Monday, May 19, 2003
consensual cave diving
Number Theory and Time
"I have sometimes thought that if we were able to perceive time in some multi-dimensional way, more like a surface than like a line, then perhaps the distributions of prime numbers would be entirely self-evident, and not seem at all mysterious to us."
"A Möbius surface has only one side and one edge. You can make a Möbius band by gluing together the two ends of a long strip of paper after giving one end a half twist."
Moebius strip + Möbius Strip -- from MathWorld
"Even atoms have structural roots. Take carbon, my personal favorite. Life is based on carbon because carbon has four outer electrons that stick like little strips of Velcro to atoms next door, allowing the atoms to form long and elaborate chains. Think of these attachment points as outstretched hands. What gives carbon this marvelous property? The electrons are anchored by the positive attraction of protons deep in the nucleus. Unlike the root of a mountain or iceberg, the root of an atom takes up but a tiny amount of space. But in mass, it accounts for nearly all of the atom's heft. The root is also the core. That's why roots have such great explanatory power. They tell us why things are the way they are."
K.C. Cole - Mind Over Matter: Conversations with the Cosmos (Harcourt, 2003, page 75)
Pattern in the chaos
Prime numbers are the atoms of arithmetic
"A chance meeting in the common room at Princeton between Freeman Dyson, a quantum physicist, and Hugh Montgomery, a mathematician interested in the primes began one of the strangest connections in science. Montgomery showed Dyson some of the patterns that he had observed in the primes. Dyson however had seen these patterns before in the physics of quantum chaos."
Values and Strange Attractors
"[...] The social and cultural dimension of language, like the neurosensory dimension, has the form of a nonlinear dynamical system with strange attractors pulling it toward certain "archetypal" forms. Those forms could be seen in the odd "targetedness" of the great sound-shifts that periodically convulse a language; they can also be observed in the way that metaphorization will take parallel paths in different languages, so that when a colorful idiom from another language is presented to us, we can almost always find an equivalent in our own. Thus the words "spirit" in English and "Atman" in Sanskrit have identical metaphoric histories, as do the words "kind," "nature," and "genus," all of which came together again in English, having led separate lives in Germanic, Latin, Greek, and other tongues for thousands of years since their original common root in Indo-European. Metaphorization and sound-changes are every new human generation's way of committing a sacrificial impiety against the tongue of its ancestors, an impiety that commutatively atones for the crime of the ancestors themselves in similarly appropriating the language for themselves from their own mothers and fathers. And since meaning dies the moment it ceases to cut slightly against all previous usage -- a valuable if over-emphasized and not entirely original contribution of Deconstruction -- it is constituted by this continual low-level feedback between the language and the world it contains.
Such might be the rudiments of a new, evolutionary poetics and a new nonlinear theory of meaning and representation.
[...] Suffice it to say here that poetic meter turns out to be a sure road to the ur-language, or to change the metaphor, meter is the lyre or golden bough or magic flute that enables us to enter the underworld of that language and to return with intelligible gifts for the community. Meter, like music and visual imagery, is an ancient psychic technology by which human nature and human culture are bridged; appropriately, and as we might imagine from our discussion of the fractal harmonics of Hebb-cell circuitry, meter is a rhythmic and harmonic system in itself, a way of inducing the wave functions of the brain. The lyre through which Rilke traces Orpheus in the Sonnets to Orpheus is the poetic form of the sonnet itself.
If the words of a poet can induce in one brain the same strange attractor that they proceeded from in the poet's brain, an extraordinary possibility presents itself. This possibility is that when those harmonics are in our heads we are actually sharing the thoughts, and indeed the subjectivity, of the poet, even if he or she is dead. The poet lives again when his or her attractors arise in another brain. Poetry, then, is a kind of artificial intelligence program, that springs into being when booted ..." Frederick Turner
Neither Christopher Columbus, nor his contemporaries, believed the earth was flat.
How has the discovery of the mind been advanced or impeded by Nietzsche, Heidegger, and Buber?
Human Rights and Ethics (pdf)
Nietzsche's thesis that "consciousness is a surface" is a major insight which highlighted the role of the un-conscious in our psychic life ...
How does the existence of an epidermis define our sense of space and time?
The boundary is the place where inside and outside meet, where subject and object conjoin.
"Today, as physics attempts to incorporate instability, the world we see outside us and the world we see within are converging. This convergence of two worlds is perhaps one of the most important cultural events of our age." Ilya Prigogine
A future that works [doc]
"In a universe essentially based on instability and creativity, humankind is in a way once again at the very centre of the fundamental laws of the universe as we understand it today." Ilya Prigogine
May you live in interesting times
While widely reported as being an ancient Chinese curse, this phrase is likely to be of recent and western origin.
