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Martin Gardner

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Popular mathematics is mathematical presentation aimed at a general audience. Sometimes this is in the form of books which require no mathematical background and in other cases it is in the form of expository articles written by professional mathematicians to reach out to others working in different areas.

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70-501: Martin Gardner (October 21, 1914 – May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing magic , scientific skepticism , micromagic , philosophy , religion , and literature  – especially the writings of Lewis Carroll , L. Frank Baum , and G. K. Chesterton . He was a leading authority on Lewis Carroll; The Annotated Alice , which incorporated

140-755: A Psi-Watcher") for Skeptical Inquirer , that organization's monthly magazine. These columns have been collected in five books starting with The New Age: Notes of a Fringe Watcher in 1988. Gardner was a critic of self-proclaimed Israeli psychic Uri Geller and wrote two satirical booklets about him in the 1970s using the pen name "Uriah Fuller" in which he explained how such purported psychics do their seemingly impossible feats such as mentally bending spoons and reading minds . Martin Gardner continued to criticize junk science throughout his life. His targets included not just safe subjects like astrology and UFO sightings , but topics such as chiropractic , vegetarianism , Madame Blavatsky , creationism , Scientology ,

210-659: A copy of Sam Loyd 's Cyclopedia of 5000 Puzzles, Tricks and Conundrums . He attended the University of Chicago where he studied history, literature and sciences under their intellectually-stimulating Great Books curriculum and earned his bachelor's degree in philosophy in 1936. Early jobs included reporter on the Tulsa Tribune , writer at the University of Chicago Office of Press Relations, and case worker in Chicago's Black Belt for

280-626: A copy of it. Over seven thousand requests came pouring in, some of them from other countries. This caused significant consternation in the US defense agencies and possible legal problems for Gardner himself. The National Security Agency (NSA) asked the RSA team to stop distributing the report and one letter to the IEEE suggested that disseminating such information might be violating the Arms Export Control Act and

350-417: A far greater debt to Martin Gardner than most conjurors realize. –Stephen Minch Martin Gardner held a lifelong fascination with magic and illusion that began when his father demonstrated a trick to him. He wrote for a magic magazine in high school and worked in a department store demonstrating magic tricks while he was at the University of Chicago. Gardner's first published writing (at the age of fifteen)

420-634: A free-standing article on hexaflexagons which ran in the December 1956 issue of Scientific American . Flexagons became a bit of a fad and soon people all over New York City were making them. Gerry Piel, the SA publisher at the time, asked Gardner, "Is there enough similar material to this to make a regular feature?" Gardner said he thought so. The January 1957 issue contained his first column, entitled "Mathematical Games". Almost 300 more columns were to follow. It ran from 1956 to 1981 with sporadic columns afterwards and

490-513: A freelance author, publishing books with several different publishers, and also publishing hundreds of magazine and newspaper articles. In 1950, he wrote an article in the Antioch Review entitled "The Hermit Scientist". It was one of Gardner's earliest articles about junk science , and in 1952 a much-expanded version became his first published book: In the Name of Science: An Entertaining Survey of

560-527: A hub of this network helped facilitate several introductions that led to further fruitful collaborations. Mathematicians Conway, Berlekamp, and Guy, who met as a result of Gardner's influence, would go on to write Winning Ways for your Mathematical Plays , a foundational book in combinatorial game theory that Gardner subsequently championed. Gardner also introduced Conway to Benoit Mandelbrot because he knew of their mutual interest in Penrose tiles . Gardner's network

630-672: A list of "Ten Red Flags of Junk Science". Another way in which causation often is undermined—also an increasingly serious problem in toxic tort cases—is the reliance by judges and juries on non-credible scientific or medical testimony, studies or opinions. It has become all too common for 'experts' or 'studies' on the fringes of or even well beyond the outer parameters of mainstream scientific or medical views to be presented to juries as valid evidence from which conclusions may be drawn. The use of such invalid scientific evidence (commonly referred to as 'junk science') has resulted in findings of causation which simply cannot be justified or understood from

