82 results found.
... , and so I multiplied 123...9 by this, a simple matter, and divided the answer by 81.'" But what, asks Smith, led Aitken to 81? To this question, which is the heart of the mystery, he commendably admits he has no reply. And the same deep mystery confronts us even after all has been said about the sur, as distinct from the underlying, structure of the processing. At the unlettered end of the spectrum of mental calculators, the ". .. ignorant vagabond, Henri Mondeux, who at the age of 14 years, before the French Academy of Sciences, was able promptly to state two squares differing by 133." Of course, some mental feats of calculation can be done consciously employing various shortcuts and mathematical tricks. The really fantastic performances, however, are accomplished unconsciously. No one knows how, even the calculators themselves. (Cohen, John; "What Makes a Calculating Prodigy?" New Scientist, 100:819, 1983.) From Science Frontiers #32, MAR-APR 1984 . 1984-2000 William R. Corliss ...
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... of-Progress Report," Skeptical Inquirer, 8:312, 1984.) Comment. If psi effects are real and also transcend our usual concept of causality and the space-time framework, the conventional scientific approach really becomes impossible. For example, the results of an experiment could be modified by someone in the future -- so-called retroactive psychokinesis! Psi when completely generalized is independent of humans and other life forms. It is then a general property of the cosmos -- a certain tendency of lists made by people, random-number generators, and similar sources to match up in non-chance ways. If this tendency is real, the laws of chance to not truly reflect the way the cosmos works. There is, after all, no absolute requirement that mathematics be a faithful mirror of reality. Reality is reality; and theory is, well, something the left side of the brain is good at generating. John Holden's rendition of 'telepathy'. From Science Frontiers #35, SEP-OCT 1984 . 1984-2000 William R. Corliss ...
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... , fever, sleeplessness, and other altered states of consciousness. Migraine headaches, too, are often presaged by floating, semicircular fields of closely spaced parallel lines or bars arranged in zigzag patterns. This geometrical visual phenomenon may, like a berserk TV screen, be diagnostic and betray regularities in the brain's circuitry. The kaleidoscopic patterns seem to occur when imput signals from the eyes are weak or suspended, leaving the brain to generate its own "favorite" patterns. (Shepard, Roger N.; "The Kaleidoscopic Brain," Psychology Today, 17:62, June 1983.) Comment. But why the elaborate geometry? Could this apparently "built-in" pattern-generating capacity manifest itself in waking humans as an urge to describe the universe in terms of regular mathematical laws and geometric models? Visual sensations induced during controlled intoxication with cocaine. (Illustration from Unfathomed Mind) From Science Frontiers #31, JAN-FEB 1984 . 1984-2000 William R. Corliss ...
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... at n = 40. An interesting consequence of Euler's formula can be made apparent when all numbers from 41 to 440 are written in a square spiral, like so: All of the numbers on the diagonal indicated are Euler formula primes, even when the spiral is expanded to 20 x 20. However, when the 20 x 20 spiral is examined closely, many of the other primes -- those not generated by Euler's formula -- also tend to line up on diagonals. This is a most intriguing characteristic, one which goes far beyond the 20 x 20 array mentioned above. The computer-generated display shown below lays out a huge square spiral, with each prime a bright dot. The picture has a pronounced diagonal texture. Why this is so is a mathematical mystery. (Crypton, Dr.; "Prime Numbers and National Security, " Science Digest, 93: 86, October 1985. ) (Does the diagonal fabric of primes have any practical significance ? At the moment no one knows. Again and again, abstruse mathematical structures have turned out to mirror phenomena in the world we call "real". WRC) From Science Frontiers #42, NOV-DEC 1985 . 1985-2000 William R. Corliss ...
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... but a serious anomaly has been found. The double star DI Herculis has a Newtonian precession rate of 1.93 degrees per century, with another 2.34 added by relativistic effects. With more than 3,000 well-observed orbits of this star system on the books, astronomers come up with only 0.64 degree per century, instead of the 4.27 predicted by theory. Something is obviously awry; and all searches for errors and other influences on the orbit have been negative. (Anonymous; "Double-Star System Defies Relativity," New Scientist, p. 23, August 29, 1985.) Comment. As a matter of record, Newtonian mechanics can account for Mercury's perihelion advance if the sun is actually an oblate spheroid instead of the mathematically perfect sphere usually assumed. Also, the gravitational theory of J. Moffat seems to explain the motions of both Mercury and DI Herculis. From Science Frontiers #42, NOV-DEC 1985 . 1985-2000 William R. Corliss ...
