Is the Universe a mathematical structure?

In his latest book, Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, Max Tegmark tries to answer what is maybe the most fundamental question in science and philosophy: what is the nature of reality?

Our understanding of reality has certainly undergone deep change in the last few centuries. From Galileo and Newton, to Maxwell, Einstein, Bohr and Heisenberg, Physics has evolved by leaps and bounds, as well as our understanding of the place of humans in the Universe. And yet, in some respects, we know little more than the ancient Greeks. Is the visible Universe all that exists? Could other universes, with different laws of physics, exist? Does the universe split into several universes every time a quantum observation takes place? Why is mathematics such a good model for physics (an old question) and could there exist other universes which obey different mathematical structures? These questions are not arbitrary ones, as their answers take us into the four levels of the multiverse proposed by Tegmark.

As you dive into it, the book takes us into an ever-expanding model of reality. Tegmark defines four level of multiverses: the first one consisting of all the (possibly infinite) spacetime of which we see only a ball with a radius of 14 billion light-years, since the rest is too far for light to have reached us; the second one which possibly holds other parts of spacetime which obey different laws of physics; a third one, implied by the many-worlds interpretation of quantum physics; and a fourth one, where other mathematical structures, different from the spacetime we know and love, define the rules of the game.

It is certainly a lot to take in, in a book that has less than 400 pages, and the reader may feel dizzy at times. But, in the process, Tegmark does his best at explaining what inflation is and why it plays such an important role in cosmology, how the laws of quantum physics can be viewed simply as an equation (the Schrödinger equation) describing the evolution of a point in Hilbert space, doing away with all the difficult-to-explain consequences of the Copenhagen interpretation, the difficulties caused by the measure problem, why is the space so flat, and many, many other fascinating topics in modern physics.

Since the main point of the book is to help is understand our place in this not only enormous Universe but unthinkably enormous multiverse, he brings us back to Earth (literally) with a few disturbing questions, such as:

  • What is the role of intelligence and consciousness in this humongous multiverse?
  • Why is this Universe we see amenable to life, in some places, and why have we been so lucky to be born exactly here?
  • Shall one view oneself as a random sample of an intelligent being existing in the universe (the SSA, or Self-Sampling Assumption proposed by Bostrom in his book Anthropic Bias)
  • If the SSA is valid, does it imply the Doomsday Argument, that it is very unlikely that humans will last for a long time because such a fact that would make it highly unlikely that I would have been born so soon?

All in all, a fascinating read, if at times is reads more like sci-fi than science!

Could Venus possibly harbor life?

Two recently published papers, including one in Nature Astronomy (about the discovery itself) and this one in Astrobiology (describing a possible life cycle), report the existence of phosphine in the upper atmosphere of Venus, a gas that cannot be easily generated by non-biological processes in the conditions believed to exist in that planet. Phosphine may, indeed, turn out to be a biosignature, an indicator of the possible existence of micro-organisms in a planet that was considered, up to now, barren. Search for life in our solar system has been concentrated in other bodies, more likely to host micro-organisms, like Mars of the icy moons of outer planets.

The findings have been reported in many media outlets, including the NY Times and The Economist, raising interesting questions about the prevalence of life in the universe and the possible existence of life in one of our nearest neighbor planets. If the biological origin of phosphine were to be confirmed, it would qualify as the discovery of the century, maybe the most important discovery in the history of science! We are, however, far from that point. A number of things may make this finding another false alarm. Still, it is quite exciting that what has been considered a possible sign of life has been found so close to us and even a negative result would increase our knowledge about the chemical processes that generate this compound until now believed to be a reliable biomarker.

This turns out to be a first step, not a final result. Quoting from the Nature Astronomy paper:

Even if confirmed, we emphasize that the detection of PH3 is not robust evidence for life, only for anomalous and unexplained chemistry. There are substantial conceptual problems for the idea of life in Venus’s clouds—the environment is extremely dehydrating as well as hyperacidic. However, we have ruled out many chemical routes to PH3, with the most likely ones falling short by four to eight orders of magnitude (Extended Data Fig. 10). To further discriminate between unknown photochemical and/or geological processes as the source of Venusian PH3, or to determine whether there is life in the clouds of Venus, substantial modelling and experimentation will be important. Ultimately, a solution could come from revisiting Venus for in situ measurements or aerosol return.

