Duncan Graham-Rowe

Astronomers are taking the search for somewhere quiet to work to new extremes with a plan to put a radio telescope on the far side of the Moon. The advantage of this unusual location is that the Moon would act as a massive shield, protecting the telescope against radio emissions from Earth. Astronomers could also listen to low radio frequencies that don't penetrate the Earth's atmosphere. Claudio Maccone, an astronomer at the Centre for Astrodynamics in Turin, Italy, is assessing the concept for the International Academy of Astronautics. He even has his eye on a plot of lunar real estate. A 100-kilometre-wide crater called Daedalus should provide enough space, he says. The crater's 3-kilometre-high rim should also help block any stray radio signals that creep around the Moon to the far side. "I do believe this will be built," says Maccone, although he admits it will probably take at least 15 years. Even if robots were used to build the observatory remotely, it would cost billions of dollars and need the backing of a large space agency like NASA or the European Space Agency. By the time the telescope could be built, the area of the Moon that's protected from radio waves is likely to be shrinking fast. This is because as orbit space for telecommunications satellites gets used up, they will have to be placed in higher orbits, so their radio emissions will reach more and more of the Moon's surface (see Graphic). So Maccone also wants to give the region around the Daedalus crater some form of protection status, to create a permanent quiet zone that would be safe no matter what technology is developed in the future. "The far side is in my opinion a unique treasure that should be preserved for the sake of humankind," he says. Setting up such a zone would probably be the responsibility of the International Telecommunications Union, which allocates the rights to use different radio frequencies. But it's far from clear whose permission would be needed to build a permanent structure on the Moon. Maccone is due to present the results of his study to the International Astronautical Congress next October. If the plans are approved, the first step will be to design a satellite probe to orbit the Moon and check there really is a quiet zone.

Jupiter's giant light show

SOMETHING strange is happening on Jupiter. Its magnetic field extends hundreds of times further out into space than previously thought, creating auroras that make the Earth's northern lights seem feeble in comparison. Jupiter is the giant of the Solar System, more than a thousand times as massive as Earth. In January 2001, the combined power of the Cassini and Galileo space probes, the Chandra X-ray telescope and the Hubble Space Telescope were all trained on the Jovian magnetosphere - the region controlled by the planet's magnetic field. Magnetic field lines fan out from a planet like the lines of iron filings from the poles of a bar magnet. Auroras are caused by ions zipping along these lines, so researchers can use the location of auroras to track how far out into space the planet's magnetic field lines can trap ions from the solar wind. Randy Gladstone and his colleagues at the Southwest Research Institute in San Antonio, Texas, used Chandra to map the Jovian auroras. Earth's northern lights shine only with visible light, but the more violent Jovian auroras emit X-rays. The X-ray auroras on Jupiter extend surprisingly far from the planet's poles, showing that field lines reach far out into space. Gladstone also found that the auroras pulsated regularly every 45 minutes in certain places he's calling "hot spots", unlike anything seen on Earth. "Those field lines go way further out than expected," says Gladstone. "Something weird is happening." Theorists have trouble explaining why Jupiter's magnetosphere is so much more powerful than Earth's, even allowing for the planet's greater size. "Jupiter's magnetosphere is like Earth's on steroids," says Thomas Hill, who works on the theory of magnetospheres at Rice University in Houston, Texas. Eugenie Samuel, Boston More at. Nature (vol 415, p 1000) [New Scientist 2 March 2002] HOW JUPITER GOT ITS STRIPES. A new study of turbulence in the atmosphere around a rotating sphere is helping to explain the dramatic stripes on Jupiter, Saturn, and the other giant planets. On Earth, turbulence caused by solar heating and friction with the ground disrupts atmospheric flows and dissipates the energy provided by the sun that might otherwise lead to the formation of circulating, global cloud bands. In the thin atmospheres of gas giants, however, energy dissipation is small, and some of the sun's energy is gradually collected in stable, global jets that trap clouds and form planetary stripes. Researchers at the University of South Florida and Ben-Gurion University of the Negev (Israel) have now developed a model that shows how planetary rotation and