Thursday, October 28, 2010

Extra-Dimensional Geometry

A direct link to the above video is at

Last week, in Thinking Bigger, we talked about how difficult it is for our monkey brains to visualize extra dimensions. On that same topic, the above video accompanies Our Universe as a Dodecahedron, a blog entry published in May of this year, and it explores something called the Poincaré Dodecahedral Space: a proposed underlying structure to our universe. I'm fascinated to read the comments for this one at YouTube - this video triggered some strong debate from people with both scientific and spiritual viewpoints.

Here's another image from theories about the geometry of extra dimensions which we've talked about before: the ten-dimensional Calabi-Yau manifold.

Michael Brooks, in his CultureLab blog for New Scientist, recently wrote about a new book by one of the co-discoverers of the above manifold: Shing-Tung Yau (the book is written in collaboration with Steve Nadis). Here's a few paragraphs from what Mr. Brooks had to say about "The Shape of Inner Space":

In case you're wondering, the geometric form known as a Calabi-Yau space (seen above) exists in multiple dimensions and is the pedestal on which string theory has been built. And in case you want to know more than that, one of the inventors (discoverers?) of the Calabi-Yau space, the geometer Shing-Tung Yau, has written a book that explains it all in exquisite detail.

The Shape of Inner Space is a hymn to geometry. Without geometry, Yau points out, we cannot account for the forces of nature. Einstein's general theory of relativity is, essentially, nothing but geometry. Yet geometry is the poor relation of modern science.

Yau is aiming to put that right. "I would go so far as to say that geometry not only deserves a place at the table alongside physics and cosmology, but in many ways it is the table," he writes.

Earlier this month, in Global Coherence, we talked about how the hard determinist viewpoint seems to be at odds with my approach to visualizing the extra dimensions. A youtube user calling themselves Der3k7r summed the viewpoint up quite nicely:
Free will is an illusion. Say a person can make a "choice". Whatever that choice may be, they would have always chosen that path because of given circumstances and how they are. Whether it be seemingly insignificant as deciding to scratch your nose, or significant like choosing a spouse.
I responded:
If that's what you believe then you're entitled to your belief. The conclusion you've reached is very much part of what the twentieth-century scientific community trained people into believing: that we are insignificant, meaningless cogs in a predetermined machine that will run down until a hopeless future of maximum entropy for our universe.
You may be surprised to hear me say that part of the hard determinist viewpoint does have a certain resonance for me: but I think it's a mistake to say that we don't have free will. As we've seen in the above explorations, there is ultimately a timeless perspective where everything becomes "just geometry" within the extra dimensions, and within that realm of timelessness it really is accurate to say that "everything that can happen has already happened". But down here in spacetime, we are each constantly navigating within that geometry, and our choice, chance, and the actions of others all contribute to cause us to be selecting one reality over another in a winding path that I would say is definitely not predetermined.

So enjoy the journey!

Rob Bryanton

Next: Just Geometry

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