23 results found.
... Science Frontiers ONLINE No. 103: Jan-Feb 1996 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects How To Find A Piece Of Pi The formula shown below allows one -- if one wishes -- to find the billionth digit of pi without first computing the preceding 999,999,999 digits. In other words, isolated digits of pi can be quickly calculated should an urgent need arise. P.B . Borwein et al, at Simon Fraser University, announced this "curious" discovery in October 1995. This is the equation mathematicians use in calculating isolated digits of pi. Innuendo aside, there is something more than "curious" here. It seems that the formula works only for hexadecimal (base-16) digits of pi. These can be easily converted into binary (base-2 ) digits. Strangely, it does not work at all for our familiar decimal (base-10) digits of pi. Not to worry though! Y. Kanada and colleagues, at the University of Tokyo, have now computed pi to 4,294,960,000 decimal digits. But, they have found a puzzling asymmetry. In the first 4 billion digits, the decimal digit 6 occurs 400,033,035 times, but 2 shows up only 399,965,405 times! Shouldn't all ten digits appear with the same frequency? Obviously, we do not appreciate all of the subtleties of pi. (Peterson, I.; "A New Formula for Picking Off Pieces of ...
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... Science Frontiers ONLINE No. 37: Jan-Feb 1985 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects The Secret Of It All Is In The Pi In the above, Pollard discoursed on the meaning of it all and how mathematics seemed to mirror reality so marvelously. Now, one fixture of mathematics is the transcendental number. The adjective "transcendental" is most appropriate here given the title of Pollard's article. Of the transcendental numbers, pi is a great favorite. Mathematicians like pi so much that they have computed it out to well beyond 10 million decimals. Are there any inklings to the meaning of it all in these 10 million-plus decimals? Well, at decimal 710,100 there are seven 3s in a row. At decimal 1,526,800, we find the digits 2718281, the first seven digits of e, the base of natural logarithms. Then at decimal 52,638 there is 14142135, the first eight digits of the square root of 2. But all these discoveries are hardly profound, for they could occur by chance -- nothing really "transcendental" so far. A more astounding discovery is that: 22(pi)4 = 2143 A few multiplications, and the 10 million-plus decimals of pi have vanished. (Can this remarkable relationship mirror some as yet undiscovered facet of physical reality?) While it is difficult to squeeze the meaning of the universe out of pi's 10 million-plus decimals, one has to admit that pi is everywhere. ...
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... Science Frontiers ONLINE No. 96: Nov-Dec 1994 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Lazzarini eats humble pi (posthumously)If you are on a desert island and have forgotten the value of pi and need it desperately, you can find it experimentally. One amusing though tedious method would require throwing a short, straight twig onto parallel lines drawn in the beach sand. You will be able to compute pi from: pi = 2lN/dH, where l = the length of the twig, which must be less than d, separation of the parallel lines. N = the number of throws. H = the number of times the twig crosses one of the lines. One famous performance of this experiment was by M. Lazzarini in 1901. He reported that in 3408 throws he got 1808 intersections, leading to: pi = 3.1415929 Actually, the final digit should be a 6. Thus, Lazzarini measured pi to a few parts in 10 million. Recently, L. Badger, Weber State University, concluded that Lazzarini probably never actually performed his experiment. His results were just too good -- too fortuitous! If the number of hits had been 1807 or 1809, pi would have been wrong by 1 part in 2,000. As it turns out, a Chinese mathematician of the 5th Century pointed out that 355/113 = 3.1415929. It is very suspicious that Lazzarini's 3408 = 355 x 16, and 1808 = 113 x 16. Badger thinks that Lazzarini ...
