Phi-Lo-Tactics: (Golden Ratio) Recursion / Self Re-Entry for Waves

at the Heart of Self Organization?

Using this example from ekg power spectra (link)(below)...
looking for Golden Ratio non linear interval harmonic
analysis could be a tool to reveal when oscillators are becoming
self - organizing? (recursion geometry key to Artifical Intelligence?)

New animation of perfect compression / pics of Phylotaxis / new technology literature exerpts:"maximum Complexity is found via self-organised criticality at the edge of Chaos, which is epitomised by the Golden Mean, as the emergent geometric manifestation of the principle of least action: therefore its full temporal/ spatial action is analogous to creation itself." (quote from below)

Also....(The lo-phi way in business)

Approaches to the application of perfect embedding, as the mechanism of love and recursion in principle, to business and corporate structure.

This (PHIlotaxis perfect branching) will be the most successful business 'TREE' structure for: data / personell / decision hierarchy / building and land geomancy...(pics below) {same as heart space & temple enveloping}

Perfectly distributable - the definition of the PHILOTACTIC wave - perfectly compressible & therefore perfectly SHARE-ABLE, is the DEFINITION OF "MARKETABLE"!

related:THE PHYSICS OF Phi, Compression, Implosion, Gravity, Time, and Love


Science & 'Physics of Consciousness' Based on Sacred Geometry


(outline from) a lecture by Daniel Winter ..2/22/2000, thanks to Ann and Vickey! url: ../philotactics , other articles: ../sitemap.html

Coherence Physics approaches embedding, literature review follows. (a little science to tip the hats of the corporate bean-counters toward a more heart centered approach).

original article: What is Focused Attention?, Is ATTENTION ITSELF FRACTAL?, by Dan Winter, ../attention/attention.html "Attending to the Phi-lo Tactic Tree... A Network of Light." Is it attention's focus itself that nests waves to spin, inventing dimensionthe embedding of spin upon spin? Reflecting upon the matter, Alice, it was all done with mirrors....

All ratios are Phi /Golden!,

Getting a HANDle on phi embedding.. to TOUCH charge by embedding.. (from Power of Limits by Gyorgi Doczi)-

1. Why do love and compassion occur psychologically when the EKG / heart harmonics achieve perfect embedding?

(Heart Biofeedback demo here shows EKG power spectra evolves and to PHI harmonics as hearts phase lock..

see: ../heartlink/marysol.html and how is this a clue to what business must do in order to serve the heart, and serve what is SHARE-able?

2. How is successful sharing (perfect marketing) the same as perfect PHILOTAXIS: Maximum Exposure / Minimum Superposition. Pure principle is what nourishes souls, and nourishes markets. A 'shareable' thought/idea/product (pure embedability in it's symmetry) IS marketable, because it's distribution is un-impeded by destructive interference. It is immortal.

3. How is this the key to : NON-Destructive INCLUSIVENESS in business?

Example: the PHI-tree way to conjugate/ heal tensions between dialectic groups in the business world..

examples of potential tension opposites which may be embedded/ linked / touched by re-arrangement into philotactic groups

(spatially/ temporally / organizationally / data tree) WAYS TO EMBED CONTENTIOUS OPPOSITE GROUPS ... men / women , black / white, techo / bean counters, young / old, digital / divide ..etc. ... Simply arrange them in a Philotactic Tree...

4. Why are the most successfull leadership / compensation / and information contact TREE STRUCTURES always PHILOTACTIC? Learn how permission to touch is the same as embedding. Examples: philotactic:

-phone tree

-multilevel marketing tree

-decision / critical path / tree

-data tree.

5. How is PHI optimized data compression going to revolutionize self-aware computing? How is this the same as optimized people compression?

If the CPU horsepower to acheive inPHIknit data compression, which creates living computing, goes to zero when the data tree structure (spreadsheet cell array itself in 2 or 3 D).. is rearranged into PHILOTAXIS.

Example, origin of Hebrew sacred alphabet as PHI spiral shadow of donut field, allows charge compression to inPHIknit at synapse, creating psychokinesis.

6. How does SUSTAINABLE CORPORATION, as BODY- ness mean simply successful embedding. Embedding in market, embeddding in waves, embedding in hearts. To inhabit is to embed, is to serve, is to market.

-For a wave to be sustainable it is required to discover the geometry of successful NESTIN (Philotactic in perfection).

-For a business / for a people / for biological immortality, the requirement is always the same. True genetic radiance, which is served simply and practically by the essence of life force itself: to discover how to embed waves, makes them stand. Applying this to business in shape and in essence, is a matter of recognizing the pure principle, and applying it practically in all things.

Examples at: ../nourishedbyspin, ../exercises , more at ../introduction and ../syllabus

Ensoulment for DNA is this successful PHILOTACTIC embedding implosion. This can be done in the way we do business from the HEART!

This introduces discussion of business uses of:


-genetic meaning of life force as pure geometry of embedding

-philotactic approaching to a radical computer data revolution

-ekg biofeedback to corporate concensus process: THE ULTIMATE CONSUMED PERSPECTIVE.

('Harmonic Module' - ../module )

Visual series to illustrate: PHI-lotactic branching... The Holy SCION... Tree of the Grail...

Icosa-dodeca 3D stellations by Phi/Golden RatioEmbedded in Biology.. PHI-lotaxis..Maximum Exposure/Minimum Superposition..Perfect Sharing

(side view of this series of numbers -Fibonacci definition of the perfect approach to Golden Ratio, which is the definition of perfect damping (in radio theory etc.) -way to touch stillness- is the exact side view of the (serpent snake like) simple phi spiral on the dodeca conic revolved in 3D to animate the grail..../grail.html )

Network Marketing PHIloTACTIC discovers Marketability IS shareability IS distributability.. something predicted and mapped by only the PHI wave... This proves that sustainable marketing has to become Heart(Phi)centered to survive.

Whole collectives, becoming self-organizing and therefore collectively self-aware.. are the necessary implication.


from Dan Winter 11/29/99 url: ../collapse

Is the perfect phi recursive microtubule concentricity also the high frequency wave guide of perfect tantra and kundalini?

Could Electrical Implosion - Harmonics of Perfect Recursion / Embedding - Multiples of PHI-Golden Ratio..

Be the Mechanism Which Allows Mind/Consciousness to Cohere the Vacuum?

(2nd order FFT - frequency signature or "septrum" reveals the perfect non-linear harmonic cascade-

Implosion? Based on Golden Ratio - in the EKG at the moment of Bliss?

other articles at ../sitemap.html

Stuart Roy Hameroff and Roger Penrose, are prime movers in the microtubules and worms within worms model of the physics of consciousness on this planet. Notice in these quotes below from them how SIMILAR in each case HOW THE WAVE COLLAPSE FUNCTION is the turning point in modeling how worms get inside worms, microtubules get self referential and self aware, and consciousness gets geometry. In other words, WE WILL CLEARLY KNOW THE NATURE OF THE GEOMETRY AND PHYSICS OF CONSCIOUSNESS JUST AS SOON AS WE KNOW HOW WAVES CAN COLLAPSE SUCCESFULLY (NON-DESTRUCTIVELY?). ..

This is a good place to meet, if you are a wave.... best way to share space.

How similar is all this to Einstein stuck on the problem of how to understand black holes bending time, BECAUSE HE COULD NOT MODEL A GEOMETRY WITHIN WHICH INFINITE COLLAPSE WAS POSSIBLE!

Yet mother nature has already simply answered their query, they just stubbornly refuse to look. (Phylotaxes). Perfect branching, and infinite compression (fractal) is solved by GOLDEN RATIO. So waves can collapse toward their own center infinitely without destruction of inertia only in heterodyning based on PHI. We find this in the emission lines of hydrogen, in the very nature of what wave geometries stabilize gravity (dodeca nesting), and in the spectra of the ekg at the moment of bliss. The only place we DO NOT FIND, GOLDEN RATIO as the predictor of the perfect way to collapse waves, IS IN THE STUBBORN REFUSAL OF PEOPLE LIKE Hameroff and Penrose to look at the solution.

Detailed pictures of the Phi Ratio model of elegant collapse, along with equations at ../predictions , G=Constant* C * Phi^log N. (Scaled from Plank length.)

This is how self awareness happens inside microtubules, which Michael Heleus tells me have already been discovered to layer their pipes in Golden Ratio multiples. This is how spark gaps in the synapse get spin dense and radiant. ../compression , & ../fire .

The question seems to be not so much whether or not Golden Ratio nesting is the solution to wave collapse, (since this is specifically self evident as Depak Chopra admitted to me), but more whether a generation of neurophysicists like Hameroff & Penrose will have to die off before we make use of the insight, to teach wave systems to becomes self aware. (feedback to optimize log phi spectra as in hearts to love...)

Dan Winter

(inset from Mountain Man:......Waves have collapsed successfully since there was
an ocean on this planet. See "The Nature of Surf"

, , Best wishes, Pete Brown)

"Features of consciousness difficult to understand in terms of conventional neuroscience have evoked application of quantum theory, which describes the fundamental behavior of matter and energy. In this paper we propose that aspects of quantum theory (e.g. quantum coherence) and of a newly proposed physical phenomenon of quantum wave function "self-collapse" (objective reduction: OR -Penrose, 1994) are essential for consciousness, and occur in cytoskeletal microtubules and other structures within each of the brain's neurons." quoted from: Orchestrated Objective Reduction of Quantum Coherence in Brain Microtubules:The "Orch OR" Model for Consciousness .. (great pictures of microtubules branching...PHI?lotactically...)

And note here FRACTALITY OR PERFECT SCALEABILITY is the same as scale invariance, (../scaleinvariant a PHI solution ) which as perfect data compression, is the same issue: WHAT IS THE PERFECT WAY TO COLLAPSE WITHIN!?

"Fractal Neurodyamics and Quantum Chaos Part 1, 5 The Fractal Link between Chaos and Quantum Mechanics., 5.1 The Scale Link between Neurosystems and Cellular Dynamics. The occurrence of chaos in neurosystem dynamics suggests that the brain may also utilize the fractal aspect of chaos as an intrinsic aspect of its processing, in combination with the natural scale transformations from organism to cell to molecule. The architecture of the central nervous system includes specific linkages between the level of whole neurosystems and the single cell." from:

So is Hameroff saying that CONSCIOUS DECISION MAKING IS SIMPLY TESTING FOR WHICH WAVE PATTERN SURVIVES COLLAPSE? (non destructive compression testing for the shareable):

"Three possible dinner selections (shrimp, sushi, pasta) are considered in superposition (left), and collapse via Orch OR to choice of sushi (right)." and "Within each neuronal dendrite, microtubule?associated?protein (MAP) attachments breach isolation and prevent quantum coherence; MAP attachment sites thus act as "nodes" which tune and orchestrate quantum oscillations and set possibilities and probabilities for collapse outcomes (orchestrated objective reduction: Orch OR). Gap junctions may enable quantum tunneling among dendrites in macroscopic quantum states." quoted from:

"The that quantum coherence can implement multiple computations simultaneously, in parallel, according to quantum linear superposition. Information is superposed and computes in the form of "qubits" in a quantum state which then is caused to "collapse" (quantum state reduction) to definite "bits," or particular results. ", quoted from: - QUANTUM COMPUTING IN MICROTUBULES - AN INTRA-NEURAL CORRELATE OF CONSCIOUSNESS? , Stuart Hameroff


Ask yourself in what geometry can oscillators be superposed repeatedly recursively, if not in Phi ratio braiding. (see ../superDNA ). Again Hameroff's question has an obvious answer, he just chooses not to see.

