The Illusion & The Ultimate Truth

The Beauty of Mathematics

 


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1. THE PHYSICAL REALITY:

Our conceivable physical universe consists of only mass and energy. Each and every mass particle is fundamentally of the same nature (being formed out of bosons, leptons, hadrons and quarks). Is there any fundamental structural difference between a man and a chair? No, they consist out of the same fundamental particles. Then what really makes them different? Humans can think. Every living organism has the Will Power unlike the inert lifeless objects. What is the origin of this extraordinary unique power? Has this power originated from the complex chemical reactions in our bodies leading to biological adaptation over millions of years? Can mere chemical reactions make us think and let us do what we want to? Does any unknown Supreme Energy thrive within us? These have been the curious questions of man for thousands of years.


2. THE ILLUSION:

From ancient Indian and Eastern philosophy, dating back to thousands of years, we find a very interesting idea about The Reality.

The Eastern philosophers say that our physical world around us is nothing but an illusion, a dream. Whatever we see, we feel, we do and we think are all done in a state of trance. But The Reality is completely different. They also say that there resides a unique energy in every living organism and they call it by the name of The Aatma (The Soul). This soul cannot feel, cannot think, cannot see, cannot perform any work. They do not have any finite shape, nor have any mass, nor occupy any space. They cannot die. They just exist. But they have only one power : The Will Power. They take a mortal form only to fulfill a task guided by their Will. Naturally, a question may arise : Why does then every living object not perform a great task during their lifetime? This is because the emotions and materialistic yearnings overdo the original Will Power and make them forget about their Task in their very short span of lifetime.

All these may seem very laughable to a scientifically oriented mind. But do all these hold any truth? Let us see.

Let us consider a picture of a sphere intersecting a plane. To any living two dimensional living object on this plane, the sphere will only appear as a circle (which gets projected on the plane). To this object The Reality is the circle. But is that the Absolute Reality? No, the Absolute Reality is the sphere. It is only limitation impressed by space that binds the living object on the plane from visualizing further.

Similarly, our existence may be the projection of an Absolute Reality from a much higher dimension. Our vision, thoughts and feelings may be an insignificant projection of a much greater, nobler cause.

Did the circle have any mass or volume? No. But the sphere did. This is what is meant by The Illusion.


3. PROCESS OF HUMAN THINKING : Philosophy, Logic and Mathematics:

Man has started to think from the first day he was able to take control over his mind. But one can never take Total Control over his mind ----- if he does so, then he would be able to recognize Himself and knowing The Ultimate Truth, he would escape from the Physical Dimensions and enter into The Absolute Reality. This is what was meant by Salvation or Moksha by the ancient Eastern Philosophers including Lord Buddha.

But for a simple common man, the magnanimity of this Reality remains unknown. He tries to reason out what he observes around him and through continuous formulation of axioms, assumptions, postulates and constructing different theories explaining the behavior of things around him, he tries to conceive his reality. Like little drops of rain which add up to a boundless deep ocean, the thoughts of hundreds of men over thousands of years, give birth to philosophy and logic and hence a path leading towards The Reality.

The concepts and theories and thoughts streaming through the human brains give birth to philosophy, which when refined and researched, get established in the rigid form of logic. But when these thoughts and theories get a complete analytic proof, then it takes the form of The Ultimate Truth, the most perfect reflection of The Absolute Reality ---- Mathematics.


4. MATHEMATICS -- THE FORMLESS BEAUTY:

"Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitutes the life, usefulness and the supreme value of mathematical science."
(Quoted from : 'What is Mathematics?' by Courant & Robbins)

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting and music, yet, sublimely pure, and capable of a stern perfection such as the greatest art can show."

"Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos, where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world."
(Both the above quotations are from the essay : 'The Study of Mathematics' by Bertrand Russell)


5. THE FRAGILE PHYSICAL WORLD :

Everything in this materialistic world is dependent on space and time. Laws of economics, geography, political sciences and even the worshipped laws of the physical sciences may not hold their present discovered truths one day. But those beautiful equations originating from hardcore logic will always dictate human ways of thinking and techno scientific inventions through all the ages. If in a different universe, Newton's Law changes to F=ma^6 then almost all the present physical laws would break down. But the elements in the set of the Real Numbers will always obey the Associative, Commutative and Distributive Laws, no matter what. This is the only field which is completely independent of the others. It is only logical thinking and hence strong human reasoning and philosophy that has led all the people and the scientists over thousands of years to formulate laws and construct axioms and postulates. Nothing other than the complete annihilation of the human race can cease this process of human thinking and hence advancement of philosophy, logic and mathematics. The truth suggested by them can be reformed but the earlier proofs can never be disregarded or discarded completely.

Emotions are nothing but secretion of different hormones from the different glands and their flow into the brain through the bloodstream. This may sound very unromantic, but this is the most scientific truth acquired from detailed study of the human anatomy. But still these emotions have enough power to make us forget The Truth and push us more and more into the dark world of The Illusion. The hormones like adrenaline, testosterone, estrogen and progesterone do nothing but distract us from our objective in life and make us dwell into our primitive wild nature.


6.CONCLUSION ---- Our goal in life :

We are a part of The Illusion. "The world is a stage and we are mere performers." But were our souls given a chance to enter this Illusion to eat, earn money, relish life and then die like zillions of insignificant insects ---- leaving no contribution ? Then why did we exist for? We must know our Goal in life, our Ultimate Task. We must blaze our locus through this illusioned world, tearing through the mere dimensions of space and time.

We must not be misled and distracted from our Task in this illusioned world which is highly temporary and unstable. We must not get incorporated into that set where exceptions rule the nature. We must construct that rigid mathematical structure that the Nature itself would not be able to falsify. We must not be lead a worthless life led by paltry emotions and hormones. We must remember : To be The One, we have to dedicate ourselves only to our mission in life. We must believe in ourselves, have Supreme Self-Confidence, unquenchable thirst for knowledge and unpenetratable reasoning power and logical abilities. Our mission in life is to advance the human mind and philosophy closer to the Ultimate Truth ; to introduce The Reality in this Illusioned world.

So, we must take this as the only challenge in our lives and devote ourselves to revolutionary and influential thinking. We must show what extraordinary capabilities we have in us. Our principle in life should be :

"Strength is Life,
Weakness is Death."

and we must overcome all the obstacles in our path towards The Ultimate Task with "nerves of steel and muscles of iron".

"Arise, Awake and stop not till the goal is reached."
(Swami Vivekananda)


THE LAST FEW WORDS :

 

"I could be bounded in a nutshell
and count myself a king
of infinite space."


(William Shakespeare : Hamlet, Act 2, Scene 2)


APPENDIX : An example of the beautiful logic and art of Mathematics

Prove : If a + b = a + c then b = c

The Proof :

The Field Axiom 5 (The existence of negatives) states that " For every real number x there is a real number y such that x + y = 0 ."

We here choose a number 'y' such that : y + a = 0 ...............(1)
Therefore, as it is given that : a + b = a + c, we can write :
y + (a + b) = y + (a + c) ..............(2)

From the Associative Law (Field Axiom 2) we can write from (2):

(y + a) + b = (y + a) + c ...............(3)


But from our earlier condition (1), it follows from (3). that :

0 + b = 0 + c ..............(4)

The Field Axiom 4 states that : " There exists a real number '0' such that for every real x, x + 0 = x ."

Therefore, we can write from (4),
b = c

Hence Proved.

In our common practice we would have just cancelled out 'a' from the left and right hand sides of the given equation and reach the conclusion, but here we have tried to show the rigorous and rigid logical route to this obvious conclusion.


Compiled and Written by : Vivek Panda
dated 31st August 2003.


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© & ® Vivek Panda : August 2003