--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
http://www.theglobeandmail.com/servlet/ArticleNews/TPStory/LAC/20040710/UNIVERSE10/TPScience/
A cosmic crisis
Does the universe look like a soccer ball? Or is it flat and infinite in size? If we don't find out soon, we may never know. SIOBHAN ROBERTS reports on the latest hypothesis
By SIOBHAN ROBERTS
Saturday, July 10, 2004 - Page F9
It used to be that, once a decade or so, scientists asked, "What is the shape of the universe?" A hypothesis would arise -- for example, that the universe was flat and infinite -- followed by a spurt of research, and that was enough to last us a while on the space-time odometer.
Since the early 1990s, however, cosmology is where much of the exciting science has been happening. "We've been looking for the shape of the universe like Columbus did the shape of the Earth," says Glenn Starkman, an astrophysicist currently based at the Conseil Européen pour la recherche nucléaire (CERN) in Geneva -- the home of the world's largest particle physics laboratory and essentially the centre of the universe for determining the content of the cosmos when it was a trillionth of a second old.
But Dr. Starkman, having cut his teeth at the Canadian Institute for Theoretical Astrophysics at the University of Toronto, is more concerned with the large-scale properties of the universe. He focuses his research on the general topology and shape of the cosmos (his regular gig is as a professor at Case Western Reserve University in Cleveland).
The "crisis" in cosmology these days, according to Dr. Starkman, speaking only somewhat with tongue in cheek, is that time is running out. "If we don't figure out the shape of the universe soon," he says, "the universe will hide this secret from us forever."
This is because the research depends on data salvaged from the microwave background, the echoes of the Big Bang that created the universe in the first place.
And as Dr. Starkman explains, "Today, the place from which the echoes come to us is moving away from us faster than the speed of light, which means we can't receive light from that place any more -- we can no longer see or learn about that place, never mind any farther away.
"We have enough data now to be able to determine the shape of the universe if the shortest distance around the universe is less than the distance across the microwave sphere of the Big Bang. But we do not have enough data if the universe is any bigger," he says, getting a tad more technical.
Max Tegmark, an astrophysicist and professor at the University of Pennsylvania, likens it to trying to figure out the shape of the Earth if you're not able to see beyond the walls of your bedroom. "Nature has a censorship where we can only see so far," Dr. Tegmark says. "We can't see anything from farther than 14 billion light-years. This limits us in what we can see and what data we can gather."
"The only way we'll have enough data," Dr. Starkman says, "is if the universe stops behaving as it is now. It might stop its accelerated expansion, but probably not for many billion years, which doesn't help us much."
Aside from finding a solution to this problem -- what to do when we can no longer receive the data -- Dr. Starkman is also involved in testing the latest prediction for the shape of the universe (based on that microwave information).
It was put forth by four Parisian cosmologists and one American "freelance" geometer (the spokesman for the group), Jeff Weeks from Canton, N.Y. Dr. Weeks, a 1999 recipient of the MacArthur Fellowship, known as the "genius prize," and his team proposed that the universe is in the shape of a 12-sided figure called a dodecahedron.
Greek philosopher Plato guessed nearly 2,400 years ago that the universe was structured like a dodecahedron.
The Greeks had recently discovered that there were only five regular polyhedra: the cube, octahedron, tetrahedron, icosahedron and dodecahedron. Plato, who believed that the properties of matter could best be understood in terms of mathematical symmetries, assigned the first four solids to the elements earth, air, fire and water, respectively, and then proclaimed that the dodecahedron was the shape of the cosmos itself.
Also in ancient Greece, using bare-hands science and the power of their imaginations, philosophers Leucippus and Democritus had differing ideas; they envisaged an infinite universe.
Aristotle thought that it was a finite ball, with the Earth at the centre. His view prevailed and went mostly unchallenged in Western society for almost 2,000 years, until the invention of the telescope by Galileo in 1608.
In 1917, when Albert Einstein applied his geometrical theory of relativity to the questions of cosmology, he recycled a three-sphere scenario previously posited by German mathematician Bernhard Riemann.
All hypotheses, dating from ancient times to today, remain contentious. But technological advances over the past decade have increased our chances of actually finding an answer to this age-old question -- that is, of course, if we manage it in time.
Currently, there are three models considered contenders: a spherical universe, a hyperbolic saddle-shaped universe and the standard and most widely accepted model, a flat universe, expanding infinitely under the pressure of an ominous and as yet inexplicable "dark energy."
