Max Tegmark

Swedish-American physicist and cosmologist

Max Tegmark (born May 5, 1967) is a Swedish-American physicist, cosmologist and machine learning researcher. He is a professor at the Massachusetts Institute of Technology and the scientific director of the Foundational Questions Institute. He is also a co-founder of the Future of Life Institute and a supporter of the effective altruism movement, and has received research grants from Elon Musk to investigate existential risk from advanced artificial intelligence.

Max Tegmark, 2006


  • I believe that consciousness is the way information feels when being processed.
    • On Math, Matter and Mind Piet Hut (IAS), Mark Alford (WashU), Max Tegmark (MIT), Foundations of Physics 36 (2006) 765-794
  • 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.
    • Interview with the Co-Founders of the Foundational Questions Institute, Dr.Max Tegmark and Dr. Anthony Aguirre.
  • 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.
    • BBC Horizons - What is Reality? (January 17, 2011)
  • ... I would rather have questions that I can't answer than answers that I can't question. (variation of a remark by Richard Feynman)
  • Yet the complexity of all this pales in comparison to the patterns of information processing in your brain. Your roughly 100 billion neurons are constantly generating electrical signals (“firing”), which involves shuffling around billions of trillions of atoms, notably sodium, potassium, and calcium ions. The trajectories of these atoms form an extremely elaborate braid through spacetime, whose complex intertwining corresponds to storing and processing information in a way that somehow gives rise to our familiar sensation of self-awareness. There’s broad consensus in the scientific community that we still don’t understand how this works, so it’s fair to say that we humans don’t yet fully understand what we are. However, in broad brush, 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.
  • Imagine all the food you have eaten in your life and consider that you are simply some of that food, rearranged.

Our Mathematical Universe: My Quest for the Ultimate Nature of Reality (2014)

