Tag Archives: men of science

Hargobind Khorana

In a recent discussion with some friends the topic drifted to Indian Nobel Prize winners. Almost everyone seemed to know about C.V Raman, or Rabrindranath Tagore and about Subramanian Chandershekhar and also their contributions. But very few of us knew much about Dr Hargobind Khorana and his contributions towards Science. In today’s VERITAS we will try to correct this situation.


        Dr Hargobind Khorana was born in 1922 at Raipur, Punjab ( this is now in Pakistan). He was born in a poor family. His father was a “patwari”

in the village. A “patwari” is an agrigulture tax collector. This is a post that is still common in Punjab villages. He was the youngest in the family of 5 children. Hargobind Khorana attended D.A.V high school in Multan. Later he studied in Punjab University at Lahore and got the MSc degree. He got a scholarship to study in England. He joined the University of Liverpool and got the Phd degree in 1948. IN 1949 he returned to India. He tried desperately to search for a job but he could not find one. He returned to England and joined Cambridge.


        At Cambridge Hargobind Khorana became interested in proteins and nucleic acids(DNA and RNA). He moved to Canada in 1952 and joined the University of British Columbia. In 1968 Khorana received the Nobel Prize in Physiology and Medicine along with Nirenberg and Holley. They were awarded the Nobel Prize for their research which led to deciphering of  the Genetic Code and helped understand its function in protein synthesis.


        Lets understand this in more detail. In 1944 Avery showed that genes are made up of Nucleic acids. Both DNA and RNA are composed of 4 nucleotide bases. DNA is composed of adenine(A), Guanine(G), Cytosine(C) and Thymine(T). DNA is composed of strings of these bases. So a DNA strand may look like AATGGGTTACCC etc. Nirenberg was the first to show that each set of 3 bases like AAA or GGG etc forms an amino acid. He formed an artificial DNA by constructing a string of a single repeating base. So Nirenberg showed how DNA/RNA is composed of repeating bases. Khorana developed this work independently and decipered the codes for several known amino acids. He discovered for example that the amino acid Glycine was  GGA etc. He did this by constructing giant nucleic acids( giant DNA and RNA) with complicated base strings. Holley succeeded in preparing something known as transfer-RNA and determined its exact structure.

Transfer-RNA is a special type of nucleic acid. It has the ability of reading genetic code from somewhere else and transforming it to form a protein.

So Hargobind Khorana was one of the scientists who succeeded in understanding the alphabet which is used to create DNA and RNA. He also managed to create DNA and RNA in his laboratory. So Hargobind Khorana is one of the pioneers of Genetic Engineering.

        Hargobind Khorana is still doing active research. I went to his webpage in the “faculty and research” section of MIT’s chemistry department. He is currently doing research on molecules that act as receptors of light in the eye- Rhodopsin, 11-cis-retinal, all-trans retinal( See VERITAS: Light and Life Part II, May 12, 2005 for details on these molecules and the bio-chemical mechanism of sight).





  Go, wondrous creature! mount where Science guides:                 

  Go, measure earth, weigh air, and state the tides:                 

  Instruct the planets in what orbs to run,                          

  Correct old time and regulate the Sun;                             


Celebrations in 2005



  Do you know that UNO has declared 2005 as the “World Year of Physics”?

This is to mark the 100th anniversary of a set of revolutions that shook the foundations of Physics and led to a complete change in man’s understanding of nature. Physics after 1905 would never be the same again.

It would be deeper, stranger and so much more beautiful. In 2005 the world will celebrate the revolution that took place in a small patent office in Switzerland in 1905. The revolution that was brought about by a clerk. The clerk who everyone later would recognize as a giant of intellect. The towering figure of Science-Albert Einstein. In today’s VERITAS we will recall that revolutionary year.

   In 1905 Einstein was a 26 year old patent office clerk in  Switzerland. He had barely passed his exams a few years back. In 1901 UNiversity of Zurich had rejected his doctoral thesis. He had difficulties finding a job as a Physics teacher. So he had joined the patent office. Einstein studied Physics in his spare time that he got from his office work and his family( Einstein was married and had a son at that time). He had access to very little Physics literature( the patent office library was strong in engineering but weak in Physics). Einstein wrote 4 papers that year. Any one of these could have ensured his name in textbooks. But they went much further. They revolutionized man’s view of nature. Only once before in human history had one year brought such a huge revolution in human thought: In 1666 Newton was confined to his country home to escape the plague. And he produced the basis of calculus, law of gravity and the theory of colours. 1666 was Newton’s “annus mirablis”( year of miracle). 1905 was Einstein’s “annus mirablis”.

      Lets take a look at the four papers of 1905:

1) “On a Heuristic Point of View Concerning Production and Transformation of Light”: In this paper Einstein solved the photoelectric effect. He applied Plank’s quanta to light. He showed that if we assume that light is quantized (consists of discrete bundles) then we can understand how light can bump off electrons to produce current. This idea would later pave the way to Quantum Mechanics and the dance of probabilities that Einstein himself hated. This paper would win him the Nobel Prize in 1922.

