Russell E. Rierson

Reality can be postulated as a complex self
organizing system. A fundamental principle would be the principle of "resonance" where the universe is held in check by complementarity. Complementarity would be the origin of resonating p-branes.

Two families of histories{or two logical frameworks} can be called complementary when they are both consistent though mutually incompatible. Non-commutativity of operators
is the origin of this "complementarity". At a particular instant in time, you can't speak of both position and momentum of electrons. Complementarity is the most
specific character of quantum logic.

For example, waves and particles have radically different behaviors and properties. How does one understand that light is both a wave and a particle? Niels Bohr explained that each description excludes the other, but both are
necessary...they complement each other.

The Schrodinger equation describes a superposition of possible outcomes and attaches a range of probabilities to each possibility.

When the quantum world is measured or observed this superposition of probabilities becomes one "actuality". The superposition of Schrodinger's cat [alive and dead]
becomes an actuality with the cat [alive or dead].

Probabilities also have axioms.

p{a} >= 0

p{I} = 1

where I is the universal proposition allowing for every possibility

If two propositions a and b are mutually exclusive then p{a or b} = p{a} + p{b}

Reality is a complex self organizing system. In general, complex systems display a property that mathematicians call
"attractors". These attractors represent states that the system eventually settles down to. For example, the pendulum of a clock is also in the grip of an attractor. As
the pendulum swings, it speeds up to the midpoint, then slows down as it reaches the top of its swing. Oscillations are between maximum speed, zero displacement, and zero
speed, maximum displacement. This pendulum is governed by a "limit cycle" attractor.

Attractors exist in what is known as phase space. Phase space allows a way to transform numbers into pictures, extracting all bits of knowledge from a dynamic system. The complete state of knowledge of a
system is collapsed to a point for one instant in time. These "strange attractors" exhibit sensitivity to initial
conditions. While attractors exist in an infinite dimensional "phase space", they themselves have only finite dimensions.

This brief essay is my search for the understanding of reality as a system at resonance. Complementarity between
"waves" and "particles" can be explained with a simple diagram.

{<-{->{<-{U}->}<-}->}

Where U stands for universe and the arrows are waves expanding outwardly with radius R and 1/R respectively. Two waves at the same frequency, in phase, moving in opposite
directions are at resonance. The intersecting waves are governed by complementarity and resonance.

The number 2 is also very important. Complementarity says that there are two ways of looking at the world. If a polyhedron has V vertices, F faces, and E edges and is
topologically equivalent to the sphere, one will always find:

V + F - E = 2

where 2 is the Euler characteristic of the polyhedron. Consider a polyhedron with the least possible number of faces - a tetrahedron. Topologically, the tetrahedron is equivalent to a sphere... The increase in information would be "exponential". 2^{n}.

Time is an iterative process. Fractal behavior in the complex number plane is produced by iterating a nonlinear
function whose variables include its own result.

Let z = 0+0i , f{z} = z^2+c

f{z} = f{0+0i} = {0+0i}^2+c = c

f[f{z}] = f{c} = c^2+c

f[f[f{z}]] = f{c^2+c} = {c^2+c}^2+c

Time is a function of time. A function of functions. The Eigenfunction diffeomorphism is basically a map between manifolds
with the term "manifold" a topological space which is locally Euclidean. An infinitely differentiable bijection also
with a differentiable inverse.

An "inverse expansion" would be material and radiative contraction. A type of mathematical "inverse" of spatial
expansion. Expansion and inverse expansion are defined by the wavefunction of the universe.

Remember the "T-Duality" of string theory? A type of isomorphism.

R<------>[1/R]

Really T-Duality says:

R<------->[{L_st}^2]/R

The physics for a circle of radius R is the same for a circle of radius 1/R .

Again, a type of diagram for the "self
organizing"{self creating}, self containing universe, would be:

{<-{->{U}<-}->}

A system that should be describable by non-linear partial differential equations. A strange attractor of finite dimensions within an infinite dimensional phase space.
Our universe, postulated as a complex self organizing system.

Russell E. Rierson
analog57@yahoo.com

References:

Chris Langan, CTMU, <a href="http://www.ctmu.org" target="_blank">http://www.ctmu.org</a>

James Gleick, Chaos, Penguin books, New York 1987.

Brian Green, The Elegant Universe W.W. Norton&Company New York 1999.