nearly two-dimensional atmospheric turbulence may combine to create large scale structures. Scientists have long suspected that the interaction between planetary rotation and large-scale turbulence governs the banded circulations on giant planets. The new research has quantified the phenomenon, leading to an equation that characterizes the distribution of energy among different scales of motion, and to simple formulae that describe basic energetic features of giant planets' circulations. The model helps explain the paradoxical observation that the outer planets have stronger atmospheric flows, even though the energy provided by the sun to maintain such flows decreases with increasing distance from the sun. The researchers (B. Galperin, bgalperin@marine.usf.edu, 727-553-1101) have found that the atmospheres of distant planets dissipate even less energy than their warmer sisters. Although the outer planets receive less energy from the sun, they keep more of the energy they receive. As a result, the model shows why Neptune has the strongest atmospheric circulation of all the gas giants even though it is the farthest of the bunch from the sun. (S. Sukoriansky, B. Galperin, N. Dikovskaya, Physical Review Letters, 16 September 2002)

Mercury and the mystery of a "planet" that disappeared

Experience has taught me that predictions of spectacular astronomical events are tantamount to long-range forecasts of bad weather: the grand alignment of five planets scheduled to take place over the western horizon tomorrow evening therefore means that gardeners should put any house plants needing a watering outside at about 8pm. The various planets, fortunately, will be dancing around each other in the same part of the sky for a few weeks, so I still hope for a glimpse of Mercury, the one planet visible to the naked eye that I have yet to see. Tomorrow's planetary alignment will form a vast celestial finger pointing to its location at the bottom of a line that baa Jupiter at its top, followed by Saturn, Mars and Venus, with the Moon just below the Red Planet. One consequence of Mercury's elusiveness is that astronomers know little about this planet. Data sent back by the only space probe to visit it, Mariner 10 in 1974, raised as many mysteries as it solved. The mass of the planet turned out to be extraordinarily high: despite being not much larger than the Moon, Mercury proved to be five times more massive - suggesting that its rocky, cratered surface covers a colossal nickel-iron ball more than 2,000 miles across. The planet also has a relatively strong magnetic field, thus cocking a snook at scientists who claim to know how such fields are generated. Standard theories link them to the spin of the planets, which creates a kind of dynamo effect within electrically conducting liquid cores. Mercury's metal core is certainly conducting, but it isn't liquid and the planet takes a leisurely 58 days to spin once on its axis (which, mysteriously, is precisely two thirds the time Mercury takes to orbit the Sun). The answers to such puzzles almost certainly lie in the proximity of Mercury to the Sun. There is no object' however, similar to Mercury hy which astronomers can test their theories. Not that this has prevented some of the more imaginative from suggesting that Mercury may not be the only object to inhabit the searing inner reaches of our solar system. During the 1840s, astronomers were struggling to understand Mercury's slow pirouettes around the Sun. Most of the rotation could be explained by known effects, but a tiny discrepancy remained. The mystery was tackled by Urbain Leverrier, the brilliant French theoretician who had in 1846 explained discrepancies in the orbit of Uranus as being due to an undiscovered planet, subsequently confirmed as Neptune. In 1859 Leverrier proposed that Mercury was being pulled off course by another undiscovered planet, duly named Vulcan. Shortly afterwards, Leverrier received a letter from a French country doctor claiming to have seen Vulcan crossing the face of the Sun in March 1859. Calculating an orbit for the object, Laverrier found that it must lie just 13 million miles from the Sun. This neatly explained why no one had seen it: Vulcan was even smaller than Mercury and would normally be lost in the Sun's glare. Not unreasonably, Leverrier went to his grave believing he had predicted the existence of two new planets. He proved to be only half right. Vulcan was never seen again, and the real explanation for Mercury's anomalous orbit turned out to be general relativistic effects unimagined in Leverrier's time. Vulcan may now reside in the wastebin of scientific history, but it is odd that the early claims to have seen it should have been so consistent. That said, readers who think they see Vulcan over the weeks ahead should probably take it as a reminder to have an eye test. [Sunday Telegraph April 14 2002] Robert Matthews invites you to send. in your questions on science, the answer's to which will soon form a regular part of his column whether you're stumped by celestial mechanics or just want to know why the sea is salty, please write to Robert Matthews at The Sunday Telegraph, 1 Canada Square, London, E14 5DT, or e-mail: robert.matthews@telegraph.co.uk