The Big Picture: On the Origins of Life, Meaning and the Universe Itself

Sean Carroll’s 2016 book, The Big Picture, is a rather well-succeeded attempt to cover all the topics that are listed in the subtitle of the book, life, the universe, and everything.  Carroll calls himself a poetic naturalist, short for someone who believes physics explains everything but does not eliminate the need for other levels of description of the universe, such as biology, psychology, and sociology, to name a few.

Such an ambitious list of topics requires a fast-paced book, and that is exactly what you get. Organized in no less than 50 chapters, the book brings us from the very beginning of the universe to the many open questions related to intelligence, consciousness, and free-will. In the process, we get to learn about what Carroll calls the “core theory”, the complete description of all the particles and forces that make the universe, as we know it today, encompassing basically the standard model and general relativity. In the process, he takes us through the many things we know (and a few of the ones we don’t know) about quantum field theory and the strangeness of the quantum world, including a rather good description of the different possibilities of addressing this strangeness: the Copenhaguen interpretation, hidden variables theories and (the one the author advocates) Everett’s many-worlds interpretation.

Although fast-paced, the book succeeds very well in connecting and going into some depth into these different fields. The final sections of the book, covering life, intelligence, consciousness, and morals are a very good introduction to these complex topics, many of them addressed also in Sean Carroll popular podcast, Mindscape.

Mindscape, a must-have podcast by Sean Carroll

Sean Carroll’s Mindscape podcast addresses topics as diverse as the interests of the author, including (but not limited to) physics, biology, philosophy, complexity, intelligence, and consciousness. Carroll has interviewed, in-depth, a large number of very interesting scientists, philosophers, writers, and thinkers, who come to talk about some of the most central open topics in science and philosophy.

Among many other, Daniel Dennett discusses minds and patterns; Max Tegmark  physics, simulation and the multiverse;   António Damásio  feeling, emotions and evolution; Patricia Churchland, conscience and morality; and David Chalmers, the hard problem of consciousness.

In all the interviews, Sean Carroll conducts the conversation in an easy and interactive mode, not imposing his own views, not even on the more controversial topics where the interviewees hold diametrically opposed opinions.

If you are into science and into podcasts, you cannot miss this one.

The Fabric of Reality

The Fabric of Reality, a 1997 book by David Deutsch, is full of great ideas, most of them surprising and intriguing. The main argument is that explanations are the centerpiece of science and that four theories play an essential role in our understanding of the world: quantum theory, the theory of evolution, the theory of computation and epistemology (the theory of knowledge).

You may raise a number of questions about these particular choices, such as why is the theory of relativity not there or why is the theory of evolution simply not a result of other theories in physics or even what makes epistemology to special. You will have to read the book to find out but the short answer is that not everything is physics and that theories at many levels are required to explain the world. Still, in physics, the most fundamental idea is quantum theory and it has profound impacts on our understanding of the universe. Perhaps the most significant impact comes from the fact that (according to Deutsch) what we know about quantum theory implies that we live in a multiverse. Each time a quantum phenomenon can conduct to more than one observable result, the universe splits into as many universes as the number of possible results, universes that exist simultaneously in the multiverse.

Although the scientific establishment views the multiverse theory with reservation, to say the least, to Deutsch, the multiverse is not just a theory, but the only possible explanation for what we know about quantum physics (he dismisses the Copenhagen interpretation as nonsense). Armed with these four theories, and the resulting conclusion that we live in a multiverse, Deutsch goes on to address thought-provoking questions, such as:

  • Is life a small thing at the scale of the universe or, on the contrary, is the most important thing on it?
  • Can we have free will, in a deterministic universe? And in the multiverse?
  • Do computers strictly more powerful than Turing machines exist, and how do they work?
  • Can mathematical proofs provide us with absolute certainties about specific mathematical statements?
  • Is time travel possible, at least in principle, either in the physical world or in a virtual reality simulator?
  • Will we (or our descendants, or some other species) eventually become gods, when we reach the Omega point?

