic or Bizspeak. It's a hybrid of both, as unintelligible as either but without the former's precision or the latter's accessibility.
Re:Not so new (Score:2)
Flight was mastered by looking at how birds fly and experimenting. So was medicine, math and every other complex system.
Oh baloney. There's no way you can convince me that medicine, math, and every other complex system was mastered "by looking at how birds fly and experimenting."
; )
"Free your mind and your ass will follow"
Re:Not so new (Score:3)
As usual, it depends. Thinking about, say, IP packets in terms of fuzzy sets is not likely to be productive. Thinking about political affiliations would be a good way to apply them. Fuzzy sets are a tool: just like any tool they are applicable to some situations and not applicable to others.
And in discussing other aspects of complex systems, even amoung the average joe, it becomes pretty clear, that people are more than well enough equipped to deal with complex systems
Among the average joe? Never mind...
Note, though, that reality itself is a very complex system. People (as well as protozoa, grasshoppers, rats, etc.) who were NOT equipped to deal with complex systems died out long time ago.
Flight was mastered by looking at how birds fly and experimenting.
Not really. Birds fly by flapping their wings and I don't know of a single successful aircraft that does this. Flight was mastered by understanding physical laws, specifically the laws of aerodynamics. These laws, by the way, are pretty crisp (=non-fuzzy).
So was medicine, math and every other complex system.
Err... so math was developed by imitating what you see, exploring the world, and experimenting? Uh, yeah, sure, right... [nods his head and slowly backs away]
Kaa
Re:Not so new (Score:2)
between fuzzy set theory and complex systems theory. Fuzzy set theory
in my opinion is based upon bad ideas about the proper form of logical
semantics and its relationship to the way we use concepts, and while
it has proven to be of some use in specifying systems in engineering,
the exaggerated claims of some of its early proponents for it to
displace traditional approaches to logic and set theory are nonsense.
Complex systems theory is a sophisticated and well-thought out
area that dates back to von Neumann, and has proven very
enlightening in a huge range of intellectual areas. It desrerves
better than the touchy-feely new-paradigm bluster that seeks to tie it
to fuzzy set theory.
ever a bad review? (Score:1)
I've bought a couple books off the reviews, and liked the ones I've gotten. But it'd be interesting to see reviews of the full range (in goodness to badness) of books--
Re:Complexity Science?!? (Score:1)
Err... "complex systems" is a very very wide term (usually meaning "I can't understand how it works and I've been looking at it for five minutes already!") and generally chaotic systems are treated as a subset of complex systesm.?
Chaos, in the sense the review meant, is a phenomenon (namely stochastic behavior in a deterministic system). A chaotic system would, then, be any system that displays the phenomenon of chaos.
A complex system usually has some chaotic behavior within it, but the chaos usually not the interesting part to so-called "complexity researchers". Rather, people like to study the emergent structures that form as a result of the interactions within the system. I think the reviewer meant to highlight the distinction, while still acknowledging that there are relationships between the concepts of complexity and chaos.
Reject the Status Quo! (Score:1)
It is time for everyone to simply think outside the BACHs!!
(Yeah, I know, but the alternative is for me to do some real work. ;-)
Re:Not so new (Score:1)
Don't run with scissors, eh?
Just that it was natural to think in fuzzy terms.
I have a nasty suspicion that it'll take us at least a dozen posts to sort out what "natural" means in this context. Besides, it's all handwaving. You say it's natural to think in fuzzy terms, I say it's natural to think in crisp terms, and how are we going to decide who is right?
I'm not sure that proves anything.
It proves that "humans are equipped to deal with complex systems" is a content-free sentence.
If you doubt that man didn't learn the concepts of flight from flying creatures, then go down to the library and research it yourself. Where do you think one would learn about concepts of aerodynamics? From creatures that have mastered it themselves, perhaps?
I don't understand what do you mean by "concepts" of flight. The concept of flight, that is, that heavier-than-air object can fly, certainly came from looking at birds. However I doubt very much that aerodynamics were developed by studying birds.