Geometry of the I Ching
The Cullinane sequence of the 64 hexagrams
On the brink of the hydrogen age
As late as the 1850's, wood, charcoal, and straw were the world's dominant fuels.
Fuel's Paradise - Wired 8.07 - July 2000
World-class contrarian Thomas Gold has a theory about life on the planet: It's pumping out of the Earth's crust - and it's swimming in oil.
Sheik Ahmed Zaki Yamani - "So, you want to talk about oil."
At this point he makes an extraordinary claim: 'I am 100 per cent sure that the Americans were behind the increase in the price of oil. The oil companies were in real trouble at that time, they had borrowed a lot of money and they needed a high oil price to save them.'
He says he was convinced of this by the attitude of the Shah of Iran, who in one crucial day in 1974 moved from the Saudi view, that a hike would be dangerous to Opec because it would alienate the US, to advocating higher prices.
'King Faisal sent me to the Shah of Iran, who said: "Why are you against the increase in the price of oil? That is what they want? Ask Henry Kissinger - he is the one who wants a higher price".'
Yamani contends that proof of his long-held belief has recently emerged in the minutes of a secret meeting on a Swedish island, where UK and US officials determined to orchestrate a 400 per cent increase in the oil price.
Sheikh Yamani predicts price crash as age of oil ends
"Thirty years from now there will be a huge amount of oil - and no buyers. Oil will be left in the ground. The Stone Age came to an end, not because we had a lack of stones, and the oil age will come to an end not because we have a lack of oil."
The Next Material World
"Fundamental shifts in civilization traditionally are initiated and designated by materials - and how an organized society masters their use."
The Real Scientific Hero of 1953 by Steven Strogatz - The New York Times, 4 March 2003
"In 1953, Enrico Fermi and two of his colleagues at Los Alamos Scientific Laboratory, John Pasta and Stanislaw Ulam, invented the concept of a "computer experiment." Suddenly the computer became a telescope for the mind, a way of exploring inaccessible processes like the collision of black holes or the frenzied dance of subatomic particles -- phenomena that are too large or too fast to be visualized by traditional experiments, and too complex to be handled by pencil-and-paper mathematics. The computer experiment offered a third way of doing science. Over the past 50 years, it has helped scientists to see the invisible and imagine the inconceivable.
Fermi and his colleagues introduced this revolutionary approach to better understand entropy, the tendency of all systems to decay to states of ever greater disorder. To observe the predicted descent into chaos in unprecedented detail, Fermi and his team created a virtual world, a simulation taking place inside the circuits of an electronic behemoth known as Maniac, the most powerful supercomputer of its era. Their test problem involved a deliberately simplified model of a vibrating atomic lattice, consisting of 64 identical particles (representing atoms) linked end to end by springs (representing the chemical bonds between them).
This structure was akin to a guitar string, but with an unfamiliar feature: normally, a guitar string behaves "linearly" -- pull it to the side and it pulls back, pull it twice as far and it pulls back twice as hard. Force and response are proportional. In the 300 years since Isaac Newton invented calculus, mathematicians and physicists had mastered the analysis of systems like that, where causes are strictly proportional to effects, and the whole is exactly equal to the sum of the parts.
But that's not how the bonds between real atoms behave. Twice the stretch does not produce exactly twice the force. Fermi suspected that this nonlinear character of chemical bonds might be the key to the inevitable increase of entropy. Unfortunately, it also made the mathematics impenetrable. A nonlinear system like this couldn't be analyzed by breaking it into pieces. Indeed, that's the hallmark of a nonlinear system: the parts don't add up to the whole. Understanding a system like this defied all known methods. It was a mathematical monster.
Undaunted, Fermi and his collaborators plucked their virtual string and let Maniac grind away, calculating hundreds of simultaneous interactions, updating all the forces and positions, marching the virtual string forward in time in a series of slow-motion snapshots. They expected to see its shape degenerate into a random vibration, the musical counterpart of which would be a meaningless hiss, like static on the radio.
What the computer revealed was astonishing. Instead of a hiss, the string played an eerie tune, almost like music from an alien civilization. Starting from a pure tone, it progressively added a series of overtones, replacing one with another, gradually changing the timbre. Then it suddenly reversed direction, deleting overtones in the opposite sequence, before finally returning almost precisely to the original tone. Even creepier, it repeated this strange melody again and again, indefinitely, but always with subtle variations on the theme."
