Is Life Possible in Fewer than Three Dimensions?

JF Ptak Science Books    Quick Post

Hell is empty and the devils are all here--The Tempest   [Dedicated to Rohan Myers for causing me   to think about this...]    See also "The Dot and the Sphere--Picturing Multiple Dimensions", here.

Listening last night to a reading of The Tempest I was very soundly struck by this famous line--it made me think not so much of hell-on-Earth and all of the other permutations in this vein, but of difficult/devilish questions.  And what came out while I was listening to the play was this, something that seems difficult to me: 

Can life as we know it exist in fewer than three dimensions?

I've never really thought about this before, even after having written a fair amount about the impact of the thinking on the Fourth Dimension in the arts and sciences as well as the history of the rediscovery of perspective in general.  So while thinking about life and living and travel and so on in higher-than-the-third-dimension, it had never really come to me about thinking if it was possible for life to exist in less-than-three-dimensions.

It seems prima facie impossible, but why?  The first thing that came into my mind was that in order for there to be a functioning brain--assuming that there could be a brain, somehow, in the second dimension--there must be a way for the brain to connect with itself.  I do not think that the universe of axons and such could do their job if they had to intersect one one another rather than going above/below/around each other.  All other things being equal, this would be a conversation killer, I think. 

Perhaps it is as difficult to imagine this as it was stupendous for the figures in the two dimensional world in Edwin Abbott's Flatland to see a three dimensional figuring rising into itself from their world.  No doubt the question above is far more interesting than my answer.

Comments

[Jeff Donlan]

The answer is: Yes.

[John F. Ptak]

Okay. Can we expand on this a little, Dr. D? AS I said, the question to me is way more interesting than the start of my answer...

[Darien Large]

My understanding is that the two-dimensional Game of Life (Conway/Guy) has been demonstrated to support a) self-reproducing patterns and b) Turing-complete computation. This may not be the existence proof you seek, but it's provocative to me at least. My hesitation extending the result from Life to general two-dimensional "worlds" has to do with questions of conservation laws, which on the level at which the Game of Life was designed, do not really exist. Of course, the conservation laws of our own universe are a lot more complicated than "matter can be neither created nor destroyed", so perhaps it's a question of scale.

[David Bimler]

Dewdney, in "The Planiverse", spent a while looking into the details of how multicellular communication might work in a 2D universe.

http://en.wikipedia.org/wiki/The_Planiverse

There's still the problem that planetary orbits don't exist in 2D (assuming that forces like gravity follow an inverse law rather than an inverse-square law).