Inversions, Reversions & Perversions

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In our childhood there was this rumor that horses harnessed to 'jhatkas' of Tirupati ran backwards when they were annoyed with their Drivers. But I never saw one nor met anyone who saw one.

In KGP in the 1960s there were a few dandies who bought the famous Rajdoot bikes and flaunted them on the road...whoosh! It used to be said that, once in a while, when the Driver sits proudly astride his Rajdoot and kicks its Starter Pedal, it starts to go backwards. I thought it was a bull till MSS, who never told a lie, said he had that experience once and explained it as due to its timer's misbehavior.

When I was a kid, we were traveling by the Madras-Howrah Mail from Nellore to Srikakulam and had to cross Waltair (Vizagh). I had slept off when the train passed Waltair and when I woke up, I started shouting to my dad that the Driver had goofed and the Mail is running back to Nellore. It took repeated journies to find out what happens at Waltair...there is a T-Junction and while reaching Waltair, the train takes the vertical leg of the T and goes in seawards. Since it can't very well drive on and drown in the Bay of Bengal, it reverses and goes back and on to Howrah...but not quite a U-Turn. Its sea-bound engine delinks and goes into its yard while a new engine is shunted to the rearmost bogie and lugs the Mail merrily on. So, if you were sitting in a North-facing seat till Waltair, you will be facing South then on...the port side turns into the starboard side...the first and last bogies are reversed and it is quite an experience to figure out the 'symmetry operation' involved in the perverted behavior of the Howrah-Mail.

As for the Electron Tube Circuits in our youth, we have the famous example of Feynman, who as a boy, 'repaired' a misbehaving radio by simply switching the tubes at the front and back ends...the hum and hiss just disappeared. And at KGP, as long as I was there, no 'Audio System' in any one of the several auditoria behaved like a Lady. First, the front-end-techno would stand in front of the mike and say: "Check..one, two, three..." and nothing happens. Then the back-end chap fiddles and twiddles his Amplifier knobs and suddenly the negative feedback goes positive at some pole or zero of the Nyquist Plot or whatever and it squeals: 'Queee!' and then fine tuning is done and "Check, one, two, three" and "thumbs up". It always happened that the Host who does the intro is super-tall like Obama while the Chief Guest is like Hitler. Since the various 'joints' in the mike are not altogether 'universal', several adjustments have to be made and the mouthpiece gets pushed into the face of the CG and after several 'sorry's the CG starts his Speech and goes: 'Queee!'. After enjoying the whole drama several times, I was at last at the wrong end of the thing when I had to 'lecture' to a Class of 350 students in the Vikramshila (or was it Takhashila?) and the techno pushed an 'Apple-Nano' thing into my shirt pocket and clipped a 'butterfly' on my button-hole thing and said 'go'...it never 'went'...I largely depended on my immense lung power.

During the 1970s I was collaborating, sort of, with my Industrial Engineer friends (it got keyboarded as fiends) at KGP. And 'discovered' a Theorem on Reversal Symmetry of Assembly Lines. Don't, please, think of pigs entering the Line at one end and pork chop cans exiting the other; and its absurd vice versa. It is much simpler than that. Suppose we have a Hair-Cutting Saloon as it is called in Hyderabad, having three chairs manned by three operators. An unending stream of customers enter the Line. The first barber 'cuts' the head. And the customer moves into the second chair and the chap there shaves his beard; and he moves into the third where his nails are clipped. And he goes out home merrily. Suppose each of the three barbers manning the Line has his own 'mean' time and distribution function...say Gaussian, Poisson or Erlang. And suppose it turns out that the mean throughput is such that in any random hour ten customers get serviced.

Now, ask the customers to enter through the nether-end...first nail-cutting, then shaving and last, head-cutting. Our theorem stated that the 'throughput' will be the same ten customers per hour. It was quite a remarkable theorem unlike what you would say: "Obvious"...for, we couldn't supply a correct general proof...we goofed. And it took another decade for our Reversal Symmetry Theorem to be proved, by an expert US Production Engineer.

Finally, those who think the 'left-right' reversal of our image in a plane mirror is passe', please stand up on the bench and keep standing the whole hour. It required Feynman again to explain it pithily as an operation of 'squashing' us back to front...read Page 331 of Genius by James Gleick.

How nice it is to be a Teacher! I opened the book after nearly two decades and found this 'dedication' on its first leaf:

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To

......Sir,

............with best wishes

..................................moitreyee



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