(The following account of ABCU is as fictitious as the canals on Mars)

Believe it or not, seven of our Delhi University students (DUS) landed up in Bollywood recently. Promptly they made a bee-line for AB, who was then shooting for his first ever Sci-Fi film `Planet of Red Tapes’.(AB, ofcourse, is THE AB and not Aharanov-Bohm of the celebrated AB-effect.) How did they manage to penetrate the security barrier surrounding cinema’s SHAHENSHAH? Easy. They simply used a STAR TREK device available on the sets and got themselves quantum tunneled through the DEEWAR to materialize before an amazed Amitabh. AB was hovering over the ground in a transparent space-capsule. He looked different, and slightly annoyed.

AB: What’s all this JALWA?

DUS: Sir, we are SAAT HINDUSTANI from Physics and Astrophysics Department. We are DUS.

AB: Bas! How can 7 be 10?

DUS: Heisenberg’s Uncertainty Principle, sir! Counting error is inevitable.

AB: Position-momentum uncertainty is NO Gush versus Bore vote counts! With such poor understanding of concepts, you deserve zeroes in exam. And, no counting error here, mind you!

DUS (impressed): You seem to be a DON in the world of physics, sir.

AB: I study the subject KABHIE KABHIE, CHUPKE CHUPKE. I can talk physics, walk physics and act physics because physics is where ACTION is! You see, the coefficient of LINEA is a juxtaposition of the haemoglobin and the atmospheric pressure in the country.

DUS: What?

AB: Excuse me please, but physics and Bollywood have quite in common. You analyse superconductors, we admire superhits; you study stars, we make them; your galaxies exhibit box orbits, while ours watch the box-office; you use floppy discs, and our discos flop!

DUS: You have an interest in astronomy too!

AB: Receiving astronomical sums of money as remuneration for my performances inevitably led me to this heavenly hobby. You may watch me in TRISHUL, driving past the Nehru planetarium near Teen Murti at Delhi. And I remember, suddenly from nowhere hoards of public descended in the area to have a dekko at me, missing a show in the sky theatre altogether. Star gazing, nonetheless!

What a bonus of a live show my fans got when I started shooting in the air – in broad daylight, they were treated to the spectacular display of a SHOOTING STAR! Hearing the thunderous applause, poor girl Poonam suffered a car accident.

DUS: Sorry to hear about her misfortune.

AB: Fortunate Miss, actually. I rescued her from that unexpected collision. Life is unpredictable. Who could have foreseen the head-on plunge of comet Shoemaker-Levy on to Jupiter?

DUS: And what could be more ridiculous than attempting to predict the fate of individuals? Astrology be damned!

AB: Yes, after all quantum mechanical indeterminism reigns supreme! Now, physics is stuck with chances and probabilities.

DUS: Yet, Einstein claimed that `God does not play with dice’.

AB: HE tosses coin, instead. Have’nt you seen me in SHOLAY doing just that? I am only a GREAT GAMBLER, while GOD is the greatest!

DUS: If unpredictability is so fundamental, why is’nt everything chaotic? Why are order and symmetry so common around us?

AB: Order and laws in the world are due to ADALAT. Now speaking of symmetry, I have often portrayed the AKS symmetry in movies by pretending to be a lefty, although in reality I am right-handed. Later I came to know that this left-right reflection symmetry is broken by weak interactions. And the mirror cracked!

Imagine my consternation. One would have thought that only strong forces could break ones left or right arm.

DUS (showing off their savvy-ness): The strong force does more, sir! It makes as well as breaks. On one hand, it causes lighter atomic nuclei to fuse to give rise to heavier elements and intense heat. This happens, for instance, in the core of stars. The chemical elements that make us have all come from the belly of stars where they were cooked by STRONG chefs. We are all star material, sir!

AB: OK! OK! What about the other hand?

DUS (there was no stopping then): On the other hand, this force may lead to a ZANJEER reaction resulting in a Hiroshima-Nagasaki kind of holocaust! One only has to recall Bertrand Russell appearing in a Bollywood masaala to warn us against the Mr.Hyde side of Dr. Strong and live in AMAN instead.

What really amazes one is that this force which is responsible for star shine is believed to be due to sparks, called gluons, flying between tiny colourful quarks, sir!

AB: I see, its merely a SILSILA of `Rang Barse …’. That certainly explains why even stars exhibit colours. Although, when I tried to figure out various hues on them through a telescope in MILI, mujhe kuchh nahi mili!

DUS: But, sir, the spectral colour of stars is due to their surface temperature. Hotter the star, bluer it is.

AB: I concede that we stars do fall ill occasionally, and run temperature as well. However, when we suffer our blues, we develop cold feet!

DUS: But when a film star is selling like hot cakes at the box office, his chest expands and he stands tall. He is cool! Pretty much the same story with stellar objects.

AB (grasping the idea fast) Listen, when you heat up a star it will expand and because of this it will become cooler, right.

DUS: Right.

AB: While if you remove heat from it, the star will contract and in the process its temperature will shoot up, right.

DUS: Right ho!

AB: All you got to do, now, is to take a hotter star and connect it to a colder one with a thermal conductor. Heat will flow from the first to the second, making the former hotter and the later cooler. In this manner, heat energy will continue flowing in the same direction, from hot to cold, as long as you wish. So, I have invented a Carnot engine which becomes more and more efficient, solving the energy crisis in the universe in one stroke, right!

DUS: Wrong. This paradoxical situation arises because stars being gravitationally bound objects have negative specific heat. Heat them, and they grow colder!

But your idea won’t work.

In the first place, the thermal conductor itself will evaporate away due to intense heat. Then, your engine cannot run indefinitely. After some time, the first star which has been progressively contracting will collapse into a BLACKHOLE! Once it becomes a KAALA PATHAR sorry GADDHAA, nothing can escape from its horizon! No heat, no light, except a Hawking perhaps!

AB (crestfallen): I thought for a moment that I will be a billionaire using this idea. Now, I have no other choice. I have to kidnap Amitabh Bachchan away with me!

DUS (utterly confused): Eh! Come again! Are’nt you AB?

AB: I am. But I am Android Bachchan from a world made of anti-matter, thousands of light-years away! Don’t you notice that I have’nt been touching anything that belongs to your world? Even a nano-second contact with matter will cause a gamma ray explosion. E=mc^2, matter-antimatter annihilation and all that!

DUS: But why do you need the real AB?

AB: Only he can reveal the secret of how to become a millionaire! Oh yes, I have been regularly watching KAUN BANEGA CROREPATI? No more wasting of time. {With a menace in his voice) Bring me Amitabh!

{DUS quickly scurried out. They soon returned with the director of `Planet of Red Tapes’, who appeared completely drained out with fatigue. Hassles with bureaucrats, technicians, censor board etc. showed clearly on him.)

Diro (to the Android): Real ETs in a Sci-Fi movie! This is too much!

You could have advanced your arrival date, saving enormous expenses on fake futuristic sets and real AB. Now, what use? There is no double role in my film.

AB: Get me AB of KBC, quick! Or else, I annihilate the entire movie set!

Diro (tearing his hair with the fear of going bankrupt): But he has been put to deep sleep through administration of morphine! Realistic filming of the spaceship hibernation scene demanded such a course of action. I belong to the neo-realistic school of movie making, you know. Coming back to the point, AB cannot be brought to a state of consciousness for another hour or two!

AB (scratching his chin): That’s alright. A comatose AB will do for the time being. He is bound to wake up sooner or later! (His eyes gleamed with hope) Then, AB will teach me the ABC of KAISE BANUNGA CROREPATI! (Menace in his voice returned) Bring him here!

(Exit DUS. A shattered Diro gazed helplessly. But our SAPTARISHI returned soon, carrying a stiff AB on their shoulder.)

AB (gloating away): Good. I will now enclose my victim within an electromagnetic bubble-shield to screen him from all the anti-matter inside my space-craft. Good bye! (With a mock politeness) You all have been most cooperative. Adieu!

(With a shrill, cricket-like HUM the anti-space capsule took off, heading towards a mysterious anti-world)

Diro (shell-shocked): First, my shooting gets delayed due to govt. red tape. Now, the hero of my film is abducted by an ET imposter! Is it curtains now?

DUS (appearing pleased as punch): Not yet, sir! The real AB is in the studio. Still hibernating. Evil Android has carried away with him only a MAYA SITA!

Diro: A what?

DUS: A wax work of Amitabh Bachchan.

Diro: Where did you get it from?

DUS: Delivered from Madame Tussaud, sir. It just arrived from London as a part of Indo-British exhibition. Then, it straight came to this studio for the approval of the real AB, naturally! (Then, looking upwards in the direction of the space vehicle) Bon Voyage.

(Two hours later, in a distant corner of this vast cosmos, there was a powerful gamma ray burst)

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The Puzzle of Fast Radio Bursts

Patrick Das Gupta

Department of Physics and Astrophysics,

University of Delhi, Delhi-110007



  1. Introduction


Most cosmic bodies emit electromagnetic radiation at various wavelengths spanning from long wavelength radio-waves to very high frequency gamma-rays. Why is that so? Imagine listening to a radio set on a stormy evening with incessant lightning and thunder going on outside while  time to time some corner of the dark sky brightens up due to a lightning flash followed by a loud thunder. In case the radio station you have tuned in is transmitting amplitude modulated (AM) signals then lightning outside, in general, is accompanied by hissing and bursting  noise coming out of the radio set.


This is  due to the fact that lightning is  largely caused by the flow of huge number of energetic electrons from the  turbulent clouds to the earth because of the  high electrical potential difference between the charged clouds and the earth. Since electric current is nothing but flow of charges, these downward moving electrons constitute enormous currents that lead to emission of light. Electric currents lasting for a short duration, each time there is a flash of lightning, generate not only   radio waves (since accelerated charge particles  radiate electromagnetic waves) but also visible light  (since collisions of energetic electrons with atoms in the atmosphere excite the atoms to higher electronic energy levels so that when these atoms get de-excited they emit visible light).


After all, most of us are familiar with  household phenomena of similar nature occurring in our day to day lives.  For example, when we see tiny sparks at night  as soon as    we take off our sweater quickly  or comb our hair in the winter season (since  cold air is  extremely dry with  humidity being  low). One may also recollect  the sparks we see near a electric switch when we turn it off. All these happen because of flow of electrons from  negative potential to the positive one. In other words, it is rather natural that electromagnetic radiation from cosmic sources, majority of  which involve  charge particles in motion, would be of broad-band spectrum with wavelengths ranging from tens of metres (radio-waves) to tiny fractions of angstrom (gamma-rays).


In fact, one of the prime motivation of the Indian space-based astronomy mission ASTROSAT is to study astrophysical objects like gamma-ray burst sources, pulsars, hot accretion discs around black holes and compact objects, binary stars, etc. at multiple wavelengths. Which is why the ASTROSAT satellite has optical, UV and X-ray telescopes on board pointing in the same direction.  One of the ways its instruments were calibrated was by observing the well studied Crab pulsar (which was formed after a supernova explosion that was seen and recorded by Chinese monks  in 1054 AD).


  1. Pulsars: Cosmic Lighthouses


Pulsars are very rapidly spinning compact objects made essentially of neutrons, formed after the compact iron core of a massive star collapses gravitationally in just few milli-seconds time interval. During the core collapse, electrons fall into the iron nuclei and undergo inverse beta decay whereby electrons combine with protons to become neutrons releasing neutrinos. Conservation of angular momentum turns an initially  slow rotating iron core into a fast spinning neutron star as the core collapses from a radius of few thousand kilometres to about 10 kilometres. This is analogous to  what happens when we sit, with our arms stretched out horizontally, in a chair that can spin about the vertical direction, with someone setting  the chair spinning.  When we bring our palms close to the chest, the chair spins faster because of angular momentum conservation and the fact that moment of inertia decreases by our action.