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... necessary nuclei. But cloud studies prove that there are about a thousand times more ice crystals than dust nuclei. Now, some are convinced that bacteria blown off plants and flung into the air by ocean waves are the true nuclei of atmospheric ice crystals. Remember this the next time you tast a handful of snow! (Carey, John; "Crystallizing the Truth," National Wildlife, 23:43, December/ January 1985.) Comment. The possibility that the fall of snow and all other forms of precipitation is largely dependent upon bacter-ia brings to mind the Gaia Hypothesis; that is, all life forms work in unison to further the goals of life. The second item is from Nature and is naturally more technical. After reviewing the great difficulties scientists are having in mathematically describing the growth of even the simplest crystal, the author homes in on one of the fascinating puzzles of snowflake growth: "The aggregation of particles into a growing surface will be determined exclusively by local properties, among which surface tension and the opportunities for energetically advantageous migration will be impor tant. But the symmetry of a whole crystal, represented by the exquisite six-fold symmetry of the standard snowflake, must be the consequence of some cooperative phenomenon involving the growing crystal as a whole. What can that be? What can tell one growing face of a crystal (in three dimensions this time) what the shape of the opposite face is like? Only the lattice vibrations which are exquisitely sensitive to the shape of the structure in which they occur (but which are almost incalculable if ...
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... Wilson has outlined the diversity of terrestrial life in a recent issue of BioScience. The earth, it appears, is a veritable Gene sis Machine; and it is only one planet among a possible infinitude. So many terrestrial species have already been described that one could easily believe that biological collectors roaming the planet's wild places have just about completed their task. Some recent totals: 47,000 species of vertebrates, 440,000 plants, and 751,000 insects. But we may not even be close to grasping life's diversity on earth! We do well in counting the large mammals and birds, but most insects and microscopic forms of life have escaped description. To illustrate, in 1964, the British ecologist C.B . Williams, combining intensive local sampling and mathematical extrapolation, extimated the insect population as 3 million species. However, by 1985, this figure has been raised ten-fold to 30 million species. Why the huge jump? For the first time, entomologists had found a way to efficiently sample the canopies of tropical forests. This rich stratum between the sunlight and gloomy forest floor 100+ feet below had been largely neglected before. The slick tree trunks and the attacking swarms of wasps and stinging ants deterred the insect counters. What the collectors did was to fire projectiles with ropes over the high branches and then haul up canisters of a knockdown gas. Insects rained down -- a cloudburst of new species -- neatly collected on sheets spread out below. Such techniques led to the 30-million figure. As Wilson put it ...
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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 A "MAGICAL GENIUS"" If ever there were an exemplar of inborn mathematical ability it would be Srinivasa Ramanujan, a poor, uneducated Indian, born 100 years ago, who was one of the greatest and most unusual mathematical geniuses who ever lived. Although he died young -- at age 32 -- Ramanujan left behind a collection of results that are only now beginning to be appreciated. "Ramanujan's story is one of the great romantic tales of mathematics, made all the more haunting because of the mystery surrounding the man. No one, no matter how much they try, has ever been able to understand the workings of Ramanujan's mind, how he came to think of his results, or the source of this incredible outpouring of mathematics." Ramanujan has been termed a "magical genius." In contrast, "ordinary geniuses" are merely an order of magnitude of two smarter than you and me. In Ramanujan's case, no one knows where his voluminous results came from. They appeared as if by magic, in a manner transcending ordinary human mental activity. Ramanujan did complete high school, but his entire mathematical education seems to have come from the reading of just two books. Nevertheless, he was invited to Cambridge on the basis of a letter he wrote to G.H . Hardy in 1913. The letter contained about 60 theorems and formulas stated without proof. After some ...
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... Science Frontiers ONLINE No. 56: Mar-Apr 1988 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Reincarnation of ramanujan?In India, Shakuntala Devi is considered to be the reincarnation of Srinivasa Ramanujan, about whom we heard in the above item. We will not comment on the reincarnation bit, but it does seem that S. Devi's remarkable capabilities are somewhat different from those of Ramanujan. The latter intuitively saw mathematical relationships as expressed in equations and identities; Devi is a mental calculator of no mean talent. In 1977, Ms. Devi beat a UNIVAC 1108 computer to the 23rd root of a 201-digit number. The machine, which required two hours to program for the task, took more than a minto solve the problem. She took 50 seconds. "And, in 1981, she made the Guinness Book of World Records as the 'Human Computer' by correctly multiplying two 13-digit numbers -- 7,686,369,774,870 times 2,465,099,745,779 -- in 28 seconds. The awesome answer? 18,947,668,177, 995,426,462,773,730." S. Devi is also a calendar calculator, being able to name the day of the week for any date in the past or future, taking into account leap years and calendar changes. She never attended school or had any formal mathematical training! (Young, Luther; "Numbers Whiz Takes Delight in Beating Computers;" Baltimore Sun ...