700-544: A lot of criticism from the advocates of alternative science and New Age philosophy . He kept up running dialogues (both public and private) with many of them for decades. In a review of Science: Good, Bad and Bogus , Stephen Jay Gould called Gardner "The Quack Detector", a writer who "expunge[d] nonsense" and in so doing had "become a priceless national resource." In 1976 Gardner joined with fellow skeptics philosopher Paul Kurtz , psychologist Ray Hyman , sociologist Marcello Truzzi , and stage magician James Randi to found

770-507: A major impact on mathematics in the second half of the 20th century. His column ran for 25 years and was read avidly by the generation of mathematicians and physicists who grew up in the years 1956 to 1981. His writing inspired, directly or indirectly, many who would go on to careers in mathematics, science, and other related endeavors. Gardner's admirers included such diverse individuals as W. H. Auden , Arthur C. Clarke , Carl Sagan , Isaac Asimov , Richard Dawkins , Stephen Jay Gould , and

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840-692: A monthly column on magic tricks called "Trick of the Month" in The Physics Teacher , a journal published by the American Association of Physics Teachers . In 1999 Magic magazine named Gardner one of the "100 Most Influential Magicians of the Twentieth Century". In 2005 he received a 'Lifetime Achievement Fellowship' from the Academy of Magical Arts . The last work to be published during his lifetime

910-583: A possibility existed that AIDS could be transmitted to schoolmates through yet undiscovered "vectors". However, five experts testified on behalf of Thomas that AIDS is not transmitted through casual contact, and the court affirmed the "solid science" (as Huber called it) and rejected Armentrout's argument. In 1999, Paul Ehrlich and others advocated public policies to improve the dissemination of valid environmental scientific knowledge and discourage junk science: The Intergovernmental Panel on Climate Change reports offer an antidote to junk science by articulating

980-404: Is spurious or fraudulent scientific data , research , or analysis. The concept is often invoked in political and legal contexts where facts and scientific results have a great amount of weight in making a determination. It usually conveys a pejorative connotation that the research has been untowardly driven by political, ideological, financial, or otherwise unscientific motives. The concept

1050-419: Is an anagram of "Mathematical Games". Virtually all of the games columns were collected in book form starting in 1959 with The Scientific American Book of Mathematical Puzzles & Diversions . Over the next four decades fourteen more books followed. Donald Knuth called them the canonical books . His depth and clarity will illuminate our world for a long time. – Persi Diaconis Martin Gardner had

1120-408: Is expected to produce the desired results) into scientific fraud (e.g., lying about the results) and pseudoscience (e.g., claiming that the unfavorable results actually proved the idea correct). Junk science can occur when the perpetrator has something to gain from arriving at the desired conclusion. It can often happen in the testimony of expert witnesses in legal proceedings, and especially in

1190-523: Is not the same as pseudoscience . Junk science has been defined as: Junk science happens for different reasons: researchers believing that their ideas are correct before proper analysis (a sort of scientific self-delusion or drinking the Kool-Aid ), researchers biased with their study designs, and/or a "plain old lack of ethics". Being overly attached to one's own ideas can cause research to veer from ordinary junk science (e.g., designing an experiment that

1260-491: Is unique – in its range, its insight, and understanding of hard questions that matter." Gardner repeatedly alerted the public (and other mathematicians) to recent discoveries in mathematics–recreational and otherwise. In addition to introducing many first-rate puzzles and topics such as Penrose tiles and Conway's Game of Life , he was equally adept at writing columns about traditional mathematical topics such as knot theory , Fibonacci numbers , Pascal's triangle ,

1330-454: The American Association for the Advancement of Science also recognized the need for increased understanding between scientists and lawmakers: "Although most individuals would agree that sound science is preferable to junk science, fewer recognize what makes a scientific study 'good' or 'bad'." The American Dietetic Association , criticizing marketing claims made for food products, has created

