Why do we live in a three-dimensional world?

Until something disrupts the rhythm of life (or you’re in the car with a five-year-old), most of us don’t stop to analyze why things are the way they are. We’re too busy navigating life to step back and ponder our reality. But let’s try it for a few minutes.

Photo by Mike Kononov on Unsplash.

We live in a universe that physicists describe as having 3+1 dimensions–three dimensions in space and one in time. But was a 3D world a foregone conclusion? Could complex life have emerged and survived in a 2+1 (2D) world? This question is at the heart of a paper recently published in the journal Physical Review Research by James Scargill, a theorist at the University of California, Davis.

Some scientists have proposed that a universe with three spatial dimensions is the most stable kind of universe or has other physical advantages. This may be the case, but physicists haven’t been able to show it mathematically. Another way to approach this question is to add a bit of philosophy. The anthropic approach starts by recognizing that the fact that we can study the universe tells us important information about the universe: We know that the universe evolved into something that supports intelligent life.

This leads to a new question. Could intelligent life have emerged in a universe with any other number of dimensions? If the answer is no, then of course we live in a place with three dimensions; if we didn’t, we wouldn’t be here to ask the question. If the answer is yes, then exploring the possible scenarios could reveal new insight on how and why the universe evolved as it did.

There’s a pretty convincing anthropic argument against life in a universe with more than three spatial dimensions. Newtonian gravity predicts that orbits aren’t stable in a universe with additional spatial dimensions. Without orbits, you don’t get galaxies, stars, planets, atoms, or life.

Stable orbits are possible in a universe with two spatial dimensions, but there are other anthropic arguments against the possibility. Here are two of the most common:

  • General relativity isn’t consistent with a 2D universe
  • Complex life can’t form in a world where things like neurons don’t cross paths.

A visualization of one object orbiting another in spacetime.

Scargill’s new research addresses these two arguments using a “big picture” approach. It would be easy to get lost in the details of how general relativity—in which gravity is described by the warping of spacetime—translates from our experience in 3D to 2D. But Scargill avoids this trap. First, he takes a step back to consider some of the key features of general relativity and neural networks that are necessary for life. Then, he goes on to see if those can be translated into two dimensions.

“It is worth noting that where comparable observations can be made, all of these theories may depart from what it observed in our universe,” he explains in the paper. “However, for the question of whether life can exist, it does not seem necessary to fully reproduce gravity as in our universe (but merely certain features, such as the existence of stable orbits).”

Using this approach, Scargill provides a detailed example of how general relativity can be modified to work with a 2D universe and how 2D networks can replicate key features of neural networks. He doesn’t present complete theories, or even show that life in a 2D universe is definitely possible. Instead, he demonstrates that the common anthropic arguments against the existence of life in a 2+1 dimensions actually don’t rule out the possibility.

Biological neural networks like the human brain are complex information processing systems composed of individual neurons and a web of connections that link them together.

Scargill puts it this way. “Overall it would seem that if one wishes to use anthropic reasoning to explain the observed dimensionality of spacetime, then the possibility of life in 2+1 dimensions requires further investigation.”

This research raises so many fascinating questions. What conditions are necessary for complex life? On the flip side, what would rule out the possibility of life? If life could have existed in 2+1 dimensions, why do we exist in 3+1? What would life look like in 2+1 dimensions?

That last question is especially brain-stretching and brings to mind a book written nearly 150 years ago by Edwin Abbott Abbott, Flatland: A Romance of Many Dimensions. The satirical story is set in a two-dimensional world in which women are lines, men are polygons, and the narrator is a square.

“I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space.”
–The square in Flatland, by Edwin Abbott Abbott

Kendra Redmond

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