It's natural for us to see things from a start to and end. The concept of eternity is a mystery for the human mind and it has crept in to mathematics as well. Infinity, as we know, is endless; not an enormous number but a representation of an eternal number.
According to definition of infinity, it's simpler than most things which have a definite beginning and ending because infinity just is and can not be measured. It's use in mathematics has been narrowed down since it can behave like a real number but does not follow the properties of a real number. In fact infinities lie beyond the boundaries of real numbers, - ∞ < x < ∞ where x is a real number.
Some properties that infinity follows are:
∞ + ∞ = ∞
-∞ + -∞ = -∞
∞ × ∞ = ∞
-∞ × -∞ = ∞
-∞ × ∞ = -∞
x + ∞ = ∞
x + (-∞) = -∞
x - ∞ = -∞
x - (-∞) = ∞
x × ∞ = ∞, x > 0
x × (-∞) = -∞, x > 0
x × ∞ = -∞, x < 0
x × (-∞) = ∞, x < 0
Functions never are able to reach infinity, since it's endless, but only reach towards and is known as approaching it's limit.
Problems involving finding limits, as it is well know, is not enjoyable and can mess with one's brain. L'Hopitals's rule attempts to make it easier. The process in l'Hopital's rule involves finding the derivatives of functions which tend to zero or infinity. And generally the derivative of a function is a measurement of it's rate, so it can be assumed that the derivative helps find the rate at which each function in consideration is reaching zero or infinity. When they are being divided, as l'Hopital's rule imposes, the ratio of the rates is being found. At times this rule can cause the problem to go in circles, but with interruptions of the rule the limit can be found.
As much as infinity and bothers us, I believe it's one of the most amazing concepts understood by humans. Because as much as everyone believes in the end of the Universe, I believe the Universe will go on forever and (until we have discovered otherwise) the Big Crunch will not take place.
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By Kowsheek Mahmood
Ryerson University, Toronto, Canada
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The Aftermath Publications, Issue 3
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Friday, March 13, 2009
The Man Every Physicist Wants to Get Married To - Einstein
We all know a thing or two about Einstein’s great works that lofted physics into great heights. But unfortunately we no almost nothing of his life apart form his works. Albert Einstein was born on March 14th 1879, of Jewish parents. He was a shy and curious child.
He attended a rigorous Munich elementary school where he showed an interest in science and math but did poorly in other areas of study. He finished high school and technical college in Switzerland. At the age of 22 he became a Swiss citizen. In 1903 he married
Mileva Marec. They had two sons but were later divorced. He later married his widowed cousin Esla in 1919. Around 1902 Einstein became an examiner in the Swiss patent office at Bern. In 1905 at the age of 26 he published five major research papers in an important German physics journal. He received a doctorate for the first paper. The next four papers that he published changed view of whole of mankind about our universe.
Esla and Einstein
The first paper provided a theory explaining Brownian motion, the zigzag motion of microscopic particles in suspension. Einstein suggested that the movement was caused by the random motion of molecules of the suspension medium as they bounced against the suspended particles.
The second paper laid the foundation for the photon, or Quantum theory of light. In it he proposed that light is composed of separate packets of energy called quanta or photons that had both particle and wave nature. This very paper redefined the theory of light.
A third paper which began with an essay Einstein had written at the age of 16 contained the “Special theory of relativity”. The last of the four papers, the fourth paper was a mathematical addition to the special theory of relativity where he presented his most famous equation E = mc2. These papers established Einstein’s status among the most respected physicists in Europe.
Albert Einstein and Rabindranath Tagore in Berlin, Germany, 14th July, 1930
Einstein and Plank
In 1916 Einstein published his general theory of relativity. In it he proposed that gravity is not a force, a previously accepted theory, but a curved field in the space-time continuum that is created by the presence of mass. Between 1909 and 1914 Einstein taught theoretical physics in Switzerland and Germany. Worldwide fame came to him in 1919 when the Royal Society of London that predictions made in his General theory had been confirmed. He was awarded the Nobel Prize for physics two years later for his work in theoretical physics. When the Nazis came to power in 1933, they denounced his ideas, seized his property and burned his books. That year he moved to USA and in 1940 became an American citizen. His later years would mainly pass by in trying to establish a formula that would explain of the properties of matter and energy. Einstein died in Princeton in April 1955. This was the story of Einstein’s life.
