Hippasus (Ancient Greek: Ἵππασος, Híppasos; 5th century BC) of Metapontum in Magna Graecia, was a Pythagorean philosopher. Little is known about his life or his beliefs, but he is sometimes credited with the discovery of the existence of irrational numbers. The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea (apparently as a punishment from the gods). However, the few ancient sources which describe this story either do not mention Hippasus by name or alternatively tell us that Hippasus drowned because he revealed how to construct a dodecahedron inside a sphere. The discovery of irrationality is not specifically ascribed to Hippasus by any ancient writer. Some modern scholars though have suggested that he discovered the irrationality of √2, which it is believed was discovered around the time that he lived.

Life[link]

Little is known about the life of Hippasus. He may have lived in the late 5th century BC, about a century after the time of Pythagoras. He probably came from Metapontum in Italy (Magna Graecia), although the nearby city of Croton is also mentioned as his birthplace.^[1] Iamblichus states that he was the founder of a sect of the Pythagoreans called the Mathematici (Greek: μαθηματικοί) in opposition to the Acusmatici (Greek: ἀκουσματικοί);^[2] but elsewhere he makes him the founder of the Acusmatici in opposition to the Mathematici.^[3]

Doctrines[link]

Aristotle speaks of Hippasus as holding the element of fire to be the cause of all things;^[4] and Sextus Empiricus contrasts him with the Pythagoreans in this respect, that he believed the arche to be material, whereas they thought it was incorporeal, namely, number.^[5] Diogenes Laërtius tells us that Hippasus believed that "there is a definite time which the changes in the universe take to complete, and that the universe is limited and ever in motion."^[6] According to one statement, Hippasus left no writings,^[7] according to another he was the author of the Mystic Discourse, written to bring Pythagoras into disrepute.^[8]

A scholium on Plato's Phaedo notes him as an early experimenter in music theory, claiming that he made use of bronze disks to discover the fundamental musical ratios, 4:3, 3:2, and 2:1.^[9]

Irrational numbers[link]

Hippasus is sometimes credited with the discovery of the existence of irrational numbers, following which he was drowned at sea. Pythagoreans preached that all numbers could be expressed as the ratio of integers, and the discovery of irrational numbers is said to have shocked them. However, the evidence linking the discovery to Hippasus is confused.

Pappus merely says that the knowledge of irrational numbers originated in the Pythagorean school, and that the member who first divulged the secret perished by drowning.^[10] Iamblichus gives a series of inconsistent reports. In one story he explains how a Pythagorean was merely expelled for divulging the nature of the irrational; but he then cites the legend of the Pythagorean who drowned at sea for making known the construction of the regular dodecahedron in the sphere.^[11] In another account he tells how it was Hippasus who drowned at sea for betraying the construction of the dodecahedron and taking credit for this construction himself;^[12] but in another story this same punishment is meted out to the Pythagorean who divulged knowledge of the irrational.^[13] Iamblichus clearly states that the drowning at sea was a punishment from the gods for impious behaviour.^[11]

These stories are usually taken together to ascribe the discovery of irrationals to Hippasus, but whether he did or not is uncertain.^[14] In principle, the stories can be combined, since it is possible to discover irrational numbers when constructing dodecahedrons. Irrationality, by infinite reciprocal subtraction, can be easily seen in the Golden ratio of the regular pentagon.^[15]

Some modern scholars prefer to credit Hippasus with the discovery of the irrationality of √2. Plato in his Theaetetus,^[16] describes how Theodorus of Cyrene (c. 400 BC) proved the irrationality of √3, √5, etc. up to √17, which implies that an earlier mathematician had already proved the irrationality of √2.^[17] A simple proof of the irrationality of √2 is indicated by Aristotle, and it is set out in the proposition interpolated at the end of Euclid's Book X,^[18] which suggests that the proof was certainly ancient.^[19] The proof is one of reductio ad absurdum, and the method is to show that, if the diagonal of a square is commensurable with the side, then the same number must be both odd and even.^[19]