1400-565: The Cato Institute , which had hosted the junkscience.com site, ceased its association with the site and removed Milloy from its list of adjunct scholars. Tobacco industry documents reveal that Philip Morris executives conceived of the "Whitecoat Project" in the 1980s as a response to emerging scientific data on the harmfulness of second-hand smoke. The goal of the Whitecoat Project, as conceived by Philip Morris and other tobacco companies,

1470-631: The Committee for the Scientific Investigation of Claims of the Paranormal (now called the Committee for Skeptical Inquiry). Intellectuals including astronomer Carl Sagan , author and biochemist Isaac Asimov , psychologist B. F. Skinner , and journalist Philip J. Klass became fellows of the program. From 1983 to 2002 he wrote a monthly column called "Notes of a Fringe Watcher" (originally "Notes of

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1540-586: The Daubert standard as too unreliable would be the testimony of a phrenologist who would purport to prove a defendant's future dangerousness based on the contours of the defendant's skull. Lower courts have subsequently set guidelines for identifying junk science, such as the 2005 opinion of United States Court of Appeals for the Seventh Circuit Judge Frank H. Easterbrook : Positive reports about magnetic water treatment are not replicable; this plus

1610-749: The International Traffic in Arms Regulations . In the end the defense establishment could provide no legal basis for suppressing the new technology, and when a detailed paper about RSA was published in Communications of the ACM , the NSA’s crypto monopoly was effectively terminated. Martin Gardner is the single brightest beacon defending rationality and good science against the mysticism and anti-intellectualism that surround us. – Stephen Jay Gould Gardner

1680-628: The Laffer curve , Christian Science , and the Hutchins-Adler Great Books Movement . The last thing he wrote in the spring of 2010 (a month before his death) was an article excoriating the "dubious medical opinions and bogus science" of Oprah Winfrey  – particularly her support for the thoroughly discredited theory that vaccinations cause autism ; it went on to bemoan the "needless deaths of children" that such notions are likely to cause. Skeptical Inquirer named him one of

1750-447: The Möbius strip , transfinite numbers , four-dimensional space , Zeno's paradoxes , Fermat's Last Theorem , and the four-color problem . Gardner set a new high standard for writing about mathematics. In a 2004 interview he said, "I go up to calculus, and beyond that I don't understand any of the papers that are being written. I consider that that was an advantage for the type of column I

1820-486: The Southern Poverty Law Center (SPLC) as an anti-gay extremist and a purveyor of "junk science". Cameron's research has been heavily criticized for unscientific methods and distortions which attempt to link homosexuality with pedophilia. In one instance, Cameron claimed that lesbians are 300 times more likely to get into car accidents. The SPLC states his work has been continually cited in some sections of

1890-404: The game of Hex invented by Piet Hein and John Nash ; Tutte's account of squaring the square ; and many other topics. The wide array of mathematicians, physicists, computer scientists, philosophers, magicians, artists, writers, and other influential thinkers who can be counted as part of Gardner's mathematical grapevine includes: These new ciphers are not absolutely unbreakable in the sense of

1960-511: The rep-tiles and pentominos of Solomon W. Golomb; the space filling curves of Bill Gosper; the aperiodic tiles of Roger Penrose; the Game of Life invented by John H. Conway; the superellipse and the Soma cube of Piet Hein; the trapdoor functions of Diffie , Hellman , and Merkle ; the flexagons of Stone , Tuckerman , Feynman , and Tukey; the geometrical delights in a book by H. S. M. Coxeter;

2030-475: The High Priests and Cultists of Science, Past and Present . The year 1960 saw the original edition of the best-selling book of his career, The Annotated Alice . In 1957 Gardner started writing a column for Scientific American called "Mathematical Games". It ran for over a quarter century and dealt with the subject of recreational mathematics . The "Mathematical Games" column became the most popular feature of