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... Science Frontiers ONLINE No. 54: Nov-Dec 1987 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Fractals, fractals everywhere Anyone who follows the popular scientific literature knows that fractals are now "in." Commonly employed to "explain" patterns in nature, fractals are, from a simplistic viewpoint, mathematical ways to predict the development of a growing structure, be it a crystalline mass, a plant, or the universe-as-a -whole. Yes, the universe-as-a -whole, the clouds of stars and clusters of galaxies, may be mimicked by cellular automata (i .e ., fractals). Imagine the universe as a cubical lattice, and start in one corner, adding one layer of cubes after another. Galaxy distribution could be simulated by using a rule telling us which of the added cubical cells had galaxies in them and which did not. "The rule actually used supposes that the question whether each point in a newly added layer will (or will not) be occupied by a galaxy is mostly determined by the occupancy of the five nearest neighbors in the previous layer, but for good measure, there is a random variable to introduce an element of white noise to the system. To make the process a little more interesting, the determination whether a new site is occupied depends on whether a number characteristic of that site, and calculated by simple arithmetic from the corresponding number for the five nearest neighbors in the preceeding layer, exceeds an arbitrarily chosen number." Comparing this ...
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... Science Frontiers ONLINE No. 63: May-Jun 1989 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Some Editorial Pedantry If you glance back quickly at the last three items on "astronomy," you will see that all three discoveries were made with computers using numerical simulation - not through direct observation. Since such simulations are built upon a foundation of accepted physical laws, to say nothing of various mathematical approximations and computer software, the discoveries made are only as good as the laws and methodology. As. A. Korzybski used to say: "The map is not the territory." Forgetting this has led experts to predict that heavier-than-air craft could never fly and that the earth could not be more than a few million years old. From Science Frontiers #63, MAY-JUN 1989 . 1989-2000 William R. Corliss ...
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... water. Using for a stepping stone the cooperative action of atoms in a laser, he leaps to the development of an embryo from a single strand of DNA! All such systems are "open"; that is, energy can flow in and out. They are also nonlinear, which means that chaotic, unpredictable action may occur. Davies implies that such action can be "creative," almost as if they possessed free will! His final example is that of the network with large numbers of interacting sites or nodes. With random inputs, large networks do exhibit self-organization. Network theory is now very popular in the field of artificial intelligence. (Remember the computer Hal in 2001?) Davies's conclusion: ". .. Neo-Darwinism, combined with the mathematical principles emerging from network theory and related topics, will, I am convinced, explain the 'miracle' of life satisfactorily." (Davies, Paul; "The Creative Cosmos," New Scientist, p. 41, December 17, 1987.) The superorganism. One week later, O. Sattaur expanded on the Gaia concept. He quotes J. Lovelock's definition: ". .. the physical and chemical condition of the surface of the Earth, of the atmosphere and of the oceans has been, and is, actively made fit and comfortable by the presence of life itself...in contrast to the conventional wisdom which held that life adapted to planetary conditions as it, and they, evolved their separate ways." Mainstream science has shown scant love ...
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... in New York City, 1928-1964. Noise or chaos? We should talk about chaos more. This subject threatens to undermine the popular notion that nature is fully deter ministic. We like to think that if we are given enough data that scientific laws will allow us to predict the future ac curately. But, unhappily, determinism stumbles when trying to cope with the weather, asteroid motion, the heart's electrical activity, and an increasing number of natural systems. Chaos lurks everywhere! The growing split in scientific outlook is seen very clearly in the statistics of New York City measles epidemics before mass vaccinations. Take a look at the graph of recorded cases. The expected peaks occur each winter, but there is a strong tendency toward alternate mild and severe years. Very nice mathematical models exist that purport to predict the progress of epidemics. They take into account such factors as the human contact rate, disease latency period, the existing immune population, etc. It is all very methodical, but it fails to account for the irregularities in actual data. Deterministic scientists claim that just by adding a little "noise" they could duplicate the observed curve. On the other hand, a very simple model that acknowledges the reality of chaos easily duplicates the measured data. Who is right? The determinists and chaosists (chaosians?) are now fighting it out. (Pool, Robert; "Is It Chaos, or Is It Just Noise?" Science, 243:25, 1989.) Comment. Much more of nature may be chaotic. Even evolution itself ...
