Registered: Jul 2004
Posts: 5

As I'm a newcomer to the forum and to the ideas of Wolfram, so, perhaps you'll forgive some naivety as to the philosophy behind NKS.

My interest is in what insights NKS has to offer in explaining how the brain and the mind function.

Wolfram's idea - that observing how a system works can tell us more than looking at the rules of the system - has many parallels in neurodynamics and theory of mind. This is often summed up by the expression "The sum is greater than the parts".

My (naive) interpretation of Wolfram's thinking is that simple mathematical rules can lead to explanations of complex biological system behavior. By inference, this implies human behavior and human thinking and decision making.

Wolfram illustrates his ideas using cellular automata, where simple rules relating to the interdependence of the cells give rise to highly complex patterns of cells in a two dimensional environment. By iteration, these patterns change over time in a deterministic manner that is not predictable by examining the underlying rules.

It is a seductive thought that, by finding the right set of rules, complex behavior in biological systems can be explained and modelled on a computer. However, current thinking in theories of mind sees this quite differently. The equations that give rise to a temporal series of patterns are not seen as explaining behavior but simply as as a means of organizing and locating the neural networks that give rise to thinking and behavior. In other words, the cellular automata diagrams are describing only the way in which the brain manages to locate and activate different combinations of areas of the brain.

This would see the two dimensional cellular automata diagrams as multiple position switches, where the on and off states of the cells activate or deactivate different areas of the brain.

This is best viewed not as a two dimensional space, but as a multiple dimension space, where the states of the cells are determined by the attractor states of a chaotic system. The reasoning here is that the millions of different inputs from our senses are reduced to a limited number of attractor states (each of which activates a specific set of neural areas).

This is exampled by the work of Walter Freeman, who used brain imaging techniques to show how different odors give rise to attractor states that activate various emotional centers in the brain.

The best (and shortest) description of this idea is Walter Freeman's 1987 paper entitled:

"Strange Attractors that Govern Mammalian Brain Dynamics Shown by Trajectories of Electroencephalographic (EEG) Potential"
_
http://sulcus.berkeley.edu/FreemanW...pts/ID1/88.html

This paper illustrates patterns of neural activity that, unmistakably, have all the hall marks of attractor basins. It was this inference that was the basis of Freeman's classic work on the olfactory system, where he was able to associate specific odors with specific attractor basins - and show new odors were presented new attractor basins were established.

As each attractor basin involves the stimulation of a unique network of neurons, it was easy to to trace - through brain imaging techniques - how different odors could activate different parts of the brain. This activation included activity in parts of the brain associated with emotions.

Since that paper was published sixteen years ago, the concept of attractors has been increasingly applied to all areas of neurology and psychology. Now, universities are buying their own PET scanners to observe brain activity patterns as they give subjects various kinds of mental tests and emotional experiences.

A typical example of how Freeman's work was regarded is shown in the article (written 2000) at
http://www.theory.org/fracdyn/neurodyn/ubichaos.html

How Walter Freeman associated attractors with emotions is detailed by him in a 1998 paper entitled: "Emotion is Essential to All Intentional Behaviors"
http://sulcus.berkeley.edu/wjf/CE.%...and.Emotion.pdf

These are the best links for starters, but there are thousands of papers that have appeared since then that expand on this work in a multitude of different ways.

If you want to go deep into Walter Freeman’s work, have a look at some of his papers - listed on his Web site at:
http://sulcus.berkeley.edu/

My question is, "How does current NKS thinking link up with these ideas?".


Peter Small

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"simple mathematical rules can lead to explanations of complex biological system behavior. "

NKS distinguishes between the kind of regularity that can be encapsulated in formula that allow prediction of a future state of the system without going through the steps the system actually passes through, and a broader class of rule-following that can be produce or simulated by following some simple algorithm, applied repeatedly. The first sort of regularity it calls "reducibility". The second sort, it calls "a computation".

As examples, I can predict the center cell of rule 250 using a formula x[i] = x1 mod 2, that does not require knowledge of the intervening steps. I can determine the center cell of rule 30 - because it does follow a definite rule - but only by explicitly emulating every step of the calculation.

