February 06, 2018 Tuesday
Bedtime Story
Continuing with Menabrea - 12
Today I am posting the table that displays
in complete detail how the machine will carry out the operations mechanically
for the function (a +bx1).(A + B Cos1 x)
I shall once again continue to quote
Menabrea from his paper “Sketch of the Analytical Engine”.
“It will now be perceived that a general
application may be made of the principle developed in the preceding example, to
every species of process which it may be proposed to effect on series submitted
to calculation.
It is sufficient that the law of formation
of coefficients be known, and that this law be inscribed on the cards of the
machine, which will then of itself execute all the calculations requisite for
arriving at the proposed result.
If, for instance, a recurring series were
proposed, the law of formation of the coefficients being here uniform, the same
operations which must be performed for one of them will be repeated for all the
others; there will merely be a change in the locality of the operation, that
is, it will be performed with different columns.
Generally, since every analytical
expression is susceptible of being expressed in a series ordered according to
certain functions of variable, we perceive that the machine will include all
analytical calculations which can be definitively reduced to the formation of
coefficients according to certain laws, and to the distribution of these with
respect to the variables.
We may deduce the following important
consequence from these explanations, viz. that since the cards only indicate
the nature of the operations to be performed, and the columns of Variables with
which they are to be executed, these cards will themselves possess all the
generality of analysis, of which they are in fact merely a translation.
We shall now further examine some of the
difficulties which the machine must surmount, if its assimilation to analysis
is to be complete.
There are certain functions which
necessarily change in nature when they pass through zero or infinity, or whose
values cannot be admitted when they pass these limits.
When such cases present themselves, the
machine is able, by means of a bell, to give notice that passage through zero
or infinity is taking place, and it then stops until the attendant has again
set it in action for whatever process it may next be desired that it shall
perform.
If this process has been foreseen, then the
machine, instead of ringing, will so dispose itself as to present new cards
which have relation to the operation that is to succeed the passage through
zero and infinity.”
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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