"O wild West Wind, thou breath of Autumn's being,
Thou, from whose unseen presence the leaves dead
Are driven, like ghosts from an enchanter fleeing....
"...Thou dirge
"Of the dying year, to which this closing night
Will be the dome of a vast sepulchre,
Vaulted with all thy congregated might
"Of vapours, from whose solid atmosphere
Black rain, and fire, and hail will burst: oh, hear!"
Ode to the West Wind, Percy Bysshe Shelley, via LoudLit.org"...Til day rose; then under an orange sky
The hills had new places, and wind wielded
Blade-like, luminous black and emerald,
Flexing like the lens of a mad eye...."
Wind, Ted Hughes"Air Pressure and Wind"
John P. Stimac, Department of Geology/Geography, Eastern Illinois University College of Sciences
"We know that standard atmospheric pressure is 14.7 pounds per square inch. We also know that air pressure decreases as we rise in the atmosphere.
"1013.25 mb = 101.325 kPa = 29.92 inches Hg = 14.7 pounds per in2 = 760 mm of Hg = 34 feet of water...."
There's quite a bit more about air pressure. Quite informative, too.
Then the page turns to wind:
"...Wind results from a horizontal difference in air pressure and since the sun heats different parts of the Earth differently, causing pressure differences, the Sun is the driving force for most winds.
"The wind is a result of forces acting on the atmosphere:
"Pressure Gradient Force (PGF) - causes horizontal pressure differences and winds
"Gravity (G) - causes vertical pressure differences and winds
"Coriolis Force (Co) - causes all moving objects, such as air, to diverge, or veer, to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.
"Friction (Fr) - very little effect on air high in the atmosphere, but more important closer to the ground.
"Centrifugal Force (Ce) - objects in motion tend to travel in straight lines, unless acted upon by an outside force.
"The Net force = PGF + G + Co + Fr + Ce...."
All of which is rather technical.
Comparisons
Which helps the reader understand wind?
The poetry?
The mathematics?
The Lemming thinks the answer is - both.
But not the same sort of understanding.
Wind in Minnesota
The Lemming, sitting by a dark window in central Minnesota, hears wind rubbing against the sky, patting the house with nebulous paws.
"A massive ridge nearly encircling Saturn's moon Iapetus is likely the remains of a mini-moon destroyed by Iapetus' gravity long ago, a new study suggests.
"This sub-moon probably formed after a giant object smashed into Iapetus, and the blasted-off pieces coalesced, according to researchers. But over time, Iapetus tore it apart and its bits slammed into the moon along its equator, forming a ridge more than twice as tall as Mount Everest.
" 'Imagine all of these particles coming down horizontally across the equatorial surface at about 400 meters per second, the speed of a rifle bullet,' study co-author William McKinnon of Washington University in St. Louis said in a statement. 'Particles would impact one by one, over and over again on the equatorial line. At first the debris would have made holes to form a groove that eventually filled up.'..."
Iapetus has a special place for the Lemming, since it's where one of the big black monoliths were in A. C. Clarke's novelization of Kubrick's 2001: a Space Odyssey. A 'making of' book that's - somewhere in the Lemming's attic - explained that Kubrick would have used Clarke's locale: but doing so would have meant special effects to make Jupiter, and then adding rings. Even Kubrick had limits, so that part of the movie was set in orbit around Jupiter.
That self-indulgent stroll down memory lane is to explain why, when the Lemming saw that ridge precisely over the equator of Iapetus, 'artifact' came to mind.
Not as a serious idea: more along the lines of 'that would make a good story.'
The Iapetus feature is unique in the Solar system - the part inside the orbits of Pluto/Charon and Neptune, anyway - but the collision that may have caused it isn't.
Not according to current best-fit models about how planets form, anyway. Right now, it looks like Earth's moon and Charon got started after major collisions kicked up moon-size divots. Debris piles, actually.
One of the reasons no other Saturnian moons have features like this ridge is - probably - that the orbit of Iapetus isn't particularly close to other moons. Other satellites didn't have that kind of elbow room.
"Saturn's famous rings are the last remaining shards of a huge moon the planet tore apart long ago, a new study suggests.
"A moon about the size of Titan — Saturn's largest satellite — likely spiraled into the giant planet about 4.5 billion years ago, scientists think. As it made its way, Saturn's powerful gravity stripped off the doomed moon's icy outer layers, thus spawning the planet's magnificent rings, according to the research. [Gallery: The Rings and Moons of Saturn]
"And, in death, this lost moon may have given other satellites life, the study suggests. Over the eons, much of the ring material has glommed together, forming the icy inner moons of Saturn.
" 'This model implies that the rings are primordial, that they formed from the same processes that left Titan as Saturn's only large satellite,' said study author Robin Canup of the Southwest Research Institute in Boulder, Colo. "'And it's the only self-consistent explanation for the ice-rich inner satellites.'..."