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By Tahsin Uddin Mullick
North South University, Dhaka, Bangladesh
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The Aftermath Publications, Issue 3
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He attended a rigorous Munich elementary school where he showed an interest in science and math but did poorly in other areas of study. He finished high school and technical college in Switzerland. At the age of 22 he became a Swiss citizen. In 1903 he married
Mileva Marec. They had two sons but were later divorced. He later married his widowed cousin Esla in 1919. Around 1902 Einstein became an examiner in the Swiss patent office at Bern. In 1905 at the age of 26 he published five major research papers in an important German physics journal. He received a doctorate for the first paper. The next four papers that he published changed view of whole of mankind about our universe.
Einstein,Gezin,Mileva
Esla and Einstein
The first paper provided a theory explaining Brownian motion, the zigzag motion of microscopic particles in suspension. Einstein suggested that the movement was caused by the random motion of molecules of the suspension medium as they bounced against the suspended particles.
The second paper laid the foundation for the photon, or Quantum theory of light. In it he proposed that light is composed of separate packets of energy called quanta or photons that had both particle and wave nature. This very paper redefined the theory of light.A third paper which began with an essay Einstein had written at the age of 16 contained the “Special theory of relativity”. The last of the four papers, the fourth paper was a mathematical addition to the special theory of relativity where he presented his most famous equation E = mc2. These papers established Einstein’s status among the most respected physicists in Europe.
Albert Einstein and Rabindranath Tagore in Berlin, Germany, 14th July, 1930
Einstein and Plank
In 1916 Einstein published his general theory of relativity. In it he proposed that gravity is not a force, a previously accepted theory, but a curved field in the space-time continuum that is created by the presence of mass. Between 1909 and 1914 Einstein taught theoretical physics in Switzerland and Germany. Worldwide fame came to him in 1919 when the Royal Society of London that predictions made in his General theory had been confirmed. He was awarded the Nobel Prize for physics two years later for his work in theoretical physics. When the Nazis came to power in 1933, they denounced his ideas, seized his property and burned his books. That year he moved to USA and in 1940 became an American citizen. His later years would mainly pass by in trying to establish a formula that would explain of the properties of matter and energy. Einstein died in Princeton in April 1955. This was the story of Einstein’s life.
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By Tahsin Uddin Mullick
North South University, Dhaka, Bangladesh
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The Aftermath Publications, Issue 3
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An Ode to CD
The CD (compact disc) a familiar name to us all, the device that gave us music, video and data storage capacity unparallel to any other previous recording device seen before.
Didn’t it bring us the tears of joy? As history would have it the CD was the combined work of two great warriors of the tech industry. One was Philips and the other was Sony. Each company had introduced a working model of an optical disc in separate dates but later collaborated to produce the master piece we have become so acquainted to.
The basic design of a CD is some what like the diagram below.
A. A polycarbonate disc layer has the data encoded by using bumps.
B. A reflective layer reflects the laser back.
C. A lacquer layer is used to prevent oxidation
D. Artwork is screen printed on the top of the disc.
E. A laser beam reads the polycarbonate disc, is reflected back, and read by the player.
The polycarbonate layer contains bumps as a single, continuous, extremely long spiral track of data. The reflective layer usually aluminum helps in reflecting the laser back. The aluminum is protected by a layer of lacquer to avoid chances of oxidation. At last the lacquer is covered by a design. The CD spirals start at the center and spread outwards.
This when taken into consideration allows CD’s to be smaller than 4.8 inches. The track is made by elongated bumps 0.5 microns wide a minimum of 0.83 microns long and 125 nanometers high and also each track is separated from one another by 1.6 microns. The picture below is a microscopic view of CD bumps.
To read data in such tiny scale requires high degree of precision. Looks like a job for laser man. The drive has three basic jobs to perform , first of is the spinning of the CD which is carried out by the drive motor . The drive motor rotates the disc at 200 to 500 rpm. The second task at hand is that of the laser and a lens system which is to focus and read the data of those very tiny bumps. The third job rests with the tracking mechanism that rotates the laser to mimic the spiral track. The tracking system has to be able to move the laser at micron resolutions.
