Proposing FTL today is pretty much a lost cause (although there are interesting ideas such as the Alcubierre Drive – at least it’s still a viable option for Sci-Fi literature). The problem is that the Einstein’s special theory of relativity (SRT) postulates that nothing is able to go faster than light (more exactly: no information can be transmitted faster than light. Spaceships and their passengers are of course matter organized in certain ways, viz information – so they can’t go faster than light).

To date, we have no observations which contradict relativity, on the contrary, SRT and GRT are highly successful and thoroughly corroborated. To put it another way, observation of an FTL object would be theoretically quite…a surprise.

The situation is very different for strong AI: first of all, there is no theory whatever which predicts that such a thing were not possible. We don’t know quite exactly how this thing called consciousness appears in the brain, but it is a very active subject of research.

But there is something more important: whereas we have not observed FTL objects, we observe strong “I’s” (intelligences) every day: your fellow humans, yourself etc.

We are conscious, and we live in this physical world, made of the same physical stuff as everything else. Our consciousness is an organizational property of the matter we are made of, not something magical tacked on as an afterthought. What a wonderful insight: we know by simple observation of our surroundings that physical matter configurations can become conscious! Easy to see, yes? But, as Aristoteles said: “Just as bats’ eyes are to daylight, so is the mind blind to that which is most obvious of all.”

Strong AI is not a problem in the sense of “could it possibly exist?”; it is evidently only an engineering problem (albeit a complex one). Maybe we will need molecular biology for solving it (meaning that AI will only run on proteins and not on silicon, which is more in line with materialism than computationalism; but it is engineering nonetheless). We just have to find out in which way matter has to interact (in a sufficiently reentrant way) to build an AI.

After all, the distinction artificial and natural is pretty thin anyway. Ants are natural. Their nests are natural. Humans are evolved, they are natural. So why should we not call their artifacts natural? It is only a philosophical word quibble – the distinction natural/artifact is sometimes interesting – for instance, when we stumble upon an artifact on an alien world, this is astounding not because an “artifact” were something “supernatural”, totally out of this world, but because an “artifact” suggests an “artificer” -  an intelligence, an agent, which made it – a natural being of some sophistication. The intelligence that made the thing would be quite a natural inhabitant of its environment. Never let the distinction artificial/natural confuse you!

So, to get back on topic: what opponents of strong AI would actually have to claim is that we will never (1000 years? 1 million years? our descendants on different planets in 5 billion years?) be able to engineer a conscious artifact because of mysterious reasons which would go against everything we know about this world. And this claim, now, seems completely ludicrous to me. And if it does not sound ludicrous to you, go look in a mirror! (you are conscious, are made of matter, but are not going faster than light ) Opponents of strong AI are fighting the same losing battle as vitalists did in the 19th/20th century.

I found this amusing quote by Francis Crick on the wikipedia article on vitalism: “And so to those of you who may be vitalists I would make this prophecy: what everyone believed yesterday, and you believe today, only cranks will believe tomorrow.”

Similar issues are raised in this blog post, which motivated me to publish this (now slightly overworked) draft (which otherwise would have slumbered for many months on my harddrive before being polished enough to publish ).

A commenter on that blog (Accelerating Future) says this:

Michael Bishop (2003). Dancing with pixies: Strong artificial intelligence and panpsychism

This paper argues against computationalism by showing it implies panpsychism.

Here it should be emphasized that in fact every realist monist naturalism (and who’s a dualist nowadays? nobody, for good reasons!) implies panpsychism – see this paper by Galen Strawson. (If you want more of this stuff, there’s also a book.) So the problem (if it is one) lies somewhere else and certainly not in positing strong AI or computationalism. The problem can be solved by a radical (“radical” in the sense of “going to the root”) monism, but on that more later, because it’s a topic of its own.

Technorati Tags: consciousness, human brain, materialism, philosophy, strong ai

(The Tegmark paper on “The Mathematical Universe” can be found on arxiv.org.)

