May 12, 2018 Saturday
Bedtime Story
Note E of Ada Lovelace - Part 3
Tonight we shall continue with the Note E
of Ada Lovelace where she is once again emphasizing the point that the
Analytical Engine is not simply a complex and sophisticated mechanical calculator
but a device that can perform both algebra and analysis.
Yet she is mindful of the fact that her
claims are tall and developing the Engine to its fullest potential, that is,
making it function truly algebraically or/and analytically would greatly extend
its mechanical complexity.
You have to pause and understand that Ada
Lovelace always perceived the Engine conceptually rather than mechanically even
though she does apparently discuss some mechanical aspects of it, her view of
it is more through the eyes of a mathematician than that of a mechanical
engineer.
“Many persons who are not conversant with
mathematical studies, imagine that because the business of the engine is to
give its results in numerical notation, the nature of its processes must
consequently be arithmetical and numerical, rather than algebraical and
analytical.
This is an error.
The engine can arrange and combine its
numerical quantities exactly as if they were letters or any other general
symbols; and in fact it might bring out its results in algebraical notation,
were provisions made accordingly.
It might develop three sets of results
simultaneously, viz. symbolic results (as already alluded to in Notes A and B),
numerical results (its chief and primary object); and algebraical results in
literal notation.
This later however has not been deemed a
necessary or desirable addition to its powers, partly because the necessary
arrangements for effecting it would increase the complexity and extent of the
mechanism to a degree that would not be commensurate with the advantages, where
the main object of the invention is to translate into numerical language
general formulae of analysis already known to us, or whose laws of formation
are known to us.
But it would be a mistake to suppose that
because its results are given in the notation of a more restricted science, its
processes are therefore restricted to those of that science.
The object of the engine is in fact to give
the utmost practical efficiency to the resources of numerical interpretations
of the higher science of analysis, while it uses the processes and combinations
of this latter.
To return to the trigonometrical series.
We shall only consider the first four terms
of the factor (A +A1cosθ + etc), since this will be sufficient to
show the method.
We propose to obtain separately the
numerical value of each coefficient C0, C1 etc of (1).
The direct multiplication of the two
factors gives
A result which would stand thus on the
engine:- “
We shall carry this forward in the nights
to come as the arrangements of these coefficients on the Variable columns are diagrammatic
and take up more space than allotted to each bedtime story.
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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