In the hands of modern writers this combination of vague ancient reports and modern guesswork has sometimes evolved into a much more emphatic and colourful tale. Some writers have Hippasus making his discovery while on board a ship, as a result of which his Pythagorean shipmates toss him overboard;^[20] while one writer even has Pythagoras himself "to his eternal shame" sentencing Hippasus to death by drowning, for showing "that √2 is an irrational number."^[21]

Proof of the irrationality of √2[link]

The reductio ad absurdum proof of the irrationality of √2 is as follows:^[22]

1. Take a right triangle whose short sides are 1 unit in length
2. By the Pythagorean theorem, the diagonal is √2
3. Suppose that √2 is the ratio of two natural numbers, √2=m/n
4. Suppose that m/n has been reduced to its lowest common form by division
5. It follows that either m and n are both odd, or that m is odd and n is even, or that m is even and n is odd (if not, we could reduce m/n even further by dividing both numbers by 2)
6. Square both sides of √2=m/n, so that 2=m²/n²
7. Then 2n²=m², so that m² is even, and therefore m is even
8. If m is even, then m=2x, where x is some other natural number
9. Squaring this, it follows that m²=4x²=2n²
10. It follows that n²=2x², and therefore n² is even, which means that n, being a natural number, must be even
11. So we've reached a contradiction: although we assumed that m and n cannot both be even, it now turns out they both are. It therefore follows that √2 cannot be expressed as the ratio of two natural numbers, and must therefore be in another class of numbers

References[link]

See also[link]

• Incommensurable magnitudes

External links[link]

• Hippasus of Metapontum at scienceworld.wolfram.com
• Diogenes Laërtius, Life of Hippasus, translated by Robert Drew Hicks (1925).

Julius Sumner Miller (May 17, 1909 – April 14, 1987) was an American physicist and television personality. He is best known for his work on children's television programs in North America and Australia.

Off-screen[link]

Julius Sumner Miller was born in Billerica, Massachusetts the youngest of nine children. His father was Latvian, his Lithuanian mother spoke 12 languages.^[1][2]

Miller graduated with a Philosophy degree and a Master's in Physics from Boston University in 1933 but due to the Depression worked as a butler for a wealthy Boston doctor for the next two years during which time he married the doctor's maid, Alice Brown; they were to have no children, but he was to go on to reach millions of children through his popular science programs.^[2]

After making over 700 applications for employment, in 1937 he was offered a place in the Physics Department of Dillard University, a private, black liberal arts college in New Orleans. During World War II he worked as a civilian physicist for the U.S. Army Signal Corps while holding fellowships in physics at the universities of Idaho and Oklahoma and was a Ford Foundation Fellow at UCLA. In 1950 he enrolled in the Institute for Advanced Studies in Princeton, N.J. where he was a student of Albert Einstein. He became a lifelong friend of Einstein and went on to amass a collection of Einstein memorabilia that included Einstein's birth certificate. Miller also taught at Princeton but disliked large institutions, leaving in 1952 to join the Physics Department at the then small El Camino College in Torrance, California (1952–1974), to maximum student enrollments due to his great popularity^[2] and where he was instantly recognizable by his casual hair and horn-rimmed spectacles.

Miller was intolerant of misspelled words and misplaced punctuation and often angered his colleagues because he charged that the students of most faculty were not learning enough. During an interview in the 1940s, he stated that intellectual life in America was in trouble, a belief he held for the rest of his life.

"We are approaching a darkness in the land. Boys and girls are emerging from every level of school with certificates and degrees, but they can't read, write or calculate. We don't have academic honesty or intellectual rigor. Schools have abandoned integrity and rigor."^[2]

From 1963 to 1986 he was the visiting lecturer for the Physics Department of the University of Sydney ^[3] and from 1965 to 1985, the US Air Force Academy.

