Characteristics of Physical Law


Despite numerous limitations, we human beings are able enough to study as well as appreciate the grandeur of the universe. Our great journey of determining scientific laws began as we understood the regular repetitions of the day and night, the annual cycle of seasons, the eclipses, the tides, the volcanoes, the rainbow and so on.


What is scientific law?

A scientific law is verbal or mathematical explanation that describes some phenomenon of the natural world. For example, Newton's law of gravity, which states that every particle attracts every other particle in the universe with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. But the law itself does not explain why the phenomenon exists or what causes it: that is really the job of theory, in this case, Einstein's theory of general relativity.

The scientific law is factual and should not be confused with logical truth. For example, "boiling point of water is 100 degrees celsius" is a law whereas "every number has a double" is logical truth and not really a law.


Constant over space and time

The same laws which apply here on earth also apply to the rest of the universe. For example, Galileo's law of falling bodies was tested on the moon by astronaut David Scott in 1971.


This is simple and yet beautiful truth, that the laws of nature are universally valid. There are no laws of nature that hold just for the planet earth or the Andromeda Galaxy, for that matter.

In addition, the laws of nature do not change as time progresses. There is a joke which goes something like this, "Before Newton discovered gravity, all things could fly." That is so not the case; there are no laws of nature that hold just for the eighteenth century or just for the Mesozoic Era.



Same for animate and inanimate

The laws are same for living beings and for inanimate objects. There is no evidence yet that what goes on in living creatures is necessarily different, so far as the physical laws are concerned, from what goes on in non-living things.

For example, conservation of angular momentum is a fundamental law of nature. A rotating ballerina spins faster when drawing her arms in.

how are physical laws symmetrical?

Similarly, the earth and other planets revolving around the sun obey the law of conservation of angular momentum, which is why, when a planet is nearer to the Sun, the orbital speed increases and when it is farther away, it slows down.


Simple in nature

Eminent kiwi physicist Ernest Rutherford used to say, "it should be possible to explain the laws of physics to a barmaid." But even though the laws themselves are so simple, their implications are far and wide.

For example, Newton's third law of motion is simply, "for every action there is equal and opposite reaction", and yet it is noticeable in many instances of life such as in walking, swimming, recoiling of gun, and most importantly, rocket propulsion.

how are physical laws symmetrical?

Similarly, Newton's second law of motion is just, F=ma, but it made possible the industrial revolution. Steam engines, locomotives, factories, machines, all of it due to the mechanics set into motion by the second law of motion.


Same in uniform motion

If we have an experiment working in a certain way and then take the same apparatus, put it in a car, and move the whole car, plus all the relevant surroundings, at a uniform velocity in a straight line, then so far as the phenomena inside the car are concerned, there is no difference.


Unification of laws

Scottish physicist James Clerk Maxwell took a set of known experimental laws such as Faraday's Law, Ampere's Law and unified them into a symmetric coherent set of equations known as Maxwell's equations.

how are physical laws symmetrical?

Maxwell's equations are also laws just like the law of gravity. They govern the behavior of electric and magnetic fields. Also, light itself is an electromagnetic wave. Therefore, Maxwell's equations have in a way unified three separate phenomena, electricity, magnetism and optics, into one.

A similar type of unification occurred in the early part of the 20th century. The laws of conservation of energy and conservation of total mass were proven to be equivalent by German physicist Albert Einstein in a simple equation, E=mc^2.


These unifications are possible because the laws of physics are symmetrical in nature. Two or more distinctly appearing natural phenomena appear to be governed by just one simple law. Thus, one day, we may be able to find an ultimate law of physics that may explain everything.

Renowned American physicist Richard Feynman had famously said, "God is always invented to explain those things that you do not understand."

Throughout history, man has credited god for this or that phenomena. For example, early Greeks believed that lightning was a weapon of Zeus. Now, when you finally discover how something works, you get some laws which you're taking away from god; you don't need god anymore.

Thus, "what one man calls god, another calls the laws of physics," or in other words, to have an understanding of the physical laws is in a way a liberation from all superstition.

How To Study Physics By Using Feynman Technique

how to learn by feynman technique

Richard Feynman was one of the world’s greatest scientists who won a nobel prize for physics in 1965. But we recognize him more as an outstanding teacher, a story-teller and an everyday joker whose life, was a combination of his intelligence, curiosity and uncertainty.