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... of its constituent protons and neutrons. Tantalizing experiments suggest other wise. Magnes ium-24, for example, may under some circumstances exist as two carbon-12 nuclei in tight orbit, as in the illustra tion. Even more startling is the "sausage" form of magnesium-24, in which six helium-4 nuclei (alpha particles) are lined up in a row. This "hyperdeformed" state has not yet been detected in the lab, but it demonstrates new thinking among the physicists. (Kenward, Michael; "Are Atoms Composed of Molecules?" New Scientist, p. 21, April 6, 1991.) Comment. Evidently we do not know everything about nuclear physics. Beyond the molecule. We are used to seeing atoms and molecules arranging themselves into mathematically regular crystals. Now it appears that particles consisting of thousands of atoms also spontaneously organize themselves. A.S . Edelstein et al find that molybdenum particles assemble themselves in cubes with two prominent edge lengths: 4.8 and 17.5 nanometers. The larger cubes show up in micrographs as 3x3x3 groupings of the smaller cubes. The smaller cubes each contain about 7000 atoms. (Edelstein, A.S ., et al; "Self Arrangement of Molybdenum Particles into Cubes," Science, 251:1590, 1991.) Comment. What are the "organizing forces" here? Why cubes? Why the heirarchy of cubes? Why 3x3x3 super cubes? From Science Frontiers #76, JUL-AUG 1991 . 1991-2000 William R. Corliss ...
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... markable of all is the use of the word "spontaneous" without philosophical comment. The stimuli for the research described are such observations as: (1 ) life exists; (2 ) life evolves; (3 ) the fossil record displays stasis, extinctions, and great gaps between phyla and lesser classifications; and (4 ) disordered molecules move smoothly and surely into the order manifest in the living cell. The question asked in the article is whether science has missed something in its description of the origin and development of life. Just what makes molecules coalesce into cells and humans? The answer given is: spontaneous self-organization ! In other words, there is no guiding external force. Molecules do this spontaneously. There are even computer models being developed, based on a branch of mathematics called "dynamical systems," that describe how this all happens - spontaneously, of course. (Waldrop, M. Mitchell; "Spontaneous Order, Evolution, and Life," Science, 247:1543, 1990.) Comment. When water molecules spontaneously cluster together to form a snowflake, with all its symmetry and order, science explains the process in terms of the properties of water molecules. The same must be true when molecules merge to form life forms. But why do atoms and molecules possess these properties that lead to bacteria, to humans, to who-knows-what's -next? "Spontaneous self-organization" is a cop out! From Science Frontiers #69, MAY-JUN 1990 . 1990-2000 William R. Corliss ...
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... Science Frontiers ONLINE No. 82: Jul-Aug 1992 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Does nature compute?Back in the 1960s, kids used to watch the TV series Lost in Space . Starring on this show was a robot which, when asked a stupid or answerless question replied, "It does not compute!" More seriously, we now ask, "Does Nature compute?" Science believes very deeply that mathematics reflects the real world, that we live in an ordered universe where everything can be reduced to mathematical expressions. The progress of science, particularly physics, seems to bear out this symbiotic relationship between mathematics and the physical world. However, P. Davies points out that that there are uncomputable numbers and operations. In fact, there are infinitudes of them. All the world's computers could chug away forever and not come up with answers in these cases. So far , Nature has been kind, or we have been lucky, because we have been able to nicely mirror Nature with "doable" math. Davies wonders if it has been entirely a matter of luck: "Einstein said that God is subtle but not malicious, and we must hope that the laws of physics will turn out to be computable after all. If so, that fact alone would provoke all sorts of interesting scientific and philosophical questions. Just why is the world structured in such a way that we can describe its basic principles using 'do-able' mathematics? How was this mathematical ability evolved in ...
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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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... -Jun 1993 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Calculating prodigies, gnats, and smart weapons In a thought-provoking letter to New Scientist, J. Margolis commences with the observation that calculating prodigies (idiot savants), who are often also mentally retarded, can easily and almost instantaneously recognize 20-digit prime numbers! Gifted mathematicians with so-called photographic memories cannot perform such mental feats using known methods for identifying primes. What do the calculating prodigies know that the rest of us do not? Better algorithms; that is, calculating methods? Margolis expands on this: "All this suggests some relatively simple, subconscious algorithms which have not, as yet, been explicitly formulated. Research in this direction might well result in new mathematical insights. "It need not be surprising that mathematical insight is more fundamental than language. Even a primitive animal brain is 'wired" to perform exceedingly complex computations essential for survival in an unpredictable environment. The latest 'smart' weapons are rudimentary compared with a humble gnat. Mathematics could be a by-product of these functions. Language is a comparatively recent evolutionary innovation and it is quite possible that conscious manipulation of abstract symbols has not caught up with an innate ability to perceive quantitative relationships." (Margolis, Joel; "What Gnats Know," New Scientist, p. 58, January 30, 1993.) From Science Frontiers #87, MAY-JUN 1993 . 1993-2000 William R. Corliss ...
