Milky Way, the large, disc-shaped galaxy, or aggregation of stars, that includes the Sun and its solar system. Its name is derived from its appearance as a faintly luminous band that can be seen stretching across the sky at night. Its hazy appearance results from the combined light of stars too far away to be distinguished individually by the unaided eye. The individual stars that we see in the sky are those in the Milky Way galaxy that lie sufficiently close to the solar system to be discerned separately.
Milky Way Galaxy Our solar system lies in one of the spiral arms of the disc-shaped galaxy called the Milky Way. This photograph looks towards the centre of the Milky Way, 30,000 light years away. Bright star clusters are visible in the image along with darker areas of dust and gas.Photo Researchers, Inc./Morton-Milon/Science Source
From the middle northern latitudes, the Milky Way is best seen on clear, moonless, summer nights, when it appears as a luminous, irregular band circling the sky from the north-eastern to the south-eastern horizon. It extends through the constellations Perseus, Cassiopeia, and Cepheus. In the region of the Northern Cross, which is part of Cygnus, it divides into two streams: the western stream, which is bright as it passes through the Northern Cross, fades near Ophiuchus, or the Serpent Bearer, because of dense dust clouds, and appears again in Scorpius; and the eastern stream, which grows brighter as it passes southward through Scutum and Sagittarius. The brightest part of the Milky Way extends from Scutum to Scorpius, through Sagittarius. The galactic centre is in the direction of Sagittarius and is about 26,000 light years from the Sun.
The Origin of the Milky Way
The origin of the name Milky Way dates back to the ancient Greeks in a myth.
This painting by Italian artist Tintoretto, completed between 1575 and 1580, depicts a legend about how the Milky Way was formed. Jupiter, hoping to immortalize his infant son Hercules (who was born to a mortal woman), placed the baby on Juno’s breast. Her milk spilled up, forming the Milky Way. The Origin of the Milky Way is in the National Gallery in London.
Corbis/Jacopo Tintoretto/The National Gallery, London
Monday, September 20, 2010
QUASARS
Quasar, acronym for quasi-stellar radio source, any of a class of blue, star-like objects that have spectra which exhibit a strong red shift and are apparently very remote and emit enormous amounts of energy. The earliest quasars to be discovered were identified as sources of intense radio emission in the late 1950s (see Radio Astronomy). In 1960, using the 200-in. (508-cm) telescope on Mount Palomar in California to observe the positions of these radio sources, astronomers discovered objects the spectra of which showed emission lines that could not be identified. In 1963 the Dutch-American astronomer Maarten Schmidt discovered that these unidentified emission lines in the spectrum of quasar 3C 273 were known lines that exhibited a far stronger red shift than in any other known object.
One known cause of red shift is the Doppler effect, which shifts the wavelength of emitted light of celestial objects toward the red (longer wavelengths) when the objects are moving away from the Earth. Distant objects, such as galaxies, are receding from the Earth because of the expansion of the universe. From the amount of red shift astronomers can calculate the recession velocity. Hubble's law (see Cosmology), which states that recession velocity caused by the expansion of the universe is directly proportional to the distance of the object, indicates that quasar 3C 273 is 1.5 billion light years from the Earth.
By the end of the 1980s, several thousand quasars had been identified and the red shifts of a few hundred determined; in a small number of these, the shift factor is greater than 4. If the red shift is assumed to be cosmological, these quasars would have velocities greater than 93 per cent of that of light. According to Hubble's law, their distances would thus be greater than 10 billion light years, and their observed light would have been travelling practically as long as the age of the universe. In 1991 a quasar 12 billion light years distant was discovered by observers at Palomar Observatory, and in 1998 a team from Princeton University found three more at around this distance during the first few months of the Sloan Digital Sky Survey. Judging from the energy received on Earth from such distant objects, some quasars produce more energy than 2,000 ordinary galaxies—one, S50014 + 81, may be 60,000 times as bright as our Milky Way galaxy. Radio measurements, however, combined with the fact that electromagnetic waves emitted by some quasars vary strongly over a period of a few months, indicate that quasars must be much smaller than ordinary galaxies. Because the size of a fluctuating radiation source cannot be much larger than the distance light would travel from one end of the object to the other during one fluctuation period, astronomers estimate that the variable quasars cannot be larger than one light year across, which is 100,000 times smaller than the Milky Way.