Feynman was once asked in an interview whether an ordinary person could understand physics like him. After a brief pause, "of course!", he replied candidly. "I was an ordinary person who studied hard."

In this post, you will learn to study physics by using the Feynman Technique, a method involving four easy steps, which was designed to help you understand concepts you don't get and to remember stuff you've already learned.

1. Write

how to learn by feynman technique

This is a no-brainer. Always write down everything you know about the topic on a notebook page. Add examples and illustrations in your notes whenever possible.

Why is it important to write? Because writing anything down makes us remember it better. This is also the reason why many life coaches advise to pen down our goals.


2. Explain

Describe whatever you have learned to an empty room. This step will not only test memorization but also help you to become a better teacher.

how to learn by feynman technique

Yes, many of you may not want to go into the teaching profession but it is a good practice to convey your learning in loud words. Remember, teaching is a powerful tool to learning.


3. Analyze

There is a famous saying which many attribute to Feynman, "If you cannot explain it simply, you do not understand it", which is fairly obvious.

how to learn by feynman technique

Did you teach it well? Where is the gap in your understanding? Identify it. Then, revisit your notes for revision.

Revision often increases your confidence because the gap in your understanding is reduced. You may even want to rewrite your notes in a more simple language than before.


4. Repeat

Because of revision, you should have a better grasp of the subject. So gather one of your friends and explain the topic once again, to him/her. This step is powerful because when one teaches, two learn.

how to learn by feynman technique

At the end, take feedback from your friend as that might help in understanding any remaining gaps. Did you know that Professor Walter Lewin, famous for his physics videos on YouTube, used to teach at least five times to an empty hall, before actually taking the class?


Summing up

Feynman had once said, "I don't know what's the matter with people: they don't learn by understanding; they learn by some other way, by rote or something. Their knowledge is so fragile!"

But if you follow what is known as the Feynman Technique, as described here, you will be able to learn more efficiently and firmly. It is a tried and tested method so please share this post with fellow students.

Who was Carl Sagan?

Carl Sagan Biography For Teenagers

As a scientist, Carl Sagan contributed enormously to our knowledge of the solar system. He correctly predicted the existence of methane lakes on Saturn's largest moon Titan. When other astronomers had imagined Venus to be a balmy paradise he showed it to be dry, thick and unpleasantly hot. Carl went on to propose that the atmosphere of the early earth must have contained powerful greenhouse gases.


When she returned, all of Carl's enthusiasm turned into utter disappointment. She had with her a book on the Hollywood stars, wait what, those weren't the kind of stars that concerned an astronomer.

The librarian, a little embarrassed, shifted her attention to a different bookshelf. After searching for a while, she brought with her the correct book, titled, "secrets of the stars". She handed it to the young astronomer. This incident made a deep and lasting impression on a young Carl Sagan.


Career at NASA

Carl Sagan attended the University of Chicago where he came under the guidance of famous physicists such as Enrico Fermi and Edward Teller. As an undergraduate he worked for geneticist H.J. Muller and wrote a thesis on the origins of life.

Carl Sagan Biography For Teenagers

Carl Sagan went on to earn a masters in physics in 1956, before earning a PhD degree in 1960.

Then he became a visiting scientist to NASA's Jet Propulsion Laboratory where he contributed to the making of the first Mariner orbiter mission to Venus.

The Mariner Orbiter confirmed his conclusions on the surface conditions on Venus in 1962. He also worked closely with NASA for the successful landing of man on the moon in 1969.


Next, he worked with NASA for the Viking space program which  was set up to explore the habitat and environment of planet Mars. For the first time in human history, a man-made object had landed on an alien world.

Carl Sagan Biography For Teenagers
viking on mars, 1976

However, the viking landing did not receive attention it deserved. The general public was widely unaware of a significant success in the field of space exploration. Was it not important to people? Was it not worth their time? These questions began to haunt Carl's imagination.

Therefore, just two years later in 1978, Carl Sagan began to work for a new TV show, Cosmos: a personal voyage. Its objective was to narrate to people the story of cosmic evolution, sciences and civilization. In 1980, the first episode of Cosmos was aired and became an instant hit.


