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.
Definition
Definition
-statements of the essential properties of a certain thing
-statement of equivalence between expression and another but usually more complex expression that give meanings on the fact.
Definiendum- thing being defined
Definiens- the definition itself
Types of definition:
1. Lexical
2. Extensional
3. Interpersonal
4. Contextual
5. Stipulative
6. Extensive
7. Operational
________________________________________________________________________
-statements of the essential properties of a certain thing
-statement of equivalence between expression and another but usually more complex expression that give meanings on the fact.
Definiendum- thing being defined
Definiens- the definition itself
Types of definition:
1. Lexical
2. Extensional
3. Interpersonal
4. Contextual
5. Stipulative
6. Extensive
7. Operational
________________________________________________________________________
Tuesday, July 20, 2010
Astronomy is the oldest of the sciences. When Stoneage humans turned to an agrarian way of life and began to settle into communities, their interest must naturally have turned to the "heavens":
1. The seasons became important; during different times of the year, different stellar patterns appear in the sky. In the spring, Virgo and her accompanying constellations signal the time to prepare the earth, to plant crops, and to be wary of floods. In the fall, Orion rises to indicate time to harvest and to prepare for winter.
2. The approximate equivalence of the human menstrual cycle and the 30 day orbital period of the Moon which produces lunar phases led to the belief that the heavens, and the Moon in particular, were related to fertility. (What is the Moon's phase right now?)
3. To early humans facing an uncertain and changeable future, the constancy of the heavens must have suggested perfection and certainly led to deification in many cultures.
4. We may expect that eclipses would have been especially frightening to early humans. After predicting the seasons, eclipse prediction may have been one of the earliest astronomical activities.
Stonehenge, constructed between 3100-2000 BCE on England's Salisbury Plain, may have been a Stoneage astronomical site (observatory is too strong a word), at least in part. Certainly the alignment of the "heelstone" with the rising Sun on Midsummer's Day (June 21, the Summer Solstice) represents a true astronomical alignment, and many other Megalithic sites have similar alignments. In Stonehenge Decoded, astronomer Gerald Hawkins argued that there exist a large number of astronomical alignments, though further study suggests that many of these are fortuitous.
Cosmologist Fred Hoyle has suggested that Stonehenge may have been used to keep track of the solar-lunar eclipse cycle. Far outside the still partially standing ring of Sarsen Stones is a ring of 56 holes, known as the Aubry holes. Hoyle has noted that movement of a marking stone by 3 positions each time the Sun rose over the heelstone (or by one position three times yearly) would complete a circle in 18.67 years -- approximately the period for the "nodes", the intercepts of the lunar and solar paths in the sky, to complete a cycle. Certainly ritual use of Stonehenge would have been more important that its astronomical functions and much of this interpretation must remain speculation. We may be certain, however, that Stonehenge was indeed constructed by Stoneage humans without the assistance of alien astronauts as suggested in some pseudo-scientific books. Visit the Complete Stonehenge
Eastern observers, notably the Chinese, kept careful track of events in the skies, particularly the appearance of "guest stars" -- comets, novae and other transients. Chinese records of the guest star that we now call Comet Halley can be traced back to 240 BCE and possibly as early as 1059 BCE. One of the most important Chinese records is of a guest star that was bright enough to be seen during the daytime for nearly a month in the constellation that we call Taurus in July 1054. We believe this to be the supernova explosion that gave rise to the Crab Nebula, and our knowledge of the date of the explosion itself is a very important key in understanding the deaths of massive stars. This event was also chronicled by the Anasazi in Chaco Canyon and by Native Americans elsewhere, but is curiously absent from European records in the Middle Ages.
As the above suggests, Archaeoastronomy is an active and exciting field of research.
Western scientific history begins with the ancient Greek civilization about 600 BCE.
The Ionian region of Asia Minor appears to have been a site of particular philosophical/scientific/mathematical activity for several centuries.
We will review the progress of science by highlighting a few key natural philosophers, scientists and mathematicians. As Isaac Newton said,"If I have seen further, it is by standing on the shoulders of Giants."
Pythagoras of Samos (~580-500 BCE)
Most famous for his theorem, little is known of his actual work. He founded a school (some would call it a cult) of natural philosophy and mysticism that attracted many followers. The Pythagoreans lived by a strict regimen including vegetarianism, silence for the first 5 years of membership, and anonymity with respect to personal accomplishments (so that it is difficult to know what to ascribe to Pythagoras as opposed to his followers). The Pythagorean Theorem was actually known to the early Babylonians, but it may be that Pythagoras was the first to prove it. The Pythagoreans recognized the existence of irrational numbers and were interested in the relationship between music and mathematics.
Pythagoras developments in astronomy built upon those of Anaximander from whom, apparently, came the idea of perfect circular motion. The Pythagoreans believed that the planets were attached to crystalline spheres, one for each planet, which produced the Music of the Spheres. These spheres were centered on the Earth, which was itself in motion. Pythagoras is also credited with recognizing that the "morning star" and "evening star" are both the planet Venus.