Mark Evans - The Music of The Spheres
"In the mid-Sixties, DuPont had been working on the cutting edge of research and development in Laser technology. They had enormous stationary lasers, some almost as big as a dynamo, in a huge 300-foot white room, in their lab in Wilmington. They did everything with those lasers that could possibly be conceived of being done. They were working the other end of the equation at the same time, developing equipment that could electronically transform light into sound.
They made the apparatus that could transform light into sound as small as possible, given the state of technology at the time - so small that it could be put into a small suitcase. Then they took that equipment up to Canada, and set it up on the tundra, west of Hudson Bay, and directed it at the Aurora Borealis - the Northern Lights. With state-of-the-art recording equipment, they monitored dozens of Auroral displays, and recorded scores of hours of Auroras on audiotape. They were amazed at what they found: the Northern Lights, electronically transformed into sound, were music, the most exquisite music one could ever possibly imagine.
At the highest echelons of DuPont, even down to the corps of engineers, this was known. Leonard Richardson himself had heard ten to twelve hours of those tapes in the lab at Wilmington. "The moment you first heard it," he said, "it sounded like a beehive. After a few moments, however, you began to realize that it was choral in nature, a highly complex, harmonious tapestry of sound." It was, in fact, a labyrinth of melodies, totally harmonious, and contrapuntal. In it could be discerned as many as sixty-four distinct, harmonious lines of counterpoint. The closest earthly music it could be compared to was Bach, perhaps the Third Brandenburg Concerto, except that it was way beyond Bach, far more liberated, and not at all lugubrious or liturgical. It was infinite. Although each manifestation of the Aurora Borealis moved in a series of movements and variations along the lines of a concerto, no two Auroral displays ever produced the same symphony; each one was entirely unique.
It became a DuPont Company secret."
Prime numbers not so random?
A kind of order may be buried in the occurrence of indivisible numbers
Report by Philip Ball
The music of the spheres
Johannes Kepler and the Music of the Spheres
The music of the spheres
"It was Heinrich Heine who gave me the highest conception of a lyrical poet. I search vainly through the kingdoms of all the ages for anything to equal his sweet and passionate music." Friedrich Nietzsche
Refreshing the search for the 'first moving thing'
A thought-experiment from medieval physics?
AI Magazine Volume 12 Number 4
This is not a medieval woodcut
Shape of the Earth
DNA computers take shape
"In the experiments, DNA molecules were applied to a small glass plate overlaid with gold. The DNA was modified so that all the possible answers to a computationally difficult problem were included. By exposing the molecules to certain enzymes, the molecules with the wrong answers were weeded out, leaving only the DNA molecules with the right answers.
The appeal of DNA computing lies in the fact that DNA molecules can store far more information than any existing computer memory chip. It has been estimated that a gram of dried DNA can hold as much information as a trillion CDs.
What is more, in a biochemical reaction taking place in a tiny surface area, hundreds of trillions of DNA molecules can operate in concert, creating a parallel processing system that resembles the processing architecture of the most powerful supercomputer.
The logic behind conventional digital computers represents information as a series of electrical impulses using ones and zeros. DNA computing depends on information represented as a pattern of molecules arranged on a strand of DNA."
DNA computers: general-purpose systems with the potential to excel where electronic computers fail
Karaki: In media interviews, I am sometimes asked if the system is really a DNA computer or just a biochemical reaction system.
Suyama: The system carries out calculations using reactions in DNA molecules, so it is indeed a reaction system. The real questions are what kind of reactions are involved, how they are implemented, and what they are all about. Basically, we choose specific reactions and use a program to control the order in which to trigger them. By modifying the program, we can carry out not just a single computation process, but many different kinds. This general-purpose quality is the key criterion for determining whether or not a system can be described as a computer.
What is a computer?
"Since we are concerned with logical behaviour and not physical behaviour, we assume that inputs, outputs, time, and other parameters of the system are quantised. That means that time proceeds in definite 'ticks'; at each tick, our black box can inspect its inputs and will find each of them in one of a number of definite 'states', will itself be in one of a number of definite states, and will set each of its outputs to one of a number of definite states.