Things looked hopeful for the dodecahedron hypothesis when its computer-generated model was compared to reality -- that is, the data from NASA's Wilkinson Microwave Anisotropy Probe. The WMAP was sent to map the cosmic echo of the Big Bang and provide information about its early history and scale.
One particularly useful indicator of universe topology is the temperature fluctuations of radiation emanating from the originating bang.
In an article in Nature magazine, Dr. Weeks and the other members of his team -- Jean-Pierre Luminet of the Paris Observatory, Roland Lehoucq of the Paris Observatory and CEA/Saclay (Atomic Energy Research Centre), Alain Riazuelo of CEA/Saclay and Jean-Philippe Uzan of the University of Paris -- explained these fluctuations by comparing them with the sound waves of musical harmonics.
"A musical note is the sum of a fundamental, a second harmonic, a third harmonic, and so on," the group's article said. "The relative strengths of the harmonics -- the note's spectrum -- determines the tone quality, distinguishing, say, a sustained middle C played on a flute from the same note played on a clarinet.
"Analogously, the temperature map on the microwave sky is the sum of spherical harmonics. The relative strength of the harmonics -- the power spectrum -- is a signature of the physics and geometry of the universe."
When the WMAP data arrived in February, 2003, it confirmed the popular infinite-flat model of the universe, but only in part. All the small and medium-sized temperature waves were present as predicted, but the model's broad wavelengths, which would have to exist in such a large and infinite universe, were much weaker than expected.
One explanation, Dr. Weeks says, is that space simply isn't that big and thus could never produce such strong large waves in the first place. "A violin is never going to play the low notes of a cello because a violin's strings aren't long enough to support such a long sound wave," he says. "It's the same with the universe. Its waves cannot be larger than space itself."
However, the behaviour Dr. Weeks predicted for a dodecahedral universe matched all the WMAP data. The model, nonetheless, is still in limbo.
It is being subjected, by Dr. Starkman and an international medley of cosmologists, to a "circles-in-the-sky test (the rest of the team is Neil Cornish, an Australian currently at Montana State but who did his PhD at the University of Toronto, David Spergel at Princeton University and Eiichiro Komatsu at the University of Texas at Austin).
If the dodecahedron model is correct, a computer-coded search should be able to detect six pairs of matching circles across the cosmic horizon -- echoes from the Big Bang vibrating against the 12 faces of the dodecahedron universe.
"As much as I love the dodecahedron model," Dr. Tegmark says, "I'm not putting my money on it. Don't get me wrong, I don't have a bias against the dodecahedron. It's a beautiful idea, it's the cutest Platonic solid -- the cube and the octahedron are a little more pedestrian.
"The most amazing thing of all is that we humans can address these questions in a scientific way; that these philosophical questions -- like, Is space infinite? -- have become scientific questions."
Though, the end result of these philosophical questions that now have scientific answers -- the so-what? factor -- is still philosophical. That is, the answers mainly just serve to satisfy the age-old and innate human curiosity, our egocentric pondering about our local place in universal scheme of existence. There is always the chance, of course, that the scientific answers will lead to more scientific questions, and then potentially more answers, but these subsequent questions and answers are in areas of science that are essentially unfathomable before we find the initial answers.
Unfortunately, the scientific data does not seem to be there supporting the dodecahedron, and thus, it has not yet been accepted as an answer. So far, for example, Dr. Starkman and the team have found no circles (they calculate that the universe can be no smaller than 78 billion light-years across, while the dodecahedron idea means the universe measures just 60 billion light-years).
"And it's not just that we haven't found any circles yet," Dr. Starkman says. "It's that we've looked, and shown that the circles that should be there -- if the universe is a dodecahedron of the size that Weeks and company said it was -- are definitively not there. And they are not hiding behind the galaxy."
But Dr. Weeks and his team are holding out hope. They speculate that one explanation for the missing circles is galactic contamination -- dust and hot electrons getting in the way of the WMAP data.
His team is also exploring other options, such as the possibility of a universe that is finite in some directions and infinite in others. "We don't want to ignore other possibilities," Dr. Weeks says. "But personally, I'm not quite ready to declare the circles missing."
One last-ditch possibility, according to a more recent discovery that Dr. Starkman is involved with (with another international cluster of cosmologists), is that there is something odd going on, perhaps a miscalculation, with the WMAP microwave data and its analysis.
The anomaly was that those weaker-than-expected broad-scale fluctuations on the microwave sky align with themselves in strange ways, and -- still more outrageously -- they seem to align with the ecliptic plane, or the plane of the solar system. This just shouldn't be. What goes on in deep space and the distant past should not be affected by the path the planets follow around the sun.