Roland Omnes, Understanding Quantum Mechanics,Princeton University Press, 1999

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Adrian Selby

I'll resist the ad hominems, but your Langan influence is abundantly clear. Ah well. Aren't you also the guy that mocked someone on the ARN by insisting that there could be no reality without Truth?


Isn't this the current explanation? Are you so sure that the necessary explanation will always be defined in terms of a problematic 'complementarity' between two what appear to be conflicting descriptions of light.

They complement each other insofar as between them we have a working explanation of photons etc. but why are you so sure a harmonic and unified explanation isn't around the corner? The point of which is that what your saying depends on this complementarity to provide evidence for the postulation that complementarity holds the universe in check. I wonder what the universe would do if a different and more unified explanation appeared. Would complementarity still apply?

Are you only confusing a current explanation with the nature of the universe?

Incidentally, you don't explain what p branes are, how can you expect someone to understand and more importantly effectively cogitate on your post if you don't qualify neologisms for the general readership here on this forum? Are you purposefully obscuring what you're saying or just lazy?

Sorry, where are the premises that conclude that reality is a self organising system? Also, on what basis, were that true, do you conclude that properties that only generally apply to complex systems, you're not saying all here are you, if so be more precise, apply to reality?

Moving on, where is your evidence that 'attractors' exist in phase space. You are talking about sets having attractors, you provide no definition of what reality's attractors are and what phase space is other than that numbers are transformed into pictures. Can you define 'pictures' in the context of reality? Only it does smack of a perspective, after all, a picture is only a picture to someone, and someone's are contingent on reality, not existent in phase space and somehow defining or causally integrated into it. Excuse my ignorance here, I'm sure mathematicians have postulated such things, have they done so such that it is ludicrous to reject? I'd appreciate some help here from anyone but as it stands what you're postulating is interesting but assuming rather a lot.

The rest of your post seems to rest on the acceptance of the points I've a problem with.

A quick request though, I have read the ctmu and gleick's chaos but i'm from a non scientific background, my issues are purely conceptual. I do hope that if you feel the need to respond you'll do so with the hope of explaining more clearly where I am mistaken. This isn't stated mockingly, as you'll see from another post I've made here on Langan's ideas, I believe he believes what he's saying, but given he's not keen on explaining that to the rest of us, I feel denied a perfectly interesting explanation of the cause of the universe. Hopefully you'll be more willing to explicate. As a teacher (not a lecturer in university), I find such things intrinsically good

Adrian

Russell E. Rierson

Yes, how can reality exist without truth?

Surely you jest, mocker, I am not.




A premise is not a conclusion.

Are you saying that reality is not a complex system?


Attractors and phase space are explained by "chaos theory".

<a href="http://www.wfu.edu/~petrejh4/Attractor.htm" target="_blank">http://www.wfu.edu/~petrejh4/Attractor.htm</a>

<a href="http://order.ph.utexas.edu/standardmap/phasespace.html" target="_blank">http://order.ph.utexas.edu/standardmap/phasespace.html</a>

Adrian Selby

that should read 'where are the premises that lead to the conclusion', my bad.

I capitalised truth, your post related to a conviction, as I read it, concerning Truth, not truth, there are many of the latter, I don't think there are any of the former, at least, if there are truths that are true for all time etc. etc. I don't think reality relies on them. Incidentally, you did mock, I recall a 'Ha!' in the post, but its my other laptop that has the text, so I can provide it in a week or so, I@m too lazy to re-look up the threads I've read on the ARN again for it.

Truth is something that applies to statements predicated regarding states of affairs. Reality does not rely for its existence on whether people make true predications concerning it. It is true that there is a state of affairs x such that there cannot simultaneously be a state of affairs that is 'not x' yet the truth is merely a statement I've made. Reality did not rely on this being the case, I observed this being the case. I do not think you can identify truth with reality unless you accept that for any given example you can show that this example is actually true such that its contrary cannot be true.

Are you confident of this with regard to p-branes, phase space et al? i.e. its all very well saying that a thing cannot be another thing, but its how we define things that could be subjective, to wit, a cave complex to us can be itself or not itself, but if pressed to say what it is, such that we can rule out what it isn't, the chances are that another species would 'see' the 'cave complex' quite differently, in part due to the categories that it applies to the same geographical location, indeed, it could have a different idea of what the space is where we humans have identified the referent to 'cave complex'. As such, exemplifying our general rule is arbitrary, and we can be contradicted. The generalisation of this instance is thus meaningless if its impossible to hold any example to support the generalisation. This is roughly expressed of course, I'm aware of that. All of which is meant to show that when attempting to create pictures of our universe that we find meaningful, its awfully anthropomorphic to think that the universe itself just is or is close to what we understand it to be, if only in virtue of the nature of our brains and sense organs. This isn't to say either that we can't be close to a statement that is Truth regarding reality. We might just have very very useful models and pictures of reality, and the framework for arbitrating for when something thats very useful becomes True is also to be considered.