These neutron stars carry tremendously large surface magnetic field strengths ranging from about 100 billion Gauss to few million billion Gauss (as in the case of magnetars, a variety of neutron stars with enormously high magnetic field strengths, discovered in 1999). These city size compact objects are found to have masses ranging from one solar mass to  just over two solar masses. But how do we know about the existence of such stars that are composed mainly of neutrons with just a fraction of protons and electrons?


Rapid  rotation of neutron stars endowed with large magnetic fields lead to incredibly high electric fields around them, since changing magnetic field gives rise to electric field (after all, generators and dynamos use this principle to create electrical energy out of  mechanical energy). Such  high electric fields cause charge particles to get accelerated along magnetic field lines that  radiate electromagnetic waves predominantly in the forward direction within a narrow cone because of Doppler effect. Hence, if the magnetic axis is inclined with respect to the spin axis of a neutron star, radiation emerging effectively out of a cone with its axis along the magnetic axis are seen  as  narrow pulses of radio-waves arriving periodically at the radio-telescope provided the precessing cone sweeps across the  line of sight that is directed from the telescope to the rotating neutron star.


Hence, rotating neutron stars  whose cone of emission intersect the line of sight periodically due to the rotation of the compact star, can be observed as pulsars. In fact, Jocelyn Bell,  a research student of radio-astronomer Anthony Hewish was the first to notice tiny periodic radio-pulses with a period of about 1.33 second from such a cosmic light-house in 1967. By now about 2300 radio-pulsars have been detected.



III. Fast Radio Bursts: A New Class of Cosmic Beasts


Around 2007, an astronomer from West Virginia university, Duncan Lorimer, was looking for  radio-pulses in the old records of Parkes telescope data. To his surprise, he along with his other team members, discovered a bright but single radio-pulse lasting for about 5 milli-seconds in the archival data. Unlike pulses arriving from a standard pulsar at regular instants of time separated by a definite period, it was just a solitary pulse!  This chance discovery has led to a new field in astrophysics – the study of Fast Radio Bursts (FRBs).


In the last 10 years or so,  astronomers have detected so far about 30 extragalactic FRBs with the help of radio-telescopes operating at frequencies ranging from about 800 MHz to about 2 GHz. A typical FRB event is characterized by a single narrow radio-pulse, few milli-seconds wide, with a peak flux density ranging from about 0.5 Jy to about 2 Jy at 1.4 GHz (1 Jy =10^{-26} W/m^2/Hz). We must note that,  in comparison, radio energy received from Sun at 1.4 GHz is more than about 600000 Jy. But this is an unfair comparison since these mysterious radio bursts are occurring way beyond the limits of Milky Way, at distances   larger than  10^{14} times Earth-Sun distance!


How does one know that these FRBs are extragalactic in nature? To understand this, one needs to consider propagation of electromagnetic waves in a cold plasma.  It so happens that the gaseous matter that is spread all over our Milky Way, the so called interstellar medium (ISM),  is mostly  in  ionized form. When radio waves propagate in such ionized ISM, high frequency components travel faster than the lower frequency ones. Radio astronomers define a quantity called the dispersion measure (DM) of a source, which is nothing but the integral of electron density over the path traversed by the waves from the source along the line of sight to the observer. Delay of arrival of low frequency waves compared to the high frequency ones is proportional to the DM.


Hence, larger the DM, more is the  lagging behind of lower frequency radio waves. The distances of Galactic pulsars are routinely estimated from such time delays. It turns out that the FRBs detected in the directions sufficiently away from  the Galactic plane have very high DM. Since these FRBs are sighted in  directions where the Galactic electron densities are extremely low,  observed large DM must be due to  the enormous distance traversed by the radio waves through tenuous and ionized intergalactic medium (IGM) that exists  between galaxies.


Therefore,  by monitoring the arrival times of radio spikes seen at different wavelengths, one can estimate how far the FRBs are.  It turns out that FRBs are located several billions of light years  away from us. From the measured radio flux densities  and estimated distances one infers that FRBs release 10^{38} erg to 10^{41} erg of energy in radio waves.  


Among all FRBs, FRB 121102 stands out. Radio bursts from this source recurs again and again. Not only that, it is found to be co-located in a dwarf galaxy which itself is a weak radio-source. As of  now, only FRB 121102 is seen to repeat, rest of the FRBs being `one-shot’ catastrophic events. So far about 200 such transient bursts  have been detected from  FRB 121102.


Understanding the physical nature of FRBs is creating great deal of excitement among the astrophysicists,  keeping them delightfully busy. Are they radiation from supramassive neutron stars or magnetars that collapse when their spins get slowed down? Could they be due to the interaction of electron winds from hot accretion discs around black holes  with pulsar magnetospheres? Exotic models like white holes, collisions of asteroids and neutron stars, etc. have also been proposed. Only future investigations would reveal the true nature of FRBs.


Several astronomers of Indian origin are involved and active in the detection and study of FRBs like S. R. Kulkarni, Pawan Kumar, Shami Chatterjee, S. P. Tendulkar, T. Vachaspati, V. Ravi,  D. Palaniswamy, J. Yadav, M. Lingam, M. Bagchi, etc. One hopes that  ASTROSAT will soon lead to some crucial breakthrough in resolving the FRB conundrum. After all, using ASTROSAT, an exciting discovery has recently been made – A. R. Rao (TIFR), Dipankar Bhattacharya (IUCAA) and their team, have detected  polarized X-rays emitted from several Gamma Ray Bursts!






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It happened when Neelketu was attempting to capture the columns of Pantheon digitally.  In order to get all the eight Corinthian style  pillars in a single frame, he had stepped back by  about two hundred feet from the main entrance.  Just when he was about to press the camera button,  lower portions of the columns suddenly metamorphosed into a sky blue Alfa Romeo.

A good looking  young man  (a rubicund  David a la  Michelangelo,  thought Neelketu at that time),  wearing a friendly smile, was gesticulating at him out of the car’s rolled down window.

`You  Indian?’, he asked,  pronouncing  the `d’ as `thee’.

Neelketu nodded and stepped forward towards the neutral geared Alfa Romeo.

`I like Indians. Had fun  recently  in Bombay. International Fashion Week, you understand’,  he brought all his fingers of the right hand together and quickly kissed their tips before flinging them out.

`Me Donato, a fashion designer from Milano.’

`I am Neelketu, a historian.’

`Aah, that’s why  you interested in  Pantheon. But you  young to be in history‘, he said with a flourish.

`You see Raphael’s tomb inside?’, asked  Donato, flicking his thumb  out at the Pantheon.

`Sure. Who would  miss paying tribute to the  creator of  `The School of Athens’?’, replied Neelketu,  with a distinct emphasis on the name of the Renaissance era painting.

‘I  like your speech style. Visit Milano, you must. It is  more beautiful than Roma’, said Donato, throwing a north-westerly  flying kiss with  passion.  Appearing  magnanimous, he said, `Look here,  Professor. You  good man. I  gift you two leather jackets, fresh from my company.’

He displayed  two glossy  plastic covers containing black colored jackets inside, after picking them up  from the side seat.

That  made Neelketu feel, inwardly  flattered and interested in the gift.  Ostensibly, however,  he launched a protest  by waving his  hands wildly, `I can’t accept your offer. These look awfully expensive!’

`No, no,  I give you free. I  come here on company work, you see. I advertise my product.  Job   done.  I  return back to Milano. Not want to carry  free samples back,‘ pointing to the packets.

Neelketu continued the appearance of vigorous protest.

`You not like favors, I can tell. But wait. I have idea. You got 50 euros?’

`Y..yes’, murmured Neelketu in an uncertain manner.

`Give me 50 euros only. I  use that money  for  petrol. Milano, long distance. And you accept  my present. Have  girlfriend or  wife? Here, I give  one more jacket. Brown-yellow, see. For her.’

Neelketu was in a quandary.  But  not willing to appear cheap, he took out his wallet and  slowly pulled out few  banknotes.  The car’s  logo depicting a green serpentine dragon swallowing a red man with his arms stretched out   caught his eye when he was handing over  the money  to the ruddy David.

`Grazie.  Have a great time in Roma. Ciao.’

Donato took the money and sped  away.

Wee bit crestfallen, Neelketu took out the jackets from their plastic wrappers one by one, and  realized that he had been had. They were  musty smelling, worn out jackets.  He felt stupid and angry. At that very instant he heard a giggle on his left. Turning towards the source of  mirth, he spotted  a fairly  pretty brunette, perhaps in her late twenties, grinning  at him. Her  hazel colored eyes with long eye lashes made her attractive. She was wearing a  mauve colored t-shirt on a pair of grey faded jeans.

Damn, his face must have given away his discomfiture, Neelketu thought.

The stranger approached him somewhat awkwardly and, raising her palms at the chest level,  said apologetically,`I am sorry. I could’nt help laughing. That was rather gross of me.’

She spoke with a clear cut diction, throwing her voice out softly but with intensity. From the sharp t’s and d’s  in her energetic manner of speaking, he  guessed that she was British.

However, her words  did not assuage his punctured ego.  Neelketu  still felt irritated.  He eyed her with a sullen expression.

The dewy lady continued, `I happened to watch the entire sequence. I was in a dilemma as to what to do. Before I could sound out  warnings, you had slipped over the bills  to the confidence trickster!‘

Struggling to find words, Neelketu spluttered, `Tricked…first time… never  before.’

The brunette  shrugged, `It can happen to anyone. I have gone through such experiences in the past.’

Hearing that, he  almost said `then we are quits’, but stopped short of acting silly the second time.

She stretched her right hand out, `Hi,  I am Agnes.’

Her name reminded him of the angelic character in David Copperfield. Letting out an embarrassed smile, he shook the offered hand and  murmured, `Neelketu.’

`I am an evolutionary  biologist from Cardiff.’  

`I specialize in ancient Indian history. I belong to Puri,’ mentioned Neelketu.

`Oh!  I know  Puri. Its  beach, from where you can view sun rise as well as set, is always so crowded with tourists,  unlike  our Penarth beach.’

`But Penarth foreshore has these rows of mysterious stakes. No one seems to know what they were meant for’,  said Neelketu in a friendly tone, and quickly added, `I have only read about them. Never been there.’

He had begun warming up to her.

`And you have  Lord Jagannath’s temple of antiquity along with  its  associated annual car festival. Not to mention the magnificent Sun temple of Konark closeby’, she argued.  

Neelketu was  pleasantly surprised by her knowledge about his hometown. He looked at her questioningly.

Agnes explained, `Neel, I was in  Puri as a participant of  a science conference several  years back. I was a PhD student then, and was  quite amazed to learn that the enormous  chariots of the car festival   gifted a word to  my mother tongue   – juggernaut.’

And then, with a twinkle in her eyes, she quipped, `I don’t mean the eponymous British  film starring Richard Harris and Omar Sharif!

Neelketu  gave out a short laughter.  Parodying the climax of the film, he said,  `Cut the blue wire!’

`Does’nt Neel in your name mean blue?’, she retorted.

Taken aback, he asked,  `Yes, but how do you know that?’

As they started sauntering in the direction of Trevi Fountain, Agnes elaborated.

`During my trip to Odisha, I had found out that Puri, many years ago,  was also called Neelachal or the blue hill, on which Lord Jagannath’s temple was erected.   I had also wondered whether Neel, the word for blue,  had anything to do with the river Nile,’ and  she immediately made a dismissing gesture saying, `Just a crazy thought.’

