December 12, 2016 Monday
Bedtime Story
The Essense of Mathematics : Deductive Reasoning
The story of mathematics is rather different and very much untold.
Most of us have been taught elementary physics and mathematics
with very little understanding of how they work.
Many of us take mathematics to be the ultimate truth and reality.
It is hardly so.
Mathematics is the most extreme game of logic and reasoning
(something like a game of chess where the only player is the mathematician
himself) but very little to do with truth and reality.
That it sometimes, or rather a lot of times, applies to physical
sciences and ends up in describing reality “is a wonderful gift which we
neither understand nor deserve”, in the enduring words of Eugene Wigner.
Theorems or rather mathematics itself begins with very basic
propositions that are called axioms and are considered to be self-evidently true.
Both time and history has shown that these assumptions can be
mistaken and hence one must always bear in mind that axioms are primarily assumptions
that rests on our evolved intuitions that at the very best work statistically
for our survival.
Axioms can also be taken as the starting rules of a game from
which the rest of it is played out.
Take for example Euclid’s very first axiom.
Things that are equal to the same thing are equal to one another.
Another example would be one of Hilbert’s axioms of geometry:
If a point B lies between point A and point C, then the points A,
B and C are three distinct points of a line, and B then also lies between C and
A.
Axioms like these do not require proof.
At least they do not seem to or we do not have them.
They are taken as established truths or facts.
Thereafter, using logic, rigorous chain of reasoning from the
axioms, theorems are built up, the classic one being the Pythagorean Theorem
for which several proofs exist using the basic axioms.
This is known as deductive reasoning and is the pillar stone for
constructing the magnificent edifice of mathematics.
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:
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