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A Geiger Counter January 28, 2012

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In my first class of the new semester, Modern Physics Lab, I finally learned about something that has intrigued me for quite some time: The Geiger Counter.

Begin at 8:40

I first heard of the Geiger Counter during an interview with Dr. Michio Kaku of CUNY City College. He mentioned it as he was describing the famous thought experiment of Schroedinger’s Cat. This thought experiment involves the decay of a radioactive atom which is detected by the Geiger Counter. Eventually, I learned that Geiger Counters measure radioactivity of radioactive materials.

In my Modern Physics Lab class, I learned how it actually worked though. A Geiger Counter typically consists of a metallic cylinder, known as a Geiger, with an opening at one end of its circular surface, known as the window. The inside of the cylinder has a rigid metallic wire running down the center and the cylinder is filled with a gas of some sort. The window is covered with a thin piece of material to prevent the gas from escaping.

When you point the probe in the direction of a radiation source, the radiation from the source travels via electromagnetic waves (such as gamma rays). These waves pass through the window, into the cylinder, and come in contact with the gas. The energy of these waves is sufficient to knock off electrons from these gas atoms (i.e. they “ionize” the gas). These freed electrons then in turn knock off other electrons of the surrounding gas atoms, creating an avalanche effect. The wire is connected to a high voltage source that makes the wire positively charged. Since it is positively charged, the freed electrons become attracted to the wire, and eventually they come in contact and the electrons travel along the wire to the rest of the device. Usually, the wire is connected to a microphone that turns the traveling electrons, or electrical current, into a sound vibration. That’s why if you’ve seen a Geiger Counter, you hear the crackling/popping noise when it is pointed closely to a radiation source.

If you come in contact with a Geiger Counter one day, you can still use it even if you are not in the presence of any obvious radiation source. Just point the counter towards the sky and you are bound to hear a few clicks. This is because the Earth is constantly hit by radiation all of the time in the form of cosmic rays. These are equally capable of setting off the Geiger counter.

My Professor had exactly one of these types of Geiger Counters yesterday that he showed the class. He played a nice trick on us by borrowing a student’s pack of cookies and placing it on a plate. The counter starting crackling quite loudly and he had us believe that the cookies contained radiation. It turned out though, that the plate he placed them on was actually made in Russia and contained some radioactive material in it.

Book Review: Death By Black Hole January 16, 2012

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Over the summer, I had the incredible privilege of meeting Dr. Neil deGrasse Tyson, astrophysicist and Director of the Hayden Planetarium of the American Museum of Natural History. I, along with my fellow Fellows of the Jeannette K. Watson Fellowship program, had a private seminar at the planetarium in his conference room. Before this meeting, I bought his book Death By Black Hole and took the opportunity to get it signed.

I began reading it during this winter break and have just completed it. It was a fun and enlightening read overall. The format of the book is mostly a collection of previous essays that Dr. Tyson has written and it is divided into chapters accordingly. Therefore, I found the transitions between each chapter a bit rough and sudden. I felt better bridges could have been built between the chapters, illustrating how the ideas/concepts discussed in one lead or relate to the next.

The other major question I had throughout was why he titled the book Death By Black Hole, as only one chapter covers this morbid, yet incredibly fascinating phenomenon. The book is primarily a discussion of astrophysics and the important events in history that lead to the development of the field, along with mentions of other scientific fields as well. My first impression by looking at the title was that the book would be an in-depth qualitative discussion of black holes.

Aside from those two concerns, I found the rest of his book informative and fun to read. Dr. Tyson certainly covers a wide range of important developments in science as well as cosmic phenomenons. A passage I enjoyed concerned Tyson’s thoughts on America’s declining role as a major leader in scientific research. He discusses the project that was canceled by Congress, known as the Super Conducting Super Collider (I would call it (SC)^2). The SC^2 was to be the most powerful particle accelerator ever created that would enable scientists to replicate the early conditions of the Big Bang, and perhaps understand how and why the universe came to be what it is, and not assume some other configuration. Tyson writes:

But in 1993, when cost overruns looked intractable, a fiscally frustrated Congress permanently withdrew funds for the $11 billion project. It probably never occurred to our elected representatives that by canceling the Super Collider they surrendered America’s primacy in experimental particle physics.

