Chaos and other big discoveries

Dream

Dream

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Please suggest the simplest and best introductions to the big theories that people need to be aware of. In this first post, I've mentioned three that I found helpful, and one is an online freebie. I wonder if anyone has run across some simple introductions other beautiful theories? Just provide what you think represents the shortest and best introduction you've found to any beautiful theory -- could be scientific, historical, or psychological, medical, cosmetic, or anything at all.

Chaos Theory: If you've never had a good straight-forward explanation of the importance of Chaos Theory or the study of Fractals (Fractionals), then you've got to follow this hypertext link Chaos Theory: A brief introduction . It is the short, simple introduction to Chaos Theory that the layperson needs to be aware of.

Apprentices of Wonder
Neural Networks are very technical but the basic principle can be understood by anybody. I thought the explanation in the book Apprentices of Wonder was very simple and also entertaining.

2.8 Angstroms
Read the first chapter or two of this book. Hubble's Constant is part of the reason that people nowadays theorize infinite universes, but before the infinite universes theory, there was a book written 10 years ago titled 2.8 Angstroms. Because of Hubble's Constant, there is some debate over whether the speed of light is the same from galaxy to galaxy -- that it may be proportional to a galaxy's acceleration. There are also other theories about the outward acceleration of the galaxies (such as the Infinite Universes theory which suggest a constant speed of light).
 
Ive always loved fractal art and fractal music. There are some great programs now that let you "fly thru" a fractal image. It makes me wish holodecks were finished. And fractal music makes me wish I had a totally top-line surround sound.
 
Wow, very cool. On that musical session, it sounds as if the bifurcations in the formula begin to grow more wild toward the end of the melody, similar to the bifurcations in the Lorentz experiment. (You can see the graph in the internet link or from pg 141 of Ian Stewart's book Does God Play Dice....Chaos).

I wonder whether Diana Dabby imprinted any music theory guidelines into her program or whether she simply used the notes as points in her formulas. I doubt that she added anything. Her program reminds me of neural network setups.

Gandalf said:
Ive always loved fractal art and fractal music. There are some great programs now that let you "fly thru" a fractal image. It makes me wish holodecks were finished. And fractal music makes me wish I had a totally top-line surround sound.
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Yeah, I remember when Fractint used to take about half an hour to bring up the Mandlebrot set on a One Megahertz machine. I played with the settings, but I still didn't have any idea what it meant or why Fractals were significant! I thought the Lorentz distribution was just a neat-o butterfly looking graphic.
 
I remember the excitement I got from my first introduction and subsequent delve into chaos theory and now revisiting it I find it strange that I have done so little to try an incorporate it into my overview. It is something I have to address.

I am only glad that Path of One does not seem to have thought much about it, or at least does not incorporate it into her descriptions to me or I would have had a much harder time giving half way credible responses. The thumbprint of God. Well it is one astounding equation.

Here is a link to an excellent documentary in 6 parts that is well worth watching if its simple introductions you are after.

YouTube - Arthur Clarke - Fractals - The Colors Of Infinity 1 of 6
 
Yes that did help explain how the Mandelbrot graph is drawn, how fractal image compression works, and also gave curious hints about mandalas and LSD trips.
 
Tao_Equus said:
I remember the excitement I got from my first introduction and subsequent delve into chaos theory and now revisiting it I find it strange that I have done so little to try an incorporate it into my overview. It is something I have to address.

I am only glad that Path of One does not seem to have thought much about it, or at least does not incorporate it into her descriptions to me or I would have had a much harder time giving half way credible responses. The thumbprint of God. Well it is one astounding equation.

Here is a link to an excellent documentary in 6 parts that is well worth watching if its simple introductions you are after.

YouTube - Arthur Clarke - Fractals - The Colors Of Infinity 1 of 6
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Wow- thanks all, for this. I've heard a little about chaos theory, but not being a mathematician by any stretch, I haven't delved into it enough. Can anyone recommend some excellent books?

I think there is so much there in this and in quantum mechanics and string theory, and I'm like a minor spectator but fascinated. (Tao, you overestimate my knowledge... :D)

This is fascinating stuff and I clearly need to learn more. I'm a visual person primarily, and the images produced here remind me deeply of some key images I've had in visions and dreams. Crazy! It also seems life itself is in the image.

This isn't the first time I wished I'd been gifted with a more mathematically oriented brain. I was that kid in math that always got As but had no clue what I was doing or what it all meant. Maybe if I'd stuck with it past college calculus, the meaning would have emerged but I'm too much of an "outdoors, action-oriented" person to ever devote so much time to equations... Still, I feel like there is something deeply spiritual and revealing in math and physics. Perhaps it's one of the few ways we can unite science and spirituality without the problems we have with uncommon language and diverse culture.