NKS posits that when we see apparently complexity, it does not mean the behavior in question cannot be formulated in terms of rules. But it does generally mean we will not be able to formulate it in terms of reductions, rules of the first 250 type rather than the second 30 type. We must model and reproduce the computation the natural system goes through itself.

As for basins of attraction, they can certainly be used to analyse system behaviors, and are particularly suited to small systems that must eventually hit some sort of cycle. However, basin analysis is not always informative, when the transients are quite long and only a small portion of the system's possible states are actually visited along any given dynamic path.

In general, NKS believes that dynamics matter, not just infinite limit behavior. Analysing systems in terms of infinite limit behaviors - a generalization of the equilibrium idea, basically - is viewed as appropriate only for a limited class of systems. And in particular, it is not expected to account for the real phenomenon that give rise to complexity.

When a system is clearly an information crusher, self organizing, showing many to one paths, basin analysis is a natural method. And there is nothing wrong with trying to emulate a biological algorithm, by trying to reproduce that algorithm as a sort among neural nets etc. But this is not general enough to be an account of the origin of complexity in formal or in natural systems.

NKS shows that complex phenomenon arise already, in cases where there is no such elaborate set up. The claim is that its general formal cause is that the algorithm being used is computationally irreducible. That does not mean "uncomputable"; it means you model the algorithm and directly trace its steps, "one to one and onto", rather than expecting to find some short cut of the whole evolution that obeys a short parameterized formula.

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At the moment I choose a special Modulation Tranfer Function and Point Spread Function Limit in gaining subject matter information. This is called a Nyquist threshold in my field. Do you think NKS will allow me to surpass this threshold and will the brain then handle the additional information?
Can you tell what wont cascade and where I might use a brain information shunt?

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Recently in two experiments I simulated CA generating action potentials. It is not difficult to simulate even an E.E.G.

http://www.what-is-cancer.com/papers/ca/ca117.htm
http://www.what-is-cancer.com/papers/ca/ca129.htm

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Jason Cawley wrote:

"But this is not general enough to be an account of the origin of complexity in formal or in natural systems. "

I have a question: Is it necessary to have an origin of complexity?

If even the elementary rules admit Garden of Eden precursors under certain conditions, is not complexity a given?

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L. J. Thaden

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L. J. Thaden asks "Is complexity a given?".

Where you have multiple interdependencies between the states of a large number of cells, complexity is a given because this is the inherent characteristic of such a system.

This is because it is computationally impractical to work out what happens when the status quo is disturbed - even though the activity is deterministic.

This leaves us with no choice other than to be concerned only with the reality of the observable transitional and steady states that occur as a result of system disturbances.

The biological system of the brain takes advantage of the fact that a disturbed complex system of interdependencies (multiple neuron connections) quickly settles into one of a large number of possible steady states. The steady state, into which the system settles, will be dependent upon which neurons are activated and is repeatable if the same combination of neurons are activated at any other time.

The nature of dynamic complex systems is such that they are tolerant of slight variations, such that small changes to the steady state might have no effect. But, some changes can cause the system to become unstable and then settle into a new and completely different steady state (which is repeatable if the same initial conditions are repeated).

The essence of this system is that complex networks of neurons in the brain will settle into a variety of steady states according to which combination of sensory inputs disturb the system. For example, the sound invoked by the word "lion" will disturb the system to activate areas of memory related to a lion. The disturbance will be much greater if sensory inputs also inform the brain that you are in a jungle clearing.

To my mind, the metaphor of cellular automata to picture this complexity is not appropriate. This is because cellular automata activity is visualized in two dimensions and is associated with sequential series of events. In reality, the neural states in the brain are multidimensional and are determined by massive parallelism.

I'm currently working on a book to explain this neuronal activity and my starting place is to describe a multidimensional space. Once this multidimensional space can be visualized, it is then possible to explain how this multidimensional space is used by the brain to locate and combine memories and turn on appropriate responses.