If you want to see the next frontier, hop a plane to Europe, which seized the opportunity to build the world’s largest particle accelerator and stake a claim of its own on the landscape of cosmic knowledge. Known as the Large Hadron Collider, the accelerator will be run by the European Center for Particle Physics. Although some U.S. physicists are collaborators, America as a nation will watch the effort from afar, just as so many nations have done before.

With the exception of the rather bleak but realistic outlook of this passage, Tyson’s enthusiasm and love of the cosmos is evident throughout the book. His pedagogical nature and at times humorous writing style will provide readers a basic understanding of the universe in a laymen fashion.

Earth’s Invisible Defender – The Magnetic Field January 9, 2012

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Earth’s magnetic field is a tireless guardsmen, protecting the inhabitants of its planet always. People often take it for granted and many do not even know it exists. To appreciate it, let us first understand what a field is. Physicists are very careful and precise about how they define things, so it is a bit difficult to formally define a magnetic field. But I can give you a qualitative understanding, or at least, a mental picture of it.

A field is the area of influence exerted by a force. Let’s take the force of gravity for instance. Back then, scientists knew that the planets orbited the Sun because the Sun exerted a gravitational force on them. It was almost as if the Sun was pulling on these planets. But the idea of an object, as if by magic, reaching out through space and instantaneously pulling on another object was absurd. To resolve this, the concept of a field was created. Imagine you had a source, that emitted this invisible “stuff” until it filled up all space. At different points in space, you would feel a certain amount of force from this source because everything is immersed in this “stuff.” This “stuff” is the field. Take the Sun as our source for example. It is a source of gravity, and the sun emits a gravitational field throughout space. If you stood close to the sun, you would feel its gravitational force (a strong one). If you stood farther away from the sun, you would still feel its gravitational force, but it might feel a lot weaker. This is why a field is considered the area of influence exerted by a force.

Magnetic fields behave similarly, except the source of a magnetic field is charges in motion (i.e. current) rather than a Sun. Therefore, if Earth has a magnetic field, there must be a source of moving charges that is generating it. Where is that source you may ask? It is believed to be coming from the Earth’s core, which is composed of mostly molten iron. The flow of liquid iron creates electric currents in the core and this creates a magnetic field around the Earth, otherwise known as the magnetosphere.

The magnetosphere is invisible to our eyes but it plays a very important role in protecting the earth against solar wind, which is a stream of charged particles (mostly electrons and protons) that is ejected from the surface of the Sun. Only charged particles are affected by magnetic forces when they enter a magnetic field. So when solar wind strikes the Earth, the magnetosphere deflects all of the charged particles away, leaving the Earth’s surface safe. If there were no magnetosphere, solar wind would damage power stations leaving everyone without electricity for months. Food would spoil and people would starve.

While the magnetosphere is associated with this morbid doomsday scenario, it can also be attributed to one of nature’s most incredible spectacles: aurora borealis, or more commonly known as the northern lights. These are the spectacular aurora displays of dancing colorful nights that usually occur at the north and south poles. These lights result when solar wind particles collide with oxygen and nitrogen atoms in the Earth’s atmospheres at high energies. These collisions excite the electrons of the oxygen and nitrogen atoms and cause them to release certain colors of light as the electrons return to their ground states. The following chart shows what colors correspond to which atoms:

Green – oxygen, up to 150 miles in altitude
Red – oxygen, above 150 miles in altitude
Blue – nitrogen, up to 60 miles in altitude
Purple/violet – nitrogen, above 60 miles in altitude

These lights primarily occur at the Earth’s poles because the magnetic field is weaker at the poles than any other part. Solar wind particles tend to collect here whereas they are strongly deflected at other parts of the magnetosphere.

VIDEO: Amazing Northern Lights Time Lapse

The Physics of the New Year December 31, 2011

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As December 31st comes to end, when the clock strikes midnight, the Gregorian calendar is reset to January 1st and another year begins. As you may have noticed, we do this every 365 days. Something must be repeating itself annually to represent the start of this new cycle. Obviously, it is a representation of the complete revolution of the Earth about the Sun.