Then, she asked,` What does ketu stand for?’

`It  refers to a comet. The body of a  serpentine dragon that  participates in causing solar and lunar eclipses,  according to Hindu mythology, is also called Ketu’, he replied. At that moment, the logo of Donato’s car flashed across  his mind.

`Blue comet. Nice name’, saying that Agnes drew an arc in the air with her right forefinger.

`Now, don’t say `Cut the blue comet!’, he exclaimed laughing, and tried teasing her by saying,

`Agnes sounds very much like Agni, the vedic fire god. I hope you are not a fiery lady!’

But she had turned contemplative. She murmured, as though speaking to herself, `Sun, moon, comets, etc. had so much influence on the primitive human psyche.  Scholars  surmise that our Stonehenge was meant  for   winter and summer solstice rituals.’

Neelketu, eager to display knowledge  of his field,  stated in a pedantic manner,  `Though built over a long period  in Salisbury, England,  when  Pharaohs were busy ruling the Nile and erecting Pyramids,   blue stones found at  Stonehenge were actually transported from Preseli mountains of your Wales, Agnes.’

`Why would anyone go through all that trouble?’, she asked.

`The same reason why people built Sun temples, I guess.  Sun worship had been  prevalent in the past. And religion can drive  humans to shift mountains’, he replied.

Agnes turned serious and said, `And yet, surprise, surprise, I was duped within the  Sun temple complex. It was worse than what happened to you few moments ago.’

He was not prepared to hear this. Neelketu  became concerned. He queried, `At Konark?’

`I was bamboozled while  I was admiring a long necked African mammal. Just imagine,  giraffe in the precinct of Black Pagoda!’

It was becoming curiouser and curiouser.  Although Neelketu  wanted to know more about the conning, he disliked appearing to be a prying type.  So, he did not utter any word and kept walking with her silently. He had noticed that Agnes did not have an easy gait but nevertheless it was enticing.

They were passing by the  Piazza di Pietra that overlooked  Temple of Hadrian. In front of the Corinthian columns,  a small crowd had gathered.  A turbaned man of Indian-origin,   wearing shiny and flowing yellow robes,  was floating in the  air. His only terrestrial contact seemed to be  a stick in his left hand that pointed downwards with its  lower end touching  the ground.

Neelketu wondered whether the tourists who had flocked around the hovering yogi,   posing for pictures,  knew the secret behind the levitation. What appeared to be an ordinary  stick was in reality a  tough steel rod emerging almost vertically out of the ground with its upper end  dovetailed to a  horizontal steel frame (hidden from view because of  the bright overflowing garment all around its edges) on which the smiling yogi was well ensconced.

`Splendid! Although I would have preferred him performing the Great Indian Rope Trick of antiquity’, she said tongue-in-cheek.

`I doubt whether such a hoary illusion was ever performed in the daylight,’ he advocated.

`Peter Lamont, a professor in Edinburgh university, has written a fascinating book on the history of Indian rope trick, linking it with the bamboo pole acrobatics that Indian street jugglers perform during the day,’ she championed.

Neelketu opined, `Here is my take on the trick:  Long long  ago,  a non-Indian  witnessed  a snake charmer inducing a   cobra that was quietly coiled up  in its  basket to rise vertically up. Naturally the stranger was bewildered to see a long rope like creature coming out of a small basket, standing tall and hissing. His anecdote must have  undergone  gradual  embellishments over thousand of years.  Simply a reverse  case of  Adi Shankara’s  rope-snake confusion!’

`Hmm.  Yes, snakes like King cobras can indeed be fifteen to twenty feet long,’ she agreed.

Few moments later, as they strolled along, she stated, `Magic tricks shown by street jugglers in India  with their limited resources are exceedingly clever and creative.’

Then she added,   `It is interesting to observe enterprising small time artisans, tailors, vendors, street conjurors  and so on, eking out their  living by introducing novel elements in their products that eventually bring about  a positive change in the  society. They are no less than your celebrated software engineers making millions in the Silicon Valley.’

`There is a word in north Indian languages for such unorganized, small scale innovations – jugaad,’ he grinned.

`At times such `jugaad’ have impact world over. Have you heard of a craftsman named Ram Chander from Jaipur?’, she asked.

`Who, the Jaipur Foot guy? But to set the record straight, Agnes, he developed the artificial limb by collaborating with established surgeons and doctors.’

`You are missing the point, Neel. It was Ram Chander who felt the need for an innovation when he saw that  imported prosthetic limbs were not only  very expensive but also extremely inconvenient for certain postures prevalent in India. Struck by a bright idea while getting his bicycle tyre repaired, he decided to  employ  soft rubber and light wood available locally to create Jaipur Foot.’

`I thought only Rama Chandra of Valmiki’s epic  is famous. I had no idea  that Ram Chander and his innovation are equally renowned,’ said a smiling Neelketu. He continued, `Interestingly, the oldest literature of Indo-Europeans, namely the Rig Veda, composed by aryan seers, speaks of an artificial limb.’

Agnes looked at him with an animated expression. Neelketu was thoroughly enjoying the moment. He gestured her to wait for a minute. He jogged up to a stall, located at a corner,  and bought two cups of gelato from a kind old Italian lady. After offering her a cup, he resumed his dialogue.

`There are several verses in Rig Veda which refer to a warrior woman named Vishpala whose  leg was severely injured in a battle. Seers extolled   the virtues of  vedic twin gods Ashvins who replaced her damaged leg with an iron limb.’

Then he added tongue-in-cheek, `First surgery in the history of mankind!’

Agnes winced. Her spoonful of gelato  stopped halfway. She wanted to change the subject. Looking down at the pavement, she asked as she walked,

`Who is Adi Shankara, Neel?’

Somewhat surprised, he uttered, `Oh,  Adi Shankara  was a Hindu philosopher  born in the present day Kerala state sometime between 800 and 900 CE.  You may find it  interesting  that he had not only visited Puri when it was a great buddhist centre but had also established a vedic monastery there which is still quite active.’

`But what about the rope-snake stuff?’, she asked.

Neelketu replied, `Shankara had posited that the perceived world is only a Maya or an illusion and, as an illustration, he had written about   mistaking a rope for a snake when it is dark. According to him, Truth or the Ultimate Reality resides in one’s own consciousness.’  

These words acted as a trigger. Agnes stopped walking. She stared at Neelketu with an unusual intensity. He felt uncomfortable. There was a firmness in her voice when she spoke,

`Do you want to know what happened to me at Konark?’

Without waiting for his reply,  she narrated the entire incident.

A fortuitous post-Christmas weekend, falling  in the middle of the  conference, had opened up a  sightseeing possibility for  Agnes.  She had been eager to explore parts of Kalinga, an ancient name of Odisha. She  boarded a tourist bus from near her hotel in Puri, early in the  morning, to visit few historical  monuments scattered in and around Bhubaneswar,  the state capital. There had been   a nip in the air.  When  she got down   at  Khandagiri,  the clear blue sky and the winter sun  made her cheery.

She took out the well wrapped chutney sandwiches and a slice of  Chhena podo (baked cottage cheese – a delicious, exclusively Odisha dessert)  from within her locally purchased backpack and started rapidly walking up towards the Khandagiri-Udaygiri caves.  She began nibbling at the sandwiches when she reached a cave.

`Yumm…’, she mentally bestowed a `thumbs up’ to  the superb chefs of the hotel  where she was put up.

King Kharavela, a zealous Jaina,  along with his queens,  had got these austere  caves dug out on the  Kumari (virgin) hill around 150 BCE for the benefit of  Jaina monks. Living systems are extremely  sacred to the ardent  followers of Jainism. They  abhor  inflicting pain on anything alive. So much so that  they would not even pluck fruits to quench their pangs of hunger,   instead  wait for the juicy bulbs  to fall naturally from the trees. Fasting is a common ritual amongst  the Jains  even today,  leading at times to fatality.

`This is  antithetical  to life’, thought Agnes.

Naturally she was surprised after  perusing   the translated version of Kharavela’s inscriptions  at Hathi gumpha (elephant cave). This  king of Mahameghavahana (the great one who rides on clouds) dynasty was an aggressive  conqueror who  boasted in his  wall writings about his victorious campaigns – how he had attacked  the Greeks in the northwest region, and  how after ransacking regions of southern India, got  donkeys to plough the land in order to humiliate the local rulers. And he claimed himself to be a Jaina!

`Why was his dynasty called Mahameghavahana? Did the cloud  in this  word symbolize  an  elephant? Could it be  that his  dynasty  owed  its origin to  a family  that had  domesticated  elephants for the first time? After all, the rain causing dark clouds were often likened to elephants by  poets,’ she mused.

It was getting late.  Agnes  entered the wide open mouth of  Bagh gumpha (tiger mouth cave), gave a cursory look  and  hurriedly went  down. She did not want to miss her bus that was scheduled to leave  for the Sun Temple shortly.

Agnes was very keen to explore the Black Pagoda at Konark.  She had read somewhere that  king Langula Narasingha deva (Man-lion god) of Puri, who lived in the 13-th century and  was  a devotee of Lord Jagannath,  developed suddenly a deep veneration for the Sun god after he was cured of leprosy through regular sun basking. So, as a tribute, he built a magnificent temple in the form of a gigantic stone chariot standing on twenty four  exquisitely carved wheels and driven by powerful stone horses.

Speculation is rife on his epithet `Langula’ , as it  refers to a tail. A  legend  speaks of Narasingha deva having an unusual tail like growth at the base of his back bone.

Agnes was fascinated by the intricate sculptures portraying  the king receiving precepts  from his guru (teacher), dancers, musicians, erotic acts  as well as Lord Jagannath along with his siblings being  worshipped.

`Were the chariots of Puri car festival inspired by the Sun temple architecture  or was it the other way round?,’ she was curious to know.

The time was about five in the evening when her eyes fell on a  relief  on the plinth  of the  temple.  It  depicted a  small size giraffe facing a mounted elephant. A person of regal bearing,  sitting on the howdah of the tusker, was pointing a bow at the giraffe. She was  intrigued by the sculpture.

`Where on earth did the giraffe come from?’,   she asked herself.

`Did  Narasingha deva earn the epithet `Langula’   for being fond of exotic animals’, she wondered while taking out a camera from .her backpack.

She was shooting the scene when a man’s voice from behind said,

`Madam, many believe that this relief speaks of the flourishing trade that ancient Odiya people had with other countries.’

She turned around and saw  a portly middle aged Indian,  in a cream color safari suit and  neatly combed hair,  addressing her in an  accent common to eastern region.

`Are you an  artist, madam?’,  he asked her politely.

Upon learning that she is a biologist, he pointed  to the sculpted  African mammal and  declared with a serious face, `I strongly believe that  this image  is that of a dinosaur of the sauropoda family, and not of a giraffe.’

He appeared to be a knowledgeable, well mannered and an affluent person.  Agnes let out a brief laughter of dissent, and  shaking her head stated,  `I doubt that.’

He snapped his fingers and asked,`Then, how do you explain the existence of a stegosaurus image on a relief?’

Blurting out a `What!’ incredulously, she almost jumped up.

`I will show you pictures, madam’ he said and started fumbling with his backpack which  was remarkably  similar to the one that Agnes was carrying.

 `But hang on! I can show you the  relief  itself. It  is closeby’, he added and urged her to follow him further south.

He ushered her towards a  dilapidated sandstone structure,  about ten feet high – a remnant of a badly damaged  pillar with  floral designs  carved on it.  Chunks of broken  stones  were lying scattered all around. The  relic was located not very far from the Mayadevi temple that  boasts of  an impressively chiseled  chlorite crocodile clasping  a  fish between its jaws.

