Thursday, November 06, 2003
The sixth sense of Henry the Sleuth
Counting Coots - By Corey S. Powell and Paroma Basu
"The coot - a clumsy bird so unloved that its name is a synonym for an eccentric old man - has a remarkable ability to recognize and count its eggs, says behavioral ecologist Bruce Lyon of the University of California at Santa Cruz. Coots need to be crafty because of the unusual way the animals compete: One coot will slip eggs into another's nest to trick the host into raising the interloper's eggs. But nest owners use their wits to fight back, Lyon finds."
The Big Question: Does the Universe Follow Mathematical Law?
In The New York Times - 10 February 1998 - George Johnson writes: " [...] In "The Number Sense: How the Mind Creates Mathematics" (Oxford University Press, 1997), Stanislas Dehaene, a cognitive scientist at the National Institute of Health and Medical Research, in Paris, marshals experimental evidence to show that the brains of humans -- and even of chimpanzees and rats -- may come equipped at birth with an innate, wired-in aptitude for mathematics.
[...] Leopold Kronecker, a 19th-century mathematician, once said: "The integers were created by God; all else is the work of man." Albert Einstein, taking a different view of whole numbers, wrote that "the series of integers is obviously an invention of the human mind, a self-created tool which simplifies the ordering of certain sensory experiences."
In "The Number Sense," Dehaene went even further. The integers -- the smallest ones, anyway -- are hard-wired into human nervous systems by evolution, along with a crude ability to add and subtract. Mathematics, he believes, is "engraved in the very architecture of our brains."
"Because we live in a world full of discrete and movable objects, it is very useful for us to be able to extract number," he argued in a ... forum published ... by the Edge Foundation. "This can help us to track predators or to select the best foraging grounds, to mention only very obvious examples."
[...] While people are born with an understanding of the rudiments of arithmetic, [Dehaene] contends, going beyond that requires learning and creativity. Multiplication, division, and the whole superstructure of higher mathematics -- from algebra and trigonometry, to calculus, fractal geometry, and beyond -- are a beautiful improvisation, the work of human culture."
Salamanders can do maths - Nature 3 May 2003
Amphibians hint that number skills evolved early. Hannah Hoag writes:
"The addition of salamanders to the list of animals with natural mathematical abilities hints that some notion of number evolved at least 28 million years ago. "It may be more ancient than we thought," agrees Marc Hauser, who studies primate math at Harvard University in Cambridge, Massachusetts. But Hauser and Leslie caution that different processes may be at work in amphibians and primates."
Monkeys Have Numerical Abilities, Two Columbia Psychologists Report [also here]
Ms. Brannon and Prof. Terrace believe that arithmetic and language evolved separately, and that number skills preceded human speech. "Language is a complex social skill, whereas counting can be learned by the individual," Prof. Terrace said. "Counting is useful in foraging for food, assessing a group of predators or ordering the number of dominant males in one's group."
Science Daily - 26 October 1998
ABC News Online - Counting coots mystify scientist
"The ability of females to count only their own eggs in a mixture of eggs is a remarkable feat that provides a convincing, rare example of counting in a wild animal." Bruce Lyon
BBC Science/Nature - Counting lions roar for help
A scientist based in the UK says she has proved that lions can count.
Biologist Karen McComb of Sussex University used a big loudspeaker and recordings of lions in various numbers to experiment with African lions. She then recorded the number and type of roars that came back from lions around.
"What they did was closely controlled by how many were roaring from the loudspeaker, and how many of themselves there were," Karen McComb of Sussex University explained to BBC World Service's Science In Action programme. "Their likelihood of approaching increased as their own group size increased - and also decreased as the number of intruders roaring from the loudspeaker increased. Their behaviour was best predicted by a variable that we called odds, which was the ratio of number of defenders to number of intruders." In other words, the lions were making decisions by working out the numbers they potentially faced.
Lab tricks show dogs can count - New Scientist - 31 July 2002 [& BBC report]
Hazel Muir writes: "Dogs can count, new work on mongrels reveals. Dogs are descended from wolves, which not only have a large neocortex - the brain's centre of reasoning - but live in large social groups. So their mathematical ability could, in evolutionary terms, have been useful for working out how many allies and enemies they had in a pack, the researchers think.
Animals such as birds and rodents can tell when one pile of objects is bigger than another. But to count, an animal has to recognise that each object in a set corresponds to a single number and that the last number in a sequence represents the total number of objects. Many primates have this basic mathematical ability. But Robert Young, an animal behaviour expert at the Pontifical Catholic University of Minas Gerais in Belo Horizonte, Brazil, suspected that dogs do too.
To test the idea, Young and his colleague Rebecca West of De Montfort University in Lincoln, UK, borrowed a technique that has been used to show that five-month-old babies can count."
Coot Birds Can Count, Study Says
James Owen reports for National Geographic: "Many animals apparently have a brain-wiring that in the right circumstances can support competent counting without verbal symbolic representation of numbers," said Malte Andersson, from the University of Gothenburg, Sweden. "Lyon's findings provide a fascinating example of how this capacity is put to good use in the wild."
"The study raises some very interesting questions about just how animals are able to assess the number of young they have - and which ones are theirs - and adjust their parental care accordingly," [John] Eadie said.
