January 24, 2017 Wednesday
Bedtime Story
Continuing with Menabrea - 2
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.
I had initially not intended to write this
treatise verbatim but having gone through it I could not resist that
temptation.
I feel that this treatise beautifully
encapsulates the origins of the idea of analytical machine and later the
principle behind it.
Of course, if later I feel that there is
something left out about the analytical engine in this treatise, I certainly
shall endeavor to cover up the deficiencies as Menabrea himself keeps insisting
that this essay is not a comprehensive description of the analytical engine but
merely its bare essentials.
But for now let us move on with the
treatise of Menabrea, the 7th Prime Minister of Italy where he is
describing the fundamentals of the difference engine of Babbage.
“By this method the question is reduced to
the primitive case of a finite polynomial.
It is this that we can calculate the succession
of the logarithms of the numbers.
But since, in this particular instance, the
terms which had been originally neglected receive increments in a ratio so
continually increasing for equal increments of the variable, that the degree of
approximation required would ultimately be affected, it is necessary, at
certain intervals, to calculate the value of function by different methods, and
then respectively to use the results thus obtained, as data whence to deduce,
by means of the machine, the other intermediate values.
We see that the machine here performs the
office of the third section of calculators mentioned in describing the tables
computed by the order of the French government, and that the end originally
proposed is thus fulfilled by it.
Such is the nature of the first machine
which Mr. Babbage conceived.
We see that its use is confined to cases
where the numbers required are such as can be obtained by means of simple
additions or subtractions; that the machine is, so to speak, merely the
expression of one particular theorem (Ada Lovelace in her notes on this same
essay elaborates further on this one particular theorem) of analysis; and that,
in short, its operations cannot be extended so as to embrace the solution of an
infinity of other questions included within the domain of mathematical
analysis.
It was while contemplating the vast field
which yet remained to be traversed, that Mr. Babbage, renouncing his original
essays, conceived the plan of another system of mechanism whose operations
should themselves possess all the generality of algebraical
notation, and which, on this account, he denominates the Analytical Engine.
Having now explained the state of the
question, it is time for me to develop the principle on which is based the
construction of this latter machine.
When analysis is employed for the solution
of any problem, there are usually two classes of operations to execute; first,
the numerical calculation of the various coefficients; and secondly, their
distribution in relation to the quantities affected by them.”
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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