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... Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects All roads lead to 123 "Start with any number that is a string of digits -- , say, 9 288 759 -- and count the number of even digits, the number of odd digits, and the total number of digits it contains. These are 3 (three evens), 4 (four odds), and 7 (seven is the total number of digits), respectively. Use these digits to form the next string or number, 347. If you repeat the process with 347, you get 1, 2, 3. If you repeat with 123, you get 123 again. The number 123, with respect to this process and universe of numbers, is a mathematical black hole." We have a black hole because we cannot escape, just as spaceships are doomed when captured by a physical black hole! You end up with 123 regardless of the number you start with. Other sorts of mathematical black holes exist, such as the Collatz Conjecture, but we must not fall into them because our printer awaits. (Ecker, Michael; "Caution: Black Holes at Work," New Scientist, p. 38, December 19/26, 1992.) From Science Frontiers #86, MAR-APR 1993 . 1993-2000 William R. Corliss ...
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... this chaos; it seems that that's the way the cosmos is constructed! However, it now seems that the situation is even worse than chaotic! Some systems, perhaps most systems, are also indeterminate, meaning that we cannot predict their qualitative behavior either. A simple example is the water swirling down the bathtub drain. This is not only chaotic but it has two qualitative final states: clockwise and counterclockwise. Regardless of which hemisphere you are in, you can change the direction of swirl with negligible effort. Each of the two final states of motion is still quanti tatively unpredictable. Systems that are more complex will possess many different final states, all chaotic. Can nature really be fundamentally chaotic as well as qualitatively uncertain? J.C . Sommerer and E. Ott have mathematically examined a relatively simple system consisting of a single particle moving in a force field, experiencing friction, and being periodically jolted. Besides settling into chaotic motion, this particle may also be forced away to infinity -- two radically different final states. The analysis revealed that for any set of initial conditions leading to the first type of behavior, there was an infinite number of slightly different initial conditions that would lead to the second type of behavior. In other words, systems that we have long thought to be deterministic, like the motions of the planets, may be not only chaotic but indeterminate. Since Sommerer and Ott found their indeterminate system easily, we must face the possibility that the future behavior of just about everything is beyond our capability to predict, even with our best instruments ...
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... pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Self-organized stone stripes "Geometrically regular stripes of stones are found on many unvegetated alpine and polar hillslopes; known as 'sorted stripes' because of the characteristic textural sorting between surface stones and fine-grained soil, they contrast markedly with the lack of order typical of natural landscapes. The spacing of the stripes can range from centimeters to meters (about 10-20 times the average stone diameter), with individual stripes extending downslope for many tens of meters. A variety of formative mechanisms have been proposed, but it is still unclear how such orderly stripes can arise spontaneously, and what dictates the spacing." B.T . Werner and B. Hallet, authors of the foregoing partial abstract, have mathematically simulated the displacement of surface stones under the forces generated by the growth of needle ice in the underlying soil. As the number of freeze-thaw cycles increases into the thousands, computer simulations show the surface stones gradually arraying themselves into linear patterns. (Werner, B.T ., and Hallet, B.; "Numerical Simulation of Self-Organized Stone Stripes," Nature, 361:142, 1993.) Reference. These stone stripes represent just one type of "patterned ground." Other examples may be found in ETP1 in our catalog: Carolina Bays, Mima Mounds, described here . From Science Frontiers #88, JUL-AUG 1993 . 1993-2000 William R. Corliss ...
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... Aug 1992 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Can you guess where this quotation comes from?THE GRADUALIST'S DILEMMA "The basic article of faith of a gradualist approach is that major morphological innovations can be produced without some sort of saltation. But the dilemma of the New Synthesis is that no one has satisfactorily demonstrated a at the population genetic level by which innumerable very small phenotypic changes could accumulate rapidly to produce large changes: a process for the origin of the magnificently improbable from the ineffably trivial. This leads to skepticism about the microevolutionary approach. Perhaps, as Waddington put it: 'the real guts of evolution -- which is, how do you come to have horses and tigers, and things -- is outside the mathematical theory.'" Did you guess a creationist publication? Sorry! (Thomson, Keith Stewart; "Macroevolution: The Morphological Problem," American Zoologist, 32:106, 1992.) (And just the other day, we read that evolution was a proven fact!) From Science Frontiers #82, JUL-AUG 1992 . 1992-2000 William R. Corliss ...
