May 03, 2018 Thursday
Bedtime Story
Note D of Ada Lovelace - Part 8
Tonight we shall continue with the Note D
of Ada Lovelace wherein she continues to describe the complex interplay between
Variable and Operation-cards in any mathematical operations.
Mathematical computations will vary in
their complexities, and therefore some variables will need to undergo similar
operations or different operations multiple number of times.
This disparity will necessitate a significant
difference in the number of Variable-cards and Operation-cards and for once we
see that the ever-bullish and buoyant Lady Ada expresses concerns over the
immense complexity the physical workings of the Engine would entail.
“Therefore, at least three times as many
Variable-cards as there are operations (not Operation-cards, for these, as we
have just seen, are by no means always as numerous as the operations) are
brought into use in every calculation.
Indeed, under certain contingencies, a
still larger proportion is requisite; such, for example, would probably be the
case when the same result has to appear on more than one Variable
simultaneously (which is not unfrequently a provision necessary for subsequent
purposes in a calculation), and in some other cases which we shall not here
specify.
We see therefore that a great disproportion
exists between the amount of Variable and of Operation-cards requisite for the
working of even the simplest question.
All calculations do not admit, like this
one, of the operations of the same nature being performed in groups together.
Probably very few do so without exceptions
occurring in one or other stage of the progress; and some would not admit it at
all.
The order in which the operations shall be
performed in every particular case is a very interesting and curious question,
on which our space does not permit us fully to enter.
In almost every computation a great variety
of arrangements for the succession of the processes is possible, and various
considerations must influence the selection amongst them for the purposes of a
Calculating Engine.
One essential object is to choose that
arrangement which shall tend to reduce to a minimum the time necessary for
completing the calculation.
It must be evident how multifarious and how
mutually complicated are the considerations which the working of such an engine
involve.
There are frequently several distinct sets
of effects going on simultaneously; all in a manner independent of each other,
and yet to a greater or less degree exercising a mutual influence.
To adjust each to every other, and indeed
even to perceive and trace them out with a perfect correctness and success,
entails difficulties whose nature partakes to a certain extent of those
involved in every question where conditions are very numerous and
inter-complicated; such as for instance the estimation of the mutual relations
amongst statistical phenomena, and of those involved in many other classes of
facts.”
With this, we come to the end of the Note
D.
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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