`Madam, the stone fragment  bearing a sculpted stegosaurus   is now lying on the top of this pillar. Let us  slowly climb up using these rubble as stairs. We can leave our backpacks here,’ he uttered,   lowering  his backpack on a pile of stones.

Agnes replaced the shooting camera in her backpack, and put it down near the stranger’s backback. She followed him, balancing herself carefully as she walked up.  Sun sets fairly early during the winter in the eastern region of India. The western sky had already developed orange stripes of various hue.

When they reached the top, the man pointed his finger towards a broken piece of relief as he stood there panting. It was turning  chilly and the sky had started  assuming a darker shade of greyish blue. Agnes  took her cellphone out of  her trouser pocket to use it as a flashlight.  She commenced her inspection of  the fragment.  A raised portion of it  seemed to depict an oval body  with petal like shapes  carved  on its rim. Agnes became excited. `Is it really the back of a stegosaurus?’, she asked herself  and resumed her investigation with gusto.

A moment later, pulling out his cellphone,  the safari suited man whispered, `Madam, I have to make a quick call.’

Agnes was totally  absorbed in studying  the relief. So, she  gave an unmindful  nod  and the man excused himself. She was focussed on  obtaining  hard  evidence of a short neck emerging out of the oval body. But there was none. Moreover, all the four  petal like  images with intricate inner decorations were of same shape and size, unlike the bony fins on a stegosaurus.

She was fully convinced that the relief simply depicted a floral design. She stood up and looked for the man to give him a piece of her mind. He was nowhere to be seen. It had already started becoming dark. She could spot  her backpack below but his  seemed missing.  Taking help of her cellphone flashlight, she came down in an unsteady manner.  When she reached  the ground level,   she  realized to her horror  that it was her backpack that was gone.

Her heart started pounding. All her money was in that backpack, both British as well as Indian currencies. Her camera, laptop, pendrive, few souvenirs, a bottle of mineral water   and two paperbacks, all gone. Thank god, her passport was still  in her trouser pocket.

Anxiety started making inroads into her mind. Did he deliberately switch the packs?   Or, did  the man  mistake her backpack with his? She frantically searched his sack in order to obtain his address and contact number. Instead she found bundles of old newspaper cuttings, pieces of stones and a packet of biscuits in  the swindler’s pack.

The descending  shroud of cold darkness added to her misery. She became delirious. Was it possible that her backpack was somehow still on the top of the pillar? Light from her mobile phone was becoming fainter as it badly needed  recharging. Using  whatever glow that was emerging out of her phone, she ran up  the pile of stones, stumbling time to time.

She looked around. There was no sign of her sack. Then her flashlight went into hibernation. It was pitch dark. In the absence of light,  Mayadevi temple appeared frightening to her. Her mind started imagining nightmarish figures akin to Francisco Goya’s Black Paintings. She felt as though some unknown danger  was closing in.

Mustering courage, she decided to get down to the ground level carefully. But her sense of direction was adversely  affected. She  took few steps towards where she thought his backpack was lying. Suddenly she tripped.  Before her reflexes could recover her balance, she fell on the jagged pieces of stone. Her body was badly bruised and there was blood here and there. Her head hurt, and there was an excruciating pain in her right foot. The sharp dip in the temperature made her shiver.

 A strange thing happened then. The severe physical pain and discomfort that  she was enduring, kicked her delirium away. Fear of the unknown had got displaced. She  regained  clarity of her thought processes. She understood that she had to take another bus to reach Puri, as the tourist bus most likely had left.  Somehow she  managed to get out of the Sun Temple precinct to reach a nearby bus stand.

The simple local folks who were waiting there were very kind and helpful to her despite the language barrier.  As she  suspected, the bus by which she  had come had already left. On enquiry, it turned out,  to her misfortune,  that none of the buses that would arrive shortly would take her to the hotel where she was staying. But few of them would go to the Puri bus stand.

After about an hour, a bus, with Puri as its destination, arrived. Agnes had no money but she had a plan. She entered the vehicle and explained her situation to the young bus conductor. He  was very understanding and he empathized with  her condition. She promised that she would  hand over the ticket fare to him as soon as the bus touched Puri. After about an hour and a half, the conveyance reached its destination. She alighted from the bus and immediately hired a cycle rickshaw that was waiting near the bus stop.

She borrowed some money from the poor and good natured old rickshaw puller to pay for her bus ticket. From the bus stand, it took only half an hour to reach her hotel. She requested the hotel reception to lend her some money  to repay the kind rickshaw puller. Seeing her poor health condition, which was getting aggravated with time,  the hotel staff  immediately got her admitted in a nursing home closeby.

Agnes had to be shifted next day to a good hospital in Bhubaneswar for proper treatment. Fortunately the conference organizers along with her compatriots lent her sufficient money to cover the medical expenses. However, to add to her woe, several of her injuries had turned septic. She spent nearly three months in the hospital before she could get her strength back and walk.

Neelketu noticed that her beautiful eyes had welled up. He touched her arm gently. He felt an urge to comfort her. Agnes put her head on his shoulder and sobbed silently. After a while, they started walking hand in hand. There was a huge crowd in front of the Trevy Fountain. The exquisitely sculptured marble structure poured out  crystal clear  water causing a blue-green pool to form in front.  There was  gaiety all around.  Young girls and boys had gone down the steps wishing to  feel the life giving water.

Neelketu too went down few steps and beckoned Agnes to follow suit. She involuntarily moved a bit forward but then stopped immediately. She shook her head. His  gaze instinctively  got directed  at  her feet.

`Oh God! You don’t mean to say… ’, he had to abruptly break his  sentence. There was a lump in his throat.

There was no sadness in her eyes then. She smiled and murmured, `Yes, Neel. Jaipur Foot.’

He walked up to her  and put his right arm around her shoulders. He observed that some of the tourists were throwing coins into the water and making wishes. Neelketu pulled out his wallet and took out a coin. He stared at Agnes with great affection. She appeared serene and  lovely, with a radiant forehead.

A courageous  and beautiful warrior, he mused.  Closing his eyes, he  tossed  the coin into the blue water below.


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Soaring high on the wings of Physics


Patrick Das Gupta
Department of physics & Astrophysics
University of Delhi, Delhi – 110 007

I. Introduction

Ancient Greeks had fantasized about Daedalus and Icarus making artificial wings and attaching them to their arms using wax to soar into the sky. Similarly, at various points of time over a period of about two thousand years, ancient Indian poets had invoked the Rig vedic twin gods Nasatyas (i.e. Ashwins) riding their flying chariots, imagined Ravana acquiring Kubera’s aerial vehicle pushpaka vimana and depicted Hanuman’s ability to cruise across the sky to reach the mythical Mount Gandhamardan, and so on.

Although taking to the air using hot air balloons was achieved early on (around 1782 by Montgolfier brothers), Wright brothers could successfully fly their `winged’ contraption only in 1903. After that, there was no looking back as far as air flights is concerned.
However, one cannot keep humans contented for long. For, space was the next destination where even the birds had not set their feet (or, fluttered their wings). Of course, dreams of conquering the space had always existed whether it is Lord Shiva’s scion Kartikeya taking off on his peacock to chart out the universe as narrated in the mythologies or H. G. Wells’ science fiction with intrepid adventurers of ‘The First Men in the Moon’ landing on our natural satellite.

Science fiction authors like Wells, Arthur C. Clarke, Asimov and others had captured the imagination of the readers with their fascinating tales of space voyages. Such fantasies metamorphosed into reality when, in 1961, the Soviet cosmonaut Yuri Gagarin became the first man to explore the outer space while manning the spacecraft Vostok 1, and whose feats were soon emulated two years later by his compatriot, cosmonaut Valentina Tereshkova, the first woman and the first civilian to journey into the outer space. Mankind’s next gigantic leap took place due to the Apollo 11 mission of 1969 when the Americans Neil Armstrong and Buzz Aldrin set their `small steps’ on the Moon, collecting lunar samples, during which time their co-astronaut Michael Collins controlled the mother spaceship while orbiting the Moon.

The juggernaut of space mission since then has become unstoppable. Thanks to the leadership of renowned scientist late Vikram Sarabhai, who established space and rocketry research in India after about a decade of our independence, the stupendous achievements of ISRO remain unparalleled. Our lunar mission was successful in its very first attempt with Chandrayaan-I providing the concrete proof of the existence of vast quantity of water on Moon. The pinnacle of glory came with the launch of Mangalyaan in 2013, with India becoming the first country in the whole universe to succeed in putting the Mars orbiter around the red planet on September 24, 2014, in her first attempt. The prestigious science journal Nature selected Dr. K. Radhakrishnan, former chairman of ISRO, as one of the top ten scientists of 2014 because of Mangalyaan’s success, making the achievements of Indian space research truly monumental.

II Skyward Ho with a fillip from Physics

Aircrafts are large and heavy objects. How do they manage to overcome the gravitational pull of Earth and fly in the atmosphere without falling? Aviation hinges on the physics of fluid dynamics. A crucial role is played by Bernoulli’s theorem which states that in a laminar flow a particular combination of pressure, density and velocity of the fluid remains a constant along a streamline, so that if the local flow speed shoots up, the corresponding pressure drops. Hence, if one designs aircraft wings such that when they move, air velocity above the wings is greater than that below, then pressure below exceeds the pressure above as predicted by Bernoulli’s theorem. The resulting pressure difference leads to an upthrust that makes the wings rise in the air. Air viscosity also plays a central role in the flight mechanism. This, in a nutshell, is the basic principle behind aviation.

On the other hand, physical principles utilized in space missions are different. In outer space, far from the Earth, density of matter is extremely low while gravity is almost nonexistent. So, once in space, one need not worry about slowing down of the spacecraft due to viscous damping or deceleration due to gravity. But how does one accelerate, decelerate or change the trajectory of the spacecraft in deep space? Here, the third law of Newtonian mechanics comes to the rescue. When the rockets at the tail end fire (action) the body of the spacecraft catapults in the opposite direction (reaction). In other words, conservation of linear momentum ensures that if the jet of ignited rocket fuel carries a large momentum in one direction, the spacecraft speeds up in the opposite direction.

In the future, if due to great technological breakthroughs one is able to travel in space with speeds close to 0.9 c, one may witness counter intuitive physical effects like time dilation, length contraction, etc. as predicted by Einstein’s special theory of relativity (see my article `An Enigma called Time’, Phyzion 2014, vol.XXIV, pp.3-4). . Furthermore, if a person, say, B’s twin A left Earth, cruising with an average speed of 0.9 c, and returned back after 20 years (as measured by A) of space voyage, he will be shocked to find that about 46 years have gone by on Earth (as measured by B) since he undertook the journey, making B much older than A. This leads to the celebrated Twin Paradox, illustrated in the next section in the form of a school kid’s micro-play.

III Space travel and Twin Paradox: A micro-play

The twin sisters Seeta and Geeta had just turned 15 on the New Year Day of y2k. The more adventurous of the two, Geeta, decided to try out something different to celebrate their joint birthday on the dawn of a new millenium. On that day, Geeta began a trip to the star Lilavati (about 2.1 light-years away; a fictitious star) on her spaceship with a speed close to that of light, leaving Seeta behind on Earth. Her idea was to orbit around the star, and then return to meet Seeta in 2005 (Earth time), so that they could celebrate the International Year of Physics together.