Television[link]

Miller began hosting his educational program, "Why Is It So?" in 1959 on KNXT Channel 2 in Los Angeles. From 1962 to 1964, Miller was Disney's "Professor Wonderful" on new introductions, filmed at Disneyland, to the syndicated reruns of The Mickey Mouse Club. During the same period, he appeared on a semi-regular basis, performing physics experiments, on Steve Allen's late night TV show in Hollywood, syndicated by Group W.

Miller's first television appearance in Australia was on Bob Sanders People in 1963. In an improvised physics demonstration he attempted to drive a straw through a raw potato. A paper straw does not have the strength but if you pinch the end, the trapped air acts as a piston, easily piercing the potato. For the first time in his career he could not get it to work and loudly exclaimed "Australian straws ain't worth a damn". The next morning, Miller arrived at his Sydney University laboratory to find one million drinking straws on the floor with a telegram reading "You might find one of these fitting your requirements". He later stated "I sat amongst the straws with straws stuck in my hair and ears. But clearly I had made a mistake. I should have said: "Australian potatoes ain’t worth a damn," and I’d have cornered the potato market!"

Shortly after, he was offered a job presenting science for ABC Television. When asked how much money he wanted he replied he never asked, he listened to an offer then "multiplied it by a factor between two and ten". Due to budget constraints the offer was withdrawn but an agreement was reached for Miller to host his own science based TV series which was filmed at the University of Sydney where he taught. Why Is It So? (his eventual stock phrase), was broadcast from 1963 to 1986 and became an instant hit known for its "cool experiments, interesting science, and fantastic hair." The 1960s program became Demonstrations in Physics (also called Science Demonstrations when it was aired on American Public television). He introduced each episode with the line: "How do you do, ladies and gentlemen, and boys and girls [sometimes adding "and teachers"]. I am Julius Sumner Miller, and physics is my business."

"My first TV series on demonstrations in physics - titled Why Is It So were now seen and heard over the land. The mail was massive. The academics were a special triumph for me. They charged me with being superficial and trivial. If I had done what they wanted my programs would be as dull as their classes! I knew my purpose well and clear: to show how Nature behaves without cluttering its beauty with abtruse mathematics. Why cloud the charm of a Chladni plate with a Bessel function?"^[4]

Miller's on-air popularity was due to an enthusiasm not normally associated with serious science. Shows would be liberally sprinkled with phrases such as "He who is not stirred by the beauty of it is already dead!" and he also liked to trick the audience. A common ploy would be to hold up an empty glass and ask guests to confirm it was empty....then chide them for not noticing it was full of air. Before each demonstration he would usually ask for a show of hands to indicate which of several results they expected. Often he would then add "hands up those who don’t care".

In 1964 Miller suffered a near fatal heart attack. Scheduled to give a lecture in Australia, he sent Sydney University a telegram saying; "I've dropped dead here." He would suffer a second heart attack in 1986.^[2]

In 1966 questions from his show with an answer to the previous day’s question were published as "Millergrams" for The Australian newspaper. 112 of these questions were published as a book "Millergrams; Some Enchanting Questions for Enquiring Minds". Further books were published in 1967: "The Second Book of Millergrams: Some More Enchanting Questions for Enquiring Minds" and 1988: "Why is it So?: The Very Best Millergrams of Professor Julius Sumner Miller".

Sample Millergram:
Q32: A juggler comes to a foot-bridge of rather flimsy design. He has in hand four balls. The maximum load is no more than the juggler himself and one ball. Can he get across the bridge by juggling the balls, always having at most one ball in the hand (and three in the air)?
A: No. A falling ball exerts a force on the hand greater than its own weight.
Rather, a 'thrown' ball exerts greater force than a 'held' one. That is, the additional force equal and opposite to that imparted to a flung ball, in addition to the juggler's mass, would exceed the bridge's tolerance (the bridge can tolerate a juggler and held ball, but not the additional downward force associated with forcing a ball 'up').

Miller appeared as "The Professor" in the Canadian series The Hilarious House of Frightenstein (1971), in a 2- to 3-minute segment each episode where he demonstrated physics experiments and explained the principles involved.

