September
09, 2017 Saturday
Bedtime
Story
From Gottlob Frege to Daniel Hillis
I
keep repeating ad nauseam that the seminal work of Gottlob Frege was
Begriffsschrift (1879), but it was in his “The Foundations of Arithmetic”
(1884) where he clearly proposes his view of logicism; that arithmetic is a
branch of logic.
He
aimed to show that arithmetic has no basis in intuition.
(Many
would disagree with Frege as several great mathematicians such as Ramanujan and
Bernhard Riemann were strongly intuitive.
Of
course, this can be counter argued with the simple fact that we do not have a
decent understanding of both intuition and workings of mind.
The
fact remains that there is nothing that a human mind can compute extra which a
computer cannot do.)
At
this point I will take the pleasure of quoting a passage from a fairly popular
book by a computer scientist Daniel Hillis named “The Pattern on the Stone: The
Simple Ideas That Make Computers Work”.
This
guy is seriously good and very oddly is the Judge Widney Professor of
Engineering AND Medicine at the University of Southern California.
He
has a formidable family background.
His
father was a US Air Force epidemiologist who took to the study of Hepatitis in
Africa and so Hillis spend many years of his childhood in Africa.
His
father also happened to be a visiting faculty at ISI, Calcutta and so Hillis
also happened some time of his childhood in Calcutta, India.
When
in Calcutta, this little boy was schooled by his mother who happened to be a
biostatistician.
It
was through his mother in this period that he developed a liking both towards
mathematics and biology; a love that is almost universally mutually incompatible
among students.
He
has two siblings, one brother and one sister.
His
brother is a professor of evolutionary biology at the University of Texas,
Austin.
His
sister is a professor of neurology at Johns Hopkins University.
Pretty
formidable family, eh!
It
was while writing about Gottlob Frege and his views on intuition and
mathematics that I recalled having read something in the book “Pattern on the
Stone” that has relevance to our bedtime story here.
The
excerpt that I am quoting is from the chapter titled “How universal are Turing
Machines?”
It,
I think, is perhaps the most interesting chapter of the book as it talks about the
universality of Turing’s computing machine, Gödel’s incompleteness theorems,
Church thesis, limitations of a universal computing machine and so on.
Since
by now, at least those of you who have diligently following my bedtime stories,
must be well versed with Gödel’s incompleteness theorems, this paragraph should
prove to be exciting.
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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