May 18, 2018 Friday
Bedtime Story
Note E of Ada Lovelace - Part 9
Tonight we shall resume with the Note E of
Ada Lovelace from where we had left last night.
Lovelace is continuing to describe how the
Analytical Engine would compute a function when the law is known for the
general term.
It would be a smart play of the
Operation-cards with the Variable-cards wherein a certain series of
Operation-cards placed in specific order would be repeated but each time with
new Variable-cards feeding it with new variables.
“To proceed: the law, according to which
the successive functions of (5) are to be developed, must of course first be
fixed on.
The law may be of various kinds.
We may propose to obtain our results in
successive powers of x, in which case the general form would be
C + C1x + C2x2
+ etc,
or in successive powers of n itself, the
index of the function we are ultimately to obtain, in which case the general
form would be
C + C1n + C2n2 + etc;
and x would only enter in the coefficients.
Again, other functions of x or of n instead
of powers might be selected.
It might be in addition proposed, that the
coefficients themselves should be arranged according to given functions of a
certain quantity.
Another mode would be to make equations
arbitrarily amongst the coefficients only, in which case the several functions,
according to either of which it might be possible to develop the nth function
of (5), would have to be determined from the combined consideration of these
equations and of (5) itself.
The algebraical nature of the engine (so
strongly insisted on in a previous part of this Note) would enable it to follow
out any of these various modes indifferently; just as we recently showed that
it can distribute and separate the numerical results of any one prescribed
series of processes, in a perfectly arbitrary manner.
Were it otherwise, the engine could merely
compute the arithmetical nth function, a result which, like any other purely
arithmetical results, would be simply a collective number, bearing no traces of
the data or the processes which had led to it.
Secondly, the law of development for the
nth function being selected, the next step would obviously be to develop (5)
itself, according to this law.
This result would be the first function,
and would be obtained by a determinate series of processes.
These in most cases would include amongst
them one or more cycles of operations.
The third step (which would consist of the
various processes necessary for effecting the actual substitution of the series
constituting the first function, for the variable itself) might proceed in
either of two ways.”
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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