Fractals: Fingerprints of God

[Gauracandra]

 

"Mathematics is the language with which God has written the universe." - Einstein

 

Fractals, chaos theory and complexity have provided a new way of looking at the universe. These components of a "new science" appear to provide fresh insights into our reality and the interconnedtedness of that reality. They also appear to be very much about that place where art and science intersect.

 

But what are they; what do they tell us about how that reality works; or are they just mathematical mind games? Some of the philosophical questions have been expressed by mathematician Brian Evans in the notes to the 1995 Fractal Calendar (Universe Publishing):

 

"With the help of a computer, mathematical processes are translated into sensory experiences. Is the realization a glimpse of reality; the apprehension of "truth"? Or is it simply a human-derived diversion? When we view the beautiful images of mathematical formulae, are we looking at something that, in some mathematical way, exists? Or is the mathematics describing nothing more than an intellectual construct, and the images simply pretty?... If the universe is ordered, how was that order created? If not, why is is possible to define, predict and discover so much of our reality with the logic and structure of mathematics?"

 

The Ultimate Paradigm Shift

 

The rapidly accelerating discoveries of Chaos are overtaking our worldview. They teach us that Newton, and indeed almost all of the pre-chaos scientists, were dead wrong in their basic view of the Universe. They thought that there was a predictable cause and effect for everything, and that everything happened according to fixed physical laws. They believed in certainties, not probabilities. Their fundamental image of the Universe was a big clock. The presence of a divine being was only necessary to make the clock and wind it up. After He created the Universe, all God had to do was sit back and watch. The laws would operate in a predictable causal fashion.

 

Old science actually used to think that if you only knew all of the initial conditions, how the clock worked, you could predict what would happen at any point in time. Science assumed that everything could be known and eventually predicted. The Universe was ruled by a detailed system of unchanging laws. Cosmos and causality reigned supreme. There was no room for chaos and so it was conveniently swept under the rug. The inevitable outcome of the ordered machine view was the complete winding down of the clock, the end of time in complete entropy - the second law of thermodynamics where everything tends to breakdown, to dissipate. This big picture of science naturally spawned the "God is dead" philosophies, nihilism, the life nausea of existentialism, behavioralism, communism and the like. Now with the Chaos theories this paradigm is itself dead. A whole new scientific view has been born, one much more in accord with an organic view, the common law, and philosophies of hope and spirit.

 

The cosmic clock image of establishment science first began to crumble at the turn of the century when physicists found that at the nuclear level the causal laws of physics didn't hold true. The behavior of the atom and individual electron could not be predicted. Still, even in the face of incontrovertible evidence of quantum physics, old ideas die hard. The static civil law mind set would not die easily. Even Einstein could not believe that God would play dice with the Universe. He searched in vain for a unified field theory that would explain away the chance and unpredictability so obvious in the subatomic world. Science struggled to maintain its centuries old view. The belief in a causal cosmos was now on shaky ground because it lacked a subatomic foundation. Still it prevailed because the rest of the world of physics seemed to follow linear, orderly and predictable clock like processes. Besides no one had articulated a different view to replace it. The subatomic world was considered an insignificant anomaly, an exception that proved the rule.

 

Then along came the Science of Chaos in the last part of this century to show that causality did not apply everywhere else as thought. In fact close measurements revealed that the unpredictable appeared in what was previously believed to be the most ordered and predictable of systems, the swinging of a simple pendulum - the very heart of a clock. As James Gleick's book Chaos shows the brave early explorers of Chaos found that Science had been fooling itself for centuries by ignoring tiny deviations in its data and experiments. If a number was slightly off what the causal laws predicted, the pre-chaos scientists simply assumed there was an error in measurement in order to uphold the sanctity of the law itself. In order to preserve their pseudo-cosmos, scientists limited their investigation to closed and artificial systems, avoiding the turbulence of open systems like the plague.

