December 31, 2016 Saturday
Bedtime Story
Paradoxical Decomposition of Hyper-Oxford
This is what we will land up with after taking out the first
redundant alphabet from each word of all the 26 volumes:
Volume A: A, AA, AAA, … , B, BA, BAA, … , C, … , Z, ZA, …
Volume B: A, AA, AAA, … , B, BA, BAA, … , C, … , Z, ZA, …
Volume C: A, AA, AAA, … ,
B, BA, BAA, … , C, … , Z, ZA, …
Volume Z: A, AA, AAA, … , B, BA, BAA, … , C, … , Z, ZA, …
Voila! They are all identical!
Moreover, each one is identical to the original hyper-Oxford!
Isn’t this a paradox?
If you are seriously interested in this paradox, I would encourage
you to read the book:
The Pea and the Sun: A Mathematical Paradox
By Leonard M. Wapner
In a way, what we did with the hyper-Oxford is paradoxical decomposition.
We broke up the first infinite set into a finite number of
disjoint infinite subsets.
The paradox is the fact that all the 26 subsets can be mapped back
into the original set using only finitely many distinct functions (like taking off
or adding on the first alphabet).
This is exactly how Felix Hausdorff defined paradoxical
decomposition.
We are going to do something similar with the sphere.
We are going to convert our hypothetical numerical sphere into
infinite points thus decomposing it into a hyper-Oxford dictionary.
The first step for that is to designate name for all the infinite
points on the sphere.
Non-mathematically it can be done by giving each point a label
depending upon how they are reached from a given starting point on the surface
of the sphere which will be origin for that case.
We shall deal with the naming of all the points on the sphere in
the nights to come.
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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