The description of this multidimensional space you will find at:
http://www.stigmergicsystems.com/st...ubsection2.html

Peter Small

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The question on the origin of complexity is a question on the origin of synergy. When you can quantify *how different* the behavior of a whole, compared to predictions based on knowledge of the parts, you'll have a metric of 'complexity,' for one is just the perception of the other.

Meanwhile, I'm curious why brain research is so focussed on the activation of areas, rather than the interference of signals.

Everything you experience, physically, exists because of a self-supporting, self-regenerating interference of events which only interact with tuned frequencies. A standing wave is the simplest example, but all particles - indeed, all observable systems - are such self-interfering interactions of events.

Are thoughts the same thing? Is that what's meant by 'attractors' and 'basins' - the shapes those self-interferings (knots) take on, physically?

Forgive me if these are newbie questions, I'm kind of new to 'NKS' - still quite skeptical about the 'N' part, in fact.

-Tom

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-Tom McWilliams

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Tom,

Complexity can be defined as a system where the state of any part is dependent upon the states of many other parts.

In such a system, altering the state of one or several parts can have a complex domino effect that can disturb the whole system. Such disturbances of mutually dependent parts can create unpredictable, chaotic series of changes.

Such chaotic disturbances do not go on forever. Systems quickly settle into a new steady state after a disturbance. These steady states are known as the system attractors. - of which there can be vast numbers, dependent upon the complexity.

The human brain is such a complex system. Sensory inputs create disturbances to this system. Different combinations of disturbances result in different steady states (characteristic of the particular disturbances).

There are many orders of magnitue less of the steady states than there are combinations of sensory inputs, thus the system acts to reduce the number of possible combinations of sensory inputs to a finite number. These steady states each correspond to the activation of particular combinations of neurons.

An attractor basin can be thought of as the variations of sensory inputs that will produce the same steady state.

Memories, thoughts, perceptions and emotions can be thought of as particular steady states - changes of which are associated with moving from one different steady state to another.

Because of the complex interdepndency of so many different parts of the brain, transference from one steady state to another can involve changes to many different areas of the brain. However, for certain mental activities or specific sensory inputs, particular areas of the brain are disturbed more than others. Brain imaging techniques can identify these highly active areas and therefore associate them with particular forms of mental processing.

Obviously, this is necessarily a very brief overview, but I hope it answers your query.

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The electric activity (EEG) of the brain may be viewed as a chaotic attractor since its oscillations occupy a relatively narrow frequency domain. Its behavior however depends not only on neurons and glia but also on the entire body. When I raise my hand my EEG shifts to a new attractor. Experiments with biofeedback show that one can learn how to shift ones EEG at will from attractor to attractor.

However there is more to it. Despite the ongoing turnover in the body it maintains its appearance. In other words our appearance is a strange attractor in a multidimensional chaotic space.
v. The streaming Organism:
http://www.what-is-cancer.com/paper...eamorganism.htm

CA provide a new tool to investigate chaotic attractors like those observed in the organism. I developed such a system. It is chaotic and when perturbed proceeds from one chaotic attractor to another.
http://www.what-is-cancer.com/papers/ca/ca125.htm

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Gershom,

It is perhaps more accurate to think of the organism as a complexity of many different attractors that are mutually dependent upon each other. In this way, organisms can be thought of as consisting of hierarchies of many different attractors - with attractors occuring at the higher levels dependent upon the nature of the attractors occurring at the lower levels.

In this way, certain disturbances might change a particular attractor in a way to localize changes of state, but, when a cetain threshhold is reached might trigger universal attractor changes that ripple through the whole system.

Such a system is not easy to imagine, as might be explained by a paper written by Chris Lucas "Quantifying Complexity Theory" - http://www.calresco.org/lucas/quantify.htm

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Who invented such clumsy language to refer to systemic behavior? Ugh!

Despite that, Peter, yours was a clear overview, answering lots of my questions, so thanks. I would suggest that 'complexity' is an adjective applicable to a system, rather than a system in it's own right, however.

Indeed, once we translate 'attractor' for 'self-interfering, self-regenerating system' I don't think anyone disagreed with anything I've said (yet). Since 'attractors' as herein described qualify as systems in their own right, I'm curious if that's standard terminology, or if 'NKS' is kind of casual about certain words.

