Sunday, October 31, 2010

Tachyon

tachyon d

According to Einstein's Special Theory of Relativity, it is possible to go slower than light and faster than light, but it is impossible to go at the speed of light. Also, there is a particle called a tachyon which is supposed to go faster than light.

Tachyons are a putative class of particles which able to travel faster than the speed of light. Tachyons were first proposed by physicist Arnold Sommerfeld, and named by Gerald Feinberg. The word tachyon derives from the Greek (tachus), meaning "speedy." Tachyons have the strange properties that, when they lose energy, they gain speed. Consequently, when tachyons gain energy, they slow down. The slowest speed possible for tachyons is the speed of light.

Tachyons appear to violate causality (the so-called causality problem), since they could be sent to the past under the assumption that the principle of special relativity is a true law of nature, thus generating a real unavoidable time paradox (Maiorino and Rodrigues 1999). Therefore, it seems unavoidable that if tachyons exist, the principle of special relativity must be false, and there exists a unique time order for all observers in the universe independent of their state of motion.

Tachyons can be assigned properties of normal matter such as spin, as well as an antiparticle (the antitachyon). And amazingly, modern presentations of tachyon theory actually allow tachyons to actually have real mass (Recami 1996).

It has been proposed that tachyons could be produced from high-energy particle collisions, and tachyon searches have been undertaken in cosmic rays. Cosmic rays hit the Earth's atmosphere with high energy (some of them with speed almost 99.99% of the speed of light) making several collisions with the molecules in the atmosphere. The particles made by this collision interact with the air, creating even more particles in a phenomenon known as a cosmic ray shower. In 1973, using a large collection of particle detectors, Philip Crough and Roger Clay identified a putative superluminal particle in an air shower, although this result has never been reproduced.

Pi

PI__3_141592653589793238462643_by_Xan2_3

Why is Pi important?

Pi is perhaps the most important mathematical constant. It appears in various formulas throughout math and science in fields as diverse as physics, statistics, and sociology. Although pi is defined in terms of the geometry of a circle, most applications of this number do not directly involve circles.

Since ancient times, people have been fascinated by pi. This is hardly a surprise, since the circle is one of the most basic, but nevertheless fascinating, geometric figures. Pi is defined as the ratio of the circumference to the diameter of a circle. (Any circle will work, since all circles are similar.) Rounded to 10 decimal places, its value is 3.1415926536.

Part of what makes pi fascinating is that it appears in several other formulas involving circles or spheres. For instance, the area of a circle is equal to pi times the square of its radius. Further, the surface area of a sphere is equal to 4 pi times the square of its radius, and its volume is equal to 4/3 pi times the cube of its radius. In fact, the formulas for the content of all higher dimensional analogs of the sphere also involve pi.

As mentioned, pi also appears in many formulas not directly involving circles or spheres. For instance, the periods of all the trigonometric functions are either equal to pi or 2 pi. Although trig functions may be defined in terms of a circle, they are usually used in contexts not directly involving circles. Another place pi is widely used is in the normal distribution, which is commonly used in statistics, whose formula involves the square root of pi.

The computation of pi has a long and fascinating history. Some of the most elaborate mathematical methods have been used in devising various formulas for pi. By the late 19th century, its value had been computed by hand to several hundred decimal places. Since the dawn of the computer age in the mid-20th century, the number of calculated digits of pi has skyrocketed. Since 2002, its value has been known to over a trillion decimal places - enough to fill a large library!

Part of the reason some mathematicians are fascinated with calculating so many digits of pi is in order to look for patterns in its digits. So far, no obvious ones have been found. It has been conjectured that pi is a normal number, meaning that every finite pattern of digits in every base occurs infinitely often in pi with the same frequency which would be expected if the digits were random.

In 1995, an amazing formula was found for pi, which allows one to compute hexadecimal (base 16) digits of pi without having to compute any previous digits. This formula was used in 2000 to compute the quadrillionth (10^15th) hexadecimal digit of pi, which happens to be 0. Several similar formulas have since been discovered, some in other bases, but none in base 10 have yet been found.