It takes the Earth approximately 365 days to revolve around the sun. But where does this number come from? In math and physics, there is a way to mathematically represent periodic systems, i.e. systems that repeat in a regular pattern. In physics, if you have a system where an object goes around in a circle, that system has a certain period, because there’s a certain amount of time it takes the object to leave one position and return to the same position. The period is represented by T. The orbits of planets are such systems and so they have a period too. It turns out that the period of an orbiting object depends on the speed of its orbit.

To find the period of the Earth, you would have to apply Newton’s law of gravitation and his 2nd law of motion. Newton’s 2nd law simply says that the forces acting on an object are equal to the mass of the object times its acceleration, F = ma. His law of gravitation says that the gravitational force between two bodies depends on their masses (their size) and the distance between them.

According to his 2nd law, we must set the gravitational force equal to the mass of the planet times the centripetal acceleration, a = v^2/R. If we solve for v, we get the orbital speed, and since the period depends on the orbital speed, we can also find the period of the orbit. Plugging all the values in such as the gravitational constant G, the mass of the sun M, and the distance of the earth from the sun R, we can calculate the value of T which comes out to be 365.5 days.

Isn’t that just amazing? Isn’t it just so incredible that with a sheet of paper and a pencil, the laws of physics gives us insight into the motion of heavenly bodies and enable us to predict something as grand as the time it takes this planet to revolve around the sun? This is the power of math. This is the power of science. Happy New Year to you all.

Albert Einstein – His Work, His Contributions, His Legacy December 25, 2011

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Albert Einstein is a household name, but few know of his work and his role in science.

When I was younger, my perception of Einstein was that he was a mad scientist who conducted all kinds of crazy experiments that led to his trademark frizzy hairstyle. But this could not be further from the truth. For Einstein was a theoretical physicist rather than an experimentalist. The only materials he required for his research were paper and pencil.

In his early years, Einstein worked in a patent office in Bern, Switzerland. Everyday, he would come into work, quickly analyze the patent applications on his desk, and proceed to secretly work on questions in theoretical physics of the day. It was here that he developed his famous theory of Special Relativity.

Relativity is one of the fields that gave rise to the Modern Physics revolution. Classical physics explains common human experiences such as falling objects, friction, electricity, and magnetism through Newton’s laws of motion and through the principles of Electromagnetism. Modern Physics explains events that are not common to our everyday experiences, such as objects traveling close to the speed of light and behaviors of atoms.

Special Relativity tells us that space and time are not static, but stretchy and dynamic. When Isaac Newton formulated his laws of motion, it was believed that time was constant throughout the universe, meaning the way one experiences time on Earth experiences it the same way on Mars. Time was seen as an arrow that when fired traveled in the same direction indefinitely. However, Einstein’s theory of Special Relativity told us otherwise. Time is not constant. People experience time differently. This was a completely non-intuitive way of understanding the universe and it shook the foundations of physics.

Special Relativity simply tells us that people in different reference frames experience things differently. Everything is relative, not absolute. Therefore, space and time are relative. The theory requires that nothing travel faster than the speed of light. But if you travel close to the speed of light, then very weird things begin to happen. Time slows down for you, and space compresses. These phenomenons are called Time Dilation and Length Contraction. Let’s suppose you stood on Earth, and I was in a space ship flying close to the speed of light past Earth. Suppose you were able to see exactly what I was doing in the space ship. If I were doing jumping jacks at a normal pace, you would actually see me doing it very very slowly. This is because time has slowed down for me in your reference frame. To myself, I would feel as if I were doing jumping jacks regularly. Not only would you see me doing jumping jacks slowly, you would notice that I am a lot thinner and contracted, like squeezing a picture together in Photoshop. This is a very bizarre and strange idea, but the mathematics indicates this.

You might say well that is nice that the math shows this, but it is all just a theory. But in fact, these effects have been experimentally verified. They tested time dilation by synchronizing two very precise atomic clocks so that they ticked in unison. One clock they left on the ground and the other they put on a PanAm aircraft. They flew this aircraft around the world in the direction of the Earth’s rotation to give it extra speed and when they brought back the clocks together, they measured the difference and the time difference was exactly the amount predicted by Einstein’s theory. Relativity has practical uses today too. You unknowingly experience these phenomenons when you use your smartphones or gps systems to navigate yourself through the world. GPS signals are provided by satellites orbiting the Earth. These satellites travel at very high speeds and as a result, they are affected by time dilation. To make sure they are synced properly, their clocks must be corrected to take these effects into account. Without Relativity, your GPS would be useless. Relativity is real.