Part of the puzzle of Saturn's rings is that they're mostly water ice. Which is odd - since mathematical models which do a good job of explaining how the outer planets formed, and observations, show that material available was ice and rock.
The new model involves a moon like Titan, with a rocky core and water ice near the surface, in a decaying orbit around Saturn. The rocky core eventually fell in, but on the way tidal forces stripped water ice off - part of which formed the rings. Some of the rest, again according to this new model, clumped together to form Saturn's inner satellites.
The new model passes the Occam's Razor test:
"..."The other theories have the rings forming from a sort of random event," Canup said. 'This model reduces the number of things that have to happen, which I think makes it more probable.'..."
"How on Earth do women walk in high heels? Seriously now . . . shouldn't they tip over?
"The answer is: Science.
"Lady Gaga's massive 10-inch tapered heels may be purely for show, rarely making an appearance outside of the artist's music videos. But three-inch or higher heels are hard for many people to understand -- even scientists.
" 'Many of my physicist colleagues have no trouble understanding quantum mechanics but can't figure out how women can wear high heels,' admitted Dr. Laura Grant, a physicist from Liverpool University...."
That equation? It comes after a description of how high heeled shoes are made.
"...Turns out, there's a formula for that. In 2004, researchers at the University of Surrey devised an equation that uses shoe size, the Pythagorean theorem, and several sociological variables to calculate how high heels can safely go: h = Q x(12+3s /8)
"Variables in the equation include aesthetic appeal of the shoe, experience in wearing high heels, how many months the shoe has been in style, and even the amount of alcohol consumed.
"Really...."
Okay: so there's an equation that describes, if somewhat subjectively, how people can stand, walk - and even dance - in heels. That still doesn't explain why anybody with a quorum of their marbles would wear the things.
Particularly considering the tradeoffs involved:
"...But wearing high heels requires more than balance. They demand sacrifice: Sacrifice in comfort. Sacrifice in practicality. Sacrifice in stability. Sacrifice in mobility. And in some cases, sacrifice in health, including knee, hip, feet, and back injury, as documented by WebMD.
"In other words, beauty is pain. Women don't wear heels because they are comfortable; they endure the pain because the tradeoff is looking really hot.
"Why all the health risks? Science can explain that too. Specifically, Newton's second law of motion, which states for every action there is always an equal and opposite reaction...."
The Lemming has lived in the American culture for the last half-century or so - I've learned that women are supposed to look better in high heels. It seems to have something to do with contraction of the calf muscle producing an illusion of greater length of the lower part of the leg.
Back in the late sixties and seventies, the Lemming thought women generally looked better in the 'before' pictures of those diet ads - and that's another topic.
Here's an insight that helps explain (part of) the situation:
"...'They have a way of making me feel better about myself,'" Dani Gooch, a high-heeled mother of two told FoxNews.com. 'In that sense, I feel more confident in them than I do in other shoes.'
"Exactly, said shoe designer Terry DeHavilland.
" 'People say they're bad for the feet, but they're good for the mind. What's more important?' "
That's - pardon the phrase - a no-brainer. For the Lemming, anyway. The mind's got priority over the feet. And is, in the Lemming's view, distinct from the brain. Yet another topic. "Mind" being distinct from "brain," that is. Not "brain" from "feet." Or, for that matter, feats. Which isn't the plural of foot: that's feet. Which is also a unit of measure.
On the other hand, "mens sana in corpore sano." (Satire X, Juvenal) The old 'healthy body in a healthy mind' thing. Or, rather, the other way around. Which is a pretty good place to start. And that's one more topic.
As to why some folks - quite a few, judging from sales figures - seem convinced that high heels don't make a woman look accident-prone, at risk for health problems, and wobbly to boot? That's a whole different topic - one more in the bailiwick of psychology or sociology than physics.
"Benoit Mandelbrot, the father of fractal geometry, has died at the age of 85, the AFP reports. The French-American mathematician discovered mathematical shapes called "fractals," and developed a geometry that was used to analyze naturally occurring shapes that were previously thought unmeasurable.
" 'Fractals are easy to explain, it's like a romanesco cauliflower, which is to say that each small part of it is exactly the same as the entire cauliflower itself,' Catherine Hill, a Gustave Roussy Institute statistician, told the AFP. 'It's a curve that reproduces itself to infinity. Every time you zoom in further, you find the same curve.'
"Fractals are said to be infinitely complex and can be found in things like clouds, snowflakes, and mountain ranges. Physics, geometry, and finance are a few of the many areas to which Mandelbrot applied the theory. According to an article in the U.K.'s Telegraph, Mandelbrot's book 'The Fractal Geometry of Nature' has sold more copies than any other book on advanced mathematics.
"Mandelbrot first started studying the concept while working as a research fellow at IBM in the 1950s, and it revolutionized the field...."