Aristotle (384-322 BCE)
Aristotle was a student of Plato, founding his own school of Natural Philosophy, the Lyceum, in Athens about 335 BCE. Aristotle's philosophy involved the qualitative study of all natural phenomena, pursued without the aid of mathematics which was deemed to be too "perfect" for application on an imperfect terrestrial sphere. In Aristotelian cosmology, the "imperfect" Earth was situated at the center of the Universe (Solar System). It was composed of the four elements: earth, air, water, and fire, each of which sought its natural place in the Universe (e.g. earthen bodies fall to Earth, rain falls from the sky, travelling through rivulets, to streams, to rivers and finally to the sea). Aristotle adopted Pythagoras' model of concentric spheres for the planets, but deduced that the Earth must be immobile. Aristotle's Natural Philosophy was embodied in the writings of St. Thomas Aquinas and became the foundation of Church doctrine and University instruction in medieval times.
Aristarchus of Samos (~310-230 BCE)
Aristarchus concluded that the Solar System must be heliocentric, following his geometrical estimates of the relative sizes and distances of the Earth, Moon and Sun. His geometrical methods were perfectly correct, but the required observations of the exact time of first and third quarter Moon and the duration of lunar eclipse were beyond the instrumental capabilities of his era. He calculated that the Sun is about twenty times farther away than the Moon, about 20 times larger than the Moon and ten times bigger than the Earth. Unfortunately, all of Aristarchus work was lost in the great fire in Alexandria which destroyed the magnificent library and its records of Greek science and culture. A lunar crater bears his name in recognition of his accomplishments.
Eratosthenes of Cyrene (276-197 BCE)
Eratosthenes was a mathematician and geographer. He developed a map of the world, a method for finding prime numbers called Eratosthenes' Sieve, and estimated the circumference of the Earth. His method involved determining the direction to the Sun in Alexandria at noon on the summer solstice and comparing this with the fact that the Sun is overhead in Syene(Aswan), about 500 miles away. Here are the results of a worldwide high school recreation of Eratosthenes' experiment along with pictures of how to do the experiment yourself.
Claudius Ptolemy (~85-165AD)
Ptolemy, Alexandrian (Greek) mathematician, geographer, and astronomer, developed the most sophisticated mathematical model of the motions of the Solar System based upon the geocentric (Earth-centered) model and the principle of perfect circular motion. His model was quite complex in order to follow the details of planetary motions, requiring circles (epicycles) upon off centered circular orbits. His major astronomical work is known as The Almagest. Here's how epicycles work to produce retrograde motion.
Ptolemy's Geography remained the principal work in that field until the time of Columbus.
Copernicus Heliocentric Solar System vs. Ptolemy's Geocentric Model
Both models employed perfect circular motion with epicycles, equants ...
Nikolas Kopernig (Copernicus, 1473-1543)
Copernicus studied mathematics and astronomy in Cracow and Italy, but spent his life as a physician, attorney and church administrator. By Copernicus' time, the Ptolemaic model could no longer reproduce the observed planetary positions. Copernicus developed a heliocentric model of the Solar System which retained the notion of perfect circular motion, but placed the Sun at the center and established the proper order of the planets outward from the Sun. Copernicus model, a mathematical tour de force (not bad for an amateur), was published in De Revolutionibus Orbium Celestium in 1543, the year of his death.
Tyge (Tycho) Brahe (1546-1601)
Danish astronomer Tycho Brahe is chiefly remembered for his meticulous observations, made with instruments of his own design before the advent of the telescope. His early observations were carried out on the island of Hven (now Swedish) where he built a pair of observatories, Uraniborg and later Stjerneborg. In 1572 he observed a supernova and in 1577 a comet. His parallax measures demonstrated that these objects were beyond the Moon, and his measures of the brightness of the supernova showed that it was clearly variable. Tycho's measurements of planetary positions were at variance with the ptolemaic model. He developed his own Solar System model in which the Sun orbits the Earth, but the remaining planets orbit the Sun. Tycho's abrasive nature ultimately led him into disfavor. He moved to the court of Rudolph II in Prague in 1599 where he would pass along his observations to Johannes Kepler. These became the basis for Kepler's Laws of Planetary Motion.
Galileo Galilei (1564-1642)
There is an exquisite WebSite, The Galileo Project about Galileo and his world put together by Rice University's History department. Many of the following links are to pages on this site. Another excellent site at Lawrence Livermore Laboratory is The Art of Renaissance Science.
Galileo was the first "modern scientist". He argued that mathematics, rather than being abstract perfection, is the true language of science. He performed many revolutionary experiments in mechanics and other fields of physics. Among his accomplishments in mechanics are:
• development of the concept of inertia, later refined by Newton.
• a variety of experiments on falling bodies which demonstrated that the acceleration of gravity is independent of mass. There is no evidence that Galileo actually dropped objects from the Tower of Pisa. Rather, his experiments were conducted with an inclined plane as shown in this animation.
• the first Theory of Relativity, valid for velocities much smaller than the speed of light.
Using telescopes of his own design and manufacture, Galileo also made many discoveries in astronomy:
• sunspots on the Sun and craters and mountains on the Moon.
• The so called "Galilean satellites" which orbit Jupiter -- Io (with the volcanos), Europa, Callisto and Ganymede. Here's more on Jupiter and her satellites from the Siderius Nuncius and an animation showing what Galileo observed.
• rings of Saturn.
• the phases of Venus.
Galileo's observations suggested that the heavens were as "imperfect" as the Earth; that other objects in the Solar System have satellites which orbit around them, and that Venus passes through a full range of phases. These observations led him to the conclusion that the Copernican Model of the Solar System is preferable to the Ptolemaic Model. Galileo published his views in Italian in Dialogues Concerning the Two Chief World Systems in 1632. They were in direct contradiction to the world-view taught by the Catholic Church, and he was called before the Italian inquisition in 1633. Galileo was forced to disavow his work, and was sentenced to house arrest for the remainder of of his life.
