Mary Mallon is depicted breaking skulls into a skillet

In the early twentieth century, a thirty seven year old Irish lady Mary Mallon worked as a cook with the wealthy banker, Charles Henry Warren in New York. Six of the eleven people of this banker’s family fell ill to typhoid in spite of the best cleanliness and hygiene being maintained in the house. Outbreak of typhoid in his family upset Warren who wanted the matter investigated in order to know the cause of disease.
George Soper was a civil engineer by qualification but was trained in the matter of public health. There could not be a better expert than Soper to investigate the cause of disease. Soper inspected the residence of Warren and found the cleanliness in order and the dishes properly cooked at high temperature ruling out any possibility bacteria affecting the residents. However, he also noticed that ice cream generally made of mashed peaches and milk was not pasteurised and that could be the only source of bacteria Salmonella typhi causing typhoid.
When Mary Mallon the cook confronted with questions, she was not cooperative. However Soper did not lose hope and traced her previous five years history of employment. His discovery was astounding. Every family where Mary had worked in earlier five years, had its members suffering from typhoid. That confirmed there was some problem with Mary and Sopore wanted to confirm that. He requested Mary to give samples of urine and feces for testing but she not only refused but came attacking Soper with carving fork. He even tried to convince Mary that he was in fact writing a book and would share royalties with her if she had cooperated. In stead she charged him of harassing her as she was hale and hearty having no symptoms of typhoid or fever of any kind.
When all attempts failed, Soper took the help of police and on examination of samples, she was found carrier of bacteria Salmonella typhi but without any symptoms. She was quarantined in a small island near New York with Terry a dog as her only companion. Not satisfied living in isolation, she moved the court and her application was dismissed holding she was a threat to the society.
Mary Mallon when in isolation, again made a petition to Health Commissioner who allowed her to lead a normal life in society on the undertaking that she would not work as a cook. Being uneducated and not convinced with her condition of asymptomatic bacteria carrier, she did not leave her profession of cooking and continued working as cook by the assumed name of Mrs Brown but in different county. As was obvious, there also she spread the disease and again the task of investigation was given to Soper who this time did not find any difficulty in reaching the conclusion that Mrs Brown aka Mary Mallon the Irish lady who had migrated to USA in her adolescence, was the cause of affliction. This time Mary was slapped with severe punishment of living in isolation where she finally died. By that time, it was widely published in the papers that Mary Mallon aka Typhoid Mary was a superspreader of the disease Typhoid.
From the life story of Typhoid Mary, it is immensely clear that she never admitted herself suffering from typhoid and even refused to get removed her gall bladder that was considered bag of bacteria Salmonella typhi. Interestingly, the same perception exists today when coronavirus has encompassed the globe. An asymptomatic infected person never gets himself tested for the novel virus and will always insist, he is healthy. One can recall such instances that recently occurred in Punjab, UP and elsewhere. Superspreaders thus infect many and will continue spreading irrespective of doctors advice.


  1. Image courtesy

Author: Narinder Kumar Wadhawan is an Electronics and Electrical Communication Engineering graduate and was earlier Scientist, then Instrument Maintenance Engineer, then Civil Servant in Indian Administrative Service (IAS). After retirement, he writes on subjects, Astronomy, Mathematics, Yoga, Humanity etc.

Human Happiness And Melancholy

Happiness is widely discussed on social media and is advocated as a solution to all ills. May it be successful life, longevity or prosperity., it is a recommended wonder pill against all maladies of life. Happiness is a goose that lays golden eggs, also a golden key that opens all doors to ones well being. One who differs with its charismatic effects is dubbed the odd man who queerly glorifies melancholy.

But to my mind in simple words, happiness is that which does not have its existence at its own, it coexists with melancholy, it is inseparable from sadness, it can only be felt when one has passed through gloominess. Happiness is akin to relief one gets with a rest of few hours after engagement in bone tiring hard work. Happiness is akin to joy one feels on finding lost valuables although net gain is nothing, Is it then not the sadness that defines happiness as situated diagonally opposite but inseparable from it? Is it not the loss that realises how happy one was without suffering it?

