May 14, 2018 Monday
Bedtime Story
Note E of Ada Lovelace - Part 5
Tonight we shall resume with the Note E of
Ada Lovelace from where we had left last night.
“We shall perceive, if we inspect the
particular arrangement of the results in (2) on the Result-columns as
represented in the diagram, that, in order to effect this transformation, each
successive coefficient upon V32, V33, etc (beginning with
V32), must through means of proper cards be divided by two; and that
one of the halves thus obtained must be added to the coefficient on the
Variable which precedes it by ten columns, and the other half to the
coefficient on the Variable which precedes it by twelve columns; V32,
V33, etc themselves becoming zeros during the process.
The series of operations may be thus
expressed:-
Fourth Series
{It should be noted observed, that were the
rest of the factor (A + A cos θ + etc) taken into account, instead of four
terms only, C3 would have the additional term 1/2B1A4;
and C4 the two additional terms, BA4, 1/2B1A5.
This would indeed have been the case had
even six terms been multiplied.}
The calculation of the coefficients C0,
C1, etc of (1) would now be completed, and they would stand ranged
in order on V20, V21, etc.
It will be remarked, that from the moment
the fourth series of operations is ordered, the variables V31, V32
etc cease to be Result-Variables and become Working-Variables.
The substitution made by the engine of the
processes in the second side of (3) for those in the first side is an excellent
illustration of the manner in which we may arbitrarily order it to substitute
any function, number, or processes, at pleasure for any other function, number
or processes, on the occurrence of a specified contingency.”
All this is of course difficult to grasp since
you do not have the model of the Analytical Engine in front of you and poor you
are left to imagine of lot, far more than can be expected of average apes.
Let it not dishearten you, for understand
the manipulation of variables by the Engine is akin to grasping the
physiological pumping of the heart through biochemical changes taking place at
the cellular level.
Let me continue with Note E.
“We will now suppose that we desire to go a
step further, and to obtain the numerical value of each complete term of the
product (1); that is, of each coefficient and variable united, which for the
(n+1)th term would be Cn . cosnθ.
We must for this purpose place the
variables themselves on another set of columns, V41, V42,
etc, and then order their successive multiplication by V21, V22,
etc, each for each.
There would thus be a final series of
operations as follows:-“
We shall study the fifth and the final
series of operations in the nights to come.
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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