2100-600: The Soma Cube . Charlotte died in 2000 and in 2004 Gardner returned to Oklahoma, where his son, James Gardner, was a professor of education at the University of Oklahoma in Norman . He died there on May 22, 2010. An autobiography – Undiluted Hocus-Pocus: The Autobiography of Martin Gardner  – was published posthumously. I just play all the time and am fortunate enough to get paid for it. – Martin Gardner, 1998 The "Mathematical Games" column began with

2170-616: The Ten Outstanding Skeptics of the Twentieth Century. In 2010 he was posthumously honored with an award for his contributions in the skeptical field from the Independent Investigations Group . In 1982 the Committee for Skeptical Inquiry awarded Gardner its In Praise of Reason Award for his "heroic efforts in defense of reason and the dignity of the skeptical attitude", and in 2011 it added Gardner to its Pantheon of Skeptics. Card magic, and magic in general, owe

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2240-408: The advent of the personal computer." Colm Mulcahy described him as "without doubt the best friend mathematics ever had." Gardner's column introduced the public to books such as A K Dewdney ’s Planiverse and Douglas Hofstadter ’s Gödel, Escher, Bach . His writing was credited as both broad and deep. Noam Chomsky once wrote, "Martin Gardner's contribution to contemporary intellectual culture

2310-601: The authors, rather than the readers, become the customer and the source of funding for the journal, so the publisher is incentivized to publish as many papers as possible, including those that are methodologically unsound. John Stauber and Sheldon Rampton of PR Watch say the concept of junk science has come to be invoked in attempts to dismiss scientific findings that stand in the way of short-term corporate profits. In their book Trust Us, We're Experts (2001), they write that industries have launched multimillion-dollar campaigns to position certain theories as junk science in

2380-588: The city's Relief Administration. During World War II , he served for four years in the U.S. Navy as a yeoman on board the destroyer escort USS Pope in the Atlantic . His ship was still in the Atlantic when the war came to an end with the surrender of Japan in August 1945. After the war, Gardner returned to the University of Chicago. He attended graduate school for a year there, but he did not earn an advanced degree. In

2450-548: The credibility of all research. In his 2006 book Junk Science , Dan Agin emphasized two main causes of junk science: fraud, and ignorance . In the first case, Agin discussed falsified results in the development of organic transistors : As far as understanding junk science is concerned, the important aspect is that both Bell Laboratories and the international physics community were fooled until someone noticed that noise records published by Jan Hendrik Schön in several papers were identical—which means physically impossible. In

2520-614: The current consensus on the prospects for climate change, by outlining the extent of the uncertainties, and by describing the potential benefits and costs of policies to address climate change . In a 2003 study about changes in environmental activism regarding the Crown of the Continent Ecosystem , Pedynowski noted that junk science can undermine the credibility of science over a much broader scale because misrepresentation by special interests casts doubt on more defensible claims and undermines

2590-622: The entire French literary group known as the Oulipo . Salvador Dalí once sought him out to discuss four-dimensional hypercubes . David Auerbach wrote: "A case can be made, in purely practical terms, for Martin Gardner as one of the most influential writers of the 20th century. His popularizations of science and mathematical games in Scientific American, over the 25 years he wrote for them, might have helped create more young mathematicians and computer scientists than any other single factor prior to

2660-455: The first chapter of his "best of" collection, The Colossal Book of Mathematics . In the 1980s "Mathematical Games" began to appear only irregularly. Other authors began to share the column, and the June 1986 issue saw the final installment under that title. In 1981, on Gardner's retirement from Scientific American , the column was replaced by Douglas Hofstadter 's " Metamagical Themas ", a name that

2730-415: The four Princeton University professors who had invented and investigated their mathematical properties. The subsequent article Gardner wrote on hexaflexagons led directly to the column. Gardner's son Jim once asked him what was his favorite puzzle, and Gardner answered almost immediately: " The monkey and the coconuts ". It had been the subject of his April 1958 Games column and in 2001 he chose to make it