ETA- I really, really would like any information on books that are intelligble to a layperson that don't miss the detail. I'm watching more of the series as we speak and a lot of the images are so exactly like ones I've had in various other contexts that I'm nearly in tears. I'm fascinated by the concept of the music as well, as I had a dream where the entire universe, including myself, was energy and music- the concept of fractal music would, I think, for the first time describe what that was like. I've tried desperately to explain what it was like to hear music that was all variants of a single "Something" and it has so far eluded me. I can recall what I experienced but I can't express it adequately to others whatsoever. I think this whole bit may be a huge missing chunk to my own understanding of my own experience, so I'm very eager to learn more. It's kind of akin to the first time I watched a PBS show on string theory and was in tears because so much of the information made scientific sense of ideas I'd long held based only on my visions that I'd had since I was a child.
 
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I've seen various books about Fractals, but I've never seen anything as straightforward as the link in the first post. The thing about the Fractal discovery, is that it seems to fill a big gap in Mathematics. There are so many things in the world that cannot be modeled by Calculus. For example: We still don't understand how bees are able to hover, because according to our Math knowledge they should be falling to the ground. Our very number system is the limitation we've reached in what can be computed.

Our Mathematics has led us to recognize fractals, however we are leaving Mathematics behind. Fractals represent something bigger than a mere number system that starts at zero. I think a Fractal could represent operations upon infinity, whereas Calculus is merely able to solve a small set of Math problems that wink at infinity. There could potentially be Fractal maps onto the individual digits of Pi, for instance.
 
Wow, just wow. I'm still on happy-high from the images. Some of them look a lot like tunnel/gate/portal type things that show up in my dreams. Also, and interestingly, they look like descriptions that people having near-death experiences have described to me.

Here's a photo I took over Bodie Ghost Town, CA as a winter storm rolled in... for some reason, the M-set makes me think of this, among many many other things...

tunneloflight.jpg


tunneloflight-1.jpg


The camera really didn't do the experience justice, but you get the idea. The entire rest of the sky was dark and that was the only spot that framed the sun. It was winter and I was snowshoeing on about 4' of snow at the time the snowstorm began to move in. It was like seeing the NDE people's description come to life, and reminded me of mandalas.

Another birth... that is what it makes me think of. A few years back I had a vision of being swallowed up by the earth and, well, it's a longish description so I won't get into it, but the message was: "It all leads to life." It was like a visual tour of the M-set, only in sets of images- alternating- creation/destruction, creation/destruction. But when I see the M-set, I see the same message. Infinite creation, in the form of fleeting figures...
 
Path,

The image is indeed fractal :)

Interesting that you relate it to dreams. I too can do the same. Infact several years before fractals were discovered, 1979 to be exact, I had the deepest and most profound "waking dream" experience of my life. One that I think has effected my whole way of thinking on everything since then. It was a visual dream, I was wide awake, and out in the hills alone lying in my survival bag on a clear cold January night with the telescope I had just got as a Christmas present. For some time before then I had been experimenting with an Indian tantric meditation technique using a set of symbols as focus. They are called tatwa cards and their purpose is to focus the mind in such a way that you could achieve an out of body experience.

I had stopped looking through my telescope and was simply laid back gazing at the bright band of the milky way overhead. I had up to that point never had any success with the cards but I knew them so well that I went into the preliminary breathing technique they required and almost immediately I was above my body. My real eyes were still open and it was like I was seeing through two set of eyes at the same time, me looking at me looking at me. I was so excited and fully concious, there was no doubt to me this was a real experience. Almost immediately my floating part began to ascend toward the stars above me and I flew not just above the Earth but very rapidly beyond our solar system. As I looked back at it what I saw was a 'halo' of living energy that was more or less a perfect 'set' in appearance. I continued my journey above the plane of the milky way and was soon gazing down on our entire Galaxy which again had its own field of energy that again resembled so closely the Mandlebrot sets we see in the images. Not a disc or globe of energy but that strange yet familiar organic insect like shape. The tendrils stretched out to touch those of neighbouring galaxies, connected them all like a ring of children holding hands. I continued my journey beyond the local cluster of galaxies and the image was repeated again, the cluster too had its field of energy that with long snaking tendrils connected to other galactic clusters.