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... Science Frontiers ONLINE No. 132: NOV-DEC 2000 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Puzzling Partitions The Indian mathematician S. Ramanujan's has been called a "magical genius" because his remarkable insights seemed to come out of the blue -- like magic. We have not neglected Ramanujan in this newsletter ( SF#53 and here ), and now we spotlight him again. First, a quick primer on a fascinating mathematical byway called "partitions." A partition is a way in which a whole number can be expressed as the sum of positive integers. For example, 5 can be partitioned in seven ways: 5 4+ 1 3+ 2 3+ 1+ 1 2+ 2+ 1 2+ 1+ 1+ 1 1+ 1+ 1+ 1+ 1 The number 4 has only five partitions. Check it out. Historically, ordinary mortals saw no patterns in the number of partitions possessed by the parade of numbers until Ramanujan came along. He had in front of him a list of the number of partitions for each of the first 200 integers. They ranged from one (for 1) to 3,972,999,029,388 (for 200). [That of a computer is itself worthy of mention!] Here is the order that Ramanujan perceived: Starting with 5, the number of partitions for every seventh integer is a multiple of 7, and starting with 6, the number of partitions for every 11th integer is a multiple of 11 ...
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... Science Frontiers ONLINE No. 128: MAR-APR 2000 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects How to Win by Loosing (twice)It's all exceedingly counterintuitive. If you switch randomly between two games of chance, each of which is guaranteed to empty your pockets if played separately, you can actually win. This phenomenon can be proved mathematically, but we will not inflict this upon our readers, even if we understood it. Two games played with coins illustrate the effect. One game employs a weighted coin such that the probability of winning is much less than 50%. If played alone, your capital decreases steadily in a rather smooth curve, with a small win now and then but many small losses. The second game requires two weighted coins and is also a losing proposition by itself. Here, though, the graph of your assets vs. the number of games played is a sawtooth. There are sharp increases and downturns, but with an average downward trend. Switching between the two games in a random manner has the effect of locking in a win before the next loss comes along. It's a ratchet effect. Your overall capital will rise, at least it does according to the equations, though your intuition cannot help but doubt it. No wonder this Is called Parrondo's paradox! (Harmer, Gregory P., and Abbott, Derek; "Losing Strategies Can Win by Farrondo's Paradox," Nature, 402:864, 1999. Anonymous; "Losing ...
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... Science Frontiers ONLINE No. 136: JUL-AUG 2001 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects The Eclipsing Of Innate Talents The age effect. An idea going the rounds holds that everyone is really a genius but that his or her innate talents have been eclipsed or suppressed. Age is one factor that is blamed. As a child develops, so goes the theory, its brain is bit by bit swamped by the high-level conceptual thinking required for survival in the modern adult world. The child's innate mathematical genius, musical capabilities, and other "low-level" talents are placed on the brain's back burner by the demands of adulthood. It is a common observation that the young assimilate foreign languages more readily than adults. A less-well-known talent, eidetic imagery (the ability to recall images with photographic precision), is found in some children, but it also usually fades with age. Now, we learn that 8-month-old babies are apparently blessed with perfect pitch, a capability they, too, generally lose as they age. (Hall, Carl T.; "Learning by Infants Isn't Just Baby Talk," The Brain, February 28, 2001. Cr. J. Cieciel.) Removal of mental blocks. Sometimes the barriers that eclipse our innate talents are removed by mental disease. The surprising enhancing effect of dementia on some "low-level" talents was mentioned in SF#133. The same mental barriers also seem to ...
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... by deep troughs. as seen in this sketch of a vessel in the notorious A gulhas Current off the coast of South Africa. (From: Earthquakes. Tides....) Just between 1969 and 1994. 60 supercarriers were lost due to sudden flooding. Of this number, 22 were apparently swallowed by rogue waves. The rogue waves appear unexpectedly. They dwarf all surrounding waves. For a long time, the rogues were said to be just chance additions of two smaller waves. But they are too big and occur too frequently to be statistical flukes. In addition, statiticians have trouble in accounting for the fabled and feared "three sisters" -- three massive waves in succession. Consequently, scientists have retreated to a now-familiar refuge: nonlinear effects. They show mathematically how small perturbations in a physical system can lead to huge consequences -- on paper at least.. (Lawton, Graham; "Monsters of the Deep," New Scientist, p. 28, June 30, 2001.) Comments. Somehow, as insinuated above, blaming monstrous waves on non-linear effects is not very satisfying in our cause-and-effect world. Twenty-two huge vessels swallowed up by giant waves! Yet, we never see notices of such events in the papers! A small tanker oil spill gets much more media attention. From Science Frontiers #137, SEP-OCT 2001 . 2001 William R. Corliss Other Sites of Interest SIS . Catastrophism, archaeoastronomy, ancient history, mythology and astronomy. Lobster . The journal of intelligence and ...