When a CD is being read, a laser is shown through the polycarbonate layer and reflected off of the reflective material. The reflected laser light is in turn detected by an optical sensor which converts the received laser signal into electricity. Depending on whether the laser was focused on a bump or not, the electrical signal will be different because the reflected laser light will be different. The difference in the electrical signals is how a computer can read data off of the CD. This is how the CD works.Till the next time stay tuned.
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By Tahsin Uddin Mullic
North South University, Dhaka, Bangladesh
----
The Aftermath Publications, Issue 3
----
Didn’t it bring us the tears of joy? As history would have it the CD was the combined work of two great warriors of the tech industry. One was Philips and the other was Sony. Each company had introduced a working model of an optical disc in separate dates but later collaborated to produce the master piece we have become so acquainted to.
The basic design of a CD is some what like the diagram below.
A. A polycarbonate disc layer has the data encoded by using bumps.B. A reflective layer reflects the laser back.
C. A lacquer layer is used to prevent oxidation
D. Artwork is screen printed on the top of the disc.
E. A laser beam reads the polycarbonate disc, is reflected back, and read by the player.
The polycarbonate layer contains bumps as a single, continuous, extremely long spiral track of data. The reflective layer usually aluminum helps in reflecting the laser back. The aluminum is protected by a layer of lacquer to avoid chances of oxidation. At last the lacquer is covered by a design. The CD spirals start at the center and spread outwards.
This when taken into consideration allows CD’s to be smaller than 4.8 inches. The track is made by elongated bumps 0.5 microns wide a minimum of 0.83 microns long and 125 nanometers high and also each track is separated from one another by 1.6 microns. The picture below is a microscopic view of CD bumps.
To read data in such tiny scale requires high degree of precision. Looks like a job for laser man. The drive has three basic jobs to perform , first of is the spinning of the CD which is carried out by the drive motor . The drive motor rotates the disc at 200 to 500 rpm. The second task at hand is that of the laser and a lens system which is to focus and read the data of those very tiny bumps. The third job rests with the tracking mechanism that rotates the laser to mimic the spiral track. The tracking system has to be able to move the laser at micron resolutions.
When a CD is being read, a laser is shown through the polycarbonate layer and reflected off of the reflective material. The reflected laser light is in turn detected by an optical sensor which converts the received laser signal into electricity. Depending on whether the laser was focused on a bump or not, the electrical signal will be different because the reflected laser light will be different. The difference in the electrical signals is how a computer can read data off of the CD. This is how the CD works.Till the next time stay tuned.
----
By Tahsin Uddin Mullic
North South University, Dhaka, Bangladesh
----
The Aftermath Publications, Issue 3
----
A Short History of Astronomy
Astronomy is one of the oldest subjects ever ventured into by ancient scholars and philosophers. Astronomical study was probably first made by the Mayans and the Aztecs either as apart of astrology where the ancients strove to predict the future, or more scientifically in knowing when to sow crops, or as a navigational aid.
Although it is often claimed that the prime scholars and philosophers who studied astronomy had their roots in Babylonian and Egyptian cultures, there is strong evidence to show that the present day astronomy started with the Greek civilization.
EGYPTIANS PLACED TOMBS IN PLACES WITH ASTROLOGICAL SIGNIFICANCE
Early thoughts in Greek astronomy originated from renowned philosophers like Plato or Eudoxus of Cnidus, the ideas of whom were concretely established later by Aristotle (384BC-322BC). Aristotle was one of the most eminent thinkers. He developed a geocentric model of the universe with the earth at its centre and the Heavens above.
Astronomical research then remained suspended for many years, due to its religious obligations until in around AD140, Ptolemy, another Greek resident took the earth centered Aristotle model and endeavored to account for the varying speeds and occasional retrograde motion of the planets. According to Ptolemy, each planet moved in a small circle (epicycle) whose centre moved on a bigger circle (the deferent).
Most of Ptolemy’s work was gathered into a book known by its Arabic title, The Almagest, which means, The Greatest. With Ptolemy’s death, classical western astronomy was slipping into the dark ages.
