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47-513: Nova (stylized as NOVΛ ) is an American popular science television program produced by WGBH in Boston , Massachusetts , since 1974. It is broadcast on PBS in the United States, and in more than 100 other countries. The program has won many major television awards. Nova often includes interviews with scientists doing research in the subject areas covered and occasionally includes footage of

94-510: A / b = c / d {\displaystyle a/b=c/d} ⁠ if and only if the ratios ⁠ n / m {\displaystyle n/m} ⁠ that are larger than ⁠ a / b {\displaystyle a/b} ⁠ are the same as the ones that are larger than ⁠ c / d {\displaystyle c/d} ⁠ , and likewise for "equal" and "smaller". This can be compared with Dedekind cuts that define

141-533: A = n ⋅ b {\displaystyle m\cdot a=n\cdot b} ⁠ , then also ⁠ m ⋅ c = n ⋅ d {\displaystyle m\cdot c=n\cdot d} ⁠ . Finally, if ⁠ m ⋅ a < n ⋅ b {\displaystyle m\cdot a<n\cdot b} ⁠ , then also ⁠ m ⋅ c < n ⋅ d {\displaystyle m\cdot c<n\cdot d} ⁠ . This means that ⁠

188-407: A general audience . While science journalism focuses on recent scientific developments, popular science is more broad ranging. It may be written by professional science journalists or by scientists themselves. It is presented in many forms, including books, film and television documentaries, magazine articles, and web pages. Before the modern specialization and professionalization of science, there

235-513: A birth year of c.  390 BC . His name Eudoxus means "honored" or "of good repute" ( εὔδοξος , from eu "good" and doxa "opinion, belief, fame", analogous to the Latin Benedictus ). According to Diogenes Laërtius, crediting Callimachus ' Pinakes , Eudoxus studied mathematics with Archytas (of Tarentum , Magna Graecia ) and studied medicine with Philiston the Sicilian . At

282-414: A divide in mathematics which lasted two thousand years. In combination with a Greek intellectual attitude unconcerned with practical problems, there followed a significant retreat from the development of techniques in arithmetic and algebra. The Pythagoreans had discovered that the diagonal of a square does not have a common unit of measurement with the sides of the square; this is the famous discovery that

329-510: A letter to philosopher William Whewell , he wrote that the general public needed "digests of what is actually known in each particular branch of science... to give a connected view of what has been done, and what remains to be accomplished." Indeed, as the British population became not just increasingly literate but also well-educated, there was growing demand for science titles. Mary Somerville became an early and highly successful science writer of

376-495: A particular discovery. Some episodes have focused on the history of science. Examples of topics covered include the following: Colditz Castle , the Drake equation , elementary particles , the 1980 eruption of Mount St. Helens , Fermat's Last Theorem , the AIDS epidemic , global warming , moissanite , Project Jennifer , storm chasing , Unterseeboot 869 , Vinland , Tarim mummies , and

423-421: A precursor to the integral calculus which was also used in a masterly way by Archimedes in the following century. In applying the method, Eudoxus proved such mathematical statements as: areas of circles are to one another as the squares of their radii, volumes of spheres are to one another as the cubes of their radii, the volume of a pyramid is one-third the volume of a prism with the same base and altitude, and

470-583: A real number by the set of rational numbers that are larger, equal or smaller than the number to be defined. Eudoxus' definition depends on comparing the similar quantities ⁠ m ⋅ a {\displaystyle m\cdot a} ⁠ and ⁠ n ⋅ b {\displaystyle n\cdot b} ⁠ , and the similar quantities ⁠ m ⋅ c {\displaystyle m\cdot c} ⁠ and ⁠ n ⋅ d {\displaystyle n\cdot d} ⁠ , and does not depend on

517-417: A simpler proof from similar triangles, which relies on ratios of line segments. Ancient Greek mathematicians calculated not with quantities and equations as we do today; instead, a proportionality expressed a relationship between geometric magnitudes. The ratio of two magnitudes was not a numerical value, as we think of it today; the ratio of two magnitudes was a primitive relationship between them. Eudoxus

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564-444: A story reported by Simplicius, Plato posed a question for Greek astronomers: "By the assumption of what uniform and orderly motions can the apparent motions of the planets be accounted for?" Plato proposed that the seemingly chaotic wandering motions of the planets could be explained by combinations of uniform circular motions centered on a spherical Earth, apparently a novel idea in the 4th century BC. In most modern reconstructions of

