Where Science and Ancient Wisdom Converge: Fractal Geometry
Both an Ancient and Universal Concept- The Microcosm/Macrocosm- The First Fractal
One of the most fully developed written versions of the idea of the Microcosm/Macrocosm we have may be from Plato (in Timaeus) in approximately the third century BCE. However, some form of the idea of the Macrocosm/Microcosm correspondence comparing human beings to the universe seems to have been common among most ancient cultures.. ancient Mesopotamia, ancient China, ancient India , ancient Greece…
One of the most fully developed written versions of the idea of the Microcosm/Macrocosm we have may be from Plato (in Timaeus) in approximately the third century BCE. However, some form of the idea of the Macrocosm/Microcosm correspondence comparing human beings to the universe seems to have been common among most ancient cultures.. ancient Mesopotamia, ancient China, ancient India , ancient Greece…
One of the most fully developed written versions of the idea of the Microcosm/Macrocosm we have may be from Plato (in Timaeus) in approximately the third century BCE. However, some form of the idea of the Macrocosm/Microcosm correspondence comparing human beings to the universe seems to have been common among most ancient cultures.. ancient Mesopotamia, ancient China, ancient India , ancient Greece…
The Buddhist Conception of the Universe- Indra's net of Jewels- 'The Fractal Web'
Indra’s net of Jewels is a Vedic teaching originally introduced in the Atharva Veda (1000 – 900BCE).
Indra, an ancient Vedic Deity in Hinduism, has an infinitely large net of cords that hangs over his palace on Mount Meru which serves as the axis of the earth (axis mundi) in Buddhist and Hindu cosmology.
In the “eye” of each net hangs a single glittering jewel.
Since the net is infinite, the jewels are infinite and each jewel reflects all of the other jewels.
The image of Indra’s net of Jewels illustrates the way the fabric of the universe is woven together. It may be likened to a spiderweb that extends into al dimensions.
“Imagine a multidimensional spider’s web in the early morning covered with dew drops. And every dew drop contains the reflection of all the other dew drops. And in each reflected dew drop, the reflections of the other dew drops in that reflection. And so ad infinitum. That is the Buddhist conception of the universe in an image.”
– Alan Watts.
Indra’s net of Jewels is a Vedic teaching originally introduced in the Atharva Veda (1000 – 900BCE).
Indra, an ancient Vedic Deity in Hinduism, has an infinitely large net of cords that hangs over his palace on Mount Meru which serves as the axis of the earth (axis mundi) in Buddhist and Hindu cosmology.
In the “eye” of each net hangs a single glittering jewel.
Since the net is infinite, the jewels are infinite and each jewel reflects all of the other jewels.
The image of Indra’s net of Jewels illustrates the way the fabric of the universe is woven together. It may be likened to a spiderweb that extends into al dimensions.
“Imagine a multidimensional spider’s web in the early morning covered with dew drops. And every dew drop contains the reflection of all the other dew drops. And in each reflected dew drop, the reflections of the other dew drops in that reflection. And so ad infinitum. That is the Buddhist conception of the universe in an image.”
– Alan Watts.
Indra’s net of Jewels is a Vedic teaching originally introduced in the Atharva Veda (1000 – 900BCE).
Indra, an ancient Vedic Deity in Hinduism, has an infinitely large net of cords that hangs over his palace on Mount Meru which serves as the axis of the earth (axis mundi) in Buddhist and Hindu cosmology.
In the “eye” of each net hangs a single glittering jewel.
Since the net is infinite, the jewels are infinite and each jewel reflects all of the other jewels.
The image of Indra’s net of Jewels illustrates the way the fabric of the universe is woven together. It may be likened to a spiderweb that extends into al dimensions.
“Imagine a multidimensional spider’s web in the early morning covered with dew drops. And every dew drop contains the reflection of all the other dew drops. And in each reflected dew drop, the reflections of the other dew drops in that reflection. And so ad infinitum. That is the Buddhist conception of the universe in an image.”
– Alan Watts.
"Indra's entire web could be described as a holographic universe where even the smallest stream of light contains the complete pattern of the whole."
"Indra's entire web could be described as a holographic universe where even the smallest stream of light contains the complete pattern of the whole."
While ‘Indra’s net of Jewels’ is an ancient Vedic teaching with close parallels to the hermetic axiom ‘As Above So Below’, the image is also a good example of ancient wisdom overlapping with modern technology. Indra’s web is a great representation of fractal geometry; a contemporary and highly utilized discipline where mathematics and biology intersect…
While ‘Indra’s net of Jewels’ is an ancient Vedic teaching with close parallels to the hermetic axiom “As Above So Below’, the image is also a good example of ancient wisdom overlapping with modern technology. Indra’s web is a great representation of fractal geometry; a contemporary and highly utilized discipline where mathematics and biology intersect.
Benoit Mandelbrot and Fractal Geometry
Fractal Geometry was discovered and developed almost entirely through the maverick-like thinking of Benoit Mandelbrot (who at first met resistance to his unorthodox ideas.)
