October 17, 2017 Tuesday
Bedtime Story
Haskell Curry Goes to Göttingen from Princeton in 1928 after the Encounter with the Paper of Moses Schönfinkel
Last night we saw that Schönfinkel had
introduced two more combinators B and C besides the already existing I, K and
S.
Schönfinkel also showed that the
combinators B and C could also be expressed using only S and K.
B = (S (K S) K)
C = (S (S (K (S (K S) K)) S) (K K))
Understandably all this is very technical
and intricate and I assume it does not make sense to you.
There is a derivation and proof for it but
since I am mostly a story teller and storytellers take certain things for
granted, we shall assume that the proof is a valid one and move on.
The point of the story was to give a taste of
the kind of work Schönfinkel had done.
He showed that the whole of combinatory
logic could be reduced to just K and S and this system was as powerful as
predicate logic.
When Haskell Curry read this paper, he left
Princeton and moved to Göttingen under the supervision of David Hilbert
somewhere in 1928.
Those were the years when the Institute for
the Advanced Study was only a figment of imagination of Abraham Flexner and Göttingen
still was the epicenter of mathematics.
Hitler then was still an unknown figure, a
dot of a figure far over the German political horizon.
Curry could not meet Schönfinkel who had
left back to Moscow but he did work with Heinrich Behmann and Paul Bernays,
both of whom were well versed with Schönfinkel’s work.
Curry eventually went on to receive his
Ph.D. in 1930 at Göttingen under the supervision of David Hilbert with his
dissertation being on combinatory logic.
On returning to the United States, Curry
hope to show that combinatory logic could provide the foundations of
mathematics.
It was not to be as Kleene and Rosser came
up with their paradox in the systems of both combinatory logic and original
lambda calculus of Alonso Church.
As we had discussed earlier, presence of
paradoxes in any formal system is a reflection of the system’s inconsistency.
Curry though disturbed by this paradox
never gave up and devoted his whole life in developing and improving
combinatory logic and its application to the foundation of mathematics.
He defended his perseverance by stating
that he did not wish to “run away from paradoxes”.
You may not recall, but in the bedtime
story of October 02, 2017 which was a Monday (at least in my time zone) I had
promised you that I will deal with Haskell Curry and his famous Y combinator or
the Y operator.
So then I went on to write about Haskell
Curry but did not touch upon the Y Combinator.
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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