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des

Fractals

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Saw this thing (beautiful!) on fractals on NOVA. I used to do mandelbrot sets on my Amiga computer (circa 1985!?). Anyway, this was interesting. At the end, there was a comment on Einstein's comment re: God does not play dice with the universe. There was discussion on how there is a science (or mathematics of chance).I have been watching with one eye tonight, pretty busy, but then the guy (?) commented, it isn't IF God plays dice but HOW God plays dice! Far out, huh?

 

 

--des

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I love fractals. :) I love chaos theory.

 

Contemplating ideas like chaos theory (which is at the heart of Taoism) connects me to God just as well (maybe better) than contemplating scripture. (Don't tell the scientists that though. They may get mad. ;) )

 

"As above, so below" is a scripture that has been rattling around in my brain over the past few days. The wave/particle duality of matter and energy is what first brought it into my mind. Fractals and chaos theory fit very nicely in there as well.

 

As a matter of fact, in the Huston Smith book I just bought, he uses pyramid imagery to describe the universe's relationship to God. (Cool eh Fred?) God is the "tip" of the pyramid where everything unites (and like a particle, has no depth, breadth, or width). As creation flows forth from God, it gets simpler and simpler, more dual, more diverse.

 

Viewed as a fractal, one might focus in on the chaos of creation, which will give way the further away from it you get, until it can all be seen as being one, united, harmonious whole. B)

 

"At any given moment, life is completely senseless. But viewed over a period, it seems to reveal itself as an organism existing in time, having a purpose, trending in a certain direction." - Aldous Huxley (1894-1963)

 

www.fractalwisdom.com is a cool webpage with lots of links. click here.

Edited by AletheiaRivers

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I actually do have the idea of a fractal consciously in my mind when I think about the basic metaphysical structures that undergird reality. The processes of differentiation, integration, and opposition, for instance. No matter what scale of reality you're looking at, they show up. Every single manifestation of them, at any scale, is completetly unique upon close inspection, even though the basic contours are the same. No matter how much you zoom in or out, the same shapes and structures keep coming into view over and over again. Things that appear to be in opposition to each other at one scale, work together to oppose something else at the next, and so on as far up or down or in or out as you'll ever have time to examine in all the ages of the universe.

 

And here's something else wicked cool: the mathematics of fractals are based upon imaginary numbers -- numbers that have a formal definition, but don't actually exist anywhere in reality. Actually they're doubly so. Even simple negative numbers don't exist in reality, which is why the discovery both of zero and of negative numbers was an enormous leap forward in the human capacity for conceptual abstraction. But even-numbered roots of negative numbers go beyond even that kind of non-existence, to the point of not even being capable of quantifying reality at all, positively or negatively!

 

Anyway, remember way back when we were discussing privation theory and the problem of evil, and I suggested that the ontological negativity which was classically called "evil" by Platonism and early Christianity had structural, but not material existence?

 

(This may have led more than one undergraduate math student to exclaim, "Imaginary numbers are evil!" But that's beside my point.....)

 

B)

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..., but then the guy (?) commented, it isn't IF God plays dice but HOW God plays dice! Far out, huh?

Hmm, that's an interesting comment, considering there's not a single random thing about a fractal. :blink:

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Here are some really gorgeous images of regions of the Mandelbrot set. There really is something mystical about it...

 

m_pine.gif

 

m_trieye.gif

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Things that appear to be in opposition to each other at one scale, work together to oppose something else at the next, and so on as far up or down or in or out as you'll ever have time to examine in all the ages of the universe.

 

Only the paradox comes anywhere near to the comprehending fullness of life. -- C.G. Jung

 

A paradox is truth standing on its head to attract attention. -- Nicholas Falletta

 

The way of paradoxes is the way of truth. To test Reality we must see it on the tight-rope. When the Verities become acrobats we can judge them. -- Oscar Wilde

 

The paradox is really the pathos of intellectual life and just as only great souls are exposed to passions it is only the great thinker who is exposed to what I call paradoxes, which are nothing else than grandiose thoughts in embryo. -- Soren Kierkegaard

 

:D

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Here are some really gorgeous images of regions of the Mandelbrot set.  There really is something mystical about it...

