February 24, 2017 Friday
Bedtime Story
What Bothered David Hilbert also Concerned Two Englishmen Alfred North Whitehead and Bertrand Russell
David Hilbert had spoken these famous two lines on September 8,
1930 at the annual meeting of the Society of German Scientists and Physicians.
These words reflected his optimism of generating that perfect
self-contained, consistent and complete formal mathematical system bereft of
any flaws, paradoxes and indecisiveness.
One of the first serious attempt to create such a perfect and
comprehensive mathematical system was the 1910 three-volume treatise by Alfred
North Whitehead and Bertrand Russell.
Agreed that Giuseppe Peano did it before them, but his work was
neither as voluminous nor as comprehensive as theirs though it must be said
that Peano’s work was one of the inspirations for these men to work on this
book.
Both these gentlemen were English, mathematicians, logicians and
philosophers, all in one.
Russell was the younger of the two and in fact was a student of
Whitehead at the Trinity College in the 1890s.
This three-volume work of these two great minds goes by the name
of Principia Mathematica and is considered one of the greatest intellectual
feats of the twentieth century.
Modern Library, the American publishing company ranks Principia
Mathematica 23rd in the list of top 100 English-language non-fiction
books.
In a way, Principia Mathematica that I shall abbreviate to PM
since it will come several times, was a product of extreme uneasiness and
discomfort with the prevailing state of mathematics of those times (late 1800s
and early 1900s) and whose (state of mathematics) most vocal proponent was
David Hilbert.
It was essentially an attempt to reduce mathematics to pure
symbolic logic.
That means even the set of axioms and inference rules were reduced
to symbolic logic and starting from them, attempt was made to prove all of the
known mathematics.
Just the nature of task that was attempted and carried out calls
out for immense respect towards these gentlemen.
The work dealt only with the set theory, cardinal numbers, ordinal
numbers and real numbers.
A fourth volume on the foundations of geometry was thought out but
by the end of the three volumes, these two remarkable men were overwhelmed with
intellectual exhaustion.
Yet they convinced the world that in principle, almost all of
known mathematics could be derived from this formal symbolic logic.
This work is almost or is essentially deduction of mathematics
using pure logic.
One of the most memorable
fact of this painstaking tedious work that is often spoken about is that it
took more than eighty pages into volume 2 to prove that 1 + 1 = 2.
This is stated as a proposition and is followed with a comment:
“This proposition is occasionally
useful”.
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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