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... Science Frontiers ONLINE No. 53: Sep-Oct 1987 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Pi And Ramanajan Someone has finally complained about an equality sign in SF#37 namely, 22[PI]4 = 2143 D. Thomas has correctly pointed out that we have here only a very good approximation. Of course, one need not do the actual calculation to prove that it is an approximation, because 2143/22 is a rational fraction which can be expressed as a repeating decimal; whereas pi is irrational. The number (2143/22) is a discovery of Ramanujan, about whom we heard on p. 000. How did he ever stumble upon this extremely accurate approximation of pi -- one that is accurate to 300 parts in a trillion? N.D . Mermin suggests that Ramanujan may have taken it from the expansion: [PI]4 = 97+ 1/(2+ 1/(2+ 1/(3+ 1/(1+ 1/(16539 +.... If 16,539 is replaced by infinity, Ramanujan's result follows. (Mermin, N. David; "Pi in the Sky," American Journal of Physics, 55:584, 1987.) From Science Frontiers #53, SEP-OCT 1987 . 1987-2000 William R. Corliss ...
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... Science Frontiers ONLINE No. 74: Mar-Apr 1991 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Pi Surprise Consider the positive integer, 8. It can be written as m 2+ n 2 , a sum of two squares of integers, in just 4 ways, namely when the pair (m , n) is (2 , 2), (2 , -2 ), -2 , 2), and (- 2 , -2 ). The integer 7, on the other hand, cannot be written as the sum of any squared integers. On the average, over a very large collection of integers from 1 to n, in how many ways can an integer be written as the sum of such squares? The answer is little short of astounding: closer and closer to pi! (Anonymous; "Closing Pi Surprise," Algorithm , p. 7, n.d . Cr. C.H . Stiles) From Science Frontiers #74, MAR-APR 1991 . 1991-2000 William R. Corliss ...
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... Science Frontiers ONLINE No. 9: Winter 1979 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Transcendental trivia?Both e (2 .7182...) and pi (3 .1416...) are transcendental numbers of great significance in mathematics and the scientific description of nature. Instead of being neat and orderly (as we devoutly hope nature will be), the decimal expansions of these two numbers are patternless, some say ugly. Faint hope arises at the 710,150th digit of pi where a satisfying string of seven consecutive 3s appears (. .. .353733333338...). More reassuring is the observation that (pi)4+ (pi)5 almost exactly equals e6 . We are sure that great truths lie hidden in these two numbers (despite their unattractive decimals) when we find that a 5x5 magic square (first row: 17, 24, 1, 8, 15) can be transformed by the alchemy of pi into an unmagic but very strange square. To do this, replace the 17 by the 17th digit of pi (this is 2); 24 by the 24th digit (this is 4); and so on. The rows and columns of the new square add up to the same numbers: columns; 17, 19, 25, 24, 23; rows; 24, 23, 25, 29, 17. (Yes, the order given is correct.) Gardner maintains that this astounding transformation is merely a coincidence, like all of the ...
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... Science Frontiers ONLINE No. 65: Sep-Oct 1989 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Pi in the mind!" Srinivasan Mahadevan, a graduate student from India at Kansas State University in Manhattan, is trying to become the fourth person to remember the first 100,000 digits to pi, the theoretically infinite computation that measures the ratio of the circumference of a circle to its diameter. He has already memorized the first 35,000 digits of pi. "Only three cases of such ability to remember have been documented in 200 years. One of these people became insane when he became unable to forget anything and his reasoning processes drowned in a flood of facts." (Anonymous; "Student's Memory Wins Bets," San Mateo Times, June 2, 1989. Cr. J. Covey) From Science Frontiers #65, SEP-OCT 1989 . 1989-2000 William R. Corliss ...
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... Frontiers ONLINE No. 29: Sep-Oct 1993 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Temptations Of Numerology "Too much innocent energy is being spent on the search for numerical coincidences with physical quantities. Would that this Pythagorean energy were spent more profitably." Following this admonition, John Maddox conceded that numerology, on rare occasions, has provided useful insights. Musings about Bode's Law are not complete wastes of time; and Prout's hypothesis that the masses of the elements would be found to be integral multiples of the mass of the hydrogen atom was not far off the mark. Certainly an entertainment factor exists, too, for Maddox cannot resist printing a curious little contribution by Peter Stanbury, entitled "The Alleged Ubiquity of pi." Stanbury has discovered a large number of relations between the masses of the fundamental particles that are closely related to pi. Four representative examples follow: The proton-to-electron mass ratio is almost exactly 6pi5 ; The sum of the masses of the basic octet pio, pi +, k +, k-, ko, k-baro is 3.14006 times the proton mass; The sum of the masses of the baryon octet is very close to pi2 times the proton mass; and The reciprocal of the fine structure constant, 137.03604 is close to 4-pi3 + pi 2+ pi , or 137.03630. There are many more such relationships. Further, the ratios 1.0345 and 1.1115 keep popping up more frequently than coincidence ...
