December 16, 2016 Friday
Bedtime Story
Story of Two Men Who Pursued the Axiom of Choice
Let me tell you a great story on one of the most dazzling
paradoxical outcomes of the axiom of choice.
Just keep in mind that such simple theorems and axioms such as
well-ordering theorem and axiom of choice lead to very powerful and counter
intuitive outcomes when taken to their logical conclusions involving
infinities.
We apes and our brain have evolved to engage with only three-dimensional,
mid-sized world and to solve problems limited to few numbers such as the number
of available mating partners or to count the pack of wolves or say mules.
So the concept of infinites are inherently difficult to grasp.
Perhaps not so for two great Polish mathematicians Stefan Banach
and Alfred Tarski.
These two great mathematicians and logicians largely unknown to
most were born in Poland 19 years apart from each other.
Stefan Banach was born in Kraków in 1892 (then part of Austro-Hungarian
Empire) and Alfred Tarski in Warsaw of 1901.
Poland, as you must be well aware, is a cursed nation with the
recent history perhaps only slightly less miserable and wretched than the
Indian subcontinent.
Banach was born out of wedlock (his father being a soldier and as
per rules was not allowed to marry) and the only time he spent with his mother
was those mandatory nine gestational months in the uterus.
He was given the first name of his father and the surname of his
mother.
He was essentially a self-studied and self-made man, supporting
his intense thirst for education by doing whatever he could find.
When the Russian Empire attacked the Austro-Hungarian Empire in
1914, he made his living doing odd jobs such tutoring, working part time in
some book shops or becoming overseer or road building crew.
During the war, in 1916 somewhere in the beautiful city park of
Krakow a professor of mathematics Hugo Steinhaus was taking a stroll when he
overheard someone speaking about Lebesgue integral, an improvement over Riemann
integral.
Steinhaus walked up to see who was discussing such an abstruse
topic and he came across two young men by the name of Otto Nikodym and Stefan
Banach.
Banach took Steinhaus by storm.
Steinhaus knew he had found a prodigy, much like the discovery of
Srinivasa Ramanujan by Hardy somewhere around that time (1913).
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
Good night and my fellow cousin ape.
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, may I
suggest this large collection of Kids Songs:
Stefan Banach was to Steinhaus in 1916 what Srinivasa Ramanujan was to G. H. Hardy in 1913
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