 

Causality was the prime assumption behind all pre-chaos science and it never occurred to anyone to question it. This conceptual bias created a blind spot of enormous proportions. But the reality of open systems, the Chaos lurking behind all order, would not be denied. The charade of perfect order and fudged experimental data could not last forever. By the nineteen seventies it began to crumble, the conceptual blinders were falling from the eyes of more and more scientists. By the nineteen eighties the fly in the ointment, the unpredictable results in what should have been perfect predictability, could no longer be denied. The Science of Chaos was born. Our understanding of the world will never be the same.

 

After nearly two decades now of work by Chaoticians made up of the leading scientists and mathematicians in a wide variety of fields, the evidence is overwhelming. The world is not a gigantic clock where everything happens in an ordered and predictable manner. The real world is fundamentally disordered, free. Chaos reigns over predictability. Simple, linear systems which are causal and predictable are the exception in the Universe, not the rule. Most of the Universe works in jumps, in a non-linear fashion that can not be exactly predicted. It is infinitely complex. Freedom and free will - the Strange Attractors - prevail over rules and determinacy.

 

Yet Chaos is no enemy and destroyer of Cosmos, for from out of Chaos a higher order always appears, but this order comes spontaneously and unpredictably. It is "self-organized." The creation of the Universe is an ongoing process, not just a one time event at the beginning. All and everything - and everyone - is part of this creative process. Over time all systems - from molecules, to life, to galactic clusters - are continually creating new organizations and patterns from out of featurelessness and chaos. The world is not a Clock, it is a Game, a Game of Chance and Choice. In the game random processes - chance and serendipity - allow room for free will, individuality and unpredictable creativity.

 

The Universe is governed by laws, but the laws are of a different kind than previously thought. Like the common law system, the Laws of Wisdom are inherently flexible. They are not written in stone, they are general. They leave infinite room for creativity within certain general parameters. A few fundamental principals exist to establish the parameters, but the Law governs much more loosely than previously thought. The Laws are subject to changes and modifications over time and depend upon the particular facts. Like the common law, the Laws of Nature appear to have flexibility; many things are decided on a case by case basis. Self organization is the rule, not the exception. Everything is not pre-determined by a rigid and complex system of detailed laws which specify exactly how everything works. There is no detailed blueprint of the universe, just a general set of Laws.

 

In the words of physicist Paul Davies in his book The Cosmic Blueprint (1988):

 

There is no detailed blueprint, only a set of laws with an inbuilt facility for making interesting things happen. The universe is free to create itself as it goes along. The general pattern of development is "predestined", but the details are not. Thus, the existence of intelligent life at some stage is inevitable; it is, so to speak, written into the laws of nature. But man as such is far from preordained.

 

The image of God playing dice with the Universe was threatening and fearful to the old scientists, even the great ones like Einstein, who incidently grew up in a civil law system. But that was only because they did not understand the order lurking in Chaos, the great beauty inherent in chance. For we now know that it is only through chance that new and unpredictable relationships can be created, entities can self organize to further evolution and create entirely new symmetries and coherence. With the image of the machine clock gone, the insights of relativity can finally be appreciated. Time is not mechanical, it depends on space. Time is flexible, essentially unpredictable from moment to moment, but this does not lead us hopelessly adrift. We can still navigate from the hidden order which appears over time, the statistics from segments of time, from iteration. The order implicit in Chaos is unpredictable on a case by case basis, but still reliable and workable on the long run.

 

God's dice liberates us from the prison of determinism, the hopeless tedium of the cosmic clock and the inevitable death of entropy. We have instead an intelligent Universe, where ever new and evolving life forms thrive on Chaos, where negentropy creates higher order from decaying forms. The clock is not winding down as the second law of thermodynamics had thought, it is ever being created anew. God is back in the picture, not just as the creator of the machine who then left - the ghost in the machine - but as the Strange Attractor, the origin of inexplicable and unpredictable order from chance.

 

This is a new kind of order, a "fractal order," based on a relatively few basic structural principals from which many transitory laws follow. The Laws of Wisdom we must learn for the journey to self realization are flexible, evolving. Like the common law, they are articulated afresh moment by moment, case by case. The laws are stable, but they do not stand still. Exactly how the basic principals will apply to form governing laws all depends upon the circumstances, the consciousness involved, the entities, the case.