For Geeta, everything went along pretty smoothly. After few revolutions around Lilavati, she turned the nose of her rocket towards the direction of the solar system. Very soon she spotted our beautiful blue planet and readied her spaceship for a comfortable landing. Back home, Seeta was eager to meet her twin sister after five long years. She saw Geeta’s space vehicle touching the land and gradually slowing down on the runway.

Few minutes later, the door of the spacecraft opened, and out came Geeta, looking for her sister. At first she could not locate Seeta. All she could see was a young lady of twenty staring at her with a bewildered expression. After gaping at the young woman for few seconds, Geeta realized to her horror that she was looking at her twin sister.

While Seeta had turned twenty in the year 2005 (as expected), Geeta was still a girl of slightly over 15 years! Quite baffled by all this, they ran to a physicist for an explanation. The physicist of course understood the cause of this bizarre incident. So, what was his verdict? He blamed it on EINSTEIN and RELATIVITY!

Physicist (P): The chief culprit is the phenomena of TIME DILATION that was proposed for the first time by the great ALBERT EINSTEIN.

Geeta (G): Eh! Time-dilation?

P: When a person A holding a clock moves with a uniform speed v relative to another person B who is at rest, wearing a wristwatch, then B sees that A’s clock is ticking at a slower rate than his own watch by a factor of under-root 1 – (v/c)^2. This is the time dilation factor (its reciprocal is called the Lorentz factor), which is very small if the speed v is large. Because of her high speed, time for Geeta ticked at a much, much slower rate than that for Seeta, as observed by the latter. As v approaches c, time in the moving frame as seen by an observer at rest, tends to stop flowing!

Seeta (S): And what is this c in the time dilation factor?

P: Well, c is the speed of light in vacuum. It is a constant, no matter in which frame you measure, and nothing can move faster than c. Suppose, a Diwali cracker at rest with respect to B suddenly explodes. Then, let’s say both A and B measure the speed of light rays shooting out of the cracker while A is travelling with a speed equal to 0.9999 c relative to B. Both A and B will find the respective speeds to be c. Amazing, is’nt it?

G: I thought that time dilation applies only to moving clocks and watches. The biological systems A and B ought to age at the same rate.

P: Not at all. Even living organisms are physical systems. They do not violate any laws of physics. If A were to age at a different rate than his clock, he can conclude by just looking at his clock that he is moving with respect to some absolute frame of rest. But we know from experience that if we are in a train that is moving with a constant speed without any jolts or shakes, we cannot ascertain without looking out of the windows that we are moving relative to the ground. All uniform motions are relative. There is NO absolute rest frame. Don’t you
remember the null result of Michelson-Morley experiment?

G: Aha! If every motion is relative, it was Seeta who was travelling with a speed close to that of light relative to me in the opposite direction. I was at rest. So the time dilation factor should have been applied to Seeta’s age. I should have aged, not she!

P: Well, you have justed stated the TWIN PARADOX. The whole thing appears paradoxical because both of you “appear” to be in identical situation. After all, if motion is relative was it Geeta who was moving or Seeta? Who was to age more?

S: So, what is the resolution of this paradox?

P: Remember, only uniform motion is relative. Geeta had to fire the rockets of her spaceship while leaving the earth as well as while returning from Lilavati. She had to undergo accelerated motion. Hence, the “apparently identical” situation was deceptive. There was no symmetry between the motions of Seeta and Geeta. Only Seeta was in a uniform state of motion (i.e. v=0 all through) without experiencing any acceleration, so she became older at a faster rate than Geeta.

As you know, if your spacecraft is accelerating in the forward direction, you feel a pseudo-force, exactly like a gravitational force, pressing you in the backward direction. Hence, you can determine that your spaceship is accelerating without looking outside. In some sense, acceleration is absolute.

S: But this time dilation factor should not be applied to Geeta, as she was not in a uniform motion. What would be v in the factor, when v is changing with time?

P: Well, in such situations, one can use this factor on infinitesimally small intervals of time over which v is almost a constant, and then integrate the factor over a large interval of time. So, non-uniform velocity can easily be incorporated in the analysis. At the end of the analysis, you will find a time dilation effect for accelerated motion.

G: Suppose two identical clocks A and B start out from a common point. Clock A moves along a complicated trajectory, sometimes accelerating and sometimes not. Meanwhile, clock B moves with a uniform speed. After some time, A changes its course so as to meet B. Then, if I understand you right, clock A should show less time than clock B.

P: You are absolutely correct. You can prove what you just said using the principle of least action. Please go and look up Feynman’s Lectures, Volume I, for a simple yet correct argument. The argument hinges on the fact that the relativistic action for a free particle is proportional to negative of the total time elapsed in the comoving frame of the particle (i.e. the proper time).

So, the actual trajectory of the free particle minimizes the action and hence maximizes the proper time. Therefore, the time elapsed for B will always be larger than that for A which is not moving in a trajectory required by the principle of least action. As they say, physics is where action is!

To sum it up, acceleration and, equivalently, gravity slow down the march of time.

S: All that is fine. How do I become as young as Geeta?

P: Elementary, my dear Seeta! Just undertake an identical return journey to Lilavati, and you are as old as Geeta.

The next thing for everyone to see was Seeta sprinting (alas, with sub-relativistic speed) towards Geeta’s spaceship.

IV Epilogue

Mangalyaan’s immaculate injection into a Martian orbit in ISRO’s maiden attempt has ignited the imagination of an uncountable number of young students, the impact of which will have a positive effect on India in the long run. Future manned missions to Moon are already in the pipeline. Now for some fantasy. It is known that after about billion years, Sun will turn into a red giant increasing its size manifold. The outer regions of this red giant will possibly engulf Earth. Will human beings circumvent the disaster by relocating themselves to another habitable planet? After all, Kepler mission has been detecting so many almost Earth like exoplanets.

First of all, it is next to impossible to imagine the state of human beings after billion years of natural and civilizational evolution. Secondly, if consciousness (memory along with other activities of the brain) is what defines an individual, it is not difficult to imagine that the future technology will probably enable people to download their consciousness in memory stick like devices, and thereby achieving virtual immortality. Then, possibly the human species will escape the red giant furnace in the form of a huge swarm of tiny flying robots each carrying the consciousness of an individual.

Quest for experimentation, innovation, travel and exploration are encoded in our genes, without which human species could not have survived for millions of years. So, space research will continue to flourish, striving to make Prometheus unbound.

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On `Time’

                                                           PATRICK DAS GUPTA,

Department of Physics & Astrophysics

University of Delhi, Delhi – 110007


Time is indeed a riddle wrapped inside a mystery. To paraphrase a savant: “Past is a collection of events that remains only in the memory and records; Future is yet to unfold and moreover, is uncertain; only Present is real and tangible.” But this Present is like a thin line shifting forever into the Future.

Causality plays a central role in our daily life. You switch on the ceiling fan, and only after that its blades start turning. It is never the other way round. Cause always precedes effect. Now, causality is intimately tied up with order of events and the march of time. It is apparent that it prohibits time travel. For, if it were possible to go back to the past, a psychotic person could (using an n-bomb like contraption) exterminate the entire humanity. A paradox ensues: Who built the time machine, in the first place, to enable a trip to the past that subsequently obliterated the cause that to begin with had led to the existence of the inventor of the time machine?

On the contrary, one can always go back and forth in space. Time and space are indeed observed to be different in this respect, although they are treated theoretically on equal footing in relativity and quantum field theory. The second law of thermodynamics states that the disorder of a system left to itself continues to increase with time. The disorder is characterized by entropy. The total entropy always increases with time, since the number of `high entropy’ states are by definition larger, so that the probability of landing on a `high entropy’ state is higher in contrast with the `low entropy’ states. Murphy’s law in management is a special case of the second law of thermodynamics.

The refrigerator tries to maintain the low entropy states of fruits and vegetables inside, while it is constantly increasing the disorder outside by despatching heat outwards. To convince oneself, one just has to feel the heat emanating from the backside of a fridge. Living systems do similar things. They grow into orderly states by consuming food and generate more entropy in the environment through respiration and perspiration, among other things. Increase of entropy provides an arrow of time. As time marches ahead, disorder of the universe  keeps increasing.

Thinking and learning lowers the entropy of our brain at the cost of creating more disorder outside (The brain has to maintain itself at the appropriate temperature, and hence the heat generated by its activity has to be transported to the environment.). Our consciousness provides another arrow of time. We know our past but are unsure about the future.

In the macroscopic domain our perception of flow of time is linked with the universe not being in a maximal entropic state. For example, if the entire universe was in thermodynamic equilibrium then for every forward process there would be a reverse process, so as to maintain the equilibrium. In that case, at a coarse grain level, there is no `happening of events’. Does it mean time has stopped in such a situation?

This is a metaphysical point, as there can be no human being or intelligence if there is a perfect thermal equilibrium. The very notion of thinking involves progress of time. It is futile to discuss Time’s halt.

From quantum mechanics, we know that any physical state is described by a wave function. Wave functions undergo unitary evolution in time, generated by the relevant Hamiltonian. Now, a quantum system interacts with the environment by means of a Hamiltonian too. As time progresses more and more quantum states of the environment get entangled with the system’s basis states. Does it mean that an arrow of time is provided by the number of systems in the environment that get entangled?

All fundamental theories are formulated in terms of differential equations consisting of a derivative (or a second derivative) with respect to time, whether it is Grand Unified theories or String Theory. Time evolution of physical states follows from such equations. If all physical states were stationary states (i.e. eigenstates of the Hamiltonian) there will be no time evolution (since in that case only the phase of the state will change linearly with time). But quantum mechanics allows superposition of different physical states. Superposed states exhibit non-trivial time evolution although each of the energy eigenstates that make up the superposition have only their phase changing with time.

We may now let our imagination run loose: Is time an external agent that uses the Hamiltonian to make a local quantum system get entangled with quantum systems of the rest of the universe? Or, is the space-time continuum an active medium that makes the quantum field operators undergo an orchestrated dance analogous to how a background music guides dancers to make correlated moves even when they are not aware of each other? Causality and time travel seem to be mutually incompatible, but can indeterminism associated with quantum theory circumvent such an impasse. Only future research will unravel the knotty issues of time.

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ASTRONOMY : Its impact on human psyche

                                                  Patrick Das Gupta

                                   Department of Physics & Astrophysics                                                                         University of Delhi, Delhi – 110 007  

I. Comets galore

The year 2013 appears to be annus comets.  Many of us are eagerly waiting to be visually  treated by three comets  – Pan-STARRS in March, Lemmon in April and ISON in November. These trio of tailed celestial strangers were discovered only  recently. Comets, in general,  are fascinating not only because they are rare visitors but also because they often develop spectacular tails as they approach Sun – rare, due to their highly eccentric orbits, and tails, because of the solar wind that pushes away cometary matter, heated and vapourized by solar  radiation, radially outwards from the sun.

A comet’s orbit is largely determined by Sun’s gravity as well as the angular momentum  and the orbital energy of the comet. But since it is a loosely bound object made of rocky material, frozen methane and ammonia,  water ice and dry ice, etc., the pressure exerted by the solar wind and mass loss experienced by it when it is near the sun, have non-negligible effects on the cometary orbit. Of course, encounters  with other members of the solar system can have drastic consequences – the comet Shoemaker-Levy 9 suffered a fatal crash in July, 1994, when Jupiter’s gravitational tidal field ripped it apart into several fragments, which were eventually swallowed by the giant planet.

