January 31, 2018 Wednesday

Bedtime Story 

Continuing with Menabrea - 7

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.

Menabrea is now considering one specific example of two first degree equations to explain the workings of the engine.

         mx + ny = d

         m’x + n’y = d’

We deduce x = (dn’ – d’n)/(n’m – nm’),

And for y an analogous expression

Let us continue to represent by V₀, V₁, V₂ etc the different columns which contain the numbers, and let us suppose that the first eight columns have been chosen for expressing on them the numbers represented by m, n, d, m’, n’, d’, n and n’, which implies that V₀ = m, V₁ = n, V₂ = d, V₃ = m’, V₄ = n’, V₅ = d’, V₆ = n, V₇ = n’.

The series of operations commanded by the cards, and the results obtained, may be represented in the following table:-

	Operation cards	Cards of	The Variables
Number of the operations	Symbols indicating nature of operations	Columns on which operations to be performed	Columns which receive results of operations	Progress of the operations
1	x	V2 x V4 =	V8…	= dn’
2	x	V5 x V1 =	V9…	= d’n
3	x	V4 x V0 =	V10…	= n’m
4	x	V1 x V3 =	V11…	= nm’
5	-	V8 – V9 =	V12…	= dn’ – d’n
6	-	V10 – V11 =	V13…	= n’m – nm’
7		V12/V13 =	V14…	= x =  (dn’ – d’n)/(n’m – nm’)

 

Since the cards do nothing but indicate in what manner and on what columns the machine shall act, it is clear that we must still, in every particular case, introduce the numerical data for the calculation.

Thus, in the example we have selected, we must previously inscribe the numerical values of m, n, d, m’, n’, d’, in the order and on the columns indicated, after which the machine when put in action will give the value of the unknown quantity x for this particular case.

To obtain the value of y, another series of operations analogous to the preceding must be performed.

But we see that they will be only four in number, since the denominator for the expression of y, excepting the sign, is same as that for x, and equal to n’m – nm’.

In the preceding table it will be remarked that the column for operations indicates for successive multiplications, two subtractions and one division.

Therefore, if desired, we need only use three operation-cards; to manage which, it is sufficient to introduce into the machine an apparatus which shall, after the first multiplication, for instance, retain the card which relates to this operation, and not allow it to advance so as to be replaced by another one, until after this same operation shall have been four times repeated.”

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:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg

January 30, 2018 Tuesday

Bedtime Story 

Note C of Ada Lovelace - 2

We are continuing with the Note C of Ada Lovelace in 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.

“This process is alluded to by M. Menabrea (as we shall see later when we get back to the writing of Menabrea), and it is a very important simplification.

It has been proposed to use it for the reciprocal benefit of that art, which, while it has itself no apparent connection with the domains of abstract science, has yet proved so valuable to the latter, in suggesting the principles which, in their new and singular piece of application, seem likely to place algebraical combinations not less completely within the province of mechanism, than are all those varied intricacies of which intersecting threads are susceptible.

By the introduction of the system of backing into the Jacquard-loom itself, patterns which should possess symmetry, and follow regular laws of any extent, might we woven by means of comparatively few cards.

Those who understand the mechanism of this loom will perceive that the above improvement is easily effected in practice, by causing the prism over which the train of pattern-cards is suspended to revolve backwards instead of forwards, at pleasure, under the requisite circumstances; until, by so doing, any particular cards, or set of cards, that has done duty once, and passed on in the ordinary regular succession, is brought back to the position it occupied just before it was used the preceding time.

The prism then resumes its forward rotation, and thus brings the card or set of cards in question into play a second time.

This process may obviously be repeated any number of times.”      

Here Lovelace makes an attempt to describe how the card system of the loom can be used in the engine to carry out repeated mathematical operations.

Now we will go back to Menabrea where he continues to describe in greater detail how the card system was proposed to be used in the analytical engine.

“Arrangements analogous to those just described have been introduced into the Analytical engine.

It contains two principal species of cards: first, Operation cards, by means of which the parts of the machine are so disposed as to execute any determinate series of operations, such as additions, subtractions, multiplications, and divisions; secondly, cards of the Variables, which indicate to the machine the columns on which the results are to be represented.

The cards, when put in motion, successively arrange the various portions of the machine according to the nature of the processes that are to be effected, and the machine at the same time executes these processes by means of the various pieces of mechanism of which it is constituted.

In order more perfectly to conceive the thing, let us select as an example the resolution of the two equations of the first degree with two unknown quantities:-

         mx + ny = d

         m’x + n’y = d’

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:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg

January 29, 2018 Monday

Bedtime Story 

Note C of Ada Lovelace

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.

At this time he is describing the punched cards automation system that was deployed in Jacquard loom.

“Supposing this process is successively repeated according to a law indicated by the pattern to be executed, we perceive that this pattern may be reproduced on the stuff.

For this purpose we need merely compose a series of cards according to the law required, and arrange them in suitable order one after the other; then, by causing them to pass over a polygonal beam which is so connected as to turn a new face for every stroke of the shuttle, which face shall then be impelled parallely to itself across the bundle of lever-arms, the operation of raising the threads will be regularly performed.

Thus we see that brocaded tissues may be manufactured with a precision and rapidity formerly difficult to obtain.”

This beautiful exposition on Jacquard’s automation was supplemented by that of Ada Lovelace in her Note C which is worth going through immediately rather than later on sequentially as we may lose the thread by then.   

Note C written by Ada Lovelace

“Those who may desire to study the principles of the Jacquard-loom in the most effectual manner, viz. that of practical observation, have only to step into the Adelaide Gallery or the Polytechnic Institution.

