May 20, 2018 Sunday
Bedtime Story
Note E of Ada Lovelace - Part 11
Tonight we shall resume with the Note E of
Ada Lovelace from where we had left last night.
Here she is giving her own mathematical notation
of varying cycles that some operations would be carried out by the Analytical
Engine.
Tonight we will be finishing off with the
Note E wherein we would have completed with Lovelace’s detailed description of
the workings of Analytical Engine using a specific example which I personally
find very endearing considering the passion with which she is chronicling very
minutiae of running of a device never invented till this day.
“But there is another description of cycles
which can only effectually be expressed, in a condensed form, by the preceding
notation.
We shall call them varying cycles.
They are of frequent occurrence, and
include successive cycles of operations of the following nature:-
(9) 
where each cycle contains the same group of
operations, but in which the number of repetitions of the group varies
according to a fixed rate, with every cycle.
(9) can be well expressed as follows:-
(10)
∑p(1, 2…m), the limits of p being from p-n to p
Independent of the intrinsic advantages
which we thus perceive to result in certain cases from this use of the notation
of the integral calculus, there are likewise considerations which make it
interesting, from the connections and relations involved in this new
application.
It has been observed in some of the former
Notes, that the processes used in analysis form a logical system of much higher
generality than the applications to number merely.
Thus, when we read over any algebraical
formula, considering it exclusively with reference to the processes of the engine,
and putting aside for the moment its abstract significations as to the
relations of quantity, the symbols +, x, etc in reality represent (as their
immediate and proximate effect, when the formula is applied to the engine) that
a certain prism which is a part of the mechanism turns a new face, and thus
presents a new card to act on the bundles of levers of the engine; the new card
being perforated with holes, which are arranged according to the peculiarities
of the operation of addition, or of multiplication, etc.
Again, the numbers in the preceding formula
(8), each of them really represents one of these very pieces of card that are
hung over the prism.
Now in the use made in the formulae (7),
(8), and (10), of the notation of the integral calculus, we have glimpses of a
similar new application of the language of the higher mathematics.
∑, in reality, here indicates that when a
certain number of cards have acted in succession, the prism over which they
revolve must rotate backwards, so as to bring those cards into their former
position; and the limits 1 to n, 1 to p, etc, regulate how often this backward
rotation is to be repeated.”
This terminates the Note E and now we can
safely return to the left-over part of the Note G from which we had rerouted to
Note E.
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.
Advertisements
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:
No comments:
Post a Comment