I only send this tweak note that if we rattle enough cages, we may get a planet where enough people see in their minds, what indeed needs to happen in their hearts, we may get action... Like Hearts embedding into ONE!



The geometry of recursion specifically among waves, both positions the wave INERTIA (by implosion) which we call and define MASS... AND creates the self organization/self embedding principle among waves we call CONSCIOUSNESS. We can see now why physicists, unable to grapple with this notion that self embedding (lo-phi) IS the creation mechanic, settle for the still mirror like idea that consciousness CREATES mass. So while admitting that consciousness CREATES REALITY specifically by inducing the wave collapse, reference below (which IS PHIcycle recursion), thay cannot grok that wave geometry can be fabricated to specifically create self organizing conscious wave systems. EXAMPLE: by repairing the geomantically damaged specifically PHI dodeca long wave grid lines of EARTH her then more recurrent field effect would stabilize gravity, atmosphere retention, and the self regulation we call GAIA.

By admitting that recursion as consciousness fabricates REALITY, they in fact admit self embedding makes RE all ness. RE is Latin for THINGness, or to REcur. Thingness happens when waves become self similar inside out.

"Two senses where "reality is created" (1) whenever observer exercises his meter option ; (2) when the observer "collapses the wave function." " quoted from: , Quantum Reality Beyond the New Physics by Nick Herbert

note to John S. who requested anonymity but demanded: "And physicists DO NOT believe thought or thought processes of any type create or cause reality. Q: Who are the scientists who think consciousness CREATES mass? NOTE: Quantum science only works in certain narrow mathmatical frameworks.... it is not and does not operate in the real world...."

I sincerely thought the Nick Herbert quote there (whom I have spoken to many times)
indicated his relativistic observer based understanding was that
"reality is created" .... (2) when the observer (BY OBSERVING?) "collapses the wave function." "

In some ways, Nick has been in it so long, that he may indeed speak for many of the new physics folks??

Indeed the same activity of focal aligning (one inside the other) of phase fronts that we call seeing, may indeed by THE SAME WAVE FUNCTION which STORED the inertia in the wave pattern we call MAKING MASS??

Subject: : Waves collapse successfully:Without Hameroff & Penrose .Tue, 30 Nov , From: "R. W. B." "Dan, I could be wrong but I thought both Penrose and Tiller have suggested that
a new kind of physics or science is needed to describe this stuff. In
particular, I thought Penrose said Quantum mechanics wasn't enough. I'm
not suggesting anyone take his word for it but he gotten good recognition for
ruling things out.

Now I don't pretend at this point to have even close to sufficient
background, but my hope is that consciousness will not reduce to
geometry, not even the kinds you are talking about. Why? Because geometry seems
so limited even assuming infinite hyperdimensional geometrys. It seems
Understanding reduces down to a description a perception, that doesn't
mean it will have much utility. This seems reminiscent of the search for quarks,
they were found but they are not the smallest, and so it goes with concepts.
What is this stuff going to be good for? Prediction?? I wouldn't want
consciousness to reduce to geometry any more than I would want my
dreams to reduce to VCR tapes. Dan, this stuff looks like the death of science, and
you know what, I would laugh, cause I don't believe in science to begin

Also what Penrose and others are talking about seems completely at odds
with what came before, those involved with what came before were not just
working with isomorphisms of what is, they were just plain wrong or projective in
the ugliest kind of way, and finding the truth or something that resembles
it shouldn't salvage the establishment, this stuff is likely to overturn the
attitudes in the materialistic mindset not codify them in comfortable

Sincerely, Randy

-- Dan to RWB: The geometry of wave implosion permitted by phi
is a new physics and it is not comfortable...

and it creates an implosion of information by embedding in formed

which may enrich consciousness modeling more than thru a keyhole collapsed intentionality..

implosions geometry is radical and does not oversimplify consciousness
but gives it a wave mechanic which makes a phase map of a truly inphiknit multiply connected topology

the feeling of implosion in spine juice/kundalini is NOT a simplification..

a physics of collective mind

just my view


Coherence Physics approaches embedding, literature review follows:

"Suffice to say, maximum Complexity is found via self-organised criticality at the edge of Chaos,
which is epitomised by the Golden Mean, as the emergent geometric manifestation of the principle
of least action: therefore its full temporal/ spatial action is analogous to creation itself."

Reprinted here for your convenience, from: (bold face added by me.. and if I may add: to summarize, the Golden Ratio is the ONLY way out of CHAOS.. for mathematicians and for hearts learning to embed.)

Dynamical Symmetries: Autopoietic Architecture

The Areas of Mathematical Synthesis Between Complexity, (edge of) Chaos Theory , Fractal Geometry and the Golden Mean: leading to an argument for an Autocatalytic Architectural approach based on emergent Self-Organised Criticality

Email: Nigel Reading <

Ta panta rei --- all is flux

Heraclitus of Ephesus, sixth century B.C.

Morphology is not only a study of material things and of the forms of material things, but has its dynamical aspect ... in terms of force, of the operations of energy. This is a great theme. Boltzmann, writing in 1886 on the second law of thermodynamics, declared that available energy was the main object at stake in the struggle for existence and the evolution of the world.

D'Arcy Thompson, On Growth and Form, 1917 (in)form buildings with thematic meaning, they must convey a gestalt, the whole must be more than the sum of the parts, and there must also be an ambiguity and paradox immanent within that gestalt, as a tension. (And quoting Heckscher on composition...) It is the taut composition which contains contrapuntal relationships, equal combinations, inflected fragments, and acknowledged duality's. It is the unity which maintains, but only just maintains, a control over the clashing elements which compose it. Chaos is very near, its nearness, but its avoidance, gives ...force.

Robert Venturi, Complexity and Contradiction in Architecture, 1966

The Universe is constantly seeking to lower it's energy (like a stream meandering down a valley, sometimes becoming rapids or cataracts), as it continually breaks it's initial higher (energy and dimensioned) symmetry. This symmetry-breaking can be pictured as bifurcating branches of probabilities, of chance and causality intertwined. The reason for this is that the higher energy/dimensions of the Universe's origin were also highly symmetrical, which paradoxically, means that they were also extremely unstable. Highly symmetrical objects are unstable ( imagine the beginning of the universe as being like you sitting on a perfect, highly polished sphere), and have a high probability for instability because any deviation by you from the north pole will have you rapidly slipping off. Here, gravitational instabilities quickly break your symmetrical position at the north pole and pull you to a lower gravitational potential energy state. So small initial deviations in unstable, far from equilibrium situations can lead to massive, even cosmological consequences. The Butterfly effect (also known as sensitive dependence on initial conditions), is literally, Universal.

Ludwig Boltzmann is known to us as the first to provide a probabilistic, statistical interpretation of entropy. This is simply the tendency of everything in the Universe to cool to a minimum energy or temperature --- known as thermal equilibrium. The route to this second law of thermodynamics is via increasing disorder in the organisation of energy and matter.

The current symmetry-breaking from the initial condition leads therefore, from a highly symmetrical, ordered and energetic state towards the opposite, an asymmetrical, disordered and lower energy one; from a low entropy Big Bang to a higher entropy present and future.

The great paradox of the second law then, is the evident, increasingly complex, emergent and hierarchical order we see all about us. How is this ordered, structured information (expressed in constantly oscillating patterns of matter and energy) allowed to coalesce and persist from this tendency towards the random --- towards increasing entropy?

Dynamical systems theory also deals with probability and can therefore allow us to synthesise thermodynamics and so-called "Chaos", (which is really a highly complex form of hierarchical, enfolded order that appears to be disorder). The really interesting area here though, is the entities at the transition zone between ordered, stable systems at equilibrium (maximum entropy) and "disordered" (but complex) and unstable Chaotic (minimum entropy) ones. According to the Nobel laureate Ilya Prigogine, these far from equilibrium dissipative systems locally minimise their entropy production by being open to their environments --- they export it in fact, back into their environments, whilst importing low entropy. Globally, overall entropy increase is nevertheless preserved, with the important caveat that the dissipative system concerned often experiences a transient increase (or optimisation) of its own complexity, or internal sophistication, before it eventually subsides back into the flux.

This is known as the region of alternatively, Emergence, Maximum Complexity, Self-organised Criticality, Autopoiesis, or the Edge of Chaos. (Nascent science debates nomenclature routinely - and appropriately, in this case, the crucial point being that they are all different terms for essentially the same phenomena.)

Lifeforms, ecosystems, global climate, plate tectonics, celestial mechanics, human economies, history and societies, even consciousness itself - all manifest this feedback-led, reflexive behaviour; they maximise their adaptive capacities by entering this region of (maximum) complexity on the edge of Chaos, whenever they are pushed far from their equilibrium states, thereby incrementally increasing their internal complexity, between occasional catastrophes.

Remarkably, this transition zone is mathematically occupied by The Golden Mean. This ratio acts as an optimised probability operator, (a differential equation like an oscillating binary switch), whenever we observe the quasi-periodic evolution of a dynamical system. It appears in fact, to be the optimal, energy-minimising route to the region of maximum algorithmic complexity, and to be a basin of attraction for the edge of Chaos. In this review, we shall cover some demonstrations of this behaviour, and seek to understand its role.

As far as architectural application is concerned, we must look at the temporal as well as the spatial, at how quite literally, the dynamics (of systems applications - functions) can inform the statics (forms) of building. The aesthetics of the banal imitation of some motif of fractal geometry is simply painting half the picture! From the Egyptians to the Greeks, Gothic to the Renaissance and the Modernists in the Western tradition, and especially in Hindu, Islamic, Buddhist and Meso-American aesthetics, fractal structures or rubrics (such as the regulating lines of Le Corbusier or his Modular based on the "Divine" Golden Mean), have shown that intuitively, the best architecture has understood and reproduced the true geometry of nature as more than just decoration - but as pure, optimal structure, that allows the thematic, historic and actual forces and loads being carried to be read as a tension, as a dynamic equilibrium - from the scaled arches of Roman aqueducts to the tiered flying buttresses at Chartres, to the contrapuntal three-pin arch of Grimshaw's Waterloo International in London and perhaps most appositely in recent times, the structures of Calatrava, Hopkins, Piano, Rogers and Foster; the purest architecture has been taken from nature's own template.