I highly recommend a tour of the Museum of the History of Science in Florence if you can tear yourself away from the Renaissance Art. Here is a tour of the Museum which has an extensive collection of Galilean exhibits including the famous middle finger. Here is their biography of Florence' greatest scientist.
Johannes Kepler (1571-1630)
Kepler came to Prague to work with Tycho Brahe and his observational data. Kepler was a mathematician and mystic, interested primarily in numerical relationships among objects in the Universe. Using Tycho's unprecedentedly accurate observations, he made highly precise calculations of planetary orbits. Although he could come very close to matching Brahe's data with perfect circlular orbits, his faith in the data led him to continue his calculations until he matched Tycho's accuracy. Kepler developed three mathematical rules for the orbits of the planets:
1. The orbits of the planets are ellipses with the Sun at one focus.
2. The planets sweep out equal areas during equal times of the orbit.
3. The square of the orbital period is proportional to the cube of the planet's distance from the Sun. (If you measure the period in Earth years and the distance in Astronomical Units (1 A.U.= the average distance of the Earth from the Sun), then Period2 = Distance 3.)
Here's a page with some nice animations of Kepler's Rules, and here is another way to play with them.
Obviously Kepler's Rules require that the Sun be the center of the Solar System, in contradiction with the Aristotilean ideal. The first rule eliminates the circular motion which had been fashionable for 2 millennia. The second replaces the idea that planets move at uniform speed around their orbits,with the empirical observation that the planets move more rapidly when they are close to the Sun and more slowly when they are farther away. The third rule is a harbinger of the Law of Gravitation which would be developed by Newton in the latter part of the 17th century.
Isaac Newton (1642-1727)
Certainly the greatest classical Physicist, Newton developed the science of mechanics as we know it. His first development was his Laws of Motion. In order to perform mechanical calculations and to understand Gravity, Newton invented a mathematical tool that he called "fluctions", now known as calculus. At the urging of Edmund Halley, Newton published his Laws of Motion and analysis of Gravity in the Principia Mathematica, probably the greatest physics text ever written, in 1687. Halley, of course, wanted to use Newton's theories to analyze orbits, particularly that of the comet of 1682 which now bears his name. More about Newton's Laws in the next tutorial.
Other pioneers and milestones in the advance of Science:
• 18th Century, William Herschel discovered Uranus, a new planet beyond Jupiter. Barely visible with the unaided eye, Herschel made the observation with his telescope .
• Early in the 19th Century Adams (English) & LeVerrier (French) independently calculated that there must be another planet beyond Uranus that was producing small gravitational disturbances in Uranus' orbit. First observed in 1846 by Hohan Galle, it was named Neptune. (It was actually spotted earlier by Challis in Cambridge, but Challis did not note his discovery until Galle reported his observation.)
• 1930 Clyde Tombaugh discovered Pluto.
• 1910 Harlow Shapley estimated the size of the Milky Way.
• W. H.Pickering and Annie J. Cannon calculated the surface temperatures of the stars.
• Einstein (1905) developed the Theory of Special Relativity, based upon the idea that light travels at the same speed in all frames of reference. Modified Newton's Theory of Gravity by developing the General Theory of Relativity (1916).
• Cecilia Payne-Gaposchkin & Henry Norris Russell determined the composition of stars.
• 1924 Edwin Hubble established that the Andromeda nebula and other "spiral nebulae" are star systems like the Milky Way at great distances.
• 1929 Hubble & Milton Humason discovered that the Universe is expanding.
• 1938 Hans Bethe determined that the Sun's energy comes from thermonuclear fusion reactions.
• 1940s Karl Jansky observed that the nucleus of the Milky Way and other celestial objects are strong sources of Radio Waves in 1931. Based on radar technology developed in WWII, Radio Astronomy becomes an active field in the late 1940s.
• 1948 George Gamov developed the Hot Big Bang Theory of the origin of the Universe.
• 1950's chemical composition of the stars; stars build the heavy elements via nuclear fusion reactions, mapped out in a famous paper by Burbidge, Burbidge, Fowler & Hoyle.
• 1954 Radio Galaxies
• 1960-63 Quasars
• 1960s X-ray & Infrared astronomy
• 1965 Arno Penzias and Robert Wilson from Bell Laboratories discovered the cosmic microwave background radiation remnant of the Big Bang.
• 1968 Jocelyn Bell (Burnell) & Anthony Hewish discovered Pulsars
________________________________________
History of Astronomy Links
• History of Astronomy at U. Bonn, maintained on behalf of IAU Commission 41 - The History of Astronomy. History of Astronomy & Archaeoastronomy Links.
• History of Mathematics at St. Andrews U., Scotland, with 1350 biographies & links, including many Astronomers & Physicists.
• The Galileo Project at Rice U.
• The Art of Renaissance Science
• Women in Science
• History of High-Energy Astrophysics
• Calvin Hamilton's History of Space Exploration - part of his Views of the Solar System
1. The seasons became important; during different times of the year, different stellar patterns appear in the sky. In the spring, Virgo and her accompanying constellations signal the time to prepare the earth, to plant crops, and to be wary of floods. In the fall, Orion rises to indicate time to harvest and to prepare for winter.