The most profound part of the experience though was not what I was seeing, it was what I was 'feeling'. It was like I was in every atom in the universe simultaneously, knowing its form, its history and its future. I describe it as living energy and it was. But I got no sense of conciousness, well at least not as we can describe it. It was like it was there because the alternative was nothingness and not because it had any purpose. It simply 'was' because nothingness was unacceptable. There was no "God" there, no creative and no destructive force was detected. There was only change like a kaleidoscope being slowly turned into infinity. The purpose of each molecule was not controlled or planned it was not purpose at all as we know it, it simply was for the alternative was nothing. And I knew then, and have believed since then, that big bang theory is wrong. And that infinity is something real, not imagined. The cycle we see, the illusion we call time, is just that, an illusion. A necessary one so that we can function on this plane of reality, but ultimately just an illusion. The atoms that make up our bodies are on another journey and they will not take "us" with them but we are a part of their journey and some part of us leaves its mark on them. But that is not anything like any concept of 'soul' that I have come across. It has no 'meaning', it simple is.

When I returned to my body I saw the Earth for the briefest of moments as an impossibly blue orb that buzzed with an energy I knew to be very very rare, but not unique. It was such a confused energy, its colour and my association with it made it beautiful, but there was something else. Something a lot more worrying. It 'buzzed' like a fly in its death throws, or like an animal at death exploding signals out to every nerve end making it twitch violently and without control. There was no place in my journey that had so much energy but it was so confused and chaotic, like it was out of control. Like an atom being agitated and compressed to the point where it must explode and annihilate itself.

Back in my body I was so exhilarated by my journey that I at the time ignored that last fraction of my journey, I had space travelled!! I had toured the local universe, had a glimpse of infinity. And it was all fractal. That experience led me to two things. One to believe Gaia theory, I believe all life on Earth is a single organism, but more closely related to a single cell automaton than a concious animal. And 2, that there is no God watching us, caring about what we say or do. In a very real sense we are alone and we will stand or fall by what we and we alone do. The Universe will persist with or without us. It will not mourn our passing. If we want to survive as a species we better learn that only our own willingness to survive can keep us going. There is no God daddy to bail us out.

tao
 
That's phenomenal, Tao. A couple things in its stood out to me...

First, the sensation of infinity. Oddly, it was white light that first gave me the sensation of infinity and eternity. I was about 10 and had a dream in which I entered a building and was immediately in infinite white light. It was the strangest sensation and I still can't really explain it. There were no points of reference. There was no sense of time, in part because there were no points of reference. It felt like standing in nothingness and yet everything around me was very alive with something. It felt like I was watched by everything, though nothing was there; the same way that I feel when I used to go to my grove in the woods, that was filled with little spirit-somethings... the feeling that I am not alone. It was disconcerting, to be honest. It felt like God but it was not a Grandpa-like, human-ish, come sit on my knee kind of God. It was a Being beyond comprehension, so foreign that I could experience nothing of it but the feeling of its consciousness of me. It was without emotion and without any message for me in that context, save one, something akin to: You are tiny, but precious. And so is everything else.

In that space, there was just... nothing else. My insignificance, and my significance- a paradox. When I say I've felt the love of God, it is at its heart this calm, constant creation. I know I'm noticed, that every single tiny being is noticed. And yet, that Beingness that was white light is completely whole and unruffled. I experience other beings that seem to have more emotion, that have more messages for me, that are my friends or my comforters... but God Itself- that white light- was completely alien. And I could never squeeze that sensation back into conventional Christianity again. It was too real.

The fractals... the M-set has always appeared everywhere to me. My studio/office is filled with shells and leaves and crystals... each reflecting the other. If you look at the speck of light in your eye in a mirror- look closer, closer, and allow that to become your entire field of vision-- oh, you'll see a very interesting and changing M-set in there... (at least I and a few friends do!) Some of my more detailed dreams and visions- of other worlds- the gates I go through to get there are like huge round-ish disks of energy, and the tendrils are alive and shift just like a M-set. The more circular parts of the M-set images recall the gates so perfectly that it is stunning. The tendrils, in the gates, reach out to draw you in. It is the sensation of an illusion (yourself) traveling to a new illusion (a different world). But the energy remains the same, a constant- ever-changing but never new- a paradox.

The blue orb... Gaia, who is a conscious being to me, or at least that is what I experience of her... I feel is shuddering, preparing to destroy and recreate. We're too unsustainable. Whether by our own hand (which is an illusion anyway) or by her, I feel that there is change coming. It can't go on like this. It is a bound animal, crazily beginning to break free from its bonds. I feel we're loved, but not privileged. That is, the Earth and God loves us, but no more than they love all beings. We have our role, our purpose. We're a bit of them that came to awareness of themselves. But that makes us no more or no less valuable to God, which is in all things. If we are too threatening to other beings, the natural progression is that we will be destroyed... make way for sustainability, for the next image in the set. Life continues with or without us.

