May 08, 2018 Tuesday
Bedtime Story
Note G of Ada Lovelace - Part 11
Tonight we shall continue with the Note G
of Ada Lovelace, which you need to read with continuous or intermittent
reference to the flowchart table that I had posted on the night of May 06, 2018
Sunday.
Here, I think, she is discussing something
very important: which in today’s computer science would be known either as
recursion or looping.
More specifically pertaining to her
logarithm, it is the steps from 13 to 23 that will keep repeating, and the
value generated will be the fodder for the next cycle.
She also explains how the number of
Operation-cards and Variable-cards that will be necessitated for the
calculation of different Numbers of Bernoulli will change as the computation
progresses.
“This identity in the columns which supply
the requisite numbers must not be confounded with identity in the values those
columns have upon them and give out to the mill.
Most of those values undergo alterations
during a performance of the operations (13…23), and consequently the columns
present a new set of values for the next performance of (13…23) to work on.
At the termination of the repetition of
operations (13…23) in computing B7, the alterations in the values on
the Variables are, that
V6 = 2n – 4 instead of 2n – 2
V7 = 6………………………………….4
V10=0………………………………….1
V13= A0 + A1B1 + A3B3 + A5B5
instead of A0 + A1B1 + A3B3
In this state, the only remaining processes
are, first, to transfer the value which is on V13 to V24;
and secondly, to reduce V6, V7, V13 to zero,
and to add one to V3, in order that the engine may be ready to
commence computing B9.
Operations 24 and 25 accomplish these
purposes.
It may be thought anomalous that Operation
25 is represented as leaving the upper index of V3 still = unity;
but it must he remembered that these indices always begin anew for a separate
calculation, and that Operation 25 places upon V3 the first value
for the new calculation.
It should be remarked, that when the group
(13…23) is repeated, changes occur in some of the upper indices during the
course of the repetition: for example 3V6
would become 4V6 and 5V6.
We thus see that when n=1, nine
Operation-cards are used; that when n=2, fourteen Operation-cards are used; and
that when n>2, twenty-five Operation-cards are used; but that no more are
needed, however great n may be; and not only this, but that these same
twenty-five cards suffice for the successive computation of all the Numbers
from B1 to B2n-1 inclusive.
With respect to the number of
Variable-cards, it will be remembered, from explanation in the previous Notes, that
an average of three such cards to each operation (not however to each
Operation-card) is the estimate.
According to this, the computation of B1
will require twenty-seven Variable-cards; B3 forty-two such
cards; B5 seventy-five; and for every succeeding B after B5,
there would thirty-three additional Variable-cards (since each repetition of
the group (13…23) adds eleven to the number of operations required for
computing the previous B).”
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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