Saturday, January 20, 2018

January 20, 2018 Saturday

Bedtime Story 


Sketch of the Analytical Engine - 1


We are continuing with the treatise of Menabrea:
“Sketch of the Analytical Engine”.

“This admitted, we may propose to execute, by means of machinery, the mechanical branch of these labors, reserving for pure intellect that which depends on the reasoning faculties.

Thus the rigid exactness of those laws which regulate numerical calculations must frequently have suggested the employment of material instruments, either for executing the whole of such calculations or for abridging them; and thence have arisen several inventions having this object in view, but which have in general but partially attained it.

For instance, the much-admired machine of Pascal is now simply an object of curiosity, which, while it displays the powerful intellect of its inventor, is yet of little utility in itself.

Its powers extended no further than the execution of the first four operations of arithmetic, and indeed were in reality confined to that of the first two, since multiplication and division were the result of series of additions and subtractions.

The chief drawback hitherto on most of such machines is, that they require the continual intervention of a human agent to regulate their movements, and thence arises a source of errors; so that, if their use has not become general for large numerical calculations, it is because they have not in fact resolved the double problem which the question presents, that of correctness in the results, united with the economy of time.”

It is worth looking back and trying to see what this first paragraph is summarizing.

Menabrea is saying that since lots of mathematics is purely mechanical calculation, mechanical machines in theory ought to be able to render us decent services at least to this aspect of mathematics.

One must keep in mind that we are talking of days where even the most basic of electronic calculators that an average shopkeeper fiddles with today was a science fiction.

Yet the machines that have been made so far have failed to achieve even this bare minimum as the best machine then, that of Blaise Pascal could only perform just the two of the four basic mathematical operations and over that it requires constant intervention of human hands which could very easily lead to errors rendering the whole process of automation futile.

But let us now continue and see what follows after the first paragraph.

“Struck with similar reflections, Mr. Babbage has devoted some years to the realization of a gigantic idea.

He proposed to himself nothing less than the construction of a machine capable of executing not merely arithmetical calculations, but even all those of analysis, if their laws are known.

The imagination is at first astounded at the idea of such an undertaking; but the more calm reflection we bestow on it, the less impossible does success appear, and it is felt that it may depend on the discovery of some principle so general, that, if applied to machinery the latter may be capable of mechanically translating the operations which may be indicated to it be algebraic notion.”

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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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