Tuesday, November 30, 2010

Same face may look male or female, depending on where it appears in a person's field of view

ScienceDaily (2010-11-28) -- Neuroscientists have made the surprising discovery that the brain sees some faces as male when they appear in one area of a person's field of view, but female when they appear in a different location.

To find out more, follow: http://www.sciencedaily.com/releases/2010/11/101124124018.htm

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Monday, November 29, 2010

The very early universe behaved like a hot liquid?!

liquiduniverse-0

Physicists from the ALICE detector team have been colliding lead nuclei together at CERN's Large Hadron Collider (LHC) in an attempt to recreate the conditions in the first few microseconds after the Big Bang. Early results have shown that the quark-gluon plasma created at these energies does not form a gas as predicted, but instead suggest that the very early universe behaved like a hot liquid.

The Large Hadron Collider enables physicists to smash together sub-atomic particles at incredibly high-energies, providing new insights into the conditions present at the beginning of the universe.

liquiduniverse

ALICE (an acronym for A Large Ion Collider Experiment) researchers have been colliding lead nuclei to generate incredibly dense sub-atomic fireballs – mini Big Bangs at temperatures of over ten million degrees.

Previous research at lower energies had suggested the hot fire balls produced in nuclei collisions behaved like a liquid, yet many still expected the quark-gluon plasma to behave like a gas at these much higher energies.

Additionally, it has been found that more sub-atomic particles are produced in the collision than some theoretical models suggested.

“Although it is very early days we are already learning more about the early Universe,” said Dr David Evans, from the University of Birmingham’s School of Physics and Astronomy, and UK lead investigator at ALICE experiment. “These first results would seem to suggest that the Universe would have behaved like a super-hot liquid immediately after the Big Bang.”

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The ALICE experiment aims to study the properties of the state of matter called a quark-gluon plasma. The ALICE Collaboration comprises around 1,000 physicists and engineers from around 100 institutes in 30 countries. During collisions of lead nuclei, ALICE will record data to disk at a rate of 1.2 gigabytes (GB), equivalent to two CDs every second, and will write over two petabytes (two million GB) of data to disk. This is equivalent to more than three million CDs, or a stack of CDs without boxes several miles high!

To process this data, ALICE will need 50,000 top-of-the-range PCs, from all over the world, running 24 hours a day.

Tuesday, November 23, 2010

First Alien Planet From Another Galaxy Discovered

HIP 13044b

Astronomers have confirmed the first discovery of an alien planet in our Milky Way that came from another galaxy, they announced Thursday.

The Jupiter-like planet orbits a star that was born in another galaxy and later captured by our own Milky Way sometime between 6 billion and 9 billion years ago, researchers said. A side effect of the galactic cannibalism brought a faraway planet within astronomers' reach for the first time ever.

The find may also force astronomers to rethink their ideas about planet formation and survival.

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Saturday, November 20, 2010

Doing Well in Calculus

calculus
  • Develop an effective and time-efficient homework/study strategy for, not only your calculus class, but other classes as well. This will help you become a more confident, successful, and well-rounded student. It will lead to a healthier balance between work time and leisure time.
  • Spend at least two to four hours on each homework assignment. This affords you extra time to work on challenging homework problems and helps you organize your thoughts, questions, and ideas. The more time you spend on homework, the more likely you are to articulate clear, concise questions to your classmates and teachers. The more time you spend on homework, the less time you will spend on frantic, last-minute preparation for exams.
  • Definitions, formulas, and theorems that are introduced in class or needed to complete homework assignments should be memorized immediately . Postponing this until it's needed for the exam will impede your work speed on homework assignments and interfere with clearer and deeper understanding of calculus.
  • Spend time working on calculus every day . Doing some calculus every day makes you more familiar with concepts, definitions, and theorems. This familiarity will make calculus get easier and easier one day at a time.
  • Find at least one or two other students from your calculus class with whom you can regularly do homework and prepare for exams. Your classmates are perhaps the least used and arguably your best resource. An efficient and effective study group will streamline homework and study time, reduce the need for attendance at office hours, and greatly improve your written and spoken communication. The best time to use your classmates as study/homework partners is after you have made an honest effort on your own to solve the problems using your own wits, knowledge, and experience. When you encounter an unsolvable problem, don't give up too soon on it. Being stumped is an opportunity for mathematical growth and insight, even if you never solve the problem on your own. If you seek help prematurely, you will never know if you could have solved a tough problem without outside assistance.
  • Begin preparing/outlining for exams at least five class days before the exam. Outlining the topics, definitions, theorems, equations, etc. that you need to know for the exam will help you focus on those areas where you are least prepared. Preparing early for the exam will build your self-confidence and reduce anxiety on the day of the exam. It's also an insurance policy against time lost to illness, unexpected family visits, and last-minute assignments in other classes. Generally speaking, pulling all-nighters and doing last-minute cramming for exams is a recipe for eventual academic disaster.
  • Prepare for exams by working on new problems . Good sources for these problems are unassigned problems from your textbook, review exercises and practice exams at the end of each chapter, old hour exams, or old final exams. Studying exclusively from those problems which you have already been assigned and worked on may not be effective exam preparation. Problems for each topic are generally in the same section of the book, so knowing how to do a problem because you know what section of the book it is in could give you a false sense of security. Working on new randomly mixed problems more closely simulates an exam situation, and requires that you both categorize the problem and then solve it.
  • Use all resources of assistance and information which are available to you. These include classnotes, homework solutions, office hours with your professor or teaching assistants, and problem sessions with your classmates. Do not rely exclusively on just one or two of these resources. Using all of them will help you develop a broader, more natural base of knowledge and understanding.
  • Expect your exams to be challenging . If they are challenging, you will be prepared. If they are not challenging, you can expect to have an easy time getting a very high score !