Does the theory warrant further scrutiny?

First of all the question was raised of what could possibly be gained by the approach favored by Max Tegmark; is it only a waste of time with no empirical consequences?

I would like to reframe the question: What does it actually mean calling reality mathematical?

1. An issue well pointed out by Max himself is maximal independence from word fluff: only relationships made explicit in formalisms, computations or structures constitute knowledge. This “making explicit” is a first boon, because when we speak in “normal” words everybody has different connotations and associations bundled with them; only by speaking in mathematics can we ensure that everybody associates the same meaning with what is said. Words are hidden inferences:
   

   Your brain doesn’t treat words as logical definitions with no empirical consequences, and so neither should you. The mere act of creating a word can cause your mind to allocate a category, and thereby trigger unconscious inferences of similarity. Or block inferences of similarity; if I create two labels I can get your mind to allocate two categories. Notice how I said “you” and “your brain” as if they were different things?

   Making errors about the inside of your head doesn’t change what’s there; otherwise Aristotle would have died when he concluded that the brain was an organ for cooling the blood. Philosophical mistakes usually don’t interfere with blink-of-an-eye perceptual inferences.

   But philosophical mistakes can severely mess up the deliberate thinking processes that we use to try to correct our first impressions. If you believe that you can “define a word any way you like”, without realizing that your brain goes on categorizing without your conscious oversight, then you won’t take the effort to choose your definitions wisely.

   In mathematics, we choose our “definitions” (rather: axioms, inference rules etc) very wisely – otherwise contradiction rears it’s ugly head. Everyday language use, on the other hand, is quite indifferent to contradiction (that is, by the way, the secret of politics ).

2. By adopting the Mathematical Universe stance, it is immediately obvious that everything we see emerges from an inside view. The “outside view” knows neither time nor space (as the concepts have meaning only in relation to structures on the inside). Think of this as a radically more extreme version of the block universe; have a look at endophysics – it is only a short wikipedia article but with nice references included. It should be obvious that a TOE (Theory of Everyting for non-physicist readers of the blog) we will develop must be endophysical – after all, we are inside the universe, and a TOE should also explain how our impressions arise from being inside this universe. Physicists usually call a TOE a theory which unites all four forces (electromagnetism, strong nuclear, weak nuclear and gravity); but I think we should adopt a broader view of TOE; maybe we should differentiate between a proximate TOE (having the usual meaning used in physics circles) and an ultimate TOE – bringing all knowledge into a coherent whole. Max’s Mathematical Universe would be an ultimate TOE.
3. The Mathematical Universe addresses the conundrum raised by many a thinker, most notably be Eugene Wigner: The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Everybody who denies the mathematical nature of reality is welcome to present more plausible alternatives for the effectiveness of mathematics. In this sense, even if the Mathematical Universe Hypothesis were wrong, it would be a good catalyst for further philosophical inquiry.
4. An important point which can’t be stressed enough because it is so deeply ingrained in our thinking: from the Mathematical Universe viewpoint immediately follows the elimination of essences. Most traditional Western philosophy is concerned with the “essence” of an object/subject; or, similarly, is occupied with categorizing things in ontological hierarchies. These approaches are largely unsuccessful and thus have lead to postmodernism and relativism. The Mathematical Universe immediately shows why these approaches have failed in the last 2500 years: because there are no essences apart from relations.Even if you are not a philosopher and have not heard of essences: if you were brought up in a Western context, it is pretty much guaranteed that you are thinking in essences; it is part of our cultural background; it shapes the way we categorize your knowledge. See Eli’s post How an Algorithm Feels From Inside for how this essence feeling arises.This predilection for essences is of course a human phenomenon, arising from our brain architecture – it applies to all people. Why do I stress a Western context then? Because Buddhists/Taoists/Zen-philosophers have, through long meditation, seen through this “mind trick” – mind as seen from the inside. This does not mean that every chinese/japanese guy you’ll encounter will have understood this: after all, the Zen masters are revered in the East, because it is so difficult to dissolve these concepts.But in the East, the dissolution of essence exists as a cultural background, ready to draw on, whereas in the West it is only a minority position not vigorously pursued.
5. So we have moved away from Aristotelian essences. But the Mathematical Universe is not traditional Platonism, which speaks of ideals and mere shadows and denies reality perfection; to quote from the Wikipedia article on Platonism:
   