However, I do think we continue with or without this life... I can't explain scientifically why this is so, though there is plenty of research on it in psychology and so forth if you care to read it. I can only say-- I have enough personal evidence to know that I've lived before, and I wager I will live again. Somehow, there is consciousness in energy. It is a different kind of consciousness than our waking consciousness here on earth, but I've experienced it and I've seen enough of my own past lives to know that I continue on, somehow. And like the M-set, the outer form changes but the inner core remains, shows up again and again. Like the M-set operating on a universal level, and within every one of the beings that is created. It's interesting that you said the earth was blue energy... I've been blue energy before. It was the dream where everything in the universe was music and energy simultaneously. The music was creating an illusion of form and distinction, but there was an awareness of the oneness of all the music, and a harmonizing as it was all from the One Song. At any rate, I was sound and energy. I was me, but I was a different kind of consciousness than I am now... I had no sensation of time, no thought of anything but a delicious now, in which I merged energy with other illusions and then came back to my own illusion-- really, just blue energy like a fireworks sparkler... but curiously like the M-set... tendrils, and all else was as well... and it all made sound. The entire "place" I was at, the most beautiful "place" I've ever been-- I could simultaneously see as an image, a piece of living art... and the underlying energy and sound... and then I knew what I was, and what God was. I understood that I wasn't only being watched by God, but that God was watching me through me... I was in God, and God was in me. The repetition of that indelible stamp in the energy in me, and the energy outside... and the beauty in those changing forms, myself a part of something fundamentally unchangeable at its core, something unified with all that is. It's one of the hardest things toexplain, but it was completely mind-blowing for me, and life-changing. Everything is beautiful images God creates because at the heart of love is beauty, and life is art. But underneath these beautiful images are God's stamp, the energy that goes on, that bears the same pattern as God Itself... that cannot be destroyed or created, but only changed and molded and crafted. I go on, but it's a different "I" than I thought I was. I'm glad "I" got to meet "her" early... the most spectacular time of my life, never wanted to come back. I knew it would change me forever when I stood in front of the gate to get there, and was offered the journey. But I had no idea how gorgeous it would be, and how comforting, given how alien it was...
 
An out of body feeling is often attributed to spiritual flight, but it could just as easily be due to the brain's left hemisphere becoming less active. Tao_Equus incorporated his knowledge of stars, the blue planet, and concerns about the world's future into his fractal. His out of body experience was probably very similar to a mandala vision but slightly less abstracted from practical knowledge as there were many identifiable objects on his journey.

Computers strain to handle all of the long division required to peer into a fractal. The computational challenge is huge, because the only devices suited to appreciate fractals are brains. Brains, with their long, fractional axons and dendrites are well suited to appreciate fractal geometry, which explains how Tao_Equus could have visualized a fractal model of the universe.

I don't know what to think about his vision, but I can understand what he's describing. It must have been a very cool thing.
 
It is true that looking at the similarities and the differences between the experiences of Path and myself our concious 'persuasion' is clearly reflected in the imagery we describe. Ever since I had it I have wondered was it real or was it an hallucination of a type that cannot be induced by drugs, for it was, (and I have more than enough experience here to determine that), in no way similar to a conventional 'trip'. A brief left brain shut down may be a good explanation for the vision but the things I saw were outside of my knowledge at that time, or perhaps in the close to 30 years since the event I have allowed some artistic retouches to be made. And at the very least I am describing it now as a 40+ not as a teenager. It was very cool and looking back at it for me it was the point when I began to have a true understanding of just how enormous the 'everything' is. Maybe that was all it was, the enormity of the cosmos hitting me like a train. But maybe it was a real experience too, some kind of surf on the quantum foam. I only had one other, very similar experience but much briefer, in Greece about 8 years later. Wish I could have them at will.


tao
 
Tao_Equus said:
It was like I was in every atom in the universe simultaneously, knowing its form, its history and its future. I describe it as living energy and it was. But I got no sense of conciousness, well at least not as we can describe it.
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Maybe you were looking for self-conciousness - which is something specific to individual beings.

It was like it was there because the alternative was nothingness and not because it had any purpose. It simply 'was' because nothingness was unacceptable. There was no "God" there, no creative and no destructive force was detected.
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That makes sense to me. Matter obeys Spirit and in fact exists in the service of spirit. Spirit is not "in" matter. Rather it animates and illminates matter when in proximity with it. This is why the concept of freeing Spirit from captivity in Matter may not be quite accurate, although the principle is important.