However, you point about steady states in the brain didn't address my question; are those steady states static, or dynamic? In physics, all seemingly-static items are actually a seething, self-interfering self-regenerating interaction of forces; a system, and from the apparent functional definition of 'attractor,' a complex one.

In the standard QM model, any entity can be treated as a collection of photons that we experience as 'stuff' because they develop into 'attractor' states; the positve and negative feedback, the positive and negative (or left-right. or up-down, etc) forces, all balance, within a minimal level of tolerance required to 'keep it together.' That's why it can push back when you push it, right? It's not just sitting there, it's constantly passing messages/forces.

My point about synergy remains; that's what 'complexity' means, since the *existence* of attractors is the 'tell' - that's how you know you are dealing with a complex system; something emergent occurs, that you can't predict from just the known elements. That is the definition of synergy.

You wrote: "Systems quickly settle into a new steady state after a disturbance"

I fear this is an extreme oversight, mistaking the operation of mind for the operation of the universal 'substrate.' I still fear that process physics is doing the same thing.

We are only able to perceive systems - those attrator states displaying a repeatable pattern - and further, can only do so within a fairly narrow range of frequencies, as Gershom points out. Our primary 'substrate' by which to explain our experiences must be those experiences themselves, not the objects we imagine causes them. NKS still inverts that relationship, and hence can never qualify as a 'paradigm shift.' That the oversight appears as an ambiguity, rather than a contradiction is an indication of how close NKS really is to the real situation.

Your statement looks like selection-bias to me; because you can only experience humanly-tunable systems, and via our bodily or other technological systems, you evidently think that all events are systems, but nothing could be further from the truth.

All *knowable* events certainly are systems, and there is some value to suggesting only those should be, or can be, subject to our consideration and efforts.

When you said "These steady states each correspond to the activation of particular combinations of neurons" you claimed almost the opposite. What we consider 'steady' depends upon our recognition of a pattern of experience, not a particular set of neural activation. A pattern in time, not in geometry. A frequency, not an angle.

Your description is a fair one, for referring to the activities of brains; the collection, sorting, storing, and recall of experiences.

But there's something missing as a description of the activities of mind; comparing those patterns, for the purposes of developing new ones requires the intentional application of the synergy principle....which gets glossed over, in NKS, as 'emergent,' which is no better, as a quantitative conceptualization, than ignoring it, as 'regular' science does.

You also said "attractors occuring at the higher levels dependent upon the nature of the attractors occurring at the lower levels" in your description of organisms, and I think that might be too strong a claim.

At some level all attractors/systems have the same nature, making your claim a tautology. "Needs water, proteins and motive power" applies to all levels of human activity, from DNA on up.

In those aspects by which they differ, I don't think such differences have any affect outside the realm of the interactions which keeps any one system stable. IOW, the way the system/attractor keeps it's integrity on *this* level has almost nothing to do with how a larger or smaller system/attractor keeps it's integrity. *Whether* the smaller systems keep their integrity certainly does matter!

A proton, for example, does not have it's structure changed by any chemical (electronic) reaction. Likewise, there is no type of light or material you can throw down a black hole that will break it. But electrons are hardly involved in nuclear interactions, and almost everything tossed into a black hole gets broken. There are always such anti-symmetric relationships involved when you talk about ensembles of attractors/systems.

Referring to the body, the way your musculature keeps things steady is different than the lipid interactions which keep cells alive, even if those muscular tensions ultimately derive from those lipids. Likewise, the ecologic and symbolic interactions which make each of us part of a community, even if those symbols or decisions happen in the realm of lipids or electrons.

Perhaps I should have just asked; what's the difference, in NKS, between an attractor and a system?

-Tom

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-Tom McWilliams

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Originally posted by Peter Small






"Such chaotic disturbances do not go on forever. Systems quickly settle into a new steady state after a disturbance. These steady states are known as the system attractors. - of which there can be vast numbers, dependent upon the complexity."


