Our entire living reality happens in a three-dimensional Universe, so naturally it's hard to imagine a universe with just two dimensions. But, according to new calculations, a 2D universe could actually support life, too.
The new paper is the work of physicist James Scargill at the University of California, Davis, who wanted to test the anthropic principle – the philosophical idea that universes can't exist if there is no life within to observe them.
In particular, Scargill examines the idea of life in 2+1 dimensions, where +1 is the dimension of time. He suggests we might have to rethink both the physics and the philosophy of living outside the 3+1 dimensions we are used to.
"There are two main arguments levelled against the possibility of life in 2+1 dimensions: the lack of a local gravitational force and Newtonian limit in 3D general relativity, and the claim that the restriction to a planar topology means that the possibilities are 'too simple' for life to exist," writes Scargill in his paper.
The calculations that Scargill works through are sophisticated ones, as you would expect, but he shows in theory that a scalar gravitational field could indeed exist in two dimensions, allowing for gravity and thus cosmology in a 2D universe.
He then goes on to another important point - for life to emerge, there needs to be a level of complexity, which in this case can be symbolised with neural networks. Our highly complex brains exist in 3D, and we might think a neural network couldn't work in just two dimensions.
But Scargill demonstrates that certain types of planar, two-dimensional graphs share properties with biological neural networks we find in life. Such graphs can also be combined in ways that resemble the modular function of neural networks, and even exhibit what are known as small-world properties, where a complex network can be crossed in a small number of steps.
Therefore, according to physics as laid out by Scargill, 2D universes could support life. That doesn't mean they exist, but the paper shows that two of the strongest arguments that fly in the face of 2+1 universes need some serious reconsideration.
While Scargill's paper hasn't yet been peer-reviewed, it has been assessed by the MIT Technology Review: "The work undermines the anthropic argument for cosmologists and philosophers, who will need to find another reason why the Universe takes the form it does."
If you're finding it difficult to get your head around the idea of living in a 2D world, consider the thought that we might already be in one. Previous research has put forward the hypothesis that we are in fact living in a giant hologram, and being fooled into believing that we exist in three dimensions (plus time).
Since we don't have any universe-traversing machines at our disposal, such work might seem extremely theoretical, but Scargill's musing do open up some interesting avenues for future research – not least whether one day we might be able to simulate a 2D universe, perhaps through the intricacies of quantum computing.
"In particular it would be interesting to determine if there might be other impediments to life which have so far been overlooked, as well as to continue to search for non-anthropic explanations for the dimensionality of space-time," writes Scargill.
The paper can be read on the pre-print server arXiv.org.