The Chaos Theory (Fractals) Part - 2
It is not that we need theories and practices to agree with each other in the way we percieve for one to have faith in God. Faith is such an enigma. It is the strong conviction in the unseen which changes it into the seen! And that is a point at which traditional science begs to differ. Science is about "seeing is believing" while faith seems to say, "believing is seeing". This is the cause for many a debate and the twain never seems to meet.
However, the great Masters have given importance to both Science and Faith. And that is because if Science is really the quest for Truth that it claims to be, it will inevitably land on the Truth - one just has to ensure that Science does not degrade into biases just as it happens at times in religion.
The Chaos theory is something that is considered Frontier Sciences. As I read more about Chaos theory, I happened to chance upon another equally fascinating and absorbing theory called the String theory. As I read about it, it felt so unifying and special.
Oh my! There is so much to write about! But the heart of the matter is that string theorists are not able to design an experiment to prove their postulates. What they say is this,
"Believe in the theory and apply it. You will see that it works!"
Now is this a theory or is this faith? I rejoiced for I felt that finally the frontiers of science were catching up with the basics of faith. Then I am shocked by the reaction that some parts of the world accords these theorists - it calls them non-scientific! What is worshiped as the pinnacle of scientific achievement by some is considered as wild imagination by some other!
At this point, I am reminded of the saying by the great saint, philosopher and scholar, Adi Sankaracharya. He says,
"Pashyanapi Na Pashyati Mudho, Mudho , Mudho".
This translates into the lament,
"You see and yet you do not see, Oh fool! Oh Fool! Oh Fool!"
Seeing through the physical eyes and through the eyes of faith are not the same things!
Again I am reminded of Swami's quote, "Munde Munde Mathir Bhinnah" - each head contains its own thoughts and opinions. So, for those who pooh-pooh spirituality, let me say that you will find enough reasons to pooh-pooh it. And for those who swear by spirituality, let me assure you that you will find enough reasons to swear by! What matters at the end of the day is the happiness and contentment levels.
Let us jump back to the orderly world of chaos!
When Bhagawan Sri Sathya Sai Baba says,
"All of you are Divine. You just have to realize it",
it seems difficult to accept. How can I be God? How can something finite like my body house something that is infinite? And yet, when we say that Divine Consciousness pervades everything in the cosmos it means that every being, living and non-living, is as powerful as the Creator - God! Allow the beauty of chaos theory to show the possibility of this concept.
In scientific terms, this would translate as each and every tiny component of any system being able to contain the entire system itself. It is like the cell has the whole body in it. (Isn't that true for the cell has the DNA which is in fact the whole body!)
Once again, this seems to be the conclusive conclusion that the frontiers of science are heading towards. Just as the "Butterfly effect" has come to symbolize connectivity, the term "fractal" symbolizes the concept of the part containing the whole. In simple terms, a fractal is "a rough or fragmented geometric shape that can be subdivided in parts, each of which is a reduced-size copy of the whole".
Imagine a triangle, each of its side a foot long. Now just take the middle one third of each side and add another similar triangle. The result is the famous star of David with twelve sides instead of the original three.
Take the twelve sides and repeat the transformation attaching a smaller triangle onto the middle third. The outline becomes more and more detailed. Continue doing this to infinity and the snowflake kind of structure that results is an example of a fractal. This has been called the Koch Curve. (see figure below)
On reflection, it becomes apparent that the Koch Curve has some interesting features.
1. The most obvious one is that since this 'triangle-adding' transformation is applied to infinity, each triangle, be it the smallest or the largest, represents the entire Koch Curve itself!!
2. Another important thing, it is a continuous loop, never intersecting itself, because the new triangles on each side are always small enough to avoid bumping into each other.
Each transformation adds a little area in the curve BUT the total area remains finite because if you drew a circle around the original triangle, the Koch Curve will never extend beyond it. And yet, the curve itself goes on adding length infinitely. So it is infinitely long - as long as a line extending to the edges of an unbounded universe!!
(Just as the first transformation replaces a one foot segment with four four-inch segments, each transformation thereafter multiplies the total length by four-thirds. And this goes on till infinity.)
These are 'paradoxical' results which state:
1) It is possible for each component of the system to contain in it the whole system!
2) Something with a finite measure (area of the circle that can be drawn around the Koch curvein this case) can contain something that is infinite (length of the Koch curve in this case!)
Let me put the self same sentences in other words
1) It is possible for each being - living and 'non-living' - to contain the universe within it.
No wonder it is said, "Treat the stone as God but do not degrade God to the level of a stone!"
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