2) “On the motion of small particles suspended in liquids at rest…”: In this paper Einstein explained Brownian Motion( how particles suspended in a liquid randomly bump into each other). This was an important contribution to statistical Physics.

3) “On the Electrodynamics of Moving Bodies”: This is the special theory of relativity paper. This was the greatest of the four that Einstein wrote that year. What can I say about this? I cannot explain it in 2-3 lines. I can only say that when I first read about relativity when I was a school kid it seemed to be the most romantic subject. Constancy of light, the fact that electricity and magnetism are one, simultaniety, moving frames of reference, twin paradox, the oneness of space and time: it is soooooo beautiful. Anyone who wants to live life fully cannot be ignorant of this theory.

4) “A new determination of molecular dimensions” : This measured the speed of diffusion. We must remember that atoms were still a controversial subject in those days. Einstein tried to show that atoms of a definite size exist.

       So the two pillars of modern Physics: Quantum Mechanics and Relativity were born(in a sense) in 1905. Relativity was expanded in 1915 to form a new theory of gravity( The General Theory of Relativity). Quantum machanics took its own road : Quantum Field Theory, Nuclear Physics, Particle Physics, Quantum Chromodynamics.

      But everything that is beautiful has a tragic component as well. The beautiful march of Physics from 1905 onward has a tragedy associated with it as well. The two theories born that year dont meet each other: Quantum Mechanics and Relativity( actually General Relativity) are inconsistent with each other. Perhaps a new revolution is needed to unite them.

        In 2005 the world will celebrate and remember that year of revolution.

        “To Einstein, hair and violin

         we give our final nod.

        Though understood by only two people:

        Himself and sometimes God”




  Go, wondrous creature! mount where Science guides:                 

  Go, measure earth, weigh air, and state the tides:                 

  Instruct the planets in what orbs to run,                          

  Correct old time and regulate the Sun;                             


Wave Function Collapse


        In the last few weeks I and a friend have had a number of discussions on this subject. I thought I should share some of these mysteries with the whole VERITAS gang.

        In quantum mechanics a particle( say an electron) is represented by a wavefunction or a state. Lets take some examples:

1)   An electron have a spin of +1/2. So we represent this electron as:

     |electron>  = |+1/2>

2) An electron may be found with a spin of -1/2. We say:

     |electron>  = |-1/2> 

3) Now there is another possibility. And this is at the core of the

   mystery of quantum mechanics. An electron may be found in the following


    |electron> =  a |+1/2>  + b |-1/2>

    This state is said to be a superposition of the +1/2 state and the

    -1/2 state. So it is neither in the +1/2 state and nor is it in the

    -1/2 state. So what happens when we measure the spin of such an

    electron? The  measurment of this electron might yield a value of +1/2

    or a value of -1/2!!! A measurment of this electron will yield +1/2

   with a probability of a^2 and will yield -1/2 with a probability of

   b^2. Of course a^2 + b^2 = 1.

      These probabilities are very different from the ones that we encounter when we toss a coin. When we toss a coin then the coin is either in a heads state or in a tails state. Our observing it reveals the state that it actually is in. So our observation just increases our knowledge about the state of the coin.

      But before we observe a quantum superposition state then the electon is NOT in a +1/2 state or in a -1/2 state. It is in a a|+1/2> + b|-1/2> state. Our observation will CREATE the |+1/2> state or the |-1/2> state.

In the language of quantum mechanics the observation COLLAPSES the wave function into the |+1/2> state or into the |-1/2> state. The observation creates the reality!

      How do we know that the electron was not in a |+1/2> or |-1/2> state before we observed it? We will not discuss that question in detail here. But this much I can tell you: There are ways to observe the electron without collapsing the wave function and such observations tell us that the electron was NOT in a |+1/2> or |-1/2> state. So the wave function collapse is for real.

      But what decides the probability of collapse into the |+1/2> or |-1/2> state. No body knows the answer to that! But we know that after an electron has collapsed into a |+1/2> state or a |-1/2> state it will stay in that state and a future observation will show you the same state with 100% probability.

      So in a sense an observation creates the reality. And nature adopts a probability in deciding what reality to create! All this seems very strange to us who are used to the deterministic world around us.

      Some people do not believe in the current theory of quantum mechanics. But in Science there is no room for belief or disbelief. These things belong to religion. In Science the validity of a theory is decided by experiments alone. And EVERY experiment ever performed to check the validity of quantum mechanics has found it to be correct. Einstein was a real scientist and instead of saying things like “I dont believe in QM”, he invented some very innovative thought experiments to show that Quantum Mechanics was conceptually wrong. But every experiment showed instead that quantum mechanics is a solid theory.


       But lots of mysteries remain to be answered. Quantum Mechanics is the theory of the universe. It is valid for everything: electrons to billiard balls, to humans to planets to galaxies. But then why dont we see superpositions around us. Why dont I see my Tv in a superposition of several states ??? How does an deterministic world around us arise from the basic principles of probability? We will study these questions in a future VERITAS. But let me tell you that there is a Decoherence theory that answers these questions. And you can derive the Newton’s laws of motion from the laws of Quantum Mechanics.

      I leave you with a few quotes on Quantum Mechanics by some eminent scientists:

“If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet.”