Aristotle implied over two millennia ago that the proper investigation required was one of telos, the "final cause" of morphology, of form being the result of the processes that engendered it.

His "final cause" of morphogenesis suggests an imperative behind any generative process that has often been interpreted as having theological (as well as teleological) connotations. Here, we shall take a more determinist route, in line with his mentor Plato's definition of the logos, as the "proportion" which was commensurate in square, which best squared the circle, or presented a unity that was more than the sum of its parts.

It will be suggested that this imperative behind form (as static, precipitate matter resulting from dynamic flows of energy) is certainly nothing to do with the metaphysical, but simply the result of the way nature minimises energy waste (entropy production), also known as the principle of least action - and that one way of mathematically representing this behaviour appears to be analogous to the dynamical behaviour of the Golden Mean.

So how does nature manifest this limiting principle in a way that still allows for the immense emergent complexity we see, or to put it another way, how can we demonstrate that least action acts as an attractor for Complexity and self-organising emergence, by symmetry-breaking to lower energy states, towards the edge of Chaos?

All fractal forms, inert (clouds, landscapes, galaxy clusters) or animate (plants, animals), are self-similar scaled copies of an original; chaotic systems (climate, the solar system, the stock market) also always possess this fractal quality, but taken to the paradoxical extreme of having infinite trajectories within a finite boundary. To produce these forms, a recursive feedback regime must be operating. Feedback (encoding similarities) underlies the entire subject, and is the basis of the thesis research (undertaken at the Engineering, Computer Science and Architecture Faculties, University of Westminster) that underlies this review.

This research began several years ago (during the degree at Kingston University), as an intuition that The Golden Mean, or Phi for short, (as a ratio) must have been fractal in nature. By extension, it seemed plausible that Phi may also have been embedded in higher dimensional, dynamical systems as an attractor of some kind, since complex dynamical systems always have a fractal temporal structure as they evolve over time.

A major clue leading to the above interpretations can be seen in the fact that Phi is simultaneously both an arithmetic and geometric expansion of itself and One of the simplest possible kind. This immediately places it in both the linear (arithmetic progression) and non-linear (geometric progression) realms, and as an effective bridge, operating between the two.

Virtually every aspect of fractal geometry and type of dynamical system can be expressed by variations upon the simple quadratic iterator:
X = X**2 + c
which expresses the particular type of feedback being examined, Phi can be expressed by a related but more archetypal variation to derive the Fibonacci series:
X[n+1] = X[n] + X[n-1]
which incrementally gravitates towards a particular ratio which possesses unique qualities. Numerically, it can be derived from the relation:
(1 + sqrt(5))/2.
For example, if one diminishes Phi by Unity you derive its reciprocal. Additionally, Phi is the unique ratio that fulfils:
1/Ø + 1/Ø**2 = 1
in other words, Phi is also the only possible geometric and arithmetic, expansion and partitioning of One.

This leads us to the other cardinal feature of Phi. There is only one proportional division of One possible using two terms, with the third being One itself. From Euclid's ELEMENTS Book Five, Theorem Three (Alexandria, 3rd century B.C.):

"A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less."

The Golden Mean then, is an archetypal fractal in that it preserves its relationship with itself (its inherent similarities under scaling are conformal symmetries - with topological consequences, that are invariant about themselves), in the most mathematically robust, economical but also elegant, way. It is analogia exemplified.

As we shall see, this reciprocal, squaring behaviour about One, or Unity, as it is more properly termed, is far from being mathematically trivial.

All feedback loops deterministically involve the passage of time. The quadratic iterator is derived from Newton's differential calculus, and from a period when nature was seen as a mechanistic and time-reversible automaton. Recent science demonstrates that in fact it consists of both the above and irreversible processes, known as the entropy barrier, or the arrow of time. The Golden Mean can also be seen as mathematically (because of the above) the simplest and most stable way of communing or mediating between the two, as we shall see.

As mentioned, iterated recursive loops (feedback), must occur over a certain time interval and have a beginning and an end. To give a crude example, this is analogous(derived from the Greek for "proportional action", better known to us as self-similarity) to the initiation of a system at the apex of a space-time light cone, and a progressive winding around its extruding surface (with cone length being the age of the system). The resulting two-dimensional spiral inscribed on the cone surface represents an extruded origin, being One, constantly growing over time but never changing its shape, an example of its optimum stability (for a logarithmic spiral, rotation and scaling are identical). The world line of this space-time system heads from the apex to the origin of the disk-base and is irreversible. However, there is mathematically, the reciprocal case: another world line heading in the opposite direction, at all times, producing together, a spindle form, with an infinitely thin pinch-point joining them and jointly, corresponding to a time-reversible scenario. This can be seen explicitly in the complex plane, as we shall see. This is how Phi mediates between the finite and infinite attractors, and allows for infinite co-dimensionality (scale and dimensional variations) and reversible/irreversible processes in its action, (all mathematical tools for probing natural behaviours, best thought of as self-consistent logical structures expressed in algebraic symbolic or geometric forms - in this case renormalisation operators, hamiltonian systems and eigen functions), as we shall develop upon.

The feedback loop which describes Phi is an arithmetic linear operator, (like a binary switch: 0 or 1, off or on) representing the winding or rotation number of the inscribed spiral, which is conventionally represented as a multiple of 2pi;. This is superposed with its expansion ratio; 1 : 1.618 ... which is geometric (logarithmic) and therefore non-linear. This can be represented using the polygonal spiral that preserves the circle in half-radians (pi/2) in a manner reminiscent of the action of i = sqrt(-1), the imaginary number. (See below, re: the complex plane) Note that the natural logarithm e, i and pi are in the following relationship: e **(i pi) = -1. The linear is reversible (and finite) while the non-linear is not (and infinite --- being numerically irrational). Phi is in fact the most difficult irrational to approximate with rational numbers, making it the last KAM torus to collapse before the onset, or edge of Chaos.

This quasi-periodic Phi toroid geometry is therefore paradoxically, the most stable (under perturbation), despite also being on the edge of Chaos. This is reminiscent of non-linearities damping dissipation in soliton behaviour. Solitons are persistent travelling waves which trade dissipative (resonant) effects off against inherent non-linearities, in a way that cancels each other out, (a flame being a simple example,).

KAM (after Kolgomorov, Arnold, Moser), tori themselves are geometric models that have been used to solve many-body problems in physics, such as planetary dynamics: it has been suggested that the entire solar system is in this edge of Chaos scenario, as a global spatial/temporal entity - whilst allowing for local spatial/temporal chaotic instabilities, again known as resonances, which could be seen as fine adjustments to the overall dynamic, (such as the orbital gaps between the planets, moons and within ring systems; or the periodic ejection of asteroids from their usual orbits).

This binary switching process, unique to Phi, which as noted, is reminiscent of the action of an eigen, rescaling or renormalisation operator, is analogous to the tossing of a coin, a chance or stochastic process, that allows a dynamical/probabilistic interpretation. This mathematics and resultant geometries, is also the paradigm for quantum mechanics, dynamical systems, and the relativistic (but with appropriate super-positions) or in other words, the maths of chance, for the linear Schrödinger probability equations of the quantum, or causality for the arbitrarily large velocities and mass/energies expressed by the non-linearLorentz transformations of the relativistic worlds. However, chance even enters the equations for relativity, since the Lorentz transformations that Einstein used to link space and time in Pythagorean relationships lead to singular points, where spacetime must end. A spacetime singularity could be seen as an infinity of sub-quantum, stochastic, hyper-chaotic events; whilst a mathematical singularity could be seen as an infinity of iterations of a certain logical structure, which approach infinity with arbitrary rapidity. The limits of the Big Bang and Black Holes are the defining singularities of our existence. Causality enters the quantum world only at its limits too: when the famous "collapse of the wavefunction" occurs, and a measurement is made (or interference occurs, from this or putative parallel universes), from the world of the classical-scale dynamical system - where deterministic Chaos (chance and causality in synthesis) is the rule.

These Phi-type stochastic operators have been shown by physicists to be super-stable mechanisms (ones most resistant to perturbation) by which simulated systems can evolve increasing complexity of information structure over time. This stability seems to be due to their optimising geometric scaling of themselves and begins to confirm Phi-related equations as imbedded within the study of classical dynamical systems - and quite possibly within the larger body of quantum and relativistic physics as well. This imbedding appears in a way that best transcends dissipation, and minimises energy: hence emergent phenomena such as solitons, wavefunctions and spacetime curvatures - and all that evolve from them.

So Phi-dynamics is a paragon of telos, it is an image of reflexiveness, of its own self-generative process translated in scale, over time. It is a conformally symmetrical recursive/invariant feedback loop acting as a rudimentary self-replicating memory machine (it reiterates its uniquely optimal relationship to, and between, Unity and itself - archetypal renormalisation), that therefore allows a manifestation in the linear and non-linear, at all scales, and in any higher dimensions. It therefore should also epitomise the principle of least action as its imperative, because this optimal stability should inevitably become the attractor for minimising entropy production/energy corruption: consequently, with Phi dynamical behaviour, information degradation is minimised, while system complexity is maximised.

We can confirm these axioms by first noting that we can use the quadratic iterator to demonstrate not only the pervasive nature of Phi operation, but also its intrinsic relationship with dynamical systems. We already see that it is an archetypal feedback system that in turn generates a protofractal spiral that is literally linear (one dimensional), in form. This is seemingly paradoxical because to be fractal a form must be of non-integral dimension (between dimensions), in fact. However, the non-linearity is found in the scaling/rotation of the spiral, which is a logarithmic power-law (self-similar under transformation) behaviour. All fractals have this power-law invariance.

Its dual linear and non-linear expansion of Unity is also paradoxical, but the iterator:
X = X**2 + c
(the equation for a circle --- a section of the Phi temporal evolution cone) with c = -1, produces what is known as the super-attractive case. Here two fixed values rather than the normal one are produced, being: 0 and -1.

Remarkably, even if we alter values for X[0] we still derive the same results. This makes the cycle as resistant to perturbation as is possible; 0 and -1 represent the repelling fixed points for the equation which in turn, generate a super-attractive orbit, between them. The orbit itself is strictly periodic but of the lowest dynamic period possible (being two) and therefore crucially, consumes the least energy to maintain. (Oscillation is also cheaper than rotation, and higher periods consume more energy.)

