April 17, 2018 Tuesday
Bedtime Story
Note A of Ada Lovelace - Part 10
Tonight we are continuing with the Note A
of Ada Lovelace wherein she is stressing on a major weakness of the Difference
Engine; that the Difference Engine, in order to work, needs a human mental
push-start, almost very literally.
The initial input values of a polynomial function
have to be mentally worked out, inserted into each of the vertical columns, and
only then cranking of the handle at the side would churn out consecutive values
of functions.
“It is true that the Difference Engine can
calculate to a much greater extent with these few preliminary data, than the
data themselves required for their own determination.
The table of squares, for instance, can be
calculated to any extent whatever, when the numbers one and two are finished;
and a very few differences computed at any part of a table of logarithms would
enable the engine to calculate many hundreds or thousands of logarithms.
Still the circumstance of its requiring, as
a previous condition, that any function whatever shall have been numerically
worked out, makes it very inferior in its nature and advantages to an engine
which, like the Analytical Engine, requires merely that we should know the
succession and distribution of the operations to be performed; without there
being any occasion, in order to obtain data on which it can work, for our ever
having gone through either the same particular operations which it is itself to
effect, or any others.
Numerical data must of course be given it,
but they are mere arbitrary ones; not data that could only be arrived at through
a systematic and necessary series of pervious numerical calculations, which is
quite a different thing.
To this it may be replied, that any
analyzing process must equally have been performed in order to furnish the
Analytical Engine with the necessary operative data; and that herein may also
lie a possible source of error.
Granted that the actual mechanism is
unerring in its processes, the cards may give it wrong orders.
This is unquestionably the case; but there
is much less chance of error, and likewise far less expenditure of time and
labour, where operations only, and the distribution of these operations, have
to be made out, than where explicit numerical results are to be attained.
In the case of the Analytical Engine we
have undoubtedly to lay out a certain capital of analytical labour in one
particular line; but this is in order that the engine may bring us in a much
larger return in another line.
It should be remembered also that the
cards, when once made out for any formula, have all the generality of algebra,
and include an infinite number of particular cases.
We have dwelt considerably on the
distinctive peculiarities of each of these engines, because we think it
essential to place their respective attributes in strong relief before the
apprehension of the public; and to define with clearness and accuracy the
wholly different nature of the principles on which each is based, so as to make
it self-evident to the reader (the mathematical reader at least) in what manner
and degree the powers of the Analytical Engine transcend those of an engine,
which, like the Difference Engine, can only work out such results as may be
derived from one restricted and particular series of processes, as those
included in
.”
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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