611-499: Is credited with defining equality between two ratios, the subject of Book V of the Elements . In Definition 5 of Euclid's Book V we read: Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of,

658-676: The Associated Press wrote of the episode " The Fabric of the Cosmos ", "Mind-blowing TV." The Futon Critic wrote of the episode "Looking for Life on Mars", "Astounding [and] exhilarating." Nova has been recognized with multiple Peabody Awards and Emmy Awards . The program won a Peabody in 1974, citing it as "an imaginative series of science adventures," with a "versatility rarely found in television." Subsequent Peabodys went to specific episodes: The National Academy of Television Arts and Sciences (responsible for documentary Emmys) recognized

705-567: The COVID-19 pandemic . The Nova programs have been praised for their pacing, writing, and editing. Websites that accompany the segments have also won awards. Nova was first aired on March 3, 1974. The show was created by Michael Ambrosino, inspired by the BBC 2 television series Horizon , which Ambrosino had seen while working in the UK. In the early years, many Nova episodes were either co-productions with

752-533: The real numbers . Craters on Mars and the Moon are named in his honor. An algebraic curve (the Kampyle of Eudoxus ) is also named after him. Eudoxus is considered by some to be the greatest of classical Greek mathematicians, and in all Antiquity second only to Archimedes . Eudoxus was probably the source for most of book V of Euclid's Elements . He rigorously developed Antiphon 's method of exhaustion ,

799-513: The square root of 2 cannot be expressed as the ratio of two integers. This discovery had heralded the existence of incommensurable quantities beyond the integers and rational fractions, but at the same time it threw into question the idea of measurement and calculations in geometry as a whole. For example, Euclid provides an elaborate proof of the Pythagorean theorem ( Elements I.47), by using addition of areas and only much later ( Elements VI.31)

846-419: The 4th century, added seven spheres to Eudoxus's original 27 (in addition to the planetary spheres, Eudoxus included a sphere for the fixed stars). Aristotle described both systems, but insisted on adding "unrolling" spheres between each set of spheres to cancel the motions of the outer set. Aristotle was concerned about the physical nature of the system; without unrollers, the outer motions would be transferred to

893-535: The BBC Horizon team, or other documentaries originating outside of the United States, with the narration re-voiced in American English . Of the first 50 programs, only 19 were original WGBH productions, and the first Nova episode, "The Making of a Natural History Film", was originally an episode of Horizon that premiered in 1972. The practice continues to this day. All the producers and associate producers for

940-561: The Eudoxan model, the Moon is assigned three spheres: The Sun is also assigned three spheres. The second completes its motion in a year instead of a month. The inclusion of a third sphere implies that Eudoxus mistakenly believed that the Sun had motion in latitude. The five visible planets ( Mercury , Venus , Mars , Jupiter , and Saturn ) are assigned four spheres each: Callippus , a Greek astronomer of

987-493: The Origin of Species (1859) by Charles Darwin . Popular science is a bridge between scientific literature as a professional medium of scientific research, and the realms of popular political and cultural discourse. The goal of the genre is often to capture the methods and accuracy of science while making the language more accessible. Many science-related controversies are discussed in popular science books and publications, such as

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1034-601: The age of 23, he traveled with the physician Theomedon —who was his patron and possibly his lover —to Athens to study with the followers of Socrates . He spent two months there—living in Piraeus and walking 7 miles (11 km) each way every day to attend the Sophists ' lectures—then returned home to Cnidus. His friends then paid to send him to Heliopolis , Egypt for 16 months, to pursue his study of astronomy and mathematics. From Egypt, he then traveled north to Cyzicus , located on

1081-404: The basis of rigorous mathematics. Some Pythagoreans, such as Eudoxus's teacher Archytas , had believed that only arithmetic could provide a basis for proofs. Induced by the need to understand and operate with incommensurable quantities , Eudoxus established what may have been the first deductive organization of mathematics on the basis of explicit axioms . The change in focus by Eudoxus stimulated

1128-462: The city assembly. While in Cnidus, he built an observatory and continued writing and lecturing on theology , astronomy, and meteorology . He had one son, Aristagoras, and three daughters, Actis, Philtis, and Delphis. In mathematical astronomy, his fame is due to the introduction of the concentric spheres , and his early contributions to understanding the movement of the planets . He is also credited, by