It is even conjectured that  the Tunguska catastrophe  of 1908 in Siberia, which mysteriously flattened about 80 million trees, was caused by a cometary fragment that exploded before hitting the  ground. Very  recently, in the month of February 2013,  a meteor streaked across the atmosphere above the Chelyabinsk region of Russia, and the resulting  shock waves  shattered window glasses, injuring many and causing much fear among the residents. This happened just hours before the asteroid 2012 DA14 cruised along, missing us by only 17230 miles, leading many to speculate whether the mid-February  meteor was a detached fragment from the asteroid. It is well known that  the extinction of cold blooded dinosaurs was brought about by either an  asteroid or  a comet colliding with the earth, leading to the formation of a dust blanket all around and  cutting out sunlight.On the other hand, it has also been posited that the origin of life on Earth is linked to crashing comets and asteroids that  time to time deposit  water and organic matter on  our planet, compounds so essential for living systems.

When a fast moving asteroid hits a nearby planet, a fragment of the latter can fly off due to the powerful impact, freeing itself altogether from the  gravitational pull if its velocity exceeds the planet’s escape velocity. Such a scenario did occur  –  in 1980s, a meteorite named ALH84001 was discovered in  Antarctica that originally hailed from  Mars.   ALH84001 was ejected out of the red planet by a crashing asteroid. In 1990s, NASA researchers, analysing  iron crystals in the carbonates from  ALH84001, claimed that such crystals could be synthesized only by certain kinds of bacteria, sparking off a debate on the possibility of  life on Mars.

II. Astronomical events and Imagination

Undoubtedly, astronomical events like the  appearance of a comet,  transit of Venus (observed recently on June 5, 2012), total solar and lunar eclipses, meteor showers, etc. cause tremendous excitement  these days,  just falling short of  mass hysteria. Of course, they had fuelled much of science-fiction writings from the days of Jules Verne, H.G. Wells, Arthur C. Clarke, Ray Bradbury and so on. Who can ever forget the eerie denouement of `Nightfall’ , a story  written by  Isaac Asimov, in which intelligent creatures living in a planet orbiting a double star,  who had never witnessed  a night sky, go berserk when there is a rare nightfall,  and they see for the  first time  myriad of twinkling stars?

What about our ancestors? Were people of ancient India affected by  heavenly incidents? Eclipses  have captivated human mind since time immemorial, as evidenced from the references to them in ancient texts and epics. Rig Veda, for instance,  described Svarbhanu,  a demon,  inflicting darkness on the sun. The demon  was   eventually  decimated by Indra and subsequently, Atri, belonging to  the vedic priestly class, retrieved Sun through chantings. This is likely to be. a   reference to  a solar eclipse of the bygone era.  Over the years, the Svarbhanu character got transformed in the puranic literature to the demon Rahu.

Now, total eclipses occur because  angular sizes of Moon and Sun are almost equal at present.  Can we attribute triggering of scientific imagination in human beings, who appeared less than  about a million years ago, to their observing the intriguing phenomena of eclipses brought about by the chance coincidence of equal angular diameters of Sun and Moon?  For,  in the past, intelligent human beings exercised their minds to understand and predict  eclipses, be it Hipparchus, Aryabhatta or Varahamihira. In other words, one wonders whether  in the absence of eclipses, there would  have been enough incentives to develop trignometry and other sophisticated calculational techniques.

We should note that  Moon is spiralling away from Earth since the former  is losing its spin angular momentum to its orbital angular momentum due to the tidal torque exerted on it by Earth (because of which now the spin period  of Moon is very close to  its orbital period, so that we see the same face of Moon every day). So, billions of years ago, the apparent size of Moon was much bigger than its present `half a degree’ angular diameter. It is amusing to imagine a poet penning down his feelings after getting emotionally affected by  a ten degree wide Moon!

III. Astronomy and Mythologies

When an orbiting Venus comes between Earth and Sun, we witness the phenomena of  Venus  transit during which  one sees a dark spot slowly sailing across the solar disc. In June, last year, Nehru planetarium in Delhi was teeming with a sea of humanity who had gone there to watch the Venus traverse across the face of the sun. The previous Venus transit had occurred on June 8, 2004, and the world will have to wait till 2117 to see the next one, when none of us will be around.

Now, some speculations –  I wonder whether the story (from Valmiki Ramayana) of a hungry, newly  born Hanuman,  leaping towards the rising red Sun, mistaking it to be a ripe fruit, was inspired by a Venus transit event of the past. The imagery of a toddler Hanuman gliding towards a rubicund sun does conjure up a picture of a transit episode. Similarly, another figment of imagination of mine is,  whether the story of Kartika competing with Ganesha and taking off on his peacock vehicle for a long round trip of the universe, while Ganesha just perumbulates around Shiva (Rudra, or Sun) and eventually winning the race, was an allusion to Mercury or Venus orbiting around the sun in shorter time period than a comet (that has a peacock like tail).

Astronomy images certainly fire our imagination. I still remember the sense of awe and mystery that stirred inside me when as a school kid I saw a photograph of the Horse head nebula. The vast night sky bejewelled with bright stars make us think of infinity and the unknown. My first lesson on cosmology was Olbers’ paradox, or why the night sky is dark? That, the entire night sky is not as bright as the surface of the sun  because of  the finite age of our universe, was a revelation to me. And, all it takes to understand Olber’s paradox is simple Euclidean geometry and the notion of luminosity and flux.

 IV. Summary

Comets and meteors have fired human imagination since the dawn of civilization. Giotto’s depiction of Halley’s comet as the star of Bethlehem in the 14th-century painting `Adoration of the Magi’ indicates the level of fascination among Renaissance painters with celestial events. Jahangir of 17th-century, a Mughal emperor ruling from Delhi, was so excited by the report of a fiery meteor event in Punjab, followed by the discovery of a hot, metallic meteorite, that he ordered his craftsmen to forge two swords, a dagger (extant in Smithsonian Institution) and a knife from the mix of  a meteorite part and iron. The amount of  nickel content discovered in a dagger from the tomb of Tutankhamen,  has led to the suggestion that it was forged from a  iron meteorite – a `thunderbolt of heaven’.

The year 2013 is significant not only because of the naked-eye sightings of  three recently discovered comets – Pan-STARRS, Lemmon and ISON, along  with the ensuing  enthusiasm of  astronomers and public, alike, but also due to the mid-February glass shattering meteor strike in the Chelyabinsk region of Russia,  just few hours before the closest encounter with  2012 DA 14, an asteroid. Comets and asteroids have been invoked to explain extinction of  dinosaurs, origin of life on earth, ejection  from Mars of ALH84001 (a meteorite discovered in Antarctica, with  NASA’s controversial claim that it bears signatures of life on Mars) and so on.

Curiously though, comets and meteors occupy an enigmatic status in Indian epics and ancient astronomy scripts.   Writings from  the times of Parasara (before 700 BC?) down to Varahamihira (6th-century) on ketu (the Sanskrit word for a comet), and its classification, pose intriguing interpretations. Ketu is  still venerated as one of the Navagrahas (or, nine planets)  deities, in almost all hindu temples. Ulkas, or  meteors,  have been referred to in Mahabharata, Ramayana and numerous puranas. Several temples from antiquity still stand all around the Lonar Lake, an impact crater in Maharashtra  (western India).

It is being said that ISON is likely to be comparable to Venus as far as brightness goes, when it grazes past the sun. Will there be a re-enactment of the Shoemaker-Levy 9 episode? Will it break into several pieces due to Sun’s tidal pull? Will it outshine the Venus? Amateur astronomers are asking such questions. Therefore, November is worth the wait. One can only imagine the thrill if, in the near future, one were to observe exo-comets given that exoplanets are routinely being detected in the vicinity of distant stars by NASA’s Kepler mission.

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On `Mathematics’

Patrick Das Gupta

   Department of Physics & Astrophysics

      University of Delhi, Delhi – 110007


With Manjul Bhargava winning the prestigious Fields Medal, Subhash Khot bagging the Rolf Nevanlinna Prize and Ashoke Sen receiving the Dirac Medal,  mathematics has become temporarily a source of  non-trivial excitement among the young, in the land  of Srinivasa Ramanujan. Ashoke Sen, an internationally renowned string theorist, is not technically a mathematician. But that is a matter of little consequence as string theory, though a branch of physics, is almost inseparable from subsets of  advanced pure mathematics. To gauge its importance to  mathematics, one may recollect that   Edward Witten, another stalwart of string theory and theoretical physics, was awarded Fields Medal   in 1990 for his seminal  papers  on    supersymmetry, Morse and Hodge-de Rham theories   that led to progress in number theory and complex analysis.

Why is it that a fraction of gifted people, however  miniscule,  keep scaling  newer  heights  of an  esoteric and difficult  subject called  mathematics? A  George Mallory type  answer `because it is there’ notwithstanding, one of  the reasons could be  the inherent affinity in many for  tackling riddles, whodunnits and paradoxes. Some may recall   cracking their heads once upon a time on conundrums associated with  unexpected-hanging puzzle or Klein bottles from Late Martin Gardner’s feature `Mathematical Games’ (which, later,  made a metamorphosis  to `Metamagical Themas’, an anagram of the original title, in the deft hands of Douglas Hofstadter, after he took charge of the column) that appeared  in every issue of the Scientific American magazine from mid-50s to 80s.  This column initiated several young students  to paradoxes like  Bertrand Russell’s alluring  poser   involving a set of barbers who shave only  those men who do not shave themselves. Should a barber, belonging to  this set, shave himself? Be prepared to tie yourself into knots fathoming  this one!  Russell’s paradox had  serious implications in  axiomatic set theory.

Returning to the main topic, evidently arithmetic and geometry  grew  out of necessity.  Early humans  not only had to keep  track of  their possessions through  counting  but  also needed to estimate directions, distances, shapes and sizes, without which hunting, exploration, building cities like that of Harappa and  Mohenjo daro, raising humongous  Egyptian pyramids, etc, would not have been possible.  Homo sapiens who could assess numbers and sizes, and discern shapes and directions, had  an evolutionary advantage  for survival during the Darwinian struggle for existence.

But as is the wont of human brain, brighter of the lot,  dealing with this  incipient subject of numbers and shapes,  perceived interesting patterns in some of these entities and   their  interrelations, that entailed  concepts  such as the  zero (an Indian gift),  prime numbers,  the Pythagorean relation between sides and the hypotenuse of  right triangles, and so on. Playing and tinkering  are  natural human instincts  and so, not surprisingly,  curious and   innovative minds  toyed around with  patterns found among the   arithmetical  and geometrical  entities to create  rich logical  systems that could establish non-trivial results (i.e. theorems) such as  the number of prime numbers being infinite or the Pythagoras theorem, by deploying  imaginative and clever tricks  on a set of very few, almost self-evident  assumptions (i.e. axioms).

The Midas touch of  mathematical minds   added  fillips  to  axiomatic systems, like for example Euclid’s geometry,  to grow wings as though of their own and fly out to magical and intangible worlds. Numbers and geometrical concepts  got  transmuted and generalized to abstract but beautiful creatures, seemingly far removed from concrete reality. To cite a case, the measure of  distance between any two points  that relied on Pythagoras theorem  in the standard  Euclidean geometry  got generalized to abstract ones involving metric tensors suitable for curved and warped spaces described by non-Euclidean geometry. The genie of mathematics was out of the bottle (Klein’s?) !

Were  human beings genetically  programmed to be abstract mathematicians or theoretical physicists?  Instead,  suppose we ask:  were we genetically wired to have been swayed emotionally by sophisticated music? Putting  forward a thesis  that music has its roots in the sequence of notes present in bird songs, and that those early humans who were sensitive to and were drawn to simple melody of a koel’s cooing or of other singing birds,  had greater chances of survival, finding mates  as well as  passing on their genes to offspring (since  birds gathered in regions where water and food are  abundant), can  explain why music affects us emotionally and why  its  primitives  are  similar to bird songs.

