January 31, 2018 Wednesday
Bedtime Story
Continuing with Menabrea - 7
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.
Menabrea is now considering one specific
example of two first degree equations to explain the workings of the engine.
mx + ny = d
m’x + n’y = d’
We deduce x = (dn’ – d’n)/(n’m – nm’),
And for y an analogous expression
Let us continue to represent by V0,
V1, V2 etc the different columns which contain the
numbers, and let us suppose that the first eight columns have been chosen for
expressing on them the numbers represented by m, n, d, m’, n’, d’, n and n’,
which implies that V0 = m, V1 = n, V2 = d, V3
= m’, V4 = n’, V5 = d’, V6 = n, V7
= n’.
The series of operations commanded by the
cards, and the results obtained, may be represented in the following table:-
|
|
Operation cards
|
Cards of
|
The Variables
|
|
|
Number of the operations
|
Symbols indicating nature of operations
|
Columns on which operations to be
performed
|
Columns which receive results of
operations
|
Progress of the operations
|
|
1
|
x
|
V2 x V4 =
|
V8…
|
= dn’
|
|
2
|
x
|
V5 x V1 =
|
V9…
|
= d’n
|
|
3
|
x
|
V4 x V0 =
|
V10…
|
= n’m
|
|
4
|
x
|
V1 x V3 =
|
V11…
|
= nm’
|
|
5
|
-
|
V8 – V9 =
|
V12…
|
= dn’ – d’n
|
|
6
|
-
|
V10 – V11 =
|
V13…
|
= n’m – nm’
|
|
7
|
|
V12/V13 =
|
V14…
|
= x = (dn’ – d’n)/(n’m – nm’)
|
Since the cards do nothing but indicate in
what manner and on what columns the machine shall act, it is clear that we must
still, in every particular case, introduce the numerical data for the calculation.
Thus, in the example we have selected, we
must previously inscribe the numerical values of m, n, d, m’, n’, d’, in the
order and on the columns indicated, after which the machine when put in action
will give the value of the unknown quantity x for this particular case.
To obtain the value of y, another series of
operations analogous to the preceding must be performed.
But we see that they will be only four in
number, since the denominator for the expression of y, excepting the sign, is
same as that for x, and equal to n’m – nm’.
In the preceding table it will be remarked
that the column for operations indicates for successive multiplications, two
subtractions and one division.
Therefore, if desired, we need only use
three operation-cards; to manage which, it is sufficient to introduce into the
machine an apparatus which shall, after the first multiplication, for instance,
retain the card which relates to this operation, and not allow it to advance so
as to be replaced by another one, until after this same operation shall have
been four times repeated.”
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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