 

The free will of the individual in connection with the infinite is now primary. All is not determined, everyone has a chance to decide their own fate. The philosophic implications of Chaos are positive and encouraging. The Universe is not a clock, its a game. Enjoy it!

[This message has been edited by Gauracandra (edited 04-19-2002).]

[Rati]

I think many people tend to confuse philosophical discourse with religious doctrine. Certainly theologians are also concerned with the same set of problems that philosophers grapple with. The difference is that religion deals more with rituals and subjective experiences of the mystical variety and one's relationship with the Deity, whereas philosophy is a discipline of logical rules and systematically defining problems with a view to formulating potential solutions to them. We see many Western bhaktas bandying about the term philosophy, but unfortunately most of them have not actually studied the discipline of philosophy itself and therefore are not familiar with the problems that discipline addresses. We see them making statements like, "The philosophy of Ksna consciousness tells us [fill in the blank]", when they really should be stating "The theology developed by Rupa and Jiva Goswami in the school of Vaishnavism founded by Sri Caitanya holds that...". One could say that I am just being pedantic and splitting hairs over semantics, and they might be right about that. The only reason I bring it up in this connection is that it can easily lead to muddled arguments in connection with the philosophy of science in particular. One can twist the meaning of the rationalist school of thought to wring out an endorsement and propagation of atheism, when in fact it might not be there at all.

 

For a medical researcher looking for a cure for some disease, the answers lie in the empirical data that will prove or disprove the efficacy of any one medicine. Does that somehow tell us something about the religious beliefs of that researcher? - hardly. The famous scientist and inventor Nikola Tessla (the man who actually invented radio, even though Marconi took all of the credit) was very mystical in his outlook and also deeply religious. He wrote that his motivation for technological innovations was for the service of mankind and a mission that was divine in nature.

 

I find Gauracandra's post to be inspiring and exciting. I hope everyone here shares my view and sees the opportunity to incorporate the philosophy of science into their personal theologies.

 

[This message has been edited by Rati (edited 04-19-2002).]

[Guest guest]

 

This is nothing new,Pythagoras and his writings are in the same vain.

The mathematical precision in nature,has been observed by Alchemists,and scientists for a long time.

The modern sciences of Metallurgy,medicine,and chemistry started with Paracelsus the medievel alchemist.

Science and spirituality were,since ancient times,seen as two sides of the same coin,the recent divide between the two,is the result of the concerted effort of those who oppose the idea of God.

They admitted to as much,they were the early proponents of Darwinism,in their writings they say, even though evolutionary theory is greatly flawed,they detest the very idea of God,and therefore went about pushing Darwinism on the population.

This is new,previous to their propaganda,the sciences were led by theistic visionary's,like Newton.

[Rati]

In a sense you are right about that, Shiva. However, the developments in particle physics and quantum mechanics in the last century are indeed very revolutionary in the context of classical Newtonian physics. The interesting thing is that they closely mirror the same types of philosophical paradoxes that ancient Eastern schools have discussed for millenia. I am not going to advise you to get out and a university degree in physics just to get your feet wet on the subject, but I do recommend some of the books out on the topic for the lay public. A number of them were cited on other threads here. If you have already done that reading, then disregard my advice.

 

[This message has been edited by Rati (edited 04-19-2002).]

[gHari]

I don't know the source of your quote, Gauracandra, but it seems that this concluding statement is complete speculation:

 

[...] All is not determined, everyone has a chance to decide their own fate. [...]

It appears to assume that we can control this chaotic mechanism. I still like Krsna's transcendental soul control theory better.

 

'Science' is like studying the motions of the balls on a billiards table without understanding that people are striking the ball from time to time. Such a closed-minded study requires fanciful theories of momentum leaps, quantum flux, and who knows what other Star Trek hocus-pocus; when all the while it was just Frank and Larry banging the balls around in a game of snooker.

[Guest guest]

 

Einstein stated he believed in Spinoza's God,which is wholly opposed to chaos theory.

As is vedanta,the problem with chaos theory is that it does not include the reality,of superconsciousness.

The universe is alive,infinity is occupied by a living consciousness.

