Tuesday, April 29, 2014

FQXi essay contest 2014: How Should Humanity Steer the Future?

This year’s essay contest of the Foundational Questions Institute “How Should Humanity Steer the Future?” broaches a question that is fundamental indeed, fundamental not for quantum gravity but for the future of mankind. I suspect the topic selection has been influenced by the contest being “presented in partnership with” (which I translate into “sponsored by”) not only the John Templeton foundation and Scientific American, but also a philanthropic organization called the “Gruber Foundation” (which I had never heard of before) and Jaan Tallinn.

Tallinn is no unknown, he is one of the developers of Skype and when I type his name into Google the auto completion is “net worth”. I met him at the 2011 FQXi conference where he gave a little speech about his worries that artificial intelligence will turn into a threat to humans. I wrote back then a blogpost explaining that I don’t share this particular worry. However, I recall Tallinn’s speech vividly, not because it was so well delivered (in fact, he seemed to be reading off his phone), but because he was so very sincere about it. Most people’s standard reaction in the face of threats to the future of mankind is cynicism or sarcasm, essentially a vocal shoulder shrug, whereas Tallinn seems to have spent quite some time thinking about this. And well, somebody really should be thinking about this...

And so I appreciate the topic of this year’s essay contest has a social dimension, not only because it gets tiresome to always circle the same question of where the next breakthrough in theoretical physics will be and the always same answers (let me guess, it’s what you work on), but also because it gives me an outlet for my interests besides quantum gravity. I have always been fascinated by the complex dynamics of systems that are driven by the individual actions of many humans because this reaches out to the larger question of where life on planet Earth is going and why and what all of this is good for.

If somebody asks you how humanity should steer the future, a modest reply isn’t really an option, so I have submitted my five step plan to save the world. Well, at least you can’t blame me for not having a vision. The executive summary is that we will only be able to steer at all if we have a way to collectively react to large scale behavior and long-term trends of global systems, and this can only happen if we are able to make informed decisions intuitively, quickly and without much thinking.

A steering wheel like this might not be sufficient to avoid running into obstacles, but it is definitely necessary, so that is what we have to start with.

The trends that we need to react to are those of global and multi-leveled systems, including economic, social, ecological and politic systems, as well as various infrastructure networks. Presently, we basically fail to act when problems appear. While the problems arise from the interaction of many people and their environment, it is still the individual that has to make decisions. But the individual presently cannot tell how their own action works towards their goals on long distance or time scales. To enable them to make good decisions, the information about the whole system has to be routed back to the individual. But that feedback loop doesn’t presently exist.

In principle it would be possible today, but the process is presently far too difficult. The vast majority of people do not have the time and energy to collect the necessary information and make decisions based on it. It doesn’t help to write essays about what we ‘should’ do. People will only act if it’s really simple to do and of immediate relevance for them. Thus my suggestion is to create individual ‘priority maps’ that chart personal values and provide people with intuitive feedback for how well a decision matches with their priorities.

A simple example. Suppose you train some software to tell what kind of images you find aesthetically pleasing and what you dislike. You now have various parameters, say colors, shapes, symmetries, composition and so on. You then fill out a questionnaire about preferences for political values. Now rather than long explanations which candidate says what, you get an image that represents how good the match is by converting the match in political values to parameters in an image. You pick the image you like best and are done. The point is that you are being spared having to look into the information yourself, you only get to see the summary that encodes whether voting for that person would work towards what you regard important.

Oh, I hear you say, but that vastly oversimplifies matters. Indeed, that is exactly the point. Oversimplification is the only way we’ll manage to overcome our present inability to act.

If mankind is to be successful in the long run, we have to evolve to anticipate and react to interrelated global trends in systems of billions of people. Natural selection might do this, but it would take too much time. The priority maps are a technological shortcut to emulate an advanced species that is ‘fit’ in the Darwinian sense, fit to adapt to its changing environment. I envision this to become a brain extension one day.

I had a runner up to this essay contribution, which was an argument that research in quantum gravity will be relevant for quantum computing, interstellar travel and technological progress in general. But it would have been a quite impractical speculation (not to mention a self-advertisement of my work on superdeterminism, superluminal information exchange and antigravity). In my mind of course it’s all related – the laws of physics are what eventually drive the evolution of consciousness and also of our species. But I decided to stick with a proposal that I think is indeed realizable today and that would go a long way to enable humanity to steer the future.

I encourage you to check out the essays which cover a large variety of ideas. Some of the contributions seem to be very bent towards the aim of making a philosophical case for some understanding of natural law rather than the other, or to find parallels to unsolved problems in physics, but this seems quite a stretch to me. However, I am sure you will find something of interest there. At the very least it will give you some new things to worry about...

