Max Tegmark Quotes

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. Nothing else has a baggage-free description. In other words, we all live in a gigantic mathematical object-one that's more elaborate than a dodecahedron, and probably also more complex than objects with intimidating names such as Calabi-Yau manifolds, tensor bundles and Hilbert spaces, which appear in today's most advanced physics theories. Everything in our world is purely mathematical-including you.

The hallmark of a deep explanation is that it answers more than you ask

For me, [John Wheeler] was the last Titan, the only physics superhero still standing.

The classification above is based on a 2011 presentation by MIT grad student David Hernandez for my cosmology class. Because such simplistic taxonomies are strictly impossible, they should be taken with a large grain of salt:

Some ancients speculated that the stars were small holes in a black sphere through which distant light shone through. The Italian astronomer Giordano Bruno suggested that they were instead objects like our Sun, just much farther away, perhaps with their own planets and civilizations - this didn't go down too well with the Catholic Church, which had him burned at the stake in 1600.

Darwin's theory thus makes the testable prediction that whenever we use technology to glimpse reality beyond the human scale, our evolved intuition should break down.

The discovery of eternal inflation has radically transformed our understanding of what's out there in space on the largest scales. Now I can't help but feel that our old story sounds like a fairy tale, with its single narrative in a simple sequence: "Once upon a time, there was inflation. Inflation made our Big Bang. Our Big Bang made galaxies." Figure 5.7 illustrates why this story is too naive: it yet again repeats our human mistake of assuming that all we know of so far is all that exists. We see that even our Big Bang is just a small part of something much grander, a treelike structure that's still growing. In other words, what we've called our Big Bang wasn't the ultimate beginning, but rather the end-of inflation in our part of space.

Physics is the ultimate intellectual adventure, the quest to understand the deepest mysteries of our Universe. Physics doesn't take something fascinating and make it boring. Rather, it helps us see more clearly, adding to the beauty and wonder of the world around us.

Economics was largely a form of intellectual prostitution where you got rewarded for saying what the powers that be wanted to hear.

Alas, I soon grew disillusioned, concluding that economics was largely a form of intellectual prostitution where you got rewarded for saying what the powers that be wanted to hear. Whatever

In other words, the idea is the there's a fourth level of parallel universes that's vastly larger than the three we've encountered so far, corresponding to different mathematical structures. The first three levels correspond to noncommunicating parallel universes within the same mathematical structure: Level I simply means distant regions from which light hasn't yet had time to reach us, Level II covers regions that are forever unreachable because of the cosmological inflation of intervening space, and Level III, Everett's "Many Worlds," involves noncommunicating parts of the Hilbert space of quantum mechanics. Whereas all the parallel universes at Levels I, II and III obey the same fundamental mathematical equations (describing quantum mechanics, inflation, etc.), Level IV parallel universes dance to the tunes of different equations, corresponding to different mathematical structures. Figure 12.2 illustrates this four-level multiverse hierarchy, one of the core ideas of this book.

But why has our physical world revealed such extreme mathematical regularity that astronomy superhero Galileo Galilei proclaimed nature to be "a book written in the language of mathematics," and Nobel Laureate Eugene Wigner stressed the "unreasonable effectiveness of mathematics in the physical sciences" as a mystery demanding an explanation?

If life were a movie, physical reality would be the entire DVD: Future and past frames exist just as much as the present one.

Please hold your hand up at arm's length and check which things around you can be blocked from view by your pinkie. Your little finger covers an angle of about one degree, which is about double what you need to cover the Moon - make sure to check this for yourself the next time you do some lunar observing. For an object to cover half a degree, its distance from you needs to be about 115 times its size,

The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and ... there is no rational explanation for it. - Eugene Wigner, 1960

The cognitive science's challenge is to link our consensus reality to our internal reality, but physics' challenge is to link our consensus reality to our external reality.

Other big questions tackled by ancient cultures are at least as radical. What is real? Is there more to reality than meets the eye? Yes! was Plato's answer over two millennia ago. In his famous cave analogy, he likened us to people who'd lived their entire lives shacked ina a cave, facing a blank wall, watching the shadows cast by things passing behind them, and eventually coming to mistakenly believe that these shadows were the full reality. Plato argued that what we humans call our everyday reality is similarly just a limited and distorted representation of the true reality, and that we must free ourselves from our mental shackles to comprehending it.

Evolution endowed us with intuition only for those aspects of physics that had survival value for our distant ancestors, such as the parabolic orbits of flying rocks (explaining our penchant for baseball). A cavewoman thinking too hard about what matter is ultimately made of might fail to notice the tiger sneaking up behind and get cleaned right out of the gene pool. Darwin's theory thus makes the testable prediction that whenever we use technology to glimpse reality beyond the human scale, our evolved intuition should break down. We've repeatedly tested this prediction, and the results overwhelmingly support Darwin. At high speeds, Einstein realized that time slows down, and curmudgeons on the Swedish Nobel committee found this so weird that they refused to give him the Nobel Prize for his relativity theory. At low temperatures, liquid helium can flow upward. At high temperatures, colliding particles change identity; to me, an electron colliding with a positron and turning into a Z-boson feels about as intuitive as two colliding cars turning into a cruise ship. On microscopic scales, particles schizophrenically appear in two places at once, leading to the quantum conundrums mentioned above. On astronomically large scales… weirdness strikes again: if you intuitively understand all aspects of black holes [then you] should immediately put down this book and publish your findings before someone scoops you on the Nobel Prize for quantum gravity… [also,] the leading theory for wha

The Canadian-Australian mathematician Norman Wildberger has posted an essay arguing that real numbers are a joke.