The Ptolemic model of the universe was not superseded until the arrival of Nikolaus Copernicus (1473-1543), the son of a rich Polish merchant. Copernicus developed a revolutionary model for the universe that was unique in its true sense. He is the one who first established the heliocentric model in which the planets travelled around the sun in circular orbits. Copernican model awakened astronomy form its dark age. All of Copernicus’s ideas were published in a book titles De Revolutionibus Orbium Coelestium (on the revolutions of the celestial spheres). The years following Copernicus’s death were to be a golden era for astronomy as it was only within a thirty year period, three major figures in the field of cosmology and astronomy were born.
Tycho Brahe (1546-1601), a Danish nobleman, made important contributions to observational astronomy by many amazing inventions. His wit and talent was enough to impress the then King Frederick II of Denmark who funded him for his research. Tycho Brahe built the very first observatories and made instruments like the quadrant which could measure the position of stars with remarkable accuracy. Tycho Brahe’s work was further carried on by his student Johannes Kepler.
Kepler deduced three, very important and immensely useful laws which hold true even today!
The laws were mainly based on observation and had no mathematical basis.
1.The orbit of a planet about the sun is an ellipse with the sun at one focus.
2.The line joining a planet and the sun sweeps out equal areas in equal times.
3.A planet’s orbital period squared is proportional to its average distance from the sun cubed.
Can you prove the Third Law using laws of Gravitation and Circular Motion?
Galileo Galilei was born shortly before the birth of Kepler in 1564 in Pisa, Italy. He investigated many aspects of physics and was probably the first astronomer to use telescopes for systematic astronomical observations. Galileo’s contribution to astronomy mainly comprised of early attempts of unifying astronomy with material sciences and inventions of more accurate astronomical devices.
Isaac Newton made astronomy a truly scientific subject. Physics and astronomy were used to be considered as separate disciplines until the time of Newton. Newton was the first philosopher or scientists who attempted for the first unification of celestial objects with that of terrestrial objects. He was successful into showing that it was not separate theories but the same, governing the behavior of objects in the universe. While trying to explain what forces cause the motions of planets, he discovered gravity, an attractive force exerted by all masses on all other masses in the universe. His ideas greatly helped in reducing anomalies and complexities in astronomy.
Most of Ptolemy’s work was gathered into a book known by its Arabic title, The Almagest, which means, The Greatest. With Ptolemy’s death, classical western astronomy was slipping into the dark ages.
The Ptolemic model of the universe was not superseded until the arrival of Nikolaus Copernicus (1473-1543), the son of a rich Polish merchant. Copernicus developed a revolutionary model for the universe that was unique in its true sense. He is the one who first established the heliocentric model in which the planets travelled around the sun in circular orbits. Copernican model awakened astronomy form its dark age. All of Copernicus’s ideas were published in a book titles De Revolutionibus Orbium Coelestium (on the revolutions of the celestial spheres). The years following Copernicus’s death were to be a golden era for astronomy as it was only within a thirty year period, three major figures in the field of cosmology and astronomy were born.
A SIMPLIFIED VERSION OF THE COPERNICAN MODEL
Tycho Brahe (1546-1601), a Danish nobleman, made important contributions to observational astronomy by many amazing inventions. His wit and talent was enough to impress the then King Frederick II of Denmark who funded him for his research. Tycho Brahe built the very first observatories and made instruments like the quadrant which could measure the position of stars with remarkable accuracy. Tycho Brahe’s work was further carried on by his student Johannes Kepler.
MANY OF TYCHO BRAHE’S INVENTIONS
Kepler deduced three, very important and immensely useful laws which hold true even today!
The laws were mainly based on observation and had no mathematical basis.
1.The orbit of a planet about the sun is an ellipse with the sun at one focus.
2.The line joining a planet and the sun sweeps out equal areas in equal times.
3.A planet’s orbital period squared is proportional to its average distance from the sun cubed.
Can you prove the Third Law using laws of Gravitation and Circular Motion?
Galileo Galilei was born shortly before the birth of Kepler in 1564 in Pisa, Italy. He investigated many aspects of physics and was probably the first astronomer to use telescopes for systematic astronomical observations. Galileo’s contribution to astronomy mainly comprised of early attempts of unifying astronomy with material sciences and inventions of more accurate astronomical devices.
