Sunday, December 31, 2006

A criminal's head is a manifold

Stupid is as stupid does. This is like a scene from A Clockwork Orange. It seems this Muslim holiday of Eid al-Adha includes sacrificing animals in remembrance of God providing to Abraham a ram when Abe was ready to offer his son. (Funny, the article reads, “a ritual commemorating the biblical account of God's provision of a ram.” Do you think they reference it out of the Bible? Oh yeah, that’s that old book that is only partially true, at least according to them.) It further seems these folks are ok on the concept of animal sacrifice, but not the reality.

“In Turkey, at least 1,179 people - dubbed "amateur butchers" by the Turkish media - were treated at hospitals across the country, most suffering cuts to their hands and legs.

“Four people were severely injured when they were crushed under the weight of large animals that fell on top of them, it was reported. Another person was hurt when a crane, used to lift an animal, tumbled onto him.

“Three people suffered heart attacks and died while trying to restrain animals, private CNN-Turk television reported.

“Two bulls escaped and caused havoc in the streets of the central Turkish city of Kayseri and in the south-eastern province of Sanliurfa, until they were caught with the help of veterinarians who fired tranquilliser darts.”

Who’s the animals?

Some people give criminals a bad name. This idiot carjacks a GMC Envoy. Can’t just find a vehicle driven by some effeminate boy that works in a florist shop making arrangements all day. No. Our criminal jacks a vehicle with five people in it. OK. Maybe has some mojo percolating inside that southern mud flap. Even busted the driver’s window and dragged the driver out. And then started punching the passengers until they left. Dufus carjacker hit a couple of vehicles on his joyride, and then wound up in another town. Actually, so far so good. Not a bad roll. But then it fell apart.

Seems the oxycontin or crack or whatever he was on began to wear off. And then his loserness began to shine through.

The pussy called the cops. Said, "Um, I committed a crime," then "I stole a vehicle."

When the dispatcher asked for his name, King allegedy said, "I'd rather do this: Could you just send the police over here?" The dispatcher then asked where the stolen car was located, to which King replied, "I couldn't even tell you. I don't even know where I'm at." He then sat on the curb next to the SUV waiting for the cops to arrive.

These girls from the hood don’t know nothing. Amazing. Never ever end a sentence in a preposition.

Here’s some fun facts about shoplifting. Total annual cost of theft from retail stores: $33.21 billion. Inventory loss ranges from 0.7% to 2.2% of gross sales with the average falling around 1.7% (but that’s only one-third of the total inventory shrinkage – so it seems stockboys steal or trash twice as much as the thieves do). Shoplifting occurs 330 - 440 million times per year. And that ain’t counting grocery-store purse-snatching pussies.

Nothing short of wow. Dumb Fluckes parks in front of Wal-Mart amongst forty (40) marked police cruisers. Forty. Each car formally held two (2) cops. That would be eighty (80) cops in total. All in uniform, and milling about the store for some kind of charity event. Seems Mr. Dumb Fluckes did his shopping and then goes to the cashier. Mr. Dumb Fluckes presented a check for payment. A stolen check in the amount of $848.00 . Well, not exactly a stolen check. A copy of a stole check. And not a good copy. Busted.

"He has to be an idiot," Lt. David G. Marker said. Well put, officer.

Did you know that the Poincaré Conjecture has a complete solution? Here’s the conjecture as written in 1904: Consider a compact 3-dimensional manifold V without boundary. Is it possible that the fundamental group of V could be trivial, even though V is not homeomorphic to the 3-dimensional sphere? More modern formulation: Every simply connected compact 3-manifold (without boundary) is homeomorphic to a 3-sphere. We on the same page now? No? Try this: In three dimensions you cannot transform a donut shape into a sphere without ripping it, although any shape without a hole can be stretched or shrunk into a sphere.

This guy, Henri Poincaré, was working on the foundations of topology. It’s interesting stuff. Three-dimensional bodies, the manifolds and spheres discussed above – like the human body – have two-dimensional surfaces. Topology studies two-dimensional bodies. They call it rubber-sheet geometry. You can’t do rips or sews in the analysis.

In topography, there is no difference between a bagel and a coffee cup with a handle. Each has a single hole and can be manipulated to resemble the other without being torn or cut. Poincaré used the term “manifold” to describe such an abstract topological space. The simplest possible two-dimensional manifold is the surface of a soccer ball, which, to a topologist, is a sphere—even when it is stomped on, stretched, or crumpled. The proof that an object is a so-called two-sphere, since it can take on any number of shapes, is that it is “simply connected,” meaning that no holes puncture it. Unlike a soccer ball, a bagel is not a true sphere. If you tie a slipknot around a soccer ball, you can easily pull the slipknot closed by sliding it along the surface of the ball. But if you tie a slipknot around a bagel through the hole in its middle you cannot pull the slipknot closed without tearing the bagel.

Poincaré proposed that all closed, simply connected, three-dimensional manifolds—those which lack holes and are of finite extent—were spheres. The conjecture is important for scientists studying the largest known three-dimensional manifold: the universe.

Seems straight forward. The problem has been that all previous calcs has dead-ended in singularities – and that’s a pinch not appropriate in a sphere. So this Russian, Grisha Perelman, lays out a proof in three pieces (one, two, and three). He modified the Ricci Flow to get around this problem.

OK. Sorry. But I thought it was pretty cool to think of topography as rubber-sheet geometry. Here is a final link that works through Perelman’s stuff.

Enough. Happy New Year.

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