The only satisfying explanation for a mechanism that could produce such amounts of energy in a relatively small volume is the swallowing of large amounts of matter by a black hole. But some astronomers suspect that the red shifts in quasars are caused by some other mechanism than the Doppler effect, and that quasars are not really very distant. The American astronomer Halton C. Arp, for example, has found large differences between red shifts of the quasars and other galaxies that nevertheless appear to be physically linked. In many other apparent pairings of quasars and ordinary galaxies, however, the red shifts do correspond. One theory gaining wide acceptance is that quasars are the superluminous cores of galaxies and that they and radio galaxies may actually be equivalent objects seen from different angles.
Microsoft ® Encarta ® Premium Suite 2005. © 1993-2004 Microsoft Corporation. All rights reserved.
One known cause of red shift is the Doppler effect, which shifts the wavelength of emitted light of celestial objects toward the red (longer wavelengths) when the objects are moving away from the Earth. Distant objects, such as galaxies, are receding from the Earth because of the expansion of the universe. From the amount of red shift astronomers can calculate the recession velocity. Hubble's law (see Cosmology), which states that recession velocity caused by the expansion of the universe is directly proportional to the distance of the object, indicates that quasar 3C 273 is 1.5 billion light years from the Earth.
By the end of the 1980s, several thousand quasars had been identified and the red shifts of a few hundred determined; in a small number of these, the shift factor is greater than 4. If the red shift is assumed to be cosmological, these quasars would have velocities greater than 93 per cent of that of light. According to Hubble's law, their distances would thus be greater than 10 billion light years, and their observed light would have been travelling practically as long as the age of the universe. In 1991 a quasar 12 billion light years distant was discovered by observers at Palomar Observatory, and in 1998 a team from Princeton University found three more at around this distance during the first few months of the Sloan Digital Sky Survey. Judging from the energy received on Earth from such distant objects, some quasars produce more energy than 2,000 ordinary galaxies—one, S50014 + 81, may be 60,000 times as bright as our Milky Way galaxy. Radio measurements, however, combined with the fact that electromagnetic waves emitted by some quasars vary strongly over a period of a few months, indicate that quasars must be much smaller than ordinary galaxies. Because the size of a fluctuating radiation source cannot be much larger than the distance light would travel from one end of the object to the other during one fluctuation period, astronomers estimate that the variable quasars cannot be larger than one light year across, which is 100,000 times smaller than the Milky Way.
The only satisfying explanation for a mechanism that could produce such amounts of energy in a relatively small volume is the swallowing of large amounts of matter by a black hole. But some astronomers suspect that the red shifts in quasars are caused by some other mechanism than the Doppler effect, and that quasars are not really very distant. The American astronomer Halton C. Arp, for example, has found large differences between red shifts of the quasars and other galaxies that nevertheless appear to be physically linked. In many other apparent pairings of quasars and ordinary galaxies, however, the red shifts do correspond. One theory gaining wide acceptance is that quasars are the superluminous cores of galaxies and that they and radio galaxies may actually be equivalent objects seen from different angles.
Microsoft ® Encarta ® Premium Suite 2005. © 1993-2004 Microsoft Corporation. All rights reserved.
Is Astrology a Science or Not?
Astrology is a system based on the belief that events on Earth are represented by the positions and movements of astronomical bodies, particularly the Sun, Moon, planets, and stars. The word astrology derives from the Greek astron (star) and logos (word, study).
Astrologers maintain that the position of astronomical bodies at the exact moment of a person’s birth and the subsequent movements of the bodies reflect that person’s character and, therefore, destiny. They are deemed to be associated with the characteristics of individuals. The celestial patterns are interpreted so as to understand, plan, or predict events on Earth. Although astrology uses systematized methods and techniques to gather valuable data, it does not utilize these data for logical explanations but for mystic readings. And because astrology bases its findings upon superstitious beliefs, it contradicts science (which rejects superstitions).
Astrologers maintain that the position of astronomical bodies at the exact moment of a person’s birth and the subsequent movements of the bodies reflect that person’s character and, therefore, destiny. They are deemed to be associated with the characteristics of individuals. The celestial patterns are interpreted so as to understand, plan, or predict events on Earth. Although astrology uses systematized methods and techniques to gather valuable data, it does not utilize these data for logical explanations but for mystic readings. And because astrology bases its findings upon superstitious beliefs, it contradicts science (which rejects superstitions).
PASCAL’S TRIANGLE
Pascal's Triangle or Arithmetic Triangle, a pattern of numbers obtained by expanding successive powers of x + y, namely (x + y)1, (x + y)2, and so on, giving the array of coefficients shown in the figure.