Cosmos

Using the word "cosmos" rather than the word universe implies viewing the universe as a complex and orderly system; the opposite of chaos. Nobody had ever explained space, in all its bewildering glory, as well as Sagan did.

Carl Sagan Biography For Teenagers
ship of the imagination

Cosmos was seen in over 60 countries by more than 500 million people. It was the biggest show of the eighties.

In the fifth episode of the series, Sagan explained the kind of experiments performed by viking on the surface of planet Mars. The episode ends with the possibility of the colonization of Mars which became inspiration for the likes of Elon Musk.


During the same time, he was also working with NASA for the voyager space program whose mission was to investigate the outskirts of the solar system for signs of life.

Voyager 1, which had completed its primary mission and was leaving the Solar System, was commanded by NASA to turn its camera around and take one last photograph of Earth across a great expanse of space, at the request of Carl Sagan.

This picture is called The Pale Blue Dot.

Carl Sagan Biography For Teenagers
consider again that dot

Our posturings, our imagined self-importance, the delusion that we have some privileged position in the Universe, are challenged by this point of pale light.

The earth is a lonely speck in the great enveloping cosmic dark. In our obscurity, in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves.


People's Astronomer

Through his appearances on TV and eloquent writings, he has shown many a times how space humbles as well as lifts. He brought astronomy into our living rooms.

Today, the word "cosmos" is on everyone's lips thanks to Carl Sagan. He made astronomy more accessible to people by popularizing it.

Carl Sagan Biography For Teenagers

In fact, Carl Sagan turned astronomy into a deep spiritual experience.

That we are not different from space but a little part of it, made from it. The nitrogen in our DNA, calcium in our teeth and iron in our blood were first forged in the interiors of the dying stars. That we are the star-stuff contemplating the stars is well and truly a great spiritual realization.

Top 10 Experiments in Physics History

all time top 10 experiments conducted in physics
Great physics experiments (image of science museum London)

Physics is an exploratory science. New experiments in physics change or expand our existing knowledge in one way or another. Let us find out how this has happened in history.


10. Galileo's Tower of Pisa experiment

Before Galileo, a majority of people used to follow the teachings of ancient Greek philosopher, Aristotle, who had proclaimed that different weights when dropped from same height experienced different amounts of attraction from the Earth thus falling at different speeds.

It is said that in 1589 Galileo climbed atop Tower of Pisa and dropped two objects of different masses in order to debunk Aristotelian belief.

all time top 10 experiments conducted in physics

In 1971, astronaut David Scott re-created Galileo's famous experiment on the moon by dropping a hammer and a feather simultaneously. You can watch it happen in this clip.



9. Faraday's law of induction

A sudden movement of a magnet through a coil produces a reading on the galvanometer meaning that a changing magnetic field can induce an electric current in the coil.

top 10 experiments conducted in physics

This observation was first made by Michael Faraday in the year 1831. Today, electric generators use the same principle to convert mechanical energy into electrical energy that powers our household electric appliances.


8. Michelson Morley experiment

Does light, like other waves, require a medium to travel? Scientists of the 19th century thought so. They proposed the existence of an invisible stationary substance permeating through all of space that they named aether.

top 10 experiments conducted in physics

In the 1880s, American physicist Albert Michelson thought of discovering the aether.

If aether really exists, Earth moving through it would cause a wind in the same way that there seems to be a wind outside a moving car.


To a person in the car, the air outside the car would seem like a moving substance. In the same way, aether should seem like a moving substance to things on Earth.

Michelson designed an interferometer to measure the speed of the "aether wind" in 1887 along with one of his colleagues, Edward Morley.

top 10 experiments conducted in physics

However, no aether wind was detected by the experimental setup making it the most famous failed experiment in history. But, it had been shown that light required no substance medium whatsoever to travel in space.


7. Double slit experiment

Newton believed that light was a stream of energy-carrying particles. But he was proven wrong by Thomas Young, in 1801, who demonstrated with experiment that light was a wave.

top 10 experiments conducted in physics

In this experiment, when light emitted from two sources is forced to interfere, an unexpected pattern is formed on a distant screen. This interference pattern can be explained by wave theory of light only.


