April 10, 2018 Tuesday
Bedtime Story
Note A of Ada Lovelace - Part 3
Tonight we are continuing with the Note A
of Ada Lovelace wherein she is emphasizing the importance of understanding the
general principles of operations that go behind analysis or mathematical calculations.
She is essentially referring to the idea of
algorithms which then was yet to get its formal definition the way we have it
today.
“In the above example, the first essential
step towards an arithmetical result would be the substitution of specific
numbers for n, and for the other primitive quantities which enter into the
function.
Again, let us suppose that for F we put two
complete equations of the fourth degree between x and y.
We must then express on the cards the law
of elimination for such equations.
The engine would follow out those laws, and
would ultimately give the equation of one variable which results from such
elimination.
Various modes of elimination might be selected;
and of course the cards must be made out accordingly.
The following is one mode that might be
adopted.
The engine is able to multiply together any
two functions of the form
a + bx + cx2
+ … + pxn
This granted, the two equations may be
arranged according to the powers of y, and the coefficients of the power of y
may be arranged according to the powers of x.
The elimination of y will result from the
successive multiplications and subtractions of several such functions.
In this, and all other instances, as was
explained above, the particular numerical data and the particular numerical
results are determined by means and portions of the mechanism which act quite
independently of those that regulate the operations.
In studying the action of the Analytical
Engine, we find the peculiar and independent nature of the considerations which
in all mathematical analysis belongs to operations, as distinguished from the
objects acted upon and from the results of the operations performed upon those
objects, is very strikingly defined and separated.
It is well to draw attention to this point,
not only because its full appreciation is essential to the attainment of any
very just and adequate general comprehension of the powers and mode of action
of the Analytical Engine, but also because it is one which is perhaps too
little kept in view in the study of mathematical science in general.
It is, however, impossible to confound it
with other considerations, either when we trace the manner in which that engine
attains its results, or when we prepare the data for its attainment of those
results.
It were much to be desired, than when
mathematical processes pass through human brain instead of through the medium
of inanimate mechanism, it were equally a necessity of things that the
reasonings connected with operations should hold the same just place as a clear
and well-defined branch of the subject of analysis, a fundamental but yet
independent ingredient in the science, which they must do in studying the
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.
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