2800-636: The general public, Mathematics, Magic and Mystery (Dover, 1956), is still considered a classic in the field. He was well known for his innovative tapping and spelling effects, with and without playing cards , and was most proud of the effect he called the "Wink Change". Many of Gardner's lifelong friends were magicians. These included William Simon who introduced Gardner to Charlotte Greenwald, whom he married in 1952, Dai Vernon , Jerry Andrus , statistician Persi Diaconis , and polymath Raymond Smullyan . Gardner considered fellow magician James Randi his closest friend. Diaconis and Smullyan like Gardner straddled

2870-589: The lack of a physical explanation for any effects are hallmarks of junk science. As the subtitle of Huber's book, Junk Science in the Courtroom , suggests, his emphasis was on the use or misuse of expert testimony in civil litigation. One prominent example cited in the book was litigation over casual contact in the spread of AIDS . A California school district sought to prevent a young boy with AIDS, Ryan Thomas, from attending kindergarten . The school district produced an expert witness, Steven Armentrout, who testified that

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2940-512: The late 1940s, Gardner moved to New York City and became a writer and editor at Humpty Dumpty magazine, where for eight years, he wrote features and stories for it and several other children's magazines. His paper-folding puzzles at that magazine led to his first work at Scientific American. For many decades, Gardner, his wife Charlotte, and their two sons, Jim and Tom, lived in Hastings-on-Hudson, New York , where he earned his living as

3010-558: The latter half of the 20th century, principally through his "Mathematical Games" columns. These appeared for twenty-five years in Scientific American , and his subsequent books collecting them. Gardner was one of the foremost anti- pseudoscience polemicists of the 20th century. His 1957 book Fads and Fallacies in the Name of Science is a seminal work of the skeptical movement. In 1976, he joined with fellow skeptics to found CSICOP , an organization promoting scientific inquiry and

3080-535: The lost continents of Atlantis and Lemuria , Immanuel Velikovsky's Worlds in Collision , the reincarnation of Bridey Murphy , Wilhelm Reich's orgone theory , the spontaneous generation of life , extra-sensory perception and psychokinesis , homeopathy , phrenology , palmistry , graphology , and numerology . This book and his subsequent efforts ( Science: Good, Bad and Bogus , 1981; Order and Surprise , 1983, Gardner's Whys & Wherefores , 1989, etc.) provoked

3150-587: The magazine and was the first thing that many readers turned to. In September 1977 Scientific American acknowledged the prestige and popularity of Gardner's column by moving it from the back to the very front of the magazine. In 1979, Gardner left Scientific American . He and his wife Charlotte moved to Hendersonville, North Carolina . He continued to write math articles, sending them to The Mathematical Intelligencer , Math Horizons , The College Mathematics Journal , and Scientific American . He also revised some of his older books such as Origami, Eleusis, and

3220-534: The material I got from them, so I owe them a big debt of gratitude." Gardner prepared each of his columns in a painstaking and scholarly fashion and conducted copious correspondence to be sure that everything was fact-checked for mathematical accuracy. Communication was often by postcard or telephone and Gardner kept meticulous notes of everything, typically on index cards. Archives of some of his correspondence stored at Stanford University occupy some 63 linear feet of shelf space. This correspondence led to columns about

3290-685: The media despite being discredited. Cameron was expelled from the American Psychological Association in 1983. In 1995, the Union of Concerned Scientists launched the Sound Science Initiative, a national network of scientists committed to debunking junk science through media outreach, lobbying, and developing joint strategies to participate in town meetings or public hearings. In its newsletter on Science and Technology in Congress,

3360-498: The most prolific popularisers of mathematics include Keith Devlin , Rintu Nath , Martin Gardner , and Ian Stewart . Titles by these three authors can be found on their respective pages. The journals listed below can be found in many university libraries. Several museums aim at enhancing public understanding of mathematics: In the United States : In Austria : In Germany : In Italy : Junk science Junk science

3430-564: The one-time pad. but in practice they are unbreakable in a much stronger sense than any cipher previously designed for widespread use. In principle these new ciphers can be broken. but only by computer programs that run for millions of years! –Martin Gardner In his August 1977 column, "A new kind of cipher that would take millions of years to break", Gardner described a new cryptographic system invented by Ron Rivest , Adi Shamir and Leonard Adleman . The system, based on trapdoor functions ,

