March 18, 2019 Monday
Bedtime Story
David Gayle and Lloyd Shapely
This stable marriage problem can be more
formally stated as follows:
Given n men and n women, where person has
ranked all members of the opposite sex in order of preference, marry the men
and women together such that there are no two people of opposite sex who would
both rather have each other than their current partners.
When there are no such pairs of people, the
set is deemed stable.
It must be stressed that the value of
number n does not matter.
In our instance we had considered a small
isolated village containing “few men and few women” but this is applicable to
the entire planet housing 7 billion people as well.
So what do you think about this problem?
Is there any possible way of making such
successful matching?
Well, I will let you that the answer to
this problem is yes which was proved way back in 1962.
Two American mathematicians and economists
by the name of David Gayle and Lloyd Shapely in the year 1962 published a paper
in the journal “The American Mathematical Monthly” that was titled “College
Admissions and the Stability of Marriage”.
What is strange about this 16-page long
mathematical paper is that it has no long gibberish equations or obscure
formulas.
The paper is so astoundingly
nonmathematical based on totally ingenious reasoning in plain and simple English
that the authors ended the paper with a final part titled “Addendum on the
nature of mathematics”.
Before we go into this paper and discuss
the solution to the problem it is worth reading this part of the paper first.
“The problem which we have discussed here
seems to be of some interest both from an abstract mathematical point of view
and from that of practical application.
There is another aspect of the problem
worth mentioning.
As an exercise in mathematical reasoning it
provides a counter example to some of the stereotypes that non-mathematicians
believe mathematics to be concerned with.
Most mathematicians at one time or another
have probably found themselves in the position of trying to refute the notion
that they are people with “a head for figures”, or that they “know a lot of
formulas”.
At such times it may be convenient to have
an illustration at hand to show that mathematics need not be concerned with
figures, either numerical or geometrical.
For this purpose we recommend the statement
and proof of our Theorem1.
The argument is carried out not in
mathematical symbols but in ordinary English, there are no obscure or technical
terms.”
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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