September
07, 2017 Thursday
Bedtime
Story
Challenge to the Axiomatic Method in late 1800s
Euclid’s
totally new approach to geometry in the Elements written in 300 BC is a
landmark in the history of Mathematics.
When
Johannes Gutenberg of Mainz, Germany developed the first metal movable-type
printing press somewhere around 1440 and when such machines went commercial
around 1480, Euclid’s Elements was one of the first mathematical works to have
gone published.
In
those days, there was just one other book in Europe that surpassed the
publication of Elements in consignment.
Can
you guess which book was that mon ami?
It
was Bible, of course.
With
human apes, as you know very well, religion is never far away.
Almost
any new technology that the human apes develop is always voraciously taken up
both for spread of religion and war.
For
nearly 2000 years the axiomatic method of Euclid remained practically unchanged
and unchallenged.
It
must be pointed out though that in that long period of two thousand years, the
axiomatic method though being popularly used was not very strictly and rigidly
formulated.
It
was in the nineteenth and twentieth century, the axiomatic method began to
undergo significant and even profound transformation.
The
changes that happened in these two centuries are very relevant for our
discussion for our notion of truth.
I
was myself surprised to that even till the very end of nineteenth century,
meaning around 1890s, the notion of truth was primarily psychological.
Needless
to say what was lacking was rigor.
Intuition
ruled.
Once
a mathematician was convinced that some statement or a theorem was most likely
to be true or if he felt so, consensus was developed to accept it as true.
It
was almost an exercise, like religion, to come to an agreement to what was felt
had to be true; it was a farcical ritual of self-convincing.
The
more the number of people accepted it as true which in turn depended how it
suited the intuition and hence mental satisfaction, the more accepted it got.
There
were no restraints on the arguments that could be deployed in such proofs.
However,
as had earlier happened in the history of mathematics, need was felt once again
for a more strict analysis to the notion of proof.
This
time there was more specific reason for it.
Thanks
to Janos Bolyai and Nikolai Ivanovich Lobachevsky who developed hyperbolic
geometry and Bernhard Riemann who developed elliptic geometry and much more all
in mid 1800s, doubts began to appear on the soundness of the assumptions made
by Euclid in his Elements.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
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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