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... Science Frontiers ONLINE No. 110: Mar-Apr 1997 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects http://www.aros.net/angio/pistuff/piquery At this Web site you can enter your Social Security Number (or telephone number, etc.) and discover if it appears among the first 1.25 million digits of pi. Perhaps when God was designing the Universe and was contemplating what the value of pi should be, he put your number somewhere in this transcendental number! (Anonymous; New Scientist, p. 64, January 4, 1997.) Comment. Of course, pi has as many digits as you care to compute (at least we think it does!) If your number is not among the first 1.25 million digits, it will certainly appear somewhere later. It's just that you are not first in line! From Science Frontiers #110, MAR-APR 1997 . 1997-2000 William R. Corliss ...
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... 2 x 272+ 0 x 271+ 3 x 270 , which equals 1461 in decimal. Now we have a way to convert numbers into words in a novel, though tedious, way, and vice versa. For example, CHAT+ TALK = WIND, which is not an unlikely word equation. Really fantastic word-number equalities can be found with the help of a computer. Who would have ever guessed that the following magic square of meaningful words could be constructed? DIM OWE TUG RAP RIG TAP DOT RAY THE TIP NAP DID PAP DUD SPY TOW The magic constant is BEAN, and all horizontal, vertical, and diagonal rows add up to this constant. The real value of this system of numerology is apparent when we turn to eternal verities: the transcendental numbers such as pi, e, and the Golden Mean (1 .618034....). The latter converts to: A.PRNTPFCUCRKDYGRYLLC-QNBIG... Ah, BIG, part of a message, no doubt! Sallows remarks, "Perhaps the first message to appear in pi is .. .GOD_EXISTS..., While that in e might be .. .PROVE_IT..." Repair to your computers to find the meaning of it all. (Stewart, Ian; "Number Mysticism for the Modern Age," New Scientist, p. 16, July 10, 1993.) From Science Frontiers #89, SEP-OCT 1993 . 1993-2000 William R. Corliss ...
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... Science Frontiers ONLINE No. 123: May-Jun 1999 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Megamemories This is not about the latest ROMs and RAMs; it's about those few pounds of gray matter sitting atop your shoulders. Every once in a while we see hints of what it can really do. At the age of eight, J. Von Neumann, the great mathematician, could just glance at a telephone book and afterward recite whole pages verbatim. (Myhrvold, Nathan; "John Von Neumann: Computing's Cold Warrior," Time, 153: 150, March 29, 1999.) Recently, H. Goto, in something like 9 hours, recited from memory the first 42,000 digits of pi. (Kaiser, Jocelyn; "Pieces of Pi," Science, 283:1975, 1999.) From Science Frontiers #123, MAY-JUN 1999 . 1999-2000 William R. Corliss ...
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... Science Frontiers ONLINE No. 74: Mar-Apr 1991 Other pages Home Page Science Frontiers Online All Issues Last Issue Next Issue Sourcebook Project Sourcebook Subjects Contents Archaeology A GOLDEN CALENDAR FOR USE AT STONEHENGE? DID THE PHARAOHS CHEAT WITH CONCRETE? Astronomy An unexplained event Gaia on mars? SOLAR ECLIPSE AFFECTS A PENDULUM -- AGAIN! Biology Eel oddities Echidna eccentricities Searching for monster sharks WHEN IDENTICAL TWINS ARE NOT IDENTICAL Geology 'TERMITE BANDS' IN SOUTH AFRICA THE MECHANICAL PARADOX IN THRUST FAULTING Geophysics NEWTONIAN GRAVITY MAY HAVE BROKEN DOWN IN GREENLAND 50-POUND 'ICE BOMB' FALLS IN WEST VIRGINIA EARTHQUAKE LIGHTS OBSERVED IN CANADA Psychology Predictive psi Maths & Logic Pi surprise Physics Repent! the phase change is coming! Cold fusion update ...
