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The Chaos Theory (Fractals) Part - 2

Updated on February 22, 2013

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!"

The Ultimate String theory too seems to come with strings attached for those who do not trust!
The Ultimate String theory too seems to come with strings attached for those who do not trust!

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".

Fractals are a way to understanding infinity
Fractals are a way to understanding infinity

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)

The first few steps of constructing the Koch Curve
The first few steps of constructing the Koch Curve
The Koch Curve grows on but is always within a circle of finite area!
The Koch Curve grows on but is always within a circle of finite area!

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.

2) Man who is finite can be the embodiment of God who is infinite.

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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    • profile image

      Tilly 2 years ago

      Your article was exeenlclt and erudite.

    • aravindb1982 profile image

      Aravind Balasubramanya 4 years ago from Puttaparthi, India

      @ Anonymous - Oh My God! Where did I ever say that "String theory is wild imagination"?

      I have the greatest regard for it and I feel the same is reflected in the article. Is it because I called it "Fantastic"? In my part of the world that word is used to denote "fascinating". I realize that in some parts of the world the same word may mean "wild imagination". I have immediately changed the word.

      Sorry for that error in language.

      I have the greatest admiration and respect for string theory and string theorists. I just stated that there are some that worship the theory but some others who consider it 'not science'.

      My opinion of it is that it is phenomenal...

    • profile image

      Anonymous 4 years ago

      With all due respect, it is not appropriate to term String Theory as wild imagination. If it were so then the best brains in the world wouldn't be working on it and the most premier research centres wouldn't be funding it. It takes years and years of hard work and toil for any major breakthrough in Science. It is only after going through a lot of advanced mathematics and physics can one start to appreciate things like quantum theory or string theory but it is equally easy to comment like a layman. This is just like how joy of God is to be experienced but it is very easy for an atheist to pass a sloppy comment. Science always progresses by reasoning and logic. This is the way it has been progressing and should progress since it solely belongs to the material domain. On the other hand, God by definition transcends this plane and hence it is impossible to rationalize which by its very definition defies logic and reasoning.

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      darshi 5 years ago

      I was wondering how I missed this part :P Honestly Anna, the theoretical parts here didn't quite jive with me (I hated Maths/Physics/Add Maths in school, it was never what I was good at!), BUT I did understand it. :)

      And the concluding sentences made a whole load of sense...its more like affirmations to things I've been reading and understanding recently. Lots to reflect :)

      As always, thank you for sharing big bro..have a good rest of the week! :)

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