It is melancholy that creates emotions of happiness. That is why wires in our brain get crossed over when one cries feeling extreme happiness. Hungarian song ‘Gloomy Sunday,’ was liked most.
Those who liked most and enjoyed it to the hilt committed suicides. Is extreme happiness not suicidal? Why are Bollywood movies, ‘Anand,’ ‘Do Ankhe, Barah Hath,’ ‘Devdas’ to name a few, liked by the audience? Why are plays of Shakespeare liked most? These all have one thing in common, it is their tragic end.

Credit To ‘Balaji Creations’ For This Video Clip Of Bollywood Melancholic Songs

Psychology says a listener involuntarily finds oneself in the situation being described. Narrator’s miseries get reflected in the mind of a listener who feels as if he were passing through the same situation being narrated and that gives rise to empathy, its repetitive occurrence in ones mind puts it in permanent memory of the brain. That is why one rarely forgets happenings that have tragic endings but easily forgets those which culminates in to happy reunions.

Father of our nation, Bapu Gandhi described in his autobiography indelible impression of pain that play Sharvana made in his mind. Scene of bind handicap old parents mourning over the death of their dutiful son who had gone to fetch water for them from a nearby pond, was killed by the arrow of King Dashratha mistaking him for an animal, was unforgettable for Gandhiji throughout his life. It evidences human empathy over the pain of others is everlasting and can never be waned or dampened. Sound of cheers, laughters are transient, momentary and short lived whereas moans of one in pain are last for ever in ones mind.

Of the literary works of C S Lewis, the most acclaimed was ‘A Grief Observed,’ written pseudonymously as N W Clerk to hide his identity. He had explored in these collections the fundamental questions of faith and theodicy. Lewis was staunch Christian, grieved and shaken to irreparable limit by the death of his wife. As resentment over the death of his wife, he cursed God saying, “We worship You, always keep You in high esteem, revere You but when we need You, Yours doors are closed and shut for us for ever.” This book in fact was his recollection of his experiences after the death of his beloved wife. It was later claimed by his step son that the book was not only the result of grief over the death of his mother but it was recollection of the the miseries suffered by the great writer throughout his life. Later on the book was republished with his actual name CS Lewis. The book moved every heart who read it and consequently a movie by the name Shadowlands was televised and later on a film of the same name. It was again the grief observed by C S Lewis that took the centre stage leaving everlasting effect upon the audience.

Melancholy, gloom or sadness are effaceable and sensible minds that keep on pondering are prone to be effected. Persons with such sensible minds think and rethink to find solution to the miseries. Overthinking by the brain defines one’s genius. More over-thinkers are more innovative. As a corollary, genius, researcher, innovator tend to be gloomy. Should then being a genius and over-thinker at the cost of gloominess be despised?

Image Courtesy TeePublic

Nay, that is what my mind says. Gloominess discovers humanity in us, it guides us to alleviate the pains of others, it evokes in us empathy for others. Melancholy unites us. Happiness gives us joy momentarily, it sets us in endless race of competition to prove one better than the other, richer than the other, stronger than the other. It puts us in competitive mode. Happiness closes the door for empathy and makes one cold shouldered and immune to human sufferings. Empathy for human sufferings is not felt at clubs, bars, extravagant theatres or hotels, it is felt in nursing homes, healthcare centres and hospitals which are synonymous with Temples, Churches, Mosques or any other place of Worship.

In the annals of literature, one finds innumerable stories, poems, essays where melancholy, suffering, gloom and sadness have given birth to talents. No art can be better reflected than by mournful cries of ones soul. No poem can be better written than expressing ones soulful agony. Maharishi Valmiki composed first Sanskrit Shaloka or verse when filled with deep agony over the death of mating crane by the arrow of the hunter and his lips cried out,

मा निषाद प्रतिष्ठां त्वमगमः शाश्वतीः समाः।

यत्क्रौञ्चमिथुनादेकमवधीः काममोहितम्॥’

mā niṣāda pratiṣṭhā tvamagamaḥ śāśvatīḥ samāḥ

yat krauñcamithunādekam avadhīḥ kāmamohitam.

You will find no rest for the long years of Eternity

For you killed a bird in love and unsuspecting.

Thus came first verse as a result of deep grief observed by Maharishi. Conclusively, melancholy, grief, gloom, sadness are universal truth, happiness is relative. Without grief, happiness does not have its legs to support upon.