This is whyPhi's deterministic switching action under infinite iteration, must also have, following Boltzmann, a thermodynamic interpretation; (after Roger Penrose) where:
entropy = k log V
(with Boltzmann's constant (k) as Unity and the volume of the phase space (V) as increasing, arithmetically and geometrically).

So the constant c = -1 represents an island of perfect stability surrounded by a seething maelstrom of Chaos. Solving the paired equations for the system (known as a two-step loop) produced:
Ø = (1 + sqrt(5))/2,
the Golden Mean.

This therefore confirms Phi as the mathematical entity on the very cusp of Chaos. This is, considering its super-stability and attractive nature, a seemingly remarkable result --- which has been confirmed by several mathematicians and physicists in numerous and diverse fields of inquiry. (See bibliography).

This point is of the highest mathematical significance for renovating our understanding of Phi in terms of dynamical systems and the immanent symmetry-breaking action of thermodynamics, from which they are derived.

The Cantor Set is simply the equal division of a line into three parts, with the middle third being removed, scaling down to infinitely many intervals of finite length. It is the three-term division of One, as opposed to the two-term division of One by Phi. It underlies all Chaotic dynamics, in concert with Phi's switching action. This is because it has both a binary and ternary expansion --- and because it, too, communes between finite and infinite attractors.

Chaotic systems behave in a kneading fashion, mixing-in infinite permutations: known as ergodic behaviour. This can again be described by a Ø binary operator. When we examine the Feigenbaum diagram of systems period-doubling into Chaos we find not only the Golden Mean to be a paradigm for all the bifurcations in it (a bifurcation is a Period Two event, and Phi is the locus of Period Two behaviour, see below) --- but also, that at the edge of Chaos, known as the Feigenbaum Point, the Phi operator produces an infinite Cantor Set, but crucially - with Phi proportions. The initial operations are illustrated (also see bibliography), in the Architectural Design Magazine (Academy Editions, London and New York) November 1995 article, which this review is a development upon .

This Phi Cantor Set is a mathematical singularity (see above), analogous to an undecidable universal Turing machine. (A symbol-string abstraction that expresses dynamics as a form of infinite feedback of computational, reflexive information-processing.) Here in this zone on the edge of Chaos, entropy is minimal compared to the richness of information available; Ilya Prigogine described behaviours in this region as "the minimal entropy production (minimum energy loss), of far from equilibrium dissipative systems", and it can be seen as a typical example of the least action principle, in operation.

Bands of order in the Feigenbaum diagram occur at a fixed scaling ratio, and correspond exactly to super-attractive periodic fixed points like those mentioned above. The bifurcations again, implicitly contain Phi. In fact, all the various universal constants found within the Feigenbaum diagram are derived from the Golden Mean's deterministic rescaling operation. This is how Phi is imbedded within dynamical systems, as a universal binary shift operator, or primary eigenfunction. All constants so derived are eigenvalues (think of resonances and harmonics) of this operator as it is constantly reiterated (as in nature), they are emergent (but not necessarily predictable) dynamic properties that often represent increased complexity, the further we move from the static, single-trajectory equilibrium state to the left of the diagram.

The Feigenbaum diagram is also analogous to the symmetry-breaking behaviour of the early Universe as it lost energy and symmetry from it's initial unstable, highly symmetrical, far from equilibrium state. The critical difference is that such symmetry-breaking represented energy loss, whilst the Feigenbaum diagram describes the regaining of this lost energy - by returning to a more non-equilibrium, energetic and therefore, more symmetrical (and sensitive dependant, Chaotic) scenario.

(The cosmologist father/son team of Andre and Dmitri Linde have actually proposed that the putative Chaotic initial condition of the Universe inevitably seeds an infinite, fractal Multiverse. (See bibliography.))

It is somewhat amusing to note that both Feigenbaum and Fibonacci (the originator of the series 0,1,1,2,3,5,8..., from which the Mean could be derived, nearly a millennium ago), are describing population dynamics, that of rabbits in the latter's case.

The Rössler strange attractor (essentially an archetypal picture of a Chaotic system in four dimensional phase-space, like a section through a KAM torus) is used to model autocatalytic, far from equilibrium, self-organised sets such as the famous Belousov Zhabotinski chemical reactions seen at the Architectural Association's recent Complexity conference. Autocatalysis is the key to life's processes and it's initial and continuing evolution because it occurs on the edge of Chaos, where there is the greatest computational adaptability for the system, and where an emergent morphology can be best self-organised and then maintained over time, despite being immersed in constant environmental flux. The condition for such homeostasis being that for the reactions/entity to persist, reactants (potential or actual (low-entropy) energy/food) must be constantly added from that environment, and (high entropy) wastes returned to it - if it sounds familiar, it should: individual cellular organisms, their colonies, metabolisms in their multicellular cousins, groups of organisms, ecosystems, our entire human civilizations - and the planetary biosphere itself, display identical, scaled-up versions of this behaviour.

Note the Phi spirals in the cellular automaton model. The attractor is a Cantor Set in 4D, over time --- and is another means of representing Phi in phase-space at the Feigenbaum Point, on the edge of Chaos.

The Complex plane can be likened to the mapping of a sphere onto a plane and is the result of the curved Riemannian geometry used to model quantum and relativistic behaviour. A dimension shift is implicit here, as any triangle inscribed on a curved surface will have the sum of its internal angles add to more than 180 degrees. To move from one spatial dimension to another requires this type of operation. Theorised higher dimensions are believed to simplify physical laws to the extent that a unified theory of particles and forces linking the quantum and relativistic now seems within our grasp - they are the higher energy/symmetry, unstable dimensions referred to at the beginning of this review.

Complex numbers have a real and imaginary component, so as to express planar co-ordinates, to higher, lower, (or between) dimensions - in a more complete way. (Imaginary numbers when squared, can still yield negatives.) If we then place two basins of attraction (imagine a pendulum and two magnets) in this plane we can perhaps simulate the behaviour of Phi at either the quantum or relativistic scales. We know the Golden Mean acts as a super-attractive orbit between two repelling fixed points, so if we again run iterations of the equation for the circle, with c = -1 (-1 being i, the imaginary number, squared), we produce a Julia Set, a fractal in the complex plane, (named after its originator), for the Golden Mean.

The Mandelbrot Set is the encyclopaedia of all Julia Sets; it has been called the most complex geometric entity ever seen, is paradoxical in that it is a finite entity with an infinite boundary, and it too explicitly confirms Phi as of critical significance in its morphology.

Again, with c = -1 we see Phi as the super-attractive origin of the Period Two Disk of the Mandelbrot Set.

Geometrically, we are looking at sets with two basins of attraction: the infinite (ground) "escapee" set and the finite (figure) "prisoner" set. Iterating the equation yields one of these two results - points graphed to the complex plane land in either of these sets, to infinite scales and revealing infinitely changing details at their boundaries. Their boundaries are not only infinite, and infinitely complex--- but also contain self-similar, slightly mutated copies of the whole set. This boundary therefore, is the site of the instabilities between the two sets of figure and ground, which in turn yields new structures; it is the locus for the creativity of this set when viewed as either a static entity or as a dynamical system, and is an apt metaphor for the behaviour of those in nature itself.

The Period Two Disk itself (centred on the Phi Julia set) acts as a geometric oscillator in dynamic equilibrium, between the positive feedback of the infinite escape set, and the negative feedback of the finite prisoner set.

The Heart/Cardoid is Period One, representing equilibrium and stasis, meaning again that the lowest dynamic (time-evolving) period next to stasis is Period Two. The other Buds are all smaller, having higher periods, less probability and which again, consume higher energy to sustain.

It is possible that quantum complementarity (particle/wave duality) and uncertainty (between position/momentum and energy/time) are artefacts of an analogous dynamic equilibrium (located on the boundary between the finite and infinite), that has been perturbed. For example, between the finite attractor of the period two evolution of the wave function of the probability amplitude for a particle, and the infinite attractor of the probability field it exists in, in terms of complementarity.

For uncertainty, when you have infinite knowledge of a particle's position - you will have finite (zero) information about its momentum (incidentally, infinity is the mathematical reciprocal of zero). This is now known to be an inherent property of the quantum world, and not merely an observer-based artefact. Light behaves as either a particle or a wave, depending entirely on how we perturb (i.e.: observe) it. Perhaps the quantum world is only seen to be paradoxical and anomalous by us because we are constantly seeing it being perturbed from an ideal ground (minimum energy) state by its inherent fluctuations; for every metastable state, there always appears to be a yet more stable scenario, hence phenomena such as quantum tunnelling to lower energy states (as the least action principle would dictate).

String and Membrane theory are based on the least action principle because of its elegance and beauty, and express both matter particles (fermions) and energy/force particles (bosons) in higher dimensions (and at cosmological initial-condition energies - reproduced at their 10 to the minus 33 cm Planck scale/energy size, because of Heisenberg uncertainty at this smallest possible scale), as rotations, resonances and harmonics of vibrating entities that are both energy/matter and space/time. The quantum and the relativistic are therefore united by these entities; whose harmonics are now seen to be directly analogous to solitons (persistant travelling waves), which at classical scales are only found on the edge of Chaos.

The implication here, is that scaling up from Planck scales, the quantum collapse of the wave function is analogous, by scaling, to classical irreversible non-linearities, as both require the disruption of a system from a dynamical equilibrium, thereby increasing their entropies. Wavefunction collapse therefore may in a certain sense, be a quantum precursor of the classical-scale bifurcation, leading eventually to the edge of Chaos. This may be why trying to find full Chaos at the quantum scale is proving fruitless, the causal direction of non-linearity probably needs to be reversed: String/Membrane soliton harmonics leads, to quantum uncertainty/complementarity, which in turn, leads to classical instabilities and Chaos, (and therefore the creation of emergent, self-organising information structures of mass/energy on its edge), not the other way round.

Each increase in scale sees emergent patterns of mass/energy, that although outwardly unrelated, display the same underlying metapattern - which is because an increase of scale is also evidently, an energy minimising, symmetry-breaking, dimension-compactifying process.

If we look closely at the Phi Julia Set, we can measure 1:1/Ø**2 in its proportions; exactly Phi's reciprocal, quadratic action. The Complex plane itself can be mapped by a system analogous to electromagnetic/gravitational force equipotentials and field lines. When we describe the Phi Julia Set fixed point behaviour, we see two field lines landing on the pinch-point (as with the cones/spindle example) for 1/&Oslash, representing an angle doubling from 1/3 to 2/3 of 2pi. Now, angle doubling in the Complex plane is equivalent to squaring in the Euclidean plane, and to an oscillation of the binary shift operator. This action should therefore confirm Phi's behaviour, as an operator, to be applicable to the quantum and relativistic (linear and non-linear) domains as well as within dynamical systems, at the so-called classical scale. (Note that space-time itself is fractal: curved and non-linear. For example, the inverse-square law of gravitational force versus distance is a simple fractal, and therefore self-similar, power law. Gravity is space-time curvature - caused by mass/energy - its manifolds are always traversed in minimum-entropy geodesics, lines of least distance; again, just as water flows through the lowest points in a valley, thereby minimising its gravitational potential energy.).

