Sunday, August 29, 2010


In 1884, Edwin Abbott Abbott (that is not a typo, two b’s, two t’s and two Abbott’s!)  wrote a charming little book called Flatland:  A Romance of Many Dimensions.  Abbott cleverly intertwines seemingly dissimilar themes of social justice, resistance to new ideas,  geometry, and how we understand physical reality.  Flatland is occupied by two dimensional shapes--triangles, squares, etc.--that are constrained to skitter around in an entirely flat world. Flatlanders can move front to back, or left to right, or on a diagonal, but not up and down.  Think of sliding checkers over a game board, without lifting them, and you’ll have the right idea. (No jumping and no kings allowed here!)

However, there  is a third dimension even if the Flatlanders don’t know  it, and eventually, Flatland is visited by a sphere from a three dimensional place called Spaceland. The sphere descends into Flatland, appearing to our two dimensional friends as a circle of changing size that mysteriously materializes out of nowhere.  Because the sphere can move in all three dimensions it can pop in and out of Flatland. The Flatlanders have no framework for understanding this  inexplicible movement;  the sphere seems to be a supernatural being.

This really intrigues me. Most of us, most of the time, are like those Flatlanders.  Our thinking is very strongly constrained by our direct perceptions and  experiences.   Not many people venture far from these familiar boundaries.  Those that do are unusually creative people- some writers, some artists, and some scientists. 

Say what? Scientists?

Yes, scientists.  As a scientist, I know that lots of people think that science is boring, dry and difficult.  Not so.  (Scientists might be.  You’d have to ask the spouses and friends of some scientists.)   Before I go on, let me distinguish science from science, a distinction analogous to that between a best-selling novel and great literature.  Science is very interesting and important - it is what improves medications, creates new materials for solar or electronic applications,  identifies new species and so on.  In fact, there is much more science done than science; but it is  science that develops the grand ideas and understanding of our universe.

Science includes evolution, quantum mechanics, general relativity, atomic theory and so on.  The really big ideas.  Science tends to remain within the parameters of direct experience, but science requires a scientist to step back and imagine what isn’t there- possibilities that not only fall outside our knowledge, but that sometimes contradict it. 

This afternoon I was reading the current issue of Scientific American and saw a news brief about some new work on a science problem that has been around a while, specifically joining the physics that describe the teeny-weeny subatomic world with the physics that explain the ginormous cosmos.   Physicists can explain both the very small and the very large, but the two theories are not consistent with each other.  Very briefly, some recent work suggests that if we use a strange type of mathematics, things might work out and a ‘theory of everything’ could emerge.  This mathematics uses eight dimensional numbers called octonions that violate many of our usual rules of arithmetic. 

I don’t want to get bogged down in detail here (would that be blogged down in detail?).   Like the Flatlanders whose ability to understand reality was shaped by their direct experience with their two dimensional world, our thinking tends to be constrained by our three dimensional world.  It appears that to really understand our physical universe, we may need to embrace a multi-dimensional mathematics that is not only different and strange, but actually contradicts our current understanding.  (Don’t worry, it won’t affect how we do our tax forms, budgets or even calculus.)  

It is probably impossible to develop a true understanding of anything from within.  Someone needs to conceive of what lies beyond the boundaries, one of those very rare individuals with the kind of brilliant and creative mind that can imagine far beyond direct experience.

Just a thought.

Today I am grateful for the times we get to really relax with good friends, sharing food, stories, ideas and laughs.

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