May 06, 2018 Sunday
Bedtime Story
Note G Of Ada Lovelace - Part 9
Note G Of Ada Lovelace - Part 9
Today we shall continue with the Note G of
Ada Lovelace, indubitably the most potent Note of all the seven notes.
I shall reprint the algorithm diagram for
calculating the Numbers of Bernoulli drawn out intricately by her.
The printing of this diagram is repeated
but one should not mind that, for it is perhaps the most salient aspect of the entire
work, all the rest merely serving as the buttress around it.
The number of operations that have been
worked out are only 25 which is a pretty good sample size to comprehend the
workings of this engine.
“But the arrangements are so made, that the
nature of the processes would be the same as for whole numbers.
In the above table and diagram we are not
considering the signs of any of the B’s, merely their numerical magnitude.
The engine would bring out the sign for
each of them correctly of course, but we cannot enter on every additional
detail of this kind as we might wish to do.
The circles for the signs are therefore intentionally
left blank in the diagram.
Operation-cards 1, 2, 3, 4, 5, 6 prepare
(-1/2)(2n-1/2n+1) or 
.
.
Thus card 1 multiplies two into n, and the
three Receiving Variable-cards belonging respectively to V4, V5,
V6, allow the result 2n to be placed in each of these latter columns
(this being a case in which a triple receipt of the result is needed for
subsequent purposes); we see that the upper indices of the two Variables used,
during Operation1, remain unaltered.
We shall not go through the details of
every operation singly, since the table and diagram sufficiently indicate them;
we shall merely notice some few peculiar cases.
By Operation 6, a positive quantity is
turned into a negative quantity, by simply subtracting the quantity from a
column which zero upon it.
(The sign at the top of V8 would
become – during this process.)
Operation 7 will be unintelligible, unless
it be remembered that if we were calculating for n = 1 instead of n = 4,
Operation 6 would have completed the computation of B1 itself, in
which case the engine instead of continuing its processes, would have to put B1
on V21; and then either to stop altogether, or to begin Operations
1, 2…7 all over again for value of n(=2), in order to enter to enter on the
computation of B3; (having however taken care, previous to this
recommencement, to make the number on V3 equal to two, by the
addition of unity to the former n =1 on that column).”
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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