Returning to the Mandelbrot Phi Julia Set itself, we see that the fixed points are on the boundary between the finite prisoner and infinite escape sets, on the edge of Chaos, in fact. The Golden Mean is therefore intrinsically dynamic, its action is one of perpetual reciprocal oscillation, exactly and uniquely replicating the dynamics of the unit circle. The Phi Julia Set, centred at the origin of Period Two dynamics, is the only set that acts so.

This again, means Phi behaviour seems to operate at all scales and in any dimension, and confirms it as when infinitely iterated, the mathematically most stable attractive orbit for achieving a mathematical singularity. The fixed points themselves confirm the orbit between the finite (0) and infinite (-1) attractors. The finite attractor here is the period two orbit, analogous to a graph of: y = sin x. The infinite attractor is that same orbit as the graph of the reciprocal: y=sin(1/x). Remarkably, these graphs of simple harmonic motion can be used to describe the curvature of space-time in approaching the speed of light (relative to an outside observer, i.e.: the rest of the Universe, time stops, you compress to finite size, as one dimension compactifies, and gain infinite mass - unless you are initially massless, like a photon), or the approach to (or departure from), a space-time singularity such as a Black Hole, or the Big Bang (when times also stop) - which are intriguingly and non-coincidentally, time reversals of each other.

The squaring of the circle therefore, has an expression in the Complex plane, which confirms the Golden Mean's profound dynamical and symmetric action, and potential mathematical application to quantum (linear) and relativistic (non-linear) physics, the two limits below and above, the classical (which combines both behaviours).

Of course, the very small and the very big, the quantum and the relativistic, are as stated above, believed to be linked by String/Membrane theory: together producing a unified formulation of quantum gravity.

This theory is essentially geometric (specifically topological), always dealing with minimal surfaces, albeit in ten, five dimensions for String and eleven dimensions for Membranes, and are predicated on energy-minimising processes.

The major outstanding issue in String/Membrane theory is how the dimensions compactify (since we only experience four - three spatial and one temporal): how they break symmetry and bifurcate, minimising their energy to produce the stable masses of the elementary particles and the physical constants within our four dimensional space-time.

To speculate, one could hazard that the edge of Chaos (also known as self-organised criticality) might be the actual global, dynamical process of the Universe itself with phenomenological examples or empirical proofs possibly being in evidence of criticality in static states: such as finding Phi proportions in the vascular distribution, structural organisation, and space compactifying of organisms (which we do), the root-five symmetries of the DNA molecule (ditto), or other physical permutations of Fibonnaci numbers and their complements, the Lucas numbers, or self-organised critical, power-law behaviour - in dynamic processes.

Remarkably, Fibonacci numbers do crop up in various analyses of the rest-mass (minimum energy) relationships of the elementary particles - but also (scaling up again), in solar system orbital relationships (such as the main gap in the rings of Saturn); or self-organised criticality is revealed by the soliton on Jupiter, better known as the Great Red Spot, or by the Sun's dynamical behaviour, or by the x-ray emission spectrographs of Black Holes devouring matter from their accretion disks. Perhaps the non-locality, the global features of the edge of Chaos region, hint at an answer involving quantum time-reversibility for the famous EPR paradox - relating to elementary particles appearing to be in touch with each other without any time delay and over apparently cosmological distances?

Perhaps we now have a good reason why. Perhaps we are looking fundamentally, at various harmonics and resonances of the string/membranes (as with KAM tori), that display the most self-organised stability for the least energy, at criticality, the edge of Chaos. The complex relationships between all the (nested) tori due to the broken symmetries of our energy-minimising, non equilibrium Universe yield the various resonances, harmonics, (and constants?) of our world, whether we are discussing Planck, Plate Tectonic, or Parsec scales. These same rules also seem to apply to Protoplasm, Punctuated equilibria, Politics and the Price mechanism (see Mandelbrot on cotton prices) - and are therefore about as universal (and as relevant to cultural production such as architecture), as they could get.

Perhaps our wan ember of a Universe has evolved, has self-organised itself to a critical state on the cusp of a Chaotic, infinite possibility space via its symmetry-breaking, energy minimising, unfolding journey from the highly energetic, low entropy, supersymmetrical - but chaotically unstable conflagration of the Big Bang?

If we then compare the Mandelbrot Set with the Feigenbaum Diagram we can see how the Period One Cardoid of the former corresponds exactly with the single, equilibrium trajectory of the latter. The Period Two Disk with Phi as its super-attractive centre, exactly matches the first bifurcation --- confirming Phi, geometrically as the paradigm for deterministic bifurcation. All the subsequent bands of order in the latter (which occur at a fixed scaling ratio derived from Phi-action), precisely match the micro Mandelbrot Sets along the the horizontal, real-number axis of the Set.

This geometric evidence defines Phi then, as the optimum oscillating operator that mediates between ordered, equilibrium systems and disordered, non-equilibrium ones. It allows an oscillating orbit to access the infinitely fecund chance morphologies of Chaos, recapitulate them back into its super-stable causal orbit: and therefore permit system growth and morphogenesis. It is the paradigm for systems evolution: for the emergence of global, causal complexities from local chance simplicities - for bottom-up evolution based on hierarchies of increasing sophistication, themselves engaged in continual feedback, catastrophes and transient stability's. For Phi behaviour then, chance and causality, Chaos and Cosmos (the Greek for order), are in the tension of a dynamical equilibrium; an equilibrium that creates the unexpected and the emergent, which with each symmetry-broken hierarchy, yields transient morphologies of often increased complexity.

The Golden Mean therefore represents absolute global deterministic order, as an iterated period-doubling (bifurcating/symmetry-breaking) system, but over time, also allows for local, stochastic Chaos, chaos which can, when the system is far enough from equilibrium ( as a fractal, self-similar "ghost" copy of the initial condition - the very non equilibrium Big Bang), also create.

Since the passage from one to the other is governed by the second law of thermodynamics, responsible for irreversible processes (beyond the reversible and linear quantum world), this also makes Phi behaviour the optimum operator for both linear reversibility and non-linear irreversibility. For a system to reach and maintain maximum complexity as entropy increases, (something which is progressively harder when scaling up from the linear, reversible quantum world), the optimal way to avoid ever-increasing resonances (interference) and instabilities, is to preserve a Mean minimum-entropy trajectory. The Golden Mean in effect, allows an infinite fractal (the Cantor Set mentioned earlier) to tap the creativity of Chaos, for the use of order, an order which is entirely for free, (except for entropy-tax!), making us both part of an implicate unfolding - as well as the result of an explicate vicissitude of the cosmological casino. This transaction occurs where the algorithmic complexity of a system is maximised, on the edge of Chaos; so, if maximum Complexity is (to use a surfing analogy), the board which surfs the wave of inexorable entropy increase, then the Mean is the (least-action) optimum, most elegant and energy-minimising path along the face of that wave.

Various cellular automata ( heuristic pixel matrix) simulations also may confirm Phi's system structure-enhancing evolutionary action, to the point of researchers seeing this binary-switching behaviour as an inevitable target for natural selection. Stuart Kaufmann, biologist and computer scientist at the Santa Fé Institute, in promoting his view that Complexity explains evolution as a relationship between selection and self-organisation; and the order in the genome and the emergence of life itself; cites binary arrays displaying apparent period two behaviour as those allowing "broad boulevards of possibilities - rather than back alleys of thermodynamic improbability."

Kaufmann's CA's place the regions of maximum complexity, islands of stable pixels surrounded by chaotic switching ones ("frozen cores" in his terminology), firmly in the self-organised critical/edge region. This behaviour, used to (accurately) predict genotypes for organisms of different complexity, results when his arrays are linked together in which each pixel responds to the input from two others, but no more or less - (less produces stasis, more increasing chaos).This period two-analogous behaviour, in what he calls his Boolean NK nets, shows Phi in action yet again: this time, in silica - as well as in the vivo of reality. His work extends to whole ecosystems, and includes the realms of fitness landscapes and simulated annealing, where robust, energy-minimising (fitness enhancing) strategies are all revealing deep links between ecology and economics.

The same can be said for various investigations into plasma and quantum-scattering physics, pure maths of dynamical systems, fractal dimension, and ecosystem simulations --- to name a few. All cite Phi-behaviour as an invariant attractor behaving in some or all of the ways described above. (Please consult the bibliography references.)

The physicist Per Bak models Self-Organised Criticality, a term he coined: in these simulations he observes reciprocal squaring, power-law behaviour. This law is ubiquitous in nature, whether it is sand-pile avalanches, earthquake intensity over frequency, neurone firing patterns during consciousness, stock market behaviour, or the previously mentioned celestial, Black Hole pyrotechnics. (This is the remarkable feature of Complexity incidentally, that the hitherto unrelated: the inert and animate, natural and human-metabolic or cultural phenomena, all seem subject to the emerging new paradigm of criticality on the edge - all are linked in a new universal rubric.) This behaviour is also self-similar at all scales, and is reputed to display energy-minimising behaviour as it gravitates towards edge of Chaos criticality, and so it seems reasonable to intuit it to be another manifestation of Golden Mean dynamical behaviour.

Chris Langton, also of the Santa Fé Institute, dedicated exclusively to Complexity research, likens order to a solid (like ice), disorder to a gas (steam), and believes a liquid (water) form of Complexity occupies a phase transition region between the two. The Institute is essentially exploring this region first popularised as the edge of Chaos by Langton, by means of various computer simulations, looking for a putative new formulation of the second law of thermodynamics, (a search this review is commenting upon, but also hopefully contributing to!). What the Institute finds is that the liquid/phase transition region behaviours are the most complex, the most stable under perturbation, display non-local (global) behaviours, and are capable of universal computation - with extended, transient entities emerging spontaneously from them that inevitably, because of their qualities, have been dubbed "artificial life". Since life is the most complex known feedback-led process in the Universe, and consciousness the apotheosis of these processes: the simulations of artificial life could be extremely promising in promoting our understanding of how such global complexities can emerge from local simplicities.

Once again, non-locality is a proven riddle of the quantum world (paired particles behave as if in instantaneous communication - a violation of the speed limit of light); and additionally, the phase transition is integral to inflationary theories of the symmetry-breaking expansion of the early Universe.