Fractal equations and computers' number-crunching capacity also brought mathematics and art together. That image displays a Mandelbrot set: created by Wolfgang Beyer with the program Ultra Fractal 3. (Beyer uploaded it to Wikimedia Commons - click the picture to see a larger version.)
At least, the Lemming thinks that's art - since it's got aesthetic appeal and was made with a human instrumentality.
There's more about Mandelbrot in the news:"Benoit Mandelbrot" Telegraph.co.uk (October 17, 2010)
"Benoit Mandelbrot, who died on October 14 aged 85, was largely responsible for developing the discipline of fractal geometry – the study of rough or fragmented geometric shapes or processes that have similar properties at all levels of magnification or across all times.
"Before Mandelbrot, mathematicians believed that most of the patterns of nature were far too complex, irregular, fragmented and amorphous to be described mathematically. Euclidian geometry was concerned with abstract perfection almost non-existent in the real world. Mandelbrot's achievement was to conceive and develop a way of describing mathematically the most amorphous natural forms – such as the shape of clouds, mountains, coastlines or trees – and measuring them. His work has become the foundation of Chaos theory – the mathematics of non-linear, dynamic systems.
"In the 1960s Mandelbrot, a research fellow with IBM, began a mathematical analysis of electronic 'noise' which was sometimes interfering with IBM electronic transmissions, causing errors. Although the nature of these errors was not understood, IBM scientists noted that the blips occurred in clusters; a period of no errors would be followed by a period with many.
"Examining these clusters, Mandelbrot noticed that they formed a pattern and that the closer they were examined, the more complex the pattern seemed to become...."
PCMag.com described Mandelbrot as a "French-American," but there's a little than that involved. As Telegraph.co.uk put it:
"...Benoit B Mandelbrot (he awarded himself a middle initial, although it stood for nothing) was born on November 20 1924 in Warsaw, Poland, into a family of Lithuanian Jewish extraction. His father made his living selling clothes while his mother was a doctor, but the family had a strong academic tradition and, as a boy, Mandelbrot was introduced to mathematics by two uncles...."
The Lemming thinks it'd be easier to say that Benoit B. Mandelbrot is from Earth, and leave it at that.
Aside from making nifty pictures, Mandelbrot's fractal math has helped solve problems - like figuring out why Earth didn't freeze, a couple billion years back. (June 6, 2010)
"Last month, astronomers announced the discovery of the first potentially habitable extrasolar planet. But this week at an International Astronomical Union meeting, doubts were raised about the existence of this exciting new planet said to be orbiting the star Gliese 581.
"Called Gliese 581g, the planet was determined to be about three times the mass of Earth, meaning it was a rocky world, not a gas giant like Jupiter.
"Rocky extrasolar planets have been found before, but the unique trait about this planet was that it orbited within the red dwarf star's habitable zone, that region of space where temperatures are sufficient for water to remain as a liquid on a planetary surface...."
Even without Gliese 581g, the Gliese planetary system is pretty exciting: with several known (and confirmed) planets in nearly-circular orbits, it's a fairly close match - on a small scale - of our Solar system.
The problem with Gliese 581g is that it's existence was found, based on some really, really, exact measurements. Or, rather, measurements of exact values - plus noise.
As the Space.com article puts it:
"...Francesco Pepe, an astronomer who works on HARPS data at the Geneva Observatory, said at the IAU meeting this week that his team could not confirm the existence of Gliese 581g.
"In e-mail correspondence with Astrobiology Magazine, Pepe said that they could not confirm the existence of planet 'f' either.
"The Geneva team, led by Michel Mayor, announced in 2009 the discovery of planet 'e' in the Gliese 581 solar system. At approximately 1.9 Earth masses, this 'e' planet is the lowest mass extrasolar planet yet found, and has a 3.15-day orbital period around the star.
" 'Since Mayor's announcement in 2009 of the lowest-mass planet Gliese 581e, we have gathered about 60 additional data points with the HARPS instrument for a total of 180 data points spanning 6.5 years of observations,' said Pepe. 'From these data, we easily recover the four previously announced planets b, c, d, and e.'
"However, he said they do not see any evidence for planet 'g,' the fifth planet in the system as announced by Vogt and his team.
" 'The reason for that is that, despite the extreme accuracy of the instrument and the many data points, the signal amplitude of this potential fifth planet is very low and basically at the level of the measurement noise, said Pepe...."
Pepe and company have a good point: the spectroscopic radial velocity measurements used to detect Gliese 581a's wobbles are measurements of very small values. There's going to be some uncertainty about the data.
Or, maybe, it's a case of 'Not Discovered Here,' a variation on the 'Not Invented Here' syndrome, where an organization denies the existence of anything its workers didn't develop.