2. The approximate equivalence of the human menstrual cycle and the 30 day orbital period of the Moon which produces lunar phases led to the belief that the heavens, and the Moon in particular, were related to fertility. (What is the Moon's phase right now?)
3. To early humans facing an uncertain and changeable future, the constancy of the heavens must have suggested perfection and certainly led to deification in many cultures.
4. We may expect that eclipses would have been especially frightening to early humans. After predicting the seasons, eclipse prediction may have been one of the earliest astronomical activities.
Stonehenge, constructed between 3100-2000 BCE on England's Salisbury Plain, may have been a Stoneage astronomical site (observatory is too strong a word), at least in part. Certainly the alignment of the "heelstone" with the rising Sun on Midsummer's Day (June 21, the Summer Solstice) represents a true astronomical alignment, and many other Megalithic sites have similar alignments. In Stonehenge Decoded, astronomer Gerald Hawkins argued that there exist a large number of astronomical alignments, though further study suggests that many of these are fortuitous.
Cosmologist Fred Hoyle has suggested that Stonehenge may have been used to keep track of the solar-lunar eclipse cycle. Far outside the still partially standing ring of Sarsen Stones is a ring of 56 holes, known as the Aubry holes. Hoyle has noted that movement of a marking stone by 3 positions each time the Sun rose over the heelstone (or by one position three times yearly) would complete a circle in 18.67 years -- approximately the period for the "nodes", the intercepts of the lunar and solar paths in the sky, to complete a cycle. Certainly ritual use of Stonehenge would have been more important that its astronomical functions and much of this interpretation must remain speculation. We may be certain, however, that Stonehenge was indeed constructed by Stoneage humans without the assistance of alien astronauts as suggested in some pseudo-scientific books. Visit the Complete Stonehenge
Eastern observers, notably the Chinese, kept careful track of events in the skies, particularly the appearance of "guest stars" -- comets, novae and other transients. Chinese records of the guest star that we now call Comet Halley can be traced back to 240 BCE and possibly as early as 1059 BCE. One of the most important Chinese records is of a guest star that was bright enough to be seen during the daytime for nearly a month in the constellation that we call Taurus in July 1054. We believe this to be the supernova explosion that gave rise to the Crab Nebula, and our knowledge of the date of the explosion itself is a very important key in understanding the deaths of massive stars. This event was also chronicled by the Anasazi in Chaco Canyon and by Native Americans elsewhere, but is curiously absent from European records in the Middle Ages.
As the above suggests, Archaeoastronomy is an active and exciting field of research.
Western scientific history begins with the ancient Greek civilization about 600 BCE.
The Ionian region of Asia Minor appears to have been a site of particular philosophical/scientific/mathematical activity for several centuries.
We will review the progress of science by highlighting a few key natural philosophers, scientists and mathematicians. As Isaac Newton said,"If I have seen further, it is by standing on the shoulders of Giants."
Pythagoras of Samos (~580-500 BCE)
Most famous for his theorem, little is known of his actual work. He founded a school (some would call it a cult) of natural philosophy and mysticism that attracted many followers. The Pythagoreans lived by a strict regimen including vegetarianism, silence for the first 5 years of membership, and anonymity with respect to personal accomplishments (so that it is difficult to know what to ascribe to Pythagoras as opposed to his followers). The Pythagorean Theorem was actually known to the early Babylonians, but it may be that Pythagoras was the first to prove it. The Pythagoreans recognized the existence of irrational numbers and were interested in the relationship between music and mathematics.
Pythagoras developments in astronomy built upon those of Anaximander from whom, apparently, came the idea of perfect circular motion. The Pythagoreans believed that the planets were attached to crystalline spheres, one for each planet, which produced the Music of the Spheres. These spheres were centered on the Earth, which was itself in motion. Pythagoras is also credited with recognizing that the "morning star" and "evening star" are both the planet Venus.
Aristotle (384-322 BCE)
Aristotle was a student of Plato, founding his own school of Natural Philosophy, the Lyceum, in Athens about 335 BCE. Aristotle's philosophy involved the qualitative study of all natural phenomena, pursued without the aid of mathematics which was deemed to be too "perfect" for application on an imperfect terrestrial sphere. In Aristotelian cosmology, the "imperfect" Earth was situated at the center of the Universe (Solar System). It was composed of the four elements: earth, air, water, and fire, each of which sought its natural place in the Universe (e.g. earthen bodies fall to Earth, rain falls from the sky, travelling through rivulets, to streams, to rivers and finally to the sea). Aristotle adopted Pythagoras' model of concentric spheres for the planets, but deduced that the Earth must be immobile. Aristotle's Natural Philosophy was embodied in the writings of St. Thomas Aquinas and became the foundation of Church doctrine and University instruction in medieval times.
Aristarchus of Samos (~310-230 BCE)
Aristarchus concluded that the Solar System must be heliocentric, following his geometrical estimates of the relative sizes and distances of the Earth, Moon and Sun. His geometrical methods were perfectly correct, but the required observations of the exact time of first and third quarter Moon and the duration of lunar eclipse were beyond the instrumental capabilities of his era. He calculated that the Sun is about twenty times farther away than the Moon, about 20 times larger than the Moon and ten times bigger than the Earth. Unfortunately, all of Aristarchus work was lost in the great fire in Alexandria which destroyed the magnificent library and its records of Greek science and culture. A lunar crater bears his name in recognition of his accomplishments.