Note: In this article, relativity of happiness to melancholy is explained, it is not the purpose of the author to propagate melancholy as a way of life.


1. First Image Courtesy AZ Quotes

2. Gloomy Sunday song by Billie Holiday

3. Credit goes to Balaji Creators for video clip

4. Image Courtesy TeePublic

5. Valmiki

About author

Author Narinder Kumar Wadhawan is an Electronics and Electrical Communication Engineering graduate and was earlier Scientist, then Instrument Maintenance Engineer, then Civil Servant in Indian Administrative Service (IAS). After retirement, he writes on subjects, Astronomy, Mathematics, Yoga, Humanity etc.

Reminiscences Of The Green And Its Club At Chevy Chase Buffalo Grove

The Green At Chevy Chase Luxury Apartments, Buffalo Grove

Buffalo Grove is a village in Lake and Cook counties in the state of Illinois and is situated in the northwest suburbs of Chicago. At Buffalo Grove, there existed “The Green, Luxury Apartments,” where I stayed for few months last year. Beside these apartments, expanse grassy land was available to the delight of golfers occasionally seen driving carriages propelled by electric machines otherwise the place presented a deserted look. One could find very few persons moving on the foot passage that went along the periphery of this “Chevy Chase Business Park.” 
Out of those few, I was the one who could be seen in the wee hours leaving for “Wheeling” suburb for morning walk but taking due precautions to be on the right of the path. That habitat was mostly populated with persons of Indian origin and in a set of four apartments, one could find three occupied by Indians. 
Apart from this oriental population of “The Green,” its remarkable feature was its club which was fully equipped for workouts, be it for toning of muscles or enhancing endurance and stamina. I had the fancy for the treadmills and used to hop on these particularly when the sky was overcast and rain imminent. That weather was sought after for me as it broke monotonous long walks which could not be undertaken in wet weather. 
Club At The Green At Chevy Chase Luxury Apartments, Buffalo Grove

Upon treadmills were fitted buttons, knobs and controls of different hues mesmerising one as if one were the pilot in the cabin about to fly the winged machine. On such days while on treadmill I used to start with a pace of 3.5 miles per hour and after a little warming to brisk walk and then finally to speed of 5 mph. But after 4.5 mph, the brisk walk turned to jog. 
One fine morning after spending a full forty minutes on the machine and surging my heart rate to 125 beats per minute at pace of 4.5 mph, I was feeling exhausted. A careful look at the indicator suggested me, maximum permissible heart rate in my case was 155. That is 220 minus my age. It was assuring I could continue but exhaustion and perspiration said something else. Sweating at an ambience of 9 degree C was overwhelming for the onlookers. 
Author In Reading Room Of Club At Chevy Chase Luxury Apartments, Buffalo Grove

Then it was time for me to photoshoot with a complimentary cup of coffee. Workout on that day had drained the energy out of my blood, however intake of the hot brew refreshed me as collecting residual energy at one place. 
Life in Buffalo Grove at that time appeared as if I was deprived of what I otherwise used to have. I often used to think when that august August will come and I will fly to my native land. 
I have been in India for the last one year, I have returned from foreign land. But my heart corrects it to state I have returned from familiar land. Now when I am in India, for reasons not known to me, my heart aches and longs for Chevy Chase Club as if treadmills  there were calling me and were asking the visitors in their humming voice of my whereabouts little knowing I was away at an unfathomable distance of seven seas. 


About author

Author Narinder Kumar Wadhawan is an Electronics and Electrical Communication Engineering graduate and was earlier Scientist, then Instrument Maintenance Engineer, then Civil Servant in Indian Administrative Service (IAS). After retirement, he writes on subjects, Astronomy, Mathematics, Yoga, Humanity etc.

Rendezvous With Factorial !

While attempting to find a general solution to cubic equations, I reached a road block where I was required to solve Binomial coefficient involving division of one factorials by the other . Search with google engine led me to a formula given by mathematician Stirling and to my disappointment, use of that formula again led me to another cubic and thus it was again of no use. However, curiosity arose in me to simplify the formula for its applicability to cubic equations. Wikipedia, it will not be exaggeration if I say, is the treasure of all knowledge, was consulted on the topic. Before I proceed further I submit, factorial is nothing but multiplication of consecutive integers starting from one and ending with the number to be factorialised. As it was expected, topic in Wikipedia had huge information from history to intricate questions on factorial and I admit that was all Greek to me, beyond my comprehension although I boast of engineering qualification. It had ‘O’ function, upper and lower bounds and asymptotic methods to solve it.