Mr. Slxpluvs in Yahoo! Answers answers:

Pi is involved with the length of the diameter a circle and it's radius. It sounds like you're in geometry, where just about all pi does is figure out the area of a circle. Later, in calculus, pi is used to go between different types of coordinates (from the grids you're used to into a system of circles that all have the same center (concentric)). There are a lot of math problems that would be almost impossible without using pi.
This doesn't sound like something that you'd use in everyday life, but it might be important when talking to someone who does work with this sort of math. Lawyers, secretaries, scientists, doctors, electricians, plumbers, warehouse workers and many other professions have to deal with (and understand!) people who use pi in everyday work. In geometry class, it's not as important to build skills you plan to use, but to understand the language of the people who do use similar (but more complicated) skills.

 

Want to memorize Pi until 9th decimal place?

here’s a solution:

If you need to remember Pi, just count the letters in each word in the sentence: "May I have a large container of coffee?" If you get the coffee and say "Thank you," you get two more decimal places. [3.141592653...]

Can you cut a cake into 8 pieces with three movements?

Yes, indeed. All you need is two vertical and one horizontal cuts:

cake

Function that demonstrates a black hole

it’s:

y=-1/(x^2+z^2)

wolframalpha-20101031152130139

which is the same:

wolframalpha-20101031152654993

Monday, August 2, 2010

Music and the Brain

Music: “a series of sounds made by instruments or voices in a way that is pleasant or exciting.” Longman Dic.
Brain: “the organ inside your head that controls how you think, feel, and move.” Longman Dic.
Einstein at violin
The brain is the center of the nervous system in all vertebrate (a living creature that has a backbone) and invertebrate animals. Some primitive animals such as Jellyfish and Starfish decentralized nervous system without a brain, while Sponges lack any nervous system at all. Musicians – from karaoke singers to professional cello players – are better able to hear targeted sounds in  noisy environment, according to new research that adds to evidence that music makes the brain work better. Music’s interconnection with society can be seen throughout history. Every known culture on the Earth has music. Music seems to be one of the basic actions of humans. However, early music was not handed down from generation to generation or recorded. Hence, there’s no official record of “prehistoric” music. Even so, there’s evidence of prehistoric music from the findings of flutes curved from bones.