 

 

Way cool guys !!! I call it complex systems theory, you call it chaos theory. Same difference. It is the analog intelligent design of things that emerge from nothingness, "creation ab nihilo".

 

Believe it or not the roots of these philosophies go back at least to the foundation of ancient Egyptian culture . The g-d Thoth, who introduced the magic of metalworking to the people would be considered the foundational character here. He also is attributed to have composed the basic rules of alchemy in a tract called "The Emerald Tablet" in the incarnation of Hermes Trigesmistrus (sp?) which contains, among other truths, the magical phrase detailing the "likeness of what is above to what is below".

 

Alchemy is thought to have originated in the middle ages in Europe where certain mystics believed that dross metals could be changed into gold and other noble metals through certain ritualistic manipulations. But the roots of alchemy and related practices extends back thousands of years earlier into the roots of the Chinese and the Indian civilizations. In each case the practice of alchemy is closely tied to the metalworking arts.

 

Alchemy formed the foundational knowledge base out of which modern physics and chemistry have grown, and Sir Issac Newton extensively studied alchemical principles and practices before changing our realities with his laws of physics. One of his best friends, George Stirk ( I think that's the name } was a well known practitioner of the alchemical arts.

 

The Mandelbrot sets, named after the mathematician Benoit Mandelbrot who first devised them, seem mystical because the spiral is the most prevalent form seen in natural systems and arises due to the prevalence of the use of Fibonacci series numbers in their design arrangements. DNA, chambered nautilus, planetary orbitals, storm systems and ocean currents, water going down a drain, galaxies, you see them everywhere in nature; and, it is one of the most prevalent decorative motifs on ancients pieces of pottery and stoneware. Spirals are definitely considered to be a sacred form by ancient cultures world wide. In SW American rock art it is extensively used as a sun symbol, and as I noted elsewhere here, it appears in grave mounds in neolithic Ireland as a sun sign.

 

Mystical indeed !!!

 

flow.... : :D

Edited by flowperson

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Flow,

 

Only you could take us from Mandelbrot, to Ancient Egypt, to Sir Isaac Newton, and back again, in about four paragraphs. :D

 

I am aware that Newton had personal ties to "esoteric arts" like alchemy and freemasonry, but I don't quite see how they form the "foundational knowledge base out of which modern physics and chemistry have grown." The more obvious tie seems to be to Enlightenment rationality and empiricism.

 

I was reading some FAQ's on fractals today, and came across some reference to the way Fibonacci series play into the contours of fractal shapes. I always forget the exact mathematical definitions of the Mandelbrot and Julia sets; and then every five years or so, something taps me on the shoulder to go remind myself (thanks des), and I am once again transported into the realm of sheer stupefaction. How the hell can imaginary numbers possibly account for this?! And yet, there it is, eternally, composed in the poetry of pure mathematics, the closest thing we've ever seen to the language of God; a tapestry of shimmering beauty transcending all the muck of space and time, just waiting for a mind capable of comprehending it. And then I'm reminded of why I'm a Platonist.

 

:)

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I'm not sure re: chaos theory and fractals. As I said, I wasn't paying 100% attention to it, as I commonly do lesson plans and watch tv at the same time. Multitasking you know. :-)

The visual images were/are arresting (much better than on the 8 bit Amiga!!). Funny thing though, when I used to play with them on the computer I never realized why if you take any section and magnify it, it looked like the rest of the image. Guess I didn't really know what a fractal was before, so I did learn something. :-)

I did really like the quote too. Someone must have sat up nights....

 

One of the neat things in the program (you should see it if you have a chance, and I might actually watch the whole thing-- it was also on during the annoying pledge drive...), was how they related the images to art. They interviewed some mathematicians, and they'd say things like "these images seemed to be familar-- I don't know how." Then they would superimpose the image on a famous sculpture or a Mandala, as well as the spiral shape of a galaxy (add in cloud patterns, ferns, etc etc.). There were many photos of mandelas shown, including those of some mental patient seen by Jung. Arthur C. Clark made the comment that these kinds of images are really deep into our being.

 

Yes, I agree they do seem mystical. It's just wild you can take imagary nos. and come up with something that is form of much of nature and art.

