Feb 01, 2018 Thursday
Bedtime Story
Continuing with Menabrea - 8
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.
“In the preceding example we have seen,
that to find the value of x we must begin by writing the coefficients m, n, d,
m’, n’, d’, upon eight columns, thus repeating n and n’ twice.
According to the same method, if it were
required to calculate y likewise, these coefficients must be written on twelve
different columns.
But it is possible to simplify this
process, and thus to diminish the chances of errors, which chances are greater,
the larger the number of the quantities that have to be inscribed previous to
setting the machine in action.
To understand this simplification, we must
remember that every number written on a column must, in order to be arithmetically
combined with another number, be effaced from the column on which it is, and
transferred to the mill.
Thus, in the example we have discussed, we
will take the two coefficients m and n’, which are each of them to enter into
two different products, that is m into mn’ and md’, n’ into mn’ and n’d.
These coefficients will be inscribed on the
columns V0 and V4.
If we commence the series of operations by
the product of m into n’, these numbers will be effaced from the columns V0
and V4, that they may be transferred to the mill, which will multiply
them into each other, and will then command the machine to represent the
result, say on the column V6.
But as these numbers are each to be used
again in another operation, they must again be inscribed somewhere; therefore,
while the mill is working out their product, the machine will inscribe them
anew on any two columns that may be indicated to it through the cards; and as,
in the actual case, there is no reason why they should not resume their former
places, we will suppose them again inscribed on V0 and V4,
whence in short they would not finally disappear, to be reproduced no more,
until they should have gone through all the combinations in which they migt
have to be used.
We see, then, that the whole assemblage of
operations requisite for resolving the two above equations of the first degree
may be definitely represented in the following table:-“
I shall put forth the complex table in the
nights to come.
The table may seem formidable for but on
closer inspection you will find it is not all that forbidding as it merely
describes in great detail how the machine with its multiple parts will assign
which number and operation to where and then to where it will move it
subsequently.
Ada Lovelace in her note D made further
changes in the table and made it even more elaborate and clearer.
Just keep in mind that in any calculation
that would be done by the engine, there will be variables that can be
essentially of the following three types:
(one) Those on which the data are inscribed
(two) Those intended to receive the final
results
(three) Those intended to receive
intermediate values of primitive data which will not have to be permanently
stored but merely used for working with so as to get the final desired results.
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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