“Am I required to know all such special functions to derive a formula as simple as multiplication of 4, 3, 2 for 4 factorial? Can mathematics be so tough in its approach as to confine derivation of a formula to knowledgeable few ? How then can it be popularised amongst masses? Can I make it simple and comprehensive to all?” were some of the questions that cropped up in my mind at that time.

Not to be trapped by the web of special functions and mathematical lexicography, I was determined to find a formula that would be simple and easy to understand. That needed, my approach must be simple and independent of earlier works an approach which should be different from traditional mathematics. At the same time, my mind should be free from from bias or prejudices that one acquired from traditional learning. I submit what colleges and Universities do to our mind, they bias us towards a particular thinking in conformity with that of peers. We lose our independent thinking, kill our creativity and move on the dotted lines to reach the set results. They ask us in examinations to derive relations of theory of relativity but never ask us whether it can be interpreted in some different form.

Coming to the derivation of formula for factorial, I had unaffected and unbiased mind, I had not learnt derivation of Stirling formula in college. It was a great plus point in my favour what others may construe my handicap. How to proceed to derive the formula was initial stumbling block. I always subscribe to axiom that sophistication manifests in simplicity. More one will be simple in ones approach, more probable is he would reach his goal. I knew, simple formulae can disentangle the web of mathematical puzzles of factorial.

It required of my understanding of number theory in simplest sense. For academic use I submit I knew numbers progress as 1, 2, 3, so on. My mind worked on what made these progress in this way. Is it not simple addition of unity to consecutive number. Can these progress by multiplication? I had found the answer. Yes, these can. I illustrate their progression by multiplication.

1 = 1,

2 = 1.(1 + 1),

3 = 1.(1 + 1).(1 + ½),

4 = 1.(1 + 1).(1 + ½).(1 + 1/3),


By mathematical induction, n can be written as

where sign of dot . means multiplication. On multiplying all these equations and by definition of factorial n written as n!, factorial n can be written as

Next hurdle was how to compute its value. For that I used simple logarithm and integration formulae

and this sum approximates as integration of ln (x) with x when x varies from x1 to x2

Noteworthy point here is, this integration gives approximation and it would be natural that value of n factorial would not be free from error as approximation does not equal to actual value. Next step was elimination of error. It is submitted plot of (n – 1).ln {n/(n – 1)} (on Y axis) with n (on X axis) is a smooth curve but n changes in steps from 1 to 2, 2 to 3 and so on. Therefore, smooth curve must conform to ladder shaped figure formed by step changes in n with smooth curve and and conformity of the two can be achieved by algebraic addition of area of triangles above the smooth curve. In this way, error although highly removed had still residual error on account of curvature of the curve. After final removal of this error, approximation of n factorial was 10 to 100 times more accurate than that given by Stirling formula. I further submit, mathematics not only expects accurate results but also appreciates neat and clean formulae for the beauty of its intrinsic value. In the scales of mathematicians, this result is clumsy and needs ornamentation. A careful look at the above said formula reveals that (1-1/n) has exponent that is n squared and to avoid that I used ‘e’ given by great Swiss mathematician Leonhard Euler. This number is given by relation, n tends to infinity, (1 + 1/n) raised to power n, tends to e.

For that I assumed n to be very large and replaced (1 + 1/n) raised to power n with e wherever it occurred. That gave the above said formula, luckily or unluckily, look resembling Stirling formula. All said and done, formula derived, next step was its publication. I would not be wrong if I state publication was the most difficult task, not that the paper was lacking in quality but there were certain other reasons that I had never anticipated.