The zodiac can at times appear predominantly masculine as most of the planets have historically been associated with male mythological figures. Until the discovery of the asteroid belt in the 19th century, the only planetary bodies which women could easily identify themselves with were Venus, the Moon and Lilith (which is considered to be Earth's ante-diluvian satellite). While women have always made significant contributions to society, it must be stressed that they traditionally played the roles of wife and mother as illustrated by Venus and the Moon respectively. The discovery of the asteroid belt brought about a balance between masculine and feminine archetypes to bring more sexual equality in our Solar system. It was also around this time that women began to take on more diversified roles and therefore needed other astrological indicators in what was to become a rapidly changing world. It is also worth noting that those men who have chosen to pursue careers which have traditionally been assigned to women will be able to relate to these more intuitive planetary bodies. The Moon The Moon is the Earth's largest satellite which governs our emotional responses. It is no secret that the close proximity of the Moon to the Earth has a strong effect on our physical environment, as evidenced by the daily motion of oceanic tides and the fact that crime has a tendency to increase during the Full Moon. The Moon relates to our emotive impulses which push us to react and in many instances it can be such a dominant feature in some horoscopes that it is actually more prominent than the Sun. This may be, as many whose natal Moon is strongly aspected in their natal chart will find to be the case, the reason why some do not show a strong affinity to their natal Sun but instead relate more to Lunar impressions. The Moon represents the relationship we have with our mother and women in general and it denotes what type of mother or parent we are likely to become. While the father is quite often associated with Saturn, those men who are more in tune with the intuitive side of themselves can just as easily identify with the Moon in relation to their parenting style. In Greek mythology, the Moon is associated with Artemis, the virgin goddess. She was considered to be eternally young and active and was equal to any man. Artemis was the twin sister of Apollo who astrologically depicts the Sun and the pair were said to have been very close. With these mythological considerations in mind, it should come as no surprise to conclude that the astrological signs of Leo and Cancer, ruled by the Sun and Moon respectively, reign side by side in the zodiac while the remaining five planets in the ancient Solar system progress outwardly from the royal pair. The planetary alignment is as follows: Mercury, the first planet away from the Sun, rules Gemini and Virgo which are one sign away from the Cancer/Leo configuration respectively. Venus, the second planet away from the Sun, rules Taurus and Libra which are two signs away from the Cancer/Leo configuration respectively. Mars, the third planet from the Sun excluding Earth, rules Aries and Scorpio which are three signs away from the Cancer/Leo configuration respectively. Jupiter, the fourth planet from the Sun excluding Earth, rules Pisces and Sagittarius which are four signs away from the Cancer/Leo configuration respectively. Saturn, the fifth planet from the Sun excluding Earth, rules Capricorn and Aquarius which are five signs away from the Cancer/Leo configuration respectively. The placement of these signs and the rulerships they were given some 2,000 years ago does seem to suggest that the Summer months were regarded as significant in the astrological year.[Predictions magazine July 1997]

Question: What is a blue moon and what is once in a blue moon? The three most popular reasons that are most often found in the literature for this so called phenomena are 1) The appearance of the moon's color due to smoke particles from forest fires, 2) The appearance of the moon's color due to particles from volcanic eruptions, or 3) The appearance of a second full moon within a calendar month. Apparently, both 1 and 2 have been known to give the moon a blue appearance. The third is the source of the popular statement "once in a blue moon" which means something happens quite rarely. It is based on the strange occurrence of having two full moons in one month. How can this happen? Since full moons actually occur every about 29.53 days, they occur about 12.36 times a year, which translates into having a double full moon month once every 