3500-402: The popular mind, often failing to employ the scientific method themselves. For example, the tobacco industry has described research demonstrating the harmful effects of smoking and second-hand smoke as junk science, through the vehicle of various astroturf groups . Theories more favorable to corporate activities are portrayed in words as "sound science". Past examples where "sound science"

3570-408: The reader to step back from the rhetoric, as "how things are labeled does not make a science junk science." In its place, he offers that junk science is ultimately motivated by the desire to hide undesirable truths from the public. The rise of open source (free to read) journals has resulted in economic pressure on academic publishers to publish junk science. Even when the journal is peer-reviewed,

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3640-530: The regulation of second-hand smoke . David Michaels has argued that, since the U.S. Supreme Court ruling in Daubert v. Merrell Dow Pharmaceuticals, Inc. , lay judges have become "gatekeepers" of scientific testimony and, as a result, respected scientists have sometimes been unable to provide testimony so that corporate defendants are "increasingly emboldened" to accuse adversaries of practicing junk science. American psychologist Paul Cameron has been designated by

3710-462: The second case, he cites an example that demonstrates ignorance of statistical principles in the lay press: Since no such proof is possible [that genetically modified food is harmless], the article in The New York Times was what is called a "bad rap" against the U.S. Department of Agriculture—a bad rap based on a junk-science belief that it's possible to prove a null hypothesis . Agin asks

3780-577: The self-serving advertising of products and services. These situations may encourage researchers to make sweeping or overstated claims based on limited evidence. The phrase junk science appears to have been in use prior to 1985. A 1985 United States Department of Justice report by the Tort Policy Working Group noted: The use of such invalid scientific evidence (commonly referred to as 'junk science') has resulted in findings of causation which simply cannot be justified or understood from

3850-619: The standpoint of the current state of credible scientific or medical knowledge. In 1989, the climate scientist Jerry Mahlman (Director of the Geophysical Fluid Dynamics Laboratory ) characterized the theory that global warming was due to solar variation (presented in Scientific Perspectives on the Greenhouse Problem by Frederick Seitz et al.) as "noisy junk science." Peter W. Huber popularized

3920-528: The term with respect to litigation in his 1991 book Galileo's Revenge: Junk Science in the Courtroom. The book has been cited in over 100 legal textbooks and references; as a consequence, some sources cite Huber as the first to coin the term. By 1997, the term had entered the legal lexicon as seen in an opinion by Supreme Court of the United States Justice John Paul Stevens : An example of 'junk science' that should be excluded under

3990-527: The text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century". He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books. Gardner was best known for creating and sustaining interest in recreational mathematics —and by extension, mathematics in general—throughout

4060-460: The two worlds of mathematics and magic. Mathematics and magic were frequently intertwined in Gardner's work. One of his earliest books, Mathematics, Magic and Mystery (1956), was about mathematically based magic tricks. Mathematical magic tricks were often featured in his "Mathematical Games" column–for example, his August 1962 column was titled "A variety of diverting tricks collected at a fictitious convention of magicians." From 1998 to 2002 he wrote

4130-590: The use of reason in examining extraordinary claims. Martin Gardner was born into a prosperous family in Tulsa, Oklahoma , to James Henry Gardner, a petroleum geologist , and his wife, Willie Wilkerson Spiers, a Montessori-trained teacher. His mother taught Martin to read before he started school, reading him The Wizard of Oz , and this began a lifelong interest in the Oz books of L. Frank Baum . His fascination with mathematics started in his boyhood when his father gave him

4200-497: Was a critic of fringe science . His book Fads and Fallacies in the Name of Science (1952, revised 1957) launched the modern skeptical movement. It debunked dubious movements and theories including Fletcherism , Lamarckism , food faddism , Dowsing Rods , Charles Fort , Rudolf Steiner , Dianetics , the Bates method for improving eyesight , Einstein deniers , the Flat Earth theory ,