There was only change like a kaleidoscope being slowly turned into infinity. The purpose of each molecule was not controlled or planned it was not purpose at all as we know it, it simply was for the alternative was nothing. And I knew then, and have believed since then, that big bang theory is wrong. And that infinity is something real, not imagined. The cycle we see, the illusion we call time, is just that, an illusion. A necessary one so that we can function on this plane of reality, but ultimately just an illusion. The atoms that make up our bodies are on another journey and they will not take "us" with them but we are a part of their journey and some part of us leaves its mark on them. But that is not anything like any concept of 'soul' that I have come across. It has no 'meaning', it simple is.
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That's brilliant Tao. I think you are describing Buddhist cosmology - i.e., cyclical universe theory, but at the microlevel:
  • This astro-physical cycle generally corresponds to the modern notion of the Big Bang, the universe expands for billions of years, then contracts to a point of complete atomization and unification of all the universe's matter/energy. Then the black hole of nuclear plasma explodes back out again to recreate galaxies, suns and planets.
Beginnings and Endings: The Buddhist Mythos of the Arising and Passing Away of the World

I wonder if this macro-level astrophysical coming-and-going gets repeated at the microlevel for individual beings who cycle in and out of existence unless they are released.
 
Netti-Netti said:
That's brilliant Tao. I think you are describing Buddhist cosmology - i.e., cyclical universe theory, but at the microlevel:
  • This astro-physical cycle generally corresponds to the modern notion of the Big Bang, the universe expands for billions of years, then contracts to a point of complete atomization and unification of all the universe's matter/energy. Then the black hole of nuclear plasma explodes back out again to recreate galaxies, suns and planets.
Beginnings and Endings: The Buddhist Mythos of the Arising and Passing Away of the World

I wonder if this macro-level astrophysical coming-and-going gets repeated at the microlevel for individual beings who cycle in and out of existence unless they are released.
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There's that fractal thing again...microlevel and macrolevel mirroring each other.
 
A thought or two: The mandelbrot and fractals are not chaotic. They are not random. They are not stochastic. They are not disordered. They are complex perhaps, yet they are ordered and deterministic. In fact they are used to characterize and to remove that order from data to compact it and make better use of the bandwidth in communications.

Chaos is in the mind of the beholder, and where a fractal or a mandelbrot is seen there is no chaos in it. Complexity perhaps, or simplicity, but not chaos. If a fractal or a mandelbrot is not seen... similarly even the consistently repeating cycle of the sun, the moon, the day, and the tides, might appear as chaotic to a person.

There is a term: 'stochastic fractal'... used within computers to manufacture life like examples of clouds or trees or mountains or waves. It is like the term 'moon light'. The light came from the moon, but the light does NOT come from the moon. The moon geometry might not change appreciably day by day, but the light that reflects off the moon is always new and unique, and originating from somewhere else. Similarly the fractal is deterministic but a seeded parameter is always new and unique, and originating from somewhere else.

The moon appears to give light and the fractal appears to give stochastic... but does it? In my mind I distinguish the light and the moon, so in a similar manner I distinguish the stochastic and the fractal. As a fractal is known, it no longer appears stochastic. The stochastic remains stochastic until it is known... if ever.
 
Cyberpi said:
The mandelbrot and fractals are not chaotic. They are not random. They are not stochastic. They are not disordered. They are complex perhaps, yet they are ordered and deterministic....Chaos is in the mind of the beholder, and where a fractal or a mandelbrot is seen there is no chaos in it.
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The fractal sets are constant, however the videos on Mandelbrot sets said that the further the computations are carried out on fractals, the more diverse the imagery becomes while still continuing to be self similar. This sounds a lot like a graph of Brownian motion to me, so is this like saying even Brownian motion deterministic? Perhaps defining fractals as chaotic is the same thing as saying there is no chaos. Well, its still a theory about chaos, so you can still call it Chaos Theory.
 
Dream said:
The fractal sets are constant, however the videos on Mandelbrot sets said that the further the computations are carried out on fractals, the more diverse the imagery becomes while still continuing to be self similar.
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It is just like trying to calculate the exact value of an irrational number. Within the mandelbrot the finer the detail examined the more information there is in the coordinate and thus the lengthier the calculation. The diversity is in the number of bits in the coordinate.

Dream said:
This sounds a lot like a graph of Brownian motion to me, so is this like saying even Brownian motion deterministic?
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No, the Brownian motion is by definition a stochastic process.
 
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