July 12, 2018 Thursday
Bedtime Story
Something Interesting Remains Left Out
Apparently it seems that we have covered
everything that I wanted to explain to you but on rechecking there is one idea
that seems to have been left out before we can meaningfully give consideration
to Noether’s theorem.
This is the idea of symmetry in nature (and
hence also in mathematics).
It generally tends to happen that
mathematical discoveries precede first which then later on find their
applications in physics.
This is so because mathematicians do not
work with reality or experimentation; they only have to start with axioms and
use pure logic to build up the edifice of their branch of their mathematics.
They need not have to worry as to whether
the theorems they churn out of logic is true in nature or whether it finds any
kind of application to other sciences as long as it is consistent and provable
within the system.
That is all the true mathematicians are
concerned about – consistency and provability starting from the axioms and
using the rules of both logic and mathematics.
Such was also the case with the idea of
symmetries.
In biology and also in the general
understanding of English language, symmetry has a different meaning, most
commonly associated with left and right equivalence.
In geometry, symmetry is seen a bit
differently in terms of division.
If a shape or object can be divided into
two or even more identical pieces, then that object has symmetry inbuilt in it.
Different types of geometrical symmetries
include reflectional, rotational, translational, helical, glide, rotoreflection
and fractals.
For instance, reflectional symmetry or
mirror symmetry is said to exist or reside in a geometrical object if a line
can be made to pass through the object or the shape which will create two
objects that are mirror images of each other.
Many animal bodies are great examples of
bilateral symmetry which is a subtype of reflectional symmetry; human face
itself is a great example of such a symmetry and greater the symmetry greater
is its attractive value in the mating market as symmetry is a great sign of
good health and therefore healthy genes, statistically speaking.
Similarly, rotational symmetry (in biology
it goes by the name of radial symmetry) is that property wherein the shape
remains the same after some degree of rotation.
In mathematics, as opposed to geometry, the
concept of symmetry is more generalized that is not very intuitive and quite
set apart from the way one would conceive in biology or even geometry.
In mathematics symmetry is defined in a
broader way in terms of mathematical operation or even a function.
A mathematical object is said to be
symmetric with respect to specific mathematical operation if it retains some
property of it after undergoing that operation.
Most of us who have never been too keen on
mathematics or who tackled mathematics just as a stepping stone to some other more
profitable career should find this definition of symmetry singular if not outright
strange.
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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