6. Discovery of electron

The atom was greatly regarded as the smallest possible structure in the universe. In 1897, however, Joseph Thomson performed a groundbreaking experiment suggesting that atom was divisible.

top 10 experiments conducted in physics

Thomson used a cathode ray tube, which is a vacuum-sealed glass tube with a cathode and anode fixed inside it. A beam of electrons was observed to move from one end to another upon the application of high voltage.

Thomson also identified that electron was not electrically neutral because he observed a deflection in the beam when an external electric field was applied.


5. Photoelectric effect

top 10 experiments conducted in physics

In 1887, German experimental physicist Heinrich Hertz stumbled upon an amazing phenomenon, the photoelectric effect. He discovered that certain metal electrodes when illuminated by the UV light produced electric sparks.

Two decades later, Einstein proposed an explanation of the photoelectric effect using a concept first put forward by Max Planck that light waves consist of tiny bundles or packets of energy known as photons or quanta.


4. Davisson Germer experiment

top 10 experiments conducted in physics

It was proposed by physicist Louis de Broglie that matter had particle as well as wave nature simultaneously. Davisson and Germer set about to test de Broglie's hypothesis in laboratory.

If electron could behave like a wave, it could interfere with another electron wave much like the light waves do. In 1925, the duo succeeded in obtaining interference pattern.

top 10 experiments conducted in physics


3. Gravity probe b

This was a satellite-based experiment which was launched on 20 April, 2004 by NASA. Its mission was to measure the space-time curvature around the earth as proposed by Einstein. Total cost of this project was about $750 million.

top 10 experiments conducted in physics

This was accomplished by measuring the tiny changes in the direction of spin of four gyroscopes contained in the satellite. Initial results confirmed the expected geodetic effect to an accuracy of about 1%.

2. Higgs boson discovery

The Higgs field is a field of energy that is thought to exist in every region of the universe. The field is accompanied by a fundamental particle known as the Higgs boson, which is used by the field to continuously interact with other particles, such as the electron.

top 10 experiments conducted in physics
Higgs interaction

In 2012, the particle was finally discovered. Peter Higgs became a worldwide sensation and a Nobel Prize winner.


1. LIGO experiment

The Laser Interferometer Gravitational-Wave Observatory is a large-scale physics observatory which was designed to detect cosmic gravitational waves as predicted by Einstein's general theory of relativity.

top 10 experiments conducted in physics

By 2017, LIGO had made five detections of gravitational waves, the first four of which were because of colliding black hole pairs. The fifth event, on August 17, 2017, was the first detection of a collision of two neutron stars.

How To Find Meaning in Life With Physics And Comedy


Einstein had once said, "Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute." That was him describing his famous theory of relativity, but if you've chuckled to yourself after reading it, then you are in good company.

Because according to physicist and comedian Rupesh Mahore, physics and comedy have helped him find purpose in life. How so?



Like others in India, Rupesh was brought up (and trained) to believe that engineering was the most respected profession ever. After many years of severe hard work, he managed to enter one of the top institutes in the country, IIT-Delhi.

And to pursue what again? A bachelors degree in textile technology; Rupesh didn't even know if that was a thing, to be honest!

Fast forward to today: Rupesh is a physics student at NIT Rourkela instead, and at the same time, one of the popular faces in Eastern India's comedy circuit, having shared the stage with likes of Zakir Khan, Atul Khatri, Sorabh Pant and others!

A trio of comics

Leading English daily The Times of India has described his humour as "intellectual and authoritative". But besides being a comic, Rupesh is an educator as well.

He says, "When teaching physics, there is deep honesty and integrity if I am able to deliver fundamentals of the universe to a student and give a better perspective to it."

Rupesh has worked under the guidance of Professor H.C. Verma, best-selling author of Concepts of Physics. Considering his research on materials science, Rupesh has been selected to work at Indian space agency's Laboratory of Electro Optical Systems (LEOS) where he would be working for the mission of Chandrayaan-2 and Gaganyaan.

With Professor Verma



But in order to be where he is at today, Rupesh has had to make bold decisions in the past. He dropped out of engineering college in 2016, "If it wasn't for physics, I wouldn't be here," Rupesh adds.

Convincing his family and asking for their support was a difficult phase in life. Talking about it further, he says, "In India, students and their guardians are not aware of the diverse range of career choices available, which has led to students ending up in a flock. We need to see sciences and arts in the right manner to actually live the best life possible."