4270-563: Was a magic trick in The Sphinx , the official magazine of the Society of American Magicians . He focused mainly on micromagic (table or close-up magic) and, from the 1930s on, published a significant number of original contributions to this secretive field. Magician Joe M. Turner said, The Encyclopedia of Impromptu Magic , which Gardner wrote in 1985, "is guaranteed to show up in any poll of magicians' favorite magic books." His first magic book for

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4340-526: Was a magic trick in the May 2010 issue of Word Ways: The Journal of Recreational Linguistics . I am a philosophical theist. I believe in a personal God, and I believe in an afterlife, and I believe in prayer, but I don't believe in any established religion. This is called philosophical theism. ... Philosophical theism is entirely emotional. As Kant said, he destroyed pure reason to make room for faith. – Martin Gardner, 2008 Popular mathematics Some of

4410-482: Was also responsible for introducing Doris Schattschneider and Marjorie Rice , who worked together to document the newly discovered pentagon tilings. Gardner credited his network with generating further material for his columns: "When I first started the column, I was not in touch with any mathematicians, and gradually mathematicians who were creative in the field found out about the column and began corresponding with me. So my most interesting columns were columns based on

4480-764: Was doing because I had to understand what I was writing about, and that enabled me to write in such a way that an average reader could understand what I was saying. If you are writing popularly about math, I think it's good not to know too much math." John Horton Conway called him "the most learned man I have ever met." He had carried on incredibly interesting exchanges with hundreds of mathematicians, as well as with artists and polymaths such as Maurits Escher and Piet Hein. – AMS Notices Gardner maintained an extensive network of experts and amateurs with whom he regularly exchanged information and ideas. Doris Schattschneider would later term this circle of collaborators "Gardner's mathematical grapevine" or "MG. Gardner's role as

4550-431: Was known as RSA (after the three researchers) and has become a component of the majority of secure data transmission schemes. Since RSA is a relatively slow algorithm it is not widely used to directly encrypt data. More often, it is used to transmit shared keys for  symmetric-key cryptography . Gardner identified the memorandum that his column was based on and invited readers to write to Rivest to request

4620-515: Was popularized in the 1990s in relation to expert testimony in civil litigation . More recently, invoking the concept has been a tactic to criticize research on the harmful environmental or public health effects of corporate activities, and occasionally in response to such criticism. In some contexts, junk science is counterposed to the "sound science" or "solid science" that favors one's own point of view. Junk science has been criticized for undermining public trust in real science. Junk science

4690-431: Was questioned by Paul D. Thacker , a writer for The New Republic , in the wake of evidence that Milloy had received funding from Philip Morris , RJR Tobacco , and Exxon Mobil . Thacker also noted that Milloy was receiving almost $ 100,000 a year in consulting fees from Philip Morris while he criticized the evidence regarding the hazards of second-hand smoke as junk science. Following the publication of this article,

4760-410: Was the first introduction of many subjects to a wider audience, notably: Gardner had problems learning calculus and never took a mathematics course after high school. While editing Humpty Dumpty Magazine he constructed many paper folding puzzles. At a magic show in 1956 fellow magician Royal Vale Heath introduced Gardner to the intricately folded paper shapes known as flexagons and steered him to

4830-478: Was to use ostensibly independent "scientific consultants" to spread doubt in the public mind about scientific data through invoking concepts like junk science. According to epidemiologist David Michaels , Assistant Secretary of Energy for Environment, Safety, and Health in the Clinton Administration , the tobacco industry invented the "sound science" movement in the 1980s as part of their campaign against

4900-472: Was used include the research into the toxicity of Alar , which was heavily criticized by antiregulatory advocates, and Herbert Needleman 's research into low dose lead poisoning . Needleman was accused of fraud and personally attacked. Fox News commentator Steven Milloy often denigrates credible scientific research on topics like global warming , ozone depletion , and passive smoking as "junk science". The credibility of Milloy's website junkscience.com

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