February 03, 2018 Saturday
Bedtime Story
Continuing with Menabrea - 9
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.
I am sure you would certainly have skipped
the menacing table of operations that I had posted last night.
That is understandable as in today’s world
of electronic gadgetry no one would be interested in knowing the details of a
theoretical universal mechanical calculating device that was never built.
“In order to diminish to the utmost the
chances of error in inscribing the numerical data of the problem, they are
successively placed on one of the columns of the mill; then, by means of cards
arranged for this purpose, these same numbers are caused to arrange themselves
on the requisite columns, without the operator having to give his attention to
it; so that his undivided mind may be applied to the simple inscription of
these same numbers.
According to what now has been explained,
we see that the collection of columns of Variables may be regarded as a store
of numbers, accumulated there by the mill, and which, obeying the orders
transmitted to the machine by means of the cards, pass alternately from the
mill to the store and from the store to the mill, that they may undergo the
transformations demanded by the nature of the calculation to be performed.
Hitherto no mention has been made of the
signs in the results, and the machine would be far from perfect were it
incapable of expressing and combining amongst each other positive and negative
quantities.
To accomplish this end, there is, above
every column, both of the mill and of the store, a disc, similar to the discs
of which the columns themselves consist.
According as the digit on this disc is even
or uneven, the number inscribed on the corresponding column below it will be
considered as positive or negative.
This granted, we may, in the following
manner, conceive how the signs can be algebraically combined in the machine.
When a number is to be transferred from the
store to the mill, or vice versa, it will always be transferred with its sign,
which will effected by means of the cards, as has been explained in what
precedes.
Let any two numbers then, on which we are
to operate arithmetically, be placed in the mill with their respective signs.
Suppose we are first to add them together;
the operation-cards will command the addition: if the two numbers be of the
same sign, one of the two will be entirely effaced from where it was inscribed,
and will go to add itself on the column which contains the other number; the
machine will, during this operation, be able, by means of a certain apparatus,
to prevent any movement in the disc of signs which belongs to the column on
which the addition is made, and thus the result will remain with the sign which
the two given numbers originally had.
When two numbers have two different signs,
the addition commanded by the card will be changed into a subtraction through
the intervention of mechanisms which are brought into play by this very
difference of sign.”
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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