The influence of music on society can be clearly seen from modern history. Music helped Thomas Jefferson write the Declaration of Independence. When he could not figure out the right wording for a certain part, he would play his violin to help him. The music helped him get the words from his brain onto the paper. Albert Einstein is recognized as one of the smartest men who has ever lived. A little known fact about Einstein is that when he was young he did extremely poor in school. His grade school teachers told his parents to take him out of school because he was "too stupid to learn" and it would be a waste of resources for the school to invest time and energy in his education. The school suggested that his parents get Albert an easy, manual labor job as soon as they could. His mother did not think that Albert was "stupid". Instead of following the school's advice, Albert's parents bought him a violin. Albert became good at the violin. Music was the key that helped Albert Einstein become one of the smartest men who has ever lived. Einstein himself says that the reason he was so smart is because he played the violin. He loved the music of Mozart and Bach the most. A friend of Einstein, G.J. Withrow, said that the way Einstein figured out his problems and equations was by improvising on the violin.
Bodily Responses to Music
In general, responses to music are able to be observed. It has been proven that music influences humans both in good and bad ways. These effects are instant and long lasting. Music is thought to link all of the emotional, spiritual, and physical elements of the universe. Music can also be used to change a person's mood, and has been found to cause like physical responses in many people simultaneously. Music also has the ability to strengthen or weaken emotions from a particular event such as a funeral.
People perceive and respond to music in different ways. The level of musicianship of the performer and the listener as well as the manner in which a piece is performed affects the "experience" of music. An experienced and accomplished musician might hear and feel a piece of music in a totally different way than a non-musician or beginner. This is why two accounts of the same piece of music can contradict themselves.
Responses to music are easy to be detected in the human body. Classical music from the baroque period causes the heart beat and pulse rate to relax to the beat of the music. As the body becomes relaxed and alert, the mind is able to concentrate more easily. Furthermore, baroque music decreases blood pressure and enhances the ability to learn. Music affects the amplitude and frequency of brain waves, which can be measured by an electro-encephalogram. Music also affects breathing rate and electrical resistance of the skin. It has been observed to cause the pupils to dilate, increase blood pressure, and increase the heart rate.
The Power of Music on Memory and Learning
The power of music to affect memory is quite intriguing. Mozart's music and baroque music, with a 60 beats per minute beat pattern, activate the left and right brain. The simultaneous left and right brain action maximizes learning and retention of information. The information being studied activates the left brain while the music activates the right brain. Also, activities which engage both sides of the brain at the same time, such as playing an instrument or singing, causes the brain to be more capable of processing information.
According to The Center for New Discoveries in Learning, learning potential can be increased a minimum of five times by using this 60 beats per minute music. For example, the ancient Greeks sang their dramas because they understood how music could help them remember more easily ). A renowned Bulgarian psychologist, Dr. George Lozanov, designed a way to teach foreign languages in a fraction of the normal learning time. Using his system, students could learn up to one half of the vocabulary and phrases for the whole school term (which amounts to almost 1,000 words or phrases) in one day. Along with this, the average retention rate of his students was 92%. Dr. Lozanov's system involved using certain classical music pieces from the baroque period which have around a 60 beats per minute pattern. He has proven that foreign languages can be learned with 85-100% efficiency in only thirty days by using these baroque pieces. His students had a recall accuracy rate of almost 100% even after not reviewing the material for four years.
In 1982, researchers from the University of North Texas performed a three-way test on postgraduate students to see if music could help in memorizing vocabulary words. The students were divided into three groups. Each group was given three tests - a pretest, a posttest, and a test a week after the first two tests. All of the tests were identical. Group 1 was read the words with Handel's Water Music in the background. They were also asked to imagine the words. Group 2 was read the same words also with Handel's Water Music in the background. Group 2 was not asked to imagine the words. Group 3 was only read the words, was not given any background music, and was also not asked to imagine the words. The results from the first two tests showed that groups 1 and 2 had much better scores than group 3. The results from the third test, a week later, showed that group 1 performed much better than groups 2 or 3. However, simply using music while learning does not absolutely guarantee recall but can possibly improve it. Background music in itself is not a part of the learning process, but it does enter into memory along with the information learned. Recall is better when the same music used for learning is used during recall. Also, tempo appears to be a key of music's effect on memory.
One simple way students can improve test scores is by listening to certain types of music such as Mozart's Sonata for Two Piano's in D Major before taking a test. This type of music releases neurons in the brain which help the body to relax. The effectiveness of Mozart's sonatas can be seen by the results from an IQ test performed on three groups of college students. The first group listened to a Mozart sonata before taking the test. The second group listened to a relaxation tape before their test. The third group did not listen to anything before the test. The first group had the highest score with an average of 119. The second group ended up with an average of 111, and the third group had the lowest score with an average of 110. And you better know that only classical music can be used to have better results but other types of music such as Jazz not only make no improvement, but also they may decrease concentration and eventually cause poor performance.
Healthy and Not So Healthy Effects



  • slow music could slow the heartbeat and the breathing rate as well as bring down blood pressure. Faster music was found to speed up these same body measurements.



  • One key ingredient to the order of music from the baroque and classical periods is math. This is realized by the body and the human mind performs better when listening to this ordered music.
      One shining example of the power of order in music is King George I of England. King George had problems with memory loss and stress management. He read from the Bible the story of King Saul and recognized that Saul had experienced the same type of problems that he was experiencing. George recognized that Saul overcame his problems by using special music. With this story in mind King George asked George Frederick Handel to write some special music for him that would help him in the same way that music helped Saul. Handel wrote his Water Music for this purpose.



