Tag Archives: Vsauce

Flat Earther

Eratosthenes calculated the circumference of the Earth without leaving Egypt. He knew that at local noon on the summer solstice in Syene (modern Aswan, Egypt), the Sun was directly overhead. He knew this because the shadow of someone looking down a deep well at that time in Syene blocked the reflection of the Sun on the water. He measured the Sun’s angle of elevation at noon on the same day in Alexandria. The method of measurement was to make a scale drawing of that triangle which included a right angle between a vertical rod and its shadow. This turned out to be about 7°, or 1/50th of the way around a circle. Taking the Earth as spherical, and knowing both the distance and direction of Syene, he concluded that the Earth’s circumference was fifty times that distance.

His knowledge of the size of Egypt was founded on the work of many generations of surveying trips. Pharaonic bookkeepers gave a distance between Syene and Alexandria of 5,000 stadia (a figure that was checked yearly).  Some say that the distance was corroborated by inquiring about the time that it took to travel from Syene to Alexandria by camel. Carl Sagan says that Eratosthenes paid a man to walk and measure the distance. Some claim Eratosthenes used the Olympic stade of 176.4 m, which would imply a circumference of 44,100 km, an error of 10%,[16] but the 184.8 m Italian stade became (300 years later) the most commonly accepted value for the length of the stade,[16] which implies a circumference of 46,100 km, an error of 15%.[16] It was unlikely, even accounting for his extremely primitive measuring tools, that Eratosthenes could have calculated an accurate measurement for the circumference of the Earth. He made three important assumptions (none of which is perfectly accurate):

  1. That the distance between Alexandria and Syene was 5000 stadia,
  2. That the Earth is a perfect sphere.
  3. That light rays emanating from the Sun are parallel.

Eratosthenes later rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia, likely for reasons of calculation simplicity as the larger number is evenly divisible by 60.[16] In 2012, Anthony Abreu Mora repeated Eratosthenes’ calculation with more accurate data; the result was 40,074 km, which is 66 km different (0.16%) from the currently accepted polar circumference of the Earth.

Seventeen hundred years after Eratosthenes’ death, while Christopher Columbus studied what Eratosthenes had written about the size of the Earth, he chose to believe, based on a map by Toscanelli, that the Earth’s circumference was one-third smaller. Had Columbus set sail knowing that Eratosthenes’ larger circumference value was more accurate, he would have known that the place that he made landfall was not Asia, but rather the New World.

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Epistemology

Is Justified True Belief Knowledge?

EDMUND GETTIER
Edmund Gettier is Professor Emeritus at the University of Massachusetts,
Amherst. This short piece, published in 1963, seemed to many decisively to
refute an otherwise attractive analysis of knowledge. It stimulated a renewed
effort, still ongoing, to clarify exactly what knowledge comprises.

Gettier problem

From Wikipedia, the free encyclopedia

The Gettier problem, in the field of epistemology, is a landmark philosophical problem with our understanding of knowledge. Attributed to American philosopher Edmund Gettier, Gettier-type counterexamples (called “Gettier-cases”) overturned the long-held justified true belief (or JTB) account of knowledge. On the JTB account, knowledge is equivalent to justified true belief, and if all three conditions (justification, truth, and belief) are met of a given claim, then we have knowledge of that proposition. In his three-page 1963 paper, titled Is Justified True Belief Knowledge?, Gettier showed, by means of two counterexamples, that there were cases where individuals had justified true belief of a claim, but still failed to know it. Thus, Gettier showed that the JTB account was inadequate—it could not account for all of knowledge. The JTB account was first credited to Plato, though Plato argued against this very account of knowledge in the Theaetetus (210a).

The term “Gettier problem”, or “Gettier case”, or even the verb Gettiered is sometimes used to describe any case in epistemology that purports to repudiate the JTB account.

Responses to Gettier’s paper have been numerous. Some rejected Gettier’s examples, while others sought to adjust the JTB account to blunt the force of counterexamples. Gettier problems have even found their way into experiments, where the intuitive responses of people of varying demographics to Gettier cases have been studied.

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a river

The ship of Theseus, also known as Theseus’ paradox, is a thought experiment that raises the question of whether an object that has had all of its components replaced remains fundamentally the same object. The paradox is most notably recorded by Plutarch in Life of Theseus from the late first century. Plutarch asked whether a ship that had been restored by replacing every single wooden part remained the same ship.

The paradox had been discussed by other ancient philosophers such as Heraclitus and Plato prior to Plutarch’s writings,[1] and more recently by Thomas Hobbes and John Locke. Several variants are known, including the grandfather’s axe, which has had both head and handle replaced.

power laws

http://en.wikipedia.org/wiki/Zipf%27s_law
http://en.wikipedia.org/wiki/Bradford%27s_law
http://en.wikipedia.org/wiki/Pareto_distribution
http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html
http://phys.ubbcluj.ro/~zneda/edu/mc/pareto.pdf

Zipf’s law /ˈzɪf/, an empirical law formulated using mathematical statistics, refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution, one of a family of related discrete power law probability distributions. The law is named after the American linguist George Kingsley Zipf (1902–1950), who popularized it and sought to explain it (Zipf 1935, 1949), though he did not claim to have originated it.[1] The French stenographer Jean-Baptiste Estoup (1868–1950) appears to have noticed the regularity before Zipf.[2] It was also noted in 1913 by German physicist Felix Auerbach[3] (1856–1933).