Having infinitely many rows, and only two sides, this is not really a triangle. The rows are numbered n = 1, 2, ... from the top downwards; the entries in row n are the coefficients of the terms in the expansion of (x + y) n. These are called the binomial coefficients, (pronounced “n choose k”). Here n! (“n factorial”) means n × (n -1) × (n -2) × ... × 2 × 1 for n≥ 1. The expression gives the number of ways of choosing k objects from a set of n objects: hence the name. For example, the coefficient of x 2y2 in (x + y)4 is
Each entry in Pascal's triangle (apart from the 1s along the sides) is the sum of the two entries to its left and right in the preceding row. Using this fact, one can construct further rows of the triangle.
Pascal's triangle displays many other interesting numerical relationships and patterns. For instance, the sum of the entries in row n is 2n. Thus the sum of the entries in row 4 is 24 = 16. Furthermore, replacing even and odd terms in Pascal's triangle with 0 and 1 respectively, we get the following self-replicating pattern:
The next eight rows consist of two adjacent copies of this triangle, with an inverted triangle of 0s between them, and so on.
History
The 17th-century French mathematician and theologian Blaise Pascal studied the binomial coefficients in connection with probability theory and games of chance; for instance, if an unbiased coin is tossed n times, the number of ways of obtaining k heads is
so the probability of this event is dependent on this number. However, Pascal was not the first to discover this array. It appeared in 1527 on the front page of the Rechnung, an arithmetic book by the German mathematician and astronomer Peter Apian (1495-1552), and the Chinese mathematician Chu Shih-Chieh referred to it in 1303, in his book The Precious Mirror, as “the old method”. The triangle probably dates from about 1100, when the Persian poet and mathematician Omar Khayyam appears to refer to it in his Algebra.
Pascal's Triangle
Pascal’s triangle is a pattern of numbers that is significant in mathematics. It is obtained very simply. The first row contains 1 twice. Each row after that is obtained by placing the sum of adjacent numbers below and between those numbers, with 1 beginning and ending each row. The resulting pattern of numbers mirrors the numbers obtained when (x + y) is multiplied by itself repeatedly. The fully written-out form of (x + y) n is called its expansion. As the comparison above shows, the numbers making up Pascal’s triangle are those appearing in the terms making up the successive expansions of (x + y) n as n takes on successive values. Pascal’s triangle has applications in various areas of mathematics, including probability theory.
Having infinitely many rows, and only two sides, this is not really a triangle. The rows are numbered n = 1, 2, ... from the top downwards; the entries in row n are the coefficients of the terms in the expansion of (x + y) n. These are called the binomial coefficients, (pronounced “n choose k”). Here n! (“n factorial”) means n × (n -1) × (n -2) × ... × 2 × 1 for n≥ 1. The expression gives the number of ways of choosing k objects from a set of n objects: hence the name. For example, the coefficient of x 2y2 in (x + y)4 is
Each entry in Pascal's triangle (apart from the 1s along the sides) is the sum of the two entries to its left and right in the preceding row. Using this fact, one can construct further rows of the triangle.
Pascal's triangle displays many other interesting numerical relationships and patterns. For instance, the sum of the entries in row n is 2n. Thus the sum of the entries in row 4 is 24 = 16. Furthermore, replacing even and odd terms in Pascal's triangle with 0 and 1 respectively, we get the following self-replicating pattern:
The next eight rows consist of two adjacent copies of this triangle, with an inverted triangle of 0s between them, and so on.
History
The 17th-century French mathematician and theologian Blaise Pascal studied the binomial coefficients in connection with probability theory and games of chance; for instance, if an unbiased coin is tossed n times, the number of ways of obtaining k heads is
so the probability of this event is dependent on this number. However, Pascal was not the first to discover this array. It appeared in 1527 on the front page of the Rechnung, an arithmetic book by the German mathematician and astronomer Peter Apian (1495-1552), and the Chinese mathematician Chu Shih-Chieh referred to it in 1303, in his book The Precious Mirror, as “the old method”. The triangle probably dates from about 1100, when the Persian poet and mathematician Omar Khayyam appears to refer to it in his Algebra.