A fractal is a subset of Euclidean space with a fractal dimension that strictly exceeds its topological dimension. Fractals appear the same at different scales. This means if you are looking at a fractal and you zoom in or out they look roughly the same.
Fractal Geometry was discovered and developed almost entirely through the maverick-like thinking of Benoit Mandelbrot (who at first met resistance to his unorthodox ideas.)
A fractal is a subset of Euclidean space with a fractal dimension that strictly exceeds its topological dimension. Fractals appear the same at different scales. This means if you are looking at a fractal and you zoom in or out they look roughly the same.
In the whole of mathematics and science,” states Mandelbrot,” Smoothness was everything. What I did was open up the roughness for investigation.
Benoit Mandelbrot developed a theory of roughness and self-similarity in nature. With fractal geometry he could precisely measure natural shapes and make calculations that could be applied to all kinds of formations.
Where do you find Fractals in Nature?
“The basic assumption that underlies classical mathematics is that you have to reduce everything to straight lines, squares, circles, rectangles, triangles etc… “Keith Devlin (British Mathematician, Stanford University)
“The patterns in nature, the things that were already on the planet before modern humans came into the picture… the trees, the clouds, the mountains.. the weather patterns.. those were OUTSIDE OF MATHEMATICS….
until the 1970’s when Mandelbrot said…”
'Hey guys, all you need to do is look at these patterns of nature in the right way and you CAN apply mathematics- THERE IS AN ORDER BENEATH THE SEEMING CHAOS. You can write down formulas that describe clouds & flowers & plants. It is just that they are different kinds of formulas and they give you a different KIND of geometry!'
‘Hey guys, all you need to do is look at these patterns of nature in the right way and you CAN apply mathematics- THERE IS AN ORDER BENEATH THE SEEMING CHAOS. You can write down formulas that describe clouds & flowers & plants. It is just that they are different kinds of formulas and they give you a different KIND of geometry!’
“The BLINDERS came off and people could see the forms that were ALWAYS there but were formerly INVISIBLE,” says Ralph Abraham, University of California.
"The key to fractal geometry and the thing that really evaded everyone was that if you look on the surface you see complexity and it looks very nonmathematical. BUT WHAT Mandebrot said was, 'think not of what you see- but WHAT IT TOOK TO PRODUCE WHAT YOU SEE.'
“The key to fractal geometry and the thing that really evaded everyone was that if you look on the surface you see complexity and it looks very nonmathematical. BUT WHAT Mandelbrot said wask, ‘think no of what you see- but WHAT IT TOOK TO PRODUCE WHAT YOU SEE.’
-Keith Devlin, Stanford University
“The key to fractal geometry and the thing that really evaded everyone was that if you look on the surface you see complexity and it looks very nonmathematical. BUT WHAT Mandelbrot said wask, ‘think no of what you see- but WHAT IT TOOK TO PRODUCE WHAT YOU SEE.’
-Keith Devlin, Stanford University
How we use Fractals and Fractal Geometry
Fractal dimension and Self Similarity– these are the mathematical terms that give us a way that is extremely precise to look at the LIVING WORLD. Since its discovery by Mandelbrot fractal geometry has inspired breakthroughs and new technologies in many areas of science and industry including: computers, cosmology, medicine, engineering, genetics, and visual art…
Fractal dimension and Self Similarity– these are the mathematical terms that give us a way that is extremely precise to look at the LIVING WORLD. Since its discovery by Mandelbrot fractal geometry has inspired breakthroughs and new technologies in many areas of science and industry including: computers, cosmology, medicine, engineering, genetics, and visual art…
Fractal mathematics has been used to describe the financial market, to diagnose disease, and to construct the networks that make up the internet. It has also had a significant impact on the world of physical chemistry, physiology, fluid mechanics and statistical mechanics (a branch of physics that combines the principles & procedures of statistics with the laws of both classical and quantum mechanics.)When coupled with chaos theory, fractal mathematics literally seems to have lifted the veil on the natural world.
To see a world in a Grain of Sand
And A heaven in a Wild Flower
Hold infinity in the palm of your hand
And Eternity in an hour
-William Blake
To see a world in a Grain of Sand
And A heaven in a Wild Flower
Hold infinity in the palm of your hand
And Eternity in an hour
-William Blake
Resources:
Fractals- Hunting the Hidden Dimension (Nova Documentary Film 53 mins 13 sec) PBS Airdate: Oct 28,2008. Produced and Directed by Michael Schwarz and Bill Jersey. Co-produced by Edward Gray. (for more information about the film: pbs.org/wgbh/nova/physics/hunting-hidden-dimension.html)
Inner Worlds, Outer Worlds. (Documentary Film 2h 2mins) 19 December 2012. Written and Directed by Daniel Schmidt. (for a full list of cast & crew: https://www.imdb.com/title/tt2415372/ )
https://en.wikipedia.org/wiki/Fractal
https://en.wikipedia.org/wiki/Fractal_analysis
https://www.bbc.com/news/magazine-11564766
https://www.britannica.com/science/fractal