   The central concept is the Theory of forms. The only true being is founded upon the forms, the eternal, unchangeable, perfect types, of which particular objects of sense are imperfect copies. The multitude of objects of sense, being involved in perpetual change, are thereby deprived of all genuine existence.

   The Mathematical Universe is in this sense very contrary to traditional Platonism: it does not say that existence is a mere shadow, an imperfect copy of some eternal object “out there” in some inaccessible realm, but in fact the platonic relations are all there is. No shadows, no caves, no torches. Only ideal structures. The moment you are currently experiencing is encoded is this Platonic mindscape. I dearly recommend reading Julian Barbour’s The End of Time and his concept of time capsules.

So, the Mathematical Universe concept promises to merge the oldest of dichotomies in Western philosophy: Aristotelianism versus Platonism. No small feat, if you ask me.

Above, we have seen that the idea of the Mathematical Universe shows much promise; so it warrants turning one’s attention to it.

Addressing some criticism

1. Bee posits The Principle of Finite Imagination; which I like very much; it was one of my own initial reactions in my first encounter with the Mathematical Universe idea; I talked with Max Tegmark in the aftermath of this conference, raising much the same issue. Bee thinks of a “Level 5: Beyond Mathematics”; but I would just call it advanced mathematics, maybe not even recognizable to us humans as mathematics yet; think of future AIs uncovering exquisite structures we have not thought
   of yet, maybe are not even capable thinking of with our little human
   brains.

   I am perfectly fine with this non-human mathematics, as I do not think that humans are the evolutionary maximum of all possible epistemic agents. But Max does not mean current mathematics, he means all possible mathematics; I think what Bee means with Level 5 is contained in Level 4 already (all mathematically possible structures).

   My other concern was: what about a universe without any structure at all? Max said that he thought that this would simply correspond to the empty set, and after thinking long and hard about this I have come to the same conclusion (in hindsight it may be obvious, trivial: but we all have our mental models of the world and some parts readjust more slowly than others; that was my personal “barrier” ).

2. Those who think the idea is too far out (Max says this is even a bonus of the theory, and I agree – why should reality correspond to our intuitions developed in a provincial evolutionary context?) should be advised of the development in philosophy of science in the scientific realism debate: structural realism. To keep things short I will only quote the first sentence from the SEP article:
   

   Structural realism is considered by many realists and antirealists alike as the most defensible form of scientific realism.

   Max’s version corresponds to the ontic variant of structural realism. But people who adhere to epistemic structural realism should think long an hard: if indeed structure is the only thing that can be known, what additional thing is there to talk about? The ontic variant is the most parsimonious version of structural realism, and in metaphysics above all we should be parsimonious, lest it degrade into mere fiction.

3. And now for the most interesting objection raised by Bee and a colleague of hers:
   

   Scientific arguments aside, my reason to not believe all of reality is maths is that for me the interesting thing about maths is not that we are able to use it. The interesting thing is what Plato above called ‘an intuitive leap’. Call it intuition, a believe, a hope, or a conjecture. The interesting thing for me is the capability of the human mind to observe, and to translate this observation into something more general, taking away clutter, finding the patters, playing around with them. It is the process of this translation that I find important, not the result, the language in which we formulate it.

   I think this is essentially also the question Olaf Dreyer has been asking in your talks here at PI, I think he asked a similar question in both talks, and I think you misunderstood the question both times. He was asking how come that we connect much more with the ‘mathematical structures’ on our notepads than the actual symbols contain. How come we are able to get an intuition for what these things ‘do’, that what makes the essential difference between mathematical proof and physics, the intuition advantage that physicists can bring into mathematics. Where does this come from? Can we ever describe this by a mathematical equation?

