July
15, 2017 Saturday
Bedtime
Story
Transiting from
There
is this strange characteristic about number theory.
It
is capable of generating such remarkably simple truths whose proofs are so
complex that they can defy generations of smartest human apes.
There
is one last bit I wish to say before I leave Gödel and his incompleteness
theorem for good.
I
am sure it must be quite visible to you that even though I have been trying to
say goodbye to Gödel since last few nights, it has not been easy doing so
simply because of the impact his work had on the foundations of mathematics.
Gödel
by his remarkable coding and self-referential arithmetic showed the limitation
of mathematics and perhaps knowledge itself.
A
lot of people (who care to read and know) take an instant gratification and
perhaps secret delight in the fact that the most secure and solid of sciences has
been shown its place.
If
mathematics has its limitations then so it must be with the other sciences too,
all awaiting their Gödelian moment to befall upon them.
And
they find it a perfect moment to bring in theology, spirituality and religion,
now that they have discovered the Achilles’ heel of the most secure of the
sciences.
Since
the truth has been delinked with the proof, it is time to debunk the notion of
evidence and proof and leap into the murky darkness of spiritualism and
religion.
Spiritualism
and religion, in my opinion, are two most successful mumbo jumbo that continue to
rule the minds of the upright hairless ape.
This
is simply because of this one immutable truth about life…That life is more
often, in fact far more often, cruel than fair.
It
would disappoint them to know that mathematics, despite Gödel, though slightly
shaken has not changed much and that it is still firmly grounded in the
axiomatic system.
Yes,
mathematicians are aware of the limitations that Gödel has cast upon
mathematics in general, but when it comes to specificities, mathematics is as
strong as ever.
There
is no working inconsistency encountered in mathematics and mathematicians are
still very proud of the soundness in what they do.
The
only other person who had had as profound an impact on the field of
mathematical logic during the mid twentieth century as Gödel was Alfred Tarski.
Tarski’s
student Vaught ranks him along with the top three greatest logicians of all
times, Aristotle, Gottlob Frege and Kurt Gödel.
Alfred
Tarski was primarily a mathematician and his collected works that run into
2,500 pages are mostly on mathematics and not logic.
If
you recall, we had encountered Alfred Tarski in our bedtime story when we were
discussing the Banach-Tarski paradox and the Axiom of Choice.
Then
we had seen him more as a mathematician than a logician though of course as now
we know better, there is no demarcation between mathematics and logic.
In
fact, some of the greatest have argued that those two are identical.
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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