With time,  simple tunes grew in richness because of the fascinating flexibility of  brain which grows  more  neuronal connections,  with extra stimuli provided by the inputs and outputs from other musically minded people,  leading to further creative activities. The ever increasing complex networks  both of inter-neuronal highways in a brain as well as of musicians resulted in increasingly sophisticated body of work in music.  Contemporary music  is obviously far more complex and richer  in comparison to the brief melody of  a bird song. It will not be far fetched to expound a similar theory  in the case of mathematics for  its ever growing complexity. So, what started with an evolutionary advantage, became richer, more abstract  and multi-layered over time.

Modern mathematics  is not  a  recondite recreation akin to the game of chess (yet another Indian innovation). It is a fact that  all fundamental laws of Nature are  expressed in mathematical terms. As pointed out emphatically by the eminent physicist  Eugene Wigner in a lecture in 1959 about `The unreasonable effectiveness of mathematics in the Natural sciences’ , that  abstract concepts and relations created in contemporary  mathematics for  its own sake, turn out at times to describe fundamental truth concerning aspects of the real universe. Although, it should be remarked that only a miniscule portion of the vast body of mathematical creations  get to enjoy this status. Therefore, one can go ahead and claim that it ought not to perplex us that a small subset of mathematical  ideas based on beauty and abstract generalization of concepts rooted to reality, get realized  in fundamental physics.

It so happens that physical entities  are measured quantitatively (i.e. in terms of numbers),  and hence  their interrelations,  including temporal cause and effect links,  better be based on a language that is numeric, precise,  logical and  unambiguous.   Clearly, mathematics is  best suited for this. One  wonders  about the effect of Godel’s theorem (which, simply stated, implies that  in a consistent logical system  there will exist  well formed expressions that  can neither be proved nor disproved) on physical theories. So,  does ambiguity in the physical world enter through a Godelian back door? Or, is it that whenever an undecidable statement springs up in a physical theory, one simply subjects it to an experimental test in order to obtain its truth value?   For, Natural science has the luxury of experimentation!

The real world has always continued to inspire  mathematicians, whether one considers  the birth of  calculus for finding trajectories of bodies moving  in gravitational field or of distribution theory that ensued from  Dirac delta function. It is common wisdom that  systematic analysis of gambling outcomes  by Fermat, Pascal and Huygens had ushered in the mathematical theory of probability.  In a lighter vein, the Mahabharata hero  Yudhisthira could have  outwitted Shakuni  in the game of dice had he brushed up on the theory of chances.

One wonders whether the chance coincidence of angular size of  sun and  moon being the same at  present,  causing  eclipses to occur, played a significant role in the development of mathematics.  After all,  mathematicians of repute  exercised their minds to understand and predict  eclipses, be it Hipparchus, Aryabhatta or Varahamihira. In other words,   it is scientifically relevant  to ask  whether  in the absence of moon occulting the sun, there would  have been enough impetus and motivation to develop trigonometry and other useful  computational techniques.  We will probably never find out.

Descartes had amalgamated algebra and geometry to create coordinate geometry. On a lighter note, combining the utterances of Descartes and Archimedes,  one may envisage the  maxim `Cogito Ergo Eureka’ for the pursuit of mathematics!

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Chapter I of “The Unicorn Valley”

Mitul found the night enchanting. She gazed at the celestial jewellery laid against the black velvetty night sky.
Myriads of stars were floating silently like glittering ships on the horizon. She could identify several constellations up there.
Hunter Orion was facing Taurus, the bull. Sirius, the dog, was close behind.

Something strange caught Mitul’s attention from the corner of her eyes. Sirius was
turning emerald green. Orion was raising his right shoulder. The string of stars that formed his belt, were now blazing blue in colour.
The eye of Taurus was glowing like a hot piece of coal. From the left, a comet appeared. It glided over Sirius. As it neared Orion, its plume started taking on hues of different colours, mimicking a rainbow.
Then, it suddenly turned into a peacock, and with a swoop, it perched on Orion’s shoulder letting out a cry – RING, RING, …!

“Wake up, Mitul!”, a distant voice called out.
“Uhh…let me sleep…”, she muttered.
Someone gently shook her. With an apparent Herculean effort, Mitul opened her eyes. It was me. Mitul sat up with a start. Taking off her glasses, she blinked. It dawned on her that all that melodrama involving Orion, Taurus and the comet was merely a dream.

Patting her head lightly, I said, “Jeet is on the line.”
The mist in her mind was clearing. It being a Sunday, her mother (and my wife) had cooked Goan fish curry, one of Mitul’s favourite, for lunch.
After a filling dose of lemon rice and fish gravy, Mitul had curled up with a book on comets. She and her classmates – Jeet,
Sahil and Kavitha, were doing a Class IX project work on comets.

Mitul remembered that Jeet and she were to go to Sahil’s place after lunch. Jeet too lived in the Mall apartments complex. They had grown up
playing and quarreling. Mostly the latter. Mitul moved towards the telephone. She picked up the receiver lying on the table, and spoke into it.

“Hello, Jeet.”

“Sahil is waiting for us at his place. Hurry!”

“How do we go there?”

“I have my bike. ”

“Bicycles! I am still groggy. I had a nap.”

“Cycling is good for health. Get your bike. It’s a 15 minutes ride.”

Mitul reluctantly agreed. Putting the receiver back in its cradle, she decided to have a cup of tea first.

It took them 30 minutes to reach there. The heavy traffic forced them to cycle carefully.
Sahil was waiting outside, near a small park-cum-playground. Half a dozen noisy kids were playing there.
After parking their bikes, Mitul and Jeet inspected Sahil’s new `toy’ with great curiosity. It was a 4 inch telescope mounted on a tripod.
Sahil suggested excitedly, “Let’s go to the top of Pir Ghaib and observe the ridge.”
Mitul added,”But be careful NOT to view the sun through the telescope. Dangerous for the eyes.”

Pir Ghaib (PG), seemingly wanting to surprise an unsuspecting visitor, was standing next to the playground. This two storeyed rugged structure, constructed with irregular stones, was built by Firoz Shah Tughlak in 14-th century. It was now surrounded on three sides by dense apartment complexes. PG had an interesting vertical `peep’ hole drilled through the ground floor ceiling to the top. Various tales were associated with PG.
Some said that Firoz Shah used it as a hunting lodge. Others claimed that it functioned as an observatory. A later legend stated that a saint vanished into thin air from PG, and hence the name. Was there a secret tunnel nearby, wondered Jeet.

Upon reaching PG, Sahil ushered them to a dark chamber with a circular dug-out on the floor. The ceiling, directly above this spot,
had a hole through which one could see a round patch of bright sky.

“Are there buried treasure around?”, asked Jeet.
“Must have disappeared along with the Pir!”, said Sahil jokingly.

The three adventurers climbed the steep rugged stairs of PG, carrying the telescope with them. Reaching the top, they quickly mounted the instrument on the three-legged stand, very close to a mound where the upper end of the `peep’ hole was located. Sahil pointed the telescope towards the green expanse of the ridge below. Mitul took off her glasses to peer through the telescope. The view was breath-taking! The green tree tops looked like round heads, adorned with leaves and exotic birds. They turned the telescope right and instantly spotted a long structure amidst transmission lines – the awesome Ashokan Pillar! It was raised by Emperor Ashoka in the second century BC, and shifted later from Meerat to Delhi by none other than Firoz Shah Tughlak.

Suddenly, Mitul felt that the roof beneath her feet was trembling. Others must have felt the same. Without raising unnecessary alarm, she said, “Let’s go down.”
Picking up the telescope, Sahil quipped,”I hope this does’nt do a vanishing act now!”
Three of them hurriedly came down the steps. When they reached the ground level, the tremors had intensified. Kids in the park stood still, taken aback by the quake.

The tremors lasted only for a minute or so. Then, Mitul noticed that everything was a blur. Upon mentioning this to her friends, it was pointed out that her glasses were missing. In her excitement, she had left behind her glasses. Before her friends could stop her, she ran towards PG to retrieve her spectacles. Mitul reached the top, panting heavily.

A bright flash from the mound temporarily blinded her. It was the reflected sunlight from her glasses. She fetched her spectacles and put them on. Mitul observed a fresh gaping crack on the mound.
“Could it be due to the earthquake? But what’s this?”, she pondered. A broken stone tablet peered through the crack. She picked it up. It had an engraved animal with a single but curved horn. Fish-shaped symbols were also etched on its top portion.

I had no idea then that I too would get sucked up in the `unicorn seal’ escapade.

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The Unicorn Valley

My daughter Mitul studies in Class IX. She and her classmates Jeet, Sahil and Kavitha are involved in a school project on comets. On the day of comet sighting, Mitul and Jeet visit Sahil’s place near the ridge to see his new telescope. They carry it to the top of Pir Ghaib, from where a saint had supposedly vanished. While the three look through the telescope, a moderate earthquake strikes Delhi. After the tremors stop, Mitul discovers a broken stone tablet in a crack. It is a unicorn seal.

Later in the evening, four of them assemble at the planetarium to participate in comet-gazing. They are astonished to find so many vans belonging to various television channels parked there. Anuj, another classmate, is also present. He, in his usual crafty way, learns about their adventure at Pir Ghaib. When the media begin their live telecast on quake and comet, Anuj maneuvers to place himself right before a TV camera. He talks about the earthquake, showing off the unicorn seal as though it was his find. Anuj also claims to have seen a live unicorn near Trevor’s Tank.

Next day, some goons try to kidnap Anuj. But the attempt is foiled by Sahil. A worried Mitul confides in me about the strange happenings. I consult Professor Natrajan, and hand over the seal to him. A week later, a history student named Sayan, discloses that Natrajan and the seal are missing. Jeet mentions that Anuj recently uploaded a picture of a unicorn standing on a hill, in his facebook profile. Police is informed. Inspector Rafi takes charge of the case.

Rafi leaves for Mt. Abu. Jeet and Sahil itch to join the investigation. They convince their parents to take them to Mt. Abu, with the pretext that it will help them study the comet better, as the hill station enjoys clearer night sky. Since Mitul and Kavitha are keen to join them, I decide to escort the two. We befriend jovial Maarich and ringmaster Mayank, who tames tigers and lions in a circus at Mt. Abu. Maarich entertains us with his comedy acts and magic tricks. Mayank suggests that we all go for a picnic. While the parents jump at the idea, the kids stay back citing their project work. Seeing through their ruse, I too decline the picnic offer.

Instead, five of us proceed towards Trevor’s Tank. Sahil spies one of the goons who had tried to kidnap Anuj, feeding the crocodiles. We decide to share this information with Rafi. Sahil and Mitul go in search of Rafi, while rest of us quietly follow the kidnapper. At the police station, the two run into Sayan. Sayan has stumbled on to a vital clue about the seal. They update Rafi with their findings.

Trailing behind the goon, we trudge along the steep path of Achalgarh. We see him enter Gopichand cave. Rafi and the young adventurers, reach the base of Achalgarh riding on a police jeep. From below, using his telescope, Sahil spots us go inside Gopichand cave. We accidentally step on a trap door. Three of us tumble down a tunnel.

When we emerge, our spines turn into jelly. We are face to face with a familiar person wearing a horned head-gear, standing amidst wild animals. Close by, we spot a large pool framed on four sides by stairs, going all the way down to the water. A figure comes up the steps, holding a live … unicorn. It is Maarich and the maya mriga.

I wonder, “ Is this just a grand illusion or is it really Mohenjo-daro? Where is Natrajan?”

