Friday, April 13, 2018

April 13, 2018 Friday

Bedtime Story 


Note A of Ada Lovelace - Part 6
  

Tonight we are continuing with the Note A of Ada Lovelace wherein last night we had left with the operations of the Difference Engine which is armed with just seven columns of discs as compared to the Analytical engine which was, at least to the mind of Babbage, projected to possess several times this number of columns.   

“It has seven columns, and a number on any column can add itself to a number on the next column to its right-hand.  

So that, beginning with column furthest to the left, six additions can be effected, and the result appears on the seventh column, which is the last on the right-hand.

The operating mechanism of this engine acts in as separate and independent a manner as that of the Analytical Engine; but being susceptible of only one unvarying and restricted combination, it has little force or interest in illustration of the distinct nature of the science of operations.

The importance of regarding the Analytical Engine under this point of view will, we think, become more and more obvious as the reader proceeds with M. Menabrea’s clear and masterly article.

The calculus of operations is likewise in itself a topic of so much interest, and has of late years been so much more written on and thought on than formally, that any bearing which that engine, from its mode of constitution, may possess upon the illustration of this branch of mathematical science should not be overlooked.

Whether the inventor of this engine had any such views in his mind while working out the invention, or he may have subsequently ever have regarded it under this phase, we do not know; but it is one that forcibly occurred to ourselves on becoming acquainted with the means through which analytical combinations are actually attained by the mechanism.

We cannot forebear suggesting one practical result which it appears to us must be greatly facilitated by the independent manner in which the engine orders and combines its operations: we allude to the attainment of those combinations into which imaginary quantities enter.

This is a branch of its processes into which we have not had the opportunity of inquiring, and our conjecture therefore as to the principle on which we conceive the accomplishment of such results may have been made to depend, is very probably not in accordance with the fact, and less subservient for the purpose than some other principles, or at least requiring the cooperation of others.

It seems to us obvious, however, that where operations are so independent in their mode of acting, it must be easy, by means of a few simple provisions, and additions in arranging the mechanism, to bring out a double set of results, viz. – 1st the numerical magnitudes which are the results of operations performed on numerical data.

(These results are the primary object of the engine.)

2ndly, the symbolical results to be attached to these numerical results, which symbolical results are not less the necessary and logical sequences of operations performed upon symbolical data, than are numerical results when the data are numerical.

If we compare together the powers and the principles of construction of the Difference and of the Analytical Engines, we shall perceive that the capabilities of the latter are immeasurably more extensive than those of the former, and they in fact hold to each other the same relationship as that of analysis to arithmetic.”

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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