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... Science Frontiers ONLINE No. 138: NOV-DEC 2001 Issue Contents Other pages Home Page Science Frontiers Online All Issues This Issue Sourcebook Project Sourcebook Subjects Born To Enumerate Einstein once said in connection with his celebrated mathematical insights: Words and language...do not seem to play any part in my thought processes. A French scientist, S. Dehaene, sees in this declaration support for his claim that human brains possess a "number sense" that is independent of language and symbols, including even the numerals we use in arithmetic! The numerals, says Dehaene, are needed only in "exact arithmetic," which is a cultural invention and unrelated to the "number sense." Exact arithmetic, in fact, is an activity of our left brain where language is processed. Our general number sense, though, is sited elsewhere; the parietal lobe, to be specific. Dehaene's experiments with babies demonstrate that, even before they can speak or do exact arithmetic, they can do "approximate arithmetic"; that is, they can distinguish between these two sequences of tones: beep-beep, beep-beep, beep-beep beep-beep, beep-beep, beep-beep-beep. This number sense is apparently hardwired in a specific part of the human brain and the brains of a few other animals that have been tested (monkeys and rats). (Baiter, Michael; "What Makes the Mind Dance and Count?" Science, 292:1635, 2001.) Comment. Superficially, distinguishing between strings of beeps would ...
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... -year-old housewife who had never had artistic training took up painting. She initially created unsophisticated images of rivers, ponds and rural settings; later, elaborate and sometimes eccentric versions of the works of great masters. Unfortunately, such new-found talents are short-lived. They, too, deteriorate. (Stein, Rob; "Patients' New Gift Paints Clearer Image of Disease," The Brain in the News, p. 7, October 30, 1998. Cr. J. Cieciel) Comment. This peeling away of mental barriers suggests that we all have hidden or suppressed capabilities. Perhaps, some day, we will know how to unlock these in normal people. It is pertinent here that in idiot savants these mental barriers are also somehow removed to expose remarkable mathematical talents, such as calendar calculating. See OUR UNTAPPED TALENTS in SF#125. From Science Frontiers #133, JAN-FEB 2001 . 2001 William R. Corliss Other Sites of Interest SIS . Catastrophism, archaeoastronomy, ancient history, mythology and astronomy. Lobster . The journal of intelligence and political conspiracy (CIA, FBI, JFK, MI5, NSA, etc) Homeworking.com . Free resource for people thinking about working at home. ABC dating and personals . For people looking for relationships. Place your ad free. ...
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... Science Frontiers The Book Strange reports * Bizarre biology * Anomalous archaeology From New Scientist, Nature, Scientific American, etc Archaeology Astronomy Biology Geology Geophysics Mathematics Psychology Physics Science Frontiers The Book Contents Science Frontiers is an indexed compilation of the first 86 issues of our Science Frontiers newsletter . Chapter 1. Archeology: Ancient Engineering Works * Small Artifacts * Epigraphy and Art * Bones and Footprints * Diffusion and Culture. Chapter 2. Astronomy: Planets and Moons * Solar System Debris * Stars * Galaxies and Quasars * Cosmology. Chapter 3. Biology: Humans .* Other Mammals * Birds * Reptiles and Amphibians * Fish * Arthropods * Invertebrates * Plants and Fungi * Microorganisms * Genetics * Origin of Life * Evolution. Chapter 4. Geology: Topography * Geological Anomalies * Stratigraphy * Inner Earth. Chapter 5. Geophysics: Luminous Phenomena* Weather Phenomena * Hydrological Phenomena * Earthquakes * Anomalous Sounds * Atmospheric Optics. Chapter 6. Psychology: Dissociation Phenomena * Hallucinations * Mind - Body Phenomena * Hidden Knowledge * Reincarnation * Information Processing * Psychokinesis. Chapter 7. Chemistry, Physics, Math, Esoterica: Chemistry * Physics * Mathematics. Comments from reviews: "This fun-to-read book may lead some to new scientific solutions through questioning the phenomena presented", Science Books and Films Publishing details: 356 pages, paperback, $18.95, 417 illus., subject index, 1994. 1500+ references, LC 93-92800 ISBN 0-915554-28-3 , 8.5 x 11. Order From:The Sourcebook Project P.O . Box ...
