April 30, 2018 Monday
Bedtime Story
Note D of Ada Lovelace - Part 5
Tonight we shall be continuing with the
Note D of Ada Lovelace wherein she is discussing the two flowchart diagrams
that I printed out for you last night.
What she is saying that though both are
analogous and both reflect each and every step that the engine would take to
perform that mathematical operation, each one has certain and disadvantage, but
together they are whole.
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She
here also describes the meaning of upper (to the left) and lower (to the
right) indices in the Vs of Menabrea.
Understanding
this notation is critical in comprehension of the flowchart tables.
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“But it was fortunately inconvenient to
print them in this desirable form.
The diagram is, in the main, merely another
manner of indicating the various relations denoted in M. Menabrea’s table.
Each mode has some advantages and some
disadvantages.
Combined, they form a complete and accurate
method of registering every step and sequence in all calculations performed by
the engine.
No notice has yet been taken of the upper
indices which are added to the left of each V in the diagram; an addition which
we have also taken the liberty of making to the V’s in M.
M. Menabrea’s table 3 and 4, since it does
not alter anything therein represented by him, but merely adds something to the
previous indications of those tables.
The lower indices are obviously indices of
locality only, and are wholly independent of the operations performed or of the
results obtained, their value continuing unchanged during the performance of
calculations.
The upper indices, however, are of a
different nature.
Their office is to indicate any alteration
in the value which a Variable represents; and they are of course liable to
changes during the processes of a calculation.
Whenever a Variable has only zeros upon it,
it is called 0V; the moment a value appears on it (whether that
value be placed there arbitrarily, or appears in the natural course of a
calculation), it becomes 1V.
If this value gives place to another value,
the Variable becomes 2V, and so forth.
Whenever a value again gives place to zero,
the Variable again becomes 0V, even if it have been nV
the moment before.
If a value than again be substituted, the
Variable becomes n+1V (as it would have done if it had not passed
through the intermediate 0V; and so on.
Just before any calculation is commenced,
and after the data have been given, and everything adjusted and prepared for
setting the mechanism in action, the upper indices of the Variables for data are
all unity, and those for the Working and Result-variables are all zero.
In this state the diagram represents them.”
(To understand this last statement you will
have to keep referring to the flowchart Table of Menabrea and watch closely how
the upper left-handed indices are changing before and after the operations In
the Variables for data, Working-Variables and Result-Variables).
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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