Einstein’s contributions extend far beyond his theory of Special Relativity. His other work includes General Relativity, the Photoelectric Effect, theoretical foundations in lasers. One could write volumes about his work, and covering it all in one blog post would be too exhausting. This is but a taste of one of Einstein’s most important contributions to physics. With it, his legacy will continue to echo throughout generations to come.

VIDEO: Einstein’s Relativity – Time Dilation

The New American Dream December 11, 2011

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My parents, and I would bargain the parents of most of my fellow Chinese, have made it through difficult challenges when they first immigrated here from China.

My father came here a poor man. He settled and he immediately looked for work which he contributed all of his earnings to his college education. He told me that he used to love eating peanut butter sandwiches but since that was the only thing he ate for a long time, because it was so cheap, he eventually got sick of it.

The only asset he had was his ability to speak English, which was a huge advantage over other immigrants. He worked in a restaurant, went home late to a dangerous neighborhood, studied for his Master’s, and went to classes. He faced other challenges along the way such as getting mugged, getting burned by a searing hot pan, and other hardships I can hardly imagine.

But eventually, he graduated, married my mother, had me and my sister, got a job at a Japanese company, got a teaching job, and bought a home and a comfortable life for his family. Considering the conditions of his own childhood background, he achieved the American dream and did his family proud. He has instilled in me a value of hard work, respect, and intelligence. Now, he and my mom have paved the way for me and my sister so that we may both live better lives.

But now that we have food, clothes, shelter, healthcare, and all these other luxuries that children like when my father was a child could barely comprehend, what does my generation have left to achieve? What is defined by a better life? Food, clothing, shelter, the basic necessities? Is it a good paying job as most Asian parents hope of their children? Have we hit the end of the road and reached the good life? Or is there another challenge that my Chinese generation must face in order to lead a better life as our parents hoped?

The challenge that I believe we face now is the glass ceiling. This arose in a discussion I had recently with my father and Uncle Charlie (not my actual uncle). We were talking about my future and career and to sum things up, Charlie is highly practical and encouraged me to pick a job that makes big money, regardless of the emotional fulfillment of the job. I told him I want to be an engineer and he told me to use my math skills as an accountant. He told me that I could not compete with foreign students in STEM fields and that the only advantage I have over them is my ability to communicate effectively in English and I needed to make use of this. I countered him saying that managers of tech businesses need both the tech knowledge as well as the communication skills.

Effectively, he told me that I did not seem like the managerial type. I was not white enough. In this society, the people at the top positions of our job markets are tall, handsome, white people. Even within our own native countries, you see white managers and CEOs in Hong Kong businesses. It is a white dominated world and I have no chance of breaking into that niche. So he encouraged me to aim a little lower than I expected, take the road of least resistance, and live a comfortable life.

Is this really what is expected of the Chinese community, even from those within our own Chinese culture? It is precisely because of this type of mindset that restricts our people from entering the ranks of high society. How are we expected to take on these roles if our own people do not believe we can acquire them? Did the Civil Rights movement take place because Dr. Martin Luther King told his people to aim for jobs as laborers and not as leaders? I am in no way comparing the difficulties of my generation to the difficulties of his, but I am drawing parallels that I see in terms of ethnic challenges that face both of our people.

It was my hopes to simply be an engineer who can build interesting technology and have a fun time doing it. But now I believe that I, and more Chinese of my generation, should aspire to be leaders in our respective fields. I believe we need to innovate and lead so that not only can our Chinese community be represented and recognized in the high ranks of society, but also so that we may serve as role models for the change and the good that we can contribute to the world.

The status quo is unsustainable. So forgive me Uncle Charlie, but I refuse to accept your advice. I refuse to aim lower than my expectations so that I can fill whatever goals I did not achieve with money. I refuse to pursue a career solely for its monetary rewards. I choose to continue on the more competitive path to being an engineer. And I choose to be one of the front runners paving the way for the future of this field. I will do what it takes to show that the Asian people are innovative, creative, strong leaders.

