ThoughtVectors2014

Order of magnitude[edit] Rømer starts with an order of magnitude demonstration that the speed of light must be so great that it takes much less than one second to travel a distance equal to Earth's diameter. The point L on the diagram represents the second quadrature of Jupiter, when the angle between Jupiter and the Sun (as seen from Earth) is 90°.[note 6] Rømer assumes that an observer could see an emergence of Io at the second quadrature (L), and also the emergence which occurs after one orbit of Io around Jupiter (when the Earth is taken to be at point K, the diagram not being to scale), that is 42½ hours later. During those 42½ hours, the Earth has moved further away from Jupiter by the distance LK: this, according to Rømer, is 210 times the Earth's diameter.[note 7] If light travelled at a speed of one Earth-diameter per second, it would take 3½ minutes to travel the distance LK. And if the period of Io's orbit around Jupiter were taken as the time difference between the emergence at L and the emergence at K, the value would be 3½ minutes longer than the true value. Rømer then applies the same logic to observations around the first quadrature (point G), when Earth is moving towards Jupiter. The time difference between an immersion seen from point F and the next immersion seen from point G should be 3½ minutes shorter than the true orbital period of Io. Hence, there should be a difference of about 7 minutes between the periods of Io measured at the first quadrature and those measured at the second quadrature. In practice, no difference is observed at all, from which Rømer concludes that the speed of light must be very much greater than one Earth-diameter per second.[5]

However Rømer also realised that any effect of the finite speed of light would add up over a long series of observations, and it is this cumulative effect that he announced to the Royal Academy of Sciences in Paris. The effect can be illustrated with Rømer's observations from spring 1672. Jupiter was in opposition on 2 March 1672: the first observations of emergences were on 7 March (at 07:58:25) and 14 March (at 09:52:30). Between the two observations, Io had completed four orbits of Jupiter, giving an orbital period of 42 hours 28 minutes 31¼ seconds. The last emergence observed in the series was on 29 April (at 10:30:06). By this time, Io had completed thirty orbits around Jupiter since 7 March: the apparent orbital period is 42 hours 29 minutes 3 seconds. The difference seems minute – 32 seconds – but it meant that the emergence on 29 April was occurring a quarter-hour after it would have been predicted. The only alternative explanation was that the observations on 7 and 14 March were wrong by two minutes.

Ole Christensen Rømer (Danish pronunciation: [o(ː)lə ˈʁœːˀmɐ]; 25 September 1644, Århus – 19 September 1710, Copenhagen) was a Danish astronomer who in 1676 made the first quantitative measurements of the speed of light.

Rømer and the speed of light

Pythagorean proof

he Pythagorean Theorem was known long before Pythagoras, but he may well have been the first to prove it.[6] In any event, the proof attributed to him is very simple, and is called a proof by rearrangement. The two large squares shown in the figure each contain four identical triangles, and the only difference between the two large squares is that the triangles are arranged differently. Therefore, the white space within each of the two large squares must have equal area. Equating the area of the white space yields the Pythagorean Theorem, Q.E.D.[7] That Pythagoras originated this very simple proof is sometimes inferred from the writings of the later Greek philosopher and mathematician Proclus.[8] Several other proofs of this theorem are described below, but this is known as the Pythagorean one.

Pythagorean triples Main article: Pythagorean triple A Pythagorean triple has three positive integers a, b, and c, such that a2 + b2 = c2. In other words, a Pythagorean triple represents the lengths of the sides of a right triangle where all three sides have integer lengths.[1] Evidence from megalithic monuments in Northern Europe shows that such triples were known before the discovery of writing. Such a triple is commonly written (a, b, c). Some well-known examples are (3, 4, 5) and (5, 12, 13). A primitive Pythagorean triple is one in which a, b and c are coprime (the greatest common divisor of a, b and c is 1). The following is a list of primitive Pythagorean triples with values less than 100: (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41), (11, 60, 61), (12, 35, 37), (13, 84, 85), (16, 63, 65), (20, 21, 29), (28, 45, 53), (33, 56, 65), (36, 77, 85), (39, 80, 89), (48, 55, 73), (65, 72, 97)

The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its value is exactly 299,792,458 metres per second, a figure that is exact because the length of the metre is defined from this constant and the international standard for time.[1]

The first quantitative estimate of the speed of light was made in 1676 by Rømer (see Rømer's determination of the speed of light).[83][84] From the observation that the periods of Jupiter's innermost moon Io appeared to be shorter when the Earth was approaching Jupiter than when receding from it, he concluded that light travels at a finite speed, and estimated that it takes light 22 minutes to cross the diameter of Earth's orbit. Christiaan Huygens combined this estimate with an estimate for the diameter of the Earth's orbit to obtain an estimate of speed of light of 220000 km/s, 26% lower than the actual value.[105]

Beginning in the 1880s several experiments were performed to try to detect this motion, the most famous of which is the experiment performed by Albert A. Michelson and Edward W. Morley in 1887.[128] The detected motion was always less than the observational error. Modern experiments indicate that the two-way speed of light is isotropic (the same in every direction) to within 6 nanometres per second.[129]

Pythagoras of Samos (/pɪˈθæɡərəs/; Ancient Greek: Πυθαγόρας ὁ Σάμιος Pythagóras ho Sámios “Pythagoras the Samian”, or simply Πυθαγόρας; Πυθαγόρης in Ionian Greek; c. 570 BC – c. 495 BC)[1][2] was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism.

Since the fourth century AD, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of the other two sides—that is,

While the theorem that now bears his name was known and previously utilized by the Babylonians and Indians, he, or his students, are often said to have constructed the first proof. It must, however, be stressed that the way in which the Babylonians handled Pythagorean numbers implies that they knew that the principle was generally applicable, and knew some kind of proof, which has not yet been found in the (still largely unpublished) cuneiform sources.[47]

Who needs dope when you go on a mind-expanding trip just sitting at your computer?

urfing the web aids in the inspiration of innovative ideas.