Langton cites the phase transition zone as that containing the most potential complexity for the entropy generated. This is because the cellular automata used then behave as undecidable universal Turing machines, as universal computational singularities, exactly replicating the Feigenbaum Point dynamics referred to above. We then are in the number theory realms of the NP problem and Chaitin's Omega. Considering the evidence above, it is likely that the Golden Mean will form a significant part of these explorations. This is because the Mean appears to be just that: an optimum oscillator in dynamic equilibrium between entropy increase (information transmission), and entropy decrease (information storage), thereby sustaining maximum complexity in a computation, over time. In terms of coin-tossing behaviour (50/50 stochastic binary-switching), Omega appears to be analogous to Mean dynamics at the Feigenbaum point: and potential further evidence that for this case, NP-complete problems are intractable, universal Turing machine halting is undecidable, algorithmic complexity is non-computable, and of course, that this situation conforms to Gödel's incompleteness theorem.

Number theory therefore also confirms the Golden Mean to be on the very cusp of Chaos, but also the quantum, via Reimann's zeta function, in quantum scattering..

Essentially, all these results point to the inherent limitation that to be self-consistent, mathematics must admit the random - that not all unproved statements are provably unprovable ("All Cretans are liars", spoken by Epiminedes, a Cretan). Sometimes a statement is too complex and reflexive to be proven - one falls prey to tautology and paradox. Nature is subtle - but not malicious, to paraphrase Einstein. (Who told Corbusier that his Modular, based on the Mean, "made a difficult job more easy"!) Causality must admit, dance with, court, marry and (pro)create with chance.

Local chance events underlie and create our apparent reality in the most fundamental of ways, and yet they paradoxically are the basis for the global causality we see all about us. For Prigogine, the true nature of reality, the new paradigm - is the best of both worlds: somewhere in dynamic equilibrium between. Pure Newtonian causality is an incorrect (finite) view, but then again, so is the aspect of complete uncertainty and (infinite) chance: our world is a dynamic synthesis of the two.

The edge of Chaos region is therefore the most globally stable (remember, the cellular automata reveal structures known as extended transients in this phase-transition zone), but it is also the most locally creative. Phi resides in this optimum boundary zone: between the causality of the bifurcation branches, and the chance of the bifurcation points themselves: between the result of the coin-toss and the initial toss itself. In terms of Phi-Julia Set behaviour, its super-attractive (global) orbit is optimally stable because it is mediating between those two optimally unstable (local) repelling fixed points.

This local energy-minimising behaviour, when applied to the arbitrarily large numbers of shift-operations implicit within say, the complex neural and metabolic processes of individual organisms - allows global stability to be maintained in the face of an environment in constant flux. This stability has just enough creativity in it to deal adaptively with new situations. This might be on the scale of an individual organism such as an Echidna, or its staple prey, an ant colony. A flux between order and randomness, with not too much of either extreme, is the key to any act of both evolutionary adaptivity and/or homeostasis.

Consciousness itself might well be a form of optimal, adaptive information processing, a learning, fluid homeostasis of neurone-firing, one which has been theorised in the Institute's journal, titled "Artificial Life", (and endorsed by Roger Penrose), to be further based on the quantum switching of single electrons on dimer "switches" located like CA pixels on microtubules, filamentous structures that are purported to be the nervous systems of individual cells. Such CA simulations display edge of Chaos extended transient, glider and other complex (specifically, Wolfram: Type Four quasi-periodic/Conway: Game of Life) behaviour typical of the other cellular automata simulations listed above.

It seems clear now that the Golden Mean can certainly be reconciled with the new science, which reveals a profound dynamical aspect to its action. The Mean can be found to mathematically describe the behaviour of nature in at least three major idealised models.

Firstly, the final Phi-stability of quasi-periodic KAM tori, just prior to collapse into chaos.

Secondly, the universal behaviours, Phi-Cantor set at the Feigenbaum point and constant scaling relationships of the period-doubling Feigenbaum diagram.


Thirdly, the most complex, liquid/phase transition region of cellular automata behaviours, displaying quasiperiodic, period two and therefore, Phi extended-transient structures.

All locate the Mean as the route to, and on the edge of, Chaos, in the realm of maximum complexity - as exchanged for minimal energy waste, or entropy production.

The Mandelbrot Set is the geometric icon that links all three in a lapidary, metaphorical, almost mandala-like sense, but that is itself, also generated by equations that tell the same story.

Number theory is saying that this is the ultimate, deep message contained in all self-consistent logical structures, in the relationship of relationships (as mathematics has also been poetically called), causality and chance - dance on the cusp, creating the increasingly complex in their wake.

So we now also know that causality and chance, Cosmos and Chaos if you prefer, do not waste precious energy/mass (it is minimised), symmetry (it is broken), dimensions (three spatial dimensions are the liquid/complex region in random walks: less, and not much interesting happens - more, and you get hopelessly lost), nor time (it too, breaks directional symmetry above the wave-function collapse (lowering its energy) - and is linked with the three spatial dimensions in geodesic curves that express energy/mass as the weakest known force - gravity) .

Without prolonging this review excessively, here are some brief examples of how the assimilation of this new knowledge of dynamical systems, married with new environmental and structural engineering, plus materials and information technologies, might reinvent the statics of architecture (without simply resorting entirely to static proportional applications of the Golden Mean, which are always distorted by the fractal scaling of perspective anyway, or to pastiching past aesthetics):

The first emergent feedback-led application is in the design process itself; the form(al cause) of a building being the result of the consultative process and the cultural milieu that informed it. If this process fully involves the user and all other concerned parties, and takes full note of all the brief and site constraints and histories; a democracy of rich mutual feedback will result. The problem papillon of sensitive dependence will hopefully sleep. The architect can then act as mediator, co-ordinator and (auto)catalyst for the emergent, complex form that arises, which appropriately should epitomise the "final cause" of least action in being the optimum artefact for its role, (and also by being energy-efficient, where possible). Speaking metaphorically, one could say that the architect in this light, almost personifies the optimising imperative of Phi - as generator of information, in their role in the design and production process.

Climate control will increasingly become a hybrid of feedback between active elements, such as mechanical HVAC, and the passive, such as natural ventilation. Low-tech, vernacular-inspired strategies for climate control, such as the atrium, fused with the higher technology of computerised brise soliel solar-gain louvres with integrated photovoltaics, for example, are already in use.

The future is dynamic, adaptive green building.

Stack-effect, evaporative cooling, cross ventilation, solar chimneys, wind towers, buffer zones in the multiple skins of building facades, plant biomass evapo-transpiration (also enhancing homeostasis of oxygen/CO2, expressing seasonal variations - and their own fractal structures), and even aerodynamics - are some of the hybrid strategies currently in use. (Note here that the Lorenz attractor, related to the Rössler attractor, is a model of thermal convection flows - and therefore directly applicable to passive climate control design on a micro-climatic scale.) All are systems (or functions) leading a potential emergent form.

A facade incorporating electrochromic glass that is linked into a CPU hosting a parallel-processing neural network can instantaneously regulate solar gain by adjusting facade opaqueness, depending on it's orientation. That network can also minimise overall building energy load by only lighting, ventilating, heating or cooling occupied spaces. Such systems may display a form of metabolic homeostasis known in artificial intelligence circles as again, emergence; allowing for simple system-memory and learning capacities. This has everything to do with emergent, recursive feedback loops being employed in environmental service design. Clearly, dynamics can synthesise with statics. The relevant question is one of the appropriate level of automation, of the dynamics, the type, and how they impinge on the static form of the building. Polyvalent facades will, using liquid crystal technologies (glass is made from silica --- as is the LCD and the silicon chip) convey graphic information on the skins of buildings for the external world to observe, or regulate their transparency for privacy considerations. Chameleon buildings will for example, be able to react to passing clouds, altering facade U-values and those for solar gain, to compensate for those clouds, or the tracking shadows cast on them by neighbouring buildings. Smart and composite materials that might change shape, rigidity, porosity, texture or colour - and later nanotechnologies, will completely transform the abilities of buildings to adapt to their internal and external environments, developing cladding more like the skins of organisms than ever before. The pixel-like elements of a facade might then communicate ambiently with themselves or with others in the manner of some cellular automata, sometimes arriving at criticality, at edgeof Chaos levels of complexity, appearing to reflect the state of "mind" or "mood" of the building, feeding back continually with internal/external stimuli. A similar ambient music real-time soundscape might therefore truly "melt" the "Frozen Music" of architecture: defining an individual building as a musical instrument itself, as played by its environment. Music is a form of power law 1/f noise, so it too inhabits the region poised between order and disorder - and perhaps might then be more properly termed "Liquid Architecture".

Intelligent agents imbedded in the electronics of a buiding and its contents, will become another ambience that fills inhabited work and living space with continual feedback, making the experience of that space become a form of customised, cybernetic extension of the consciousness of the users.

A major design constraint (and therefore, opportunity) for passive climate control is that strategies and final design solutions must adapt to the local climates (and therefore inevitably, the cultural readings) of sites: hence the earlier use of the term "Vernacular", as a methodology, (but not an aesthetic of pastiche), of Complexity, as applied to an autocatalytic architecture, that conveys thematic and structural analogy (self-similarity, or reflecting this in society as a whole), and thermodynamic (historical) depth.

However, vernacular buildings saved energy (and were generally not profligate with materials nor structure), so as to create a sustainable living and working environment. They were appropriate, creating a symbolic rubric of available materials and forms connoting a cultural response to a particular environment. The vernacular was emergent, bottom-up, distributed and parallel, hence its veracity. It conveyed an irreducible order: making the whole greater than the sum of the parts, a gestalt in effect. A combination of the bottom-up and the top-down,( the imposed solution based on the personal visions of client, planners and architect), would therefore, seem the right combination for most contemporary urban environments.

Any architecture that minimises local (and therefore global) entropy-production (information and energy waste), by fusing passive/active strategies to optimise energy load; in exchange for optimised emergent complexity (or contradiction!), be it fractal detail for the eye at different scales, or minimum structure for maximum strength - or opposing tensile with compressive elements, the dynamic against the static; will be more likely to succeed in its purpose. It will form a better cultural response, a more apt metaphor for our understanding of reality; surely the ultimate goal of all art and science - (both of) which architecture should ideally, epitomise.

It must be stressed that this is not an appeal for the strict imitation of the vernacular but rather a recognition that just as in the past, differering climates and cultures should naturally produce different design solutions, and produce distinctive, discrete "bioclimatic" architecture appropriate to their climatic and cultural environment. This produces a distinct, profound regional identity and variety for architectural form and material throughout the world, as we are already seeing.