2.77 years or so, quite infrequently, obviously. With the event occurring approximately every 33 months, it is easy to see how the statement "once in a blue moon" could have originated. It might also just be the case that some specific second full moons in months past did, in fact, occur right after a forest fire or volcanic eruption, providing some credibility to all three. It is interesting to note that in a year where a full moon does not occur in February, both January and March will have two full moons, a rare event indeed. Prepared by AACTchWill and AACTutorNY, AAC Staff, Use of this material is protected under America Online and other copyright. Any use of this material must cite AOL's Academic Assistance Center and the authors as a source. (edited by AACDrAnne)

The Golden age of Brum A subject for discussion at the Lunar Society A 1749 experiment using boys to transmit electricity John Adamson praises the elegant study of the friends who meet once a month to change the world [The Lunar Men:The Friends who made the future by Jenny Uglow Faber £25,518pp] EXCEPTIONAL times, in fortunate places, nature and nurture combine to produce a superabundance of talent that is wholly out of scale with what can reasonably be expected of mortal men. Historical moments such as the 5th century BC in Athens or the later 15th century Florence have long been regarded with reverential awe. This new book makes a compelling case for adding another - one that, hitherto, has been relatively overlooked. The time is the second half of, the 18th century, and the place -improbably - Birmingham, then a semi-rustic town with a population under 50,000 people. Between the 1760s and the early 1800s, there clustered here one of history's most exceptionally gifted networks of friends. Their energy, ideas and inquisitiveness "made the future" - to use this book's fully justified subtitle: from the development of the steam engine, through to the development of mass-market capitalism, and even in the development of the theory of evolution. These were the Lunar Men: a dozen or so luminaries who, from 1775,met together as the Lunar Society of Birmingham (so named because they met monthly, on the Monday closest the full moon). At its core was its genial pater familias the portly Erasmus Darwin (1731-1802) - physician, botanist, best-selling poet, balloonist, and grandfather of Charles. Around him clustered the talented friends with whom he shared his enthusiasms: the pottery tycoon Josiah Wedgwood, the silversmith Matthew Boulton, the inventor James Watt, the chemist and Nonconformist divine Joseph Priestley; and a series of less well-known but equally able colleagues. Indeed, no single epithet does any of them justice, as the Lunar Men were polymaths all. The intellectual heirs of Newton in science and Rousseau and the French Encyclopaedists in philosophy, they were buoyed by the belief that every aspect of the physical world would eventually yield up its secrets to well directed experiment and enquiry. Superstition (if not yet Christianity as a whole) was their enemy. As Josiah Wedgwood put it mischievously, their ambition was to "rob the Thunderer of his Bolts"; Erasmus Darwin revelled in "the slightly blasphemous glamour of scientific 'miracles'". And so they experimented, annotated, compared results, drank claret and, above all, talked. To read Jenny Uglow's book is to eavesdrop on conversations about an astonishingly diverse array of enquiries, schemes and projects: from how to get the correct glaze for Wedgwood's Portland Vase; to schemes for moving manure using hot-air balloons; on to Erasmus Darwin's conclusion, reached during the 1770s, that all life must have had a single microscopic common ancestor: the first coherent theory of evolution. What shines through, however, in all their correspondence, is the invigorating excitement of the chase, the magpie-like, omnium-gathering nature of their curiosity. When Boulton went searching for the mineral Blue John (to fashion into ormolu-mounted vases), he also collected rocks and fossils in the hope of gauging the age of the earth. And between seeing patients as a physician, Darwin was making notes on everything from telescopic candlesticks to "5-inch worms in cats". In politics, too, the Lunar Men aspired to change the world. Whigs almost to a man, they supported the American colonists against the government in 1776 ("What will become of button-making?" exclaimed Boulton, the society's token Tory, as he contemplated the drop in demand for uniforms); and Wedgwood spoke enthusiastically of 1789 as "that glorious revolution that has taken place in France". Ironically, this political and religious radicalism indirectly proved to be the Lunar Society's undoing. In 1791, Birmingham's Church-and -King mobs turned their anger on the heretical Priestley (who denied the divinity of Christ), burning his house and forcing him to flee in fear of