  • 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... On astronomically large scales... weirdness strikes again: if you intuitively understand all aspects of black holes... put down this book and publish your findings before someone scoops you on the Nobel Prize for quantum gravity… [also,] the leading theory for what happened [in the early universe] suggests that space isn’t merely really really big, but actually infinite, containing infinitely many exact copies of you, and even more near-copies living out every possible variant of your life in two different types of parallel universes.
  • 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.
  • [W]hat I had been missing... and what Feynman realized: physics is the ultimate intellectual adventure, the quest to understand the deepest mysteries of our Universe. ...[I]t makes us see more clearly, adding to the beauty and wonder of the world ...[T]he lens of physics adds more beauty to the world ...
  • So this book... [is] my personal quest for the ultimate nature of reality.
  • We're all born with curiosity, but at some point, school usually manages to knock that out of us. ...[M]y main responsibility as a teacher isn't to convey facts, but to rekindle that lost enthusiasm for asking questions.
  • [W]e've repeatedly underestimated not only the size of our cosmos, but also the power of our human mind to understand it.
  • There's no better guarantee of failure than convincing yourself that success is impossible...
  • Eratosthenes... knew that the Sun was straight overhead in... Syene at noon on the summer solstice, but that it was 7.2 degrees south of straight overhead in Alexandria, located 794 kilometers farther north. He concluded... 794 kilometers corresponded to 7.2 degrees out of the 360 degrees... around Earth's circumference, so that the circumference must be... 39,700 km...
  • Aristarchos of Samos... was able to use trigonometry to figure out... the distance between the Earth and the Sun. His conclusion... the Sun was about twenty times farther... than the Moon and therefore twenty times bigger than the Moon. In other words, the Sun was... over five times bigger than the Earth in diameter. This insight prompted Aristarchos to propose the heliocentric hypothesis long before Nicolaus Copernicus... It turned out to be quite difficult to tell precisely when the Moon was 50% illuminated, and the correct Sun-Moon angle... isn't 87 degrees but about 89.85 degrees... This makes... the Sun... almost twenty times further away... and about 109 times larger than the Earth... [T]his wasn't corrected until almost two thousand years later, so when Copernicus came along... the overall scale of his Solar System model was about twenty times too small...
  • Some ancients speculated that the stars were small holes in a black sphere through which distant light shone through. ...Giordano Bruno suggested that they were... like our Sun, just much farther away, perhaps with their own planets and civilizations... the Catholic Church had him burned at the stake in 1600.
  • The very fabric of our physical world, space itself, could be a purely mathematical object in the sense that its only intrinsic properties are mathematical... as dimensionality, curvature and topology.
  • Friedrich Bessel... achieved a breakthrough. Please hold your thumb at arm's length and alternate closing your left and right eyes a few times. ...[Y]our thumb appears to jump left and right by a certain angle relative to the background... [M]ove your thumb closer... and you'll see this jump angle growing. Astronomers call this jump angle parallax... [W]e can... compare telescopic photographs taken six months apart, when Earth is on opposite sides of the Sun. ...Bessel noticed ...61 Cygni ...moved a tiny angle, revealing its distance to be almost a million times that to the Sun... Now that Bessel knew the distance he used... [the] inverse-square law to figure out how luminous it was... in the same ballpark as the Sun... Giordano Bruno had been right after all!
  • In 1814... Joseph von Fraunhofer invented... a spectrograph, which let him separate white light into into a rainbow of colors... He discovered mysterious dark lines in the rainbow... and... the detailed positions of these lines... depended on what the light source was made of, constituting a kind of spectral fingerprint. During the following decades such spectra were measured and catalogued for many... substances. ...Sensationally, the spectrum of sunlight revealed that the Sun... contained elements... such as hydrogen. Moreover... it revealed that stars are made of roughly the same mixture of gases as the Sun! This clinched it in favor of Bruno: stars are distant suns...
  • (…) 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.
  • It’s absolutely crucial that we don’t conflate this internal reality with the external reality that it’s tracking, because the two are very different. My brain’s internal reality is like the dashboard of my car: a convenient summary of the most useful information.' Just as my car’s dashboard tells me my speed, fuel level, motor temperature, and other things useful for a driver to be aware of, my brain’s dashboard/reality model tells me my speed and position, my hunger level, the air temperature, highlights of my surroundings and other things useful for the operator of a human body to be aware of.
  • (…) 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.
  • A famous thorny issue in philosophy is the so-called infinite regress problem. For example, if we say that the properties of a diamond can be explained by the properties and arrangements of its carbon atoms, that the properties of a carbon atom can be explained by the properties and arrangements of its protons, neutrons and electrons, that the properties of a proton can be explained by the properties and arrangements of its quarks, and so on, then it seems that we’re doomed to go on forever trying to explain the properties of the constituent parts. The Mathematical Universe Hypothesis offers a radical solution to this problem: at the bottom level, reality is a mathematical structure, so its parts have no intrinsic properties at all!
  • (…) 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.
  • This implication of the Mathematical Universe Hypothesis is pretty radical, so please pause (…) take it in and think about it. What you’re aware of right at this moment feels not like a photo but like a movie clip. This movie isn’t reality—it exists only in your head, as part of your brain’s reality model. It contains lots of information about the actual external physical reality—as long as you aren’t dreaming or hallucinating—but still constitutes only a very heavily edited version of reality, akin to the evening news on TV, mainly featuring certain highlights of patterns nearby in space and time that your brain thinks are useful for you to be aware of.
  • (…) no spectator is needed, because your consciousness basically is your reality model. I think that consciousness is the way information feels when being processed in certain complex ways. Since the different parts of your brain interact with each other, different parts of your reality model can interact with each other, so the model of you can interact with your model of the outside world, giving rise to the subjective sensation of the former perceiving the latter.
  • 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.
  • We humans replace the bulk of both our "hardware" (e.g., our cells) and our "software" (e.g., our memories) many times in our life span. Nonetheless, we perceive ourselves as stable and permanent. Likewise, we perceive objects other than ourselves as permanent. Or rather, what we perceive as objects are those aspects of the world that display a certain permanence. For instance, when observing the ocean, we perceive the moving waves as objects because they display a certain permanence, even though the water itself is only bobbing up and down. Similarly (…) we perceive only those aspects of the world that are fairly stable against quantum decoherence.
  • If there’s a singularity, would the resulting AI, or AIs, feel conscious and self-aware? Would they have an internal reality? If not, they’re for all practical purposes zombies. Of all traits that our human form of life has, I feel that consciousness is by far the most remarkable. As far as I’m concerned, it’s how our Universe gets meaning, so if our Universe gets taken over by life that lacks this trait, then it’s meaningless and just a huge waste of space.
  • But I’ve suddenly changed my mind and turned more optimistic about our cosmic significance. Why? Because I’ve come to believe that advanced evolved life is very rare, yet has huge future potential, making our place in space and time remarkably significant.