The Internet has become an essential propagator of knowledge, both through free as well as paid services. The credibility of this form of education and whether it is safe, secure, and trustworthy, is usually proven through the quality and authenticity of content presented by each website. The World Wide Web has become a remarkable avenue for the academically unprivileged, to amass greater knowledge and know-how on subjects.

The Internet has become an essential propagator of knowledge, both through free as well as paid services. The credibility of this form of education and whether it is safe, secure, and trustworthy, is usually proven through the quality and authenticity of content presented by each website. The World Wide Web has become a remarkable avenue for the academically unprivileged, to amass greater knowledge and know-how on subjects.

The Internet has become an essential propagator of knowledge, both through free as well as paid services. The credibility of this form of education and whether it is safe, secure, and trustworthy, is usually proven through the quality and authenticity of content presented by each website. The World Wide Web has become a remarkable avenue for the academically unprivileged, to amass greater knowledge and know-how on subjects. The entire scope of homeschooling has expanded because of increased accessibility to videos of teachers giving lectures, showing diagrams and explaining concepts, much like a real classroom. Nonprofit organizations too have opened websites that seek volunteers and donations in order to help the ones in need. There are also sites like Wikipedia, Coursera, Babbel, Archive, and Teachertube, among others, that have dedicated themselves to the art of imparting knowledge to people of all age groups.

Surfing the Internet has become a daily routine of the new generation.

The present generation especially the college students are well versed with the new technologies and their application in present networked society

Now the potential reader can access and browse the online information from the whole web while using his/her terminal at home.

ng form of wiki-surfing in particular is Path-Finding [also called 'trail-blazing' or 'railroading'], which is a form of link-surfing where the user deliberately looks for dead links or 'wipe-out pages'. Then, upon finding these links, fills in the relevant information if possible. This is a morally uplifting activity since it gives the internet user pride in the possibility that they are aiding the travels of a fellow link-surfer. As such, path-finding is encouraged in the link-surfing community.

Home/Magazine Archive/July 2009 (Vol. 52, No. 7)/Are We Losing Our Ability to Think Critically?/Full Text News Are We Losing Our Ability to Think Critically? By Samuel Greengard Communications of the ACM, Vol. 52 No. 7, Pages 18-19 10.1145/1538788.1538796 Comments (3) View as: Print ACM Digital Library Full Text (PDF) In the Digital Edition Share: Send by email Share on reddit Share on StumbleUpon Share on Tweeter Share on Facebook More Sharing ServicesShare Society has long cherished the ability to think beyond the ordinary. In a world where knowledge is revered and innovation equals progress, those able to bring forth greater insight and understanding are destined to make their mark and blaze a trail to greater enlightenment. "Critical thinking as an attitude is embedded in Western culture. There is a belief that argument is the way to finding truth," observes Adrian West, research director at the Edward de Bono Foundation U.K., and a former computer science lecturer at the University of Manchester. "Developing our abilities to think more clearly, richly, fully—individually and collectively—is absolutely crucial [to solving world problems]." To be sure, history is filled with tales of remarkable thinkers who have defined and redefined our world views: Sir Isaac Newton discovering gravity; Voltaire altering perceptions about society and religious dogma; and Albert Einstein redefining the view of the universe. But in an age of computers, video games, and the Internet, there's a growing question about how technology is changing critical thinking and whether society benefits from it. Although there's little debate that computer technology complements—and often enhances—the human mind in the quest to store information and process an ever-growing tangle of bits and bytes, there's increasing concern that the same technology is changing the way we approach complex problems and conundrums, and making it more difficult to really think. "We're exposed to [greater amounts of] poor yet charismatic thinking, the fads of intellectual fashion, opinion, and mere assertion," says West. "The wealth of communications and information can easily overwhelm our reasoning abilities." What's more, it's ironic that ever-growing piles of data and information do not equate to greater knowledge and better decision-making. What's remarkable, West says, is just "how little this has affected the quality of our thinking." According to the National Endowment for the Arts, literary reading declined 10 percentage points from 1982 to 2002 and the rate of decline is accelerating. Many, including Patricia Greenfield, a UCLA distinguished professor of psychology and director of the Children's Digital Media Center, Los Angeles, believe that a greater focus on visual media exacts a toll. "A drop-off in reading has possibly contributed to a decline in critical thinking," she says. "There is a greater emphasis on real-time media and multitasking rather than focusing on a single thing." Nevertheless, the verdict isn't in and a definitive answer about how technology affects critical thinking is not yet available. Instead, critical thinking lands in a mushy swamp somewhere between perception and reality; measurable and incomprehensible. It's largely a product of our own invention—and a subjective one at that. And although technology alters the way we see, hear, and assimilate our world—the act of thinking remains decidedly human. Back to Top Rethinking Thinking Arriving at a clear definition for critical thinking is a bit tricky. Wikipedia describes it as "purposeful and reflective judgment about what to believe or what to do in response to observations, experience, verbal or written expressions, or arguments." Overlay technology and that's where things get complex. "We can do the same critical-reasoning operations without technology as we can with it—just at different speeds and with different ease," West says. What's more, while it's tempting to view computers, video games, and the Internet in a monolithic good or bad way, the reality is that they may be both good and bad, and different technologies, systems, and uses yield entirely different results. For example, a computer game may promote critical thinking or diminish it. Reading on the Internet may ratchet up one's ability to analyze while chasing an endless array of hyperlinks may undercut deeper thought.

Reading on the Internet may ratchet up one's ability to analyze while chasing an endless array of hyperlinks may undercut deeper thought.