Innovation is not difficult, it may be meritorious, it may be easily comprehensible but if it is not referred to earlier works, it is likely to be trashed and junked. Academicians want, a researcher must walk on the dotted lines imprinted by peers to reach his findings and any deviation from that path leads one to nowhere. A number of references means researcher has put in lot of hard work and more meritorious is the submission. Can one imagine a research paper being rejected on account of the fact author’s contribution in theory or its application was significant? Yes, it is a valid ground for rejection. Papers are rejected as the authors have contributed significantly? What is the inference? Don’t contribute significantly. But then who will contribute to make research a quality research? Natural corollary is to take the support of peers and limit your contribution to minimum. Question that arises is whether such untenable rejections will not retard the progress of Scientific inventions for betterment of mankind? Should independent and creative thinking not be encouraged? Should the rejections for the sake of proving the journal is the best and strict acceptance is adhered to, not be discouraged? But who will bell the cat?

Coming to the publication of this paper, I passed through all the hurdles, journals wanted me to describe the upper bound in deriving the formula, others wanted me to draw the graph with computer and as graph drawn manually was not acceptable. I explained in details my paper is not based on set procedure whereby upper and lower bounds were considered and it is not required of me to explain matters which did not form parts of my paper. Further I had derived the formula considering as if Stirling formula were never given. I lament I could not satisfy them and suffered rejections. Initially, rejections were upsetting but when I again checked my paper, I was reassured there was no fault with paper, probably actual fault was their age old procedure of assessment.

Finally I came across a journal that did not raise any objection and accepted my paper which was then published. Repeated rejections in fact made me stronger and more trustful of my work. I could do a work using elementary functions what others did standing with the supports of ‘O’ functions, upper and lower bounds. I could not resist my urge to refer to Friedman great conjecture here.

“Every theorem published in the Annals of Mathematics whose statement involves only finitary mathematical objects (i.e., what logicians call an arithmetical statement) can be proved in EFA. EFA is the weak fragment of Peano Arithmetic based on the usual quantifier-free axioms for 0, 1, +, ×, exp, together with the scheme of induction for all formulas in the language all of whose quantifiers are bounded.” All theorems are provable by simple elementary functions. There is no limitation, you, he and I can prove any theorem by use of elementary functions provided we resort to proper reasoning, concentration, patience and determination. Let us think differently, all are endowed with some special qualities which differ from one to other. Let us explore and utilise that special quality and not surrender before fighting. It also reminds me of Steve Jobs who was not even graduate in qualification but what he did astonishes us all even the peer in the fields.

“They teach you how other people think, during your most productive years,” he said. “It kills creativity. Makes people into bozos.” Lisa Brennan-Jobs daughter of Steve jobs recalls her father in her book and its abstract was published in Times Of India. That was my unforgettable experience with factorial and it taught me to continue my journey following untouched and virgin paths of mathematics.


1. Wadhawan Narinder, Wadhawan Priyanka, A New Approach To Approximation Of Factorial Using Elementary Functions Only, International Journal Of Engineering And Future Technology 2020

2. Title Figure courtesy Factorial Me: Alexa Skills


Writer Narinder Kumar Wadhawan is an Electronics and Electrical Communication Engineering graduate and was earlier Scientist, then Instrument Maintenance Engineer, then Civil Servant in Indian Administrative Service (IAS). After retirement, he writes on subjects, Astronomy, Mathematics, Yoga, Humanity etc.

Was Steve Jobs Right?

Lisa Brennan-Jobs With Her Father Steve Jobs

“They teach you how other people think, during your most productive years,” he said. “It kills creativity. Makes people into bozos.” Lisa Brennan-Jobs daughter of Steve jobs recalls her father in her book and its abstract was published in Times Of India.

How true it is about our education system! This system makes us think on the lines others have already thought. There is no scope of independent thinking, young minds are biased and made to think in a particular direction and memorise certain theorems to fetch good marks.

Where is creativity? Will education system ever change and create a platform for independent and creative thinking? Or will the generations continue to toe the lines already drawn and dance like puppets with the strings in the hands of those who had already done work on it?

Georg Ferdinand Ludwig Philipp Cantor

It reminds me of German mathematician Georg Ferdinand Ludwig Philipp Cantor whose original revolutionary idea of existence of infinite infinities of different sizes, was detested by mathematicians particularly his colleague Kronecker who jeered at calling him Mr Many Infinities. He was so devastated and depressed that he offered to quit teaching his parent subject mathematics and preferred philosophy. History reveals new creative ideas are always mocked at. Ironically the same ideas after the death of the inventors, are respected as new breakthroughs and followed in toto.

