June 27, 2018 Wednesday
Bedtime Story
Ernst Mach on Lagrange and Mécanique Analytique
We shall continue with what Lagrange had to
say of the revolutionary nature of his own work that he published as Mécanique
analytique:
“The methods that I explain require neither
geometrical (he surely wasn’t very fond of geometry if you may recall), nor
mechanical, constructions or reasoning, but only algebraical operations in
accordance with regular and uniform procedure.
Those who love Analysis (he surely was
deeply in love with it) will see with pleasure that Mechanics has become a
branch of it, and will be grateful to me for having thus extended its domain.”
This complete absence of any form of
modesty has a very sound reason; for the claim made by Lagrange is absolutely
accurate.
Lagrange was essentially a very modest and
shy man, but it is specially such unassuming men who are keenly aware of any
kind of monumental intellectual work, either somebody else’s or their own.
If you see from his perspective, it was an
achievement very close to his tastes; Here was a man who from his very
childhood was fascinated with analysis and had an odd dislike bordering on
contempt for geometry.
On these very lines Lagrange redefined the
mechanics of Newton that to a large extent uses geometry in the form of vectors
and trigonometry.
This is what Ernst Mach (a critique of
Newtonian physics) had to say of Lagrangian mechanics.
“The value of his work [Mécanique
Analytique] consists in the exposition of a general method by which every
mechanical question may be stated in a single algebraic equation.
The entire history of any mechanical
system, as for example, the solar system, may thus be condensed into a single
sentence; and its detailed interpretation becomes simply a question of algebra.
No one who has not tried to cope with the
difficulties presented by almost any mechanical problem can form a just
appreciation of the great utility of such a labor-saving and thought-saving
device.
It has been well called ‘a stupendous
contribution to the economy of thought’.”
You might not be aware, but Ernst Mach is
known for his Mach’s principle or Mach’s conjecture that was labeled by
Einstein as such.
This principle became the guiding force for
Einstein in framing his theory of relativity.
This is how Mach himself thought and wrote
about it:
“Investigator must feel the need
of…knowledge of the immediate connections, say, of the masses of the universe.
There will hover before him as an ideal
insight into the principles of the whole matter. From which accelerated and
inertial motions will result in the same way.”
I will try to explain to you in the nights
to come what Mach was trying to convey.
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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