                                                                Niels Bohr


“Here lies the revolution. Quantum theory says that what happens to any individual photon is genuinely and inescapably unpredictable. It has a 95 per cent chance of being reflected, and a 5 per cent chance of being transmitted or absorbed, and that’s all there is to it. There’s nothing about any photon, no secret property or hidden clue, that can tell you any more precisely than that what it will do. The unpredictability is innate.”


                                                                Max Plank


“God does not play dice with the world.”

-Albert Einstein


“Einstein, don’t tell God what to do.”

-Niels Bohr in response to Einstein


“I think it is safe to say that no one understands quantum mechanics.”

                                                -Richard Feynman


“I believe that the existence of the classical ‘path’ can be pregnantly formulated as follows: The ‘path’ comes into existence only when we observe it.”







  Go, wondrous creature! mount where Science guides:                 

  Go, measure earth, weigh air, and state the tides:                 

  Instruct the planets in what orbs to run,                          

  Correct old time and regulate the Sun;                             


Francis Bacon’s Method


      Today we see Science that is free. A Science that relies on observation, on experimentation, on constant discussion, point and counterpoint. However it was not always this way. There was a time( in not too distant past) when people thought that the only way to achieve knowledge was to discuss and interpret holy texts and the writings of Greek Scolars like Aristotle. A person with more knowledge had read these texts deeper than the others.

      One man who helped changed all this was Francis Bacon. He is regarded by many as the “Father of Modern Scientific Method”.

      Francis Bacon was born in 1561. He was only 12 years old when he entered Cambridge University. He was not impressed by his teachers.

This is what he said about them :” Men of sharp wits, shut up in their cells of a few authors, chiefly Aristotle, their dictator”. Bacon rejected a blind faith in Aristotle’s writings.

      At the age of 18 his father died. Francis Bacon joined law and by the age of 23 he was a member of the British parliament. He rose to the post of Lord Chancellor of England. But politics caused his downfall. He was accused of taking a bribe and he lost his post and his honour. In a way this was a good thing. THis allowed Bacon to write more and with more thought. His writings before the bribe scandal were more of works of spare time. After the scandal his writing and philosophy became much deeper.

      Our aim in today’s VERITAS is not to examine the personal life of Francis Bacon in detail. Our aim is to examine his philosophy and its impact on Science.

      Bacon believed that true knowledge was empirically rooted in nature and observation of nature could enable man to master it. He coined the famous expression “knowledge is power”.

Bacon’s first work came out in 1605. It was called “The Advancement of Learning”. In 1620 Bacon published the Novum Organum(The new organ(tool). This contained a new method to acquire and develop knowledge and was designed to replace Aristotle’s methods. Bacon considered himself the inventor of the new method which would “kindle a light in nature, a light that would bring to sight all that which is most hidden in nature”. His method was: collection of data, careful interpretation of data, experimentation, understanding nature by a careful observation of its regularities.

      See the attached picture. It appeared on page one of Novum Organum. It shows a ship passing through the pillars of Hercules, which symbolized for ancient greeks the limits of man’s explorations. Bacon wrote ” For why should a few received authors stand up like Hercules columns, beyond which there should be no sailing or discovering?”. The latin phrase at the bottom of the picture means “Many will pass through and knowledge will be increased”.

      Bacon’s thoughs inspired a whole generation of people to give up just learning ancient texts and go out there and observe.

Bacon died in 1626…. ironically it was his love for experimentation that killed him. He wanted to study the effects of ice on the decay of meat. He stuffed a fowl with snow while travelling. He caught a cold and died of bronchitis a few days later.  

      Lets look at the difference between Bacon’s method and Aristotle’s method. Bacon’s method was the inductive method and Aristotle’s was the deductive method. The deductive method takes a small set of axioms and derives facts based on these. The inductive method takes a huge number of observations and then tries to make a theory that contains the reason for all these observations.

Bacon realized that there are no logical inconsistencies in Aristotle’s deductive method and it would work very well for mathematical sciences. But for the study of nature you would need a more observational technique and not based on logic alone and this is the inductive method.

      Here are some famous Francis Bacon quotes:

Books must follow sciences, and not sciences books.

Reading maketh a full man, conference a ready man, and writing an exact man


No pleasure is comparable to the standing upon the vantage-ground of truth





  Go, wondrous creature! mount where Science guides:                 

  Go, measure earth, weigh air, and state the tides:                 

  Instruct the planets in what orbs to run,                          

  Correct old time and regulate the Sun;                             


The Story of Phosphorus


   In today’s VERITAS we will study the remarkable element Phosphorus.

We will study the history of its discovery and some of the properties that make it so useful and also so dangerous.

   Before the study of chemicals became a science it used to be a field for people with more monetary interests. Alchemists were about the only people who studied chemicals and they had only two aims: to find a way to make gold from other metals/elements and to find a chemical that would make man immortal. Hennig Brand was just another alchemist and he was trying to find new ways of making gold. In a crazy experiment he filled a tub with human urine. He boiled it into paste. He hoped that he would heat the paste and condense the fumes and these condensed fumes would be gold.

To his disappointment he obtained a white waxy substance. But this substance had a remarkable property: it glowed in the dark. Brand had discovered Phosphorus.

