Eratosthenes (Ἐρατοσθένης)
Portrait of Eratosthenes
Born	276 BC Cyrene
Died	194 BC Alexandria
Ethnicity	Greek
Occupation	Scholar, librarian, poet and inventor

Eratosthenes of Cyrene (Ancient Greek: Ἐρατοσθένης, IPA: [eratostʰénɛːs]; English /ɛrəˈtɒsθəniːz/; c. 276 BC^[1] – c. 195 BC^[2]) was a Greek mathematician, geographer, poet, athlete, astronomer, and music theorist.

He was the first person to use the word "geography" and invented the discipline of geography as we understand it.^[3] He invented a system of latitude and longitude.

He was the first person to calculate the circumference of the earth by using a measuring system using stades, or the length of stadiums during that time period (with remarkable accuracy). He was the first to calculate the tilt of the Earth's axis (also with remarkable accuracy). He may also have accurately calculated the distance from the earth to the sun and invented the leap day.^[4] He also created the first map of the world incorporating parallels and meridians within his cartographic depictions based on the available geographical knowledge of the era. In addition, Eratosthenes was the founder of scientific chronology; he endeavored to fix the dates of the chief literary and political events from the conquest of Troy.

According to an entry^[5] in the Suda (a 10th century reference), his contemporaries nicknamed him beta, from the second letter of the Greek alphabet, because he supposedly proved himself to be the second best in the world in almost every field.^[6]

Life[link]

19th century reconstruction of Eratosthenes' map of the known world, c. 194 BC

Eratosthenes was born in Cyrene (in modern-day Libya). He was the third chief librarian of the Great Library of Alexandria, the center of science and learning in the ancient world, and died in Alexandria, then the capital of Ptolemaic Egypt.

Eratosthenes studied in Alexandria, and claimed to have also studied for some years in Athens. In 236 BC he was appointed by Ptolemy III Euergetes I as librarian of the Alexandrian library, succeeding the second librarian, Apollonius of Rhodes.^[7] He made several important contributions to mathematics and science, and was a good friend to Archimedes. Around 255 BC he invented the armillary sphere. In On the Circular Motions of the Celestial Bodies, Cleomedes credited him with having calculated the Earth's circumference around 240 BC, using knowledge of the angle of elevation of the sun at noon on the summer solstice in Alexandria and on Elephantine Island near Syene (now Aswan, Egypt).

Eratosthenes criticized Aristotle for arguing that humanity was divided into Greeks and barbarians, and that the Greeks should keep themselves racially pure, believing there was good and bad in every nation.^[8] By 195 BC, Eratosthenes became blind. He died in 194 BC at the age of 82.

Eratosthenes' measurement of the Earth's circumference[link]

Measurements taken at Alexandria (A) and Syene (S)

Eratosthenes calculated the circumference of the Earth without leaving Egypt. Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet (known in Greek as Syene, and in the modern day as Aswan) on the Tropic of Cancer, the sun would appear at the zenith, directly overhead (he had been told that the shadow of someone looking down a deep well would block the reflection of the Sun at noon). He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the sun was 1/50th of a circle (7°12') south of the zenith on the solstice noon. Assuming that the Earth was spherical (360°), and that Alexandria was due north of Syene, he concluded that the meridian arc distance from Alexandria to Syene must therefore be 1/50 = 7°12'/360°, and was therefore 1/50 of the total circumference of the Earth. His knowledge of the size of Egypt after many generations of surveying trips for the Pharaonic bookkeepers gave a distance between the cities of 5000 stadia (about 500 geographical miles or 800 km). This distance was corroborated by inquiring about the time that it takes to travel from Syene to Alexandria by camel. He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is frequently argued. The common Attic stadion was about 185 m,^[9] which would imply a circumference of 46,620 km, i.e. 16.3% too large. However, if we assume that Eratosthenes used the "Egyptian stadion"^[10] of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 2%.^[11]

Other astronomical distances[link]

This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (March 2009)

Eusebius of Caesarea in his Preparatio Evangelica includes a brief chapter of three sentences on celestial distances (Book XV, Chapter 53). He states simply that Eratosthenes found the distance to the sun to be "σταδίων μυριάδας τετρακοσίας και οκτωκισμυρίας" (literally "of stadia myriads 400 and 80,000") and the distance to the moon to be 780,000 stadia. The expression for the distance to the sun has been translated either as 4,080,000 stadia (1903 translation by E. H. Gifford), or as 804,000,000 stadia (edition of Edouard des Places, dated 1974–1991). The meaning depends on whether Eusebius meant 400 myriad plus 80,000 or "400 and 80,000" myriad.