Actually, and directly related to the fact that complex behavior can come from simple initial conditions. this is only true with systems of a limited size.

An example, say a steady background ({{1,1,0,0},{0,0,2,2}}) is being generated by some rule (1599). With just a single bit of disturbance, you can get this.

But in a system of limited size, that will never happen; there will always be some repetitive state that is reached.

And as for the speed at which all given states converge to these attractors, there is tremendous variation. That's evident in cellular automata. Just look at some of those totalistic rules like 2049. They may never reach a repetitive state.

However it is true that any amount of infinite repetitive perturbation, so long as it happens from the start, will indeed guarantee any such system to eventually terminate, like this one.


"The human brain is such a complex system. Sensory inputs create disturbances to this system. Different combinations of disturbances result in different steady states (characteristic of the particular disturbances)."


Right on. This is pretty much what using simple programs with live input to model brain behavior is about. Not sure about what the best way to implement it is. LCAs are my attempt at making them look nice. I think there's ways to make even the nastiest implementations look nice and convey information well.

--

Tom,

I think the something that's missing as a description of the activities of the mind is actually there when you attribute complex behavior as a lone cause for what really happens. It's the understanding of what simple rules do in practice that we all lack today that makes us think that there should be more at work.

Last edited by Jesse Nochella on 02-22-2005 at 03:27 PM

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Interesting conversation.

Well, I am interested to know how the brain finds a solution to a problem, or creates someting new. Here are two examples.

Somehere I heard how Gabriel Garcia Marquez came to the idea of writing "One hundred years of solitude". He said that he was driving down on the trans-american highway somewhere in South Mexico and as he came to a turn on the top of a small hill he looked down into an incredible green valley and right there in that moment the whole idea of the book just came into his mind, and from there on he did nothing else in the next three months than to sit down and write the whole thing down from start to finish. So the question is what kind of internal or external events opened the gate that all the story of the book with all the characters just jumped into his head, just like Pallas Athene jumped out of Zeus head ?

Once I asked a few of my favorite professors back in the seventies, how did they do their discoveries. One of them told that most of his discoveries came as he was driving the tram from his house to the Institute of Experimental Physics. He told that he just grabbed a straphanger and looked out of the window as the tram was trambling the half hour drive from his house to the Institute and at some point - although he was not thinking about them - suddenly the solutions to his problems just came to him without much thinking. Then when he arrived to the Institute most of the next two hours he spent to formulate and write down all which came into his mind on the tram in a blink of an eye.

So, what I would like to say here is that the brain is working at its fullest when we do not "think" and it is working VERY FAST. The brain just has to be brought into a stage when it can think without we force it to think.

Going futher. Where the brain gets all the solutions and where those solutions "were"/"are" before the brain gets them. Is it possible that when the brain is in this "discovery stage" then it just opens a "chanel" to that place where the solution is and the information just flow between that place and the brain till our " conscious thinking", cuts that chanel down ? I might be in Platonic territory, but I much favour that idea thet our brain is a tool which connects us to a wast "Information Ocean" when a chanel established between our brain and that "Information Ocean". Roger Penrose argues in one of his books that our brain has to do quantum computation to be able to get all the discoveries we have. I do not know if I agree to it or not. He cites some research which inticates that the microtubulies in every cell are computational devices and not just that but they are also quantom mechanical computational devices. One thing is sure. You have to have either a very high capacity communication chanel into this "Information Ocean" to get a whole book into your mind under a milisecond, or you have to able to tap into very high speed of computing with your brain to siphon out perfect solutions to very hard problems which sucessfully resist any conscious tries for months or years.

As we are all different, our brains are also all different. There was some discussion about how Einstein brain - which was reserved by the pathologist who did his autopsy - is different from other people's brain and the consesuss was that those parts of his brain which we associate with higher learning were much different in Einstein's brain. May be his brain was better suited to the communication to "Information Ocean". May be his brain was capable to do more effective "quantum computation" to unearth the theories of relativity.

