March 19, 2019 Tuesday
Bedtime Story
What is mathematics?
Tonight I shall continue with the last part
of the paper of David Gayle and Lloyd Shapely titled “Addendum on the nature of
mathematics”.
The title of the paper itself is “College
Admissions and the Stability of Marriage”.
“Knowledge of calculus is not presupposed.
In fact one hardly needs to know how to
count.
Yet any mathematician will immediately
recognize the argument as mathematical.
What then, to raise the old question once
more, is mathematics?
The answer it appears is that any argument
which is carried out with sufficient precision is mathematical, or, or has been
remarked not entirely facetiously, the difference between mathematicians and
other people is that a mathematician is able to conceive of an argument
requiring more than two steps.”
Now perhaps, with this message in mind from
the authors of the paper, the reader will be more inclined to go through the
solution proposed by Gale and Shapley.
I recommend that you also go through the
original paper if time permits as it is one of those rare top-class
mathematical papers that is understandable to almost anybody.
Even though the paper is of 16-pages length
it is not all that long as you might expect it to be as the words per pages are
even less than 300 and the language is kept extremely Spartan and unpretentious
but most crucially a-mathematical if there exists such a word.
Even someone as pathetic as an innumerate
should be able to digest it provided he has the ability to reason (which I
think is even rarer a trait to seek out).
First, they proved that for any equal
number of men and women with their preferences set it is possible to solve the
stable marriage problem.
So it does not matter how large the number
of pairs are but as long as there preferences are clearly stated in order there
exists a solution to their marriage being arranged in a stable manner.
They devised their solution in a form of
algorithm that would involve number of rounds or iterations as they are called
in the world of computer science.
Although algorithm is a neat, clean and
simple one it is not much of a fun and hence I would like to tell you the
solution in my usual form of bedtime narration.
This is one of those mathematical problems
whose solution can actually be explained out in any natural languages that have
evolved over time in our human civilizations.
In the paper Gale and Shapley after stating
the problem and then with some examples showing the difficulties that one
encounters in trying to arrive at the solution stated their solution in the
form of a theorem.
They call this Theorem 1 which states that
there always exists a stable set of marriages.
Stay tuned to the voice of an
average story storytelling chimpanzee or login at http://panarrans.blogspot.com
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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