Max Tegmark Quotes & Sayings

The laws of economics tell us that atoms are expensive if they're rare, and the laws of physics tell us that they're rare if they require unusually high temperatures to make. Putting this together tells us that if atoms could talk, the priciest ones would tell the best stories. Garden-variety atoms such as carbon, nitrogen and oxygen (which together with hydrogen make up 96% of your body weight) are so cheap because garden-variety stars such as our Sun can produce them in their death throes, after which they can form new solar systems in a cosmic recycling event. Gold, on the other hand, is produced when a star dies in a supernova explosion so violent and rare that it, during a fraction of a second, releases about as much energy as all the other stars in our observable Universe combined. No wonder making gold eluded the alchemists. — Max Tegmark

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

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. — Max Tegmark

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. — Max Tegmark

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. — Max Tegmark

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 shackled in 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 begin comprehending it. — Max Tegmark

Our external physical reality is a mathematical structure. — Max Tegmark

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. — Max Tegmark

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. — Max Tegmark

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 — Max Tegmark

Amusingly, Christopher Columbus totally bungled this by relying on subsequent less-accurate calculations and confusing Arabic miles with Italian miles, concluding that he needed to sail only 3,700 km to reach the Orient when the true value was 19,600 km. He clearly wouldn't have gotten his trip funded if he'd done his math right, and he clearly wouldn't have survived if America hadn't existed, so sometimes being lucky is more important than being right. — Max Tegmark

When I bike to work int he fall, I see beauty in the trees tinged with red, orange and gold. But seeing these trees through the lens of physics reveals even more beauty, captured by the Feynman quote that opens this chapter. And the deeper I look, the more elegance I glimpse: we'll see in Chapter 3 how the trees ultimately come from stars, and we'll see in Chapter 8 how studying their building blocks suggests their existence in parallel universes. — Max Tegmark

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

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

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. — Max Tegmark

There's no better guarantee of failure than convincing yourself that success is impossible, and therefore never even trying. — Max Tegmark

So with each advance in understanding come new questions. So we need to be very humble. We shouldn't have hubris and think that we can understand everything. But history tells us that there is good reason to believe that we will continue making fantastic progress in the years ahead. — Max Tegmark

The challenge for physics is deriving the consensus reality from the external reality, and the challenge for cognitive science is to derive the internal reality from the consensus reality. — Max Tegmark

The core of a scientific lifestyle is to change your mind when faced with information that disagrees with your views, avoiding intellectual inertia, yet many of us praise leaders who stubbornly stick to their views as "strong." — Max Tegmark

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, — Max Tegmark

Generations of physicists and chemists have studied what happens when you group together vast numbers of atoms, finding that their collective behavior depends on the pattern in which they're arranged: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. — Max Tegmark

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. — Max Tegmark

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) — Max Tegmark

Third, this allowed us to propose what we called the cosmological interpretation of quantum mechanics. Here we interpret the wavefunction for an object as describing not some funky imaginary ensemble of possibilities for what the object might be doing, but rather the actual spatial collection of identical copies of the object that exist in our infinite space. Moreover, quantum uncertainty that you experience simply reflects your inability to self-locate in the Level I multiverse, i.e., to know which of your infinitely many copies throughout space is the one having your subjective perceptions. — Max Tegmark

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

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. — Max Tegmark

As we discussed in Chapter 7, we physicists still haven't found a mathematical structure that can describe all aspects of reality, including gravity, but so far, there's no indication that string theory or any of the other most actively pursued candidates for such a description are any less mathematical than quantum field theory. — Max Tegmark

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. — Max Tegmark

In infinite space, even the most unlikely events must take place somewhere. — Max Tegmark

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

Real knowledge is to know the extent of one's ignorance. - Confucius The highest form of ignorance is when you reject something you don't know anything about. - Wayne Dyer — Max Tegmark

It's easy to make money when you have a lot of it. — Max Tegmark

If I get a parking ticket, there is always a parallel universe where I didn't. On the other hand, there is yet another universe where my car was stolen. — Max Tegmark

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? — Max Tegmark

This brief century of ours is arguably the most significant one in the history of our universe. We'll have the technology either to self-destruct, or [to] seed our cosmos with life. The situation is so unstable that I doubt we can dwell at this fork in the road for more than another hundred years. But if we end up going the life route instead of the death route, then in a distant future our cosmos will be teaming with life, all of which can be traced back to what we do-here and now. I don't know how we'll be thought of, but I'm sure that we won't be remembered as insignificant. — Max Tegmark

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

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. — Max Tegmark

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

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

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. — Max Tegmark

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. — Max Tegmark

We discussed the spatial part of this paradox in Chapter 9, and concluded that your consciousness is actually observing not the outside world, but rather an elaborate reality model contained in your brain which is continually updated via input from your sensory organs to track what's actually taking place in the outside world. — Max Tegmark

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 — Max Tegmark

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

I feel that my main responsibility as a teacher isn't to convey facts, but to rekindle that lost enthusiasm for asking questions. — Max Tegmark

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. — Max Tegmark

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! — Max Tegmark

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

Our physical world not only is described by mathematics, but that it is mathematics, making us self-aware parts of a giant mathematical object. — Max Tegmark

All too often, schools resemble museums, reflecting the past rather than shaping the future — Max Tegmark

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: — Max Tegmark

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. — Max Tegmark

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 — Max Tegmark

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? — Max Tegmark

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

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. — Max Tegmark