May 17, 2018 Thursday
Bedtime Story
Note E of Ada Lovelace - Part 8
Tonight we shall resume with the Note E of
Ada Lovelace from where we had left last night and this one should really make
you feel a nincompoop illiterate if you had not been feeling already so.
Tonight Lovelace introduces the notion of ‘cycles’
and ‘cycles of cycles’ which today all computer scientists and even average programmers
will recognize this idea as loops and nested loops.
Lovelace develops a mathematical notation
for them - which to most of us who are either mathematically illiterate or handicapped
but in all likelihood both, Mon Ami being an exception – will find it
impossible to comprehend.
It is much like presenting a text in the
ancient Dravidian Tamil to a modern housewife from Netherlands; I can bet you
1000 USD that the reaction will be no different in the two cases.
Ada herself warns the reader that he should
have some minimum mathematical literacy in order to comprehend and appreciate
what she is trying to point out below.
“The whole of the processes therefore that
have been gone through, by the time the second partial quotient has been
obtained, will be, -
(3)
2{(÷),P(
x, -)} or 2{(1), p(2, 3)},
which is a cycle that includes a cycle, or
a cycle of the second order
The operations for the complete division,
supposing we propose to obtain n terms of the series constituting the quotient,
will be, -
(4) n{÷},
p( x, -)} or n{(1), p(2,3)}
It is of course to be remembered that the
process of algebraical division in reality continues ad infinitum, except in
the few exceptional cases which admit of an exact quotient being obtained.
The number n in the formula (4) is always
that of the number of terms we propose to ourselves to obtain; and the nth
partial quotient is the coefficient of the (n-1)th power of x.
There are some cases which entail cycles of
cycles of cycles, to an indefinite extent.
Such cases are usually very complicated,
and they of extreme interest when considered with reference to the engine.
The algebraical development in a series of
the nth function of any given function is of this nature.
Let it be proposed to obtain the nth
function of
(5)
Φ(a, b, c,…,x) x being the variable
We should premise, that we suppose the
reader to understand what is meant by the nth function.
We suppose him likewise to comprehend
distinctly the difference between developing an nth function algebraically, and
merely calculating an nth function arithmetically.
If he does not, the following will be by no
means very intelligible; but we have not space to give any preliminary
explanations.”
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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