The Universe Learns

In August 2020, Vitaly Vanchurin, a theoretical physicist at the University of Minnesota, posted a paper on arXiv with a title that made his colleagues’ eyes twitch: “The World as a Neural Network.”

The title reads literally: “The World as a Neural Network.” Ontologically, without analogies: the world is a neural network.

People noticed. Reactions fell into three categories. Physicists said, “Interesting, but how do you disprove it? — if you can’t, it isn’t science.” Machine-learning specialists said, “Sounds insane, but the math is consistent.” Science journalists said, “We live in the Matrix?!” (No. Not the Matrix. But we’ll get back to that.)

Vanchurin’s claim starts from a question physics has been asking itself for a hundred years and still can’t answer.

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Here’s the question: why do quantum mechanics and gravity refuse to get along?

Quantum mechanics — the best theory of the small: it describes atoms, photons, and electrons to twelve decimal places of precision, and in a hundred years not a single experiment has found a deviation from its predictions.

General relativity — the best theory of the big: it describes gravity, spacetime, black holes, and the expansion of the Universe, confirmed by gravitational waves (LIGO, 2015) and the photograph of a black hole (Event Horizon Telescope, 2019).

Both work perfectly, each in its own domain.

The problem is that they are incompatible. Quantum mechanics says spacetime is the background on which events happen; general relativity says spacetime is a participant in events — it bends, stretches, and vibrates. When you try to apply quantum rules to spacetime itself, the math breaks, returning infinities, divergences, and meaningless answers.

Over the past half-century the best minds have thrown themselves at this problem — string theory, loop quantum gravity, causal dynamical triangulation, noncommutative geometry. The output has been modest: elegant formalisms, zero experimental predictions, and one Nobel Prize (for the related mathematics, not the physics).

Vanchurin proposed approaching it from the diametrically opposite direction: what if quantum mechanics and gravity are two regimes of one and the same process, and sixty years of collective glue spent on their “unification” went to waste because there was, on the whole, nothing there to glue?

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That process is learning; it makes sense to set down Vanchurin’s idea in one paragraph first, and then unfold it piece by piece.

The world is a neural network with variables of two types: fast ones (neuron states) and slow ones (connection weights). The dynamics of the world turn out to be the optimization of a loss function — that is, learning. When fast variables dominate, we see quantum mechanics — superpositions, probabilities, Born’s rule; when slow variables dominate, we see gravity — geometry, curvature, Einstein’s equations. One and the same network, two different limiting regimes of its behavior.

(You’re thinking right now: “Hold on, quantum mechanics and gravity are sworn enemies, people have been trying to unify them for sixty years, and nobody has pulled it off.” That’s the point: everyone has been trying to unify two things, and Vanchurin is saying you don’t need to unify them at all, because they are already one — two regimes of one system. Nobody “unifies” ice and steam: that’s water in different states.)

What follows is an unpacking layer by layer: first the fast variables with their quantum mechanics, then the slow ones with gravity, then multilevel learning, into which biological evolution falls with all its mutations and selections.