The Lemming doesn't think so: this looks like the sort of double-checking (and triple-checking, and quadruple-checking, and so on) of data that's supposed to happen in scientific inquiry.
It's still something of a letdown.
Now, we wait to see if a third party comes up with a 'we found it,' using another method of analysis - or maybe new data.
"Have you ever noticed how the last bits of cereal in the bowl always seem to cling to one another, making it easy to spoon up the remaining stragglers? Physicists have -- and they've given it a name: the 'Cheerios effect.'
"This effect isn't exclusive to breakfast cereals, however. It also reveals itself in the way particles move in the air, pollen floats on the surface of water and galaxies cluster throughout the universe.
" 'If you put Cheerios in a bowl, they aggregate,' said Arshad Kudrolli, a physicist at Clark University in Worcester, Mass. 'Or if you look at foam floating on a beer, you get clumps. That's because of surface tension.'..."
It seems that pollen grains, Cheerios, and galaxies clump together in somewhat the same way. The forces involved are different at different scales - but the underlying math may be very similar.
And, worth studying.
Which is where these researchers come in. The Inside Science News Service article isn't too technical, and gives a pretty good overview of what the scientists are studying - and how they're doing it. A funnel is involved, by the way.
"...The design of the Cockpit and barrier construction consists of a building integrated into an acoustic barrier. The barrier runs alongside the A2 highway in the centre of Holland. The aim is to separate industrial and residential districts by muffling sound, while also producing an architectural construction that people can enjoy.
"The acoustic barrier and the Cockpit are designed with drivers in mind, allowing for a car to pass at a speed of 120km/h and guaranteeing a smooth appearance of the structure.
"The Cockpit houses a showroom and garage for luxury cars for Hessing Holding BV. It is positioned 15m from the side of the A2 highway. Drivers can view the cars as they pass by.
"The highway side is composed of a triangular system of glass elements..."
(from designbuild-network.com, used w/o permission) "The Cockpit houses a showroom and garage for luxury cars for Hessing Holding BV."
(from designbuild-network.com, used w/o permission) "The acoustic barrier runs alongside the A2 highway in Holland."
(from designbuild-network.com, used w/o permission) "Complex structures can be built and managed using simple engineering methods."
This is 'way beyond the sound-reflecting walls we see along urban Interstate in America. The Cockpit's design is, apparently, something really new: "...Non-Standard Architecture (NSA) realised on a large scale. The basic principle of NSA is that all compiled components are different...." The designbuild-network.com article mentions the new technology and programming that went into designing and building The Cockpit.
Manufacture of the structure involved something called a "point cloud system." If this catches on, it could be as faddish - and useful in some cases - as Fuller's geodesic domes. As the article said:
"...This shows that within a regular budget large complex structures can be built and managed using simple engineering methods."
The Cockpit was finished in November of 2005.
One thing that bothers me about the design is this sentence: "Drivers can view the cars as they pass by." They're going 120 kph. That's about 75 miles an hour - a sensible freeway speed in my part of the world. Provided that the drivers are watching the road and traffic.
I'm not entirely convinced that it's a good idea to encourage rubbernecking on a high-speed road.
Still, it's been almost five years since the thing was finished - and I haven't heard of any major accidents in central Holland.
"The infamous Mars hoax that widely circulated on the Internet since its first appearance in the summer of 2004 is rearing its head again. It comes in the form of an e-mail message titled "Mars Spectacular," originating from an unknown source.
"The Mars hoax e-mail has been passed on to countless others who haven't been able to resist forwarding it to their entire address book. In some cases, the message has been turned into a full-blown PowerPoint presentation, accompanied by snazzy-looking graphics seemingly providing a sense of authenticity to the message.
"The e-mail declares that on the night of Aug. 27, the planet Mars will come closer to Earth than it has in 60,000 years, thereby offering spectacular views of the Red Planet. The commentary even proclaims, with liberal use of exclamation marks, that Mars will appear as bright as (or as large as) the full moon...."
I think this recurring hoax depends of most folks:
Not being terribly interested in
Astronomy
Orbital mechanics
Math, particularly
Algebra
Geometry
Having short memories for anything that's not on their 'top priority' list
The psychological quirks that make scams work
Back to the Space.com article:
"...The problem is that 'Aug. 27' is actually Aug. 27, 2003. Mars made a historically close pass by Earth that night (34.6 million miles, or 55.7 million km). The Hubble Space Telescope used the opportunity to make some great images of Mars. But even then, to the naked eye Mars appeared as nothing more than an extremely bright yellowish-orange star, not at all like the full moon...." (Space.com)
The article tells you where to look for Mars in the sky - and assumes that you're in the northern hemisphere of Earth. If you live near or south of the equator, you're probably used to that sort of hemispheric parochialism by now.
Mars is bigger than our moon: Almost twice Luna's diameter.
