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Our Simulated Universe

January 2, 2013

Although I sometimes think in images, most of the time I'm having a conversation with myself in my mind. It's apparent, at least to me, that it's hard to think about things for which there are no words. Words act as a convenient shorthand for rather complex ideas. For example, consider the word, "elephant." It's a paragraph of description contained within eight letters.

There's an entertaining episode of Star Trek: The Next Generation entitled "Darmok." This episode concerns the language of a people called the Tamarians. In our language, isolated words encode larger combinations of other words, as in the elephant example above. The Tamarian language, instead, is built on metaphor in which the title of a folk tale expresses a complex concept. This is similar to the way that mentioning Dickens' story, "A Christmas Carol," brings to mind a slew of ideas and a valuable lesson.

For us, folk tales are collections of words, so how could such a metaphor language develop? Just as some programming languages are written in themselves, building more complex functions from simpler ones, we can imagine complex metaphors being described using simpler metaphors. These simple metaphors would themselves be built from more primitive metaphors, like a falling rock, or a pin prick.

Plato's Allegory of the Cave is an exploration of how the human mind builds its knowledge of the world on what it experiences, just as the Tamarians express new ideas in terms of old. The cave allegory, a part of Plato's Republic, describes a group of men who have lived their entire lives chained in a cave. Their only vista is a blank wall on which are projected shadows of things passing between them and a fire.

They understand their world only through knowledge derived from these shadows. If one of them became unchained and is able to see the objects, themselves, and not just their shadows, he wouldn't understand what he was looking at. The vocabulary in his mind has no way to codify these things, so they can't be comprehended.

Section 514a of Plato's Republic
The introduction to Plato's Allegory of the Cave in Plato's Republic. (Section 514a, via Project Perseus.)[1]

The descriptions of our present world, and our understanding of it, are enhanced by our use of technology metaphors. When we say that our last experiment turned out to be a train wreck, we can use the expression, "train wreck," since both we and our audience know what a train wreck is. Now that computers are ubiquitous, our palette of metaphors includes ideas of computation and information theory that were not available to Plato. This new vocabulary has given rise to the idea that we might all be much like Plato's prisoners; but, instead of being chained in a cave, we're trapped in a computer simulation.

In 2003, Nick Bostrom, a philosopher at Oxford University, published an article that contained the idea that it's more likely than not that our world is a computer simulation. In a form of argument not used by scientists, Bostrom wrote that "the belief that there is a significant chance that we will one day become posthumans who run ancestor simulations is false, unless we are currently living in a simulation."[3] The question arises as to whether we could ever determine whether we are a simulation. Since we would be inside the simulation, that seems impossible, doesn't it?

Well, we scientists do the impossible every day, don't we? We just need to consider the possibilities. Our own simulations do not treat their phase space as a continuum. We need to break things into a lattice of points, do our calculations at each point, and hope for the best. If our points are really close together, our finite element analysis, for example, approximates real mechanics quite well. Our Simulator Overlords might have phenomenal computers that allow a very close spacing of lattice points, but there should always be a limit.

We've actually made some progress ourselves in simulating small pieces of our universe, up to about 10-14 meter in size, or 1020 Planck lengths (1.6 x 10-35 meter). Advances in computation should someday push the simulation size up to a molecule, then a cell. Simulation of an entire cell seems like a fantasy to us, now, but consider the advances we've made in computation since the ENIAC days.

Physicists at the University of Washington and the University of New Hampshire have examined the detection of our being simulated as a problem of detecting the simulation lattice, a cubic space-time lattice.[3-4] Their conclusion, as posted in a paper on the arXiv Preprint Server,[4] is that we should look at the g-factor of the muon, every physicist's favorite dimensionless quantity, the fine-structure constant, and the energy distribution of the highest energy cosmic rays.[4]

The highest energy cosmic rays have an energy of 1011 GeV, so they would be at the limits of a simulation. The highest-energy cosmic rays would travel diagonally in the lattice, and not along the edges. Furthermore, their interaction with other particles would be anisotropic.[3] The arXiv paper has a simple graphic showing the differences that would be observed (see figure).

Figure captionThe red surface is a representation of energy-momentum space in a non-simulated universe, while the blue surface is the case for a simulation running on a cubic space-time lattice.

(Fig. 2 of ref. 4, via the arXiv Preprint Server.)[4]

Zohreh Davoudi, a coauthor of the arXiv paper, had the interesting observation that our universe might be just one of many running on the mainframe of our Simulator Overlords.
"Then the question is, 'Can you communicate with those other universes if they are running on the same platform?'"[3]


  1. Paul Shorey, Translator, Plato in Twelve Volumes, vols. 5 & 6 (Harvard University Press, Cambridge, MA; William Heinemann Ltd., London), 1969; Greek text.
    Picture men dwelling in a sort of subterranean cavern with a long entrance open to the light on its entire width. Conceive them as having their legs and necks fettered from childhood, so that they remain in the same spot...
  2. Nick Bostrom, "Are You Living In a Computer Simulation?" Philosophical Quarterly, vol. 53, no. 211 (2003), pp. 243-255.
  3. Vince Stricherz, "Do we live in a computer simulation? UW researchers say idea can be tested," University of Washington Press Release, December 10, 2012.
  4. Silas R. Beane, Zohreh Davoudi and Martin J. Savage, "Constraints on the Universe as a Numerical Simulation," arXiv Preprint Server, November 9, 2012.

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