This idea is much more familiar to us today than it was to mathematicians in the 1930s when these ideas were first being discussed. Many apparently continuous devices [photographs, telephone conversations, gramophone records, handwriting] are routinely handled by digital means today [television raster scans or CCD arrays, computerised telephone exchanges, CDs, keyboards]. Early papers spend much time explaining how a continuous function can be approximated by a sufficiently fine set of discrete values." Dr A. N. Walker
David Deutsch: The Discrete and the Continuous
"A journey of a thousand miles begins, obviously, with a single step. But isn't it equally obvious that a step of a single metre must begin with a single millimetre? And before you can begin the last micron of that millimetre, don't you have to get through 999 other microns first? And so ad infinitum? That "ad infinitum" bit is what worried the philosopher Zeno of Elea. Can our every action really consist of sub-actions each consisting of sub-sub-actions ... so that before we can move at all, we have to perform a literally infinite number of distinct, consecutive actions?
Zeno's paradox is the earliest known critique of the common-sense idea that we live in a "continuum" -- an infinitely divisible, smoothly structured space. It highlights one of several awkward problems with that concept, which would be considered fatal flaws if there were a reasonable alternative. But the only alternative is that space is not infinitely divisible but discrete, and the flaw in that is a killer too: if there are only finitely many points -- actions, changes, or whatever -- between one place and another, how can you ever get from one to the next? There is, by definition, nothing in between, nowhere to be while you cross the gap. You start having not yet crossed; then you have crossed. Period.
This dilemma kept coming up in various guises: does matter consist of atoms? how many angels can stand on the head of a pin? In the nineteenth century the continuum seemed to have won, with the triumph of the wave theory of light -- though Darwin knew that there was a problem with evolution if, as he thought, inherited traits are continuously variable. He needn't have worried. When Max Planck solved the black body problem by postulating that atoms could absorb or emit energy only in discrete amounts, the quantum age began. The idea of quantization -- the discreteness of physical quantities -- turned out to be immensely fruitful. Niels Bohr used it to construct the first successful model of the internal structure of atoms. Albert Einstein used it to analyse the photoelectric effect. However, escaping from the infinities of continuous motion again raised the question "how do you get from A to B?" Modern quantum theory gives an answer of sorts. Remarkably, it describes a reality in which observable quantities do indeed take discrete values, yet motion and change are nevertheless continuous.
How can that be?"
American Scientist Online - The Square Root of NOT
"Digital computers are built out of circuits that have definite, discrete states: on or off, zero or one, high voltage or low voltage. Engineers go to great lengths to make sure these circuits never settle into some intermediate condition. Quantum-mechanical systems, as it happens, offer a guarantee of discreteness without any engineering effort at all. When you measure the spin orientation of an electron, for example, it is always either "up" or "down," never in between. Likewise an atom gains or loses energy by making a "quantum jump" between specific energy states, without passing through intermediate energy levels. So why not build a digital computer out of quantum-mechanical devices, letting particle spins or the energy levels of atoms stand for binary units of information?
One answer to this "Why not?" question is that you can't avoid building a quantum-mechanical computer even if you try. Since quantum mechanics appears to be a true theory of nature, it governs all physical systems, including the transistors and other components of the computer on your desk. All the same, quantum effects are seldom evident in electronic devices; components and circuits are designed so that the quantum states of many millions of electrons are averaged together, blurring their discreteness.
In a quantum computer, the basic working parts would probably have to be individual electrons or atoms, and so another answer to the "Why not?" question is that building such a machine is simply beyond our skills. And even apart from the challenges of atomic-scale fabrication, there are some ticklish conceptual issues. Quantum systems have some famously weird behavior, such as the phenomenon called quantum interference. Two nearby transistors can switch on and off independently, but two adjacent quantum objects (such as two electrons) are inextricably coupled, so that the future state of one electron cannot be predicted without taking into account the surrounding electrons. Indeed, an isolated electron can interfere with itself!
A third answer to the "Why not?" question is "Why bother?" Until recently there was no reason to believe that a quantum computer could do anything a classical computer couldn't. This situation has now changed dramatically. The exact place of quantum technology in the overall hierarchy of computing machines is still not settled, but a few recently discovered algorithms offer intriguing hints. It turns out that a program written for a quantum computer can factor large numbers faster than any known algorithm for a classical machine. The quantum factoring algorithm makes essential use of interference effects, which become a source of parallelism, allowing the computer to explore all possible solutions to a problem simultaneously. Factoring is a task of much theoretical interest, and it also has practical applications in cryptography, so these discoveries have attracted considerable notice."