Isaac Newton made astronomy a truly scientific subject. Physics and astronomy were used to be considered as separate disciplines until the time of Newton. Newton was the first philosopher or scientists who attempted for the first unification of celestial objects with that of terrestrial objects. He was successful into showing that it was not separate theories but the same, governing the behavior of objects in the universe. While trying to explain what forces cause the motions of planets, he discovered gravity, an attractive force exerted by all masses on all other masses in the universe. His ideas greatly helped in reducing anomalies and complexities in astronomy.
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By Mahmud Hasan
The Aftermath Publications
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The Aftermath Publications, Issue 3
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Laser
LASER. At the first instant the name reminds me of my childhood days when I used to fancy about sci-fi robots, extra-terrestrials and heroes with mighty powers. I still remember watching numerous shows like Startrek or Galactica back in the 90s. An integral part of all those shows was the “Laser” which was used either in the form of weapons of mass destruction by perilous space beings or even in the form of “teleporters”.
Little did I know that the laser had even more important and mind boggling applications in our daily lives than in amusing but apocryphal science fictions. From checking out the shopping at the supermarket to precision hospital surgery, from printing our homework to communicating along thin strands of glass---laser is all around us.
LASER is an acronym for Light Amplification by Stimulated Emission of Radiation. Most lasers share the following components:
1. A lasing medium
2. An energy source
3. A resonator
Conventional lasing mediums consist of mixtures of helium and neon gases. In normal conditions the atoms of the gases are all in their ground states. The lasing medium is enclosed within a discharge tube with highly reflecting mirrors at two ends of the tube along with arrangements for the application of high voltages.
This high voltage arrangement acts as an energy source. When a high voltage is applied across the ends of the tube containing the gas, an electric current is caused to flow through it, thereby exciting the electrons in the atoms of the lasing medium to higher energy levels---a situation termed as Population Inversion.
When the excited atoms decay to the ground state, they emit photons of light spontaneously. However, if this photon of light then meets another excited atom, it stimulates the excited atom to drop to its ground state. In this process, another photon of light is emitted (by stimulated emission).
Einstein showed in his papers that both the stimulating and the stimulated photons have:
The same wavelength
The same phase
The same direction of travel
The emitted photons can be allowed to bounce back and forth along the axis of the tube by means of highly reflecting mirrors which act as resonators. This avalanche effect produces more and more photons until a beam of monochromatic laser light is allowed to emerge from any one end of the discharge tube.
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By Mahmud Hasan
The Aftermath Publications
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The Aftermath Publications, Issue 3
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Little did I know that the laser had even more important and mind boggling applications in our daily lives than in amusing but apocryphal science fictions. From checking out the shopping at the supermarket to precision hospital surgery, from printing our homework to communicating along thin strands of glass---laser is all around us.
SPECTACULAR LASER SHOWS ARE A COMMON PUBLIC ATTRACTION TODAY
LASER is an acronym for Light Amplification by Stimulated Emission of Radiation. Most lasers share the following components:
1. A lasing medium
2. An energy source
3. A resonator
Conventional lasing mediums consist of mixtures of helium and neon gases. In normal conditions the atoms of the gases are all in their ground states. The lasing medium is enclosed within a discharge tube with highly reflecting mirrors at two ends of the tube along with arrangements for the application of high voltages.
This high voltage arrangement acts as an energy source. When a high voltage is applied across the ends of the tube containing the gas, an electric current is caused to flow through it, thereby exciting the electrons in the atoms of the lasing medium to higher energy levels---a situation termed as Population Inversion.
When the excited atoms decay to the ground state, they emit photons of light spontaneously. However, if this photon of light then meets another excited atom, it stimulates the excited atom to drop to its ground state. In this process, another photon of light is emitted (by stimulated emission).
THE SCHEMATIC DIAGRAM SHOWS: 1. LASING MEDIUM
2. ENERGY SOURCE; 3,4. MIRROR RESONATORS; 5. EMERGENT LASER LIGHT
Einstein showed in his papers that both the stimulating and the stimulated photons have:
The same wavelength
The same phase
The same direction of travel
The emitted photons can be allowed to bounce back and forth along the axis of the tube by means of highly reflecting mirrors which act as resonators. This avalanche effect produces more and more photons until a beam of monochromatic laser light is allowed to emerge from any one end of the discharge tube.
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By Mahmud Hasan
The Aftermath Publications
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The Aftermath Publications, Issue 3
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