1175-402: The contents of Phaenomena , for Eudoxus's prose text was the basis for a poem of the same name by Aratus . Hipparchus quoted from the text of Eudoxus in his commentary on Aratus. A general idea of the content of On Speeds can be gleaned from Aristotle 's Metaphysics XII, 8, and a commentary by Simplicius of Cilicia (6th century AD) on De caelo , another work by Aristotle. According to

1222-415: The didactic poem " Phenomena " written a century later and commented on by Hipparchus . Explaining science in poetic form was not uncommon, and as recently as 1791, Erasmus Darwin wrote The Botanic Garden , two long poems intended to interest and educate readers in botany. Many Greek and Roman scientific handbooks were written for the lay audience, and this "handbook" tradition continued right through to

1269-434: The existence of a common unit for measuring these quantities. The complexity of the definition reflects the deep conceptual and methodological innovation involved. The Eudoxian definition of proportionality uses the quantifier, "for every ..." to harness the infinite and the infinitesimal, similar to the modern epsilon-delta definitions of limit and continuity. The Archimedean property , definition 4 of Elements Book V,

1316-591: The first and third; likewise form the equimultiples ⁠ n ⋅ b {\displaystyle n\cdot b} ⁠ and ⁠ n ⋅ d {\displaystyle n\cdot d} ⁠ of the second and fourth. If it happens that ⁠ m ⋅ a > n ⋅ b {\displaystyle m\cdot a>n\cdot b} ⁠ , then also ⁠ m ⋅ c > n ⋅ d {\displaystyle m\cdot c>n\cdot d} ⁠ . If instead ⁠ m ⋅

1363-399: The following condition: For any two arbitrary positive integers ⁠ m {\displaystyle m} ⁠ and ⁠ n {\displaystyle n} ⁠ , form the equimultiples ⁠ m ⋅ a {\displaystyle m\cdot a} ⁠ and ⁠ m ⋅ c {\displaystyle m\cdot c} ⁠ of

1410-599: The inner planets. A major flaw in the Eudoxian system is its inability to explain changes in the brightness of planets as seen from Earth. Because the spheres are concentric, planets will always remain at the same distance from Earth. This problem was pointed out in Antiquity by Autolycus of Pitane . Astronomers responded by introducing the deferent and epicycle , which caused a planet to vary its distance. However, Eudoxus's importance to astronomy and in particular to Greek astronomy

1457-466: The invention of the printing press, with much later examples including books of secrets such as Giambattista Della Porta 's 1558 " Magia Naturalis " and Isabella Cortese 's 1561 " Secreti ". The 17th century saw the beginnings of the modern scientific revolution and the consequent need for explicit popular science writing. Although works such as Galileo 's 1632 " Il Saggiatore " and Robert Hooke 's 1665 " Micrographia " were read by both scientists and

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1504-408: The latter equimultiples respectively taken in corresponding order. Using modern notation , this can be made more explicit. Given four quantities ⁠ a {\displaystyle a} ⁠ , ⁠ b {\displaystyle b} ⁠ , ⁠ c {\displaystyle c} ⁠ , and ⁠ d {\displaystyle d} ⁠ , take

1551-473: The long-running debates over biological determinism and the biological components of intelligence, stirred by popular books such as The Mismeasure of Man and The Bell Curve . The purpose of scientific literature is to inform and persuade peers regarding the validity of observations and conclusions and the forensic efficacy of methods. Popular science attempts to inform and convince scientific outsiders (sometimes along with scientists in other fields) of

1598-529: The nineteenth century. Her On the Connexion of the Physical Sciences (1834), intended for the mass audience, sold quite well. Arguably one of the first books in modern popular science, it contained few diagrams and very little mathematics. Ten editions of the book were published, and it was translated into multiple languages. It was the most popular science title from the publisher John Murray until On

1645-483: The original Nova teams came from either England (with experience on the Horizon series), Los Angeles or New York. Ambrosino was succeeded as executive producer by John Angier, John Mansfield, and Paula S. Apsell , acting as senior executive producer. Rob Owen of Pittsburgh Post-Gazette wrote, "Fascinating and gripping." Alex Strachan of Calgary Herald wrote,"TV for people who don't normally watch TV." Lynn Elber of

