February 09, 2018 Friday
Bedtime Story
Continuing with Menabrea - 15
We are continuing with the treatise of
Menabrea:
“Sketch of the Analytical Engine” that was
translated into French by Ada Lovelace and published along with her notes in
1842.
“Nevertheless,
when the cos of n = 1/0 has been foreseen, a card may immediately order the
substitution of the value of pi (pi being the ratio of circumference to the
diameter), without going through the series of calculations indicated.
This would merely require that the machine
contain a special card, whose office it should be to place the number pi in a
direct and independent manner on the column indicated to it.
And here we should introduce the mention of
a third species of card, which may be called card of numbers.
There are certain numbers, such as those expressing
the ratio of circumference to the diameter, the Numbers of Bernoulli, etc,
which frequently present themselves in calculations.
To avoid the necessity for computing them
every time they have to be used, certain cards may be combined specially in
order to give these numbers ready made into the mill, whence they afterwards go
and place themselves on those columns of the store that are destined for them.
Through this means the machine will be
susceptible of those simplifications afforded by the use of numerical tables.
It would be equally possible to introduce,
by means of these cards, the logarithms of numbers; but perhaps it might not be
in this case either the shortest or the most appropriate method; for the
machine might be able to perform the same calculations by other more
expeditious combinations, founded on the rapidity with which it executes the
first four operations of arithmetic.
To give an idea of this rapidity, we need
only mention that Mr. Babbage believes he can, by his engine, form the product
of two numbers, each containing twenty figures, in three minutes.
Perhaps the immense number of cards
required for the solution of any rather complicated problem may appear to be an
obstacle; but this does not seem to be the case.
There is no limit to the number of cards
that can be used.
Certain stuffs require for their
fabrication not less than twenty thousand cards, and we may unquestionably far
exceed even this quantity.”
At this point it is worth referring to the
Note F of Ada Lovelace that follows the translation of Menabrea’s treatise.
In this she elaborates on the vexing
problem of the number of punching cards that would be required for different
mathematical problems.
So now let us proceed to Note F of Lady
Lovelace.
You may find my frequent interruptions of
main treatise of Menabrea with the Ada’s notes irksome but I think the
knowledge one gains is worth the pain of interruptions.
“There is in existence a beautiful woven
portrait of Jacquard, in the fabrication of which 24,000 cards were required.”
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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