April 11, 2017 Tuesday
Bedtime Story
New Non-Euclidean Geometry Raised Doubts About Its Consistency
In proposing the parallel postulate, Euclid had made one
assumption that was very intuitive and obvious and yet it was hugely flawed.
The new kind of mathematics that Hilbert was proposing was
certainly not easy, when one has to dismiss the cozy familiarity and stick to
the rigorous axiomatic definitions.
But that unease is compensated by the new vistas that this new
mathematics is capable of unfolding.
With Peano, Hilbert and Russell came intense formalization of
mathematics that gave rise to completely unheard kind of algebras and geometry.
The interpretations of this new stuff was certainly not very
intuitive or commonsensical.
And as we all know, intuition has always been an enemy of reason
and science.
Moreover, intuition is a relative that can change or does alter
with increasing knowledge, awareness and education.
Take a devise as elementary as a simple calculator.
We all handle it with extreme ease yet given to an individual
belonging to eighteenth century would leave him flummoxed and bewildered.
Similarly the idea of time to me as a young boy was absolute.
I recall as a very young boy reading a large science book that
discussed the theory of relativity and the concept of time dilating and
contracting.
It was then simply impossible to grapple with this idea.
How the hell can time shrink or expand!
It would contradict my whole understanding of the world no matter
how limited it was then!
I am sure it would be same for most grownups as well even today
who have not been introduced to this fascinating theory.
Yet now here I am, at far more ease of coming to terms with the
time dilation under the influence of both speed and gravity.
So as mathematics got new wings with abstraction, some worries
began to creep in.
You see, Euclidian geometry was based on very middle-earthly
measurements, and hence its conclusions were never dubitable.
There was a kind of assured blind belief that the axioms of
Euclidean geometry would never lead to mutually contradictory results.
With the entry of non-Euclidean geometry, all the Euclidean certainty
began to dissipate since there was no real earthly model on which it was based.
Apparently this new geometry had apparently nothing to do with the
universe that we live in.
So what was the guarantee that this kind of geometry was as
consistent as Euclidean?
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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