May 01, 2018 Tuesday
Bedtime Story
Note D of Ada Lovelace - Part 6
Tonight we shall continue with the Note D
of Ada Lovelace wherein she is exhorting the virtues of the upper case indices
to the left of the letter V used by Menabrea and herself in their flowchart tables.
Their chief importance lies as a tracking
device as they provide the means of back-tracking and tracing out how the
result was derived at.
This, I must warn you, is no more an easy
reading now as it requires backtracking and doing some metal work yourself.
“There are several advantages in having a
set of indices of this nature; but these advantages are perhaps hardly of a
kind to be immediately perceived, unless by a mind somewhat accustomed to trace
the successive steps by means of which the engine accomplishes its purposes.
We have only space to mention in a general
way, that the whole notation of tables is made more consistent by these
indices, for they are able to mark a difference in certain cases, where there
would otherwise be an apparent identity confusing in its tendency.
In such a case as Vn = Vp
+ Vn there is more clearness and more consistency with the usual
laws of algebraical notation, in being able to write m+1Vn
= qVp + mVn.
It is also obvious that the indices furnish
a powerful means of tracing back the derivation of any result; and of
registering various circumstances concerning that series of successive
substitutions, of which every result is in fact merely the final consequence;
circumstances that may in certain cases involve relations which it is important
to observe, either for purely analytical reasons, or for practically adapting
the workings of the engine to their occurrence.
The series of substitutions which lead to
the equations of the diagram are as follows:-“
(Ada Lovelace recommends that you actually
go back to the table of Menabrea and try to trace the successive substitutions
backwards from equations (1) to (4).
This can be easily done by means of the
upper and the lower indices.
It will give you an insight how V in each
stage undergoes transformation into two other Vs in some other column of the table,
until after some time the Vs of the original data are arrived at.)
“There are three successive substitutions
for each of these equations.
The formulae (2.), (3.) and (4.) are
implicitly contained in (1.), which latter we may consider as being in fact the
condensed expression of any of the former.
It will be observed that every succeeding
substitution must contain twice as many V’s as its predecessor.
So that if a problem requires n
substitutions, the successive series of numbers for the V’s in the whole of
them will 2, 4, 8, 16…2n.”
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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