Fail to iclude this reality in any theory of cosmic law,and it will be flawed.

The appearence of freedom and ever expanding potential,is an illusion,Maha-maya,Spinoza and Vedanta agree on this point,knowing the influence of the universal consciousness.

Everything is set,and controlled,the desire of the soul in material consciouness, is to be independent, and free from the influence of the controller of the universe.

Therefore God obliges,an illusory state of reality is given ,so that the soul can feel himself to be independent.

This is the function of Maha-maya,to delude the souls desirous of independence.

This delusional power is manifested in the myriad philosophies that one can adhere to.

Eventually the conditioned soul is liberated from the desire for independence,and God consciousness is realized.

The absolute reality,trenscendental to chaos theory, is that we are living inside the consciousness of the universe,the quanta themselves are a transformation of that consciouness,from a subtle to material state.

This is why they are unpredictable,or predi ctable,they are alive,and part of a unified field of consciousness,this is the unified field theory,or theory of everything scientists have been searching for.

There is unlimited potential for God,the universe is a part of that reality,Unpredictability is only an illusion,to us what is unpredictable,is to God,very predictable.

[Rati]

Have you come up with any thought experiements (ala Einstein) to prove your unified field theory, Shiva?

 

One problem with unpredictability is that it only states that exact predictions fail, whereas there are parameters in which the outcome of events will inevitably occur all of the time, so there is always some level of predictability, never zero. If any one event were entirely unpredictable (viz. no parameters), then that would truly be a state of chaos. It is the sum of all events within a system that makes it chaotic, rather than any single occurance.

 

What are your thoughts on 'influence at a distance' as demonstrated by the experiments where single photons are beamed through a slit? That has been a particularly knotty problem for rationalists.

 

[This message has been edited by Rati (edited 04-20-2002).]

 

[This message has been edited by Rati (edited 04-20-2002).]

[Guest guest]

The double slit test has explanations that differ from my understanding,one is that they are entering different dimensions,then reapearing,another is that they respond to a conscious viewer,another rationalizes it with the quanta cancelling each other out, or something like that.

The truth is that they are alive,part of God,and under his control,doing as he pleases.

Chaos theory is only a tool for understanding reality,without the appreciation of the absolute control of all phenomena by God,any theory is faulty.

The unified field,is best summizied I think by David Bohm,as the sub-quantum sea of potential,manifesting quanta,I would add,as the manifested ability of the universal consciousness,which the unified field of energy is comprised of .

[Guest guest]

as for a thought experiment,that is what yoga is,Through the yoga process one is educated as to how the world and all phenomena are directly controlled at all times.

Your ability to percieve this truth,factually rather then philosophically,is only possible with the consent and arrangement of God.

This simple truth is needed to be understood,then you are able to appreciate the truth,directly.

The Bhagavad Gita says " the enlightened seer sees everything equally",this means when others see random events transpiring,the enlightened seer,sees the controller,rather then the controlled,if this ability is yours,then God is able to communicate to you, through the varied phenomena this world presents.

[Gauracandra]

Just to make clear, I didn't write that article that I posted. I found it on my harddrive as I was cleaning it up (defrag etc..). The thing about fractal programs for instance, is that when you create a fractal I believe you have to put in a 'seed' number or some mathematical formulas to get it started. The way I see it God creates that seed in the universe.

 

As for the double slit test, I remember reading about that in relation to multi-verse theory. I don't recall the details, but basically some suggested it (a particle of light) has its own counterpart in another universe etc... It was rather weird to think about.

[Rati]

Your thought experiment disappoints, Shiva. I was looking more for something along the lines of Einstein's thought experiment on relativity about people going off on a space voyage and aging at a slower rate than the people they left behind on earth. Put on your thinking cap and try again.

 

[Guest guest]

sorry to disapoint,here try this,it is the only proof of god on earth.

http://communities.msn.com/WalkinsWanderersandstarseeds

 

It's a weird little community i found,I'm shiva there also,Go the general messages board,go to the "shiva's map" thread,see what you think.

Or else i can email my map to you,I call it the new hitchhikers guide to the universe.