The idea of the multiverse is required to answer most, if not all, of these questions. Deutsch is certainly not a parsimonious person when he uses universes to answer questions and to solve problems. The multiverse allows you to have free will, solves the paradoxes of time travel and makes quantum computers possible, among many other things. One example of the generous use of universes made by Deutsch is the following sentence:

When a quantum factorization engine is factorizing a 250-digit number, the number of interfering universes will be of the order of 10 to the 500. This staggeringly large number is the reason why Shor’s algorithm makes factorization tractable. I said that the algorithm requires only a few thousand arithmetic operations. I meant, of course, a few thousand operations in each universe that contributes to the answer. All those computations are performed in parallel, in different universes, and share their results through interference.

The fact that Deutsch’s arguments depend so heavily on the multiverse idea makes this book much more about the multiverse than about the other topics he addresses. After all, if the multiverse theory is wrong, many of Deutsch’s explanations collapse, interesting as they may be.

Still, the book is full of great ideas, makes for some interesting reading, and presents many interesting concepts, some of them further developed in other books by Deutsch, such as The Beginning of Infinity.

The Beginning of Infinity

David Deutsch‘s newest book, The Beginning of Infinity is a tour de force argument for the power of science to transform the world. Deutsch’s main point is that human intelligence, once it reached the point where it started to be used to construct predictive explanations about the behavior of nature, became universal. Here, “universal” means that is can be used to understand any phenomenon and that this understanding leads to the creation of new technologies, which will be used to spread human intelligence throughout the known universe.

The Beginning of Infinity is not just one more book about science and how science is transforming our world. It is an all-encompassing analysis of the way human intelligence and human societies can develop or stagnate, by adopting or refusing to adopt the stance of looking for understandable explanations. Deutsch calls “static” those societies that refuse to look for new, non-supernatural explanations and “dynamic” those that are constantly looking for new explanations, based on objective and checkable evidence. Dynamic societies, he argues, develop and propagate rational memes, while static societies hold on to non-rational memes.

In the process, Deutsch talks authoritatively about evolution, the universality of computation, quantum mechanics, the multiverse and the paradoxes of infinity. They are not disparate subjects since they all become part of one single story on how humanity managed to understand and control the physical world.

Deutsch is at his best when arguing that science and technology are not only positive forces but that they are the only way to ensure the survival of Humanity in the long run. He argues, convincingly, against the myth of Gaia, the idea that the planet is a living being providing us with a generous and forgiving environment as well as against the related, almost universal, concern that technological developments are destroying the planet. This is nonsense, he argues. The future survival of Humanity and the hope of spreading human intelligence throughout the Cosmos reside entirely in our ability to control nature and to bend it to our will. Otherwise, we will follow the path of the many species that became extinct, for not being able to control the natural or unnatural phenomena that led to their extinction.

Definitely, the book to read if you care about the Future of Humanity.

 

LIFE 3.0: Being Human in the Age of Artificial Intelligence

Max Tegmark’s latest book, LIFE 3.0: Being Human in the Age of Artificial Intelligence, is an enthralling journey into the future, when the developments in artificial intelligence create a new type of lifeform on Earth.

Tegmark proposes to classify life in three stages. Life 1.0, unintelligent life, is able to change its hardware and improve itself only through the very slow and blind process of natural evolution. Single cell organisms, plants and simple animals are in this category. Life 2.0 is also unable to change its hardware (excepto through evolution, as for Life 1.0) but can change its software, stored in the brains, by using previous experience to learn new behaviors. Higher animals and humans, in particular, belong here. Humans can now, up to a limited point, change their hardware (through prosthetics, cellphones, computers and other devices) so they could also be considered now Life 2.1.

Life 3.0 is the new generation of life, which can change both its software and its hardware. The ability to change the computational support (i.e., the physical basis of computation) results from technological advances, which will only accelerate with the advent of Artificial General Intelligence (AGI). The book is really about the future of a world where AGI enables humanity to create a whole range of new technologies, and expand new forms of life through the cosmos.

The riveting prelude, The Tale of the Omega Team, is the story of the group of people who “created” the first intelligence explosion on planet Earth makes this a “hard-to-put-down” book.  The rest of the book goes through the consequences of this intelligence explosion, a phenomenon the author believes will undoubtedly take place, sooner or later. Chapter 4 focus on the explosion proper, and on how it could happen. Chapter 5, appropriately titled “Aftermath: The Next 10,000 Years” is one of the most interesting ones, and describes a number of long term scenarios that could result from such an event. These scenarios range from a benevolent and enlightened dictatorship (by the AI) to the enslaved God situation, where humanity keeps the AI in chains and uses it as a slave to develop new technologies, inaccessible to unaided humanity’s simpler minds. Always present, in these scenarios, are the risks of a hostile takeover by a human-created AGI, a theme that this book also addresses in depth, following on the ideas proposed by Nick Bostrom, in his book Superintelligence.