It's also a whole lot farther away. A whole lot farther:
"...The average distance of the moon from Earth is 238,000 miles (382,900 km). For Mars to appear to loom as large as the moon does, it would have to be about twice the Moon's distance, or roughly 476,000 miles (766,000 km).
"In fact, this week the Red Planet is 198 million miles (318 million km) from Earth...." (Space.com)
Okay, let's review that.
To look as big as our moon, Mars would have to be
476,000 miles away from us
Today, Mars is about
198,000,000 miles away from us
Nope, Mars will not seem to be as big as the moon. Not even close.
"Earth-like exoplanets could announce their presence through trailing clumps of dust — and new observations of the Earth's own dust cloud could provide a way to find them. Over the course of five years, the Spitzer Space Telescope drifted through a diffuse but extensive ring of dust particles that orbit the sun in lockstep with the Earth, showing astronomers for the first time what the dusty signature of an exo-Earth might look like.
" 'For the first time we can measure the structure of that cloud along the Earth's orbit, using this moving space probe that travels through the cloud,' said astronomer William T. Reach of the Universities Space Research Association, the author of a paper to appear in the journal Icarus. 'We can use that as a key, as a template, to understand the dust around other stars.'..."
This isn't the zodiacal cloud, that pancake of dust that surrounds our sun, or isn't the entire cloud at any rate.
This ring of dust orbits with Earth, with the thickest concentration just behind our planet. Back to the article:
"...Most of the dust in the plane of the solar system, called the zodiacal cloud, will eventually spiral into the sun. But particles of the right size, tens of micrometers across, can feel a little gravitational push as they float by the Earth. That push counteracts the sun's pull just enough to hold the dust particles in a loose halo around the sun. The subtle interactions of the Earth and the dust grains' movements lead to the backward-facing clump...."
Using data from the Spitzer Space Telescope, researchers can make models of what dust rings of planets like Earth, orbiting other stars, might reasonably look like to out telescopes. This could be a useful tool in detecting "exo-Earths."
Or any other relatively small, rocky planet at about our distance from its star. Existing methods for finding exoplanets are pretty good at finding really big ones that are very close to their stars. The sort of world we're standing on - not so much.
This could lead to the discovery of many more planets - or, maybe, add evidence for the argument that the sort of planetary system we're in is rare.
"If you're a long-time reader, you may remember the great leftover Easter Peeps microwave experiment. Well, today we're going to be nuking leftover Valentine's Day chocolate to demonstrate one of the constants of physics, the speed of light. Chocolate makes a very appropriate medium, because the heating property of microwaves was first discovered by a scientist whose candy bar melted in his pocket when he got too close to a microwave device being tested for use in radar...."
The author tells what's involved in the physics, how to set up the microwave oven - and how to avoid "familial strife" over chocolate.
And (kudos!) tells where she found the information.
If you've heard of this before: I'm not surprised. As Ceceri says, "it can be found all over the Internet".
Bottom line? This looks like fun, it's educational - and you can eat the results. Not bad at all.
"Galaxies come in many shapes and sizes, but until recently astronomers have been at a loss to explain why.
"Now scientists have used dark matter theory to predict the menagerie of galaxies found in the universe. Their new model reproduces 13 billion years' worth of cosmic evolution, resulting in a surprisingly accurate tally of the different kinds of galaxies we see.
" 'We were completely astonished that our model predicted both the abundance and diversity of galaxy types so precisely,' said researcher Nick Devereux of Embry-Riddle University in Arizona...."
The article does a pretty good job of explaining the basics of how galaxies are sorted out by shape: and what the latest mathematical model is.
The bottom line:
"...Researchers created a new supercomputer model, based on observational data and the "Lambda Cold Dark Matter" theory of the universe. This theory suggests that about 72 percent of the cosmos is made of up a mysterious force called dark energy, while another 23 percent is composed of an invisible type of matter called dark matter. That leaves only 4 percent of the universe made of normal, visible matter, including all the stars and planets that we see...."
And, despite that "solved" in the headline, the scientists are still firmly connected to the space-time continuum:
"...'These new findings set a clear direction for future research,' Devereux said. 'Our goal now is to compare the model predictions with observations of more distant galaxies seen in images obtained with the Hubble [Space Telescope] and those of the soon-to-be-launched James Webb Space Telescope.'..."
Right now, it looks like dark matter, and dark energy, work very well as explanations for why the universe looks the way it does now. Not all that long ago, a substance called phlogiston was a pretty good explanation to explain why fire works the way it does. Then, in 1772, tests demonstrated that something called oxygen was involved. As it turns out, phlogiston doesn't exist.
But it worked for quite a while as an adequate model to explain combustion.
Dark Matter, Dark Energy, Galaxies, Mathematics and Observations
It's looking more and more like dark matter and dark energy really exist. Or, if they don't, that something that acts a whole lot like them does.