"It's a mystery," Dr. Starkman says. "There seems to be something, I hesitate to say wrong, but very odd about what's been measured, which if it is a reflection of the universe, is inconsistent with our present understanding."
He stumbled upon this anomaly when he was trying to figure out a way to determine the shape of the universe if it is too big for circles to be seen.
Which seems to indicate that while the shape of the universe may or may not be finite and dodecahedral, the search for the shape of the universe is most definitely circuitous, the astrophysicist chasing our cosmic tail to infinity.
Cosmology 101
There are three main possibilities for the shape of the universe:
Sphere
A spherical universe has positive curvature: It is finite in size, but without boundaries, like a balloon.
In a so-called closed universe, you could, in principle, fly a spaceship in one direction and eventually get back to where you started from.
A closed universe is also closed in time: It eventually stops expanding, then contracts in a "Big Crunch."
In such a universe, parallel lines eventually converge (e.g. longitudinal lines are parallel at the equator, but converge at the poles) and large triangles have more than 180 degrees.
Flat
You can imagine this kind of universe by cutting out a piece of balloon material and stretching it with your hands. The surface of the material is flat, not curved, but you can expand and contract it by tugging on either end.
A flat universe is infinite in size, and has no boundaries.
In such a universe, parallel lines are always parallel and triangles always have 180 degrees.
A flat universe expands forever, but the expansion rate approaches zero.
Saddle
Such a universe has negative curvature: It is infinite and unbounded.
In a so-called open universe, parallel lines eventually diverge, and triangles have less than 180 degrees.
An open universe expands forever, with the expansion rate never approaching zero.
-- Staff
Siobhan Roberts is a freelance writer based in Toronto.
--------------------------------------------------------------------------
http://www.dfw.com/mld/dfw/living/9168914.htm?1c
Guidance? Just Do the Math
By Maggie Ross McNeely
Special to the Star-Telegram
When the midsummer sun strikes, we Southern gardeners become as housebound as Northerners do in winter. With the onset of cabin fever comes a different phase of gardening, planning for autumn projects.
When planning, we can turn to an ancient law of proportionality for guidance. The golden section is a mathematical principle first documented 2,000 years ago by Vitruvius, Julius Caesar's chief architectural engineer. It is more famously known by Leonardo da Vinci's 1509 Vitruvian Man drawing of the The Divine Proportion, illustrating the human geometry by way of a male figure graphed onto a circle within a square.
Also known as the two-thirds rule and the golden mean, the golden section describes portions of an object in the ratio of 1:1.618, and is applied in approximation as the fraction 2/3. This ratio, represented by the Greek letter phi, occurs in all forms of nature as a mathematical code of design and function.
It is no wonder the number has a universal appeal, considering its repeated occurrence throughout the cosmos. Phi has been identified in the structure and growth pattern of all living things from sunflowers to seashells and in the physics of lightning, water bubbles and mineral formations.
Our very anatomy relates to the code, with the proportions of the human appendages and the spacing between our facial features arranged according to the two-thirds rule.
Humans identify harmony in the two-thirds proportion in nature and apply the same order, either consciously or otherwise, in their creations. Mathematicians have identified the formula in proportions in ancient and modern architecture, and in the rhythms of classical music, poetry and literature, as well as the visual arts.
Applying the 2/3 standard to any visual will create a pleasing proportion between two objects and their relationship to the remainder. The principle is often illustrated by academics using old masters paintings. Divide the artwork into nine equal blocks with two horizontal lines and two vertical lines, and we find that places of emphasis often occur where the lines cross.
The same technique can be applied to designing a garden scene with a photo of the area taken from a favorite viewpoint. Divide the image into nine blocks with two equally spaced horizontal lines and two vertical. Where the lines intersect indicates the best places to site prominent objects.
In garden terms, they are described by that much-used horticultural phrase "focal point." Garden structures such as birdbaths, statuary, gazebos, windmills, benches or even humble bottle trees can be dominant, eye-stopping objects. Each block on the image can be further divided by two-thirds to indicate the positioning of more details.
In the plant category, a focal point is often described as a "specimen" tree or plant that, because of its strong form, color or other outstanding attribute, can visually stand alone in a scene or rise above the others. Garden-sized trees such as Japanese maples or desert willows, and large topiaries or espaliered plants, yucca-shaped growths and tall ornamental grasses are examples of bold specimens that are described by another widely used term, "architectural plants."