   First of all, one must be careful not to confuse the modes of “being” and “knowing”. “Knowing” is a subset of being; there is being without knowing (that is Max’s External Reality Hypothesis), but no knowing without being (a contradiction in terms/concepts).

   When we think about mathematical structures, make intuitive leaps etc, this is a mode of being (encoded in the Mathematical Universe); but when we make the connection to reality (physics) this is a mode of knowing: a mathematical structure (knower) reflects parts of his local mathematical surroundings (world) – this is then called knowledge, and is together again encoded in the “bird” structure.

   Notice how the Mathematical Universe raises interesting research questions: why do some structures find themselves in the proximity of others etc? (I can’t help from feeling very excited by these prospects; the Mathematical Universe idea seems to give a first handle on truly fundamental questions.) I will elaborate on this being/knowing distinction and how they can be visualized in the Mathematical Universe in future posts.

   To clarify, I repeat the above phrased a bit differently: Thoughts are reflections of mathematical structures. Thoughts which do not correspond to our immediate reality may correspond to other parts of modal reality, inaccessible from here, but no less real for that (this will have beautiful consequences when extrapolating further -> see a future post).

   We have the power to reflect on many structures: that is why mathematics is about ultimate creativity: it is exploration of all possibilities. Indra’s net is a good intuition pump. Maybe we humans can’t yet explore them all (Bee’s “Level 5″) but by further evolving, constructing AIs etc we will increase the accessible mindscape.

   To answer Bee’s and Olaf’s question directly: the ability of humans to play with ideas, connect with reality, translate and transform etc is a mode of being in the mathematical universe; when it is well done, that is, mathematical structures are successfully reflected in the cognitive system, the result is knowledge. Inaccurate reflections are dreams.

4. Bee also raises the question on how our thoughts could be mathematical structures when they are inconsistent, wrong or undefined? The answer is related to my explication above.”Undefined”, “illogical” thoughts happen when you reflect mathematical structures incompletely. An example: say you view an object through a mirror, but part of it is cut off: your “undefined” or “inconsistent” mathematical thought would be the system:
5. Are we leaving the domain of science with all this (this is a valid criticism!)? Depends on how you think scientific knowledge is defined (ie falsificationism vs confirmation theory).But even if we are leaving the precints of hard fact and the core of the natural sciences: certainly we are not leaving the domain of philosophy. And philosophy is about making sense of the world. And good philosophy is philosophy which does not contradict scientific evidence, on the contrary, which is even supported by scientific evidence. I have made a little diagram to make my point (it is not intended to be in any way canonical, only illustrative):
   

   Circle of Knowledge

   Here the texts for people reading with a text browser (the image shows outward moving circles representing different levels of scientific certainty (A) to (D) and three circles apart representing unscientific positions (E) – (G) ):(A) Hard empirical facts.
   (B) Less certain empirical facts.
   (C) Logical deductions from empirically successful theories.
   (D) Plausible reasoning using the same assumptions that lead to empirically successful theories.

   (E) Implausible reasoning.
   (F) Bad reasoning.
   (G) No reasoning.

   The Mathematical Universe Hypothesis is located roughly in the (C)/(D) section, supported by evidence from (A) and (B); as we move outward from the inner core (A) things get less and less sure. But we should not refrain from reasoning especially in the (D) section, because it is indeed here that new ideas for unification in science or even new experiments arise. (D) is the fecund field for discovering new knowledge.

   The problem is that most people who don’t agree with the Mathematical Universe don’t argue from (A), (B), or (C); not even from (D) actually.

   Rather criticism is raised from (E), (F) or (G), because of philosophical or personal considerations. So I would urge to constructively criticize, coming from (D).

