Monday, April 9, 2018

April 09, 2018 Monday

Bedtime Story 


Note A of Ada Lovelace - Part 2


Tonight we will continue with note A of Ada Lovelace which is invaluable in understanding the huge leap that had taken place even in the intellectual conception of the Analytical Engine by Charles Babbage.

For the first time a true universal calculating device had been conceived which was capable of performing, in theory, all possible mathematical analysis given right input through the sequentially placed punching cards devised on the principle of weaving looms that had become a huge hit in the contemporary France as it allowed the production of intricate weaving designs at a substantially lower costs.     

“It (the Difference engine) can therefore tabulate accurately and to an unlimited extent, all series whose general term is comprised in the above formula; and it can also tabulate approximately between intervals of greater or less extent, all other series which are capable of tabulation by the Method of Differences.

The Analytical Engine, on the contrary, is not merely adapted for tabulating the results of one particular function and of no other, but for developing and tabulating any function whatever.

In fact the engine may be described as being the material expression of any indefinite function of any degree of generality and complexity, such as for instance,

                      F(x, y, z, log x, sin y, xp etc.)

which is, it will be observed, a function of all other possible functions of any number of quantities.

In this, which we may call the neutral or zero state of the engine, it is ready to receive at any moment, by means of cards constituting a portion of its mechanism (and applied on the principle of those used in the Jacquard-loom), the impress of whatever special function we may desire to develop or to tabulate. 

These cards contain within themselves (in a manner explained in the Memoir itself) the law of development of the particular function that may be under consideration, and they compel the mechanism to act accordingly in a certain corresponding order.

One of the simplest cases would be, for example, to suppose that

F(x, y, z, & etc.)

Is the particular function

                                    \Delta^nu_z=0 

which the Difference Engine tabulates for values of n only up to 7.

In this case the cards would order the mechanism to go through that succession of operations which would tabulate

                             uz = a + bx + cx2 + … + mxn-1

where n might be any number whatever.

These cards, however, have nothing to do with the regulation of the particular numerical data.

They merely determine the operations to be affected, which operations may of course be performed on an infinite variety of particular numerical values, and do not bring out any definite numerical results unless the numerical data of the problem have been impressed on the requisite portions of the train of mechanism.”

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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