Monday, March 26, 2018

March 26, 2018 Monday

Bedtime Story 


Re-initiating Note G of Ada Lovelace - 4

 
I shall renew my quotation of Note G of Lovelace which is both technical and mathematical but I owe it to sapiens apes to republish the first ever algorithm.

This part also reflects the depth of knowledge of Ada Lovelace both in mathematics as well as the proposed analytical engine of Babbage.

The notes of Ada Lovelace do not make for an easy reading as not only it is highly mathematical but it is mathematical algorithm applied to a universal Turing machine that to this very day has never got itself invented.

This is not to say that it will never be constructed for as I write this bedtime story a movement is gathering steam around one John Graham-Cumming, a British computer programmer and writer who in October 2010 initiated a program of reconstruction of Charles Babbage’s Analytical Engine. 

The design that he is hoping to recreate goes by the name of Plan 28 which would involve three crucial steps:

(a) Deciphering of the writings and illustrations of Babbage

(b) Building a 3 D simulation of the engine and

(c) Construction of the actual mechanical steam-powered universal computing machine

Just as an addition, John Graham-Cumming also happens to be the guy who initiated the successful petition to the British government seeking an apology for its persecution of Alan Turing.

I promise that after quoting the various Notes of Ada Lovelace starting from Note G and then going along as the need warrants, I will describe the essence of all her notes in a much more simpler, modern and non-mathematical English.

Till then please bear with me.

Re-initiating the Note G:

“The simplest manner of computing these numbers (Bernoulli’s) would be from the direct expansion of

\frac{x}{\epsilon^x-1}=\frac{1}{1+\frac{x}{2}+\frac{x^2}{2\cdot 3}+\frac{x^3}{2\cdot 3\cdot 4}+{\rm \ETC}}

                (1.)

Which is in fact a particular case of the development of

\frac{a+bx+cx^2+\RMETC}{a'+b'x+c'x^2+\RMETC} 

mentioned in Note E

Or again, we might compute them from the well-known form

{\rm B}_{2n-1}=2\cdot\frac{1\cdot 2\cdot 3\ldots 2n}{(2\pi )^{2n}}\cdot\left\{1+\frac{1}{2^{2n}}+\frac{1}{3^{2n}}+\cdots\right\} 
      (2.)

Or from the form

 
  (3.)

Or from many others

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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