A mathematician’s and a physicist’s dilemma

In the end, the question for critics remains: how do physical brains of mathematicians come to know about acausal, atemporal abstract objects (as the traditional Platonist view will have mathematical objects)?
(BTW, If you still believe that thoughts are independent of physical brains I recommend this entertaining book: Oliver Sacks: The Man who mistook his wife for a hat; or Phantoms in the Brain by V.S. Ramachandran; you should seriously reconsider any dualisms).

The immediate objection which comes to mind is that one could adopt another philosophy of mathematics (not Platonism) and then simply regard the success of math as successful pattern matching. That is the way I took first; but, of course, it does not work. The way leads wonderfully back to the Mathematical Universe; but that is for a future post.

The physicicst is actually in an even worse situation: he/she is using a tool which “magically” works and he doesn’t even know why: no, she doesn’t even think about it: why mathematics works is a metaphysical question, not science, and therefor best not thought about (or so the argumentation goes)!

Conclusion

Why should we ignore knowledge? That mathematics works to describe reality is an empirically confirmed fact! Use this knowledge, do not ignore it! This is indeed one of the major principles of rationality: never ignore knowledge!

Let evidence guide our beliefs, and not a priori beliefs (=childhood beliefs, cultural background) guide the way we weigh evidence.

I have hinted at some future posts above, where I hope to clarify some issues which may have remained dark or only hinted at in this first outline.

But enough for today.

Technorati Tags: mathematical universe

Technorati Tags: mathematics, phd, philosophy, philosophy of science, physics

Towards a Psychology of Philosophy?

A question that I find particularly interesting is, do attitudes about science, such as naturalism vs. anti-naturalism, correlate with levels of scientific education and talent for science and math? Could it be that one factor behind the (seemingly prejudicial) anti-naturalist attitudes that are still very influential in many areas of philosophy have to do with insufficient education in the sciences?

Where I disagree is with the exposure to math/scientific education part being the main cause of anti-naturalism. It is rather a matter of trust being shaken or of having the luck of growing up in rational environments in the first place.

Resistance to naturalistic positions does not exist because the people do not know the science – it exists because it goes against ingrained, deeply conditioned beliefs.

Childhood Origins of Adult Resistance to Science
Paul Bloom and Deena Skolnick Weisberg
Science 18 May 2007:
Vol. 316. no. 5827, pp. 996 – 997
DOI: 10.1126/science.1133398

Resistance to certain scientific ideas derives in large part from assumptions and biases that can be demonstrated experimentally in young children and that may persist into adulthood. In particular, both adults and children resist acquiring scientific information that clashes with common-sense intuitions about the physical and psychological domains. Additionally, when learning information from other people, both adults and children are sensitive to the trustworthiness of the source of that information. Resistance to science, then, is particularly exaggerated in societies where nonscientific ideologies have the advantages of being both grounded in common sense and transmitted by trustworthy sources.

Technorati Tags: phd, philosophy

Overcoming Bias: Heading Toward Morality

Why? Because that is the conclusion he is drawing to:

Artificial Intelligence melts people’s brains. Metamorality melts people’s brains. Trying to think about AI and metamorality at the same time can cause people’s brains to spontaneously combust and burn for years, emitting toxic smoke – don’t laugh, I’ve seen it happen multiple times.

But the discipline imposed by Artificial Intelligence is this: you cannot escape into things that are “self-evident” or “obvious”. That doesn’t stop people from trying, but the programs don’t work. Every thought has to be computed somehow, by transistors made of mere quarks, and not by moral self-evidence to some ghost in the machine.

If what you care about is rescuing toddlers from burning orphanages, I don’t think you will find many moral surprises here; my metamorality adds up to moral normality, as it should.

snip

Yet there is also a good deal of needless despair and misguided fear of science, stemming from notions such as, “Science tells us the universe is empty of morality”. This is damage done by a confused metamorality that fails to add up to moral normality. For that I hope to write down a counterspell of understanding. Existential depression has always annoyed me; it is one of the world’s most pointless forms of suffering.

