March 29, 2017 Wednesday
Bedtime Story
This Bourbaki group introduced the notation 𝝓
More importantly, the Bourbaki group laid a great emphasis on the
use of notations and minimizing imprecise language wherever possible.
It was finally this group that made mathematics possess that scary
look that sets fear in the hearts of the bravest of men.
This is clearly visible if you make a study of papers on pure mathematics
that was published before the 1940s and after.
Post Bourbaki, pure mathematics papers had a dramatic reduction in
texts and a manifold increase (to borrow a term from mathematics) in the
notations.
With this huge increase in notation, came the great division.
Now clearly, there were two kinds of people in the world; People
who understand and are at ease with the mathematical notations and the rest who
aren’t.
Clearly I like most average apes fall in the second category.
This is all that I have to say about mathematical notations.
Now it’s time I take you to Kurt Gödel and his incompleteness
theorem.
This is a difficult subject to write upon so please bear with me
if you are left dissatisfied.
Of course, I will time and again need to digress since without
laying the foundations and establishing the background, the understanding of
the incompleteness theorems will leave you discontented.
Moreover, it does not make for a good story telling if one does
not have the liberty to back track and shift the background sceneries.
It was in 1931, just when the Nazis were appearing on the horizon,
that a young man of 25 at the University of Vienna published a paper in a
German scientific magazine.
The paper was titled: “On Formally Undecidable Propositions of
Principia Mathematica and Related Systems”.
Now you can see why I had to tell you so much about the history of
mathematical notations and the daunting work of Alfred North Whitehead and
Bertrand Russell.
It was and still is a preeminent masterpiece of mathematical logic
and foundations of mathematics.
Masterpiece it may have been, but Gödel seemed to have found
something not quite right about it.
That itself speaks volumes about the beautiful mind; the audacity
to challenge the prevailing authority, even someone as towering as Bertrand
Russell.
As you all know, mathematics, more particularly geometry, is not
an experimental science which are often described as inductive.
In other inductive sciences, there are theories that rest on the
outcomes of experiments.
Mathematics is totally deductive.
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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