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... Oct 1990 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Nature Communicates In Mysterious Ways Most of us will recall that the wings of butterflies and moths sometimes display eyespots, which, according to current thinking, are designed to startle potential predators. Perhaps so, but butterfly and moth wings can convey a wide range of "signals." K.B . Sandved, a nature photographer, has also found remarkable renditions of all the letters in the English alphabet (one at a time, of course) on the wings of these insects. In fact, he has accomplished this several times over using different species. He has found all the Arabic numerals, too, as well as ampersands, question marks -- you name it! Although Greek pi and capital omega have turned up, butterflies and maths are clearly trying to impress people who utilize the Roman alphabet. After all, it is difficult enough to evolve an ampersand; generating Chinese characters would strain credulity too much. (Amato, Ivan; "Insect Inscriptions," Science News, 137: 376, 1990.) Comments. Incidentally, of what survival value are these wing symbols? Obviously, the butterflies and moths have not got their act completely together as yet. Words and phrases will come soon, we are certain. Look at the eggplants for example. They have specialized in Arabic. It has recently been reported in British newspapers and on BBC Radio 4 that when the Kassam family sliced up an eggplant, the patterns of seeds spelled out "Ya-Allah ...
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... Science Frontiers ONLINE No. 96: Nov-Dec 1994 Other pages Home Page Science Frontiers Online All Issues Last Issue Next Issue Sourcebook Project Sourcebook Subjects Contents Archaeology That little "roman" head from precolumbian mexico The "kites" or "keyhole" structures of the middle east Astronomy On the sun, south is almost everywhere The moon: still partly molten? Lunar crater chains Biology Too identical! Why do flying fish have such colorful wings? "ADAPTIVE" MUTATION Electric snakes Geology Satellite spies strange stripes Two really deep oceans Geophysics The 536 ad dust-veil event Underwater thumps Remarkable straw fall Unusual lunar halo Psychology Psi phenomena and geomagnetism Physics Cold fission? Mathematics Lazzarini eats humble pi (posthumously) Unclassified A CURIOUS STRING OF COINCIDENCES Close encounters with unknown missiles ...
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... Science Frontiers ONLINE No. 53: Sep-Oct 1987 Other pages Home Page Science Frontiers Online All Issues Last Issue Next Issue Sourcebook Project Sourcebook Subjects Contents Archaeology A TSUNAMI AND A PERUVIAN CULTURAL GLITCH Lenses in antiquity Strange craters Astronomy Hypnotic mars The perseus flasher: mystery solved! Three planetary notes Biology Has the second law been repealed? Human direction finding Magnetic "dead" reckoning Another tale of ogopogo Geology Meteor-impact winters, magnetic field reversals and tektites Tektite-like objects at lonar crater, india Geophysics Are the soviet plumes only orographic clouds? Lightning triggered from the magnetosphere Psychology Magnetic fields and the imagination Men in black (mibs) Folie a famille A "MAGICAL GENIUS" Pi and ramanajan A MODEST EXAMPLE OF THE LONG ARM OF SYNCHRONICITY ...
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... Science Frontiers ONLINE No. 65: Sep-Oct 1989 Other pages Home Page Science Frontiers Online All Issues Last Issue Next Issue Sourcebook Project Sourcebook Subjects Contents Archaeology The samurai and the ainu Breaking the 12,000-bp barrier Astronomy Sweeping anomalies under the rug Fossil from mars? Biology The wood turtle stomp Why the hammer head? Initial bipedalism! Microorganisms at great depths Geology Fossil ufos Chemical surprises at the k-t boundary Geophysics Unusual sounds preceding lightning Books about the crop circles Psychology Pi in the mind! Calendar calculating by "idiot savants" General How fares cold fusion? How fares benveniste? ...
