April 27, 2018 Friday
Bedtime Story
Note B of Ada Lovelace - Part 7
Tonight we shall continue with the Note B
of Ada Lovelace which we shall pick up from the sketch of Lovelace that
represented 9 Variable-columns of the mill that is handling not one but three
functions with 6 variables, namely axn, bpy and then axn/bpy
and the six variables being a, x, n, b, p and y.
The point she is making is that with multiple
columns of vertical discs, multiple functions can be carried out by the machine
as long as these columns get the right feed of orders from the Operation-Cards
and appropriate values of variables via Variable-cards, though of course, she
is evasive of the mechanical means of carrying these out out which perhaps she
had left it to Charles Babbage to work it all out and maybe he had.
“We may now desire to combine together
these two results, in any manner we please; in which case it would only be
necessary to have an additional card or cards, which would order the requisite
operations to be performed with the numbers on the two result-columns V4 and
V8, and the result of these further operations to appear on a new column, V9.
Say that we wish to divide axn
by bpy.
The numerical value of this division would
then appear on the column V9, beneath which we have inscribed axn/bpy.
The whole series of operations from the
beginning would be as follows (n being = 7):
{7 (x), 2 (x),
},
or {9(x),
}
This example is introduced merely to show
that we may, if we please, retain separately and permanently any intermediate
results (like axn, bpy) which occur in the course of processes
having an ulterior and more complicated result as their chief and final object
(like axn/bpy).
Any group of columns may be considered as
representing a general function, until a special one has been implicitly
impressed upon them through the introduction into the engine of the Operation
and Variable-cards made out for a particular function.
This, in the preceding example, V1, V2, V3,
V5, V6, V7 represent the general function
(a,
n, b, p, x, y) until the function axn/bpy has been determined on,
and implicitly expressed by the placing of the right cards in the engine.
The actual working of the mechanism, as
regulated by these cards, then explicitly develops the value of the function.
The inscription of a function under the
brackets, and in the square under the result-column, in no way influences the
processes or the results, and is merely a memorandum for the observer, to
remind him of what is going on.
It is the Operation and the Variable-cards
only which in reality determine the function.
Indeed it should be distinctly kept in
mind, that the inscriptions without any of the squares are quite independent of
the mechanism or workings of the engine, and are nothing but arbitrary
memorandums placed there at pleasure to assist the spectator.
The further we analyze the manner in which
such an engine performs its processes and attains its results, the more we
perceive how distinctly it places in a true and just light the mutual relations
and connection of the various steps of mathematical analysis; how clearly it
separates those things which are in reality distinct and independent, and
unites those which are mutually dependent.”
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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