February 08, 2018 Thursday
Bedtime Story
Continuing with Menabrea - 14
We are continuing with the treatise of
Menabrea:
“Sketch of the Analytical Engine” that was
translated into French by Ada Lovelace and published along with her notes in
1842.
“Up to this point the process presents no
difficulties; but suppose that we have m=p and n=q, and that we wish to reduce
the two middle terms to a single one (Ab + bA)xm+q.
For this purpose, the cards may order m+q
and n+p to be transferred into the mill, and there subtracted one from the
other; if the remainder is nothing, as would be the case on the present
hypothesis, the mill will order other cards to bring it to the coefficients Ab
and Ba, that it may add them together and give them in this state as a
coefficient for the single term xn+p = xm+q.
This example illustrates how the cards are
able to reproduce all the operations which intellect performs in order to
attain a determinate result, if these operations are themselves capable of
being precisely defined.
Let us now examine the following
expression:-
Which we know becomes equal to the ratio of
the circumference to the diameter, when n is infinite.”
(Pi is a mathematical constant whose
original definition still remains the most popular one, which is the ratio of
circumference of a circle to its diameter.
It has fascinated the great mathematicians
of all times and has never lost its charm till today.
Numerous approaches have been used to get
to the value of pi including continued fraction, infinite series, polygonal
geometry, prime numbers and now with computers iterative algorithm.
The above expression found in the paper of
Menabrea is just one amongst them.
With computer algorithms the number of
known decimal digits of pi have increased dramatically though it’s not sure
what’s the reason for the obsession among the mathematicians to find out more
and more accurately the value of pi.
According to some theoretical physicists,
thirty nine digits of pi would suffice for most cosmological calculations as
that much accuracy of pi is sufficient to calculate the circumference of the
observable universe to the precision of one atom!
This clearly explains why mathematicians
are such a rare breed for pure mathematicians have never cared for the utility
of their discoveries. Storytelling chimpanzee)
“We may require the machine not only to
perform the calculation of this fractional expression, but further to give
indication as soon as the value becomes identical with that of the ratio of the
circumference to the diameter when n is infinite, a case in which the
computation would be impossible.
Observe that we should require of the
machine to interpret a result not of itself evident, and that this is not
amongst its attributes, since it is no thinking being.”
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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