So if we want to emulate with a CA or with a group of CAs how the brain gets it discovery, then we should concentrate on to discover how let say rule 110 is capable to tell us something which we do not know and which we think rule 110 is not capable to tell. Telling otherwise, to look for phenomena in the CA's "Computational Universe" which we cannot predict and we think the CA cannot do, but despite of it the CA still will able to produce. I tell ahead, I have no clue, and that might be a good sign :) One way I would start if I would have the resources to cram CAs into silicon - the way CAs wanted to be crammed, which might be different how microprocessors and memory in silicon are created nowdays - and shrink them down as much that they might able to do the same thing as the mictotubulies can, that is to establish an "entanglement" and in the process of the entanglement speak to the quantum world and get information out which is impossible via macroscopic methods.

J‡nos

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"..because Annushka has already bought
sunflower oil, and not only bought it, but
spilled it too."
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Attractors do not exit as such in our organism. You may detect in the organism many so called attractors, like EEG, blood glucose, hormone levels red blood cell count etc. However neither is independent from the other. They all interact, which means that each determines the attractor state of all the others. There does not exist an attractor hierarchy from lower attractors upwards.

At best the attractor concept is a metaphor which assists us to grasp the complexity of the organism. You may regard the organism as a self organizing complexity. This capability to organize itself I attribute to a wisdom which I call Wisdom of the Body (WOB). It is a metaphor which highlights the fact that one wisdom controls all the putative sub-attractors. It is inborn and evolves from birth to death. At any instant it selects the most optimal attractor for our existence.

Medicine still operates under the spell of attractor hierarchies which it inherited from the exact sciences.
Take for instance diabetes mellitus which according to medicine is a disease of the glucose attractor, while in reality it is a disease of the entire organism. The preoccupation of medicine with the glucose attractor harms patients and is discussed in depth in my site:

http://www.what-is-cancer.com/paper.../diabetes0.html

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It is pretty clear that each of the contributors to this discussion have their own unique visualization of complexity and the way in which it can explain life in general and the workings of the human mind in particular.

As a writer, I've been searching for several years to find explanations that are based upon fundamental principles. My current approach is to view the system of life and mind as an information space of infinite dimensions.

Within this space is every possible combination of matter and every possible combination of rules that can be applied to this matter. The trick then is to find a logical explanation as to how a process manages to evolve such as to manifest the exact combination of matter and rules that result in human life as we know it.

A description of this information space - based upon the concept devised by the great German mathematician, David Hilbert (1862-1943) - can be found at:
http://www.stigmergicsystems.com/st...on1.html?349882

Clearly, Nature has found a way of negotiating this information space. The task then becomes one of trying to work out Nature's strategy. This can loosely be described as being a strategy of trial and error and selecting for increasing organization and efficiency - the evolutionary strategy.

It has become apparent, over the last couple of decades, that the evolutionary strategy.involves progressing a dynamic system through a series of stable states - with each successive stable state selected according to an improvement over an existing state. In other words, being a dynamic system, it progresses over a series of attractor states.

The mechanics of this process is described as a system in a stable attractor state being changed in such a way as to drive it into a new attractor basin. If the new attractor basin is superior, its form is retained. If not, it is abandoned. Evolution progresses through many similar individuals in a stable attractor state, but with some of them deliberately made chaotic in order to try out different attractors.

This visualization of progression from one stable state to another by means of de-stabilization and selecting for improvements can be applied to any dynamic system. It applies to all social and business organizations.

Similarly, it can be applied to the human brain and thinking processes.

Our experience of the world is not any actuality. Our perceptions are made up totally of artificial representations as defined in terms of neuron states (much the same as information fed into a computer is turned into the on and off states of bits). All sensory inputs are transformed into the activation of neuronal attractor states within the brain. The activity of perception, thinking and imagination is the result of combinations of different attractors in the brain interacting with each other.

The ability to be creative is the ability to be able to disturb certain attractor states and select those disturbances that evoke attractor states that perceive superior solutions.

This way of describing biological systems is not off of the top of my head. There is a vast and rapidly expanding body of research that supports this viewpoint - much of it inspired by observations made using advances in brain imaging techniques, which show evidence of attractors being the main mechanisms responsible for perception, thoughts and emotions.

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