Wednesday, November 17, 2010

Saturday, November 13, 2010

CERN

SWITZERLAND CERN BIG BANGCentre Européen de Recherche Nucléaire (=European Nuclear Research Centre); a large scientific organization based in Geneva, Switzerland, that studies particle physics. It operates the world's largest particle physics laboratory. Its members are from 20 European countries, and it is famous for building very large and powerful particle accelerators (=special machines for making very small pieces of matter move at very high speeds). Its new accelerator, the Large Haydron Collider (LHC), is the most powerful in the world."

Tuesday, November 9, 2010

Wormhole

wormhole_graphic A hypothetical "tunnel" connecting two different points in space-time in such a way that a trip through the wormhole could take much less time than a journey between the same starting and ending points in normal space. The ends of a wormhole could, in theory, be intra-universe (i.e. both exist in the same universe) or inter-universe (exist in different universes, and thus serve as a connecting passage between the two).
Wormholes arise as solutions to the equations of Einstein's general theory of relativity. In fact, they crop up so readily in this context that some theorists are encouraged to think that real counterparts may eventually be found or fabricated and, perhaps, used for high-speed space travel and/or time travel. However, a known property of wormholes is that they are highly unstable and would probably collapse instantly if even the tiniest amount of matter, such as a single photon, attempted to pass through them. A possible way around this problem is the use of exotic matter to prevent the wormhole from pinching off.

Many physicists believe wormholes (a "shortcut" through space and time) exist all around us but they are smaller than atoms.

Klein Bottle

According to www.wordnetweb.princeton.edu/perl/webwn,

Klein bottle is “a closed surface with only one side; formed by passing one end of a tube through the side of the tube and joining it with the other end”

klein_bottle klein_bottle_st

Klein bottle parametric equations:

wolframalpha-20101109140510368

Klein bottle Cartesian equation:

wolframalpha-20101109140753575

Sunday, November 7, 2010

What is algebra and why do students find it so hard?

OLYMPUS DIGITAL CAMERA Algebraic thinking is not just arithmetic with letters standing for numbers. It is a different kind of thinking.
Many people find arithmetic hard to learn, but most succeed, to varying degrees, though only after a lot of practice. What makes it possible is that the basic building blocks of arithmetic, numbers, arise naturally in the world around us, when we count things, measure things, buy things, make things, use the telephone, go to the bank, check the baseball scores, etc. Numbers may be abstract — you never saw, felt, heard, or smelled the number 3 — but they are tied closely to all the concrete things in the world we live in.
Algebra is thinking logically about numbers rather than computing with numbers. In algebra you are a second step of abstraction removed from the everyday world: those x’s and y’s usually denote numbers in general, not particular numbers. In algebra you use analytic, qualitative reasoning about numbers, whereas in arithmetic you use numerical, quantitative reasoning with numbers. For example, you need to use algebraic thinking if you want to write a macro to calculate the cells in a spreadsheet like Microsoft Excel. It doesn’t matter whether the spreadsheet is for calculating scores in a sporting competition, keeping track of your finances, running a business, or figuring out the best way to equip your character in World of Warcraft, you need to think algebraically to set it up to do what you want — that means thinking about or across numbers, rather than in terms of numbers. When students start to learn algebra, they inevitably try to solve problems by arithmetical thinking. That’s a natural thing to do, given all the effort they have put into mastering arithmetic, and at first, when the algebra problems they meet are particularly simple (that’s the teacher’s classification), this approach works. In fact, the stronger a student is at arithmetic, the further they can progress in algebra using arithmetical thinking. (Many students can solve the quadratic equation x2 = 2x + 15 using basic arithmetic, using no algebra at all.) Paradoxically, or so it may seem, however, those better students may find it harder to learn algebra. Because to do algebra, for all but the most basic examples, you have to stop thinking arithmetically and learn to think algebraically.

