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Gifts from the sixth dimension
A clear 3-inch cube contains a Calabi-Yau manifold, the 3-D cross-section of a 6-D space.

String theorists say we may live in a 10-dimensional universe, with six of those dimensions rolled up so tightly that we can never see them. So how can you possibly visualize six-dimensional space? This year's top gift for science geeks can help.

The 2009 geek-gift competition resulted in a repeat (geek-peat?) of last year's outcome: Andrew Meeusen of Mesa, Ariz., received the most votes once again, this time for suggesting the Calabi-Yau manifold crystal.

Bathsheba Grossman creates the crystals from glass and offers them on her Web site for $72. They're also available for $89.95 from Edmund Scientific.

So... what the heck is a Calabi-Yau manifold?

That's where extradimensional physics enters the picture: As string-theory fans know all too well, there are inconsistencies between small-scale and large-scale physics that could best be resolved if the universe as we know it has 10 dimensions, including time and the three spatial dimensions with which we're familiar.

So what's up with the other six dimensions? Theorists would say we're just not built to perceive those dimensions, perhaps because they folded down to sub-sub-submicroscopic size as the universe took shape. A couple of mathematicians named Eugenio Calabi and Shing-Tung Yau worked out the geometry for how such folded-up extradimensional spaces might behave, and that's how Calabi-Yau manifolds got their name.

What's captured in Grossman's crystals is a three-dimensional cross-section of a six-dimensional space. Theorists say that every point in our 3-D world (well, 4-D if you count time) incorporates six additional curled-up dimensions, as shown in this animated visualization. To get a better grasp on the concept, watch this segment from the "Nova" documentary series based on Brian Greene's "The Elegant Universe." (And check out my 2007 interview with Greene.)

You could say that at the most fundamental level, our universe is built up from myriads upon myriads of Calabi-Yau manifolds. If the crystals seem beautiful (and they do), that may reflect our appreciation of the deep (and deeply weird) geometry of the cosmos.

Here are a few alternative gift ideas for entering the extradimensional universe:

To reward such a smashing suggestion, Meeusen will be getting a signed copy of my newly published book, "The Case for Pluto." I'm gratified to see the positive reviews that the book has received, including the latest links from Samizdata, Instapundit and ScienceBlogs' Dynamics of Cats. Check "The Case for Pluto" Web site for ordering information and upcoming tour stops (including a soon-to-be-scheduled talk by my Second Life avatar, Boole Allen).

Because I want to spread the wealth, I'll be sending another copy of "The Case for Pluto" to the runner-up in the geek-gift contest, Buddha Dude, who suggested the Star Wars Force Trainer. The SWFT is one of the first toys to capitalize on brainwave training, and it's available from a wide array of retailers.

If you're not that taken with the "Star Wars" branding, there's another game called Mindflex Brainwave that is based on the same principle. Gizmodo's Sean Fallon gave the game a "meh" review. "Mindflex seems like something you would whip out at a party to impress your friends until everyone got a headache and stopped after 30 minutes," he wrote. But just knowing that such games exist make my brain smile.

For more geek-gift ideas, make sure you review the earlier stages of this year's contest (the initial suggestions as well as the finalists). Then move on to our Tech Holiday Gift Guide. If you still need more hints after all that, check out these links:

Join the Cosmic Log team by signing up as my Facebook friend or following b0yle on Twitter. And pick up a copy of my new book, "The Case for Pluto." If you're partial to the planetary underdogs, you'll be pleased to know that I've set up a Facebook fan page for "The Case for Pluto."