But: "Solved"? What we've got now is a better explanation - and one that can be tested.
"Just how Earth survived the process of its birth without suffering an early demise by falling into the sun has been something of a mystery to astronomers, but a new model has figured out what protected our planet when it was still a vulnerable, baby world.
"In short, temperature differences in the space around the sun, 4.6 billion years ago, caused Earth to migrate outward as much as gravity was trying to pull it inward, and so the fledgling world found equilibrium in what we now know to be a very habitable orbit.
"Planets like the Earth are thought to form from condensing clouds of gas and dust surrounding stars. The material in these disks gradually clumps together, eventually forming planetesimals – the asteroid-sized building blocks that eventually collide to form full-fledged planets.
So far, so good: that's pretty much what astronomers and planetary scientists have figured for some time now. There's just one catch to this established model, and it's a big one.
The math says that as planets form, they also migrate inside the disk of dust. Specifically, the math says they migrate towards the star. Then they fall in. According to the mathematical models.
Obviously, since I've written this post, and you're reading it, there's something wrong with this picture. Earth is rather definitely here, philosophy 101 freshman-baiting notwithstanding.
Or, as one of the astronomers put it:
"...'Well, this contradicts basic observational evidence, like We. Are. Here,' said astronomer Moredecai-Mark Mac Low of the American Museum of Natural History in New York...."
The existing mathematical models didn't take temperature differences within the dust disk into account. Turns out, the disk is opaque - and quite a bit hotter near the star. Factor that into the equations, and you don't have Earth falling into the sun a bit over 4,000,000,000 years back.
The new mathematical models predict that planets are pulled in - just like in the earlier models - and that temperature differences push them away from the star. Each planet, again in the newer model, reaches an equilibrium point where its orbit stays stable - and eventually the dust dissipates.
Wait a few billion years, and you've got trilobites, dinosaurs - and us.
Since the model that Mac Low and his colleagues came up with doesn't have Earth plunging into the sun long before life got started, it would seem that it's a closer match with reality than previous ones.
Particularly since it's becoming quite obvious that stars with planets orbiting them aren't anywhere near the 'chicken teeth' rarities they were supposed to be, not all that many decades back. (But aren't as common as they might be, either - More about that, tomorrow morning.)
Exciting times, these that we live in.Related posts, at
"Buckminster Fuller's geodesic domes have reached new heights: as tree houses for the rich and famous. Arboreal architect Dustin Feider is installing them all over the Los Angeles area. Producer and writer Mark Levin has two in his backyard. The LA County Museum of Art has exhibited one. And the nest shown here belongs to Doors guitarist Robby Kreiger...."
(from Brent Humphreys, via Wired Magazine, used w/o permission)
Looks like the geodesic dome is cool again. I remember, back in the sixties, if memory serves, when dome homes were going to be the Next Big Thing in domestic architecture. There's one northeast of the small central Minnesota town I live in, and another off the Interstate between here and Fargo, North Dakota.
After being a prominent feature in 'house of the future' articles and science fiction stories, people noticed something about dome homes. Cool as a geodesic dome looks, and efficient as it is in encompassing a given volume with the least materials, that round shape is hard to divide into rooms. Rooms that people can use easily, anyway.
For applications like radomes, auditoriums, railroad roundhouses, and other buildings where you want a building that's essentially one huge room: geodesic domes are great. And, as Disney World Florida demonstrated: they look really cool.
I think the elite of Los Angeles have found a splendid new way to use Buckminster Fuller's geodesic dome. The spherical shape and recurring angles are, I think, a fine aesthetic match for the shape of many urban trees.
And, as usual with a design using Fuller's geoids, they look cool.
"1790: Mathematician, astronomer and physicist August Ferdinand Möbius is born in Schulpforta, Saxony (in modern-day Germany).
"Möbius has name recognition today because of the Möbius strip, which is a clever topological surface with only one side and only one edge.
"Speaking of name recognition, Möbius probably pronounced the name something like MER-bee-oos (first syllable rhymes with her, but with the r barely spoken). Webster's New World College Dictionary recommends pronouncing it MAY-bee-us or MOE-bee-us. But you often hear MEE-bee-us, and you sometimes see the alternate spelling Moebius.
"As for the Möbius strip (or Möbius band), many budding young topologists have discovered that it's possible to create one of these seemingly impossible objects with nothing more than..."
The Möbius strip may actually be the Listing strip. Another topologist, Johann Benedict Listing. This Wired article has a truly painful play on words, involving the lesser-known topologist's name. See if you can spot it.
The article itself is mostly about August Ferdinand Möbius, who was born on this day in 1790. And, of course, his famous one-sided band.
Which really does have one side and one edge. Putting one together, following the (really simple) instructions in the Wired article, you can try drawing a line down the center of just one side of the paper strip. The results are a bit counter-intuitive.