Life 3.0: Being Human in the Age of Artificial Intelligence (2017)

  • Let’s instead define life very broadly, simply as a process that can retain its complexity and replicate. What’s replicated isn’t matter (made of atoms) but information (made of bits) specifying how the atoms are arranged. When a bacterium makes a copy of its DNA, no new atoms are created, but a new set of atoms are arranged in the same pattern as the original, thereby copying the information. In other words, we can think of life as a self-replicating information-processing system whose information (software) determines both its behavior and the blueprints for its hardware.
  • How is technology changing the hierarchical nature of our world? History reveals an overall trend toward ever more coordination over ever-larger distances, which is easy to understand: new transportation technology makes coordination more valuable (by enabling mutual benefit from moving materials and life forms over larger distances) and new communication technology makes coordination easier. When cells learned to signal to neighbors, small multicellular organisms became possible, adding a new hierarchical level. When evolution invented circulatory systems and nervous systems for transportation and communication, large animals became possible. Further improving communication by inventing language allowed humans to coordinate well enough to form further hierarchical levels such as villages, and additional breakthroughs in communication, transportation and other technology enabled the empires of antiquity. Globalization is merely the latest example of this multi-billion-year trend of hierarchical growth.

Max Tegmark & Eric Weinstein (2020)

: AI, Aliens, Theories of Everything, and New Year’s Resolutions! Dr Brian Keating YouTube channel, Dec 31, 2020. A source.
  • Why is entropy at the beginning of time so low, and the entropy in a black hole so high? ...We ...don't know that the entropy was low ...We don't even know if there was a beginning of time. ...[E]ntropy this measure of how messy things are, so my room ...tends to get higher and higher entropy, messier and messier. Why... eggs fall on the floor and break, and not fly up and unbreak? People argued about that for a very long time until the shocking insight... that it was very low 13.4 billion years ago at the time when those baby pictures of the universe were given off... the cosmic microwave background. So our flow of time... has something to do with the origin of our universe? That... we have learned. ...[I]f you take seriously the idea of inflation and also the theory that the wave function does not collapse, according to Hugh Everett, you can do some math and get an explanation... but... it's a wonderful mystery, and I'm open to all ideas... and black holes... there are great truths yet to be discovered.
  • For Neils Bohr and the Copenhagen interpretation, I respond with Hamlet, "Something is rotten in the state of Denmark." ...The wave function does not collapse. ...There is absolutely no experimental evidence for it. It appears to collapse, yes, but what Hugh Everett showed so beautifully... in the... 50s and 60s is that even if it does not collapse... If you just drop that entirely and just... go with the Schrödinger equation all the way, it's going to appear like it collapses... according to all the usual Copenhagen interpretation rules... [I]t doesn't even have anything particularly fundamental to do with quantum mechanics. ...If you have any sort of physics which lets you make copies of an observer, classically or quantum mechanically, you will experience apparent randomness. ...Suppose you ...clone yourself you can get twice as much done? ...One copy ...wakes up in Room 1 and the other... in Room 2... Are you going to see... a sign that says Room 1 or will you see a 2? You cannot predict this... because... there will be two experiences. ...It seems random. I'm going to see either... with equal probability. This is what fundamentally is happening in quantum physics too. The quantum reality is just bigger than the one we thought we lived in before quantum mechanics, and it has this ability that it can start with something which is one way and make [it] effectively being in two ways. [W]hen we make a measurement, sometimes we find out which copy we were. So I wouldn't worry too much about the way a function collapse[s].
  • It depends... on what you measure outrageousness in... If what you mean is that something is more extravagant if it... involves somehow having more particles, or reality being bigger... then sure. But... maybe the kind of simplicity that we should value with Occam's razor is rather that the math is simple. The equations are simple.
  • Here... is the Schrödinger equation [ ]... and what it's actually saying is that the state of the world, that's this Greek letter Ψ there with the bracket around it... It's saying that the rate of change of it... depends on the current state of the world, when you do this operation on it and for the math nerds, this is a linear operation... and what that just means is, as Everett has pointed out and many others have known for a very long time is that, in some circumstances, two different solutions to this can do their parallel thing. We can talk at... length about the discoveries... about decoherence and why it is that sometimes these different parallel branches are unaware or each other, but my point is... if you give a science nerd colloquium... at a physics department... ideally, you should also start in the same way you start discussing this with your grandma. Just at a very high level... here are the cool ideas, and then you can go as deep as the audience or the listener wants, from there.