With a stadium of 185 meters, 804,000,000 stadia is 149,000,000 kilometers, the modern distance from the earth to the sun.

The NASA site gives the modern distance from the earth to the moon as "English: 238855 miles. Scientific Notation: 3.84400 x 10^5 km". [3]

Prime numbers[link]

Eratosthenes also proposed a simple algorithm for finding prime numbers. This algorithm is known in mathematics as the Sieve of Eratosthenes.

In mathematics, the sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), one of a number of prime number sieves, is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e. not prime) the multiples of each prime, starting with the multiples of 2. The multiples of a given prime are generated starting from that prime, as a sequence of numbers with the same difference, equal to that prime, between consecutive numbers.[1] This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime.

Works[link]

• Περὶ τῆς ἀναμετρήσεως τῆς γῆς (On the Measurement of the Earth)^[12] (lost, summarized by Cleomedes)
• Geographica (lost, criticized by Strabo)
• Arsinoe (a memoir of queen Arsinoe; lost; quoted by Athenaeus in the Deipnosophistae)
• A fragmentary collection of Hellenistic myths about the constellations, called Catasterismi (Katasterismoi), was attributed to Eratosthenes, perhaps to add to its credibility.

Things Named after Eratosthenes[link]

Eratosthenes (crater) on the moon

• Eratosthenes (crater) on the moon
• Eratosthenian period in the lunar geologic timescale
• Eratosthenes Seamount in the eastern Mediterranean Sea

See also[link]

Atlas portal

• History of geodesy

Notes[link]

Further reading[link]

External links[link]

Wikimedia Commons has media related to: Eratosthenes

Wikisource has original works written by or about: Eratosthenes

• Bernhardy, Gottfried: "Eratosthenica" Berlin 1822 Reprinted Osnabruck 1968 (German text)
• Bernhardy, Gottfried: Eratosthenica Berlin, 1822 (PDF) (Latin/Greek)
• Eratosthenes' sieve in Javascript
• Eratosthenes' sieve as a simple algorithm
• About Eratosthenes' methods, including a Java applet
• How to measure the earth with Eratosthenes' method
• How the Greeks estimated the distances to the moon and sun
• Eratosthenes on PBS.org
• Measuring the earth with Eratosthenes' method
• List of ancient Greek mathematecians and contemporaries of Eratosthenes
• New Advent Encyclopedia article on the Library of Alexandria
• Eratosthenes' sieve explored and visualised in Flash
• Eratosthenes' sieve in classic BASIC all-web based interactive programming environment
• Following in the footsteps of Eratosthenes : project fr:La main à la pâte.

Carl Sagan
Sagan in 1980
Born	(1934-11-09)November 9, 1934 Brooklyn, New York, U.S.
Died	December 20, 1996(1996-12-20) (aged 62) Seattle, Washington, U.S.
Residence	United States[1]
Nationality	United States
Fields	Astronomy, astrophysics, cosmology, astrobiology, space science, planetary science
Institutions	Cornell University Harvard University Smithsonian Astrophysical Observatory University of California, Berkeley
Alma mater	University of Chicago (B.A.), (B.Sc.), (M.Sc.), (PhD)
Known for	Search for Extra-Terrestrial Intelligence (SETI) Cosmos: A Personal Voyage Cosmos Voyager Golden Record Pioneer plaque Contact Pale Blue Dot
Notable awards	NASA Distinguished Public Service Medal (1977) Pulitzer Prize for General Non-Fiction (1978) Oersted Medal (1990) National Academy of Sciences Public Welfare Medal (1994)

Carl Edward Sagan ( /ˈseɪɡɪn/; November 9, 1934 – December 20, 1996) was an American astronomer, astrophysicist, cosmologist, author, science popularizer, and science communicator in astronomy and natural sciences. He published more than 600 scientific papers^[2] and articles and was author, co-author or editor of more than 20 books. He advocated scientifically skeptical inquiry and the scientific method, pioneered exobiology and promoted the Search for Extra-Terrestrial Intelligence (SETI).