After dropping out, Rupesh started teaching physics to high school students in his locality earning a bare minimum. Then, one thing led to another and he began performing on stage.

canvas laugh club

In the midst of recognition and fame on stage, Rupesh did not forget his love for physics. To carry out his interests in it, he joined the course of integrated physics at NIT in Rourkela. Here, he completed writing his first research paper on nano-fabrication.

Rupesh says, "For me, physics has allowed me to understand the world for better and stand-up comedy a liberating art form has given me solace." Clearly, his example is enough to inspire any physics student (who also has some sense of humour).

A Universe of Atoms, An Atom In The Universe

poem an atom in the universe by richard feynman

American physicist Richard Feynman was a man who always jumped into an adventure. He was an artist, a story-teller and an everyday joker whose life was a combination of his intelligence, curiosity and uncertainty.

In the summer of 1955, Feynman wrote a poem about the earth and its development as a planet of activity, of living things and ultimately of beings who would be able to think and wonder. This poem came right after the discovery of Miller-Urey experiment.


Feynman says,

I stand at the seashore, alone, and start to think.
There are the rushing waves
mountains of molecules
each stupidly minding its own business
trillions apart
yet forming white surf in unison.

poem an atom in the universe by richard feynman

Ages on ages,
before any eyes could see
year after year,
thunderously pounding the shore as now.
For whom? For what?
On a dead planet
with no life to entertain.

Never at rest
tortured by energy
wasted prodigiously by the sun
poured into space.
A mite makes the sea roar.

Deep in the sea
all molecules repeat
the patterns of one another
till complex new ones are formed.
They make others like themselves
and a new dance starts.


Growing in size and complexity
living things
masses of atoms
DNA, protein
dancing a pattern ever more intricate.

Out of the cradle
onto dry land
here it is
standing:
atoms with consciousness;
matter with curiosity.

Stands at the sea,
wonders at wondering: I
a universe of atoms
an atom in the universe.

poem an atom in the universe by richard feynman

In a free verse poem Feynman has demonstrated once again the great extent of his intellect and imagination.

Earth was once a lifeless planet.

A whole lot of activity was still made possible because of the presence of the sun. This went on for "ages and ages" meaning for the amount of time we cannot comprehend since we can only think about in days, weeks and months.


Then, deep in the sea, under conditions as described by British-Indian biologist Haldane, a whole range of organic molecules began to mature as discovered by Miller-Urey experiment in 1952.

A whole lot of activity happened in a distant past to give birth to creatures who could think and wonder today. Feynman ends the story by saying, "My mortal body is indeed a universe of atoms but I am just an atom in the universe myself," which is a great realization.

10 Greatest Women Physicists You Didn't Know

10 greatest women physicists on international women's day

Planck, Einstein, Bohr, Heisenberg, Dirac, Feynman and we can go on and on. You all identify them very well as the heroes of physics and astronomy.

It is however a disappointing fact that the sheroes of physics and astronomy remain uncelebrated still. So, we feel it duty to bring to you a list of ten greatest women physicists.


10. Lisa Randall


Lisa researches particle physics and cosmology at Harvard University, where she is a professor of theoretical physics. She contributed to the Randall–Sundrum model with Indian-American physicist Raman Sundrum.

10 greatest women physicists on international women's day

Randall-Sundrum model in physics describes the various aspects of particle physics, for instance, supersymmetry, in terms of a warped-geometry higher-dimensional universe. First published in 1999, this model of the universe has since generated thousands of citations.

Lisa explained her most acknowledged work at a non-technical level in the book, Unraveling the Mysteries of the Universe's Hidden Dimensions, which went on to become world's first successful book on theoretical physics by a female author.

9. Helen Quinn


Helen is an Australian-born particle physicist and educator known for contributions to both fields.

10 greatest women physicists on international women's day

Working with Howard Georgi and Steven Weinberg, Quinn showed how the three types of particle interactions which look very different as we see their impact in the world around us, become very similar in extremely high-energy processes.

Her most significant contribution to theoretical physics include the Peccei-Quinn theory which implies a matter-antimatter symmetry and the possible source of the dark matter that pervades the universe.


8. Jocelyn Bell


Jocelyn Bell Burnell is an Irish astrophysicist who discovered the first radio pulsar, a highly-magnetized rotating neutron star, in 1967. She was a postgraduate student at the time of discovery.