The last paragraph nicely illustrates the goal of my thesis. Much of resistance encountered to scientific thinking stems from confused thinking about existential questions, morality and the meaning of life etc. This pre-scientific – mostly magical and inconsistent – thinking can and should be dispelled.

On a side note:

As you will have noticed I often quote Eli’s posts – simply because he has eloquently written down what I only have been thinking about. Most of the times when I want to write something down I realize I can’t explain it in a few sentences or even a few paragraphs – NOT because it is confused or not coherent yet, but rather because after years of thinking on these subjects I have dissolved many mental categories, rewired others and created new ones. Then I fall into a kind of despair and write nothing (I really have to work on this).

The funny thing is that Eli Yudkowsky (and many others who also have not written yet, but are among the OB readers or elsewhere strewn over the internet) have undergone similar mental evolutions. So much for multiple discovery.

While many scientists and philosophers have “problems” with multiple discovery because they are concerned over priority, I think it is a happy thought that ideas are discovered simultaneously in many places when the time is ripe. It shows that intellectual progress is robust against individual chance events.

My main problem is how I will deal with this inferential gap issue in my thesis: while people working within traditional philosophical schools simply refer to their “founding fathers” – for instance Kant – and their advisors immediately know what they are talking about (indeed, they taught it to their students!), I can’t simply refer to Eli’s posts in my thesis – most people do not know him – not yet, anyway , maybe in 20 years time.

So I will either have to bite the bullet and write a huge expository chapter; or wait until Eli writes his book and ask my advisors to read it before I have my defensio (I guess that would be a quite cheeky approach – I’ll probably settle with the expository thing )

A last remark: why this large deviation from standard philosophy? Because standard philosophy misses some major insights, namely those gleaned from AI research of the last fifty years. Every philosopher should plow through this book (Russell & Norvig: Artificial Intelligence. A Modern Approach. 2nd Ed. 2002) before commenting on issues such as rationality or free will.

Funnily enough, Eastern Philosophy (Taoism, Buddhism) does not have this problem: that is because they stressed meditation, which is empirical/rational introspection versus the rather naive introspection performed in the West. Thus, the sages of Zen discovered many things about themselves which escaped the likes of Descartes, Kant etc.

Technorati Tags: artificial intelligence, phd, philosophy

But the structure now contains the arguments which are most important for me to make and which fit best into the current scientific/philosophical landscape.

My task for the next years (?) will be to flesh everything out – although, I don’t want to make the dissertation too big; so I will concentrate on one of the subaspects – time will tell which.

Technorati Tags: phd

Is a house real? Its constituent parts (cement, bricks)? Does one have to go further down? Is only a completely reductionist account real?

No – all constructions. I propose a minimalist ontology:

There exists a world.

Do not take this sentence literally -> it is an approximation to the unspeakable. To quote from the first verse of the Dao De Jing of Lao Dsi:

“The Dao that can be named is not the eternal Dao.”

It is an assertion of the reality which we are experiencing. All else is a construction, which is true (and therefor knowledge) if it captures aspects of reality relevant for the concrete observer (very related to Nietzsche’s Perpectivism; identical to it? I don’t know yet – have to read and think more ).

Technorati Tags: phd, philosophy of science

BBC NEWS | Science/Nature | Firm rockets into space tourism

What really pleases me is that this is a european effort. Such cool ideas usually only come to fruition in the U.S. – I hope this works out.

Technorati Tags: entertainment

This is because my thesis work concerns looking at “human” systems (many individual agents acting independently – ok, so they’re pseudo-humans ). I am especially interested in the relationship of “rational” agents and “irrational agents” – for instance, if irrational agents can survive in the long run if they have to compete against rational ones, or even if irrational agents threaten the survival of rational agents (because they are aggressive toward rational ones). This of course means I have to define a rationality criterion in the model, or ensure that it emerges (now that would be difficult!).

