Rachel, Blog: Evolving Connection
Random and Ineffecient?
What I learned about Fractal Geometry?
I can just hear all the friends and teachers who, with great frustration helped me to get through high school math deacdes ago, saying, "You? You actually learned something about geometry? How can that be?"
Yes...yes I learned that the basic blocks of the universe are simple, self-similar patterns that repeat themselves into infinity. It follows the simple formula Z=z2( as in squared)+C. And to boot...I actually know what that means!!! (well not the math part). I can relate it to life. Pretty impressive huh?
There is an Order, a Design and a Pattern
The universe that looks so chaotic and complex, or what Mendelbrot himself referred to as "roughness" actually isn't all that mixed up. There is actually a design, a simple repeating pattern to all that exists. In 1980 Mandelbrot prooved that in his experiments on computers at IBM, creating beautiful eloquant designs of repeating shapes by using the simple formula above, inputing numbers of roughness on the plane rather than on the line. Each piece in the shapes created repeated itself, identical to the whole but smaller.
Bottomless Wonders
Good example of which, that occurs in the real world, would be a cauliflower...break away one piece of the cauliflower and it is just like the whole cauliflower, one piece of that...again the cauliflower shape but smaller. Take a piece off of that and there again the cauliflower but even smaller. He called this pheneomena the "Bottomless wonder" because it seemed to go to infinitity. The pieces in this equation either get smmaler and smaller or larger and larger until we cannot see them but still...they exist. They never stop repeating.
Now, this repeating pattern seems "rough" and chaotic for sure when we look out at a craggy mountain scape or the coast line of an ocean. That makes it very challenging to meausre it in traditional ways but if we measure it according to its practical roughness: D...than it changes everything.
Intelligent Use of Energy
Just because it looks chaotic doesn't mean there isn't some intelligent design to it. There is a purpose to the rough shaping. If we were to look at the branching in the bronchioles of the lung all the way to the air sacs with our eyes ( which are so limited in percieving whole picture) we would probably view a rough, complex and chaotic mess that would seem to be a waste of energy and requiring more energy for the body in the long run. Just the opposit is true...By that intricate branching system we create more opportunity for alveoli ...more air sacs to take in oxygen...more opportunity for mucous production which is extremely necessary for cleaning and warming air...more opportunity for the cilia to pick up debris before the air hits the alveoli. Perfectly, intricately but actually very simply designed...same repeating pattern....it just looks messy to our eyes.
Is the shortest distance between two points a straight line?
Now if you were to look at a mountain stream pouring from the mountain peak to the ocean...most of us would say that the shortest distance is always straight but as Rachel, in her blog Evolving Connection,points out ...that doesn't account for obstacles along the way. Straight does not mean it is the path of least resistance. Nature is effecient! She chooses the easiest path. It would actually take much more energy for that water to get over the natural obstacles , burrow through the rock by going straight than it would in accounting for nature's grooves. Those grooves, those shapes are there to create ease and allow for efficient use of energy not to randomly complicate. They quickly and efficiently take us around the obstacles. As Mendelbrot states the most effecient measuring takes in account "the Forces of God" even if we are simply determing how our stocks are doing on a chart.
Wow! So what does all that fractal math stuff mean to us in our lives?
I couldn't say it any better than Rachel in the above quote does. The chaos has a purpose, a shape and an intricate but simple design to it. Trust that!
All is well.
Daniel Schmidt (2012) Inner World, Outer World. Amazon Prime Movies
Blog: Evolving Connection (March 2015) Fractal God: How Math Met SPIRIT and Had a Baby Called Destiny. http://www.rachelthor.com/blogposts/2015/8/4/fractal-god-how-spirituality-met-math-and-had-a-baby-called-the-universe
Benoit Mandelbrot: Fractals and the Art of Roughness (July 6, 2010) TED Talk
https://www.youtube.com/watch?v=ay8OMOsf6AQ&list=FLjmYO8qecRJgz_y0ZCO-xng&index=17
Good example of which, that occurs in the real world, would be a cauliflower...break away one piece of the cauliflower and it is just like the whole cauliflower, one piece of that...again the cauliflower shape but smaller. Take a piece off of that and there again the cauliflower but even smaller. He called this pheneomena the "Bottomless wonder" because it seemed to go to infinitity. The pieces in this equation either get smmaler and smaller or larger and larger until we cannot see them but still...they exist. They never stop repeating.
Now, this repeating pattern seems "rough" and chaotic for sure when we look out at a craggy mountain scape or the coast line of an ocean. That makes it very challenging to meausre it in traditional ways but if we measure it according to its practical roughness: D...than it changes everything.
Intelligent Use of Energy
Just because it looks chaotic doesn't mean there isn't some intelligent design to it. There is a purpose to the rough shaping. If we were to look at the branching in the bronchioles of the lung all the way to the air sacs with our eyes ( which are so limited in percieving whole picture) we would probably view a rough, complex and chaotic mess that would seem to be a waste of energy and requiring more energy for the body in the long run. Just the opposit is true...By that intricate branching system we create more opportunity for alveoli ...more air sacs to take in oxygen...more opportunity for mucous production which is extremely necessary for cleaning and warming air...more opportunity for the cilia to pick up debris before the air hits the alveoli. Perfectly, intricately but actually very simply designed...same repeating pattern....it just looks messy to our eyes.
Is the shortest distance between two points a straight line?
Now if you were to look at a mountain stream pouring from the mountain peak to the ocean...most of us would say that the shortest distance is always straight but as Rachel, in her blog Evolving Connection,points out ...that doesn't account for obstacles along the way. Straight does not mean it is the path of least resistance. Nature is effecient! She chooses the easiest path. It would actually take much more energy for that water to get over the natural obstacles , burrow through the rock by going straight than it would in accounting for nature's grooves. Those grooves, those shapes are there to create ease and allow for efficient use of energy not to randomly complicate. They quickly and efficiently take us around the obstacles. As Mendelbrot states the most effecient measuring takes in account "the Forces of God" even if we are simply determing how our stocks are doing on a chart.
Wow! So what does all that fractal math stuff mean to us in our lives?
I couldn't say it any better than Rachel in the above quote does. The chaos has a purpose, a shape and an intricate but simple design to it. Trust that!
All is well.
Daniel Schmidt (2012) Inner World, Outer World. Amazon Prime Movies
Blog: Evolving Connection (March 2015) Fractal God: How Math Met SPIRIT and Had a Baby Called Destiny. http://www.rachelthor.com/blogposts/2015/8/4/fractal-god-how-spirituality-met-math-and-had-a-baby-called-the-universe
Benoit Mandelbrot: Fractals and the Art of Roughness (July 6, 2010) TED Talk
https://www.youtube.com/watch?v=ay8OMOsf6AQ&list=FLjmYO8qecRJgz_y0ZCO-xng&index=17
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