Off the top of my head (and I freely admit that I could be 100% wrong) I would think that aerodynamics developed from fluid dynamics, which are much easier to observe and, until the invention of aircraft, were much more useful. As to the fluid dynamics, I again doubt that they developed from looking at fish. Most likely they developed by putting simple physical objects into a stream and looking at what happens. Add to that a lot of practical experience with boats and ships of all kinds and you have a pretty good base.
The flaw in your argument is that living things are usually very complicated and it's not trivial to derive laws of physics from looking at them. It's usually easier to observer a much simpler system, work out how it works, and then complexify (sic!) the experiments until you think you have a reasonable grasp on what's happening. Understanding how living things work usually comes very late in the process. Remember the (in)famous bumblebee case? Until recently (10-20 years ago?) according to then-current aerodynamics the bumblebee could not fly: it was too heavy and its wings could not -- theoretically! -- generate sufficient lift to keep it in the air. It turned out that the bumblebee does some very, very complicated things (dealing with turbulence at wing edges AFAIK) that allow it to fly. But my point is that trying to derive *basic* aerodynamics from observing the bumblebee is impossible -- you would never get off the ground
Kaa
Re:Complexity Science?!? (Score:1)
Strictly speaking, you cannot have stochastic behavior in a deterministic system. What you have is that the behavior is non-computable and so we are forced to rely on stochastic methods to evaluate it.
But in any case the concept of chaos is wider. Chaos is usually defined as specific property of a system (as well as the resulting behavior of the system) and is commonly used to mean high sensitivity to inital conditions -- "the butterfly effect" -- and/or nonlinear feedback loops. There are both deterministic chaotic systems and stochastic chaotic systems (which are pretty much unanalyzable given the current state of the art).
I think the reviewer meant to highlight the distinction, while still acknowledging that there are relationships between the concepts of complexity and chaos.
Pardon me for bluntness, but I didn't get the impression that the reviewer understood anything. I think that the reviewer has a very vague and muddled idea of what is complexity, what is chaos, and what is the relationship between them.
Kaa
information wants to be free so that... (Score:2)
Re:Not so new (Score:1)
Agreed.
Fuzzy set theory in my opinion is based upon bad ideas about the proper form of logical semantics
Huh? Fuzzy set theory is based on the idea that you could express membership in a set not as a boolean value (0 or 1), but as a real number (e.g. 0.33). From here comes the notion of partial membership in multiple sets and off you go into fuzzy logic. Computationally it's very similar to dealing with a bunch of random variables the distribution of which you know.
Which *bad* ideas are you talking about?
Complex systems theory is a sophisticated and well-thought out area that dates back to von Neumann
You probably mean cybernetics which does date back to von Neumann. However, in our context "complex system theory" means somewhat completely different, although also frequently involving feedback loops. Treat this a semantic contamination...
Kaa
Re:Not so new (Score:2)
The book focuses on complex (not just complicated) systems. Complex systems have certain properties that differentiate them from merely complicated systems. Complicated often means "having many moving parts" for example. By complex, the authors are referring to systems in which the interaction among components often heavily influence later probabilities.
Having read the book, I think it does a good job of distilling some of the subtleties of complex systems, focusing on things that a manager could affect, such as the effects of proximity (both physical and conceptual), and interaction patterns.
The book extracts some useful things out of complexity theory. Things that could conceivably be harnessed (rather than controlled). The book is surprisingly sparce on the buzz words and hand waving that I usually associate with complexity books.
My main criticism is that I don't think most managers are as smart as Axelrod and Cohen give them credit. They explicitly point out that the book doesn't have a list of 4 or 8 or 12 things a manager can do to be successful.
Unfortunately, most (not all) managers I've worked with were better suited to a dilbert cartoon than a book like this.
Anyway, this isn't a book for someone looking to model complex systems, or someone who just wants to learn about the latest research in the field in an accessible way. It really focuses on some general principles of complex systems, and what they can mean to organizations.
Also, it has a really good index...
Complex,chaotic, or genetic???? (Score:1)
What's the other one? (Score:1)
So... what's the other type?