 

Note: I found this quote on the page. I think it nicely explains how randomness isn't really random. I think that was the point of the dice quote:

"Of course, not all patterns in nature are regular. Billowy clouds, flickering flames, lightning bolts, the pattern of veins on a leaf, the architecture of the lung's passageways — these are examples of patterns without obvious regularity. But looks can be deceiving. Many irregular patterns are not simply random. They often display an underlying structure, a kind of regular irregularity that can be mathematically described. Such objects have been called fractals, a term coined by Benoit B. Mandelbrot of IBM's Watson research center meaning broken or fragmented."

There are some beautiful natural images here. It's slow to load on dial up.

http://www.scottcamazine.com/personal/DesignNature/

 

Yikes, I tried to google fractals+ chaos theory, and got a lot more than I can deal with.

Nighty night.

 

 

 

 

--des

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It is the analog intelligent design of things that emerge from nothingness, "creation ab nihilo".

 

Exactly! And the cool thing is it goes both ways - inward and outward.

 

Again using the analogy that Smith used: If you "look heavenward" the "pyramid's" base is creation, and it gradually becomes unified until you get to God. If you look inward, the individual is the pyramid's base (it's inverted), and the deeper you go, the more unified it gets, until you get to God. :) As above, so below.

 

I guess that analogy really doesn't have anything to do with fractals or chaos theory, other than fractals appear to be chaotic from one view, but then are found to be not when examined from another view. So it is the same with creation.

 

There, I think I tied the whole thing together. :D

Edited by AletheiaRivers

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I was reading some FAQ's on fractals today, and came across some reference to the way Fibonacci series play into the contours of fractal shapes.

I have a free DVD from The Teaching Co on mathematics that is all about the Fibonacci sequence and Phi. I haven't watched it yet. I think I'll do that today. The only thing I know is what I read in DaVinci and the research it prompted me to do.

 

and then every five years or so, something taps me on the shoulder to go remind myself (thanks des), and I am once again transported into the realm of sheer stupefaction. 

Did anyone notice that my avatar was a fractal for a while? Thanks from me too Des. I absolutely love this stuff.

Edited by AletheiaRivers

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I'm not sure re: chaos theory and fractals.

I found this quote on the page. I think it nicely explains how randomness isn't really random:  "... Many irregular patterns are not simply random. They often display an underlying structure, a kind of regular irregularity..."

Yikes, I tried to google fractals+ chaos theory, and got a lot more than I can deal with.

Your comment about "how randomness isn't really random" and the quote you quoted IS what chaos theory is in a nutshell.

 

One web definition is: "an orderly pattern in seemingly disordered conditions."

 

Have you seen the movie "Butterfly Effect?" That is an interesting (and entertaining) look at one aspect of chaos theory. The idea is that a butterfly flaps its wings in Brazil and causes a storm in New Mexico. Things seem random (and chaotic), but there is actually an underlying cause (and order) to it all.

 

Fractals are the epitome of "regular irregularity", ie chaos theory. :)

Edited by AletheiaRivers

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Flow,

 

Only you could take us from Mandelbrot, to Ancient Egypt, to Sir Isaac Newton, and back again, in about four paragraphs. :D

 

I am aware that Newton had personal ties to "esoteric arts" like alchemy and freemasonry, but I don't quite see how they form the "foundational knowledge base out of which modern physics and chemistry have grown."  The more obvious tie seems to be to Enlightenment rationality and empiricism.

 

:)

 

 

Of course rationality and empiricism are the most important components of Physics and Chemistry in a modern or neo modern sense. But there is a line in the sand that happened about the time of Galileo, Copernicus, Kepler, Leewenhouck, Newton, etc. where ideation and conception transformed into formal experimentation as far as research-based science was concerned.

 

The importance of alchemy to the roots of science was to give great thinkers the impetus to look for the "causes" of material transformation in the world and universe around them, and to help them to invent the "tools" to do so. When they did the process of discovery evolved from the mystical incantations and rituals of the alchemical arts into the repetitive and rigorous practices of experimental routines, results, and duplication by others through the sharing of circulated papers of successful experimentalists.