Practice finding an ideal garden arrangement with objects resembling the size and shape of a bottle, a teacup and an egg. Imagine them as prominent features such as a tree, bench and shrub, and move them around a table to find the golden means.
Some people are born with the gift of recognizing this universally satisfying balance, subconsciously applying the formula to all aspects of their surroundings. They are the gifted few known as "born artists." Everything they assemble in life has a magical appeal. Their creative mind and intuitive eye know exactly where each piece belongs to make a satisfying composition. In the garden, they know precisely which limbs to cut from a giant oak or a potted bonsai, and how to place and shape any flower bed, arbor or garden pond. For those not born with this innate knack, the two-thirds rule will unlock the universal aesthetic code.
If we apply the rule as a tool in our summer schemes and dreams, whether they are conceived in doodles, Autocad, photos or intrinsic mental images, we'll know exactly where to sink the shovel on the next blissfully cool day. That is one of the many returns of a garden -- there is always something to aspire to, like a rainbow at the end of a rainy June.
--------------------------------------------------------------------------
http://www.blackvoicenews.com/modules.php?op=modload&name=News&file=article&sid=2166&mode=thread&order=0&thold=0
For ancient Black Egyptians, a state of order (or harmony or balance) was so foundational in their lives that they divinely personified the abstract concept of order in the form of the...
... goddess Maat.
In her original role as goddess in mortuary mythology, she was depicted as wearing an ostrich plume (feather) on her head. A picture of this feather was often used as the hieroglyphic symbol for both her name and for "truth."
Her origin dates (?5500 B.C. in the pre-Egypt area) to that period when priest-astronomers had already charted the stars and planets, had noted the earth responded to these orbits, and had devised units of measurements (e.g. arithmetic and geometry) based upon the observed periodicity of astronomic events.
These measurements so matched the celestial order as to itself amount to a revelation regarding the organizing principle by which the Egyptians realized and recognized their own latent harmony in the sense of the "law of sympathy" (all God's creations are related).
So wondrous were the cycles of celestial bodies -- and their even greater, more majestic, and infinitely widening cycles -- that the priest inferred laws by which gods came into being and then disappeared. These laws were "hooked" up to the new mathematical insights into the earlier-known mystery of biological death and generation.
Thought to arise from the lunar rhythm of the womb as a result of cosmic order, the goddess Maat, through a mathematical law, was viewed as a correspondent between the earth and celestial realms. Since all Egyptians anticipated becoming part of the cosmos when they died, Maat and her principles were used to make this happen.
By putting pertinent mathematical connections into philosophical words, the Egyptians formulated Maat laws. Strict adherence to Maat's laws and manifestations represented a frame within which the Egyptians could use as a standard and guide for living so as to feel secure about conforming to the divine plan for all creation.
As an expression of God's love in the world, ancient Africans believed Maat was the true essence of creation (Bunson, Encyclopedia Ancient Egypt, p. 152) and believed that every descendant of Africans contained in his/her mind and physical body the manifestations of Maat -- truth, wisdom, justice, balance, and all the power, strength, and courage needed for getting through life.
Since the heart was said to be the center of thought, memory, and emotion -- and thus associated with intellect and character -- the Egyptians originated the first concept of a Judgement Day for the dead.
The resultant ceremony, called the Weighing of the Heart, took place in presence of Osiris, god of the dead and in the Hall of Two Truths. On a pair of enormous scales, the heart was weighed against Maat's feather (the symbol of justice). If the heart was heavy with the weight of wrongdoings, the balance would sink.
Then the "she-monster" Am-Mut (eater of the dead) would immediately devour that heart. Otherwise, the deceased entered the Afterlife -- a great achievement. Since the Egyptians were the only ones around the Mediterranean "pond" to hold a happy view of death, they were quite willing to be wise and virtuous for a chance at eternal bliss.
--------------------------------------------------------------------------
--------------------------------------------------------------------------
This "Afterlife" concept was borrowed into the religions of Christianity, Islam, Zoroastrianism, and Orphism -- but not by the Greeks. Maat was generally depicted holding the magic cross of life in one hand and the Papyrus Scepter (representing the book of the law) in the other -- the entire picture being borrowed into Greece to represent the Scale of Justice.
Website: jablifeskills.com
Joseph A. Bailey, II, M.D
--------------------------------------------------------------------------
--
The Design-L list for art and architecture, since 1992...
To subscribe, send mailto:design-l-subscribe-request@xxxxxxxxxxxxx.
To signoff, send mailto:design-l-unsubscribe-request@xxxxxxxxxxxxx.
Visit archives: http://lists.psu.edu/archives/design-l.html
