April 11, 2018 Wednesday
Bedtime Story
Note A of Ada Lovelace - Part 4
Tonight we are continuing with the Note A
of Ada Lovelace where she is writing about the science of mathematical
operations which in modern mathematics is represented with omega sign as a
function.
So ω is a function of the form ω: V →
In computer science the term branch is used
for any instruction in a computer program that can make the computer to begin
to execute a difference sequence of instructions from what it was running
previously.
“The confusion, the difficulties, the
contradictions which, in consequence of a want of accurate distinctions in this
particular, will at once occur to the reader who is at all versed in this
science, and would alone suffice to justify dwelling somewhat on the point, in
connection with any subject so peculiarly fitted to give forcible illustration
of it as the Analytical Engine.
It may be desirable to explain, that by the
word operation, we mean any process which alters the mutual relationship of two
or more things, be this relation of what kind it may.
This is the most general definition, and
would include all subjects in the universe.”
(Note Mon Ami that Ada Lovelace is referring
to a universal machine here, a computer science foundational concept that would
be firmly established a century from her time – Remark of the storytelling
chimpanzee).
“In abstract mathematics, of course alter
those particular relations which are involved in the considerations of number
and space, and the results of operations are those particular results which
correspond to the nature of the subjects of operation.
But the science of operations, as derived
from mathematics more especially, is a science of itself, and has its own
abstract truth and value; just as logic has its own peculiar truth and value,
independently of the subjects to which we may apply its reasonings and
processes.
Those who are accustomed to some of the
modern views of the above subject, will know that a few fundamental relations
come true, certain other combinations of relations must of necessity follow;
combinations unlimited in variety and extent if the deductions from the primary
relations be carried on far enough.
They will also be aware that one main
reason why the separate nature of science of operations has been little felt,
and in general little dwelt on, is the shifting meaning of many of the symbols
used in mathematical notation.
First, the symbols of operation are
frequently also the symbols of the results of operations.
We may say that these symbols are apt to
have both a retrospective and a prospective signification.
They may signify either relations that are
the consequences of a series of processes already formed, or relations that are
yet to be effected through certain processes.
Secondly, figures, the symbols of numerical
magnitude, are frequently also the symbols of operations, as when they are the
indices of the powers.”
Wherever terms have a shifting meaning,
independent sets of considerations are liable to become complicated together,
and reasonings and results are frequently falsified.”
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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