  • Another key to the order in music is the music being the same and different.
      An Australian physician and psychiatrist, Dr. John Diamond, found a direct link between muscle strength/weakness and music. He discovered that all of the muscles in the entire body go weak when subjected to the "stopped anapestic beat" of music from hard rock musicians, including Led Zeppelin, Alice Cooper, Queen, The Doors, Janis Joplin, Bachman - Turner Overdrive, and The Band. Dr. Diamond found another effect of the anapestic beat. He called it a "switching" of the brain. Dr. Diamond said this switching occurs when the actual symmetry between both of the cerebral hemispheres is destroyed causing alarm in the body along with lessened work performance, learning and behavior problems in children, and a "general malaise in adults." In addition to harmful, irregular beats in rock music, shrill frequencies prove to also be harmful to the body. Bob Larson, a Christian minister and former rock musician, remembers that in the 70's teens would bring raw eggs to a rock concert and put them on the front of the stage. The eggs would be hard boiled by the music before the end of the concert and could be eaten. Dr. Earl W. Flosdorf and Dr. Leslie A. Chambers showed that proteins in a liquid medium were coagulated when subjected to piercing high-pitched sounds.
On Animals and Plants, Too!
Tests on the effects of music on living organisms besides humans have shown that special pieces of music (including The Blue Danube) aid hens in laying more eggs. Music can also help cows to yield more milk. Researchers from Canada and the former Soviet Union found that wheat will grow faster when exposed to special ultrasonic and musical sounds. Rats were tested by psychologists to see how they would react to Bach's music and rock music. The rats were placed into two different boxes. Rock music was played in one of the boxes while Bach's music was played in the other box. The rats could choose to switch boxes through a tunnel that connected both boxes. Almost all of the rats chose to go into the box with the Bach music even after the type of music was switched from one box to the other.
Research took a new avenue when in 1968 a college student, Dorthy Retallack, started researching the effects of music on plants. She took her focus off of studying the beat and put in on studying the different sounds of music. Retallack tested the effects of music on plant growth by using music styles including classical, jazz, pop, rock, acid rock, East Indian, and country. She found that the plants grew well for almost every type of music except rock and acid rock. Jazz, classical, and Ravi Shankar turned out to be the most helpful to the plants. However, the plants tested with the rock music withered and died. The acid rock music also had negative effects on the plant growth.
Relationship to Language
Linguistic processing has generally been attributed to the left side of the brain, especially to the Broca's Area, and the left planum temporale within Wernicke's area. Musicians have been shown to have significantly more developed left planum temporales, and have also shown to have a greater word memory (Chan et al.). Chan’s study controlled for age, grade point average and years of education and found that when given a 16 word memory test, the musicians averaged one to two more words above their non musical counterparts.
Memory
Musical training has been shown to aid memory. Altenmuller et al. studied the difference between active and passive musical instruction and found both that over a longer (but not short) period of time, the actively taught students retained much more information than the passively taught students. The actively taught students were also found to have greater cerebral cortex activation. It should also be noted that the passively taught students weren’t wasting their time; they, along with the active group, displayed greater left hemisphere activity which is typical in trained musicians.
Conclusions:
One cannot deny the power of music. High school students who study music have higher grade point averages that those who don't. These students also develop faster physically. Student listening skills are also improved through music education. The top three schools in America all place a great emphasis on music and the arts. Hungary, Japan, and the Netherlands, the top three academic countries in the world, all place a great emphasis on music education and participation in music. The top engineers from Silicon Valley are all musicians. Napoleon understood the enormous power of music. He summed it up by saying, "Give me control over he who shapes the music of a nation, and I care not who makes the laws" .
Some of the most well-known personalities in music history:

Questions & Answers:
Q: How does music grow our brain and is its growth like a muscle?
A: This growth occurs when the demand is put upon the body and nerve system to carry out such a complex function. In some ways the brain and nervous system have growth similar to a muscle. If you use it, it grows to accommodate the use.
Q: Does a violin learner increase his/her brain connections?
A: Interesting phenomenon: While sitting at your desk, lift the right knee so the foot is off the floor. Then begin rotating the foot and lower leg in a clock-wise circle. Without stopping the lower leg rotation, pick up a pencil and write the number 6.Did you notice your leg stop and reverse direction of rotation? Most people do. This shows many things about brain connections. Maybe we can write more on it later.Remember, anyone studying the violin will increase these brain connections. Even adults. Yes, a child can benefit in growth by a greater amount than an adult, but it has been shown that adults also have ability to grow more brain connections.
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