While I am not yet sure as to how detailed my models will be and how useful this research into rationality will be for my models, I am very interested in principle what constitutes rational behaviour in the first place, and what makes us human rational or irrational.

Technorati Tags: phd, rationality

Heylighen F. (2001): “The Science of Self-organization and Adaptivity”, in: L. D. Kiel, (ed.) Knowledge Management, Organizational Intelligence and Learning, and Complexity, in: The Encyclopedia of Life Support Systems ((EOLSS), (Eolss Publishers, Oxford)

@INCOLLECTION {Heylighen2001,
title = {The science of self-organization and adaptivity},
author = {Heylighen, Francis},
editor = {Kiel, L. D. },
booktitle = {Knowledge Management, Organizational Intelligence and Learning, and Complexity},
series = {The Encyclopedia of Life Support Systems},
year = {2001},
publisher = {EOLSS Publishers},
address = {Oxford},
}

I would like to let the abstract speak for itself:

The theory of self-organization and adaptivity has grown out of a variety of disciplines,
including thermodynamics, cybernetics and computer modelling. The present article reviews its
most important concepts and principles. It starts with an intuitive overview, illustrated by the
examples of magnetization and B{\’e}nard convection, and concludes with the basics of mathematical
modelling. Self-organization can be defined as the spontaneous creation of a globally coherent
pattern out of local interactions. Because of its distributed character, this organization tends to be
robust, resisting perturbations. The dynamics of a self-organizing system is typically non-linear,
because of circular or feedback relations between the components. Positive feedback leads to an
explosive growth, which ends when all components have been absorbed into the new
configuration, leaving the system in a stable, negative feedback state. Non-linear systems have in
general several stable states, and this number tends to increase (bifurcate) as an increasing input of
energy pushes the system farther from its thermodynamic equilibrium. To adapt to a changing
environment, the system needs a variety of stable states that is large enough to react to all
perturbations but not so large as to make its evolution uncontrollably chaotic. The most adequate
states are selected according to their fitness, either directly by the environment, or by subsystems
that have adapted to the environment at an earlier stage. Formally, the basic mechanism
underlying self-organization is the (often noise-driven) variation which explores different regions in
the system’s state space until it enters an attractor. This precludes further variation outside the
attractor, and thus restricts the freedom of the system’s components to behave independently. This
is equivalent to the increase of coherence, or decrease of statistical entropy, that defines selforganization.

The author’s homepage.

Technorati Tags: complexity, paper of the week, phd

First I would like to introduce

Abraham, R. H. 2002. The Genesis of Complexity.

@INCOLLECTION {Abraham2002,
title = {The Genesis of Complexity},
author = {Abraham, Ralph H. },
editor = {Montuori, Alfonso},
booktitle = {Advances in Systems Theory, Complexity, and the Human Sciences},
year = {2002},
note ={verify citation: only from pdf file, not original source}
}

The article gives a nice historical overview from 1925 to early 90s.

He develops a beautiful tree metaphor regarding complex systems science – Complexity Science is described as a trunk with many branches, and three roots (in braces some important researchers):

• Cybernetics (Math: Wiener, von Neumann, Pitts; Engineer.: Bigelow, Shannon; Neuro: Rosenblueth, McCulloch, de No Anthro: Gregory Bateson and Margaret Mead -> Macy Conferences 46-53),
• General Systems Theory (von Bertalanffy, Waddington -> Serbelloni meetings 66-70),
• System Dynamics (Chaos, Catastrophe Theory; Poincare, Jay Forrester -> SD Group 1968 -> Sloane School of Mgmt of MIT)

Some of the branches of complexity according to the article: Artificial Neural Networks, Cellular Automata, Cellular Dynamical Systems, Catastrophe Theory, Chaos, Theoretical Biology, Biospherics, Ecology, Synergetics, Autopoiese, General Evolution Theory, and Gaia Theory.

The website cited in the article:
VMI Complexity

The site of Ralph Abraham, where you can also download the article.

Technorati Tags: complexity, paper of the week, phd