Being a cosmologist, Tegmark could not leave out the question of how life can spread through the Cosmos, a topic covered in depth in chapter 6, in a highly speculative fashion. Tegmark’s view is, to say the least, grandiose, envisaging a future where AGI will make it possible to spread life through the reachable universe, climbing the three levels of the Kardashev scale. The final chapters address (in a necessarily more superficial manner) the complex topics of goal setting for AI systems and artificial (or natural) consciousness. These topics somehow felt less well developed and more complete and convincing treatments can be found elsewhere. The book ends with a description of the mission of the Future of Life Institute, and the Asilomar AI Principles.

A book like this cannot leave anyone indifferent, and you will be likely to take one of two opposite sides: the optimistis, with many famous representatives, including Elon Mush, Stuart Russel and Nick Bostrom, who believe AGI can be developed and used to make humanity prosper; or the pessimists , whose more visible member is probably Yuval Noah Harari, who has voiced very serious concerns about technology developments in his book Homo Deus and in this review of Life 3.0.

Bell’s Theorem, or why the universe is even stranger than we might imagine

The Einstein-Podolsky-Rosen “paradox” was at first presented as an argument against some of the basic tenets of quantum mechanics.

One of these basic tenets is that there is genuine randomness in the characteristics of particles. For instance, when one measures the spin of an electron, it is only at the instant the measure is taken that the actual value of the spin is defined. Until then, its value was defined by a probability function, that collapses when the measurement is taken.

The EPR paradox uses the concept of entangled particles. Two particles are “entangled” if they were generated in such a way that they exhibit a totally correlated particular characteristic. For instance, two photons generated by a specific phenomenon (such as an electron-positron annihilation, under some circumstances) will have opposite polarizations. Once generated, these particles can travel vast distances, still entangled.

If some particular characteristic of one of these particles is measured (e.g., the polarization of a photon) in one location, this measurement will, probabilistically, result in a given value. That particular value will determine, instantaneously, the value of that same characteristic on the other particle, no matter how far the particles are. It is this “spooky action at a distance” that Einstein, Podolsky and Rosen believed to be impossible. It seems that the information about the state of one of the particles travels, faster than light, to the place where the other particle is.

Now, we can imagine that that particular characteristic of the particles was defined the very instant they were generated. Imagine you have one bag with one white ball and one black ball, and you separate the balls, without looking at them,  and put them into separate boxes. If one of the boxes is opened in Australia, say, and it is white, we will know instantaneously the color of the other ball. There is nothing magic or strange about this. Hidden inside the boxes, was all along the true color of the boxes, a hidden variable.

Maybe this is exactly what happens with the entangled photons. When they are generated, each one already carries with it the actual value of the polarization.

It is here that Bell’s Theorem comes to show that the universe is even stranger than we might conceive. Bell’s result, beautifully explained in this video, shows that the particles cannot carry with them any hidden variable that tells them what to do when they face a measurement. Each particle has to decide, probabilistically, at the time of the measurement, the value that should be reported. And, once this decision is made, the measurement for the other entangled particle is also defined, even if the other particle is on the other side of the universe. It seems that information travels faster than light.

The fact is that hidden variables cannot be used to explain this phenomenon. As Bell concluded “In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, …

A very easy and practical demonstration of Bell’s theorem can be done with polarized filters, like the ones used in cameras or some 3D glasses. If you take two filters and put them at an angle, only a fraction of the photons that go through the first one make it through the second one. The actual fraction is given by the cosine squared of the angle between the filters(so, if the angle is 90º, no photons go through the two filters). So far, so good. Now, if you have the two filters at an angle (say 45º, so that half the photons that pass the first go through the second filter) and put an additional filter between them, at an angle of 22.5º, it happens that roughly 85% of the photons go through the (now) second filter. Of these, roughly 85% go through the third filter (which used to be the second). That means that, with the three filters in place, roughly 72% of the photons go through, way more than if you had just the two first filters, which were not changed in any way. This, obviously, cannot happen if the decision of the photons was determined from the start.

Do look at the video, and do the experience yourself.