Miller was also an occasional guest in the 1970s on The Tonight Show Starring Johnny Carson in the United States.

Commercials[link]

During the 1980s Miller appeared in a famous series of Australian television commercials for Cadbury chocolate, using his stock phrase "Why is it so?", demonstrating a simple scientific principle, and describing how each block of chocolate "embraces substantial nourishment and enjoyment," and contained "a glass and a half of full-cream dairy milk."

While in Australia, Miller also appeared in ads for non-stick saucepans and Ampol Petroleum which included demonstrations of real principles of physics, albeit briefly. The ads were sufficiently popular to be played for some years after his death.

Foundations[link]

In February 1987 Miller became ill while visiting Australia and returned to the United States where he was diagnosed with leukemia. Miller died six weeks later on April 14, 1987, in San Jose, California. Miller willed his body to the University of Southern California's School of Dentistry, no services were held at his request.^[2] Professor Miller's wife, Alice Brown Miller, wanted to perpetuate the memory and achievements of her husband, and so conceived the idea of the Julius Sumner Miller Foundation, which was established in 1998.^[1]

Through an offer by Cadbury-Schweppes Pty Ltd, the Cadbury-Julius Sumner Miller Scholarship for Academic Excellence was set up to provide undergraduate scholarships in the School of Physics at the University of Sydney.

In 1993 the Australian Science Foundation for Physics established the Julius Sumner Miller Fellowship in his memory. The fellowship is currently held by Karl Kruszelnicki, best known as "Doctor Karl" for his appearances on Australian radio and television as a science commentator and author.

Popular culture[link]

In 1966 Miller devised a word game "Milleranagrams" which was published in Australia by John Sands Limited. The game, whose only materials were 200 Scrabble-like letter tiles, required players in their turn to draw an unseen tile from the "pool" then either make a word from their stock of tiles or add a tile to a word already on the table (rearrangement of the letters being permitted, hence the name) to form another word.

Miller remains popular in Australia, where he is still quoted. As Professor Julius Sumner Miller often asked, "Why is it so?" and its variations are still often used in newspaper articles that pose questions unrelated to science.^[5]

Bibliography[link]

• Millergrams; Some Enchanting Questions for Enquiring Minds, Ure Smith, 1966
• The Second Book of Millergrams: Some More Enchanting Questions for Enquiring Minds, Ure Smith, 1967
• Quiz Questions in Physics, Horwitz-Martin, Australia 1967
• Why It Is So, ABC books, 1971 ISBN 0-642-97296-6
• The Kitchen Professor, ABC books, 1972 ISBN 0-642-97352-0
• Why It Is So: Heat and Temperature, ABC books, 1973 ISBN 0-642-97496-9
• Why It Is So: Sound and Electricity & Magnetism, ABC books, 1973 ISBN 0-642-97584-1
• Why It Is So: Mechanics, Heat & Temperature, Sound and Electricity, ABC books, 1978 ISBN 0-642-97523-X
• Enchanting Questions for Enquiring Minds, Currey/O'Neil, 1982 ISBN 0-85902-280-3
• Why is it so?: the very best Millergrams of Professor Julius Sumner Miller, Australian Red Cross Society, Ringwood, Vic; Penguin Books, 1988
• The Days of My Life: an autobiography, Macmillan, 1989. ISBN 0-333-50337-6

References[link]

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External links[link]

Wikiquote has a collection of quotations related to: Julius Sumner Miller

• Julius Sumner Miller Foundation
• Australian Julius Sumner Miller tribute page
• Julius Sumner Miller page at a Hilarious House of Frightenstein tribute site
• Julius Sumner Miller at TV.com
• Julius Sumner Miller at the Internet Movie Database
• Why is it so? site at Australia's ABC.net.au featuring original episodes
• http://www.physics.usyd.edu.au/foundation/Outreach/DRK/jsm.pdf Julius Sumner Miller 1909 - 1987, Physics Department, University of Sydney.