Sagan is known for his popular science books and for the award-winning 1980 television series Cosmos: A Personal Voyage, which he narrated and co-wrote.^[3] The book Cosmos was published to accompany the series. Sagan wrote the novel Contact, the basis for a 1997 film of the same name.

Early life[link]

Carl Sagan was born in Brooklyn, New York,^[4] to a Ukrainian Jewish family. His father, Sam Sagan, was an immigrant garment worker from Kamenets-Podolsk, Ukraine;^[5] his mother, Rachel Molly Gruber, a housewife. Carl was named in honor of Rachel's biological mother, Chaiya Clara, in Sagan's words, "the mother she never knew." Sagan graduated from Rahway High School in Rahway, New Jersey, in 1951.^[6]

He had a sister, Carol, and the family lived in a modest apartment near the Atlantic Ocean, in Bensonhurst, a Brooklyn neighborhood. According to Sagan, they were Reform Jews, the most liberal of the three main Jewish groups. Both Sagan and his sister agree that their father was not especially religious, but that their mother "definitely believed in God, and was active in the temple ... and served only Kosher meat."^[6]:12 During the height of the Depression, his father had to accept a job as a theater usher.

According to biographer Keay Davidson, Sagan's "inner war" was a result of his close relations with both his parents, who were in many ways "opposites." Sagan traced his later analytical urges to his mother, a woman who had known "extreme poverty as a child," and had grown up almost homeless in New York City during World War I and the 1920s.^[6]:2 She had her own intellectual ambitions as a young woman, but they were blocked by social restrictions, because of her poverty, her being a woman and wife, and her Jewish ethnicity. Davidson notes that she therefore "worshiped her only son, Carl. He would fulfill her unfulfilled dreams."^[6]:2

However, his "sense of wonder" came from his father, who was a "quiet and soft-hearted escapee from the Czar." In his free time, he gave apples to the poor, or helped soothe labor-management tensions within New York's "tumultuous" garment industry.^[6]:2 Although he was "awed" by Carl's "brilliance, his boyish chatter about stars and dinosaurs," he took his son's inquisitiveness in stride, as part of his growing up.^[6]:2 In his later years as a writer and scientist, Sagan would often draw on his childhood memories to illustrate scientific points, as he did in his book, Shadows of Forgotten Ancestors.^[6]:9 Sagan describes his parents' influence on his later thinking:

My parents were not scientists. They knew almost nothing about science. But in introducing me simultaneously to skepticism and to wonder, they taught me the two uneasily cohabiting modes of thought that are central to the scientific method.^[7]

1939 World's Fair[link]

Sagan recalls that one of his best experiences was when he was four or five years old, his parents took him to the 1939 New York World's Fair. The exhibits became a turning point in his life. He later recalled the moving map of the "America of Tomorrow" exhibit: "It showed beautiful highways and cloverleaves and little General Motors cars all carrying people to skyscrapers, buildings with lovely spires, flying buttresses—and it looked great!"^[6]:14 At other exhibits, he remembered how a flashlight that shined on a photoelectric cell created a cracking sound, and how the sound from a tuning fork became a wave on an oscilloscope. He also witnessed the future media technology that would replace radio: television. Sagan wrote:

Plainly, the world held wonders of a kind I had never guessed. How could a tone become a picture and light become a noise?^[6]:14

He also saw one of the Fair's most publicized events, the burial of a time capsule at Flushing Meadows, which contained mementos of the 1930s to be recovered by Earth's descendants in a future millennium. "The time capsule thrilled Carl," writes Davidson. As an adult, Sagan and his colleagues created similar time capsules, but ones that would be sent out into the galaxy. These were the Pioneer plaque and the Voyager Golden Record records, all of which were spinoffs of Sagan's memories of the World Fair.^[6]:15