Möbius Strip

1. Start with a long rectangle (ABCD) made of paper.

2. Give the rectangle a half twist.

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3. Join the ends so that A is matched with D and B is matched with C.

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This curious surface is called a Möbius Strip (pronounced UK: /ˈmɜːbiəs/ or US: /ˈmoʊbiəs/ in English, [ˈmøːbi̯ʊs] in German) or Möbius Band, named after August Ferdinand Möbius, a nineteenth century German mathematician and astronomer, who was a pioneer in the field of topology. Möbius, along with his better known contemporaries, Riemann, Lobachevsky and Bolyai, created a non-Euclidean revolution in geometry.

Möbius strips have found a number of surprising applications that exploit a remarkable property they possess: one-sidedness. Joining A to C and B to D (no half twist) would produce a simple belt-shaped loop with two sides and two edges -- impossible to travel from one side to the other without crossing an edge. But, as a result of the half twist, the Möbius Strip has only one side and one edge!

To demonstrate this, (1) start midway between the "edges" of a Möbius Strip and draw a line down its center; continue the line until you return to your starting point. Did you ever cross an edge? (2) Next, hold the edge of a Möbius Strip against the tip of a felt-tipped highlighter pen. Color the edge of the Möbius Strip by holding the highlighter still and just rotating the Mobius Strip around. Were you able to color the entire edge? (3) Now, with scissors cut the Mobius Strip along the center line that you drew. Then draw a center line around the resulting band, and cut along it. Did you predict what would happen?

Giant Möbius Strips have been used as conveyor belts (to make them last longer, since "each side" gets the same amount of wear) and as continuous-loop recording tapes (to double the playing time). In the 1960's Sandia Laboratories used Möbius Strips in the design of versatile electronic resistors. Free-style skiers have christened one of their acrobatic stunts the Möbius Flip.

The famous artist, M.C. Escher, used mathematical themes in some of his work, including a Möbius parade of ants. His flight of swans looks like it might be a Möbius Strip, but it's not. Can you see why not?

 

MobiusAnts 

Martin Gardner wrote an amusing short story based on the Möbius Strip called "The No-sided Professor," which you can find in Fantasia Mathematica, a book edited by Clifton Fadiman.

The no-sided Professor: amazon_logo

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Wednesday, November 3, 2010

Why is the sky blue?

Skyblueanim Sunlight is made up of all the colors of the rainbow: red, orange, yellow, green, blue, and violet. The gas molecules in the atmosphere interact with the sunlight before the light reaches our eyes.

The gas molecules in the atmosphere scatter the higher-energy (high frequency) blue portion of the sunlight more than they scatter the lower-energy red portion of the sunlight (this is called Rayleigh scattering, named for the physicist Lord John Rayleigh). The Sun appears reddish-yellow and the sky surrounding the Sun is colored by the scattered blue waves.

When the Sun is lower in the horizon (near sunrise or sunset), the sunlight must travel through a greater thickness of atmosphere than it does when it is overhead, and even more light is scattered (not just blue, but also green, yellow, and orange) before the light reaches your eyes. This makes the sun look much redder.

Tuesday, November 2, 2010

Does the 4th dimension of time exist?