  • We don't know for sure that the Schrödinger equation is actually that accurate a description of nature either. That's why it's so exciting to see what's going to happen with the quantum computer efforts... Will they ultimately fail because physics isn't fully described by the Schrödinger equation, or will they actually succeed... This is where ultimately our experimental friends will... give us crucial insights...
  • I'll be the first to admit that we ultimately don't know what's going on exactly with quantum mechanics, and my personal guess... is that even quantum mechanics is probably an emergent theory, maybe an approximation of... something deeper. Maybe we can get it out of GU somehow, but... I also would guess... the opposite of Roger Penrose... that gravity doesn't really have much to do with this. I think you can... be in a spaceship far away... from any... important gravitating objects and do your little quantum experiments with a Schrödinger-like apparatus and you would get all the same fascinating things happening. So... ignoring gravity... ignoring relativistic effects altogether, you still have this thing people love fighting about. Does the wave function collapse or not, and that's why I'm so interested in this kind of discussion...
  • [I]t's... a big mistake as a species if we don't create institutions and governments which support science. There have been a number of... economic studies that have shown... that investing in basic science is the highest return on investment, basically ever... Inventing the transistor... just basic... physics research... has benefited us so much, in so many ways... Inventing calculus... didn't cost that much, but it's... so, so valuable... This comes back to the whole media question again. There are much more people who have heard about the Kardashians than... can name three living scientists... let alone twenty. ...[W]e've created a culture where scientists... not only are they not particularly known... or viewed as role models or heroes, but they are even very actively attacked by... folks with power with whom what scientists are saying is inconvenient... One of the best things we can do for science funding is to create a less screwed-up media landscape where we actually appreciate how much we benefit from scientific research. That governments will actually support it again. ...We spend two billion dollars a day or more, in this county alone, on military... If you can get a puny, puny fraction of that into scientific research, we wouldn't even be having to have this conversation about how we get funding.
  • My favorite movie of all time is... Life of Brian. We really should try and reenact this epic skit, "What have the Romans ever done for us?" by saying "What has physics ever done for us? ...But ...besides ...the internet and transistors, what has physics ever done for us?"
  • Physicists, we have a sort of arrogance... which has harmed us a lot. ...We forget that we're in a bubble and ...that there's actually a science of how you persuade people ...of how to communicate, and other people have studied that at great length. ...[T]he average person who works making cigarette ads is much more scientific about the way they get their message out than the average physicist. ...[I]t comes not from stupidity ...but from arrogance ...We're not going to stoop so low that we're going to be scientific about how we communicate... about how we advocate. We have to get off our high horses... If you get invaded by Hitler's army, you shouldn't just say... "Tanks are immoral, we're going to fight them with swords." We have to be scientific also about standing up for ourselves and our ideas... A second mistake... spending much more time infighting within our community of physicists, or... having one science pitted against another... for a few more tax dollars... losing sight of the fact that there's a tiny trickle of money that flows to all of the sciences combined... compared to... generic fruits of... corporate lobbying and random waste... So, get out of our bubble again. If we look at the big picture, it's kind of pathetic... that you have physicists, biologists, chemists, who together have built up most of the wealth of the world, and managed to be so incredibly navel-gazing and busy with infighting, and old-fashioned in how they communicate, that they have to come begging for money, and people don't listen to them.

Quotes about Tegmark

  • Tegmark’s career is a rather unusual story, mixing reputable science with an increasingly strong taste for grandiose nonsense. In this book he indulges his inner crank, describing in detail an utterly empty vision of the "ultimate nature of reality." What's perhaps most remarkable about the book is the respectful reception it seems to be getting... Before publishing his first paper, he changed his name from Shapiro to Tegmark (his mother’s name), figuring that there were too many Shapiros in physics for him to get attention... A very odd aspect of this whole story is that while Tegmark's big claim is that Math=Physics, he seems to have little actual interest in mathematics and what it really is as an intellectual subject. ...[W]hile "mathematical structures" are invoked in the book as the basis of everything, there's little to no discussion of the mathematical structures that modern mathematicians find interesting (although the idea of "symmetries" gets a mention). ...Perhaps the explanation of all this is somehow Freudian, since Tegmark’s father is the mathematician Harold Shapiro.

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