Our Mathematical Universe: My Quest for the Ultimate Nature of Reality

by Max Tegmark

How far could you rotate the dark-energy knob before the “Oops!” moment? The current setting of the knob, corresponding to the dark-energy density we’ve actually measured, is about 10−27 kilograms per cubic meter, which is almost ridiculously close to zero compared to the available range: the natural maximum value for the dial is a dark-energy density around 1097 kilograms per cubic meter, which is when the quantum fluctuations fill space with tiny black holes, and the minimum value is the same with a minus sign in front. If rotating the dark-energy knob in Figure 6.6 by a full turn would vary the density across the full range, then the actual knob setting for our Universe is about 10−123 of a turn away from the halfway point. That means that if you want to tune the knob to allow galaxies to form, you have to get the angle by which you rotate it right to over 120 decimal places! Although this sounds like an impossible fine-tuning task, some mechanism appears to have done precisely this for our Universe.

So what are we to make of this fine-tuning? First of all, why can’t we just dismiss it all as a bunch of fluke coincidences? Because the scientific method doesn’t tolerate unexplained coincidences: saying, “My theory requires an unexplained coincidence to agree with observation” is equivalent to saying, “My theory is ruled out.”

In summary, nature has a hierarchical Lego structure.

Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth. —Galileo Galilei, The Assayer,

The Mathematical Universe Hypothesis combined with our subjective experience tells us that there are very complex braidlike structures in spacetime that are self-aware and subjectively feel like observer moments.

Stephen Hawking famously asked, “What is it that breathes fire into the equations and makes a universe for them to describe?” In the context of the MUH, there’s thus no fire-breathing required, since the point isn’t that a mathematical structure describes a universe, but that it is a universe. Moreover, there’s no making required either. You can’t make a mathematical structure—it simply exists. It doesn’t exist in space and time—space and time may exist in it.

As we saw in Chapter 6, the discovery that a physical parameter seems fine-tuned to allow life can be interpreted as evidence of a multiverse where the parameter takes a broad range of values, because this interpretation makes it unsurprising that a habitable universe like ours exists, and predicts that this is where we’ll find ourselves.