April 09, 2017 Sunday
Bedtime Story
The Axiom Wobbled and Mathematics Stood Redefined
Besides revolutionizing mathematics, the other thing that these
great minds of the nineteenth century managed to achieve (albeit accidentally)
was to bring down Euclid from the exalted pedestal of mathematical angel down
to the level of a fallible ape.
Not only was the fifth postulate not provable, but replacing it
with something very contrary, gave rise to geometry of totally new universe
never seen or heard-of before.
For the first time the old-age belief that the axioms were
self-evident truth was totally shaken.
From then on, it became clear that the axioms need not have
anything to do either with truth or with reality; they just need to be taken
for what they are, pure assumptions.
The job of mathematicians then, is to start from these agreed
basic assumptions and derive theorems following the rules of the game.
That some mathematics finds applications in real world physics is
simply accidental and a privilege that we neither understand nor deserve.
In the endearing words of Eugene Wigner that I simply love to
quote ceaselessly, “The miracle of the appropriateness of the language of
mathematics for the formulation of the Laws of physics is a wonderful gift
which we neither understand nor deserve.”
The whole understanding of mathematics went a transformative
change by the termination of that century.
Earlier it was understood as “science of quantity” and to some a
“study of patterns”.
To my mind, both these understanding of mathematics is neither
deserving not adequate.
My whole interest in studying and writing about mathematics
stemmed from the natural curiosity that behoove to seek answer to this
elemental question, “What is mathematics?”
Now finally I can say with pride that without even having the
basic knowledge of mathematics, and having no serious training in mathematics,
I can answer this question better than most mathematicians.
For it, I had to discard the problem-solving mentality and study
mathematics from a whole new perspective through the minds of mathematicians themselves.
Mathematics is the quintessential exercise in logic that starts
from basic assumptions and uses strict rules to build or arrive at conclusions
whatever they may be.
To assign any meaning to the mathematical inference would be a
huge mistake that one would commit at his own peril.
Assigning meaning should in fact be left to physicists.
Mathematics then, is far more abstract and formal than many would
like to believe or accept but that is what came out to be the fact in the
middle of the twentieth century.
It is abstract because its conclusions can be extremely
counter-intuitive and apparently nothing to belong to the universe that we live
in.
The most famous example is the Banach-Tarski paradox published in
1924 to which I had given considerable consideration and had paused to linger several
nights going over it.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
Good night mon ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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