Eratosthenes of Cyrene (276-197 BCE)
Eratosthenes was a mathematician and geographer. He developed a map of the world, a method for finding prime numbers called Eratosthenes' Sieve, and estimated the circumference of the Earth. His method involved determining the direction to the Sun in Alexandria at noon on the summer solstice and comparing this with the fact that the Sun is overhead in Syene(Aswan), about 500 miles away. Here are the results of a worldwide high school recreation of Eratosthenes' experiment along with pictures of how to do the experiment yourself.
Claudius Ptolemy (~85-165AD)
Ptolemy, Alexandrian (Greek) mathematician, geographer, and astronomer, developed the most sophisticated mathematical model of the motions of the Solar System based upon the geocentric (Earth-centered) model and the principle of perfect circular motion. His model was quite complex in order to follow the details of planetary motions, requiring circles (epicycles) upon off centered circular orbits. His major astronomical work is known as The Almagest. Here's how epicycles work to produce retrograde motion.
Ptolemy's Geography remained the principal work in that field until the time of Columbus.
Copernicus Heliocentric Solar System vs. Ptolemy's Geocentric Model
Both models employed perfect circular motion with epicycles, equants ...
Nikolas Kopernig (Copernicus, 1473-1543)
Copernicus studied mathematics and astronomy in Cracow and Italy, but spent his life as a physician, attorney and church administrator. By Copernicus' time, the Ptolemaic model could no longer reproduce the observed planetary positions. Copernicus developed a heliocentric model of the Solar System which retained the notion of perfect circular motion, but placed the Sun at the center and established the proper order of the planets outward from the Sun. Copernicus model, a mathematical tour de force (not bad for an amateur), was published in De Revolutionibus Orbium Celestium in 1543, the year of his death.
Tyge (Tycho) Brahe (1546-1601)
Danish astronomer Tycho Brahe is chiefly remembered for his meticulous observations, made with instruments of his own design before the advent of the telescope. His early observations were carried out on the island of Hven (now Swedish) where he built a pair of observatories, Uraniborg and later Stjerneborg. In 1572 he observed a supernova and in 1577 a comet. His parallax measures demonstrated that these objects were beyond the Moon, and his measures of the brightness of the supernova showed that it was clearly variable. Tycho's measurements of planetary positions were at variance with the ptolemaic model. He developed his own Solar System model in which the Sun orbits the Earth, but the remaining planets orbit the Sun. Tycho's abrasive nature ultimately led him into disfavor. He moved to the court of Rudolph II in Prague in 1599 where he would pass along his observations to Johannes Kepler. These became the basis for Kepler's Laws of Planetary Motion.
Galileo Galilei (1564-1642)
There is an exquisite WebSite, The Galileo Project about Galileo and his world put together by Rice University's History department. Many of the following links are to pages on this site. Another excellent site at Lawrence Livermore Laboratory is The Art of Renaissance Science.
Galileo was the first "modern scientist". He argued that mathematics, rather than being abstract perfection, is the true language of science. He performed many revolutionary experiments in mechanics and other fields of physics. Among his accomplishments in mechanics are:
• development of the concept of inertia, later refined by Newton.
• a variety of experiments on falling bodies which demonstrated that the acceleration of gravity is independent of mass. There is no evidence that Galileo actually dropped objects from the Tower of Pisa. Rather, his experiments were conducted with an inclined plane as shown in this animation.
• the first Theory of Relativity, valid for velocities much smaller than the speed of light.
Using telescopes of his own design and manufacture, Galileo also made many discoveries in astronomy:
• sunspots on the Sun and craters and mountains on the Moon.
• The so called "Galilean satellites" which orbit Jupiter -- Io (with the volcanos), Europa, Callisto and Ganymede. Here's more on Jupiter and her satellites from the Siderius Nuncius and an animation showing what Galileo observed.
• rings of Saturn.
• the phases of Venus.
Galileo's observations suggested that the heavens were as "imperfect" as the Earth; that other objects in the Solar System have satellites which orbit around them, and that Venus passes through a full range of phases. These observations led him to the conclusion that the Copernican Model of the Solar System is preferable to the Ptolemaic Model. Galileo published his views in Italian in Dialogues Concerning the Two Chief World Systems in 1632. They were in direct contradiction to the world-view taught by the Catholic Church, and he was called before the Italian inquisition in 1633. Galileo was forced to disavow his work, and was sentenced to house arrest for the remainder of of his life.
I highly recommend a tour of the Museum of the History of Science in Florence if you can tear yourself away from the Renaissance Art. Here is a tour of the Museum which has an extensive collection of Galilean exhibits including the famous middle finger. Here is their biography of Florence' greatest scientist.
Johannes Kepler (1571-1630)
Kepler came to Prague to work with Tycho Brahe and his observational data. Kepler was a mathematician and mystic, interested primarily in numerical relationships among objects in the Universe. Using Tycho's unprecedentedly accurate observations, he made highly precise calculations of planetary orbits. Although he could come very close to matching Brahe's data with perfect circlular orbits, his faith in the data led him to continue his calculations until he matched Tycho's accuracy. Kepler developed three mathematical rules for the orbits of the planets:
1. The orbits of the planets are ellipses with the Sun at one focus.
2. The planets sweep out equal areas during equal times of the orbit.
3. The square of the orbital period is proportional to the cube of the planet's distance from the Sun. (If you measure the period in Earth years and the distance in Astronomical Units (1 A.U.= the average distance of the Earth from the Sun), then Period2 = Distance 3.)