The year was 1669. And this was the first element that was isolated since the days of ancient civilizations( who knew about gold, silver , iron etc).It was named phosphorus( meaning light bearer). Soon this chemical became famous with chemists the world over. Robert Boyle in England did a lot of research on it.

      If you are thinking that Alchemists were a few crazy people with some crazy interests you are wrong. Alchemy had a huge following at that time. People knew that gold was a substance and iron was a substance.

They knew that water was a substance and salt was a substance. They knew how to get salt from sea water. So they thought that they were converting one substance to another. They wondered if they could find a substance that could be converted to gold. They lacked that one critical piece of knowledge that we have : gold is an element and water is a compound.

You can get oxygen from water but Gold is not composed of anything else.

You cannot create a gold atom from another element’s atom. People at that time did not know about atoms and about the impossibility of such a conversion. Even the great scientist Isaac Newton was an Alchemist. When he was not doing Physics he was trying to mix substances to try and make gold.

      For about a 100 years the only way to extract Phosphorus was from urine.

In 1770 some scientists realized that animal bones contained Phosphorus and found ways of extracting it.

 Phosphorus has a tendency to burst into flames. There are 4 kinds of Phosphorus: white, red, black and violet. White Phosphorus is the most volatile. In its pure form it has to be carefully controlled. It is usually stored in oil baths. As soon as it comes in contact with air it bursts into flames.  This property of phosphorus inspired scientists. Red phosphorus is more stable and can be controlled more easily.

      Think for a moment about how difficult it would be to light a fire.

You need a spark. Can you imagine yourself going to a jungle and creating a fire with just rocks and dry leaves…. Now imagine doing it everyday!

The invention of matches was a great boon to mankind. It made burning fires so much easier… a routine task.   In 1827, John Walker the English chemist discovered that if he coated the end of a stick with certain chemicals and let them dry, he could start a fire by striking the stick anywhere. These were the first friction matches. In 1830, the French chemist, Charles Sauria, created a match made with white phosphorus. Sauria’s matches had no odor, but they made people sick with a ailment dubbed “phossy jaw”.White phosphorus is extremely poisonous! In 1855, safety matches were patented by Johan Edvard Lundstrom of Sweden. Lundstrom put red phosphorus on the sandpaper outside the box and the other ingredients on the match head, solving the problem of “phossy jaw” and creating a match that could only be safely lit off the prepared, special striking, surface.

Now Phosphrous is explosive and also very poisonous. 50 mg of phosphorus is a fatal dose. People started using Phosphorus in bombs and tracer bullets.

They also started making chemical weapons using Phosphrous.

In the second world war the German city of Hamburg was destroyed by phosphorus derived bombs. 80,000 phosphorus bombs and 500 phosphorus drums were dropped on Hamburg for three days. 40,000 men were killed, a further 40,000 wounded and 900,000 were homeless or missing. In three nights Hamburg was wiped out.

 Some scientists believe that Phosphorus limits life on earth. It is required by all organisms but it is extremely rare. It is a part of all bones and cells.

Recently a book on this history of this element has been released :” The Shocking History of Phosphrous: A biography of the Devil’s Element” by John Emsley.


      The discovery of the glowing Phosphrous by Alchemists from urine has also been the subject of a very famous painting: “The Alchemist” by Joseph Wright (1771). A print of the painting is attached with this VERITAS mail.





  Go, wondrous creature! mount where Science guides:

  Go, measure earth, weigh air, and state the tides:

  Instruct the planets in what orbs to run,

  Correct old time and regulate the Sun;


The path finder

This post was written on  Wednesday, February 05, 2003.


Imagine …. You are born into a very poor family. Your mother leaves you when you are three. You suffer from small pox before you are five and are nearly about to die. You suffer from serious fever attacks, painful skin eruptions and stomach disorders throughout life. You want to become an astronomer but you have a very poor eyesight and cannot see the stars. Employment is always uncertain for you. You have to earn a living by doing something you do not believe in. You are a deeply religious person but throughtout life you are persecuted for following your faith.
Your wife dies at a young age. Half of your children die before the age of 10. Your superiors treat you badly. It is a time of conflict and war. Sometimes you have to do your work with soldiers living in your house. Your mother is accused of witchcraft and you have to spend several years defending her in court. You are banished from two cities and your property is confiscated.

       A tragic life. A life which would be a good excuse for anyone to complain and feel miserable about himself. Anyone but not Johannes Kepler! Kepler went through all this with his love for his work and he changed the way we understand the heavens. His story is the story of great determination and love for Science. He did not let the troubles of life affect his Science

       Einstein once said:” A scientist must be unencumbered by cares, must avoid all disturbing conflicts of life, must bear with all humiliations from his opponents in order to safeguard the precious something that he bears in his soul.”  Kepler did exactly this.

       Kepler was born on Dec 27, 1571 in Weil( southwest Germany). At the age of three he contracted smallpox and nearly died. His father was a soldier and his mother left with him for a long period of time leaving Johannes with his grandfather. Johannes joined the local school and later the University of Tubingen. He studied theology, mathematics, greek and latin. Kepler was on his way to become a priest. All he wanted to do was to serve God. He was deeply religious.

