January 25, 2018 Thursday
Bedtime Story
Continuing with Menabrea - 3
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.
Now Menabrea is writing about the
analytical engine and its conceptual designing.
“If, for example, we have to obtain the
product of two binomials (a + bx) (m + nx), the result will be represented by
am + (an + bm)x + bnx2, in which expression we must first calculate
am, an, bm, bn; then take the sum of an + bm; and lastly, respectively
distribute the coefficients so obtained among the powers of the variable.
In order to reproduce the operations by
means of a machine, the latter must therefore possess two distinct set of
powers: first, that of executing numerical calculations; secondly, that of
rightly distributing the values so obtained.”
Here mon ami, you should get the beauty of
this paper; the highlight of this paper is the way it dissects the problem that
the analytical machine sought to take care of.
This paper comes at the time when the
analytical machine was only in the air so to speak and the problems that the
earliest computer scientists were grappling with.
“But if human intervention were necessary
for directing each of these partial operations, nothing would be gained under
the heads of correctness and economy of time; the machine must therefore have
the additional requisite of executing by itself all the successive operations
required for the solution of a problem proposed to it, when once the primitive
numerical data for this same problem have been introduced.
Therefore, since, from the moment that the
nature of the calculation to be executed or of the problem to be resolved have
been indicated to it, the machine is, by its own intricate power, of itself to
go through all the intermediate operations which lead to the proposed result,
it must exclude all methods of trial and guess-work, and can only admit the
direct processes of calculation.
It is necessary thus; for the machine is
not a thinking being, but simply an automaton which acts according to the laws
imposed upon it.
This being fundamental, one of the earliest
researches its author had to undertake, was that of finding means for effecting
the division of one number by another without using the method of guessing
indicated by the usual rules of arithmetic.
The difficulties of effecting this
combination were far from being among the least; but upon it depended the
success of every other.
Under the impossibility of my here
explaining the process through which this end is attained, we must limit
ourselves to admitting that the first four operations of arithmetic, that is
addition, subtraction, multiplication and division, can be performed in a
direct manner through the intervention of the machine.
This granted, the machine is thence capable
of performing every species of numerical calculation, for all such calculations
ultimately resolves themselves into the four operations we have just named.”
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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