October 26, 2017 Thursday
Bedtime Story
Y Combinator has a Biological Analog
I have found it interesting that most
computer scientists and very smart men such as Alan Turing, Erwin Schrödinger,
Claude Shannon and John von Neumann among others have found strong association
between living and non-living, between humans and machines and between
computers and brain.
Once they saw that if out of mathematics
can arise mathematical logic, and electrical circuits arranged in specific ways
can make intelligent decisions, then surely from the far more enormous complexities
of cellular machinery and neurons can far easily arise life and consciousness.
If Erwin Schrödinger defined life in terms
of thermodynamics then John von Neumann invented the concept of cellular automata.
Alan Turing though widely known for his
Turing Machine and cryptanalysis was perhaps one of the first mathematical
biologists who published his masterpiece “The Chemical Basis of Morphogenesis”
in 1952 at the age of 39.
With his two-part article published in
1948, “A Mathematical Theory of Communication”, Claude Shannon introduced the
information theory that is the converging intersection of man fields ranging
from mathematics to biology, from computer science to neurobiology and from
pattern recognition to natural language processing.
Like all these great men listed above,
someone else noticed a connection between the loop function/Y combinator of Haskell
Curry and a fundamental element of biology.
Have a look at them once again carefully.
rec = λf. (λx. f (x x)) (λx. f (x x))
loop = (λx.x x) (λx.x x)
In both of them we have two functions lying
next to each other and both these either enable loop or recursion.
Now where in biology can you imagine
something very similar happening at a very fundamental level?
If you are not able to get it, let me give
you a hint.
Look at the sequence below.
(5’->3’) ATGGAATTCTCGCTC (coding strand)
(3’->5’) TACCTTAAGAGCGAG (template
strand)
Now you will get it!
It is the DNA, the code of life!
DNA is double helix structure with two
coils of information lying side by side which enables them to replicate with
high fidelity.
The Y combinator in an eerily similar
manner has two pieces of information lying side by side that enables recursion
not only in lambda calculus but all functional programming languages.
Self replication and recursion in a way are
very similar process and this may not be a mere coincidence.
May be I can say as a conjecture that at a
very fundamental lever there could be a connection between pure abstract
mathematics and information theory and biology.
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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