This, I believe, is the new American Dream that we should strive to achieve. Our parents have climbed the financial obstacles to get us to the base of the mountain. Now it is our turn to overcome the social barriers that we face. It’s time to break the glass ceiling and enjoy the view from up top.

Science Details of the Nobel Prize December 4, 2011

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In my previous post, I mentioned that I would go further into the scientific details of the 2011 Nobel Prize in Physics. As a reminder, the winners of the prize, Saul Perlmutter, Brian Schmidt, and Adam Reiss were awarded for their discovery of the accelerating expansion of the universe. This was actually a surprising result that came out of their data, since what was believed for the last century was that the expansion of the universe was decelerating due to the inward pull of gravity.

To measure this supposed deceleration, they needed something known as a standard candle, an object that always shines with the same brightness. For their standard candles, they used Type Ia Supernovae. A supernova is the explosion of a star when it reaches the end of its life. Regular supernovae explode with different brightness depending on the surrounding conditions, making them unreliable standard candles. But Type Ia Supernovae have an interesting property that they always explode with the same brightness.

Type Ia Supernovae are the explosions of white dwarf stars. Near the ends of its lifetime, a star’s outer layer becomes very gaseous and it expands. What remains in the center is a very hot, dense, and white core composed of carbon and oxygen. Water has a density of 1 gram per cubic cm. A white dwarf has a density of 3 million grams per cubic cm. Our sun’s outer layer one day will expand and its circumference would engulf the orbit of the earth and it too will become a white dwarf. Type Ia Supernovae occur in binary star systems, a star system where two stars orbit each other. Since the white dwarf is so dense, its gravity becomes so strong that it sucks the material of its companion star causing the white dwarf to grow. When it grows and reaches the Chandresekhar limit (1.4 times the size of our sun), the white dwarf rips apart and explodes in a blast so powerful it can outshine an entire galaxy. It is believed that white dwarfs get their intrinsic brightness because they only explode when they reach this characteristic limit.

The laureates used two pieces of information of the supernova in order to determine the expansion rate: the brightness and the cosmological redshift. Redshift is a phenomenon where the wavelength of light gets elongated causing it to appear red (red light has long wavelengths, blue light has short). When light travels through space, it gets elongated because space itself is expanding. This causes it to appear red and thus this is cosmological redshift.

By comparing the observed brightness to the intrinsic brightness of the supernova, they determined how far away it was. And using the redshift, they determined how much the universe has expanded since that supernova occurred (as you look farther out in space, you look further back in time). Their plan was to observe supernovae at different distances, therefore different times, and compare them to each other to see how the expansion rate has changed. As you move standard candles farther away from you, they get less bright (imagine a flashlight moving away from you). Since they expected that the universe was decelerating, they also expected that the brightness of the supernova would get less bright more slowly. But what they found was that as they looked further out in space, the brightness became less much faster than they expected. Therefore the only conclusion they could reach was that the universe was expanding at an accelerating rate!

Expansion Into Infinite Oblivion November 20, 2011

Posted by peterxu422 in astronomy, cosmos, Science.
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Can you name 5 Nobel Laureates? It turns out not many people can answer this question. The works of Nobel Laureates are quite remarkable and they make great contributions to society’s collective understanding. Therefore, I feel it is important that I remain aware about the news of the Nobel world, in particular the prize in physics. So let me share with you some fascinating information about this year’s Nobel Winners in Physics and their mind blowing work. It’s literally bigger than anything in the entire universe.

The Nobel Prize in Physics were awarded one half to Saul Perlmutter (UC Berkeley) and the second half jointly to Brian Schmidt (Australian National University) and Adam Riess (Johns Hopkins University) for the discovery of the accelerating expansion of the universe.