As the ancient Greeks replaced myth-based explanations with mechanistic models of the Solar System, their emphasis shifted from asking why to asking how.

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, 1623

We're all born with curiosity, but at some point, school usually manages to knock that out of us.

The various approximations that constitute our current physics theories are successful because simple mathematical structures can provide good approximations of how a self-aware substructure will perceive more complex mathematical structures. In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics!

Some key physical entities such as empty space, elementary particles and the wavefunction appear to be purely mathematical int he sense that their only intrinsic properties are mathematical properties.

… when people ask about the meaning of life as if it were the job of our cosmos to give meaning to our existence, they're getting it backward: It's not our Universe giving meaning to conscious beings, but conscious beings giving meaning to our Universe.

All of the patterns we've discussed of course exist in four dimensions rather than three, and the metaphors about braids, cables and trees, shouldn't be taken too literally. The key point is simply that you can be an unchanging pattern in spacetime-the specific details of this pattern are less important for the points we're making. This pattern is part of the mathematical structure that is our Universe, and the relations between different parts of the pattern are encoded in mathematical equations. As we saw in Chapter 8, Everett's quantum mechanics endows you with an even more interesting-but no less mathematical-structure, since a single you (the tree trunk) can split into many branches, each feeling that they're the one and only you
we'll return to this later.

The apparent incompatibility between the abundance of habitable planets in our Galaxy and the lack of extraterrestrial visitors, known as the Fermi paradox, suggest the existence of what Hanson calls a "Great Filter," an evolutionary/technological roadblock somewhere along the developmental path from nonliving matter to space-colonizing life. If we discover independently evolved primitive life in our Solar System, this would suggest that primitive life is not rare, and that the roadblock lies after our current human stage of development-perhaps because assumption 1 is false, or because almost all advanced civilizations self-destruct before they are able to colonize. I'm therefore crossing my fingers that all searches for life on Mars and elsewhere find nothing: this is consistent with the scenario where primitive life is rare but we humans got lucky, so that we have the roadblock behind us and have extraordinary future potential.

Whereas the complexity of an object measures how complicated it is to describe, its information content measures the extent to which it describes the rest of the world. In other words, information is a measure of how much meaning complexity has.

All such uncertainties about undecidability and inconsistency apply only to mathematical structures with infinitely many elements. Are infinities, undecidability and potential inconsistency really inherent in the ultimate physical reality, or are they merely mirages, artifacts of our playing with fire and using powerful mathematical tools that are more convenient to work with than those that actually describe our Universe? More specifically, how well defined do mathematical structures need to be to be real, i.e., to be members of the Level IV multiverse?

So I feel that the experimental verdict is in: the world is weird, and we just have to learn to live with it.

Figure 3.3: Since it takes time for distant light to reach us, looking farther away means looking farther back in time. Beyond the most distant galaxies, we see an opaque wall of glowing hydrogen plasma, whose glow has taken about 14 billion years to reach us. This is because the same hydrogen that fills space today was hot enough to be plasma about 14 billion years ago, when our Universe was only about 400,000 years old. (Credit: Adapted from NASA/WMAP team)

In 2056, I think you'll be able to buy T-shirts on which are printed equations describing the unified laws of our universe.

The core idea is that for an information processing system to be conscious, it needs to be integrated into a unified whole that can't be decomposed into nearly independent parts. This means that all parts need to compute jointly with lots of information about each other-otherwise there would be more than one independent consciousness, such as in a room full of people or, perhaps, in the two brain halves of a patient whose connecting corpus callosum has been cut out. If there are fairly independent parts that are too simple, then these won't be conscious at all, like the independent pixels of a video camera.

These electric and magnetic fields can be elegantly unified into what's known as the electromagnetic field, represented by six numbers at each point in spacetime. As we discussed in Chapter 7, light is simply a wave rippling through the electromagnetic field, so if our physical world is a mathematical structure, then all the light in our Universe (which feels quite physical) corresponds to six numbers at each point in spacetime (which feels quite mathematical). These numbers obey the mathematical relations that we know as Maxwell's equations, shown in Figure 10.4.

Accidental nuclear war between two superpowers may or may not happen in my lifetime, but if it does, it will obviously change everything. The climate change we're currently worrying about pales in comparison with nuclear winter, where a global dust cloud blocks sunlight for years, much like when an asteroid or supervolcano caused a mass extinction in the past. The 2008 economic turmoil was of course nothing compared to the resulting global crop failures, infrastructure collapse and mass starvation, with survivors succumbing to hungry armed gangs systematically pillaging from house to house. Do I expect to see this in my lifetime? I'd give it about 30%, putting it roughly on par with my getting cancer. Yet we devote way less attention and resources to reducing the risk of nuclear disaster than we do for cancer. And whereas humanity as a whole survives even if 30% get cancer, it's less obvious to what extent our civilization would survive a nuclear Armageddon. There are concrete and straightforward steps that can be taken to slash this risk, as spelled out in numerous reports by scientific organizations, but these never become major election issues and tend to get largely ignored.

This really drove home to me that Hugh Everett was no exception: studying the foundations of physics isn't a recipe for glamour and fame. It's more like art: the best reason to do it is because you love it. Only a small minority of my physics colleagues choose to work on the really big questions, and when I meet them, I feel a real kinship. I imagine that a group of friends who've passed up on lucrative career options to become poets might fell a similar bond, knowing that they're all in it not for the money but for the intellectual adventure.

However, in broad brushstrokes, we might say this: You're a pattern in spacetime. A mathematical pattern. Specifically, you're a braid in spacetime-indeed one of the most elaborate braids known.

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