October 10, 2017 Tuesday
Bedtime Story
Mathematics as Language
Mathematics as Language
As I was saying last night, mathematical
logic like pure mathematics also has the concept of free and bound variables.
Consider the following expression of formal
logic:
∀x ∃y [𝜙(x,y,z)]
In this expression, of the three variables
x, y and z, only z is free variable as the other two are tied down to
existential quantifier and “for all” quantifier.
So the expression primarily depends on the
value of z.
If you thought that bound and free
variables can exist only in mathematics, you could not have been more wrong.
They are found even in natural languages if
you care to analyze them through formal semantics.
After all, mathematics is also a language.
If you doubt that mathematics is a
language, think carefully of any language, specially your mother tongue that
your mother cooed into your ears since the moment you were born.
Now think carefully about that language and
you will both realize and accept that it is has within the following six
components that are part of any natural language:
(a) A vocabulary of symbols or words
(b) A grammar consisting of rules of how to
use these symbols or words
(c) A syntax which is a special kind of
grammar that decides the structure of a sentence and determines what comes
where in a sentence
(d) A ‘discourse’ or a ‘narrative’ which is
basically strings of syntactical propositions
(e) A group of people who use and
understand the above four elements of language
(f) A range of meanings that can be passed
on among the users of languages
Mathematics contains all the above six
qualities and hence logically qualifies to be a language.
One English mathematician Schwarzenberger
and a former President of Mathematical Association of UK has to say this about
mathematics as a language:
“My own attitude, which I share with many
of my colleagues, is simply that mathematics is a language.
Like English, or Latin, or Chinese, there
are certain concepts for which mathematics is particularly well suited: it
would be as foolish to attempt to write a love poem in the language of
mathematics as to prove the Fundamental Theorem of Algebra using the English
Language.”
So since mathematics is a language, let us
see if mathematical ideas can be applied to languages.
In this case let us consider the idea of
free and bound variables in a natural language English.
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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