1692-435: The poet Aratus , with having constructed a celestial globe . His work on proportions shows insight into irrational numbers and the linear continuum : it allows rigorous treatment of continuous quantities and not just whole numbers or even rational numbers . When it was revived by Tartaglia and others in the 16th century , it became the basis for quantitative work in science, and inspired Richard Dedekind 's work on

1739-568: The program with awards in 1978, 1981, 1983, and 1989. Julia Cort won an Emmy in 2001 for writing "Life's Greatest Miracle." Emmys were also awarded for the following episodes: In 1998, the National Science Board of the National Science Foundation awarded Nova its first-ever Public Service Award. Popular science Popular science (also called pop-science or popsci ) is an interpretation of science intended for

1786-456: The public, Newton's 1687 Principia was incomprehensible for most readers, so popularizations of Newton's ideas soon followed. Popular science writing surged in countries such as France, where books such as Fontenelle 's 1686 Conversations on the Plurality of Worlds were best-sellers. By 1830, astronomer John Herschel had recognized the need for the specific genre of popular science. In

1833-400: The ratio of the first to the second, ⁠ a / b {\displaystyle a/b} ⁠ , and the ratio of the third to the fourth, ⁠ c / d {\displaystyle c/d} ⁠ . That the two ratios are proportional, ⁠ a / b = c / d {\displaystyle a/b=c/d} ⁠ , can be defined by

1880-646: The results. Statements in the scientific literature are often qualified and tentative, emphasizing that new observations and results are consistent with and similar to established knowledge wherein qualified scientists are assumed to recognize the relevance. By contrast, popular science often emphasizes uniqueness and generality and may have a tone of factual authority absent from the scientific literature. Comparisons between original scientific reports, derivative science journalism, and popular science typically reveals at least some level of distortion and oversimplification . Eudoxus of Cnidus Eudoxus, son of Aeschines,

1927-434: The scientific literature. Some usual features of popular science productions include: The purpose of scientific literature is to inform and persuade peers regarding the validity of observations and conclusions and the forensic efficacy of methods. Popular science attempts to inform and convince scientific outsiders (sometimes along with scientists in other fields) of the significance of data and conclusions and to celebrate

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1974-431: The significance of data and conclusions and to celebrate the results. Statements in the scientific literature are often qualified and tentative, emphasizing that new observations and results are consistent with and similar to established knowledge wherein qualified scientists are assumed to recognize the relevance. By contrast, popular science emphasizes uniqueness and generality, taking a tone of factual authority absent from

2021-640: The south shore of the Sea of Marmara, the Propontis . He traveled south to the court of Mausolus . During his travels he gathered many students of his own. Around 368 BC, Eudoxus returned to Athens with his students. According to some sources, c.  367 he assumed headship ( scholarch ) of the Academy during Plato's period in Syracuse, and taught Aristotle . He eventually returned to his native Cnidus, where he served in

2068-415: The volume of a cone is one-third that of the corresponding cylinder. Eudoxus introduced the idea of non-quantified mathematical magnitude to describe and work with continuous geometrical entities such as lines, angles, areas and volumes, thereby avoiding the use of irrational numbers . In doing so, he reversed a Pythagorean emphasis on number and arithmetic, focusing instead on geometrical concepts as

2115-560: Was born and died in Cnidus (also transliterated Knidos), a city on the southwest coast of Anatolia . The years of Eudoxus' birth and death are not fully known but Diogenes Laërtius gave several biographical details, mentioned that Apollodorus said he reached his acme in the 103rd Olympiad (368– 365 BC ), and claimed he died in his 53rd year. From this 19th century mathematical historians reconstructed dates of 408– 355 BC , but 20th century scholars found their choices contradictory and prefer

2162-417: Was credited to Eudoxus by Archimedes. In ancient Greece , astronomy was a branch of mathematics; astronomers sought to create geometrical models that could imitate the appearances of celestial motions. Identifying the astronomical work of Eudoxus as a separate category is therefore a modern convenience. Some of Eudoxus's astronomical texts whose names have survived include: We are fairly well informed about

2209-442: Was often little distinction between "science" and "popular science", and works intended to share scientific knowledge with a general reader existed as far back as Greek and Roman antiquity. Without these popular works, much of the scientific knowledge of the era might have been lost. For example, none of the original works of the 4th century BC Greek astronomer Eudoxus have survived, but his contributions were largely preserved due to

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