Re:After reading the book... (Score:1)
Re:Not so new (Score:1)
You're right. You are 100% wrong. The concept of flight was first concieved of, and attempting to imitate birds. Which is why so many people died in the attempt. I'm not at all sure where the fixed wing concept came from, but it was tested in wind tunnels, as well as on rocky hills soon to be covered in bloody piles of bodies. It wasn't until much much later, probably near WWII that fluid dynamics entered the picture at all. Wilber and Orvil were, after all, bicycle makers with a hobby.
Kaa, you seem to have a problem with the reviewer and it would probably be in your best interest and get help.
Re:Not so new (Score:2)
well-known to attempts to develop probablility theory as a version of
multi-valued logic: total orderings, like the interval of the real
line [0,1], do not support a semantics for implication, and similarly
you can't quantify over fuzzy sets.
As I understand it, systems theory is a synonym for cybernetics.
It is proposed because it is more suggestive of the subject matter.
If this is wrong, I'd be delighted to know what the difference is.
Re:Not so new (Score:1)
>>>> Flight was mastered by looking at how birds fly and experimenting.
>> Not really. Birds fly by flapping their wings and I don't know of a single successful aircraft that does this. Flight was mastered by understanding physical laws,
Actually, all heavy birds are mostly gliders, save the takeoff and landing. Take storks, for instance. They fly thousands of kms in a few weeks twice a year (well, for the 5% that survive the electric wires in Europe and the insecticids in Africa), almost without flapping.
What all gliding birds do, however, is to use variable geometry to achieve control. Copying that was a bad idea (Ader's plane did made a few bumps, replicas did fly, but that wasn't an efficient idea), but Ader plane replicas have shown that this was feasible, even with 1895 technology.
Re:Not so new (Score:1)
If you were bothered to read what I have written, you would have noticed that I was NOT talking about the idea of flying. I was talking about aerodynamics, a branch of physics, and how it developed.
Which is why so many people died in the attempt.
Which goes to show that observing nature and blindly trying to imitate it is not always a good thing, right?
It wasn't until much much later, probably near WWII that fluid dynamics entered the picture at all.
Any proof? References? As you noticed, I can make unsubstantiated statements as well as you.
Kaa, you seem to have a problem with the reviewer
Well, yeah. I know a little about the subject -- enough to understand that the reviewer has no clue, that is as in "no clue at all", about complex systems and the current research in this area. Still, he presumed that just because he picked a book at a bookstore he was qualified to write a review and put it on Slashdot. To put it bluntly, he is NOT qualified. Besides, the review itself is a piece of crap -- it contains very little useful information and wonderful sentences such as "The important message here is that complex systems are not beyond our understanding, though it may be tough." Bletch.
it would probably be in your best interest and get help.
and get help? me? [maniacal laughter in the distance] I am BEYOND help, you worm! My plans for world domination through posting to Slashdot are almost complete! You'll all be petrified! Yes! And some select ones will be both naked and petrified! Yaaaaaah!
Kaa
Re:Not so new (Score:1)
Well, yeah, fuzzy logic is not a complete drop-in replacement for "normal" logic, no question about it. I was not arguing that -- I was just surprised to see you say that it grows out of some "bad" ideas.
you can't quantify over fuzzy sets.
What do you mean?
As I understand it, systems theory is a synonym for cybernetics.
Systems theory, yes. Complex system threory, no. They are two different beasts.
Kaa
Re:Not so new (Score:1)
PII, PIII (Score:1)
Re:Not so new (Score:2)
Bart Kosko) who have claimed that fuzzy logic/set theory `generalised'
conventional logic/set theory. The people who just argue that it is
useful in specifications, but isn't a general purpose logic, I have no
problem with.
As for complex systems theory vs. cybernetics, the stuff about
variation, interaction and selection described in the article occurs
in cybernetics. Do you have a reason for believing the two to be
different or not? I'd be interested to know what reserach falls under
one and not the other, but I am not interested in bald assertions that
the two are different.
Books on complexity... (Score:2)
...and business are not common at this point, but there have been several good books about emergent phenomena and complexity-theory attempts to explain them:
Complexity: the Emerging Science at the Edge of Order and Chaos by M. Mitchell Waldrop is my favorite. It's very readable and a good introduction for the layperson.