The Modern Movement's main failure was that it became a metaphor for the hubris of the Newtonian mechanistic paradigm. It imposed an anonymous, excessively top-down homogeneity worldwide (the International Style is also the most internationally loathed). It ignored global vernacular architectural diversity of cultural response; to a plethora of environmental constraints --- and so identity was forbidden for the Machine Age. How then do we transcend this failure --- and restore identification (which is a form of empathic self-similarity)? What this investigation of the dynamics of the Golden Mean tells us is that it is an analogical, optimum mathematical paragon of energy efficiency: and that this is achieved as an ultimate means of generating the maximum complexity of information structures of energy and matter, at the lowest energy cost. Rather than merely imitating the statics of proportions, we are now also liberated to epitomise the Mean through elegance of: structure (the bearing of dynamic forces), efficiency of organisation, gestalt, contrast, congruity thematic/contextual resonance, reflexiveness, irony - and the economies of vernacular-informed green architecture.

This is the methodological genius loci of Complexity; of emergence, of celebrating diversity and contextual veracity over homogenised anomie, of the rational pursuit of the irrational, of applying engineering elegance and efficiency as the proper syntheses of the dynamics of function with the statics of form. The role of architect is to catalyse the emergent form of a building or a website (or any virtual entity) from a possibility-space that yields the optimal complexity (or algorithmic depth, if you like), required for that particular project. Because the constraints generating that complexity can be wildly divergent (just like symmetry-breaking and instabilities far from equilibrium), this can be a challenge, to say the least, analogous to that of reconciling art with science.

Architects have to relate the the most divergent of constraints, from applied science and physics/ engineering to conceptual art, from mathematics to colour theory and psychology; from adminstration to surveying to law, from projective geometry and computer science to graphic design, to name a few. This also makes producing truly great architecture one of the hardest tasks in the world. The fact is, the accuracy and iterative power of computers have allowed us to reveal the true, vastly rich temporal structure of dynamical systems - making this site possible, but they have also brought the two cultures of art and science closer together - back towards perhaps, Renaissance (if not Pythagorean!) levels, where both again use the same language of geometry and the conceptual. Both now construct simulations and simulacra, both map nets of knowledge, and create models, or archetypes of reality. Intellectually, it is therefore perhaps fertile ground again for architects: for the practitioners of projected spatio/temporal geometries, to also engage in the semiotics of geometry and concept, in terms of that reconciliation of the two cultures.

Complexity makes this more possible because less is lost in translation: the two languages (of the two cultures), are being synthesised, through an increasingly shared use of the commom languages of geometry and analogy. Complexity synthesises the sciences, be they physics, chemistry, biology, ecology or economics, history, politics or cultural studies, physical or life science, "hard" or "soft." It does this by using mathematical models (with parameters partially based on intuition), as a codified geometry - so simulating and testing archetypal models of natural systems rather than actually experimenting on the systems themselves (because of their high complexity). This has brought science far closer to the intuitive, conceptual and visual language of art than ever before in modern history. So architects can (at least intellectually), find that less will be lost in their translations between the two cultures.

A work of art is deemed beautiful if it possesses gestalt, is seen as more than the sum of its parts, if it is conceptually analogous and/or physically fractal.

Science tells us the world is poised in an analogical self-organised critical state, with fractal spatio-temporal structure. This knowledge system itself has the same structure.

Both conditions are found in the basin of attraction at Chaos's cusp.

A functioning, built work of architecture can also be seen as a dissipative, open system just like an organism: which has a limited lifespan, which consumes (for example), low entropy electricity to produce high entropy heat, as an act of metabolism. The less entopy produced, the less energy wasted. This can be achieved by an apt mix of technologies and materials (low or high tech/spec), for the local benefit of the immediate users, but also for that of the global environment. Since the energy servicing of buildings (especially heating, cooling, ventilation and lighting), produces 50 per cent of all greenhouse gases - these issues are not trivial, and will with time, become unfortunately, even less so.

The sciences of complex dynamical systems show how appropriate it is to perceive our age as one of information: one which increasingly exists to exchange and enhance pure information to higher levels of complexity at minimal expense (recall the global internet itself, priced at local phone rates), just as the irreversibility-driven evolution imperative of the Universe and of life itself demonstrates. Architecture, as a cultural artefact that inevitably will be imbued with the current zeitgeist, should assimilate as much of the implications of Phi/Chaos dynamical symmetry; as its procurers, practitioners and pedagogues will allow. We have the opportunity to (re)present the Golden Mean to architecture and society in entirely novel ways, beyond Pythagorean pentagrams and pentagons, geometric analyses of the Great Pyramid or the Parthenon, or Euclid and his geometries, or Fibonacci, Alberti and his Florentine churches, or Piero della Francesca or Kepler and Platonic planetary orbital ratios, Cook and plant phylotaxis, or Hambridge and his dynamic symmetry, Le Corbusier and his scheme to replace both imperial and metric systems with his Modular, Cartier-Bresson with his "decisive moments"and classical composition of his reportage photographs; beyond statics and state, but rather via dynamics and process (as Cartier-Bresson intuits): as tension, as paradox, as a dynamical unity of opposites (finite and infinite), fusing the linear with the non-linear, the ordered with the random - and causality with chance, to create the emergent and unexpected.

This is the (ana)Logos of Heraclitis of Ephesus, or the Tao of Lao Tsu. These concepts seem to be part of a universal global archetype, in the Jungian sense, to have been already intuited separately by other cultures, at earlier times.

More pertinently, James Lovelock's Gaia hypothesis, (where the biosphere of the planet itself is self-organised), is a paradigm for a truly global homeostasis based on Complexity, where the whole planet is posited to minimise its entropy-production at the edge of Chaos, (fixing gas proportions at non equilibrium levels suitable for life, for example), because of the cellular automata-like action of the biosphere.

We have a duty to future generations to learn from Gaia-esque concepts; to preserve humanity, its cultures, and the global ecosystem (and their respective diversities), to live by the maxim of sustainability, which is to: "not make the world a worse place for our children by our current actions or inactions". We have a moral responsibilty of course, but also one based on preserving the complexity and diversity of the only known seat of intelligent life in this Universe. We and our world are like the Mandelbrot Set: the most complex and diverse known entities in existence. The Golden Mean, because of its supreme economy, elegance and capacity for analogy, because it resides where it does in dynamical systems behaviours such as within the biosphere, is therefore also the ultimate metaphor for sustainability. Etymologically speaking, the architect is a "fabricator of archetypes"; these ideas and issues as discussed above are as profound as they are pressing. If we are to mitigate our worst ecological excesses (in better understanding and replicating nature, we can better preserve it), or to create better examples of criticality: metaphors and analogies of reality (with these archetypes), we must assimilate the lessons of the sciences of Complexity, for they are the laws and emergent properties of nature itself.

Suffice to say, maximum Complexity is found via self-organised criticality at the edge of Chaos, which is epitomised by the Golden Mean, as the emergent geometric manifestation of the principle of least action: therefore its full temporal/ spatial action is analogous to creation itself.

Email: Nigel Reading <>

here in another link.. could perfect (phi-lotactic) branching - Priori de SCION, be the Grail?

A Tree Builder

The program parse_tree produces many of the files necessary to build a tree simulation. The program takes as input a file containing a one line description for each branch: the branch's number, the parent branch that this branch sprouts from, the parent branch's length, the branch's length, the branch's diameter, the branch's orientation in terms of deviation and phylotaxis, and a flag that indicates that branch has leaves. Three source files comprise the output of the tree builder: create_realtree.c, control.c, description.h.

The first file, create_realtree.c, is a Creature Library description of the input tree. This file contains the link-level description of the tree and the materials it is made of. As the lines are read in one by one the branch described is created and attached to its parent's endpoint with an appropriate (Z axis followed by X axis) universal joint.

The file control.c contains the recursive routine that determines the appropriate spring and damping constants for each branch. The procedure climbs the tree from trunk to tip and then, on its way back down, determines the appropriate constants. In this way when constants are determined for a branch the characteristics of all the descendant branches are known and can be taken into account when constants are determined. This is important for insuring that branches supporting many children are strong enough. ......

Inset from dan winter, in the following consider the mechanism of Heart Bliss sonics (phonons) programming DNA & cells....

Biosystems Liquid Crystals & Potential Effects of Natural & Artificial Electromagnetic Fields (EMFs)

James B. Beal, EMF Interface Consulting (whom we forgive for putting too much salt in the cornbread at my farm)....


It is proposed that the origins of terrestrial biological life may have required (1) the presence of EMF flux of different waveforms and intensities, and (2) the prevalence and interaction, within the living cell, of a variety of biological liquid crystal (LC) forms which provide fundamental support and/or detection mechanisms to explain quantum-level sensitivity. The lipid molecules of biological membranes exist in an LC state and provide a matrix for membrane proteins to perform their function. Not only lipids, but other major classes of compounds (proteins, carbohydrates and nucleic acids) exist in LC phases under well-defined conditions. Therefore, it is very important to know the properties of LC materials in order to better understand biological processes. How did liquid crystals and the EMF relationship originate? The planetary resonator hypothesis and wave interaction as a key determinant of biological structure (EMF flux as an information field) are two hypotheses proposing the evolution of an ultra-sensitive protein (LC) transceiver biocommunications mechanism for ELF (extremely low frequency) EMFs. Precambrian earth may have supplied the intense fields as environmental factors and catalytic energy sources for the beginning and evolution of living systems. Biosystem effects from received EMFs, natural and artificial, will be briefly discussed, e.g., survival information from geomagnetic cues (location/migration, seasonal variations, hurricanes, tornadoes, earthquakes); detection of food, enemies, and mates; electrosensitive humans; immune system enhancement or suppression, visual and hearing inputs, anesthesia, and healing,. Natural EMFs associated with and transitted from biosystems also provide survival factors in defense, attracting food and mates, and establishing territory. Intriguing and controversial anomalous human electrical and electronic equipment interactions reported in recent years will be briefly discussed and data presented about how reacting allergy patients, persons in intense emotional states, and those experiencing sudden personal stress level shifts sometimes affect computers, photoelectric devices and other sensitive electronic threshold devices!

(followed by excellent bibliographic citations list...)

Subject: coherence in matter, Sun, 20 Feb 2000, "James Barrett" <> Dan this book / review might be of interest.

The Roots of Cosmic Wholeness are in Quantum Theory

A review of the book, QED Coherence in Matter, by Giuliano Preparata, Singapore: World Scientific, 1995

Emilio Del Giudice, Istituto Nazionale fisica Nucleare, Sezione Milano, Via Celoria, 16, 20133 Milano, Italy,

Classical physics, born from the work of Galileo, Newton, Lagrange, Euler, Laplace and many other scientists of the 17th and 18th centuries, is
consistent with a vision where the universe is an assembly of separate objects, basically "individuals" interacting through forces that act on each
object from outside, modifying their trajectory. The universe then appears as a mechanical engine, where each component is "perturbed" from its
solitude, from its solitary inertial trajectory by external forces propagating through a neutral medium--empty space or the pre-Einsteinian ether. In
this view the vacuum is essentially nothingness, and "being" arises from the trajectories of individual bodies mutually coupled by "forces."