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Galaxies: A Freudian primer

[The other day, I was having tea in the university coffee house (an oxymoronic act, if you will), when there was a typhoon in my cup! I felt a hard thump on my back. It was Fraud. He was grinning from ear to ear. I call him Fraud, as he is our local expert on Freudian psychoanalysis.]

Fraud (visibly pleased, seeing that I had spilt tea on my T-shirt): Say, what is a galaxy?

I (trying to keep cool, said): Has your subconscious been dreaming about one, lately?

F (as if he did’nt hear me, continued): I was holidaying with friends in Nainital, few days back. The night sky there was really starry and superb. One evening, a friend of mine pointed his finger excitedly in the direction of an oval silvery fuzz, exclaiming, “There’s Andromeda!”

Looking upwards, expecting something as pretty as the damsel in distress of Greek mythology, but finding just a white smudge, I remarked, “That milky smear of a thumb can in no way represent the dream heroine of Perseus.”

(Then, becoming sullen, Fraud continued)

Upon hearing that, every one burst out laughing. Later, I was told that this celestial fuzz was Andromeda, a spiral galaxy. And hence, my question: What is a spiral galaxy?

I (sympathizing with him): Well, galaxies are gigantic swarms of stars held together by their mutual gravitational attraction. The same force that glues us to the surface of the earth. Just switch off gravity (if it was possible at all), and feel being hurled out from the merry-go-round (our spinning Earth)! Stars and gas in a galaxy too feel the same attractive force.

F: A fatal attraction, eh? But where do spiral staircases come in?

(His mind still under the Pavlovian conditioning caused by spiraling stairs in murder mysteries that he often reads.)

I: Most galaxies are of spiral type. Use a powerful telescope to look at a spiral galaxy from top, face on, and what do you see – a cosmic whirlpool of light! A vortex of bright, young stars bunched in spiral patterns.

The side view of a spiral galaxy gives you the feeling that it is a fried egg – a disc with a bulge at the centre, where the yellow yolk is supposedly located.

F: Disc dislocated? Does a spiral galaxy suffer from Freudian slips or what? (Then, remembering the fried egg, he summoned a waiter) Food talk makes me hungry. I need to develop a bulge in the middle, too. (After ordering an egg dish, he cheerfully resumed his monologue) So the spiral structure lends the galaxy its ego. It thumps its belly-bulge and proclaims, “Hey, I am a rich spiral!”

I: Spirals are indeed rich in gas. The gaps between the spiral arms contain older stars and gas, mostly hydrogen. The disc stars, both young and old, as well as the gaseous matter go around the centre, making a complete circle roughly once every 100 million years! Gravity providing the centripetal force, and all that.

F (becoming animated): I get it! The stars in the pirouetting spiral arms are like bright and cheerful thoughts running through the conscious part of the brain. While the darker regions resemble the gloomy and mysterious subconscious!

I (hurrying to return to the galactic theme): Rotation of matter around the galactic centre gives rise to an outgoing spiral density wave. When this density wave sweeps across the inconspicuous but gas rich regions, it compresses the dark gas clouds so that they undergo gravitational collapse. The giant molecular gas clouds thereby collapse to form stars. That’s how bright stars are born.

F: Ah, like a bright thought popping out of the subconscious during a Freudian slip!
So, the density wave is like a psychoanalyst who prods a client’s subconscious to let out a repressed thought into the conscious realm.

I: Density waves are actually travelling compressors. When they cross clouds of gas, the latter get compressed to smaller sizes. After that, gravity takes over making the gas balls contract.

F: Rather strange. Normally, external pressure or stress leads to depression. A depressed mind seldom dazzles like a bright star!

Take a look at yourself, for example.

I (coldly): Here, we are talking about compression of a gas cloud. Hit by the density wave, the cloud size reduces but its weight remains the same. Gravitational pull between different parts of the cloud then increases. So, the giant ball of gas contracts further. This goes on till the density and temperature inside the cloud becomes so high as to trigger a nuclear reaction.

The core of the cloud becomes something like a hydrogen bomb. Continuous nuclear fusion stop the cloud from collapsing further. For the time being, gravity has been check-mated by nuclear force. Now, the object starts shining radiantly due to all those hydrogen nuclei fusing to become helium, releasing nuclear energy. That’s the MAIN SEQUENCE of events.

F (not convinced): A confusing sequence, mainly! But wait a minute. May be one can think of the density wave going round as some kind of a creative force, causing first a turmoil in the subconscious. Out of this fusion or confusion, a bright idea is born in the conscious. Eureka, there we go!

I (showing signs of impatience): See, there are about 100 billion stars in a galaxy! Please don’t bring in the “mind”. Sheer size of a galaxy is mind-boggling.

F (absolutely ecstatic): What a coincidence! There are that many neurons or brain cells inside our skull cave!

I (trying hard to outwit Fraud): Astronomers have also discovered supermassive blackholes at the centres of galaxies, weighing more than a million suns. The ultimate collapsed objects, these blackholes! Chandrasekhar thought that they were the most perfect macroscopic objects, characterized completely by mass, spin and charge. These powerful monsters remember nothing else but their strong gravitational identity, not letting even light to escape from their clutches.

F: Then, these supermassive blackholes are the “super-egos”! What are their inherited “id”, I wonder?

I (by now resigned): They are more like Vakasura, devouring anything and everything in their horizon. Stars, gaseous matter and radiation get sucked into their stomach, making them grow heavier day by day.

F (chuckling): The rogues have huge libido for gobbling up matter, eh! (Clucking and shaking his head) Eating all the time. Must be a worried lot, them blackholes.

I (trying my best not to digress): Astronomers are now confident that heavier the bulge of a spiral, more massive is the central blackhole. You know, bulges and blackholes appear in, roughly, 1000 to 1 mass ratio. No one seem to know why.

F (nonchalantly): Elementary, my dear what’s-your-name! Bigger the bulge of the wallet, richer is the spiral. More wealth, greater is the super-ego! So, what is the big deal? And, why bring in the battle of the bulge, pray?

I (with exasperation): LISTEN, apart from spirals there are other types of galaxies, too!

F (excitedly): Don’t tell me, don’t tell me. Let me guess, let me guess!

I (eyeing him suspiciously): Alright. After spirals, what?

F (with a bright expression): Viral galaxies!

I (throwing up my hands): Afflicted by viral brain-fever, have you been? First of all, there are elliptical galaxies – normals, giants and dwarfs. Their shape resembles a triaxial ellipsoid. Hence, cannot be generated by rotating an ellipse about its major or minor axis. While the normal ones have about hundred billion stars, the giants may have more than hundred times this number. On the other hand, the dwarf ellipticals, discovered only about a decade back, have less than a billion stars! Then, there are …..

F (interrupting me): Imagine galaxies being epileptic. Had he known this, Julius Caesar would be in fits!
(Then, in a cautious tone) Please don’t try spinning an epileptic Caesar.

I (with a seemingly unperturbed voice): … irregulars. With no well defined structure. Large and Small Magellanic clouds are two such galaxies. They are the companions of the spiral galaxy we inhabit, called the Milky Way. The gravitational tidal force due to the Milky Way is believed to be responsible for disrupting LMC and SMC. Like the way moon’s (as well as sun’s) tidal pull causes upheaval in our oceans!

F: Yes, bullies do bring about identity crisis among individuals. Highly irregular, these domineering acts!

I (speaking at cross-purpose): At times, when galaxies approach each other, powerful tidal forces tear apart a loosely bound galaxy! Reminds you of the fate of Jarasandha during his combat with Bheema.
According to the prevailing merger theory, elliptical galaxies are formed when two spirals come close and merge into one. In the beginning, the resulting object is all messed up and resembles an irregular due to mutual tidal tugs. But because of Chandrasekhar’s dynamical friction resulting from gravitational interactions between unequal masses, it relaxes into a smooth elliptic structure.

F (highly skeptical): How can an epileptic state be relaxing? These tidal influences cause a lot of mental untidiness.

I: There is Lynden-Bell’s violent relaxation too! The time varying gravitational potential cause transfer of energy among stars, leading to an eventual relaxation.

F (incredulously): Hah, bullies and violence bringing relaxation, it seems!

I (in a pedantic manner): The elliptical galaxies don’t seem to exhibit much organized rotational motion, while a single spiral possesses a lot of spin. But when two distinct spirals, each with mutually uncorrelated spin axis, merge there is very little rotation left. Indeed, it fits with the observation that ellipticals have less angular momentum.

F (making up his mind once for all): From this angle, everything is crystal clear to me. Galaxies are like individual minds. Young, bright stars make the conscious part while gaseous matter and old, faint stars, the subconscious. Density waves are the prime mover of creativity. They shock the subconscious in producing bright ideas, I mean, stars. At the heart of a galaxy is a super-egoistic and libidinous blackhole.

Two spirals merging is like two identities in one mind. That’s split personality, of course! After the merging, what you have is a epileptic galaxy undergoing fits!

(Then, in a puzzled tone) But surely something is missing. What about the completely hidden unconscious part?

I (deciding to play along): Well, that is your “missing matter”! All galaxies possess dark matter. Sometimes these are referred to as missing or hidden mass. They don’t give out light, but their presence is nevertheless felt due to their strong gravitational pull on visible matter like stars and gas clouds.

In fact, they outweigh shining matter by more than a factor of ten! In clusters of galaxies, which contain about thousand galaxies running helter-skelter but bound and confined by the universal gravitational attraction, the amount of dark matter is even more than hundred times the matter that gives out light. (Shaking my head) No one yet knows what this dark matter is made of. No need to despair though, experiments are underway.

F : Who is despairing? (mockingly) We don’t need no experiments. Freudian mind is supreme. We just use our head (then, cart-wheeling Descartes on his head) I think, therefore the galaxy is!

I (scratching my chin): Interesting. Immanuel Kant, the ideal philosopher, believed that space, time and matter are all due to an innate structure of human mind. He had already foreseen that the wispy fuzz one observes in the night sky are separate `island universes’, much before they were identified by astronomers as distinct galaxies.

F (favouring dystopia over utopia of Huxley): Why bring in the “islands” when we are discovering “brave new worlds”? Why insinuate about the smudge called Andromeda?

I : Look here, although, “no man is an island …”, Kantian “island universes” are galaxies. Whether it is “treasure Island” or islet of Langerhans or galaxies, experimental observations are of paramount importance. Experimentation, tinkering and exploration are indispensable for unlocking the secrets of Nature. Do you think “Descent of Man” or the “Struggle for existence”, would have materialized without Darwin’s voyage to the Galapagos island.

F (visibly irritated): I would rather have YOU deported to Pagal-log’s island than allowing you to utter sacrilegious stuff!

I (sarcastically): Mad about the idea, I am. So, when do we start? Islands usually have clear skies. We can sky gaze, and observe Andromeda and Whirlpool galaxies.

F: We? What makes you so sure that I too will drown in the whirlpool?

I: Fraud, “we” are “I” – the alter ego of one another! We possess distinct egos but are bound to one physical brain. And like Edgar Alan Poe’s protagonist in Maelstrom, we are trapped in a whirlpool – getting gradually sucked towards the eye of the whirlpool, into an unknown abyss. Two spirals merging – their central cores coalescing into a gargantuan, spinning supermassive blackhole……….!

[Engulfed by the blackhole event horizon of the mysterious mind, Fraud disappears. I am left alone, holding a cup of tea.

I confess: Fraud and myself are two distinct identities residing in the same brain. Just an ordinary case of split personality that I suffer from. All the conversations above were mere soliloquy.
So, you find the end somewhat chilling, eh? Reminded of Sybil?]

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