May 02, 2018 Wednesday
Bedtime Story
Note D of Ada Lovelace - Part 7
Tonight we shall continue with the Note D
of Ada Lovelace wherein she describes in great detail how the vertical columns
that have been represented by the Vs interact with Variable-cards and
Operation-cards to perform mathematical operations.
Each time an operation is “ordered” by an
Operation-card, immediately two Variable-cards feed in the required two
variables, since each operation must be performed on two variables in our given
example.
The result that ensures after each
operation is taken up by the Receiving Variable-card, which “marks” it so that
its proper physical location is known, as this result may go on to become a
variable for further operations until the ultimate result is obtained.
“The substitutions in the preceding
equations happen to be of little value towards illustrating the power and uses
of upper indices, for, owing to the nature of these particular equations, the
indices are all unity throughout.
We wish we had space to enter more fully
into the relations which these indices would in many cases enable us to trace.
M. Menabrea incloses the three center columns
of his table under the general title Variable-cards.
The V’s however in reality all represent
the actual Variable-columns of the engine, and not the cards that belong to
them.
Still the title is a very just one, since
it is through the special act of certain Variable-cards (when combined with the
more generalized agency of Operation-cards) that every one of the particular
relations he has indicated under that title is brought about.
Suppose we wish to ascertain how often any
one quantity, or combination of quantities, is brought into use during a
calculation.
We easily ascertain this, from the
inspection of any vertical column or columns of the diagram in which that
quantity may appear.
Thus, in the present case, we see that all
the data, and all the intermediate results likewise, are used twice, excepting
(mn’ – m’n), which is used three times.
The order in which it is possible to
perform the operations for the present example, enables us to effect all the
eleven operations of which it consists with only three Operation cards; because
the problem is of such a nature that it admits of each class of operations
being performed in a group together; all the multiplications one after another,
all the subtractions one after another, etc.
The operations are {6(x), 3(-), 2(
)}.
Since the very definition of an operation
implies that there must be two numbers to act upon, there are of course two
Supplying Variable-cards necessarily brought into action for every operation,
in order to furnish the two proper numbers.
This has been dealt in Note B.
Also, since every operation must produce a
result, which must be placed somewhere, each operation entails the action of a
Receiving Variable-card, to indicate the proper locality for the result.”
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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