Here's a page with some nice animations of Kepler's Rules, and here is another way to play with them.
Obviously Kepler's Rules require that the Sun be the center of the Solar System, in contradiction with the Aristotilean ideal. The first rule eliminates the circular motion which had been fashionable for 2 millennia. The second replaces the idea that planets move at uniform speed around their orbits,with the empirical observation that the planets move more rapidly when they are close to the Sun and more slowly when they are farther away. The third rule is a harbinger of the Law of Gravitation which would be developed by Newton in the latter part of the 17th century.
Isaac Newton (1642-1727)
Certainly the greatest classical Physicist, Newton developed the science of mechanics as we know it. His first development was his Laws of Motion. In order to perform mechanical calculations and to understand Gravity, Newton invented a mathematical tool that he called "fluctions", now known as calculus. At the urging of Edmund Halley, Newton published his Laws of Motion and analysis of Gravity in the Principia Mathematica, probably the greatest physics text ever written, in 1687. Halley, of course, wanted to use Newton's theories to analyze orbits, particularly that of the comet of 1682 which now bears his name. More about Newton's Laws in the next tutorial.
Other pioneers and milestones in the advance of Science:
• 18th Century, William Herschel discovered Uranus, a new planet beyond Jupiter. Barely visible with the unaided eye, Herschel made the observation with his telescope .
• Early in the 19th Century Adams (English) & LeVerrier (French) independently calculated that there must be another planet beyond Uranus that was producing small gravitational disturbances in Uranus' orbit. First observed in 1846 by Hohan Galle, it was named Neptune. (It was actually spotted earlier by Challis in Cambridge, but Challis did not note his discovery until Galle reported his observation.)
• 1930 Clyde Tombaugh discovered Pluto.
• 1910 Harlow Shapley estimated the size of the Milky Way.
• W. H.Pickering and Annie J. Cannon calculated the surface temperatures of the stars.
• Einstein (1905) developed the Theory of Special Relativity, based upon the idea that light travels at the same speed in all frames of reference. Modified Newton's Theory of Gravity by developing the General Theory of Relativity (1916).
• Cecilia Payne-Gaposchkin & Henry Norris Russell determined the composition of stars.
• 1924 Edwin Hubble established that the Andromeda nebula and other "spiral nebulae" are star systems like the Milky Way at great distances.
• 1929 Hubble & Milton Humason discovered that the Universe is expanding.
• 1938 Hans Bethe determined that the Sun's energy comes from thermonuclear fusion reactions.
• 1940s Karl Jansky observed that the nucleus of the Milky Way and other celestial objects are strong sources of Radio Waves in 1931. Based on radar technology developed in WWII, Radio Astronomy becomes an active field in the late 1940s.
• 1948 George Gamov developed the Hot Big Bang Theory of the origin of the Universe.
• 1950's chemical composition of the stars; stars build the heavy elements via nuclear fusion reactions, mapped out in a famous paper by Burbidge, Burbidge, Fowler & Hoyle.
• 1954 Radio Galaxies
• 1960-63 Quasars
• 1960s X-ray & Infrared astronomy
• 1965 Arno Penzias and Robert Wilson from Bell Laboratories discovered the cosmic microwave background radiation remnant of the Big Bang.
• 1968 Jocelyn Bell (Burnell) & Anthony Hewish discovered Pulsars
________________________________________
History of Astronomy Links
• History of Astronomy at U. Bonn, maintained on behalf of IAU Commission 41 - The History of Astronomy. History of Astronomy & Archaeoastronomy Links.
• History of Mathematics at St. Andrews U., Scotland, with 1350 biographies & links, including many Astronomers & Physicists.
• The Galileo Project at Rice U.
• The Art of Renaissance Science
• Women in Science
• History of High-Energy Astrophysics
• Calvin Hamilton's History of Space Exploration - part of his Views of the Solar System
Saturday, July 17, 2010
written report ko na kinopy paste lng talaga
Laguna State Polytechnic University
Sta. Cruz, Laguna
A written report submitted in partial fulfillment of the course requirements in Philosophy and History of Science (Physics M1)
Submitted by:
Joshua Vir Aldrew A. Porca
Submitted to:
Prof. Vilma M. Geronimo
Lesson Proper
What is classification?
Classification is the distinction, identification, and organization of two or more items, information, and facts according to their similarities which are determined through comparison. It gives a closer view on the link between the objects being compared.
According to Gottfried Wilhelm von Leibniz, no two things are “ever exactly alike” that if ever there would be two objects which were so alike that they could not be told apart, they would be the same object. There is always an essential dissimilarity even in a pair of apparently identical objects.
Plato’s theory of universals
1. Theory of “universalia ante rem” (universals before the things)
The link between members of a class is that they are all imitations of an archetype which existed before the world as we know it was made.
2. Theory of “universalia in re” (universals in the things)
Everything is a combination of two things, form and matter.
3. Theory of “universalia post rem” (universals after the things)
Nothing general exists, only particulars.
Four types of similarity (in descending order of usefulness for purposes of identification)
1. Genetic similarity – similarity of objects having similar origins
2. Structural similarity – similarity of objects having similar constituent parts
3. Functional similarity – similarity of objects having similar behavior
4. Apparent similarity – similarity of objects having similar external features
Sta. Cruz, Laguna
A written report submitted in partial fulfillment of the course requirements in Philosophy and History of Science (Physics M1)
Submitted by:
Joshua Vir Aldrew A. Porca
Submitted to:
Prof. Vilma M. Geronimo
Lesson Proper
What is classification?
