July 19, 2018 Thursday
Bedtime Story
P. W. Anderson's Philosophy of Science
I shall not go into the details behind the
idea of symmetry breaking though it is important to stress that it is this idea
that led to the development of the Standard Model and later to the theory
behind the Higgs mechanism thereby giving a theoretical explanation for the
generation of mass in the elementary particles.
That story on symmetry breaking perhaps
will be attended to in some future nights provided I live long enough or I
continue to keep writing as regularly as I have been doing so for the past two
years.
In his popular exponentiation of science Anderson
has made a strong pitch for the idea of emergent phenomena and to consider
science at its various hierarchical levels.
The idea is that while mathematics and
mathematical physics is the basis of understanding the fundamental laws of
nature, they will have to be pushed aside when studying subjects such as
biology where the complexity gives rise to emergent phenomena that are beyond
the limits of mathematical physics in spite of the fact that any biological
object or rather organism is made up of elementary particles.
Hence there is a limit to the usefulness of
reductionism and science at each level of hierarchy needs to be played by
different set of rules.
Now
let us leave P. W. Anderson aside for now and return back to symmetry.
My principle concern as of now is to
discover the link that connects the mathematics of symmetry to the mathematics
of group theory.
It has not been very easy for me to
understand this link and so what I will place in front of you may appear to be
not so smoothly interwoven and certainly not the way I desire in my writings.
Symmetry is all about transformation or
invariance.
Some transformations are continuous such as
rotation of a circle whereas as certain transformations are discrete such as a
rotation of a regular polygon.
Symmetries that are found in the processes
of continuous transformations give rise to continuous symmetries that are
described by Lie groups whereas those that are found in the processes of
discrete transformations are known as discrete symmetries and are best
described by finite groups.
What I mean by the so called Lie Groups and
finite groups will be discussed later and for now simply keep it somewhere in
the corner shelf of your mind.
So with the term symmetry in mathematics,
there are several crucial terms associated with it such as “operation”,
“transformation”, “mapping”, “invariance”, “affine” and so on.
I think you would now be familiar with the
terms “operation” or “transformation” which mathematically is best described in
terms of a function or mapping.
The terms operation, transformation are
often used interchangeably.
Today due to shortage of time I could not
frame my bedtime story and my sincere apologies for the same.
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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