May 05, 2018 Saturday
Bedtime Story
Note G of Ada Lovelace - Part 8
As I had explained last night, of all the
Notes of Ada Lovelace from A through G, the only one that we have never
broached upon is the Note E.
It will probably worthwhile to go through
the Note E as well which I may begin following the completion of Note G.
For now we shall resume with the Note G
from where we had left it on the night of March 29, 2018 Thursday.
You may wish to read back on Note G to
revivify your memories on the primary idea of this Note, and for that you will
need to rewind to the bedtime story of February 14, 2018 which was a Wednesday
night though gain after February 16 I had digressed to Jacob Bernoulli and his
family to understand the numbers based upon him and on which Ada Lovelace formulated
her algorithm on.
Note G forms the essential core of Ada
Lovelace wherein she works out the logarithm that the Analytical Engine would
need to execute to derive the Numbers of Bernoulli.
We had walked out mid-way from the
algorithm.
“Six numerical data are in this case
necessary for making the requisite combinations.
These data are 1, 2, (n=4), B₁, B₃, B₅.
Were n=5, the additional datum B₇ would be
needed.
Were n = 6, the datum B₉ would be needed;
and so on.
Thus the actual number of data needed will
always be n +2, for n = n; and out of these n + 2 data, 
of them are successive Numbers of Bernoulli.
of them are successive Numbers of Bernoulli.
The reason why the Bernoulli Numbers used
as data are nevertheless placed on Result-columns in the diagram, is because
they may properly be supposed to have been previously computed in succession by
the engine itself; under which circumstances each B will appear as a result,
previous to being used as datum for computing the succeeding B.
Here then is an instance (of the kind
alluded to in note D) of the same Variables filling more than once office in
turn.
It is true that if we consider our
computation of B₇ as a perfectly isolated calculation, we may conclude B₁, B₃,
B₅ to have been arbitrarily placed on the columns; and it would then perhaps be
more consistent to put them on V₄, V₅, V₆ as data and not results.
But we are not taking this view.
On the contrary, we suppose the engine to
be in the course of computing the Numbers to an indefinite extent, from the
very beginning; and that we merely single out, by way of example, one amongst
the successive but distinct series of computations it is thus performing.
Where the B’s are fractional, it must be
understood that they are computed and appear in the notation of decimal
fractions.
Indeed this is a circumstance that should
be noticed with reference to all calculations.
In any of the examples already given in the
translation and in the Notes, some of the data, or of the temporary or
permanent results, might be fractional, quite as probably as whole numbers.”
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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