his life. After that traumatic moment, the society's meetings never quite regained their former energy or conviviality, and the society eventually petered out and died. Not everything convinces. Uglow stresses that the Lunar Men were mostly non-Oxbridge, non-London, and from "outside the Establishment "- something that proved a real strength, since they were unhampered by old traditions of deference and stuffy institutions". Yet the Hanoverian Establishment was itself highly heterogeneous; and, for their part, the friends were often reliant on aristocratic patronage (the Duke of Bridgewater's, for instance, in their canal projects) and were quite happy to lay obsequiousness on with a trowel whenever it looked advantageous to do so. Wedgwood assiduously toadied to royal patrons and took pride in his title, "Potter to the Queen". Moreover, while there are moments when the book's torrent of detail threatens to overwhelm the reader, there are also some major omissions. Most seriously, there is not a word about the Deism, the heterodox contemporary religious movement that identified God with Nature. which pervades so many of the Lunar friends' attitudes and beliefs. This remains, however, a magnificently accomplished and enjoyable book. And if it highlights the Lunar Men's prodigious learning, it also demonstrates the exceptional abilities of at least one Lunar Woman. For in the sheer range of Jenny Uglow's erudition, her obvious delight in the inquisitiveness of her savants, and in her high skills as a writer, she has proved herself a worthy member of that distinguished club. John Adamson is a fellow of Peterhouse Cambridge A subject for discussion at the Lunar Society [The Sunday Telegraph Sep 15 2002]

DEEP SPACE SECRETS Over 130 molecules have been identified in interstellar space so far, including sugars and ethanol. Now Lewis Snyder and Yi-Jehng Kuan of the National Taiwan University say they have spotted the amino acid glycine. Amino acids in deep space are a particularly important discovery because they link up to form proteins. If the finding stands up to scrutiny it will add oomph to ideas that life exists on other planets, and even that molecules from outer space kick-started life on Earth. FEEL THE FORCE Pioneer 10 was the first spacecraft to fly past Jupiter. Pioneer 11 went on to visit Saturn. Out at the darkest edge of the Solar System beyond Pluto, there should be nothing to slow the probes down except the feeble gravity of the receding Sun - yet a mysterious extra force seems to be tugging on them. "For the life of me, I can't think what it could be," says Michael Martin Nieto from Los Alamos National Laboratory in New Mexico. But "I admit I want it to be something profoundly important, some entirely new physics," he adds. And he just may be in luck...

QUADRATURE OF LUNES Somewhat younger than Anaxagoras, and coming originally from about the same part of the Greek world, was Hippocrates of Chios. He should not be confused with his still more celebrated contemporary, the physician Hippocrates of Cos. Both Cos and Chios are islands in the Dodecanese group; but Hippocrates of Chios in about 430 B.C. left his native land for Athens in his capacity as a merchant. Aristotle reports that Hippocrates was less shrewd than Thales and that he lost his money in Byzantium through fraud; others say that he was beset by pirates. In any case, the incident was never regretted by the victim, for he counted this his good fortune in that as a consequence he turned to the study of geometry, in which he achieved remarkable success-a story typical of the Heroic Age. Proclus wrote that Hippocrates composed an "Elements of Geometry," anticipating by more than a century the better-known Elements of Euclid. However, the textbook of Hippocrates-as well as another reported to have been written by Leon, a later associate of the Platonic school-has been lost, although it was known to Aristotle. In fact, no mathematical treatise from the fifth century has survived; but we do have a fragment concerning Hippocrates which Simplicius (fi.. ca. 520) claims to have copied literally from the History of Mathematics (now lost) by Eudemus. This brief statement, the nearest thing we have to an original source on the mathematics of the time, describes a portion of the work of Hippocrates dealing with the quadrature of lunes. A lune is a figure bounded by two circular arcs of unequal radii; the problem of the quadrature of lunes undoubtedly arose from that of squaring the circle. The Eudemian fragment attributes to Hippocrates the following theorem: Similar segments of circles are in the same ratio as the squares on their bases. The Eudemian account reports that Hippocrates demonstrated this by first showing that the areas of two circles are to each other as the squares on their diameters. Here Hippocrates adopted the language and concept of proportion which played so large a role in