Will there be education system where creativity not only appreciated but encouraged also? Would that day arrive when success in examinations will depend upon one’s innovation and creations instead of proving Bernoulli’s theorem on dotted lines.

This text is written on being inspired by thoughts of Steve Jobs that colleges and universities bias the minds of students in the direction of particular thinking killing true creativity.


Title Image and text Courtesy Times Of India Newspaper link

Second Image Courtesy


Writer Narinder Kumar Wadhawan is an Electronics and Electrical Communication Engineering graduate and was earlier Scientist, then Instrument Maintenance Engineer, then Civil Servant in Indian Administrative Service (IAS). After retirement, he writes on subjects, Astronomy, Mathematics, Yoga, Humanity etc.

This Is His Existence

(Universe: The Hubble Ultra-Deep Field image shows some of the most remote galaxies visible with present technology, each consisting of billions of stars)

It  was dark, pitch dark and presumably nothing existed and the darkness indicated absence of everything. Then there appeared a ray of light 13.8 billion years back. Source was an unknown point. A point that has no volume but was dense enough to assimilate infinite energy in it. What sourced that infinite thermal energy is not known. This question is unanswered and still baffles those who curiously look into to it to know its origin. What existed prior to 13.8 billion years, is also not known. But 13.8 billion years back, first ray of light appeared with unprecedented Big Bang and in a fraction of second, it spread infinite heat and formed basic particles of existence. Those particles then fused to form atoms which gushed out in all directions, spreading and ever spreading to endless destination. First atom that was born was hydrogen, the lightest atom of our material world. Creation started with the winking of an eye. Hindu’s scripture, “Manu Samiriti’s” description is no different. There is no discernible change in explanation of evolution of universe except eulogisation of the primordial ray of light with Lord Brahma. After Big Bang, atoms continued to evolve, from hydrogen to helium, helium to carbon, carbon to nitrogen, nitrogen to oxygen so on by fusion of nuclei under intense heat. From lighter to heavier, different atoms continued evolving. Now the infinitely large heat that was compressed in dot of zero volume was spreading after transforming to mass but that amalgamation still had major share of energy. Atoms of different elements were still evolving.

With the birth of mass from energy, gravity evolved. This attractive force of gravitation lumped the atoms forming dense spots in the clouds of energy and atoms. Lumps being heavier gravitated more strongly and garnered more atoms in it and the process increased the size of lumps. This regenerative action went on enlarging the lumps till that stage reached when the lump got so massive that it started compressing its own contents by the process of self gravitation. Self gravitation heated up the lumps to the temperature so high that it started radiating heat that was generated from compression. Thus first star was born.

Self gravitation was compressing the atoms thereby raising the temperature and rise in temperature was causing its expansion. A tug of war in this way started between gravitation and thermal energy. And that adjusted the size of the star when an equilibrium reached where thermal energy equalled the gravitational energy. That formed a stable star. But some stars were not lucky and could not muster sufficient thermal energy. There gravitation won. Gravitation shrunk the size of the star and with each shrinkage, gravitation got stronger. Now the gravity was so huge that the star started mauling whatsoever was with in its vicinity and with each capture, mass of the star was increasing and finally it did not remain a star, it was a monster star, a celestial demonic monster which was capable of devouring even the light rays if that had passed in its event horizon. This monster ‘Blackhole’ ruled over the celestial empire and took central place in the clusters of stars. The stars started revolving around it like servants move around their masters to fulfil his wishes. 


(NGC 4414, a typical spiral galaxy in the constellation Coma Berenices, is about 55,000 light-years in diameter and approximately 60 million light-years away from Earth.)

Tug of war between the gravity and thermal energy did not end with culmination of star or Blackhole. The lump of masses which failed to gather sufficient mass to fructify into a star, gravity lost the war. The lump reduced to the status of a planet. Jupiter is a fine example of a failed star.