Classification is the distinction, identification, and organization of two or more items, information, and facts according to their similarities which are determined through comparison. It gives a closer view on the link between the objects being compared.
According to Gottfried Wilhelm von Leibniz, no two things are “ever exactly alike” that if ever there would be two objects which were so alike that they could not be told apart, they would be the same object. There is always an essential dissimilarity even in a pair of apparently identical objects.
Plato’s theory of universals
1. Theory of “universalia ante rem” (universals before the things)
The link between members of a class is that they are all imitations of an archetype which existed before the world as we know it was made.
2. Theory of “universalia in re” (universals in the things)
Everything is a combination of two things, form and matter.
3. Theory of “universalia post rem” (universals after the things)
Nothing general exists, only particulars.
Four types of similarity (in descending order of usefulness for purposes of identification)
1. Genetic similarity – similarity of objects having similar origins
2. Structural similarity – similarity of objects having similar constituent parts
3. Functional similarity – similarity of objects having similar behavior
4. Apparent similarity – similarity of objects having similar external features
lesson plan ko kay maam geronimo
I. Objectives
At the end of the lesson, the students should be able to:
1. Define classification;
2. Identify Plato’s theories of universals;
3. Differentiate the four types of similarity in descending order of usefulness;
4. Understand the importance of classification in philosophy.
II. Subject Matter
A. Topic: Classification
B. References:
1. Philosophy of Science by Caus
2. Microsoft Encarta Premium Suite 2005
3. http://www.google.com
C. Instructional Materials:
1. cartolina
2. black marker
3. tape / double – adhesives
III. Learning Strategies
A. Daily Routine:
1. Prayer
2. Greetings
3. Checking of attendance
B. Review of past lesson:
1. What is language?
2. Why is language important in the study if philosophy?
C. Motivation
The teacher will ask two students to volunteer for the said activity. While the two volunteers are standing in front of the class, the rest of the class will compare them in terms of physical, social , and other attributes.
The activity will test the student’s ability to compare, which is a very useful tool in classification.
D. Lesson Proper
What is classification?
Classification is the distinction, identification, and organization of two or more items, information, and facts according to their similarities which are determined through comparison. It gives a closer view on the link between the objects being compared.
According to Gottfried Wilhelm von Leibniz, no two things are “ever exactly alike” that if ever there would be two objects which were so alike that they could not be told apart, they would be the same object. There is always an essential dissimilarity even in a pair of apparently identical objects.
Plato’s theory of universals:
1. Theory of “universalia ante rem” (universals before the things)
The link between members of a class is that they are all imitations of an archetype which existed before the world as we know it was made.
2. Theory of “universalia in re” (universals in the things)
Everything is a combination of two things, form and matter.
3. Theory of “universalia post rem” (universals after the things)
Nothing general exists, only particulars.
Four types of similarity (in descending order of usefulness for purposes of identification):
1. Genetic similarity – similarity of objects having similar origins
2. Structural similarity – similarity of objects having similar constituent parts
3. Functional similarity – similarity of objects having similar behavior
4. Apparent similarity – similarity of objects having similar external features
IV. Generalization
1. What is classification?
2. Enumerate Plato’s theories of universals and explain each.
3. Differentiate the four types of similarity in descending order of usefulness for purposes of identification.
V. Evaluation
For the teacher to test whether the students understood the lesson, the following examination will be given:
Test I. Multiple Choice
1. It is the distinction, identification, and organization of two or more items, information, and facts according to their similarities which are determined through comparison.
a. classification c. identification
b. comparison d. similarity
2. According to Gottfried Wilhelm von Leibniz, no two things are “ever exactly alike” that if ever there were two objects which were so alike, that they could not be told apart, they would be the same object.
a. Plato c. Socrates
b. G. W. Leibniz d. Wittgenstein
3. The link between members of a class is that they are all imitations of an archetype which existed before the world as we know it was made.
a. universalia in re c. universalia per rem
b. universalia post rem d. universalia ante rem
4. Nothing general exists, only particulars.
a. universalia in re c. universalia per rem
b. universalia post rem d. universalia ante rem
5. Everything is a combination of two things, form and matter.
a. universalia in re c. universalia per rem
b. universalia post rem d. universalia ante rem
Test II. Identification.
6. What is G. W. Leibniz’s full name? Gottfried Wilhelm von Leibniz
7. similarity of objects having similar constituent parts Structural similarity
8. similarity of objects having similar behavior Functional similarity
9. similarity of objects having similar external features Apparent similarity
10. similarity of objects having similar origins Genetic similarity
At the end of the lesson, the students should be able to:
1. Define classification;
2. Identify Plato’s theories of universals;
3. Differentiate the four types of similarity in descending order of usefulness;
4. Understand the importance of classification in philosophy.
II. Subject Matter
A. Topic: Classification
B. References:
1. Philosophy of Science by Caus
2. Microsoft Encarta Premium Suite 2005
3. http://www.google.com
C. Instructional Materials:
1. cartolina
2. black marker
3. tape / double – adhesives
III. Learning Strategies
A. Daily Routine:
1. Prayer
2. Greetings
3. Checking of attendance
B. Review of past lesson:
1. What is language?
2. Why is language important in the study if philosophy?
C. Motivation
The teacher will ask two students to volunteer for the said activity. While the two volunteers are standing in front of the class, the rest of the class will compare them in terms of physical, social , and other attributes.
