January 26, 2018 Friday
Bedtime Story
Continuing with Menabrea - 4
We are continuing with the treatise of
Menabrea:
“Sketch of the Analytical Engine” that was
translated into French by Ada Lovelace and published along with her notes in
1842.
“To conceive how the machine can now go
through its functions according to the laws laid down, we will begin by giving
an idea of the manner in which it materially represents numbers.
Let us conceive a pile or vertical column
consisting of an indefinite number of circular discs, all pierced through their
centers by a common axis, around which each of them can take an independent
rotator movement.
If round the edge of each of these discs
are written the ten figure which constitute our numerical alphabet, we may
then, by arranging a series of these figures in the same vertical line, express
in this manner any number whatever.
It is sufficient for this purpose that the
first disc represents units, the second tens, the third hundreds, and so on.
When two numbers have been thus written on
two distinct columns, we may propose to combine them arithmetically with each
other, and to obtain the result on the third column.
In general, if we have series of columns
(what Menabrea is contemplating was defined by Ada in her notes as the
storehouse which we shall go through in greater detail later – storytelling
chimpanzee) consisting of discs, which columns we will designate as V1, V2, V3,
V4 etc, we may require, for instance, to divide the number written on the
column V1 by that on the column V4, and to obtain the result on the column V7.
To effect this operation, we must impart to
the machine two distinct arrangements; through the first it is prepared for
executing a division, and through the second the columns it is to operate on
are indicated to it, and also the column on which the result is to be
represented.
If the division is to be followed, for
example, by the addition of two numbers taken on other columns, the two
original arrangements of the machine must be simultaneously altered.
If, on the contrary, a series of operations
of the same nature is to be gone through, then the first of the original
arrangements will remain, and the second alone must be altered.
Therefore, the arrangements that may be
communicated to the various parts of the machine may be distinguished into two
principal classes:
First, that relative to the Operations
Second, that relative to the Variables
By the latter we mean that which indicates
the columns to be operated on.
As for the operations themselves, they are
executed by a special apparatus, which is designated by the name of mill, and
which itself contains a certain number of columns, similar to those of the
Variables.
When two numbers are to be combined
together, the machine commences by effacing them from the columns where they
were written, that is, it places zero on every disc of the two vertical lines
on which the numbers were represented; and it transfers the numbers to the
mill.
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