       In 1594 Kepler was asked to go to a Lutherian high school in Graz, Austria to replace a mathematics teacher. Kepler felt led by God to teach these students and he left the university.

       The mathematics teacher was also supposed to work as a district mathematician( create calendars, survey fields, predict weather, make astrological charts). Kepler did not believe in astrology but all his life he would be asked to make these charts. People in those times thought that study of stars except for astrological purposes is useless.


       Kepler was a deeply religious man and believed that the universe was created in a planned and orderly fashion by God. And that man could find this order. Kepler studied Euclid’s works on geometry and found that there are six regular solids:
sphere, cube, tetrahedron, dodecahedron , icosahedron and the octahedron. Also there were 6 known planets at that time. Why only 6 planets? Why only 6 regular solids? For the religious mind of Kepler there seemed relationship between the orbits of these planets and the sizes of these
perfect spheres. He wanted to find the relationship. He believed that this relationship would be a study of how God made the universe perfect!

       In 1596 he came up with a pretty wierd theory in which he explained the orbits of the planets in relationship to the sizes of these solids if put inside each other. Nobody beileved this theory. Kepler wanted more data to prove his theory. His eyesight was too weak and he could not observe the stars. He knew that the great astronomer Tycho Brahe had been observing the planets for several years and had made detailed calculations about their positions. Kepler needed Tycho’s data. But Tycho would not just hand it over to him.
Kepler took up a job under Tycho Brahe. Now Tycho was a pretty arrogant  and cranky person and used Kepler for all sorts of petty jobs as well( see the VERITAS on Tycho Brahe March 27 2000).


6 solids in a planet:


       In 1601 Tycho died. There was dispute among Tycho’s family on who would own his instruments and his observatory. In the middle of this Kepler used Tycho’s observations to sketch the orbit of Mars. He took him about a 1000 pages of calculations to come up with the final answer: the orbit is a ellipse with the sun at one of the focii. This was different from the general belief that it would be circular. Even Kepler would have liked a more “perfect” orbit. He now wanted to test the elliptical orbit theory with the rest of the planets. He also found that a planets sweep equal areas in equal times along its orbit. He published these two laws in 1609.

Tycho Brahe


       In 1611 the king of Prague died. His brother succeeded him. The king was a Catholic and Kepler was a protestant. Kepler was asked to leave Prague. His wife and son died. Kepler went to Linz and became the Imperial astrologer. His job was to predict the king and the kingdom’s future. Ten years later he came up with his third law of planetary motion. All this time he battled with his health and health/death of his children.

       Kepler decided to write a book on his three laws called: “On the Harmony of The World”. While he was working on his book his mother was charged with witchcraft. If the charge was proven she could be burnt alive. She was imprisoned and tortured and asked to confess. Kepler fought a long legal battle to save his mother.

       Kepler made several other contributions to Science: He proved why logarithms should work(Napier had proposed the idea of logrithms but he had not given any mathamatical reason). He published the Rudholphine Tables which contained Tycho’s observations and Kepler’s logarithmic calculations. He also proposed a new construction of the astronomical telescope.

       Kepler died in Regensburg in 1630. He was buried in a church. His tomb was destroyed in the thirty years war.
Kepler’s scheme to plot the earth’s orbit




 Go, wondrous creature! mount where Science guides:
 Go, measure earth, weigh air, and state the tides:
 Instruct the planets in what orbs to run,
 Correct old time and regulate the Sun;


Creative Commons License
Veritas by Kanwarpreet Grewal is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.

The Brachistochrone Problem


      You should be very careful when you talk about a scientist named Bernoulli. Because  Bernoulli was not one famous scientist. The Bernoullis  were a family of mathematicians and  scientists.

In three generations the Bernoulli family produced 8 eminent mathematicians. Most of them did not choose mathematics as their profession but “drifted into it inspite of themselves as a dipsomaniac returns to alcohol”(E.T Bell). They fought with each other over mathematics. Once Johannes Bernoulli threw his son out of the house because the son had won a mathematics prize for which the father had also competed! “After all, if rational human beings get excited over a game of cards, why should they not blow up over mathematics which is infinitely more exciting?”(E.T Bell) 🙂

        In the year 1696 Johann Bernoulli challenged the mathematicians of Europe with a problem:”If two points are fixed at random(one at a lower height than the other but not vertically below) then what is the shape of the incline along which a body should slide so that it reaches the other point in the least possible time?” The answer, VERITAS readers is not a straight line! The mathematicians spent six months trying to solve this problem but they all failed. One evening this problem reached the great Newton. Newton had just returned from his duties as the warden of the royal mint. He was tired but not tired enough for mathematics. The problem was solved after dinner and the correct answer was despached anonymously to Bernoulli.

Bernoulli on reading the solution immediately recognised that it was Newton who had solved the problem. He said “one can recognise the lion by the impression of his paws”!