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... 1985 Other pages Home Page Science Frontiers Online All Issues Last Issue Next Issue Sourcebook Project Sourcebook Subjects Contents Archaeology A Disaster-driven Early Civilization Another Remarkable Specimen of Ancient Man Astronomy The Puzzle of the Moon's Origin When Mars Had Lakes Why Aren't the Martian Craters Worn Down? Flip-flop Radio Jets? Biology The Genome's Responses to Challenges "hopeful Monsters" in Iceland? Parasites May Reprogram Host's Cell Geology More Doubts About Asteroids The Earth is Expanding and We Don't Know Why The Grand Canyon Conundrum Evidence for A Giant Pleistocene Sea Wave Recent Pulsations of Life Geophysics "Crystal" Ball Lightning The Big Divot! Shower of Coke Chemistry & Physics Squarks and Photinos At Cern? What Does it All Mean? The Secret of it All is in the Pi ...
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... Science Frontiers ONLINE No. 103: Jan-Feb 1996 Other pages Home Page Science Frontiers Online All Issues Last Issue Next Issue Sourcebook Project Sourcebook Subjects Contents Archaeology A REMARKABLE MAYAN SUSPENSION BRIDGE Did irish monks build this new england chamber circa 700 ad? Two probable frauds Astronomy Einstein's nemesis: di herculis A BRIEF HISTORY OF QUANTIZED TIME Biology Passenger pigeons not extinct! I HISS THEREFORE I AM Geology Target: south america Fossil mantle plume under south america But what about the hawaiian volcanic chain? Geophysics A SUBTERRANEAN TROMBONE Anomalous radar echoes and visual phenomenon "BLUE JETS" EMITTED UPWARD FROM TOPS OF THUNDERCLOUDS Stythe = choke damp Psychology Seeing is feeling Mathematics How to find a piece of pi ...
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... ) Dermo-Optical Perception (BHT8] Remote Viewing Clairvoyance Clairaudience Clairsentience Object Reading (Psychometry) Scrying [PLS] PHP VISIONS OF THE PAST AND FUTURE Precognition Prophecy Augury (Precognition Using Props) Precognition during Trances Precognition during Hypnosis Precognition during Dreams Pre-Disaster Syndromes Precognition Affected by Geomagnetism Premonitions of Death Prediction of Random Processes Retrocognition Hypnotic Regression Scrying [PLS] PHR REINCARNATION PHENOMENA Memories of Previous Lives Hypnotic Regression Xenoglossy Birthmarks As Proofs of Reincarnation Life after Death PHT ANOMALOUS INFORMATION TRANSFER Ordinary Telepathy Twin Telepathy Long-Distance Mass Telepathy Experiments Transfer of Physical Sensations Transfer of Emotions (Not Folie a Deux or Mass Hysteria) Dream Telepathy Remote Viewing Telepathy Affected by Magnetic Fields Role of Quantum Mechanics in Telepathy Ganzfield Experiments Animal Telepathy Telepathy under Hypnosis Atavistic Nature of Telepathy Geomagnetic Enhancement of Telepathy Psychic Odor/Taste PI INFORMATION PROCESSING PIB INPUT/OUTPUT ANOMALIES Word Blindness Dyslexia Autism Typing Skills Tip-of-the-Tongue Phenomenon Mirror Script Braille and the Brain Optical Illusions Generation of Random Numbers Cocktail-party effect Stuttering Difficulty of Learning English Brain Modularity Attentional Blink Revelation Intuition PIC ANOMALOUS INFORMATION PROCESSING Mathematical Savants Calendar Calculators Musical Prodigies Mechanical Savants Subconscious Time-Reckoning Mental Processing during Sleep Chess Prodigies Accelerated Mental Processes Mnemonists PIG MYSTERIES OF GENIUS AND CREATIVITY Early Appearance of Genius Genius and Mental Illness Origin of "Strokes of Genius" Periodicity in Creativity Humor and Creativity Genius and Season of Birth Aesthetics and Creativity Dream Creativity PII EIDETIC AND AFTER IMAGES Eidetic Imagery Vivid Afterimages Eidetic Imagery and Retardation Eidetic Imagery and Hallucinations Recovery of Eidetic Imagery through Hypnosis PIK CONSCIOUSNESS Consciousness and Hypnosis Nature of Consciousness Free Will Consciousness and Quantum Mechanics [ ...