World War II[link]

During World War II, Sagan's family worried about the fate of their European relatives. Sagan, however, was generally unaware of the details of the ongoing war. He writes, "Sure, we had relatives who were caught up in the Holocaust. Hitler was not a popular fellow in our household ... But on the other hand, I was fairly insulated from the horrors of the war." His sister, Carol, said that their mother "above all wanted to protect Carl ... She had an extraordinarily difficult time dealing with World War II and the Holocaust."^[6]:15 Sagan's book, The Demon-Haunted World (1996), included his memories of this conflicted period, when his family dealt with the realities of the war in Europe, but tried to prevent it from undermining his optimistic spirit.^[7]

Inquisitiveness about nature[link]

Soon after entering elementary school, he began to express a strong inquisitiveness about nature. Sagan recalled taking his first trips to the public library alone, at the age of five, when his mother got him a library card. He wanted to learn what stars were, since none of his friends or their parents could give him a clear answer:

I went to the librarian and asked for a book about stars ... And the answer was stunning. It was that the Sun was a star but really close. The stars were suns, but so far away they were just little points of light ... The scale of the universe suddenly opened up to me. It was a kind of religious experience. There was a magnificence to it, a grandeur, a scale which has never left me. Never ever left me.^[6]:18

About the time he was six or seven, he and a close friend took trips to the American Museum of Natural History in New York City. While there, they went to the Hayden Planetarium and walked around the museum's exhibits of space objects, such as meteorites, and displays of dinosaurs and animals in natural settings. Sagan writes about those visits:

I was transfixed by the dioramas—lifelike representations of animals and their habitats all over the world. Penguins on the dimly lit Antarctic ice; ... a family of gorillas, the male beating his chest, ... an American grizzly bear standing on his hind legs, ten or twelve feet tall, and staring me right in the eye.^[6]:18

His parents helped nurture his growing interest in science by buying him chemistry sets and reading materials.^[8] His interest in space, however, was his primary focus, especially after reading science fiction stories by writers such as Edgar Rice Burroughs, which stirred his imagination about life on other planets, such as Mars. According to biographer Ray Spangenburg, these early years as Sagan tried to understand the mysteries of the planets, became a "driving force in his life, a continual spark to his intellect, and a quest that would never be forgotten."^[7]

Education and scientific career[link]

He attended the University of Chicago, where he participated in the Ryerson Astronomical Society,^[9] received a bachelor of arts in self-proclaimed "nothing" with general and special honors in 1954, a bachelor of science in physics in 1955, and a master of science in physics in 1956 before earning a PhD in astronomy and astrophysics in 1960.^[10][11][12] During his time as an honors program undergraduate, Sagan worked in the laboratory of the geneticist H. J. Muller and wrote a thesis on the origins of life with physical chemist H.C. Urey. From 1960 to 1962 Sagan was a Miller Fellow at the University of California, Berkeley. From 1962 to 1968, he worked at the Smithsonian Astrophysical Observatory in Cambridge, Massachusetts.

Sagan lectured and did research at Harvard University until 1968, when he moved to Cornell University in Ithaca, New York. He became a full Professor at Cornell in 1971, and he directed the Laboratory for Planetary Studies there. From 1972 to 1981, Sagan was the Associate Director of the Center for Radio Physics and Space Research at Cornell.

Sagan was associated with the US space program from its inception. From the 1950s onward, he worked as an advisor to NASA, where one of his duties included briefing the Apollo astronauts before their flights to the Moon. Sagan contributed to many of the robotic spacecraft missions that explored the solar system, arranging experiments on many of the expeditions. He conceived the idea of adding an unalterable and universal message on spacecraft destined to leave the solar system that could potentially be understood by any extraterrestrial intelligence that might find it. Sagan assembled the first physical message that was sent into space: a gold- anodized plaque, attached to the space probe Pioneer 10, launched in 1972. Pioneer 11, also carrying another copy of the plaque, was launched the following year. He continued to refine his designs; the most elaborate message he helped to develop and assemble was the Voyager Golden Record that was sent out with the Voyager space probes in 1977. Sagan often challenged the decisions to fund the Space Shuttle and Space Station at the expense of further robotic missions.^[13]

Sagan taught a course on critical thinking at Cornell University until he died in 1996 from pneumonia, a few months after finding that he was in remission of myelodysplastic syndrome.