(Then, try cutting Möbius strips in two, lengthwise: first, by cutting it down the middle of the strip; then, with a fresh strip, cutting it lengthwise, about a third of the way in from one side.)
Moving along:
Somewhere in the sixties or seventies, I ran into a bit of verse that went something like this:
A mathematician named Klein
Thought the Moebius strip was divine.
Said he: "If you glue
The edges of two
You'll get a weird bottle like mine!" (John Baez[!], This Week's Finds in Mathematical Physics (Week 155), Department of Mathematics, University of California, Riverside (August 16, 2000))
Several places sell what they call Klein bottles - or Klein-somethings:
Acme Klein Bottle
Widest selection of the lot, including a Klein Stein
4Physics Store
With an explanation of the bottle's (inaccurate) name
Actually, those products are models of Klein bottles (properly, Klein surfaces), projected onto the three spatial dimensions we're familiar with. Just like that picture of a Möbius strip isn't a Möbius strip, but a projection of one onto the two spatial dimensions of the picture.
This post is getting dangerously close to being 'educational.'
bothmer, YouTube (November 8, 2006)
video, 1:23 (no sound)
"The Klein Bottle is a surface on which you can move from outside to inside without crossing an edge. This shows that inside and outside are not universal concepts.
"In this movie Klein's Bottle is constructed by gluing an rectangle along the edges. Then the bottle is cut up again to yield a Moebius-strip.
This is one of the best visual presentations of a Klein surface I've seen. What's missing is an explanation of what's happening, when the cylinder seems to go through itself.
The "Klein bottles" we have are projections into three-dimensional space of an object that needs four spatial dimensions. The Klein surface doesn't got through itself, any more than the Möbius strip does - although it seems to, on the two dimensions of that picture.
Here's another video of a rotating (projection of a) Klein bottle: in Christmas colors, yet. It's 'squishier' than most. And, again, silent.
wh8191, YouTube (September 27, 2008)
video, 1:21 (no sound)
"Rotating Klein bottle, rendered in POV-Ray"
A reasonable question is "are Möbius strips and Klein bottles real?" The answer is yes and no.
Yes, we can make models of them. It's quite easy in the case of the Möbius strip - and fairly straightforward for Klein bottles, as long as we accept the fact that we live in three spatial dimensions.
No, Möbius strips and Klein bottles aren't "real" in the sense that there's a perfect Möbius strip and an ideal Klein bottle somewhere. Unless Plato was right about that sort of thing. In the case of the Klein bottle (properly, Klein surface), even if there was a "real" one, we could only see a projection of it onto the three-dimensional space we live in.
Both the Möbius strip and Klein bottle are mathematical models.
"Four spatial dimensions?!" It's possible to make mathematical models of objects in four dimensions, just like we do for three- and two-dimensional objects. A sort of Topology 101 explanation is this:
Take a point. Move it. You've got a line that has one spatial dimension. a point on the line can move either one way or the other, in one dimension.
Take the line. Move it at right angles to the one dimension of the line. You've got a surface. A point on the surface can move in either - or both - of the two dimensions.
Take the surface. Move it in a direction that's at right angles to both of the surface's dimensions. You've got a volume. (Or, a surface three-dimensions?!) A point in this volume can move in any - or all - of the three dimensions.
Take the volume. Move it in a direction that's at right angles to all of the three dimensions (yes, it's possible - for a mathematical model). You've got a (volume with four dimensions). A point in this (volume with four dimensions) can move in any - or all - of the four dimensions.
This fourth spatial dimension may or may not reflect something in the physical world. It's not the same thing as time - although quite a number of entertaining stories have been written which assume that to be so - but time can be considered as a "fourth dimension" - as Einstein did, about a century back now.
"NASA has long followed the water and chemical building blocks of life in the course of space exploration. But most computer simulations that help scientists understand how planetary systems form usually overlooked the chemistry of planets, at least until now.
"A new study has looked for the first time at the dynamics and chemistry of how Earth-like planets form. The approach shows how rocky planets form from the manic swirl of gas and dust in the early planetary systems, and also what chemical building blocks existed in the planets that emerged from the chaos.
'If we're looking for Earth-like planets, it'd be nice to know the chemistry we're after,' said Jade Bond, a planetary scientist at the University of Arizona in Tucson and a lead author on the study.
"Such a first step has only assessed the chemistry of Earth's solar system, and still needs testing across more dynamical models...."
Well, it's a start. A few philosophy 101 students notwithstanding, we know that Earth exists and that there's life here. It makes sense to start making a model, by starting with the one place we know supports life.
"...Scientists have found that certain temperature profiles reliably match certain chemical profiles, after studying material from meteorites that fell to Earth. Some meteorites still hold the chemical profiles of the early solar system, and can serve as useful real life comparisons for simulations.