In each of these valuable repositories of scientific illustration, a weaver is constantly working at a Jacquard-loom, and is ready to give any information that may be desired as to the construction and modes of acting of his apparatus.”

(I am not sure if the tradition continues till this day though it may be possible that such displays still go on knowing how much Europeans are seeped into history and what passion that have for museums – Storytelling Chimpanzee).

“The volume on the manufacture of silk, in Larder’s Cyclopaedia, contains a chapter on the Jacquard-loom, which may also be consulted with advantage.

The mode of application of the cards, as hitherto used in the art of weaving, was not found, however, to be sufficiently powerful for all the simplifications which it was desirable to attain in such varied and complicated processes as those required in order to fulfill the purposes of an Analytical Engine.

A method was devised of what was technically designated backing the cards in certain groups according to certain laws.

The object of this extension is to secure the possibility of bringing any particular card or set of cards into use any number of times successively in the solution of one problem.

Whether this power shall be taken advantage of or not, in each particular instance, will depend on the nature of operations which the problem under consideration may require.”

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:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg

January 28, 2017 Sunday

Bedtime Story 

Continuing with Menabrea - 6

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.

We will continue with his description of the automation in Jacquard’s Loom.

“Formerly, this process was lengthy and difficult, and it was requisite that the workman, by attending to the design which he was to copy, should himself regulate the movements the threads were to take.

Thence arose the high price of this description of stuffs, especially if threads of various colors entered into the fabric.

To simplify this manufacture, Jacquard devised the plan of connecting each group of threads that were to act together, with a distinct lever belonging exclusively to that group.”

(As you would recall from my own bedtime stories of past, Joseph Marie Jacquard merely happened to be at the right place at the right time.

He had simply rediscovered and assembled the cornucopia of discoveries that were already in place in the Paris museum by the cumulative innovations of Basile Bouchon, Jean-Baptiste Falcon and Jacques Vaucanson.

Napoleon Bonaparte needed to boost the French Silk Industry as the country was in serious financial crisis post revolution and multiple wars.

On a visit to Lyon he had approved of the contraption that Jacquard had set up for display to the visiting royalties.

The rest, as they say, is history – Storytelling Chimpanzee).   

“All these levers terminate in rods, which are united together in one bundle, having usually the form of a parallelepiped with a rectangular base.”

(A parallelepiped is any three-dimensional figure with sex faces, each of which is a parallelogram – Storytelling Chimpanzee).

“The rods are cylindrical, and are separated from each other by small intervals.

The process of raising the threads is thus resolved into that of moving these various lever-arms in the requisite order.

To effect this, a rectangular board of pasteboard (card stocks like those that you see in business cards or playing cards) is taken, somewhat larger in size than a section of the bundle of lever-arms.

If this sheet be applied to the base of the bundle, and an advancing motion be them communicated to the pasteboard, the latter will move with it all the rods of the bundle, and consequently the threads are then connected with each of them.

But if the pasteboard, instead of being plane, were pierced with holes corresponding to the extremities of the levers which meet it, then, since each of the levers would pass through the pasteboard during the motion of the latter, they would all remain in their places.

We thus see that it is easy so to determine the positions of the holes in the pasteboard, that, at any given moment, there shall be a certain number of levers, and consequently of parcels of threads, raised, while the rest remain where they were.

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:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg

January 27, 2018 Saturday

Bedtime Story 

Continuing with Menabrea - 5

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.

I hope that now that you have a picture or rather a caricature of the analytical engine, you will be able to have a better understanding of the different parts of it that Menabrea is talking about such as ‘The Mill’, ‘The Store’, ‘Variable Cards’ and so on.

“There, the apparatus having been disposed suitably for the required operation, this latter is effected, and, when completed, the result itself is transferred to the column of Variables which shall have been indicated.

Thus the mill is that portion of the machine which works, and the columns of Variables constitute that where the results are represented and arranged.

After the preceding explanations, we may perceive that all fractional and irrational results will be represented in decimal fractions.

Supposing each column to have forty discs, this extension will be sufficient for all degrees of approximation generally required.

It will now be required how the machine can of itself, and without having recourse to the hand of man, assume the successive dispositions suited to the operations.

The solution of this problem has been taken from Jacquard’s apparatus, used for the manufacture of brocaded stuffs, in the following manner:-“

To explain the concept of automation in the analytical machine, meaning how the engine will automatically by itself handle the necessary successive operations without bringing humans into picture Menabrea goes into great detail of the automation mechanism that was incorporated in the Jacquard loom.

As if Menabrea’s description was not enough, even Lovelace devoted some effort in clarifying the concept through her notes (Note C).

Considering the value of automation in the analytical engine, I too had narrated in a detailed and pain staking manner not only in the history of automation pertaining to loom and weaving, but the very idea of automata itself.

After the general analysis of automata, I had honed into the process of weaving and the evolution of automation in weaving devices most notably in the city of Lyon of France.

Let us see how my writing compares with those of Menabrea and Ada Lovelace with respect to Jacquard’s loom.

First we will study the writing of Menabrea and follow it up with the notes of Lovelace.

“Two species of threads are usually distinguished in woven stuffs: one is the warp or longitudinal thread, and other the woof or transverse thread, which is conveyed by the instrument called the shuttle, and which crosses the longitudinal thread or warp.

When a brocaded stuff is required, it is necessary in turn to prevent certain threads from crossing the woof, and this according to a succession which is determined by the nature of the design that is to be reproduced.”

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.

Rendition of Analytical Engine by Sydney Padua

                           

  

                

             

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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:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg

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:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, I recommend this large collection of Halloween Songs for Kids:

https://www.youtube.com/channel/UCd14DRdYKj454znayUIfcAg