"Reductio ad absurdum": A Mathematician's delight & a Philosopher's quest!!

   Philosophy & Mathematics share such an extraordinary rapport that they have shaped up civilizations, spurred up intellectual revolutions and at times together have surmounted the seemingly unsurmountable.

   Despite arguments that Philosophy & Maths(Science in general) are at loggerheads with each other in terms of perspectives & interpretations, to a lot of us with interdisciplinary interests, they are different faces of the same coin. In the words of Will Durant - "Philosophy seems to stand still, perplexed, but only because she leaves the fruits of victory to her daughters the Sciences, and she herself passes on divinely discontent, to the uncertain & unexplored."

  One such aspect of immense interest in both the disciplines is "Reductio ad absurdum"(Latin for 'reduction to the absurd'). Its a form of argument in which a proposition is disproven by following its implications logically to an absurd consequence. Familiar to students of Mathematics as "Proof by contradiction".

  Now the beauty of this form of argument is two folded. One in the perspective of Math and the other in the light of Philosophy.

  To illustrate the Math perspective, Hardy does it best in his famous statement - " Reductio ad absurdum, which Euclid loved so much, is one of Mathematician's finest weapons. It is a far finer gambit than any chess gambit; A chess player may offer the sacrifice of a pawn or even a piece, but a Mathematician offers the game." In the method of proof by contradiction, the very first statement would be to assume what is to be proved true as false!! Like if you had to prove the number of primes was infinite, you start by assuming the number of primes is finite(crazy!) and then prove the assumption to be false(crazier!). Maybe rather than being a method of proof, it is a method of disproving the false and thereby acting as an implied proof of the truth!! There lies the beauty for the beholder!!

  In the light of Philosophy, the argument has rendered a lot of interesting twists in the tale. Consider Neils Bohr's statement: "The opposite of every great idea is another great idea." Carl Sagan used a reductio ad absurdum argument to counter this claim. If this statement is true, then it would certainly qualify as a great idea - it would automatically lead to a corresponding great idea for every great idea already in existence. But if the statement itself is a great idea, its opposite must also be a great idea. The original statement is disproven because it leads to an absurd conclusion: that an idea can be great regardless of whether it is true or false. Now what is true and what is false has been Philosopher's quest for over centuries. But how the approach of argument renders interpretation is interesting.

  "If the windows of perception are cleansed, everything would appear as it is - infinite.

                                                                                            - William Blake"

To us, who read and relish..

        The beauty of literature lies not in the huge volumes, but in small phrases.. "Small is beautiful".. Its those small phrases which make up a beautiful composition, an extraordinary novel, a brilliant write up.. "Dedications" are such small but profound and impact making pieces found in literature.. Its been a habit of mine to read "dedications" of books and movies.. In the intriguing journey of life, here are my pick of the interesting dedications I have come across..

1.Nani A.Palkhivala in We, the People


"TO MY COUNTRYMEN
   who gave unto themselves the Constitution
      but not the ability to keep it,
   who inherited a resplendent heritage
      but not the wisdom to cherish it,
   who suffer and endure in patience
      without the perception of their potential."



2.C.S.Lewis in The Lion, the Witch and the Wardrobe

"To Lucy Barfield

My dear Lucy,

I wrote this story for you, but when I began it I had not realized that girls grow quicker than books. As a result you are already too old for fairy tales, and by the time it is printed and bound you will be older still. But some day you will be old enough to start reading fairy tales again. You can then take it down from some upper shelf, dust it, and tell me what you think of it. I shall probably be too deaf to hear, and too old to understand a word you say, but I shall still be

your affectionate Godfather,

C. S. Lewis"


3. Ayn Rand in the first edition of Atlas Shrugged (The words and sentences in bold were deleted from editions printed after 1968.)


"To Frank O'Connor and Nathaniel Branden."

"I knew what values of character that I wanted to find in a man. I met such a man -- and we have been married for twenty-eight years. His name is Frank O'Connor. When I wrote The Fountainhead, I was addressing myself to an ideal reader -- to as rational and independent a mind as I could conceive of. I found such a reader -- through a fan letter he wrote me about The Fountainhead when he was nineteen years old. He is my intellectual heir. His name is Nathaniel Branden."

4. Anurag Kashyap in the Hindi movie Gulaal

"To all those poets of pre-independent India who wrote songs of freedom and had a vision of free India, which we could not put together."


5.Will Durant in The Story of Philosophy


"TO MY WIFE
   Grow strong, my comrade.. that you may stand
   Unshaken when I fall: that I may know
   The shattered fragments of my song will come
   At last to finer melody in you;
   That I may tell my heart that you begin
   Where passing I leave off, and fathom more."

6.Captain Gopinath in Simply fly


"To my father:
   Who taught me that:
    I must dream but not envy.
    I must lose myself in action but not in despair.

  To my wife:
   Who sacrificed everything and stuck with me and my 'madness'
       and displayed stoic courage.
......."

7.Dr.APJ Abdul Kalam in Wings of fire


" To the memory of my parents

My Mother

Sea waves, golden sand, pilgrims’ faith,
Rameswaram Mosque Street, all merge into one,
My Mother!

You come to me like heaven’s caring arms.
I remember the war days when life was challenge and toil—
Miles to walk, hours before sunrise,
Walking to take lessons from the saintly teacher near the temple.
Again miles to the Arab teaching school,
Climb sandy hills to Railway Station Road,
Collect, distribute newspapers to temple city citizens,
Few hours after sunrise, going to school.
Evening, business time before study at night.
All this pain of a young boy,
My Mother you transformed into pious strength
With kneeling and bowing five times
For the Grace of the Almighty only, My Mother.
Your strong piety is your children’s strength,
You always shared your best with whoever needed the most,
You always gave, and gave with faith in Him.
I still remember the day when I was ten,
Sleeping on your lap to the envy of my elder brothers and sisters
It was full moon night, my world only you knew
Mother! My Mother!
When at midnight I woke with tears falling on my knee
You knew the pain of your child, My Mother.
Your caring hands, tenderly removing the pain
Your love, your care, your faith gave me strength
To face the world without fear and with His strength.
We will meet again on the great Judgement Day, My Mother!

                                                                                       - APJ Abdul Kalam"