Complexity: Life at the Edge of Chaos by Roger Lewin takes a more biological perspective, using the Cambrian explosion and subsequent extinctions as a primary theme of inquiry. I haven't finished it yet, but find it almost as interesting as Waldrop's book. (Personally Lewin's style is chatty for my taste with its constant recreation of his conversations with various scientists.)
Lewin and Birute Regine have recently written a book called The Soul at Work, but I haven't read it yet. It may prove interesting since Regine's area of specialty is developmental psychology (which is a natural for complexity studies, but whose practitioners have not yet become interested in studying emergence). This book is perhaps the most direct competition for this book being reviewed. I hope someone who has read it will post something to this discussion.
John Holland has two good books out which may /.ers may relate more directly to, since he is a bit of a renagade in the computer science community (or was until he started turning out to be proven right). His books are very good for the detail (and even some math). But they are almost written from a lab-notebook perspective, recreating the evolution of his thought even to the point of exploring dead ends which he later abandons.
Given all this, I have some difficulty with this reviewer's blanket denunciation of the field. None of these books is long on business-babble or psycho-pspeak, so I'm at a loss to understand his generalization.
I will check this book out, but I would offer the following caveat: Complexity science is an interesting outgrowth of chaos theory which is still controversial within the scientific community. It's on the bleeding edge of current scientific thought and may yet pan out to be a dead end (or a world-changing advance).
I am personally following it with considerable interest and have already come up with a number of applications which helped with both my programming and my business. But anyone who makes blanket evaluations of it (pro or con) is probably exaggerating their actual knowledge.
Re:Not so new (Score:2)
In actuality, we generate lift with airfoils in the same way--by creating circulation. We just do it with thrust. =) And as for the laws of aerodynamics being "pretty crisp", Kaa, please tell me how to model turbulent behavior past the stall point of an airfoil.
--
Re:Not so new (Score:1)
If she weighs the same as a duck, then she's made of wood...and therefore....a witch!
Re:Not so new (Score:1)
No, I don't subscribe to this particular belief that "normal" logic is a subset of fuzzy logic. It's fairly hard to substantiate, isn't it?
As for complex systems theory vs. cybernetics, the stuff about variation, interaction and selection described in the article occurs in cybernetics.
The review sucks heavily. I don't think the reviewer understands what he is talking about.
Now, AFAIK, cybernetics is mostly concerned with control systems with feedback loops. You have a system with inputs and outputs, and the outputs affect (with a suitable time delay) either the inputs, or the parameters of the system itself.
Complex systems is not really about this. They are, basically, about modeling highly nonlinear systems, ones where plain ol' regression just doesn't cut it. It's not a unified field by any stretch of imagination. Most research concentrates on:
(1) Optimization techniques, preferably non-linear and global. Here you have genetic algorithms, simulated annealing, partly neural networks.
(2) Emergent behavior, where you typically have multiple simple agents interacting and complex behaviour spontatneously emerges out of these interaction.
(3) Chaotic systems, which is usually taken to mean either sensitivity to inital conditions (butterfly effect) and/or nonlinear feedback loops.
(4) Misc other stuff.
For an example of a complex system look at stock market. This is very noisy nonlinear unstable system with a tendency towards feedback loops and reversion towards the mean. If you manage to model it successfully, you won't have to work any more...
Kaa
Re:Not so new (Score:1)
Well, the result is the same -- flow (and not circulation, btw) over the airfoil. The mechanism of achieving the flow, however, is rather different.
And as for the laws of aerodynamics being "pretty crisp", Kaa, please tell me how to model turbulent behavior past the stall point of an airfoil.
"Crisp" does not mean "able to calculate everything to the n-the degree of accuracy". "Crisp" is a term from fuzzy logic and refers to old/normal/conventional logic, specifically to values '1' and '0'. These values are "crisp", while real numbers, like 0.5, are "fuzzy".
Kaa
The difference between complexity and chaos theory (Score:1)
Re:Books on complexity... (Score:1)
Also, John Holland is the H in BACH, the group that Cohen and Axelrod are the A and C of respectively. He's obviously had a large influence on their thoughts here.