Pythagorean thought. In fact, it is thought by some that Hippocrates became a Pythagorean. The Pythagorean school in Croton had been suppressed (possibly because of its secrecy, perhaps because of its conservative political tendencies), but the scattering of its adherents throughout the Greek world served only to broaden the influence of the school. This influence undoubtedly was felt, directly or indirectly, by Hippocrates. The theorem of Hippocrates on the areas of circles seems to be the earliest precise statement on curvilinear mensuration in the Greek world. Eudemus believed that Hippocrates gave a proof of the theorem, but a rigorous demonstration at that time (say about 430 B.C.) would appear to be unlikely. The theory of proportions at that stage probably was established for commensurable magnitudes only. The proof as given in Euclid XII.2 comes from Eudoxus, a man who lived halfway between Hippocrates and Euclid. However, just as much of the material in the first two books of Euclid seems to stem from the Pythagoreans, so it would appear reasonable to assume that the formulations, at least, of much of Books III and IV of the Elements came from the work of Hippocrates. Moreover, if Hippocrates did give a demonstration of this theorem on the areas of circles, he may have been responsible for the introduction into mathematics of the indirect method of proof. That is, the ratio of the areas of two circles is equal to the ratio of the squares on the diameters or it is not. By a reductio ad absurdum from the second of the two possibilities, the proof of the only alternative is established. From this theorem on the areas of circles Hippocrates readily found the first rigorous quadrature of a curvilinear area in the history of mathematics. He began with a semicircle circumscribed about an isosceles right triangle, and on the base (hypotenuse) he constructed a segment similar to the circular segments on the sides of the right triangle. (Fig. 5.1). Because the segments are to each other as squares on their bases, and from the Pythagorean theorem as applied to the right triangle, the sum of the two small circular segments is equal to the larger circular segment. Hence, the difference between the semicircle on AC and the segment ADCE equals triangle ABC. Therefore, the lune ABCD is precisely equal to triangle ABC; and since triangle ABC is equal to the square on half of AC, the quadrature of the lune has been found. Eudemus describes also an Hippocratean lune quadrature based on an isosceles trapezoid ABCD inscribed in a circle so that the square on the longest side (base) AD is equal to the sum of the squares on the three equal shorter sides AB and BC and CD (Fig. 5.2). Then, if on side AD one constructs a circular segment AEDF similar to those en the three equal sides, lune ABCDE is equal to trapezoid ABCDF. That we are on relatively firm ground historically in describing the quadrature of lunes by Hippocrates is indicated by the fact that scholars other than Simplicius also refer to this work. Simplicius lived in the sixth century, but he depended not only on Eudemus (fi. ca. 320 B.C.) but also on Alexander of Aphrodisias (fi. ca. A.D. 200), one of the chief commentators on Aristotle. Alexander describes two quadratures other than those given above. (1) If on the hypotenuse and sides of an isosceles right triangle one constructs semicirdes (Fig. 5.3),then the lunes created on the smaller sides together equal the triangle. (2) If on a diameter of a semicircle one constructs an isosceles trapezoid with three equal sides (Fig. 5.4), and if on the three equal sides semicircles are constructed, then the trapezoid is equal in area to the sum of four curvilinear areas: the three equal lunes and a semicircle on one of the equal sides of the trapezoid. From the second of these quadratures it would follow that if the lunes can be squared, the semicircle-hence the circle-can also be squared. This conclusion seems to have encouraged Hippocrates, as well as his contemporaries and early successors, to hope that ultimately the circle would be squared. CONTINUED PROPORTIONS The Hippocratean quadratures are significant not so much as attempts at circle-squaring as indications of the level of mathematics at the time. They show that Athenian mathematicians were adept at handling transformations of areas and proportions. In particular, there was evidently no difficulty in converting a rectangle of sides a and b into a square. This required finding the mean proportional or geometric mean between a and b. That is, if a:x = x:b, geometers of the day easily constructed the line x. It was natural, therefore, that geometers should seek to generalize the problem by inserting two means between two given magnitudes a and b. That is, given two line segments a and b, they hoped to construct two other segments x and y such that a:x = x:y = y:b. Hippocrates is said to have recognized