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... formed by counting the number of letters in each word of the first square, thus: 4 9 8 11 7 3 6 5 10 This square is also magic, adding up to 21 in all directions! Just a fluke, you say? Not so. You can even construct alphamagic squares in different languages. In his column in Scientific American, I. Stewart provides examples in French, German, Welsh, and even Swahili! In German, there are no less than 221 alphamagic squares using numbers under 100. (Stewart, Ian; "Alphamagic Squares," Scientific American, 276:106, January 1997.) Comment. The "deep meaning" of alphamagic squares is about the same as that associated with the existence of your Social Security Number in the decimal expansion of pi! From Science Frontiers #110, MAR-APR 1997 . 1997-2000 William R. Corliss ...
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... Science Frontiers ONLINE No. 148: Jul-Aug 2003 Other pages Home Page Science Frontiers Online All Issues Last Issue Next Issue Sourcebook Project Sourcebook Subjects Contents Archaeology Who or What Exterminates the Pleistocene Megafauna? Illinois's Ancient Maginot Line A Cold Barrier to Internal Parasites Astronomy Are there no other Earths out there? Where's the Fuzz? Biology Snakes Aloft Woman's Barr Bodies The Eyes have it A Major Problem for Darwinism Geology Why are old Mountains High? Subterranean Ecosystems Geophysics Milky-sea Phenomenon Is the Min Min Light a Fata Morgana (mirage)? Pre-Quake Anomalies Psychology Correlations of Brain Activity Physics A Revolution in Electrostatics Mathematics Ordering a Piece of Pi Prime Squares ...
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... Science Frontiers ONLINE No. 86: Mar-Apr 1993 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Math's mystery In extolling J. Barrow's new book, Pi in the Sky , T. Siegfried first reiterates a point made in past issues of SF, namely, that mathematics is a logical system and that we have no right to expect it is correspond structurely with a physical system. In other words, math and nature are fundamentally different entities. Nevertheless, as Barrow stated in a recent interview: "If we were just inventing mathematics from our everyday experience, we would find that it would work really rather well in those areas from which that intuition was gained. But we find almost the opposite...It works most powerfully and persuasively in areas that are farthest removed from the everyday experience that has led to it." Mathematics, for example, leads to verities in quantum mechanics far outside the realm of daily experience. Why is this so? The puzzle deepens when one discovers that there are different kinds of math based upon different forms of logic (as in Euclidian and non-Euclidian geometries). Some brands of mathematics mirror reality better than others. Why? In trying to dispose of these "whys," both matematicians and scientists fall back on the anthropic principle with all its unsatisfying tautological overtones: ". .. the universe is the way it is because that's the way it has to be for anybody to be around to study it. And perhaps math works ...
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... Science Frontiers ONLINE No. 65: Sep-Oct 1989 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Calendar calculating by "idiot savants"M.J .A . Howe and J. Smith have reported on an extensive study of calendar-calculating by individuals with otherwise subnormal intelligence. It is very clear that these so-called "idiot savants" use a variety of mental techniques, all rather different from rote memory, such as employed by memorizers of pi. First, we present Howe-and-Smith's abstract; then, a particularly interesting specific case. "A number of mentally handicapped individuals are able to solve difficult calendar date problems such as specifying the day of the week for a particular date, sometimes over spans of more than 100 years. These individuals are self-taught and do not follow procedures at all similar to the usual, published, algorithms. An investigation of one individual revealed that he retained considerable information about the structure of days in particular months, probably as visual images. His skill closely depended on the extent and form of his knowledge of calendars, and his errors were often a consequence of lack of knowledge about a particular time period. Mentally retarded individuals who perform calendar date feats are often socially withdrawn and devote considerable periods of time to calendar dates. The most capable calendar-date calculators are usually individuals who have a strong interest in calendars as such." Although some calendar calculators may use visual imagery - perhaps something like eidetic imagery - at least one calendar calculator was ...
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