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

by Max Tegmark

That is, we don’t invent mathematical structures—we discover them, and invent only the notation for describing them.

So the bottom line is that if you believe in an external reality independent of humans, then you must also believe that our physical reality is a mathematical structure.

In other words, the Mathematical Universe Hypothesis implies that we live in a relational reality, in the sense that the properties of the world around us stem not from properties of its ultimate building blocks, but from the relations between these building blocks.

First his special relativity theory said that we live in a Minkowski space (including time as a fourth dimension), then his general relativity said that we instead live in a Riemann space, which meant that it could be curved.

Then, as we saw in Chapter 7, quantum mechanics came along and said that we’re really living in a Hilbert space. Again, the points in these spaces aren’t made of anything, and have no color, texture or other intrinsic properties whatsoever.

In summary, time is not an illusion, but the flow of time is. So is change. In spacetime, the future exists and the past doesn’t disappear. When we combine Einstein’s classical spacetime with quantum mechanics, we get quantum parallel universes as we saw in Chapter 8.

There’s also a pressure field: at each point, there’s a pressure number which you can measure with a barometer—or with your ear, which will hurt if the number is too extreme and which can detect sound if the pressure is fluctuating over time.

this temporal-reality model with its sequence of memories gives you the subjective feeling of time flowing through a sequence of events even while your mind is actually looking at the reality model in your brain in a single observer moment.

even though an observer moment objectively occupies less than a liter of volume and a second of time, it subjectively feels as if it occupies all the space you’re aware of and all the time you remember.

I think that consciousness is the way information feels when being processed in certain complex ways.

The complexity of something is usually defined as the smallest number of bits required to fully describe it (a bit is a zero or a one).

Whereas the complexity of an object measures how complicated it is to describe, its information content1 measures the extent to which it describes the rest of the world.

the key difference between a solid, a liquid and a gas lies not in the types of atoms, but in their arrangement.

My guess is that we’ll one day understand consciousness as yet another phase of matter. I’d expect there to be many types of consciousness just as there are many types of liquids, but in both cases, they share certain characteristic traits that we can aim to understand.

The same thing happens with classical cloning as in Figure 8.3: cloning with determinism is perceived as uniqueness with randomness.

When the number of yous decreases, you perceive subjective immortality.

Why do we perceive the world as stable and ourselves as local and unique? Here’s my guess: because it’s useful.

More generally, any SAS that’s either evolved or engineered with a purpose might have self-awareness as a by-product of having an internal model of the world and itself.

For us humans, I find it interesting that our bodily defense against microscopic enemies (our highly complex immune system) doesn’t appear to be self-aware even though our defense against macroscopic enemies (our brain controlling various muscles) does. This is presumably because the aspects of our world that are relevant in the former case are so different (e.g., smaller length scales, longer time scales) from that of the latter that sophisticated, logical thinking and the accompanying self-awareness aren’t needed.

In other words, the SSSA allows us to make statements about what’s going on even in places that we can’t observe.

If you ask the question “What sort of entity should I expect to be?,” then your reference class clearly needs to be restricted to entities that ask such questions—and ants don’t!

And then it will do it again, infinitely many times over, so that for every copy of you that has evolved and lived a real life, there are infinitely many delusional disembodied Boltzmann

we know that there are infinitely many primes—a fact that Euclid proved over two thousand years ago.

we still don’t know whether there are infinitely many twin primes.

other words, we physicists traditionally call the regularities that we understand “laws” and dismiss much of what we don’t understand as “initial conditions.” The laws let us predict how these conditions will change over time, but give no information about why they started out the way they did.

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.

After this, the standard models of particle physics and cosmology revealed new “unreasonable” mathematical order to a spectacular extent, from the microcosm of elementary particles to the macrocosm of the early Universe, arguably enabling all physics measurements ever made to be successfully calculated from the 32 numbers listed in Table 10.1. I know of no other compelling explanation for this trend than that the physical world really is completely mathematical.

For example, a convincing demonstration that there’s such a thing as fundamental randomness in the laws of nature (as opposed to deterministic observer cloning that merely feels random subjectively) would therefore refute the MUH.

Intelligent life appears to be rare, with most of Levels I, II and IV being uninhabitable.

The CUH/FUH may help solve the measure problem and explain why our Universe is so simple.

The MUH implies that there’s no fundamental randomness: randomness is simply the way cloning feels subjectively.

collection of things can be simpler to describe than one of its parts.

in Scientific American by the relativity pioneer George Ellis, which I highly recommend reading (see http://tinyurl.com/antiverse

Level I (other such regions far away in space where the apparent laws of physics are the same, but where history played out differently because things started out differently), Level II (regions of space where even the apparent laws of physics are different), Level III (parallel worlds elsewhere in Hilbert space where quantum reality plays out) and Level IV (totally disconnected realities governed by different mathematical equations).

evolution endowed us with intuition only for those everyday aspects of physics that had survival value for our distant ancestors, leading to the prediction that whenever we use technology to glimpse reality beyond the human scale, our evolved intuition should break down.

One could therefore imagine galaxy-dwelling observers happily surviving long after intergalactic space has undergone a Big Snap, as long as deleterious effects from these faraway regions don’t propagate into the galaxies.

I think we’re due for a breakthrough on the nature of space, and that the Big Snap paradox is an interesting hint.

Instead of colliding, most stars will intermingle to form a single new galaxy, “Milkomeda.” However, as we’ll see next, this may exacerbate problems with supernovae and asteroid impacts.

Another astronomical suspect, a gamma-ray burst from a supernova explosion, has been blamed for the second-largest recorded extinction, which took place about 450 million years ago. Although the forensic evidence is currently too weak for a guilty verdict, the suspect certainly had the means and a plausible opportunity.

If such a killer beam hit Earth, it would deliver a one-two punch: it would both zap us directly and destroy our ozone layer, after which our Sun’s ultraviolet light would start sterilizing Earth’s surface.

For example, the star Gliese 710 is predicted to pass within a light-year of us in about 1.4 million years, four times closer than our current nearest neighbor, Proxima Centauri.

This galactic collision will also cause gas clouds to collide, triggering a burst of star formation, and the heaviest newborn stars will soon explode as supernovae, which may be too close for comfort.

Such a super-eruption in Siberia is widely blamed for the greatest recorded extinction of all, the “Great Dying,” which wiped out 96% of all marine species about 250 million years ago.

believe that consciousness is the way information feels when being processed.

The ability to readily copy information and software between AIs would probably reduce the strong sense of individuality that’s so characteristic of our human consciousness: there would be less of a distinction between you and me if we could trivially share and copy all our memories and abilities, so a group of nearby AIs may feel more like a single organism with a hive mind.

Logic forms the basis of scientific reasoning, yet wishful thinking, irrational fears and other cognitive biases often dominate decisions.

By undercutting fundamentalism and intolerance, education would curtail violence and war. By empowering women, it would curb poverty and the population explosion.

For example, although dinosaurs ruled Earth for over 100 million years, a thousand times longer than we modern humans have been around, evolution didn’t seem to inevitably push them toward higher intelligence and inventing telescopes or computers.