time What is Time?
Time is our way of keeping track of changes; changes that are constantly happening in the universe. Time arises due to the dynamic nature of the universe or one could say, dynamism of universe is possible because there is time!
In a way time must have been invented so that all things do not happen at the same moment and space was made so that all things do not happen at the same place. By time, we mean a series of changes or events that occur. Those events that happen periodically like the rising and setting of the Sun, the rotation of the Earth and revolution of the Earth around the Sun are used as references to calibrate and measure time. Our clocks are synchronized with these periodically repeating events to keep track of time.
What Does a Dimension Mean?
A dimension is a degree of freedom of a system. In simple words, it means the number of ways or directions in which change can take place in a system. Let us understand what do we mean by the dimension of our universe, our world. Imagine an ant walking on a very thin thread. The width of the thread is such that it can either move forward or backward on the thread, it cannot move sideways. That is its 'freedom of movement' is restricted to 'one dimension'. It has one degree of freedom and therefore one dimension. Similarly, an ant moving on a flat disk can move straight or sideways but not up and down, so its degrees of freedom is two. Hence it's moving on a two dimensional object.
Now imagine a flying ant like 'atom ant', it can move straight ahead or back, sideways, as well as up and down. Its degree of freedom is three, so it's moving as we all do in three space dimensions because the degree of freedom is three!
How is Time the 4th Dimension?
Now ask yourself, how would movement in all these dimensions be possible, if there was no concept of time? You will find that dynamism in space would not be possible if there was no time! When all of those ants were moving, they 'moved' in time too! So the ant on the thread had not one but two degrees of freedom! One was space and the other, time. That is, it was moving in two dimensions. Similarly in this world, we move in three space dimensions plus one 'time dimension'.
However, time as a dimension is unique and different from other space dimensions. In space dimension, you can move ahead and backwards, there is no restriction on that. However in time, you can only move in one direction. In time, you cannot move backwards, only forward! This has far reaching implications which we will discuss further, but first let us understand how Einstein's special relativity changed our perceptions of space and time.
Einstein and the Unification of Space Time
In 1905, a Swiss patent clerk, Albert Einstein put forth a theory called special relativity which dealt the fatal blow to the old established bastion of Newtonian mechanics which had the perception of an 'absolute time'. The theory revolutionized the way we see nature and the universe.
The basic postulate of special relativity is that no information can travel faster than the velocity of light in vacuum and it is constant. The second postulate is that all laws of the physical world should remain the same in any inertial reference frame. By inertial reference frame, we mean a co-ordinate system of reference moving at a constant velocity or which is stationary. Any other co-ordinate system moving with constant velocity with respect to a co-ordinate system at rest is also an inertial reference frame.
Newton's mechanics had the concept of absolute time. That is, no matter which reference frame people are using, their clocks if compared show the same time. Special relativity changed this perception. The necessity that the speed of light should be constant forces us to abandon the absoluteness of time! That is different observers in different reference frames show different times in their watches, but the laws of physics will remain the same. In fact the faster you move in space, the slower you move in time! This is often called time dilation. Time was not absolute, it became relative!
This forced the world to abandon the concept of separate ideas of space and time and a single unified concept of spacetime came into existence. Some found it in Einstein's name itself. 'Ein' means 'one' in German. Split up his name as ' EIN+ST+EIN', ST meaning space time. If you see, it literally means 'one space time'; just a lucky coincidence one would say! Time was realized as the 4th dimension.
Let us try to understand what it really means by 'time dilation'. We are all continuously moving not just in three dimensional space but in four dimensional space time. Consider a racing car moving on an absolutely straight race track at a constant velocity. It is moving in one dimension and takes some time to reach the finish line. Now consider that it's trying to reach the finish line, but on an oblique path. Its velocity is now distributed over two dimensions and therefore it's taking longer for the car to cover the same distance. Its velocity in the original one dimension has reduced.
In a similar way, all objects in the real world are moving in a four dimensional space time at a constant velocity as that of light! Sounds astounding but it's true. Only the velocity is distributed over dimensions and most of it is in the time dimension.
When the objects are at rest, they are moving only in the time dimension. Now when they start moving, their velocity increases in the three space dimensions, and therefore it slows down in the time dimension! Therefore the faster you move in three space dimensions, the slower you go in the time dimension! This causes time dilation. This is a bit difficult to understand but if you give it adequate time to sink in, it's simple.
The uniqueness of time dimension is that you can travel only forward in time, not backward. This fact has profound implications. It protects causality, that is the law of cause and effect. That is, cause should precede effect and it should not be the other way round. This irreversibility of time is inbuilt through the concept of entropy. If you study thermodynamics, you will come across the law that entropy or disorder in the universe always increases, never can it decrease. That is, a cup falling down and breaking can never be restored to the same condition, with every atom in place, as it was. For every system, disorder always increases. Entropy increase is unidirectional just as the unidirectionality of time. Thus it is no coincidence that the thermodynamically arrow of time and the arrow of time flow point in the same direction as they both preserve causality!
Creatures living in a two dimensional flat world will find it difficult to imagine what a three dimensional world would look like. Similarly, we, living in a world of three space dimensions find it impossible to imagine four dimensional spacetime! Still, through many indirect experimental tests the idea of four dimensional space time has been tested beyond doubt!
Concept of time as the fourth dimension is very subtle and elusive. I hope the time you have spent reading this article has made it a bit less mysterious now!