Lyon believes visual egg-counting could be a skill common to many birds.
Crow Makes Wire Hook to Get Food
"A squire was determined to shoot a crow which made its nest in the watch-tower of his estate. Repeatedly he had tried to surprise the bird, but in vain: at the approach of man the crow would leave its nest. From a distant tree it would watchfully wait until the man had left the tower and then return to its nest. One day the squire hit upon a ruse: two men entered the tower, one remained within, the other came out and went on. But the bird was not deceived: it kept away until the man within came out. The experiment was repeated on the succeeding days with two, three, then four men, yet without success. Finally, five men were sent: as before, all entered the tower, and one remained while the other four came out and went away. Here the crow lost count. Unable to distinguish between four and five it promptly returned to its nest."
Tobias Dantzig - Number: The Language of Science (George Allen and Unwin, 1962, page 3)
How to count in oil and stone
"Numbers unfold their peculiarities to people who think about them as individuals, instead of as anonymous markers on a notched line leading to infinity ... There is a certain truth to the habit of sticking to smaller numbers, since the unaided human mind can rarely hold more than three or four ideas at once. (According to the psychoanalyst Jacques Lacan [Sokal hoax], the numbers zero to six are a special key to the psyche because the unconscious can't count beyond six.) The basic idea of this book is a duality (painting and alchemy), and as I write I might be able to keep a half-dozen of its themes in my head at once. But no one except the odd number genius has theories that depend on 1000 or 1729 ideas."
James Elkins - What Painting Is (Routledge, 2000, pages 42-43)
"Man thinks in two kinds of terms: one, the natural terms, shared with beasts; the other, the conventional terms (the logicals) enjoyed by man alone."
William of Ockham
What Is a Number, that a Man May Know It?
"The numbers from 1 through 6 are perceptibles; others, only countables. Experiments on many beasts have often shown this: 1 through 6 are probably natural terms that we share with the beasts. In this sense they are natural numbers. All larger integers are arrived at by counting or putting pebbles in pots or cutting notches in sticks, each of which is - to use Ockham's phrase - a conventional term, a way of doing things that has grown out of our ways of getting together, our communications, our logos, tricks for setting things into one-to-one correspondence."
Warren S. McCulloch - Embodiments of Mind (MIT Press, 1988, page 7)
I must lie down where all the ladders start,
In the foul rag-and-bone shop of the heart.
A problem squared
Marcus du Sautoy finds poetry has links with calculations in Imagining Numbers: Particularly the Square Root of Minus Fifteen by Barry Mazur
"If mathematics is an art then it is art created under huge logical constraints. This is perhaps what makes poetry or music, with boundaries of metre or harmony, good analogies for the mathematical creative process. But ultimately what sets mathematics apart from other creative disciplines is the fact that ambiguity is anathema to the mathematician, while it is one of the joys of poetry."
John Burnside - Journey to the centre of the Earth
"On an open stage in a meadow above Kafjord, northern Norway, in July, Muscogee poet Joy Harjo and her band, Poetic Justice, have the whole crowd up and dancing ..."
John Burnside continues: "I listen and watch as a group of Kamchatkan dancers perform a dance that is as close as I can imagine coming to a living enactment of the Orpheus mystery, a shamanic tale of dismemberment and renewal that acknowledges a darkness present in the song of the earth and in our own hearts and minds.
All the time, what I am listening for is something I can barely talk about. A shared sense of home, yes; but also the acknowledgement that, while it perplexes and disturbs us, the darkness is both necessary and good. A passionate and truly rational invocation of justice, but also an acceptance of the provisional nature of human existence. By contrast, where I come from, home means something that mistakes itself for permanence: it means possession, it means consumption. Where I come from, darkness is "evil". Where I come from, we want everything, especially our own lives, to last for ever.
So while I don't want to romanticise this, Riddu Riddu, a small festival on the rim of the Arctic tundra, has revealed to me that I belong to the wrong world."
Multiple Versions of the World
"What bonus or increment of knowing follows from combining information from two or more sources?
[...] Von Neumann once remarked, partly in jest, that for self-replication among machines, it would be a necessary condition that two machines should act in collaboration.
Fission with replication is certainly a basic requirement of life, whether it be for multiplication or for growth, and the biochemists now know broadly the process of replication of DNA. But next comes differentiation, whether it be the (surely) random generation of variety in evolution or the ordered differentiation of embryology. Fission, seemingly, must be punctuated by fusion, a general truth which exemplifies the principle of information processing we are considering here: namely that two sources of information (often in contrasting modes or languages) are enormously better than one."
Gregory Bateson - Mind and Nature: A Necessary Unity (Fontana 1980, page 89)
Diversity: Multiple ways of knowing & multiple worldviews by Shamim Bodhanya
"Bohm's causal interpretation of quantum physics, rivals the more dominant ... Copenhagen interpretation of Niels Bohr, Werner Heisenberg and others. [David] has indicated that there is only a single undivided wholeness in the universe. It is we, as observers that fragment the world through the categories that we impose. He uses the metaphor of the hologram to describe this undivided wholeness."
Hedy Lamarr - an engineering pioneer
posted by Andrew 11/06/2003 04:24:00 PM