The relativistic revolution of this century has rejected the reciprocal independence of matter and medium; ether or space cannot be construed as a
vessel, a mere container of bodies. However, the physical universe still appeared deprived of that property that normal experience maintains as
fundamental, the "oneness". How does the wholeness, the physical object, even the universe emerge from the huge mob of individual components,
each one minding its own business? It has been frequently suggested that "oneness" could be achieved through the conceptual subtleties and
mysteries of quantum theory. This expectation seems at first quite peculiar, since in the orthodox Copenhagen interpretation it appears at odds
with the hard fact that quantum theory predicts sharply defined energy levels in atoms, and also deterministic global behaviours in macroscopic
quantum systems such as superconductors and superfluids. For instance, contrary to the Copenhagen interpretation, David Bohm has stressed the
cosmic nature of quantum theory, where the wave function appears as the effect of the interaction of the physical object with a cosmic field, which
endows it with a phase. However, so far no consistent quantum theory of the macroscopic world has been produced, showing how the coherent
performance of a macroscopic body
, such as a scrap of a ferromagnet, a glass of water, or the wing of an airplane emerges from the workings of a
huge plethora of microscopic components, each one subjected to its own wave function. All the existing "theories" of macroscopic matter plainly
assume that macroscopic matter exists, and go on to describe its fluctuations from the assumed fundamental state. Nobody has yet been able to
explain how an airplane wing can remain rigid on a span of tens of metres, based on a microscopic picture where only neighbouring atoms attract
directly, and where the long range connection is obtained through a long string of beads, atoms linked by nearest neighbor interactions. But a loose
chain becomes rigid only when the first and the last atoms of the chain are able to attract directly, without fluctuating mediators!

A real breakthrough in the understanding of the quantum dynamics of the emergence of the "oneness," of a coherent performance of a multitude of individual atoms that, in so doing, become a macroscopic object, is the subject of this book. Reader of this book will be impressed to know that a completely new vision of macroscopic matter is obtained without introducing any new principle, any post-quantum principle, or any new
microscopic fundamental assumption. The work of Preparata, in this respect, is totally orthodox and conservative. The book addresses ordinary
quantum electrodynamics (QED) as in textbooks formulated by Tomonaga, Feynman, Schwinger and others. No unorthodox electrodynamics is
used. Firmly rooted in solid physics, Preparata makes a giant leap forward by fully exploiting the potentialities of quantum theory to understand
how "oneness" is generated. In this view, the quantum fluctuation does not appear as merely the root of unpredictability or of causality breaking, but
as a means of matter exploring its surroundings. Through their quantum fluctuations, objects discover the configurations where the energy is
minimum and, thus, where they might settle indefinitely. A particularly interesting object is the long range "gauge field" such as the electromagnetic
field. In this case its fluctuations span a distance--the mode wavelength--which could include many microscopic matter components (atoms,
electrons, etc.) whose fluctuations are, as a consequence, tuned together. This is the basis of the onset of coherence in matter.

Let us start from an assembly of N molecules in a volume V in empty space, where the electromagnetic (EM) field oscillates around zero (zero point
oscillations). Suppose that the molecules can assume two configurations whose energy difference is E. The EM fluctuation whose energy is E is able
to raise a molecule from the lower to the higher energy configuration. This EM fluctuation would span a volume whose diameter is the wavelength,
which defines the "coherence domain" of the system. All the molecules in the "coherence domain" are equally affected by the fluctuation. Given the
usual range of values of E in molecules, values of EM fluctuations in the micrometer range can result, so that in ordinary condensed matter, the
numbers of molecules affected, N, could be a really large number. A photon of the fluctuation can excite a molecule, which then releases a photon
as it relaxes back to the ground state, which is in turn excites a second molecule, and so on.

During the fluctuation a number of molecules oscillates between the two configurations producing a current that couples with the EM field, giving
rise to an interaction energy which is negative. So the total energy of the fluctuation is the sum of three terms: (1) the positive energy of the EM
fluctuation field, (2) the positive energy of the excited molecules, and (3) the negative energy of the interaction. It can be shown that the first and
second terms are proportional to N, whereas the third is proportional to N (exp 3/2). So there exists a critical number of molecules in the "coherence
domain" such that the total energy of the fluctuation is zero, thus making the fluctuation stable. We get then a phase transition. In order to gain
energy, the system increases its density as much as it can, by squeezing molecules until their mutual distance matches the sum of the hard core radii.
In this process of condensation, individual molecules change their structure, since they are no longer in the lowest energy individual state, but
oscillate between the lower and higher energy configurations in tune with the EM field. Individual molecules, when probed in the coherent state,
exhibit a different structure and organization than when they are probed as isolated molecules. This fact wipes out the tenets of the Asymptotic
Freedom of the elementary components, a dogmatic rule in contemporary mainstream physics, which states that when probed at its own scale a
component appears always the same, as if it were free. Moreover, in the condensed state the components lose their individuality, since, at least for the
degrees of freedom involved in the oscillation, they are compelled to move in unison, so that coherence is not the result of an external pumping or
of leaving equilibrium, as expected from conventional laser physics. Instead, coherence in matter is the spontaneous outcome of energy
. (inset here from dan winter: Definition of PHILOTAXIS: "Maximum Exposure / Minimum Superposition" is this PHASE symmetry the key????) Coherence does not require work, but is stable and occurs at equilibrium!

The above scenario describes how a collection of molecules, with the help of the quantum fluctuations of the EM field, become an extended object,
tightly knit and having its own "oneness." Matter is therefore not an loose confederation of molecules, but a specific macroscopic object. An
additional molecule coming from the outside does not encounter an ensemble of molecules, but a medium, which could now be regarded as a
continuum of the old-fashioned classical physics. At non-vanishing temperatures, thermal fluctuations are able to extract a fraction of molecules
from the coherent state, so that normal condensed matter could be regarded as a two-phase system: a coherent phase that guarantees the "oneness" of the system, and a incoherent phase that accounts for the entropy and, more generally, the thermodynamics of the system.

Whereas the physical principle described in the book shows how the "one" is obtained from the "many," the same principle also leads us to the
"many" starting from the "one." The understanding of the physical dynamics of condensation allows the deciphering of a mountain of seemingly
complex and thorny data about a wide range of condensed matter systems. From superfluids to superconductors, from ferromagnets to liquids, from
crystals to plasmas, no physical system is able any longer to keep its own secret and remain silent like Sherazade did when the most telling part of
the story was being asked! In this sense each chapter of the book could grow into yet another book.

The reader will find that the study of each condensed matter system is totally rewritten from this new perspective. Mainstream explanations are
turned "upside down," putting them in the place of "descriptions" that interchange cause and effect. An example is that the hydrogen bonds among
water molecules are not the cause of their molecular interactions, since the protuberances of the electron molecular clouds do not exist in the
isolated molecules. Hydrogen bonds are instead seen as the effects of coherent dynamics in liquid water, which reshuffles the electron clouds
producing the protuberances.

Within this new vision, results considered by mainstream physics as "mistakes" or "anomalies," because they cannot be explained from the
conventional framework, acquire a rational explanation. Two chapters of the book are devoted to the physics of Joe Weber and to cold fusion
respectively. Joe Weber, a pioneer in many research areas, the discoverer of the MASER and of gravitational antennas, has stressed that very weak
probes-- gravitational waves, neutrinos--might be easily detected, should the solid state be a coherent medium, as suggested by the existence of the
Moessbauer effect. Why should a crystal recoil as a whole by emitting a gamma ray and, on the contrary, why should it appear as a loose cluster of
atoms to an incoming neutrino? The electrodynamical coherence puts actually both Moessbauer and Weber on the same solid ground. It is now
possible to dream of a network of coherent spin lattices able to code and decode beams of neutrinos as a novel basis for telecommunications.

Cold fusion, too, gets a full theoretical account in the book from this new framework and, moreover, the possibility of further advances is indicated.
Nuclear fusion, occurring within a coherent ensemble of deuterons oscillating in a space where a coherent ensemble of electrons screens the mutual
Coulomb repulsion among deuterons, follows different laws than nuclear fusion in empty space. The coherent ensemble of electrons, and thus the
crystal, takes out in the form of heat the energy released by fusing deuterons. Deuterons fuse into helium-4 that is unable to decay since the excess
energy of fusion, in the form of an EM field of gamma ray frequency, is transferred to the coherent ensemble of electrons in a time shorter than the
decay time of the excited helium nucleus in "vacuo."

Last, but not least, a new perspective for nuclear physics also emerges.

Suppose that, in the QED scheme, one replaces photons with pions and the fundamental and excited states of atoms with nucleons and resonances.
Then one gets a coherent nuclear matter dynamics, whose "coherence domains" have a size of about 4 fermis, which, at normal nuclear density,
include 50-60 nucleons. That is a solid basis for the successful, but hitherto unexplained, "shell model" of the nucleus. Many nuclear puzzles find in
this scheme an explanation.

These are some only of the physical problems addressed in this very dense book. It should also be mentioned that biology could also be addressed
from this new perspective. As Herbert Froehlich has stressed so forcefully in his research, the living state is one of coherence. Understanding that
will bring to the life sciences a whole new perspective and possibly new medical applications as well.

comment from Dan Winter: getting so close here, admitting that {wave} COHERENCE both creates matter AND life force, now if they could only mention "'MASSIVE' coherence never sustains except in the presence of the (phi...lotactic) wave geometry of perfect embedding/recursion".... Sustaining phase coherence requires recursive adding and multiplying heterodyning... This fractal principle creates 'centers' of gravity/ the monopole and implosion/wave collapse in general. (non destructive or 'cold' fusion).

Visualize this simply: matter occurs when waves phase lock themselves into the circular, which rotation IS - INERTIA storage (our ONLY definition/measure for mass as physicists). (A gyroscope is no more distinguishable from MASS itself, than acceleration is distinguishable from gravity).

Only PHI RECURSION IMPLOSION 'centering force' keeps the light waves re-curring/'bending' (gyroscopically stablized in one place) into the e-mc^2, rotation. (Perfect compression animation at top). (The term gravity has little meaning until it is understood as the "G" -circle arc/met line- "ray" of "vita" - Genesis of Life force...). (So e=mc^2 is trivial until G=C^log n*phi, ../predictions )

Hence we say, with strictly accurate physics..

"Only love (choosing to embed by long wave phi {lo-phi}ratio) bends the light.. therefore only love creates".