March 26, 2017 Sunday
Bedtime Story
How Peano and Principia Mathematica (1910) Revived Begriffsschrift (1879)
As I had stated, the outstanding Begriffsschrift got scant
attention.
It was the student of Gottlob Frege Rudolf Carnap, along with
Ludwig Wittgenstein and of course the monumental Principia Mathematica that
revived and gave this treatise a new breath of life and deserving recognition.
After Gottlob Frege, Peano further worked on these notations.
In fact, all of the notations that I had used in my previous
bedtime stories were not that of Frege but more of Peano’s.
The notations that were used by Gottlob Frege had a strange
two-dimensional layout that not only made reading it cumbersome but printing it
out economically impossible.
Peano went through the notations of Frege and transformed them to
a more linear, more manageable and far more aesthetically refined.
As I had narrated once, so obsessed was Peano was with
mathematical notations that he devised a whole new language Interlingua that
was essentially Latin but bereft and denuded of all grammar.
Which means to say not only was Peano unhappy with the state of
mathematics but also with daily use of language.
He also summarized all of the known mathematics till then in his
Formulario Mathematico.
The notation that he used in this Formulario Mathematico caught on
really well (unlike his Interlingua), and was used by Bertrand Russell and
Whitehead in the Principia Mathematica.
This use of notations was not casual; Russell had met Peano in the
famous twin conferences of philosophy and mathematics in 1900 that were held in
Paris.
(Yes Sir, the same one where David Hilbert set the agenda for the
mathematicians of the time and those to come by announcing his list of 23
unsolved problems.)
As I had stated before, at the onset of the conference Peano
offered Russell a copy of his Formulario Mathematico.
Russell was deeply and profoundly impressed by Peano’s notation
and it was this encounter that probably implanted the seed in the mind of
Russell that would flower on to become Principia Mathematica.
When it comes to mathematical notation, there is no text that can
match the sheer intensity, depth and extent that was deployed in Principia
Mathematica.
In fact, some claim that it is the most notation-intensive work
ever generated by a non-machine (considering the fact that computers use codes
all the time).
You really need to see just one page of this monumental work; it
is simply incomprehensible for the mind of an average ape.
Sometimes one wonders whether Whitehead and Russell ever meant it
to be read by the human apes.
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.
A Typical Page from Principia Mathematica
List of "Definitions" (about 500) are listed at the end of Volume 1 with most fanciful notations possible. No wonder very few human apes have ever went on to go through this landmark work.
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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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