The activity will test the student’s ability to compare, which is a very useful tool in classification.
D. Lesson Proper
What is classification?
Classification is the distinction, identification, and organization of two or more items, information, and facts according to their similarities which are determined through comparison. It gives a closer view on the link between the objects being compared.
According to Gottfried Wilhelm von Leibniz, no two things are “ever exactly alike” that if ever there would be two objects which were so alike that they could not be told apart, they would be the same object. There is always an essential dissimilarity even in a pair of apparently identical objects.
Plato’s theory of universals:
1. Theory of “universalia ante rem” (universals before the things)
The link between members of a class is that they are all imitations of an archetype which existed before the world as we know it was made.
2. Theory of “universalia in re” (universals in the things)
Everything is a combination of two things, form and matter.
3. Theory of “universalia post rem” (universals after the things)
Nothing general exists, only particulars.
Four types of similarity (in descending order of usefulness for purposes of identification):
1. Genetic similarity – similarity of objects having similar origins
2. Structural similarity – similarity of objects having similar constituent parts
3. Functional similarity – similarity of objects having similar behavior
4. Apparent similarity – similarity of objects having similar external features
IV. Generalization
1. What is classification?
2. Enumerate Plato’s theories of universals and explain each.
3. Differentiate the four types of similarity in descending order of usefulness for purposes of identification.
V. Evaluation
For the teacher to test whether the students understood the lesson, the following examination will be given:
Test I. Multiple Choice
1. It is the distinction, identification, and organization of two or more items, information, and facts according to their similarities which are determined through comparison.
a. classification c. identification
b. comparison d. similarity
2. According to Gottfried Wilhelm von Leibniz, no two things are “ever exactly alike” that if ever there were two objects which were so alike, that they could not be told apart, they would be the same object.
a. Plato c. Socrates
b. G. W. Leibniz d. Wittgenstein
3. The link between members of a class is that they are all imitations of an archetype which existed before the world as we know it was made.
a. universalia in re c. universalia per rem
b. universalia post rem d. universalia ante rem
4. Nothing general exists, only particulars.
a. universalia in re c. universalia per rem
b. universalia post rem d. universalia ante rem
5. Everything is a combination of two things, form and matter.
a. universalia in re c. universalia per rem
b. universalia post rem d. universalia ante rem
Test II. Identification.
6. What is G. W. Leibniz’s full name? Gottfried Wilhelm von Leibniz
7. similarity of objects having similar constituent parts Structural similarity
8. similarity of objects having similar behavior Functional similarity
9. similarity of objects having similar external features Apparent similarity
10. similarity of objects having similar origins Genetic similarity
Philosophical analysis, knowledge, perception, thought,concept, and percepts
Philosophical Analysis is the general term used by philosophers in the analytic tradition that involves breaking down of philosophical issues.
Functions:
• To construct theories about man and the universe
• To examine very carefully everything offered for a belief and its own theories
Analysis – from the Greek word analusis, meaning “to break down”
– the process of breaking down topics or substances into smaller parts to gain a better understanding
Methods of forming analysis:
• Explication
• Redefinition
• Illustration
Knowledge – the expertise and skills acquired by a person through experience or education.
– confident understanding of a subject with the ability to use for a specific purpose.
*acquisition involves complex cognitive processes
Four matters of fact:
• That something exist
• That something can be known
• That there is something which matters
• That something includes the foregoing statements
Other sources of knowledge:
• Customs and traditions
• Sensation and perception
• Intuition
Perception – the process of attaining awareness or understanding of sensory information.
– receiving, collecting, action and taking possession, and apprehension with the mind or senses.
perception experience knowledge science
*Edmund Hasserl
Bracketing – reducing, eliminating past experiences to learn something new that is presented to avoid prejudice.
Thought – are acts of thinking
– opinions and reflections
Concepts – habits of expectation
– serves as representations of objects
– ideas or mental images
Percepts – views, reflections, and impressions
People to remember:
• Titchener – image theory
• Hume –introspecting to discover what the self looked like
– “boundless perception”
• Heraclitus – perception is more or less arbitrarily caused out of the continous stuff.
Functions:
• To construct theories about man and the universe
• To examine very carefully everything offered for a belief and its own theories
Analysis – from the Greek word analusis, meaning “to break down”
– the process of breaking down topics or substances into smaller parts to gain a better understanding
Methods of forming analysis:
• Explication
• Redefinition
• Illustration
Knowledge – the expertise and skills acquired by a person through experience or education.
– confident understanding of a subject with the ability to use for a specific purpose.
*acquisition involves complex cognitive processes
Four matters of fact:
• That something exist
• That something can be known
• That there is something which matters
• That something includes the foregoing statements
Other sources of knowledge:
• Customs and traditions
• Sensation and perception
• Intuition
Perception – the process of attaining awareness or understanding of sensory information.
– receiving, collecting, action and taking possession, and apprehension with the mind or senses.
perception experience knowledge science
*Edmund Hasserl
Bracketing – reducing, eliminating past experiences to learn something new that is presented to avoid prejudice.
Thought – are acts of thinking
– opinions and reflections
Concepts – habits of expectation
– serves as representations of objects
– ideas or mental images
Percepts – views, reflections, and impressions
People to remember:
• Titchener – image theory
• Hume –introspecting to discover what the self looked like
– “boundless perception”
• Heraclitus – perception is more or less arbitrarily caused out of the continous stuff.
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