Also, I'm not saying reality isn't complex, you made a statement that there were properties of complex systems that generally applied, as opposed to universally, I questioned how you were sure that the system 'reality' contained said properties, given your only explanation was that, from there being features of systems that 'generally applied' these features applied to reality.

OK, I can see from your links how phase space relates to two dimensional representations of position and speed of objects, but are there real spaces that are only two dimensional, and is the link really positing that what you're calling phase space is more than just a model for understanding complex systems?

Now assuming that what you're trying to do is only to provide a model that gives 'all bits of knowledge' from a dynamic system, I have to ask whether or not you could both be clearer with regard to whether your extracting information from a system, as knowledge implies a knower, and information implies that the information processor, perhaps the knower, has a definition of information we've not covered but somehow agreed on, but also what these bits of knowledge consist of, and how you can be sure that collapsing the system to one point in time is indeed ever going to provide a model of reality. Under what circumstances could all such bits of knowledge be collected? Is it in principle possible?

I can't be sure where the use of concepts like phase states and attractors as things that create pictures and reality itself as having phase states and attractors differs, they seem blurred.

Of course, its us in a part of reality postulating that these things are or aren't the case, but reality is not dependent on what we postulate.

Russell E. Rierson

The question becomes: Is reality "true" to itself?

It must be.

Yes, reality is not self contradictory.


Branes: Objects, which appear to be fundamental ingredients of M-Theory, that can have a variety of spatial dimensions. In general, a p-brane has length in p-directions. A 1-brane is a string, a 2-brane is a surface or a membrane, etc.


Also, mental thought processes are chemical(particle) interactions within our minds. A "particle" has the property of wave-particle duality.

Therefore our thought processes are also waves spreading out through space and time.
These waves interact with other waves.

If consciousness is also a wave property spreading throughout the universe then consciousness is ubiquitous.

If reality is a self similar system, the general rules are "universally distributed".


We live in a 4D universe with "time" as the fourth temporal dimension. Actual reality is more than 2 dimensions. The 2 dimensional representations would be extended to "n" dimensions. 2D modelling is helpful.


Usful data could possibly be generated with different "mathematical" phase space representations.

Interesting...

Russ

Adrian Selby

Consciousness a wave property? Interesting...

I'm not sure consciousness is a wave property? Property of what? a brain? consciousness is an emergent property of functioning brains. Synapses firing in complex neural nets are what consciousness is, if the explanation for consciousness you're looking for answers 'what are the necessary and sufficient conditions for the emergent property of consciousness'

Consciousness is a property of highly complex living organisms. Rocks are not conscious, neither are stars, thus, consciousness is not ubiquitous. I'm sure the particles that synapses are constituted of are 'wavicles' that spread throughout the universe but you cannot conclude from this that consciousness itself spreads throughout the universe. Particles are everywhere, chocolate and opera and me aren't, though we're all made of these particles. This is a category mistake. Read some Gilbert Ryle.

I am interested in what, if my thought processes interact with other thought processes, happens to these processes, and what happens when they meet up with other particles, do my thoughts change?

I'm a little concerned about your use of the word 'mind'. What do you think a mind is?

edited to add: thank you for your explanations of your concepts such as p-branes, it helps a great deal.

[ December 22, 2002: Message edited by: Adrian Selby ]</p>

Beoran

Russel, most of what you say sounds scientifically soun... but what is your point exactly? Sure, the universe is a complex self organising system. That's trivially observable by looking outside the window. N reason to state the obvious, I reckon? I think philosophy should be about wisdom, not words. "Less talkie, more cookie." (Brian Clevinger)

Russell E. Rierson

Yes, can new information be derived from these "trivial truths"?

Maybe...

Russ

John Page

Chemicals are not synonymous with particles.
Therefore everything, whether defined aa a wave or a particle, spreads everywhere!

Russell E. Rierson

All matter consists of quarks and leptons.

Chemicals are "particles".

Russ