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Book Hangover

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Thursday, July 29, 2010

The Symmetries of Things

Human have used symmetrical patterns for thousands of years in both functional and decorative ways. Now, a new book by three mathematicians offers both math experts and enthusiasts a new way to understand symmetry and a fresh way to see the world. In The Symmetries of Things, eminent Princeton mathematician John H. Conway teams up with Chaim Goodman-Strauss of the University of Arkansas and Heidi Burgiel of Bridgewater State College to present a comprehensive mathematical theory of symmetry in a richly illustrated volume. The book is designed to speak to those with an interest in math, artists, working mathematicians and researchers.

“Symmetry and pattern are fundamentally human preoccupations in the same way that language and rhythm are. Any culture that is making anything has ornament and is preoccupied with this visual rhythm,” Goodman-Strauss said. “There are actually Neolithic examples of many of these patterns. The fish-scale pattern, for example, is 22,000 years old and shows up all over the world in all kinds of contexts.” Symmetrical objects and patterns are everywhere. In nature, there are flowers composed of repeating shapes that rotate around a central point. Architects trim buildings with friezes that repeat design elements over and over. Mathematicians, according to Goodman-Strauss, are latecomers to the human fascination with pattern. While mathematicians bring their own particular concerns, “we’re also able to say things that other people might not be able to say. “The symmetries of Things contribute a new system of notation or descriptive categories for symmetrical patterns and a host of new proofs. The first section of the book is written to be accessible to a general reader with interest in the subject. Sections two and three are aimed at mathematicians and experts in the field. The entire book, Goodman-Strauss said, “is meant to be engaging and reveal itself visually as well.” 

Book Information:

Authors: John Horton Conway, Heidi Burgiel, Chaim Goodman- Strauss
Publisher: A K Peters Ltd
Keywords: things, symmetries
Number of Pages: 448
Published: 2008-05-02
List price: $75.00
ISBN-10: 1568812205
ISBN-13: 9781568812205

EBook link here.

Thursday, July 22, 2010

Some Excellent Snaps ...

The photographs collected by NAINA KAUR and posted by me. I just captured the snaps on behalf of NAINA KAUR for her excellent collections.

Saturday, July 17, 2010

How Big is Infinity?

Most of us are familiar with the infinity symbol – the one that looks like the number eight tipped over on its side. The infinite sometimes crops up in everyday speech as a superlative form of the word many. But how many is infinitely many? How far away is “from here to infinity”? How big is infinity?

You can’t count to infinity. Yet we are comfortable with the idea that there are infinitely many numbers to count with: no matter how big a number you might come up with, someone else can come up with a bigger one: that number plus one – or plus two, or times two. Or times itself. There simply is no biggest number. Is there?

Is infinity a number? Is there anything bigger than infinity? How about infinity plus one? What’s infinity plus infinity? What about infinity times infinity? Children, to whom the concept of infinity is brand new, pose questions like this and don’t seem to have very much bearing on daily life, so their unsatisfactory answers don’t seem to be a matter of concern.

At the turn of the century, in Germany, the Russian – born mathematician George Cantor applied the tools of mathematical rigor and logical deduction to questions about infinity in search of satisfactory answers. His conclusions are paradoxical to our everyday experience, yet they are mathematically sound. The world of our everyday experience is finite. We can’t exactly say where the boundary line is, but beyond the finite, in the realm of the transfinite, things are different.

Saturday, July 10, 2010

Mathematics of DNA

Why is DNA packed into twisted, knotted shapes? What does this knotted structure have to do with? How DNA functions? How does DNA ‘undo’ these complicated knots to transform itself into different structures? The mathematical theory of knots, links and tangles is helping to find answers.

 In order to perform such functions as replication and information transmission, DNA must transform itself from one form of knotting or coiling into another. The agents for these transformations are enzymes. Enzymes maintain the proper geometry and topology during the transformation and also ‘cut’ the DNA strands and recombine the loose ends. Mathematics can be used to model these complicated processes.

The description and quantization of the three-dimensional structure of DNA and the changes in DNA structure due to the action of these enzymes have required the serious use of geometry and topology. This use of mathematics as an analytical tool is especially important because there is no experimental way to observe the dynamics of enzymatic action directly.

A key mathematical challenge is to deduce the enzyme mechanism from observing the changes the enzymes bring about in the geometry and topology of the DNA. This requires the construction of mathematical models for enzyme action and the use of these models for enzyme action and the use of these models to analyze the results of topological enzymology experiments. The entangled form of the product DNA knots and links contains information about the enzymes that made them.

Friday, July 2, 2010

Martian moon mystery

The Martian moon Phobos is cratered, lumpy and about 16.8 miles long. According to a study, the moon is also unusually light. Planetary scientists found that Phobos is probably not a solid object, and that as much as 30 percent of the moon’s interior may be empty space.

That doesn’t mean that Phobos is an empty shell where we could, say, set up a rest stop for spaceships on their way to the outer planets. But the new finding probably does mean that Phobos was not an asteroid that got caught in Mars’ gravity as it floated by the planet.

Phobos is the larger of Mars’ two moons, and astronomers have had many ideas about where it came from. Previous studies have suggested that Phobos was an asteroid. Other studies suggest the moon formed from bits of Martian rock that were sent into space after a giant object, like an asteroid, crashed in Mars. The new study suggests that neither of these ideas is completely correct. The truth might be some combination of the two.

Scientists may never know how Phobos came to be a Martian satellite, but the new study may help eliminate some possibilities. A planetary geophysicist is a scientist who studies physical properties, such as rocks and appearance, to understand more about celestial bodies such as planets and moons.

The Mars Express, a spacecraft that orbits Mars and takes measurements. That spacecraft left Earth in 2003 and is a project by the European Space Agency. In March, Mars Express flew closer to Phobos than any spacecraft ever had before, ESA reports.

The scientists wanted to learn the density of Phobos. Density measures how close together, on average, are the atoms in an object. If two objects are the same size but have different densities, the denser object will have more mass — which means it will feel heavier when you’re holding it on Earth. Density is found by dividing mass by volume. Since the scientists already had a good idea of the volume of Phobos, they just had to find its mass in order to figure out its density.

They made their mass measurements by studying the gravitational force of Phobos. Gravity is an attractive force, which means anything with mass attracts anything else with mass. The more mass an object has, the stronger its gravitational force. Since a large body like the Earth has a lot of mass, it has a strong gravitational force.

When Mars Express flew close to Phobos, the small moon’s gravity attracted the spacecraft. By studying changes in the motion of Mars Express, the scientists were able to estimate the gravitational tug of Phobos. Once they knew the strength of its gravity, they could find its mass.

They found that Phobos has a density of about 1.87 grams per cubic centimeter. The rocks in the crust of Mars, for comparison, are much denser: about 3 grams per cubic centimeter. This difference suggests that Phobos is not made of rocks from the surface of Mars.

Some asteroids have densities of about 1.87 grams per cubic centimeter, but those asteroids would be broken apart by Mars’ gravity — a fact that probably rules out the possibility that Phobos was once a free-floating asteroid.

Some scientists don’t mind giving up the idea that Phobos was once an asteroid. Finally we’re drifting away from the idea that the Martian moons are captured asteroids. We happy to see that Phobos and Deimos [Mars’ other moon] are getting a lot of attention these days.