May 15, 2018 Tuesday

Bedtime Story 

Note E of Ada Lovelace - Part 6

Tonight we shall resume with the Note E of Ada Lovelace from where we had left last night.

These are difficult parts I very much understand, but then the gadgets that you hold in your hands today arose out of such or similar complexities and that alone justifies writing bedtime stories about them.

I personally am not very much interested in the frying-pan-kind-of-science bedtime stories that talk about direct practical benefits; that can be gleaned out of most popular type of writings spread out all over.

I find it extremely appealing and scintillating just writing about these unsung heroes with superhuman intellect and brain/mind who accidentally, out of sheer chance, ended up in gifting to the world powerful computers in their hands (only to highly misused I dare say).  

                 “Fifth and Final Series of Operations

                          ²V₂₀ x ⁰V₄₀ = ¹V₄₀

                          ³V₂₁ x ⁰V₄₁ = ¹V₄₁

                          ³V₂₂ x ⁰V₄₂ = ¹V₄₂

                          ²V₂₃ x ⁰V₄₃ = ¹V₄₃

                          ¹V₂₄ x ⁰V₄₄ = ¹V₄₄

(N.B. that V₄₀ being intended to receive the coefficient on V₂₀ which has no variable, will only have cos 0θ(=1) inscribed on it, preparatory to commencing the fifth series of operations).

From the moment that the fifth and the final series of operations is ordered, the Variables V₂₀, V₂₁, etc, then in their turn cease to be Result-Variables and become mere Working-variables; V₄₀, V₄₁, etc, being now the recipients of the ultimate results.

We should observe, that if the variables cosθ, cos2θ, cos3θ, etc are furnished, they would be directly placed upon V₄₁, V₄₂, etc like any other data.  

If not, a separate computation might be entered upon in a separate part of the engine, in order to calculate them, and place them on V₄₁ etc.

We have now explained how the engine might compute (1) in the most direct manner, supposing we know nothing about the general term of the resulting series.

But the engine would in reality set to work very differently, whenever (as in this case) we do know the law for the general term.

The first two terms of (1) are

            (4) 

And the general term for all after these is

                               (5)

Which is the coefficient of the (n+1)th term. 

The engine would calculate the first two terms by means of a separate set of suitable Operation-cards, and would then need another set for the third term; which last set of Operation-cards would calculate all the succeeding terms ad infinitum, merely requiring certain new Variable-cards for each term to direct the operations to act on the proper columns.”

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