     The problem is known as the brachistochrone(“shortest time”) problem . And the correct answer to the problem is a cycloid. So if the shape of the curve between the two points is a cycloid then the body will take the least time to travel between the two points. See attached file to find what a cycloid looks like.  The cycloid and similar curves were studied extensively by the Bernoillis. They also found that the cycloid is also a tautochrone i.e a body placed at any height on a cycloid would take the same time to come down! See attached figure:

if a body is placed at the highest point A or a point lower than A (near B) the time taken to come to the bottom of the curve under gravity would be the same!

      The branch of mathematics that deals with finding the path of least/most length or least/most time between two points under various conditions is called the calculus of variations. The Bernoullis laid the foundations of this branch of mathematics.

      Now I shall attempt to shock you, VERITAS readers.  There is a principle in Physics called “Fermat’s principle of least time”. According to this principle light travels along a path between two points which takes it least time. Note that this is true even if light has to bend or pass throught objects of different kinds. Light chooses the path that will take the least time! This principle is so deep and fundamental that you can derive the laws of reflection and refraction of light using this principle alone! How much does light bend when it goes into a material such as water. It will take the path that will minimise time and you will know how much it will bend! How does light decide which path to take? Surely light cannot select paths! Is there intention in nature? Does light make decisions? The answer to this question lies deep inside the laws of Quantum Mechanics. Such minimum principles are fundamental in nature and surprise everyone including most Physicists. 

                  Give me to learn each secret cause;

                  Let number’s, figure’s, motion’s laws

                  Reveal’d before me stand;

                  These to great Nature’s scenes apply,

                  And round the globe, and thro’ the sky,

                  Disclose her working hand

                              –Mark Akenside

(Most of the material for this VERITAS has been taken from the book “Men of Mathematics” by ET Bell and the book “Classical Mechanics” by Herbert Goldstein)





  Go, wondrous creature! mount where Science guides:                 

  Go, measure earth, weigh air, and state the tides:                 

  Instruct the planets in what orbs to run,                          

  Correct old time and regulate the Sun;                              


Discovery of The Diabetes Treatment


     Diabetes is a widespread disease. All of us know someone or the other who has diabetes. There are an estimated 150 million million people with diabetes worldwide. People who suffer from this disease depend a lot on insulin injections to regulate the amount of sugar in their blood. And insulin was discovered in the year 1921.

Before 1921 people with diabetes lived terrible lives. They were forced to starve because most foods increase the amount of sugar in the blood. And people who starved were prone to other illnesses. Most people died soon after getting diabetes.

    Who was the person who discoved insulin? Who was the scientist who gave hope to the suffering millions worldwide? Today in VERITAS we turn the pages of medical history to find how insulin was discovered. And we find a remarkable story of a very stubborn young doctor.

    Frederick Banting was born in the year 1891. He joined medical school and became a surgeon. He enlisted in the Medical Corps during world war I.

He suffered a serious injury during the war and his arm was about to be amputated.But he requested the doctor not to do it. The hands are very important for a surgeon. He was stubborn and he risked his life.

But everything went well and he recovered.

   After the war he started his own practice. He was not successful.

He decided to become a part time lecturer in a local college. He became the lecturer of pharmacology (This is to make you regret not having taken this up Anjum! :-)). Now Banting had very little knowledge of pharmacology so he had to study a lot. During his studies he became interested in the subject of diabetes. In textbooks diabetes was listed as “fatal disease-remedy unknown”. Doctors knew that the pancreas are responsible for burning and thus checking the sugar in the blood. Doctors even tried to feed diabetic patients the pancreas of animals but it did not work. There was a chemical in the pancreas that did all the work.

But nobody knew how to isolate this chemical or how to administer this chemical.

   Banting’s friend Joe Gilchrist was suffering from diabetes. He was starving himself and was dying a slow death. Bantin wanted to help.

Banting studied more and realized that scattered on the pancreas are small spots(islands) that shrink for people who suffer from diabetes.  He thought that somewhere in these islands lies the secret and the treatment of diabetes. (These islands are called Isles of Langerhans).

Banting decided to try and find the chemical that does all the sugar burning. He wanted to see what is inside these islands.

      He requested permission to experiment on dogs. He knew that scientists were trying experiments for years on the pancreas but they had all failed. But he was stubborn. He sold off his furniture and bought surgical equipment. He hired a fresh doctor Charles Best to assist him. They started experiments on dogs. From 10 the number of dogs rose to 91. But still no result (VERITAS readers, patience is a very important attribute of a scientist!). The problem was that as soon as they removed the pancreas to study the island chemical the island chemical was destroyed by an enzyme in the pancreas. You had to first kill the enzyme to be able to get to the chemical in the islands. No one knew how to do this.

     Banting found a way of doing this. He would tie the duct of the pancreas in living dogs. After a few weeks the pancreatic enzyme would die. At this time the pancreas can be removed and the chemical in the islands can be extracted. They tried this theory on the 92nd dog. They removed the dog’s pancreas. The dog started suffering from severe diabetes. At this time it was injected the island chamical taken out from the pancreas of another dog. And wow! the dog started barking and wagging its tail again! However the joy was shortlived. The dog died after 20 days due to severe diabetes. Banting had not given the dog enough of the island chemical.

   So Banting had found the chemical that would control diabetes but he did not know the right amount to be injected? And he did not know how to obtain large amounts of this chemical. More research was needed.