Scientific achievements[link]

Sagan's contributions were central to the discovery of the high surface temperatures of the planet Venus. In the early 1960s no one knew for certain the basic conditions of that planet's surface, and Sagan listed the possibilities in a report later depicted for popularization in a Time-Life book, Planets. His own view was that Venus was dry and very hot as opposed to the balmy paradise others had imagined. He had investigated radio emissions from Venus and concluded that there was a surface temperature of 500 °C (900 °F). As a visiting scientist to NASA's Jet Propulsion Laboratory, he contributed to the first Mariner missions to Venus, working on the design and management of the project. Mariner 2 confirmed his conclusions on the surface conditions of Venus in 1962.

Sagan was among the first to hypothesize that Saturn's moon Titan might possess oceans of liquid compounds on its surface and that Jupiter's moon Europa might possess subsurface oceans of water. This would make Europa potentially habitable.^[14] Europa's subsurface ocean of water was later indirectly confirmed by the spacecraft Galileo. The mystery of Titan's reddish haze was also solved with Sagan's help. The reddish haze was revealed to be due to complex organic molecules constantly raining down onto Titan's surface.^[15]

He further contributed insights regarding the atmospheres of Venus and Jupiter as well as seasonal changes on Mars. Sagan established that the atmosphere of Venus is extremely hot and dense with pressures increasing steadily all the way down to the surface. He also perceived global warming as a growing, man-made danger and likened it to the natural development of Venus into a hot, life-hostile planet through a kind of runaway greenhouse effect. Sagan and his Cornell colleague Edwin Ernest Salpeter speculated about life in Jupiter's clouds, given the planet's dense atmospheric composition rich in organic molecules. He studied the observed color variations on Mars' surface and concluded that they were not seasonal or vegetational changes as most believed but shifts in surface dust caused by windstorms.

Sagan is best known, however, for his research on the possibilities of extraterrestrial life, including experimental demonstration of the production of amino acids from basic chemicals by radiation.^[16]

He is also the 1994 recipient of the Public Welfare Medal, the highest award of the National Academy of Sciences for "distinguished contributions in the application of science to the public welfare."^[17] He was denied membership in the Academy, reportedly because his media activities made him unpopular with many other scientists.^[18]

Scientific advocacy[link]

Planetary Society members at the organization's founding. Carl Sagan is seated on the right.

Sagan's ability to convey his ideas allowed many people to better understand the cosmos—simultaneously emphasizing the value and worthiness of the human race, and the relative insignificance of the Earth in comparison to the universe. He delivered the 1977 series of Royal Institution Christmas Lectures in London.^[19] He hosted and, with Ann Druyan, co-wrote and co-produced the highly popular thirteen-part PBS television series Cosmos: A Personal Voyage modeled on Jacob Bronowski's The Ascent of Man.

Cosmos covered a wide range of scientific subjects including the origin of life and a perspective of our place in the universe. The series was first broadcast by the Public Broadcasting Service in 1980, winning an Emmy and a Peabody Award. It has been broadcast in more than 60 countries and seen by over 500 million people,^[3][20] making it the most widely watched PBS program in history.^[21] In addition, Time magazine ran a cover story about Sagan soon after the show broadcast, referring to him as "creator, chief writer and host-narrator of the new public television series Cosmos, [and] takes the controls of his fantasy spaceship."^[22]

Sagan was a proponent of the search for extraterrestrial life. He urged the scientific community to listen with radio telescopes for signals from potential intelligent extraterrestrial life-forms. Sagan was so persuasive that by 1982 he was able to get a petition advocating SETI published in the journal Science and signed by 70 scientists including seven Nobel Prize winners. This was a tremendous increase in the respectability of this controversial field. Sagan also helped Dr. Frank Drake write the Arecibo message, a radio message beamed into space from the Arecibo radio telescope on November 16, 1974, aimed at informing potential extraterrestrials about Earth.

