May 09, 2018 Wednesday
Bedtime Story
Note G of Ada Lovelace - Part 12
Tonight we shall continue with the Note G
of Ada Lovelace, which you will need to read with continuous or intermittent
reference to the flowchart table that I had posted on the night of May 06, 2018
Sunday.
In today’s bedtime story, Ada Lovelace is
elaborating on the concept of ‘cycle of operations’ which the Analytical Engine
will necessary need to perform in many if not all of its computations.
“But we must now explain, that whenever
there is a cycle of operations, and if these merely require to be supplied with
numbers from the same pairs of columns, and likewise each operation to place
its result on the same column for every repetition of the whole group, the
process then admits of a cycle of Variable-cards for effecting its purposes.
There is obviously much more symmetry and
simplicity in the arrangements, when cases do admit of repeating the Variable
as well as the Operation-cards.
Our present example is of this nature.
The only exception to a perfect identity in
all the processes and columns used, for every repetition of Operations (13…23),
is, that Operation 21 always requires one of its factors from a new column, and
Operation 24 always puts its result on a new column.
But as these variations follow the same law
at each repetition (Operation 21 always requiring its factors from a column one
in advance of that which it used the previous time, and Operation 24 always
putting its results on the column one in advance of that which received the
previous result), and they are easily provided for in arranging the recurring
group (or cycle) of Variable-cards.
We may here remark, that the average
estimate of three Variable-cards coming into use to each operation, is not to
be taken as an absolutely and literally correct amount for all cases and
circumstances.
Many special circumstances, either in the
nature of a problem, or in the arrangements of the engine under certain
contingencies, influence and modify this average to a greater or less extent; but
it is a very safe and correct general rule to go upon.
In the preceding case it will give us
seventy-five Variable-cards as the total number which will be necessary for
computing any B after B3.
This is very nearly the precise amount
really used, but we cannot here enter into the minutiae of the few particular
circumstances which occur in this example (as indeed at some one stage or other
of probably most computations) to modify slightly this number.
It will be obvious that the very same
seventy-five Variable-cards may be repeated for the computation of every
succeeding Number, just on the same principle as admits of the repetition of
the thirty-three Variable-cards of Operations (13…23) in the computation of any
one Number.
Thus there will be a cycle of a cycle of
Variable-cards.
If we now apply the notation for cycles, as
explained in Note E., we may express the operations for computing the Numbers
of Bernoulli in the following manner:-“
At this point I am forced to leave the Note
G and go to Note E to understand how the notation of cycles works.
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.
Advertisements
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:
No comments:
Post a Comment