May
16, 2017 Tuesday
Bedtime
Story
Jules Richard and Louis Olivier
And
yet, Jules Richard was not “merely” a secondary school teacher but also a
thinker.
I
mean, besides fulfilling his duties as a teacher, he thought deeply about
mathematics and its underlying philosophy.
All
this displays characteristics of a mind that is not only interested in
mathematics and science, but is curious about truth and ways of finding it out.
Before
I go on to state his paradox, I wish to share with you his views on the
foundations and philosophy of mathematics.
I
shall summarize them into following four points:
[1]
Geometry is founded on arbitrarily chosen axioms – there are infinitely many
equally true geometries.
[2]
The axioms of geometry are founded on human experience.
[3]
The axioms of geometry are like definitions.
[4]
Axioms are neither experimental nor arbitrary, they force themselves on us.
Whatever
the reality may be, these views of his on geometry reveal depth in his thinking
on the origins of geometry and its axiomatic system.
Now
with this background we are ready to go into the paradox that was first stated
by him in 1905 in a letter addressed to Louis Olivier.
Louis
Olivier was a French scientist born in 1854 who at the age of 35 gave up
research and devoted himself to popularizing science.
In
1890 Olivier invested a large part of his fortune to create and establish the
scientific journal “General Review of Pure and Applied Sciences”.
This
journal later went on to become the primary site where major scientific
advances were first reported.
One
can still read two science essays contributed by him to the journal Popular
Science Monthly; one in volume 23, May 1883 and one in volume 37 October 1890.
The
first one is titled, “Microscopic Life in Air” and the second one is titled,
“The Evolution of Chemical Truth”.
Both
are a fascinating reads and is a reflection on the intellect of this man Louis
Olivier with whom our protagonist Jules Richard corresponded to reveal his
paradox.
This
paradox finds itself a place in Principia Mathematica along with six other
paradoxes which were used by Whitehead and Russell to put forward the problem
of self reference.
More
importantly to our story and more, this paradox inspired two greatest logicians
of those times, Alan Turing and Kurt Gödel to their seminal work.
Moreover,
Kurt Gödel explicitly sites Richard’s Paradox in the introduction of his paper as
the semantical analog to his syntactical incompleteness result. (This is an intriguing
statement).
This
paradox is very closely related to Cantor’s diagonal argument of 1891 which was
a mathematical proof for the existence of uncountable sets.
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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