May 04, 2018 Friday
Bedtime Story
Transiting from Note D to Note G
Last night we had finished Note D.
It was on the night of March 29, 2018
Thursday that we had moved away from the Note G to Note D for understanding the
nature and the notation used in the table to calculate the Numbers of Bernoulli.
By now, those upper and lower indices
surrounding the letter V should not scare you anymore.
Just to recapitulate, and I think some
things are worth repeating, the lower indices are indices of locality only and in
way depend on the operations performed or of the results obtained, their value
continuing unchanged during the performance of calculations.
The upper indices, however, are of a unique
nature.
The upper indices 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 had 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.
The initial setting before any calculation
is commenced, and after the data entered in the vertical columns, 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.
This is the part that understandably is
extremely tenuous to grasp as not only it is absolutely mathematical, but is
describing how these mathematical operations would be performed by the
hypothetical Analytical Engine.
You might feel frustrated at not getting
the flow of thoughts of Ada Lovelace, but that should not be of great concern
as Lady Ada Lovelace worked very hard on these Notes and often corresponded
with Babbage to clear off her doubts whenever they struck her and obstructed
her flow of ideas.
You yourself need to go back and forth
between notes and tables to understand what is going on with the numbers of
indices, the symbols, and how different types of cards are interacting with
vertical columns of discs to produce the results desired.
So now very soon I shall resume the Note G
from where I have left.
At this point it would be diligent of me to
point out that the Notes of Ada Lovelace starts off with A and go on till G,
thus making them seven in total.
We have gone through all of them except for
one, which is Note E wherein Lovelace describes step-by-step how the Analytical
Engine would carry out a computation that involves a trigonometrical function
as it was the choice of Menabrea in his example.
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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