"Model results showed that Earth and other rocky planets in the solar system formed 'wet,' with perhaps enough water to sustain life. But important elements such as nitrogen and carbon did not accumulate during simulated planet formation, which suggests that they needed to arrive by other means to kick start the development of life on Earth...."
Which means there's still quite a bit to learn. Which, in turn, means that this should be an exciting field, at least until what's unknown now becomes known. By which time we'll have discovered more facets of reality that we didn't know existed - and know very little about.
Exciting.
The article does a pretty good job of explaining what the researchers are trying to do - and how it ties in with the fast-growing list of exoplanets that have been spotted.
"Next time you're stuck on the moon and running out of oxygen, you'd better run, not walk, back to your lunar module — especially if you're wearing a space suit.
"Scientists say those giant, bulky suits actually make running easier and walking more difficult on the moon. By combing through video and audio recordings from Apollo moonwalks, researchers have devised a mathematical method to explain how space suits affected lunar gait during the Apollo missions, and how future space suits might change the way we get around on Mars.
"'Space suits are effectively reducing the gravity level by supporting part of the weight of everything that's being transported,' said space physiology researcher Christopher Carr of the Massachusetts Institute of Technology, who co-authored the paper published Wednesday in the journal PLoS ONE. 'When you're out there, it's like wearing a backpack with a bunch of helium balloons attached to it.'..."
Things are different on the Moon. This Wired article is a pretty good overview of what's involved in dealing with 1/6 the force of gravity - in a space suit - with a heavy backpack that acts like it's attached to helium balloons.
Although I'm sure it's important to work out equations for deciding when to stop walking and when to start running on the Moon and, eventually, on Mars: I've got a notion that people 'on the ground' there would be able to figure it out on their own. My guess is that working out the math will be useful for equipment design.
"During this scene from the Apollo 16 mission, astronaut Charles Duke drops a hammer on the lunar surface and has a tough time picking it up. To overcome the self-support of the space suit, he has to jump repeatedly in order to compress the suit's knee joint and pick up the hammer."I wrote another micro-review of this article for another post:
"The power of computer processing could one day solve the riddle of life's origin.
"Scientists think life appeared about 4 billion years ago, and ancient rocks on Earth can give us some idea of what the environment was like. Life may have originated in an ocean rich in chemicals. This primordial soup may have been simmering, or it may have been zapped by lightning. Certainly energy of some sort must have helped drive a simple chemical system into a more complex state. But the clues are few, and the picture remains hazy.
"Enter the Evogrid, a computer creation concept that would be a digital version of the primordial soup. The EvoGrid was dreamed up by a group of international advisors and Bruce Damer, the founder of a research company that creates 3-D spacecraft and mission simulations for NASA and the space community. Damer and his chief architect, Peter Newman, are developing the EvoGrid concept by adapting GROMACS, a powerful open source molecular dynamics simulator originally developed at The University of Groningen in the Netherlands...."
The article gives a pretty good overview of current informed speculations about how life may have started on Earth, and how Evogrid, software using distributive computing, would simulate today's models in a virtual 'primordial soup.'
Even with a million computers working on the simulation, the software's simulated ocean may mimic chemical reactions much more slowly than they work in the real world. Even so, I think this looks like a good way of testing mathematical models of how complex molecules may have combined to form the basic machinery for life.For what it's worth, posts from another blog:
"ALMOST 20 years of painstaking intergalactic measuring using pulsating stars to calculate the age of the universe has brought a $US500,000 ($630,000) payoff for three astronomers, including Australian Jeremy Mould.
"Professor Mould, 59, of Melbourne University, is set to receive about $200,000 after he and two colleagues in the US and Britain were awarded the US-based Gruber Foundation's cosmology prize.
"The award recognises their work in discovering one of the most important numbers in astronomy - the rate at which the universe is expanding.
"Using data from the Hubble telescope, which was sent into orbit in 1990, the astronomers discovered over a period of 10 years almost 800 pulsating stars, known as Cepheid variables...."
If you're still reading this post, you're one of those people who really care that the universe is roughly 13,700,000,000 years old, and whether or not it's rate of expansion is increasing, decreasing, or staying the same.
None of which will help you find minestrone soup at the grocery, or which brand of toothpaste is best.
This article is a good overview of what the three scientists found, and what some current thoughts on what dark matter is and how it works.
I understand that dark matter is a viable way of explaining what astronomers have observed, now that we've been able to make more precise measurements of some features in the universe. And, the dark matter and dark energy models may reflect something that's real.
On the other hand, I remember phlogiston. There may be better models, which more accurately reflect the underlying reality.
Whether you call it trafficking in persons, human trafficking, or slavery, buying and selling people isn't nice. And, in quite a few cou...
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Actually, some of yesterday's news may be here. Or maybe last week's. The software and science stuff might still be interesting, though. Or not. The Lemming thinks it's interesting: Your experience may vary.
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