Quest for the Quantum Computer by Julian Brown
"In "The Garden of Forking Paths," written back in the 1950s, an illustrious Chinese governor is said to have written a strange kind of novel constructed as a kind of labyrinth. "In all fictional works, each time a man is confronted with several alternatives, he chooses one and eliminates the others; in the fiction of Ts'ui Pen, he chooses -- simultaneously -- all of them," Borges wrote. By writing a novel that pursued all possible story lines simultaneously, Borges's fictitious author, Ts'ui Pen, could have been writing a script for the multiverse.
[...] Imagine living in a small house for many years and then discovering in the basement a trapdoor that opened onto a colossal subterranean world of rooms that appeared to stretch on into infinity. For physicists and computer scientists that, in some sense, is what the arrival of the first quantum computer would be like. [...]
Exploring Hilbert Space
Interpretations aside, it's long been known that at the atomic level waves can behave like particles, and particles have waves associated with them. A single entity such as an electron, for example, can travel along many different routes simultaneously as if it were really a spread-out phenomenon like a wave. The essential idea of quantum parallelism advanced by Deutsch was this: If an electron can explore many different routes simultaneously, then a computer should be able to calculate along many different pathways simultaneously too. (H&C note: Consider this paper by Andrew Steane.)
[...] On hearing Deutsch's grand vision for the future of quantum computation, I'm reminded of the scene in Stanley Kubrick's 2001: A Space Odyssey when those strange-looking apes discover for the first time the power of wielding a bone as a weapon. What a powerfully symbolic moment that was, with the future of humanity hanging in the balance between aggression and creativity. These hominids had taken their first step toward understanding and exploiting nature. Suddenly the picture cuts from a bone spinning in the air to a futuristic spinning space station orbiting the Earth ..."
Jill Matus - Proxy and Proximity: Metonymic Signing
"Metaphor is recognizable, captivating. Despite its assertion of illogical identity for the purposes of illuminating, it is a comparison between things different yet similar which enables us to see, in Kenneth Burke's phrase, the 'thisness of a that or the thatness of a this.'
[...] There are countless ways to condense the relationships and associations between one thing and another. Metonymic relationships ought to raise the question, 'Why this connection rather than that?' By exposing what we take as absolute to be relative, a scrutiny of metonymic relationships leads to a decentring perspective without which the danger is that what is habitual and conventional comes to be seen as inevitable. It is a blindness of insight, in de Man's terms, to see metonymy as dependent on contingent relationships but then to deny significance to the fact that the perception of relationships is not automatic. We have to be taught to see the connections among things, which is why games -- jigsaw puzzles, sequences, patterns, sorting and grouping on the basis of context and extrinsic connection -- inculcate in children such perceptual skills."
Games as Jazz + Standing Waves
"Great paintings shouldn't be in museums. Museums are cemeteries. Paintings should be on the walls of restaurants, in dime stores, in gas stations, in men's rooms ... It's not the bomb that has to go, man, it's the museums."
Bob Dylan - 1965
The World is Sound + The Circle is Unbroken
"Now, we daily see what science is doing for us. This could not be unless it taught us something about reality; the aim of science is not things themselves, as the dogmatists in their simplicity imagine, but the relations between things; outside those relations there is no reality knowable."
Henri Poincaré : Preface to Science and Hypothesis (1905)
Not Just Genes
"In the view of some biologists, nothing would better suit the DNA industry than a genuine midlife crisis, a realization that this most mythologized of bio-abbreviations may not, after all, be the fulcrum around which the Milky Way wheels. As these biologists see it, DNA may be elegant, but it often has been accorded far greater powers than it possesses.
With all the breathless talk of human DNA as a grand epic written in three billion runes, the scientists complain that an essential point is forgotten: DNA, on its own, does nothing. It can't make eyes blue, livers bilious or brains bulging. It holds bare-bones information - suggestions, really - for the construction of the proteins of which all life forms are built, but that's it. DNA can't read those instructions, it can't divide, it can't keep itself clean or sit up properly - proteins that surround it do all those tasks. Stripped of context within the body's cells, those haggling florid ecosystems of tens of thousands of proteinaceous fauna, DNA is helpless, speechless - DOA. By the same token, cells need their looping lanyards of genes and would grow as dull as hairballs without them." Natalie Angier
From Artificial Life to Semiotic Agent Models - Luis Mateus Rocha
"The integration or aggregation of agents in multi-agent systems is most often non-linear, in the sense that the resulting behavior cannot be linearly decomposed into the behavior of individual agents. This also implies that multi-agent systems lead to network causality, as effect and cause of agent behavior follow circular loops that cannot be linearly decomposed into traditional cause and effect chains."
Primordial soup or primordial pizza?
posted by Andrew 5/19/2003 02:08:00 PM