that this problem is equivalent to that of duplicating the cube; for if b = 2a, the continued proportions, upon the elimination of y, lead to the conclusion that x3 = 2a3. There are three views on what Hippocrates deduced from his quadrature of lunes. Some have accused him of believing that he could square all lunes, hence also the circle; others think that he knew the limitations of his work, concerned as it was with some types of lunes only. At least one scholar has held that Hippocrates knew he had not squared the circle but tried to deceive his countrymen into thinking that he had succeeded. There are other questions, too, concerning Hippocrates' contributions, for to him has been ascribed, with some uncertainty, the first use of letters in geometric figures. It is interesting to note that whereas he adyanced two of the three famous problems, he seems to have made no progress in the trisecting of the angle, a problem studied somewhat later by Hippias of Elis. HIPPIAS OF ELIS Toward the end of the fifth century B.C. there flourished at Athens a group of professional teachers quite unlike the Pythagoreans. Disciples of Pythagoras had been forbidden to accept payment for sharing their knowledge with others. The Sophists, however, openly supported themselves by tutoring fellow citizens-not only in honest intellectual endeavor, but also in the art of "making the worse appear the better." To a certain extent the accusation of shallowness directed against the Sophists was warranted; but this should not conceal the fact that Sophists usually were very widely informed in many fields and that some of them made real contributions to learning. Among these was Hippias, a native of Elis who was active at Athens in the second half of the fifth century B.C. He is one of the earliest mathematicians of whom we have firsthand information, for we learn much about him from Plato's dialogues. We read, for example, that Hippias boasted that he had made more money than any two other Sophists. He is said to have written much, from mathematics to oratory, but none of his work has survived. He had a remarkable memory, he boasted immense learning, and he was skilled in handicrafts. To this Hippias (there are many others in Greece who bore the same name) we apparently owe the introduction into mathematics of the first curve beyond the circle and the straight line. Proclus and other commentators ascribe to him the curve since known as the trisectrix or quadratrix of Hippias.2 This is drawn as follows: In the square ABCD (Fig. 5.5) let side AB move down uniformly from its present position until it coincides with AC and let this motion take place in exactly the same time that side BA rotates clockwise from its present position until it coincides with DC. If the positions of the two moving lines at any given time are given by A 'B' and BA" respectively and if P is the point of intersection of A 'B' and DA", the locus of P during the motions will be the trisectrix of Hippias-curve APQ in the figure. Given this curve, the trisection of an angle is carried out with ease. For example, if PDC is the angle to be trisected, one simply trisects segments B'C and A 'D at points R, S, T, and U. If lines TR and US cut the trisectrix in V and W respectively, lines VD and WD will, by the property of the trisectrix, divide angle PDC in three equal parts. The curve of Hippias generally is known as the quadratrix, since it can be used to square the circle. Whether or not Hippias himself was aware of this application cannot now be determined. It has been conjectured that Hippias knew of this method of quadrature but that he was unable to justify it. Since the quadrature through Hippias' curve was specifically given later by Dinostratus, we shall describe this work in the next chapter. Hippias lived at least as late as Socrates (~399 B.C.), and from the pen of Plato we have an unflattering account of him as a typical Sophist-vain, boastful, and acquisitive. Socrates is reported to have described Hippias as handsome and learned, but boastful and shallow. Plato's dialogue on Hippias satirizes his show of knowledge, and Xenophon's Memorabilia includes an unflattering account of Hippias as one who regarded himself an expert in everything from history and literature to handicrafts and science. In judging such accounts, however, we must remember that Plato and Xenophon were uncompromisingly opposed to the Sophists in general. It is well to bear in mind also that both Protagoras, the "founding father of the Sophists," and Socrates, the archopponent of the movement, were antagonistic to mathematics and the sciences. With respect to character, Plato contrasts Hippias with Socrates, but one can bring out much the same contrast by comparing Hippias with another contemporary-the Pythagorean mathematician Archytas of Tarentum. 1See Bjornbo's article "Hippocrates" in Pauly-Wissowa, Real-Enzykiopadie der klassisehen Altertumswissenschaft, Vol. VIII, p.1796. 2An excellent account of this is found in K. Freeman, The Pre-Socratic Philosophers. A Companion to Diels, Fragmente der Vorsokratiker (1949), pp.381-391. See also the article on Hippias in Pauly-Wissowa. op. cit.. Vol. VIII, pp. 1707 ff. Carl C Boyer " A History of Mathematics " p 65-69

