February 15, 2018 Thursday
Bedtime Story
Note G of Ada Lovelace - 2
We shall continue with the last and the
final Note G of Ada Lovelace.
“No reply, entirely satisfactory to all
minds, can be given to this query, excepting the actual existence of the
engine, and actual experience of its practical results.
We will however sum up for each reader’s
consideration the chief elements with which the engine works:-
1. It performs the four operations of
simple arithmetic upon any numbers whatever.
2. By means of certain artifices and
arrangements (upon which we cannot enter within the restricted space with such
a publication as the present may admit of), there is no limit either to the
magnitude of the numbers used, or to the number of quantities (either variables
or constants) that may be employed.
3. It can combine these numbers and these
quantities either algebraically or arithmetically, in relations unlimited as to
variety, extent, or complexity.
4. It uses algebraic signs according to
their proper laws, and develops the logical consequences of these laws.
5. It can arbitrarily substitute any
formula for any other; effacing the first from the columns on which it is
represented, and making the second appear in its stead.
6. It can provide for singular values.
Its power of doing this is referred to M.
Menabrea’s memoir, where he mentions the passage of values through zero and
infinity. (If you recall or go back to past bedtime stories, you will find it
there already dealt with).
The practicality of causing it arbitrarily
to change its processes at any moment, on the occurrence of any specified
contingency, at once secures this point.
The subject of integration and
differentiation demands some notice.
The engine can effect these processes in
either of two ways:-
First. We may order it, by means of the
Operation and the Variable-cards, to go through the various steps by which the
required limit can be worked out for whatever function is under consideration.
Secondly. It may (if we know the form of
the limit for the function in question) effect the integration or
differentiation by direct substitution.
The engine cannot of course compute limits
for perfectly simple and uncompounded functions, except in this manner.
It is obvious that is has no power of
representing or of manipulating with any but finite increments or decrements,
and consequently that wherever the computation of limits (or of any other
functions) depends upon the direct introduction of quantities which either
increase or decrease indefinitely, we are absolutely beyond the sphere of its
powers.
Its nature and arrangements are remarkably
adapted for taking into account all finite increments or decrements (however
small or large), and for developing the true logical modifications of form or
value dependent upon differences of this nature.”
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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