I would post it here,but i am not good at making it come out legible,if you want, post it here.

 

 

 

[This message has been edited by shiva (edited 04-22-2002).]

[Avinash]

As for the double slit test, I remember reading about that in relation to multi-verse theory. I don't recall the details, but basically some suggested it (a particle of light) has its own counterpart in another universe etc... It was rather weird to think about.

 

It was me who posted that. Interference requires two things. One explanation is the multiuniverse theory. According to it, the photon interacts with another photon in a different universe. Well, it is just one of the explanations. There are more and all of them you will find as weird.

 

[Avinash]

Fractals definitely represent our universe much more closely than regular shapes, like circles, triangles etc. One interesting thing. Fractals have fractional dimensions like 1.6 2.7 etc. Could it be that our universe has fractional dimensions?

[gHari]

I got heavily into fractals several years back. Mathematicians have actually proven that there are an unlimited number of those nodule things in the Mandelbrot fractal - the first fractal discovered by Mr. Mandelbrot in the early eighties. Some are expecting fractals to produce the next wonder invention that will stun us beyond even the computer's impact on the world.

 

Gauracandra, I'm glad you didn't write that piece, because I thought it was gobbledygook - just too polite to say.

 

BTW, for a real wonder, download a fractal MPG movie file from the net and zoom into a fractal. It is quite amazing - the only way to know a fractal.

 

[This message has been edited by gHari (edited 04-23-2002).]

[Avinash]

Quantum Physics has been mentioned in this thread. Quantum Physics was very special not only in that it gave lots of new equations, but also that it forced scientists to look at the world in a completely different way. Classical Physics followed Descartes reductionism. In this approach, any problem is broken down into many smaller sub problems, then the sub-problems are solved in isolation and then their solutions are clubbed to get the solution of the original problem. Not only that, it was assumed that any part of the universe has some intrinsic propertie which can be studied by ignoring the rest of the universe. This worked quite well for many years and was instrumental in the development of science. But it also had one disadvantage which was faced when atoms were studied in detail. The exploration of atomic and subatomic world shattered the foundations of existing world views and forced scientists to think in entirely new ways. Every time they asked nature a question, nature answered with a paradox. The more they tried to clarify the situation, the sharper the paradoxes became. Then they became aware that their whole way of thinking was inadequate to describe atomic phenomena. It took them years to realize that the paradoxes were essential aspect of the real world, and that they arise whenever one tries to apply classical Physics to atomic phenomena. One this was realized, they began to ask right questions and could thus avoid contradictions. Then precise and consistent mathematical formulation of Quantum Physics could be developed.

 

Even after the mathematical formulation was completed, its concepts were difficult to grasp. The new Physics necessiated radical changes in the concepts of space, time, matter, cause and effect.

 

In contrast to classical view which was reductionistic, the new view can be termed as holistic. The universe can not be seen as a machine having lots of parts that do their jobs independently, but it has to be seen as an indivisible whole. The parts of the universe was essentially interrelated. Quantum Physics tells us that neither electron nor anything else has any intrinsic properties independent of its environment. Whatever properties some object has, depends on the rest of the universe.

[Avinash]

I have a belief. The more I study Quantum Physics, the stronger that belief becomes. The belief is that the idea that atomic phenomena cannot be studied by considering indpendent things, but as relation between things, should be applicable for everything in the universe. By everything, I do not just mean matter, but mind also. I am also including in it emotions, our behaviour. I believe that whatever I do, whatever I think has bearing on whole of the universe. That bearing may be very small initially, but as the study of chaos theory shows, it will become significant in the long run.

[Rati]

What fractals demonstrate is an underlying order that can be actually patterned or modeled by mathematical equations, despite the appearance of totally random or chaotic phenomena. Mandelbot applied such equations to correctly forecast levels of the Nile river (after taking measurements made over a few thousand years) and cotton prices. What is really remarkable is the fractal program he wrote to simulate random lines resembling ocean coasts that he left running over the weekend. When he came back in on the following Monday morning there on the computer screen was clearly visible among the various strange continents a shape that looked uncannily similar to New Zealand!