It is almost widely known that the universe has been expanding for the last 5 million years. Space itself has been stretching and expanding. Imagine a balloon that has been partially blown up, with the surface representing our universe. If you draw dots with a marker on various locations of the surface, and you blow the balloon again, you will find that the marks are further apart from each other than they were initially. The space between them has expanded. This is the same thing that is happening to our universe. The space between our galaxy and all other galaxies are stretching and we are getting further away from each other. You may ask why is it that we do not notice this stretching on Earth? Locally, the stretching is so small and insignificant that it cannot be noticed. But since the universe is very large, over a lot of space all these contributions add up and become noticeable (think calculus).

Naturally, the second question would be to ask, “How fast is it expanding or how fast is the expansion slowing down?” which was exactly what Perlmutter, Schmidt, and Reiss sought to answer. It was believed that the expansion rate would slow down as the amount of matter accumulates in the universe and as the strength of gravity increases, the inward pull of gravity would slow down the expansion, eventually to a stop, and if powerful enough, revert the expansion and cause the universe to collapse in on itself in a Big Crunch.

The three measured this by using the brightness of Type IA supernovas (explosion of stars near the end of their lifetime) which are explosions of white dwarf stars. They also used the redshift of these stars to determine how fast they were moving away from the Earth. With these two pieces of information, they would be able to determine how fast the universe is accelerating. But their results showed that the brightness that they observed was less than what they expected, which meant that the universe’s expansion is not slowing down, but speeding up. Space itself was getting stretched faster. The laureates were actually on competing teams attempting to answer the same question, Perlmutter on one team and Schmidt and Riess on the other. Their results were so astonishing that the two teams needed to confirm each other’s results in order for it to be accepted by the scientific community.

The result of the accelerating expansion of the universe carries enormous implications. As space expands, the distance between galaxies are expanding faster and faster too. Galaxies are rushing away from us so quickly than in the distant future, their light will not even be able to reach the Earth. The universe will become a cold dark and lonely place and future astronomers will only be aware of the existence of other galaxies by the textbooks that described them in the past. The universe will not end in a Big Crunch, but a Big Rip as the expansion rate speeds out of control and rips the fabric of space time. Like a balloon being filled too quickly until the rubber membrane which holds its form tears.

Aside from this morbid interpretation, their work has also opened the doors to exciting new questions and discoveries in physics. For example, the real question was, what is driving this accelerating expansion? There must be some kind of energy in the vacuum of space that is counter-acting the inward pull of gravity, and this energy must be a lot stronger than all of the gravity in the universe. As a placeholder for this mysterious energy, physicists have dubbed it Dark Energy. Dark Energy makes up 75% of the entire universe. Another 20% is to another mysterious substance called Dark Matter, and the last 5% is to all physical matter. That means the total material composition of the stars, galaxies, planets only make up a small fraction of the composition of the entire universe. Physicists don’t know what is Dark Energy, and they cannot see it (hence ‘Dark’), but they know it’s there.

The work of Perlmutter, Schmidt, and Reiss has changed our outlook on the universe. Whether their work will have any practical applications in our life is not explicit. But the spirit of science is not to make a profit off our power to manipulate nature. It is about the quest to understanding nature through reasoning, experimentation, and asking questions. Perlmutter, Schmidt, and Reiss have certainly given us some fun questions to think about. Congratulations to the Nobel Laureates.

In my next post, I will explain in a bit more detail the actual science behind the work.
VIDEO: Dark Matter

What Is Calculus About? November 13, 2011

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For those of you who have studied calculus, how many of you have asked yourself this question? I first learned calculus at Brooklyn Technical High School in my AB Calculus class taught by an excellent teacher named Mr. Raftery.

But while I knew the algorithmic steps behind taking limits, finding derivatives, calculating integrals, I did not quite understand what was the motivation and purpose for calculus. It was not until I went well into my math and physics courses in college that I realized what it is about.

Calculus was invented at roughly the same time independently by two people, the mathematician Gottfried Leibniz and the great mathematician, physicist Sir Isaac Newton. Everyone knows the famous story of the apple falling on Newton’s head that lead him to realize that the force bringing the apple to the ground was the same force as that which governed the motion of the planets. In order to describe this phenomenon mathematically, Newton invented a completely new branch of mathematics (calculus) that would change the way people saw the world.