The Pink "pirate" who sailed the southern stars Comet man Halley also blazed a trail on Earth in a search for Antarctica

ONE day in l700 a fishing vessel was at work off the Newfoundland coast when a ragged looking craft bore down on it. Fearing piracy, the fisherman opened fire. The result was a torrent of foul language from the "pirate's" commander, the astronomer Edmond Halley. Halley was not only famous for predicting the appearance of his comet. He was also a bold explorer, travelling the world in search of scientific information, who nearly lost his life trying to find Antarctica a century before Captain Cook arrived. His extraordinary exploits are revealed in the latest issue of Astronomy Now by the scientific historian Dr Ian Seymour, who relates that Halley was not only a precursor of Cook but, in being faced with a mutiny that he himself partly provoked, of Captain Bligh too. In his second voyage, begun in 1698, he set out in a Royal Naval vessel called the Paramour Pink. "Pinks", flat-bottomed ships 52 feet long and 18 feet broad, -specially designed for sailing in shallow seas and almost unknown in the Navy, were often mistaken for pirates sailing under false colours. The crew numbered 20, making the vessel extremely cramped, and the first officer, a certain Harrison (no relation to the inventor of the marine chronometer) was a professional seaman who despised the "academic" Halley from whom, he complained with gross unfairness, "much is expected and little or nothing appears". During this voyage Halley did in fact make extensive observations of the Earth's magnetic fields which, Dr Seymour says, "remained indispensable shipboard companions for more than a century". But he was an appallingly bad commander. Despite his naval authority, he never had a man flogged and attempted to enforce discipline with sarcastic and foul-mouthed abuse. Harrison, openly insubordinate, countermanded orders and told the crew that Halley had only been given command because of his wealthy connections, since he was useless for any other occupation. One day Harrison told Halley in the presence of all the crew that he was "not only uncapable to take charge of a Pink, but even of a longboat". Halley had him confined to his cabin for the rest of the voyage. At the subsequent court martial the Admiralty appeared to recognise Halley's faults, for the mutinous officer escaped with only a reprimand. On a subsequent voyage in a Pink, this time with a more agreeable first officer, Halley put in at Recife, Brazil, where he fell foul of the English consul, a Mr Hardwicke; whom he afterwards alleged was an imposter. He told Hardwicke that the purpose of the voyage was to observe the stars in the southern skies. (Halley, in fact, had earlier won election to the Royal Society for identifying 341 southern stars from the murky skies of Saint Helena.) Halley: storm-tossed life Hardwicke said this story was too ridiculous to be believed. Citing the suspicious appearance of Halley's ship, he ordered him to be arrested as a pirate. Halley was released after a few hours at the intervention of the city's governor but,incensed and refusing to accept apologies, he set off into stormy seas. He was soon in the Southern Ocean hoping to find the fabled Lost Continent. The ship's lookouts reported seeing three large islands, unmarked on any map. They were all "flat at the top, covered with snow, milk-white, with perpendicular cliffs all around them". Surrounded by these icebergs and by thick fog, the ship was soon in deadly peril. For "between 11 and 12 days", Halley wrote in the log, "we were in imminent danger of the inevitable loss of all of us in case we starved, being alone without a consort". They were saved by the smallness of the ship, which made it responsive to controls, and by its shallow draft. Halley, who lived to 86, was one of the most remarkable scientists of all ages. A friend of Isaac Newton - probably the only friend that cantankerous man ever had - he was influential in securing the publication of his Principia, that basis of all celestial laws. He also discovered the first known globular cluster whose ancient stars today defy our attempts to age the universe. And he was a great character too, as shown by his entertainment, when Astronomer Royal, of the visiting Russian tsar Peter the Great. They ended up drunk in a ditch. Adrian Berry This is utter stupidity. The moon is a moon because of its secondary orbit around a planet which orbits a star.Unless you orbit a star,you are a moon not a planet.

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