April 14, 2018 Saturday
Bedtime Story
Note A of Ada Lovelace - Part 7
Tonight we are continuing with the Note A
of Ada Lovelace in which she exalts the virtues of the Analytical Engine in
contrast with the Difference Engine; she castigates, almost humiliates the
Difference Engine as being merely a tabulating device at the very same time
venerating the Analytical Engine to be “material and mechanical representative
of analysis”.
“The Difference Engine can effect but one
particular series of operations, viz. that required for tabulating the integral
of the special function.
and as it can only do this for values of n
up to 7, it cannot be considered as being the most general expression of even
one particular function, much less as being the expression of any and all
possible functions of all degrees of generality.
The Difference Engine can in reality (as
has already been partly explained) do nothing but add; and any other processes,
not excepting those of simple subtraction, multiplication, division, can be
performed by it only just to that extent in which it is possible, by judicious
mathematical arrangement and artifices, to reduce them to a series of
additions.
The method of differences is, in fact, a
method of additions; and as it includes within its means a large number of
results attainable by addition simply, than any other mathematical principle,
it was very appropriately selected as the basis on which to construct an Adding
Machine, so as to give to the powers of such a machine the widest possible
range.
The Analytical Engine, on the contrary, can
either add, subtract, multiply or divide with equal facility; and performs each
of these four operations in a direct, without the aid of any of the other
three.
This one fact implies everything; and it is
scarcely necessary to point out, for instance, that while the Difference Engine
can merely tabulate, and is incapable of developing, the Analytical Engine can
either tabulate or develop.
The former engine is in its nature strictly
arithmetical, and the results it can arrive at lie within a very clearly
defined and restricted range, while there is no finite line of demarcation
which limits the powers of the Analytical Engine.
These powers are co-extensive with our
knowledge of the laws of analysis itself, and need be bounded only by our
acquaintance with the latter.
Indeed we may consider the engine as the
material and mechanical representative of analysis, and that our actual working
powers in this department of human study will be enabled more effectually than
heretofore to keep pace with our theoretical knowledge of its principles and
laws, through the complete control which the engine gives us over the executive
manipulation of algebraical and numerical symbols.
Those who view mathematical science, not
merely as a vast body of abstract and immutable truths, whose intrinsic beauty,
symmetry and logical completeness, when regarded in their connection together
as a whole, entitle them to a prominent place in the interest of all profound
and logical minds, but as possessing a yet deeper interest for the human race,
when it is remembered that this science constitutes the language through which
alone we can adequately express the great facts of the natural world, and those
unceasing changes of mutual relationship which, visibly or invisibly,
consciously or unconsciously to our immediate physical perception, are
interminably going on in the agencies of the creation we live amidst: those who
thus think on mathematical truth as the instrument through which the weak mind
of man can most effectively read his Creator’s work, will regard with special
interest all that can tend to facilitate the translation of its principles into
explicit practical forms.”
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