  This chemical was named insulin(latin for island chemical). And Banting found that cattle pancreas can yield a good supply of insulin.

     He now started experiments on human patients. His friend Gilchrist was one of the first patients on whom this new treatment was tried.

The patients were administered insulin everyday and results noted.

The patients suffered no illusions: this was still an experiment. A dosage of insulin taken in very small quantities is ineffective. The dosage taken in large quantities is dangerous and patient can die of convulsions. So the experiments was to find the right quantity to be administered. Banting’s research found the right quantity.

    Eminent people like King George V of England, HG Wells and Dr. George Minot were saved from death due to diabetes by Banting and his team. Thanks to the insulin Dr Minot was spared to discover an equally important treatment: liver treatment for pernicious anaemia.

    Banting became famous and received the Nobel Prize. One man’s stubbornness (it is no joke cutting up 92 dogs and waiting for weeks on each dog) helped millions live normal lives.

    One remarkabe thing about true scientists is that they spend their lives solving problems which they themselves do not know can be solved.

In Science you cannot make project plans… no .mpp files. You have to to base your work on passion and love for knowledge. The results may never come so you have to be happy in your constant pursuit of knowledge.

   (Most of the information for this VERITAS has been taken from:

the book: Living Biographies of Great Scientists by Henry Thomas and Dana Thomas, the Nobel Prize site (www.nobel.se) and the International Diabetes Foundation(www.idf.org))




  Go, wondrous creature! mount where Science guides:                 

  Go, measure earth, weigh air, and state the tides:                 

  Instruct the planets in what orbs to run,                          

  Correct old time and regulate the Sun;                             


Nicola Tesla


      Today’s VERITAS is about a genius who changed the way we live. And yet very few people know about him.

      What inspires a genius? What does he work for? Why is he happy without sleep and without money? Why does he seemingly torment himself and live so close to madness? All these questions baffle us. The answer to these questions seems to me this: genius is the fire that needs no other fuel. Genius(the faculty) needs no outside reason to work. It is a self driven force that works without an end in mind. This theory of mine is supported by the life of Nicola Tesla.

        Tesla was born in 1856 in Yoguslavia. His early education was in a village school. When he was seven the family moved to the city of Gospic. It is at this age that Tesla showed his first sign of genius.

A new fire brigade decided to have a public demonstration of its new pump that would replace the old buckets of water. The whole town came to see. Telsa and his parents were also there. Tesla became instantly attracted to the big red water pump. The pump was huge. The aim of the demonstration was to connect one side of the pump to the river and from the other end a stream of water would be shot skywards by 16 firemen.

But when the demonstration began there was not a drop of water coming out of the nozzle. The firemen starting pumping faster but nothing happened. It was becoming a great embarrasment. Tesla was inspired by the problem. He took off his clothes and jumped into the water. At the end of the pipe he found that the pipe had twisted and kinked. He straightened it and the water shot skyward from the other end!

Tesla became a hero. He had solved a problem at the age of 7. The joy of problem solving would guide the rest of his life. 

      Tesla studied math, physics, and mechanics at the Polytechnic Institute at Graz. He displayed an extraordinary memory and was able to solve most math problems without writing them down. He also mastered 6 languages.

      During college Tesla first saw a DC machine: a machine that could be used as a dynamo or as a motor. Tesla was impressed but something told him that the DC machine was not the best way to produce electricity. After several years of research he invented the A.C induction motor. He however did not reveal his results to anyone.

       Tesla Joined the French branch of the Edison Electric company. He was given the duty of repairing an electric plant at Strassburg. AFter the completion of the work Edison’s company refused to pay him the money. Tesla left and migrated to America. He started working for Edison. Edison had several problems with his DC motors and told Tesla to improve them. He also offerred a prize of 50,000$ if he could. Tesla improved Edison’s motors but in the end Edison refused to pay and said that the promised prize was just “American Humour”. Tesla quit immediately.

      However Tesla could not find a job and he had to dig ditches for two years to support himself. However he knew that he was worth more. He would dig ditches but his brain was full of dreams of experiments he would do if he got the money.

       Tesla found work in the Westinghouse’s Pittsburgh labs. He told Westinghouse about his idea of AC electricity. He demonstrated that AC current can be used to transmit power to large distances which DC failed at. Westinghouse immediately liked the idea and paid a good sum to Tesla for the idea.

      Edison had invested a lot of money on DC power and he tried his best to show that AC power is not a good idea. He even burnt animals using AC power to show that AC is too dangerous to be used in homes. The press believed Edison …. he was really famous! Tesla did not give up. At a fair in Chicago he even passed AC current through his own body to light electric bulbs to show the world that it is not so dangerous.

     Tesla also invented transformers to step up and step down Electric power. Westinghouse with Tesla’s help started generating electric power from Niagra falls. Soon America’s homes had electricity!

    With the money Tesla set up his own electric company and started inventing a lot of exotic electric machines. But he was careless with money. Westinghouse one day decided to pay Tesla no more( The initial contract was to pay $2.50 for each KW of energy sold). Tesla did not bother. He only wanted enough money for his experiments. 