Complexity theory is unquestionably valid.... (Score:1)
Complexity theory is NOTChaos Theory.... (Score:1)
It is definitely, absolutely NOT chaos theory, which I've never formally studied but which I'm given to understand involves order spontaneously emerging out of disorder. Two totally different things from what I understand....
Fuzzy: good and bad (Score:2)
Which *bad* ideas are you talking about?
I'd agree that the notion of partial set membership is a Good Idea.
However (I would say) the rules used for doing computations with fuzzy membership numbers -- at least, the ones typically advocated -- are arbitrary, ad-hoc, and fundamentally plain wrong. Sometimes they are useful as a very rough and ready engineering fix when nothing can go too badly adrift, but basically they are Not A Good Thing At All.
A more principled way to deal with fuzzy numbers is to use the machinery of Bayesian calculation, treating fuzzy values as ordinary probabilities, but relating to a wider ontology than just the physical state of reality.
Such extended ontologies arise very naturally from communication theory when we try to summarise data. For example, consider transmitting a set of points on a 2D grid using a mixture of Gaussians model. For each point, one sends the probability that it was generated by Gaussian A rather than B (less than one bit, using BitsBack), followed by the bit string to code its position using one or the other Gaussian.
Gaussians extend to infinity, so we can never definitiely allocate a point to one bump or the other -- it is always a mixture of the two. Thus even a knowledge of the whole of reality is not sufficient to resolve the probability to a definite 0/1 state. "Generation by bump A rather than bump B" is therefore technically a fuzzy proposition, rather than a classical one -- the variable is part of our description of the system (our extended ontology), rather than underlying reality.
In summary:
Endnotes:
1. All of which is entirely irrelevant to the subject of far-from-equilibrium pattern formation (which is what complex systems theory is mostly all about?).
2. For a more extensive discussion of Bayesian inference and fuzzy systems, there are classic papers by Cheeseman.
Re:Not so new (Score:1)
Most everybody takes a dump, too, but that doesn't mean it's tightly coupled with human cognitive capacity.
Pete
Re:Not so new (Score:2)
dynamics'? Or did they, too, decide they wanted a new name?
For an example of a complex system look at stock market. This is :-)
very noisy nonlinear unstable system with a tendency towards feedback
loops and reversion towards the mean. If you manage to model it
successfully, you won't have to work any more...
Ah. Sitting on my desk I have a powerful stock market simulator.
It performs calculations capable of reliably determining tomorrows
stock market prices from a sample of today's data. Unfortunately it
takes 100 years to complete its calculations...
Re:Fuzzy: good and bad (Score:2)
binary notion of truth-value can be replaced by the smooth real
interval. Unfortunately this generalisation breaks the semantics of
implication, and a similar problem breaks quantification over fuzzy
sets with the naive semantics.
A Bayesian approach to `fuzzy' set theory/logic is an interesting
idea, but unlike the fuzzy logicians, most Bayesians are radical
subjectivists. I think this gives it a chance of success (the
smenatics of conditionals can be described in terms of what a given
observer learns in learning that the condition is true), but it is a
much more complex approach, and it isn't obvious that it will nicely
generalise the successes of fuzzy set theory in the specification of
simple engineering systems.
The stuff you describe doesn't sound so subjectivist. Could you
give a more detailed reference to Cheesman?
Aerodynamics (WAS Re:Not so new) (Score:1)
I don't argue the difference in the mechanism--I made that point myself. And, circulation is indeed present over the wing surface. I'm betting here that you haven't taken a course in aerodynamics. It's circulation that accelerates and decelerates the flow to create the pressure gradient across an airfoil.
Last I checked, the laws of aerodynamics don't accurately model separated flow. You can make a stab at it, but you don't get anything near "conventional"--at least not yet. Separated and turbulent flows are a bitch to model. Laminar flow is easy--and crisp.
--
good book but thin on content (Score:1)
Re:Complex,chaotic, or genetic???? (Score:1)
Re:Complexity theory is Chaos Theory.... (Score:1)