March 20, 2019 Wednesday
Bedtime Story
Proof of Theorem 1
To arrive at the solution of this vexing
marriage problem every man has to propose to a woman for a hand in marriage but
even more importantly he has to thick skinned so as not be offended when
rejected.
It can also be done other way around with
each woman first proposing to a man that is on top of her matching list but we
all are fully aware that this is hardly natural as it is always the millions
and billions of sperms that compete for a single precious egg.
So we shall stick with the men proposing to
the women as was the case in the original paper of 1962.
I must tell you beforehand that there is an
inherent asymmetry in the benefits that accrues to these two sets of people -
namely the group that proposes versus the group that is being proposed to -
which is not very apparent until you try the whole process out.
But we shall come to that later.
In the first round every man will propose
to his girl of first choice.
This will naturally mean that some girls
will get more than one suitors and perhaps many proposals whereas there will be
others who will get a few or no proposal.
The women who get several proposals on the
other hand have to only accept one man who is on top of their love list and
reject the others.
Remember that this does not mean that all
the women have got their number one ranking man for their will be few most
sought after men who would have been picked by at their first proposal.
The other thing is that in this first round
only tentative pairing is being done and the assigned men to particular women
are only their tentative husbands.
You as a matchmaker or the yenta are
explicit about that to everybody so that they are all aware of the provisional
nature of pairing in the rounds/iterations that follow.
So the men are proposing and are either
being rejected or being held on the string of women (as the authors had put it
in their paper) only waiting to dump him if a better suitor comes in the next
round.
If this reminds you of the real life do not
be surprised as mating games are absolute brutal for after all they determine
the most important aspect of biology – the quality of offspring and their
chances of survival!
A mistake in the choice of the partner or a
faulty mating strategy can be potentially disastrous not only for the
individual female (such as sick offspring with genetic disorders) but for the
species in general.
This sets the stage for the second round or
the second iteration.
In this round all the men who were rejected
now propose to the women of their second choice.
It does not matter if those women are
single or paired since you would recall that the pairing in the first round was
only a tentative one.
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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