May 11, 2018 Friday
Bedtime Story
Note E of Ada Lovelace - Part 2
Tonight we shall continue with the Note E
of Ada Lovelace.
Lovelace treads very gently, in the very
beginning explaining in simple terms what computation of numerical results of
an analytical formula entails.
Here she is trying to explain the
fundamental that exists between the sciences of arithmetic and algebra and that
between numbers and analysis.
Very broadly speaking, arithmetic is about
numbers and very concrete whereas algebra is about variables and symbols and is
capable extreme high levels of abstractions.
Analysis is perhaps even harder to define
but is deeply integrated with the concept of mathematical function which is
very simple to define but results in unimaginable complexities and abstractions
and this is exactly the point that I think Lovelace is trying to hammer into
our brains.
Ada Lovelace is stressing that though the
Analyitcal Engine may appear to be yet another mechanical computing devise just
because it seems to be an advanced version of the Difference Engine, it is in
fact far from so.
So let us read in.
“This trigonometrical series is not only in
itself very appropriate for illustrating the processes of the engine, but is
likewise of much practical interest from its frequent use in astronomical
computations.
Before proceeding further with it, we shall
point out that there are three very distinct classes of ways in which it may be
desired to deduce numerical values from any analytical formula.
First. We may wish to find the collective
numerical value of the whole formula, without any reference to the quantities
of which that formula is a function, or to the particular mode of their
combination and distribution, of which the formula is the result and
representative.
Values of this kind are of a strictly
arithmetical nature in the most limited sense of the term, and retain no trace
whatever of the processes through which they have been deduced.
In fact, any one such numerical value may
have been attained from an infinite variety of data, or of problems.
The values for x and y in the two equations
come under this class of numerical results.
Secondly. We may propose to compute the
collective numerical value of each term of a formula, or of a series, and to
keep these results separate.
The engine must in such a case appropriate
as many columns to results as there are terms to compute.
Thirdly. It may be desired to compute the
numerical value of various subdivisions of each term, and to keep all these
results separate.
It may be required, for instance, to
compute each coefficient separately from its variable, in which particular case
the engine must appropriate two result-columns to every term that contains both
a variable and coefficient.
There are many ways in which it may be
desired in special cases to distribute and keep separate the numerical values
of different parts of an algebraical formula; and the power of effecting such
distributions to any extent is essential to the algebraical character of the
Analytical Engine."
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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