Pascal's Triangle
Pascal’s triangle is a pattern of numbers that is significant in mathematics. It is obtained very simply. The first row contains 1 twice. Each row after that is obtained by placing the sum of adjacent numbers below and between those numbers, with 1 beginning and ending each row. The resulting pattern of numbers mirrors the numbers obtained when (x + y) is multiplied by itself repeatedly. The fully written-out form of (x + y) n is called its expansion. As the comparison above shows, the numbers making up Pascal’s triangle are those appearing in the terms making up the successive expansions of (x + y) n as n takes on successive values. Pascal’s triangle has applications in various areas of mathematics, including probability theory.
Importance of Studying the History of Science
1. To give credit to those people who contributed even a bit to its advancement
2. To trace back where a certain idea originally came from (because many concepts were renamed after its pioneer has died)
3. Because history repeats itself, knowing the history of science had helped present scientists to minimize errors in their research work.
4. In connection with number 3, analyzing the mistakes of the past and the present scientists will help future scientists and technologists to reduce inaccuracies and miscalculations in their experiments.
5. To be amazed of the breakthrough that people had achieved
6. To compare the past and present (and probably, even the future) sciences and they aid people in different aspects of their lives.
7. To be entertained while studying it
2. To trace back where a certain idea originally came from (because many concepts were renamed after its pioneer has died)
3. Because history repeats itself, knowing the history of science had helped present scientists to minimize errors in their research work.
4. In connection with number 3, analyzing the mistakes of the past and the present scientists will help future scientists and technologists to reduce inaccuracies and miscalculations in their experiments.
5. To be amazed of the breakthrough that people had achieved
6. To compare the past and present (and probably, even the future) sciences and they aid people in different aspects of their lives.
7. To be entertained while studying it
Saturday, July 24, 2010
Axioms and Theorems
Axioms and Theorems
Axioms or postulates – proposition which are not yet proven but consider being self- evident or subjecting to necessary decision.
Theorems- statements which have been proven on the basis of previously established statements such as other theorems, and previously accepted statements such as axioms.
Brief Backgrounds of Axiom
The early Greeks developed a logico- deductive method whereby conclusions follow from premises.
Common notions by Euclid:
a. Things which are equal to the same thing are also equal to one another.
b. If equals be added to equals, the wholes are equal.
c. If equals be subtracted to equals, the remainders are equal.
d. Things which coincide with one another are equal to one another.
e. He whole is greater that part.
Axiomatic System
-any set of axioms from which some or all axioms can be used in conjunction to logically derived theorem.
Properties of an Axiomatic System:
1. consistent if it lacks contradiction
2. complete if for every statements, either itself or its negotiation of contradiction is derivable
3. independent if it is not a theorem that can be derived from other axioms in the system
Indicative conditional
Many theorems are of the form of an indicative conditional: if A, then B. In this case, A is called the hypothesis (antecedent) of the theorem and B the conclusion (consequent)
*Theorems are true precise in the sense that they posses proofs.
Axioms or postulates – proposition which are not yet proven but consider being self- evident or subjecting to necessary decision.
Theorems- statements which have been proven on the basis of previously established statements such as other theorems, and previously accepted statements such as axioms.
Brief Backgrounds of Axiom
The early Greeks developed a logico- deductive method whereby conclusions follow from premises.
Common notions by Euclid:
a. Things which are equal to the same thing are also equal to one another.
b. If equals be added to equals, the wholes are equal.
c. If equals be subtracted to equals, the remainders are equal.
d. Things which coincide with one another are equal to one another.
e. He whole is greater that part.
Axiomatic System
-any set of axioms from which some or all axioms can be used in conjunction to logically derived theorem.
Properties of an Axiomatic System:
1. consistent if it lacks contradiction
2. complete if for every statements, either itself or its negotiation of contradiction is derivable
3. independent if it is not a theorem that can be derived from other axioms in the system
Indicative conditional
Many theorems are of the form of an indicative conditional: if A, then B. In this case, A is called the hypothesis (antecedent) of the theorem and B the conclusion (consequent)
*Theorems are true precise in the sense that they posses proofs.
Meaning of language
Language
- abstract system of words, meanings and symbols of aspects of cultures.
- includes speech written characters, numerical symbols, gestures, and expressions of non- verbal communication.
Ordinary Language Analysis
-an argument of any language which is adequately strands as the transmitter of differences and styles of meaning on which everyday connection must be fluid.
- abstract system of words, meanings and symbols of aspects of cultures.
- includes speech written characters, numerical symbols, gestures, and expressions of non- verbal communication.
Ordinary Language Analysis
-an argument of any language which is adequately strands as the transmitter of differences and styles of meaning on which everyday connection must be fluid.
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