Calculus takes algebra to a new level. With algebra, we could calculate things that were “easy to work with” such as lines, squares, triangles, etc. But as we all know, the real world is much more complicated than this. The real world consists of curves, changes, and weird geometries. Calculus empowers us to calculate and identify the rich mathematical properties of these irregular forms. It does this by considering changes in the structure or form that are infinitesimally small, meaning smaller than anything you can think of greater than 0. By looking at things in infinitesimally small changes and combining their contributions, you can learn about complex systems without examining the irregularities head on.

To further illustrate the idea behind calculus, imagine I have a nice straight line and a very nasty confusing curve and I want to find the lengths of both. For the straight line, this is trivial. I take a ruler and measure it. To measure the curve is not as simple. But what I can do is zoom in on a very very tiny segment of the curve, so tiny that it almost a perfectly flat line. This I can measure. I do this for every other segment on the curve until I measure the whole thing. Then I add all of their contributions and I get the length of this complicated shape. The tinier I take these segments, the more accurate the measured length will be. This is the idea behind calculus. You look at small changes and see how they contribute as a whole. Calculus is about finding the behavior of continuously changing systems. This was an ingenious way of looking at the world, and it eventually changed it.

The main application of calculus was initially to physics. Back then, if I dropped a ball from the top of my house and I wanted to know its speed, I would take the distance it fell and divide it by the time it took to fall and I would get the speed. But this is only the average speed. Calculus enables us to find the exact speed at any point of the ball’s fall, and the ball’s speed is constantly changing since it is accelerated by gravity. It turns out that studying changes in a system reveal interesting properties that enable us to make accurate predictions about how it will behave in the future. Calculus has a broad range of applications to any type of changing system including chemistry, population growth, probability, finance, and statistics.

When I realized its purpose, perhaps a little later than I should have, I developed an incredible appreciation for the field because it was such a creative insight and it revolutionized the world. Its invention has enabled us to warm our homes, power our lives, move our cars, peer into the universe, probe the atom, remain connected in a world of disconnect. It has allowed me to deliver this message to you.

Watch an excellent explanation of the motivation behind calculus starting at 13:20.
VIDEO: Newton’s Dark Secrets

Re-Starting With Why November 3, 2011

Posted by peterxu422 in Business, Entrepreneurship, Science.
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Why. How. What. The Golden Circle rule. A simple concept that could change the way you view your life for the better. The creator of this concept is a man named Simon Sinek, an inspirational speaker and ethnographer, someone whose work I greatly admire. I first became familiar with Simon when I watched a TED talk titled “How Leaders Inspire Action.” It was the most thought provoking and incredible TED talk I have ever listened to. Simon came to speak at my school today and I was lucky to be there for it.

I have watched his TED talk about 3 times already and I was expecting him to speak about similar topics. He talked about the exact same things, using almost the same language. I was already familiar with everything he said today. However, I went there not for the content, but for the subjective energy and connection that I felt in that room on a human level. Simon speaks with confidence, clarity, and complete honesty in what he believes, and that in turn re-inspired my outlook on life.

The main chord he hit that really reverberated within me was understanding what you believe in, being clear about what you believe in, and remaining authentic on how you show your beliefs. This, he believes, is how businesses and people who make impact think.

For the past few months, I lost some motivation to continue my work. It was beginning to pile up, and my mindset was such that I was in it for something else. I fear that I became too focused on the rewards of my work that I began living to wait for the prizes. I wanted to push through and get to the end quickly because I was tired of waiting. My concentration on the result made me less focused on the present, and consequently, made me less motivated to work.

Today, Simon helped get me back on track. He preached that the ultimate fuel for oneself is understanding exactly what they believe and why. It is the difference between someone who gets up and goes to work excited to accomplish something as opposed to someone who gets up and goes to work hoping to get through the day. It is the difference between leaders and those who lead. And when you find those who share your vision and wish to make it theirs, you begin to have the capacity to create movement and impact.

I believe in a world that appreciates science and technology and supports its continued innovation to do good and to further the potential of humankind. This is what gets me up in the morning. This is what gets me to class. This is what gives me hope for a better future. Thanks for coming to Queens College Simon. Please come back at some point. Maybe the next time we meet it will be at Columbia.

Watch an amazing and inspiring talk.
VIDEO: How Great Leaders Inspire Action

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