Sagan was chief technology officer of the professional planetary research journal Icarus for twelve years. He co-founded the Planetary Society, the largest space-interest group in the world, with over 100,000 members in more than 149 countries, and was a member of the SETI Institute Board of Trustees. Sagan served as Chairman of the Division for Planetary Science of the American Astronomical Society, as President of the Planetology Section of the American Geophysical Union, and as Chairman of the Astronomy Section of the American Association for the Advancement of Science.

At the height of the Cold War, Sagan became involved in public awareness efforts for the effects of nuclear war when a mathematical climate model suggested that a substantial nuclear exchange could upset the delicate balance of life on Earth. He was one of five authors—the "S" of the "TTAPS" report as the research paper came to be known. He eventually co-authored the scientific paper hypothesizing a global nuclear winter following nuclear war.^[23] He also co-authored the book A Path Where No Man Thought: Nuclear Winter and the End of the Arms Race, a comprehensive examination of the phenomenon of nuclear winter.

Sagan also wrote books to popularize science which reflected and expanded upon some of the themes of A Personal Voyage, and became the best-selling science book ever published in English;^[24] The Dragons of Eden: Speculations on the Evolution of Human Intelligence, which won a Pulitzer Prize; and Broca's Brain: Reflections on the Romance of Science. Sagan also wrote the best-selling science fiction novel Contact in 1985, based on a film treatment he wrote with his wife in 1979, but he did not live to see the book's 1997 motion picture adaptation, which starred Jodie Foster and won the 1998 Hugo Award for Best Dramatic Adaption.

Pale Blue Dot: Earth is a bright pixel when photographed from "Voyager 1" six billion kilometers out (past Pluto). Sagan encouraged NASA to generate this image.

He wrote a sequel to Cosmos, Pale Blue Dot: A Vision of the Human Future in Space, which was selected as a notable book of 1995 by The New York Times. He appeared on PBS' Charlie Rose program in January 1995.^[25] Sagan also wrote an introduction for the bestselling book by Stephen Hawking, A Brief History of Time. Sagan was also known for his popularization of science, his efforts to increase scientific understanding among the general public, and his positions in favor of scientific skepticism and against pseudoscience, such as his debunking of the Betty and Barney Hill abduction. To mark the tenth anniversary of Sagan's death, David Morrison, a former student of Sagan, recalled "Sagan's immense contributions to planetary research, the public understanding of science, and the skeptical movement" in Skeptical Inquirer.^[26]

Sagan hypothesized in January 1991 that enough smoke from the 1991 Kuwaiti oil fires "might get so high as to disrupt agriculture in much of South Asia ..." He later conceded in The Demon-Haunted World that this prediction did not turn out to be correct: "it was pitch black at noon and temperatures dropped 4°–6 °C over the Persian Gulf, but not much smoke reached stratospheric altitudes and Asia was spared."^[27] A 2007 study noted that modern computer models have been applied to the Kuwait oil fires, finding that individual smoke plumes are not able to loft smoke into the stratosphere, but that smoke from fires covering a large area, like some forest fires or the burning of cities that would be expected to follow a nuclear strike, would loft significant amounts of smoke into the stratosphere.^{[28][29][30][31]}

In his later years Sagan advocated the creation of an organized search for near Earth objects that might impact the Earth.^[32] When others suggested creating large nuclear bombs that could be used to alter the orbit of a NEO that was predicted to hit the Earth, Sagan proposed the Deflection Dilemma: If we create the ability to deflect an asteroid away from the Earth, then we also create the ability to deflect an asteroid towards the Earth—providing an evil power with a true doomsday bomb.^[33][34]

Billions and billions[link]

Sagan with a model of the Viking Lander probes which would land on Mars. Sagan examined possible landing sites for Viking along with Mike Carr and Hal Masursky.

From Cosmos and his frequent appearances on The Tonight Show Starring Johnny Carson, Sagan became associated with the catchphrase "billions and billions". Sagan stated that he never actually used the phrase in the Cosmos series.^[35] The closest that he ever came was in the book Cosmos, where he talked of "billions upon billions":^[36]