10 greatest women physicists on international women's day

She helped in building the 16,000 m² radio telescope over two years and was the first person to notice the anomaly, sometimes reviewing as much as 29 meters of paper data per night.

Her discovery was recognized by the award of the 1974 Nobel Prize in Physics, but despite the fact that she was the first to observe the pulsars, Bell was excluded from the recipients of the prize.

7. Chien-Shiung Wu


10 greatest women physicists on international women's day
Chinese experimental physicist

She is best known for conducting the Wu experiment, which contradicted the most revered law of conservation of parity. This discovery resulted in her colleagues Lee and Yang winning the 1957 Nobel Prize in physics. Wu was not publicly honored until 1978.


6. Vera Rubin


American astronomer Vera Rubin uncovered the discrepancy between the predicted angular motion of galaxies and the observed motion, by studying galactic rotation curves.

10 greatest women physicists on international women's day

By observing the minor deviations from Hubble's law in galaxies, Rubin provided evidence for the existence of galactic superclusters. Her most significant discovery was providing the first evidence for dark matter.

Vera Rubin spent her life advocating for women in science and was known for her mentorship of aspiring women astronomers.


5. Lise Meitner and Andrea Ghez


Position 5th is a tie: Along with long-time collaborator, Otto Hahn, Austrian-Swedish physicist Lise Meitner led a small group of scientists who became the first to discover the nuclear fission of Uranium.

10 greatest women physicists on international women's day

Otto Hahn was recognized with 1944 Nobel Prize in Chemistry but Meitner's contributions overlooked. Today, nuclear fission is used to produce electricity in the nuclear power plants.

According to Physics Today, Meitner's exclusion from the most coveted award may well be summarized as a mixture of disciplinary bias, political obtuseness, ignorance, and haste.

Andrea Ghez is an American astronomer, who is known for her research on Milky Way galaxy. She has won the Nobel Prize for physics and is only the fourth woman to win the highest honors.


4. Donna Strickland


10 greatest women physicists on international women's day
Canadian physicist

Donna is a pioneer in the field of pulsed lasers and winner of the Nobel Prize in physics in 2018 for the invention of chirped pulse amplification.

Its creation has enabled doctors to perform millions of corrective laser eye surgeries. She said that after developing the technique they knew it would be a significant discovery.

She became the third woman ever to be awarded Nobel Prize in Physics, after Marie Curie in 1903 and Maria Goeppert Mayer in 1963.


3. Maria Goeppert Mayer


Maria Goeppert was a German-born American scientist and Nobel prize winner in Physics (1963) for proposing the nuclear shell model of the atomic nucleus.

10 greatest women physicists on international women's day

The nuclear shell model is a model of the atomic nucleus which uses the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels.


2. Emmy Noether


Emmy Noether was a German mathematician known for contributions to theoretical physics. She was described by Albert Einstein as the most important woman in the history of mathematics.

As one of the leading mathematicians of her time, she developed the theories of rings and fields in abstract algebra. In physics, Noether's theorem explains the connection between symmetry and conservation laws.

10 greatest women physicists on international women's day

When she was recruited by University of Göttingen, one faculty member protested, "What will our soldiers think when they return to the university and find that they are required to learn at the feet of a woman?"


Completely unegotistical and free of vanity, she never claimed anything for herself, but promoted the works of her students above all. A teacher of such quality is not readily available these days.


1. Marie Curie


10 greatest women physicists on international women's day
Polish physicist and chemist

Marie SkÅ‚odowska Curie was denied admission to college because she was a woman, but she persisted, and went on to become the only person in history to win Nobel Prize in two different sciences.

Her achievements included the development of the theory of radioactivity, a term that she coined, techniques for isolating radioactive isotopes, and the discovery of two elements, polonium and radium.

10 greatest women physicists on international women's day
Pierre and Marie Curie

While a French citizen by marriage, Marie never lost her sense of Polish identity. She named the first chemical element she discovered, Polonium, after her native country.

She had famously said, "Life is not easy for any of us, but what of that? We must have perseverance and above all confidence in ourselves. We must believe that we are gifted for something, and that this thing, at whatever cost, must be attained."
© 2019-2022
made with by vedang