February 12, 2018 Monday
Bedtime Story
Note F of Ada Lovelace - 3
Tonight we are continuing with the Note F
of Lady Lovelace where she takes on the vexing issue of multiple punched cards
required for mathematical operations.
“If we take n simple equations containing n-1
variables, n being a number unlimited in magnitude, the case becomes still more
obvious, as the same three cards might then take the place of thousands of
millions of cards.
We shall now draw further attention to the
fact, already noticed, of its being by no means necessary that a formula
proposed for solution should ever have been actually worked out, as a condition
for enabling the engine to solve it.
Provided we know the series of operations
to be gone through, that is sufficient.
In the foregoing instance this will be
obvious enough on a slight consideration.
And it is a circumstance which deserves
particular notice, since herein may reside a latent value of such an engine
almost incalculable in its possible ultimate results.
We already know that there are functions
whose numerical value it is of importance for the purposes of both of abstract
and practical science to ascertain, but whose determination requires processes
so lengthy and so complicated, that, although it is possible to arrive at them
through great expenditure of time, labor and money, it is yet on these accounts
practically almost unattainable; and we can conceive there being some results
which it may be absolutely impossible in practice to attain with any accuracy,
and whose precise determination it may prove highly important for some of the
future wants of science, in its manifold, complicated and rapidly-developing
fields of inquiry, to arrive at.
Without, however, stepping into the realm
of conjecture, we will mention a particular problem which occurs to us at this
moment as being an apt illustration of the use to which such an engine may be
turned for determining that which human brains find it difficult or impossible to
work out unerringly.
In the solution of the famous problem of
The Three Bodies, there are, out of 295 coefficients of lunar perturbations
given by M. Clausen (Astro. Nachrichten, No. 406) as a result of the
calculations by Burg, of two by Damoiseau, and of one by Burckhardt, fourteen
coefficients that differ in the nature of their algebraic sign; and out of the
remainder there are only 101 (or about one-third) that agree precisely both in
signs and amount.
These discordances, which are generally
small in individual magnitude, may arise either from an erroneous determination
of the abstract coefficients in the development of the problem, or from
discrepancies in the data deduced from observation, or from both causes
combined.
The former is the most ordinary source of
error in astronomical calculations, and this the engine would entirely obviate.
We might even invent laws for series or
formulae in an arbitrary manner, and set the engine to work upon them, and thus
deduce numerical results which we might not otherwise have thought of
obtaining; but this would hardly perhaps in any instance be productive of any
great practical utility, or calculated to rank higher than as a philosophical
amusement.”
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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