 

So I believe we're looking at a process, like the evolving pattern of most important things in life, from feeling around in the darkness for the mystical roots of something to discovering the important aspects of its realities through experimentation, observation, and the sharing of information regarding its nature among ourselves over time. This is the process that makes the unknown generally known over time and helps to advance civilizations forward in time.

 

As I suggested elsewhere on the board, anyone interested in pursuing the origins of the new science of "chaos theory" should start by obtaining and reading the book, Chaos, Making a New Science, by James Gleick, a former science writer for the New York Times. The book was written in the 80"s but I believe that it is still in print and avaiable. Have fun smart people !!

 

flow.... :)

Edited by flowperson

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Chaos, Making a New Science, by James Gleick

 

I've owned it for about 6 years. :D

Yes, but have you READ it? :lol:

 

 

Reading and comprehension are two different things, but I'm sure it's been comprehended from what's been said on the thread.

 

Oh, I almost forgot to say that I met Mitch Feigenbaum once. The prototype frizz- haired, distracted scientist-mathematician, but seemed like a nice guy.

 

 

flow.... :D

Edited by flowperson

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Reading and comprehension are two different things, but I'm sure it's been comprehended from what's been said on the thread.

 

flow....  :D

Ahhhh, thanks Flow. :wub:

 

Fred knows that I have a tendency to buy books and add them to my "to read" pile. ;)

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I read it in college when it first came out... oops, dating. :D

 

It was fascinating and illuminating then, but I thought chaos theory was "out of vogue"???? I haven't been sure (or apparently interested enough to research) whether it was "disproven" or replaced, or just old hat. Anybody know?

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Yes, hence the neat little quote re: HOW God plays dice. Yes, God plays very well. :-)

God is also a beautiful dice player, huh? :-) These images in the mandelbrot set, Julia sets, and in real life are absolutely amazing!!! Yes, mystical too.

 

Didn't see the Butterfly Effect, am wondering if it had anything to do wtih the Bradberry short story... They create a time machine, go back in time. Nothing is supposed to be changed, but some guy goes off the track and kills a butterfly that should not have died. When they come out from the time machine, there is a Hitler like dictator instead of a

democratic, normal government. The story is called Sound of Thunder.

 

 

Yes, guys thanks. I love this kind of stuff too!!

 

BTW, I have heard weather science is the most quintesential example of chaos theory. One or two degree difference in temp. or some minor difference in clouds effects everything/ changes everythign. I think some butterflies have been flappign lately. Certainly is cold here in NM!!

 

 

--des

 

Your comment about "how randomness isn't really random" and the quote you quoted IS what chaos theory is in a nutshell.

 

One web definition is: "an orderly pattern in seemingly disordered conditions."

 

Have you seen the movie "Butterfly Effect?" That is an interesting (and entertaining) look at one aspect of chaos theory. The idea is that a butterfly flaps its wings in Brazil and causes a storm in New Mexico. Things seem random (and chaotic), but there is actually an underlying cause (and order) to it all.

 

Fractals are the epitome of "regular irregularity", ie chaos theory.  :)

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Didn't see the Butterfly Effect, am wondering if it had anything to do wtih the Bradberry short story...

Not exactly, but it's still based on the same thematic idea of small changes having large-scale effects. I tried not to get my hopes up too much about it, as I wasn't sure how well Ashton Kutcher would pull off a semi-serious role, but I actually really liked it.

 

I think some butterflies have been flappign lately. Certainly is cold here in NM!!

Boo hoo! It took me an hour and a half to get home from work in the snow last night! <_<

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I think some butterflies have been flappign lately. Certainly is cold here in NM!!

Boo hoo! It took me an hour and a half to get home from work in the snow last night! <_<

 

Well yes, but remember I moved away from all that on purpose. :-) And yes, our weather is STILL better than Chicago though.

 

Though I miss things like architecture and pizza, not necessarily in that order.

 

 

--des

Edited by des

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You live in Sin City Flow? I got married in Sin City. The hubby and I have discussed coming back to Mandalay Bay for a second honeymoon/vacation. :) (There is only one sin city right? I mean you don't live in another sin city do you?)

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