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... Mathematics Psychology Physics Other pages Home Page Science Frontiers Online Science Frontiers: The Book Sourcebook Project Sourcebook Subjects Photocopied Classic Books These important old books from the anomaly literature used to be available, photocopied and bound in heavy, printed covers. Format: 8.5 " x 11. They are no longer available. Ancient Monuments of the Mississippi Valley View Cart Buy online via PayPal with MC/Visa/Amex E.G . Squier and E.H . Davis. 376 pp., 1848, $29.95p One of the most remarkable archeological books ever published in America! Its appearance in 1848 created a great sensation. For, as America moved west, the remnants of the great civilization of the Moundbuilders raised much speculation. Even today we marvel at their immense, flat-topped temple mounds, the huge earthen enclosures, and the meticulously wrought artifacts of copper, mica, and clay. Squier and Davis objectively described the features of this New World civilization in words and drawings. It is the drawings, though, that really capture the reader. They are superb, almost overwhelming. Rude Stone Monuments in all Countries: Their Age and Uses View Cart Buy online via PayPal with MC/Visa/Amex J. Fergusson, 1872, 578 pp., $26.95p Fergusson's famous compilation of worldwide megalithic monuments is a fit complement to our photocopied edition of Ancient Monuments of the Mississippi Valley, from 1848. Fergusson has filled his book with 233 line drawings of artifacts from the megalithic period. The emphasis is on the massive monuments, but you ...
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... Science Frontiers Sourcebook Project Strange reports * Bizarre biology * Anomalous archaeology From New Scientist, Nature, Scientific American, etc Archaeology Astronomy Biology Geology Geophysics Mathematics Psychology Physics Guides available Biology Catalogs Biology Handbook Archeology Handbook Geophysics Catalogs Geological Catalogs Astronomy Catalogs Astronomy Handbook Science Frontiers Sourcebooks Ordering details Omni Edge Science Winner December 1996 Publishing History 2007: Dark Days, Ice falls, Firestorms and Related Weather Anomalies (Geophysics) 2006: Archeological Anomalies: Graphic Artifacts I 2003: Archeological Anomalies: Small Artifacts 2003: Scientific Anomalies and other Provocative Phenomena 2001: Remarkable Luminous Phenomena in Nature 2001: Ancient Structures (Archeology) 1999: Ancient Infrastructure (Archeology) 1998: Biological Anomalies: Birds 1996: Biological Anomalies: Mammals II: 1995: Biological Anomalies: Mammals I 1994: Science Frontiers, The Book 1994: Biological Anomalies: Humans III 1993: Biological Anomalies: Humans II 1992: Biological Anomalies: Humans I 1991: Inner Earth: A Search for Anomalies (Geological) 1990: Neglected Geological Anomalies 1989: Anomalies in Geology: Physical, Chemical, Biological 1988: Carolina Bays, Mima Mounds, Submarine Canyons (Geological) 1987: Stars, Galaxies, Cosmos 1986: The Sun and Solar System Debris 1985: The Moon and the Planets 1984: Rare Halos, Mirages, Anomalous Rainbows (Geophysics) 1983: Earthquakes, Tides, Unidentified Sounds (Geophysics) 1983: Tornados, Dark days, Anomalous Precipitation (Geophysics) 1982: Lightning, Auroras, Nocturnal Lights (Geophysics) 1982: Unfathomed Mind 1981: Incredible life (Biology) 1980: Unknown Earth (Geological) 1979: Mysterious Universe ...
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... Science Frontiers The Unusual & Unexplained Strange Science * Bizarre Biophysics * Anomalous astronomy From the pages of the World's Scientific Journals Archaeology Astronomy Biology Geology Geophysics Mathematics Psychology Physics About Science Frontiers Science Frontiers is the bimonthly newsletter providing digests of reports that describe scientific anomalies; that is, those observations and facts that challenge prevailing scientific paradigms. Over 2000 Science Frontiers digests have been published since 1976. These 2,000+ digests represent only the tip of the proverbial iceberg. The Sourcebook Project, which publishes Science Frontiers, also publishes the Catalog of Anomalies, which delves far more deeply into anomalistics and now extends to sixteen volumes, and covers dozens of disciplines . Over 14,000 volumes of science journals, including all issues of Nature and Science have been examined for reports on anomalies. In this context, the newsletter Science Frontiers is the appetizer and the Catalog of Anomalies is the main course. Subscriptions Subscriptions to the Science Frontiers newsletter are no longer available. Compilations of back issues can be found in Science Frontiers: The Book , and original and more detailed reports in the The Sourcebook Project series of books. The publisher Please note that the publisher has now closed, and can not be contacted. Designed and hosted by Knowledge Computing Other links Science Frontiers On Line Browse or search over 2100 free reports, and discover the unusual in archaeology, astronomy, biology, chemistry, geology, geophysics, mathematics, psychology and physics. Search site for: Science Frontiers: The Book and Science Frontiers II An indexed compilation of the first 86 issues of our Science Frontiers newsletter, and ...
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