 Apart from evolution of stars, blackholes or planets, these continued to be members of the cluster subservient to Blackhole at its centre. This clusters formation continued and is still continuing. Such clusters were called galaxies and our star sun and its family is also a member of the galaxy called ‘Milky Way.’ The spreading of energy that started with Big Bang is still continuing. Galaxies are spreading out, better to say, are receding from each other and the infinitely high temperature at the start of Big Bang is lowering. It is approximately 2.7 degree Kelvin as is measured from ‘Cosmic Microwave Background Radiations CMBR.’  CMBR is average residual radiations of space that exists now. These radiations are omnipresent and are tell tales signs that once the universe was hot and its temperature has lowered to 2.7 degree K. It is likely to further go down as the galaxies recede. CMBR is a yardstick to calculate the age of the universe.

Can you guess how many galaxies are there in the universe? These are 100 billions which is written as one followed by eleven zeros 100000000000. With better instrumentation resulting in better detection, the figure is likely to increase to 200 billions. Wow, a mammoth figure, isn’t it?

Can you have an idea of number of number of stars present in a galaxy? On an average, it can be taken as if a galaxy has 10 billion stars that is 10000000000. Again it is a mammoth figure. About number of planets, it can be assumed that a star has on an average 10 planets.

Multiplication of these figures gives us the estimate of 10000000000000000000000 planets in the universe leaving aside gaseous diffused matter. It is extremely high a figure and is not comparable with materialistic possessions. Considering surface area of a planet as 5490000000000000 square feet, total surface area of all planets calculate as 5490000000000000000000000000000000000 square feet. Assuming surface area of a man as 5 square feet and on comparing it with surface area of all planets of the universe, ratio is 1 to 100000000000000000000000000000000000. For all intent and purposes, it is tending to zero, a big cipher, a man is insignificant.

Strangely, inspite of its size approaching to zero, he is self centred, greedy and runs a never ending rat race. He shows his oneupmanship over others, enslaves weak and deceives others for petty gains. He feels pride in stating, this is mine, that is mine, he will further acquisition that. Did he ever realise his existence in the grandeur design of the universe? Will his acquisition change the status of his existence. Nay, No. Zero added to zero is no more than a zero. His pursuit of acquisition is mirage, it is never ending, appearance of water at a distance is illusion. His existence as compared to the universe is null, a void and a big nothing. This is his existence. Will he ever realise?



1) Title image of the universe courtesy

2) Galaxy image courtesy 


Writer Narinder Kumar Wadhawan is an Electronics and Electrical Communication Engineering graduate and was earlier Scientist, then Instrument Maintenance Engineer, then Civil Servant in Indian Administrative Service (IAS). After retirement, he writes on subjects, Astronomy, Mathematics, Yoga, Humanity etc.


What Is The Existence Of Man?

This question has innumerable philosophical answers. Ignoring those for time being, I concentrate upon the answer, the physical science would give. On an average, man can be considered 5 feet 6 inches tall, weighing 62 Kilograms. How much space does a man then require for his existence? This has been aptly replied by Great author Leo Tolstoy.

But science differs with those dimensions. You will agree with me if I say, his existence in terms of flesh, blood and bones can be confined to a small canister. No you are wrong, it is still less.

Then his existence must be limited to occupation of space by atoms of elements carbon, hydrogen, oxygen, nitrogen, calcium likewise that immensely constitute his body. Still, it is not the right answer.

Elementary physics says, an atom has its mass concentrated in its nucleus and electrons swarm around it. Electrons taken together, have very very small mass as compared to that of nucleus and that mass can be neglected. However these form a fluffy cloud of electricity around the nucleus.

Strange but true, volume of nucleus is .0000000000004 percent of the atom. Or one can say, an atom is 99.9999999999996 percent hollow but its structure still forms solid matter. Strictly speaking, solids are not solids, these are hollow, sheer emptiness. Sofa set, table, eatables kept in your fridge and what you see all around, are all mostly emptiness.

The man is just a speck, no more than a dot the pen marks when its point touches the paper. THIS IS HIS EXISTENCE. With such diminutive existence, no more than a speck on a piece of blank paper, is it worth while for the man to be arrogant and haughty?


1) Image Courtesy

2) Solids are mostly empty space at


Writer Narinder Kumar Wadhawan is an Electronics and Electrical Communication Engineering graduate and was earlier Scientist, then Instrument Maintenance Engineer, then Civil Servant in Indian Administrative Service (IAS). After retirement, he writes on subjects, Astronomy, Mathematics, Yoga, Humanity etc.