    In 1900 he got finance from JP Morgan to setup the world’s first wireless broadcasting system tower. The dream was to be able to transmit information to the whole world. JP Morgan soon realized that this system would mean free information to the whole world and they would not be able to get any money out of it. So they stopped the finance. And the project stopped. Tesla had created wireless about 10 years before Marconi!

   In his lab Tesla was using fluorescent bulbs in his lab some forty years before industry “invented” them.

    He even created an artificial earthquake in New York. He did this by vibrating a stream driven oscillator at the same frequency as the natural frequency of the earth!

     In his Colorado Springs lab in 1899, he sent waves of energy all the way through the Earth, causing them to bounce back to the source (providing the theory for today’s accurate earthquake seismic stations). When the waves came back, he added more electricity to it.The result? The largest man-made lightning bolt ever recorded – 130 feet! -a world’s record still unbroken! The accompanying thunder was heard 22 miles away.

   However all his life Edison kept says things against Tesla. He made sure that the press and the people think of Tesla as an eccentric crank and not as a great inventor.

   In the year 1912 Edison and Tesla were to share the Nobel Prize in Physics. But they did not want to share the prize with each other. So none of them got the prize.

   In his life Tesla recorded over 800 patents. He was only stopped from Edison’s record number by a constant lack of money.

  His notes even contain the principles of superconductivity. And this was about 30 years before it was discovered.

 Tesla however was also a bit eccentric. He never married and had only a few friends. A lot of his proposed inventions were more like flights of fancy.

 At this time when power distribution seems to be the talk to the town(New Delhi 🙂 ) lets remember the great Genius who made this all possible.




  Go, wondrous creature! mount where Science guides:                 

  Go, measure earth, weigh air, and state the tides:                 

  Instruct the planets in what orbs to run,                          

  Correct old time and regulate the Sun;                             



History of Set Theory


      Today in VERITAS we investigate how the theory of sets orignated. The story of the set theory is also the story of the struggles, the genius and the torment of Georg Cantor. Today’s VERITAS is inspired by a chapter from the the wonderful book “Men of Mathematics” written by the eminent Mathematician E.T Bell.

        In 1874 the 29 year old Cantor published a very controversial paper that marked the beginning of the set theory. The concept of sets was known earlier but Cantor gave it mathematical rigor and made it a branch of mathematics. Cantor however was not thinking about sets.

He was trying to prove something else. This paper was on algebric numbers. Any number( natural or otherwise) which is the solution of any algebric equation (with whole number coefficiants) is said to be an  algebric number. For example take the equation:

x+5 = 0

The solution to this equation is x = -5 so -5 is a algebric number.

Now isnt it obvious that algebric numbers are more than natural numbers?! To see this we notice that the set of algebric numbers includes all whole numbers since they are solutions of x-n = 0 Also algebric numbers contains the solutions of all quadratic equations with whole number coeffs + solutions of all cubic equations with whole number coeffs+ etc etc .

But to everyone’s surprise Cantor proved that the set of all algebric numbers has the same number of elements as the set of natural numbers. He did this by forming a one to one correspondence between the two infinite sets.

In another paper Cantor showed that the number of transcendental numbers is infinitely more numerous than the number of natural numbers. This did this again by doing a one to one correspondence between the two sets. THis result was a shocker!!! Mathematics had still not proved that transcendental numbers exist!

Cantor was not working on a set theory but his methods of investigations into sets of infinite numbers created the mathematical theory of sets.

A denumerable set is a set whose elements can be counted as 1,2,3 etc. So a denumerable set has less than or equal numbers as the set of natural numbers. A non-denumerable set has more numbers than a set of natural numbers. Do non-denumerable sets exist? Cantor proved that they do. He also showed that the set of points in any line segment(no matter how small) is non-denumerable. 

Note that the set of natural numbers has infinite numbers. So a non-denumerable set is also has infinite elements but the number is more infinite than the set of natural numbers.

So Cantor was dealing with more infinite and less infinite and infinitely infinite in his theories. WoW!

He proved these results and several others in a set of papers from 1879 to 1884. These papers started the theory of sets.

Several mathematicians and the great Kronecker in particular rejected Cantor’s mathematical theories. Kronecker was particularly against his methods of reasoning, his treatment of dealing with infinities and his theory of transcedental numbers. “How can anyone prove that transcedental numbers are infinitely more than natural numbers when we still doubt their existance”. But Cantor’s proof did not require that transcedental numbers exist!

Kronecker was an extremely influential mathematician and made Cantor suffer a great deal by convincing other mathematicans that Cantor’s work is nonsense.

Cantor was a very sensitive man and had several mental breakdowns. He would spend some years in mental asylum , get cured and do more math and Kronecker would hate him more and Cantor would go back to the asylum.

The problem with Cantor was that Kronecker’s criticism would make him doubt his own work and he would drive himself crazy.

But by the turn of the century Cantor’s theory of sets became acceptable to mathematicians and his work came to be regarded as the work of a genius.




  Go, wondrous creature! mount where Science guides:                 

  Go, measure earth, weigh air, and state the tides:                 

  Instruct the planets in what orbs to run,                          

  Correct old time and regulate the Sun;