Saturday, April 26, 2014

Academia isn’t what I expected

The Ivory Tower from
The Neverending Story. [Source]
Talking to the students at the Sussex school let me realize how straight-forward it is today to get a realistic impression of what research in this field looks like. Blogs are a good source of information about scientist’s daily life and duties, and it has also become so much easier to find and make contact with people in the field, either using social networks or joining dedicated mentoring programs.

Before I myself got an office at a physics institute I only had a vague idea of what people did there. Absent the lauded ‘role models’ my mental image of academic research formed mostly by reading biographies of the heroes of General Relativity and Quantum Mechanics, plus a stack of popular science books. The latter didn’t contain much about the average researcher’s daily tasks, and to the extent that the former captured university life, it was life in the first half of the 20nd century.

I expected some things to have changed during 50 years, notably in technological advances and the ease of travel, publishing, and communication. I finished high school in ’95, so the biggest changes were yet to come. I also knew that disciplines had drifted apart, that philosophy and physics were mostly going separate ways now, and that the days in which a physicist could also be a chemist could also be an artist were long gone. It was clear that academia had generally grown, become more organized and institutionalized, and closer linked to industrial research and applications. I had heard that applying for money was a big part of the game. Those were the days.

But my expectations were wrong in many other ways. 20 years, 9 moves and 6 jobs later, here’s the contrast of what I believed theoretical physics would be like to reality:
  1. Specialization

    While I knew that interdisciplinarity had given in to specialization I thought that theoretical physicists would be in close connection to the experimentalists, that they would frequently discuss experiments that might be interesting to develop, or data that required explanation. I also expected theoretical physicists to work closely together with mathematicians, because in the history of physics the mathematics has often been developed alongside the physics. In both cases the reality is an almost complete disconnect. The exchange takes place mostly through published literature or especially dedicated meetings or initiatives.

  2. Disconnect

    I expected a much larger general intellectual curiosity and social responsibility in academia. Instead I found that most researchers are very focused on their own work and nothing but their own work. Not only do institutes rarely if ever have organized public engagement or events that are not closely related to the local research, it’s also that most individual researchers are not interested. In most cases, they plainly don’t have the time to think about anything than their next paper. That disconnect is the root of complaints like Nicholas Kristof’s recent Op-Ed, where calls upon academics: “[P]rofessors, don’t cloister yourselves like medieval monks — we need you!”

  3. The Machinery

    My biggest reality shock was how much of research has turned into manufacturing, into the production of PhDs and papers, papers that are necessary for the next grant, which is necessary to pay the next students, who will write the next papers, iterate. This unromantic hamster wheel still shocks me. It has its good side too though: The standardization of research procedures limits the risks of the individual. If you know how to play along, and are willing to, you have good chances that you can stay. The disadvantage is though that this can force students and postdocs to work on topics they are not actually interested in, and that turns off many bright and creative people.

  4. Nonlocality

    I did not anticipate just how frequent travel and moves are necessary these days. If I had known about this in advance, I think I would have left academia after my diploma. But so I just slipped into it. Luckily I had a very patient boyfriend who turned husband who turned father of my children.

  5. The 2nd family

    The specialization, the single-mindedness, the pressure and, most of all, the loss of friends due to frequent moves create close ties among those who are together in the same boat. It’s a mutual understanding, the nod of been-there-done-that, the sympathy with your own problems that make your colleagues and officemates, driftwood as they often are, a second family. In all these years I have felt welcome at every single institute that I have visited. The books hadn’t told me about this.

Experience, as they say, is what you get when you were expecting something else. By and large, I enjoy my job. Most of the time anyway.

My lectures at the Sussex school went well, except that the combination of a recent cold and several hours of speaking stressed my voice box to the point of total failure. Yesterday I could only whisper. Today I get out some freak sounds below C2 but that’s pretty much it. It would be funny if it wasn’t so painful.

You can find the slides of my lectures here and the guide to further reading here. I hope they live up to your expectations :)

Monday, April 21, 2014

Away note

I will be traveling the rest of the week to give a lecture at the Sussex graduate school "From Classical to Quantum GR", so not much will happen on this blog. For the school, we were asked for discussion topics related to our lectures, below are my suggestions. Leave your thoughts in the comments, additional suggestions for topics are also welcome.

  • Is it socially responsible to spend money on quantum gravity research? Don't we have better things to do? How could mankind possibly benefit from quantum gravity?
  • Can we make any progress on the theory of quantum gravity without connection to experiment? Should we think at all about theories of quantum gravity that do not produce testable predictions? How much time do we grant researchers to come up with predictions?
  • What is your favorite approach towards quantum gravity? Why? Should you have a favorite approach at all?
  • Is our problem maybe not with the quantization of gravity but with the foundations of quantum mechanics and the process of quantization?
  • How plausible is it that gravity remains classical while all the other forces are quantized? Could gravity be neither classical nor quantized?
  • How convinced are you that the Planck length is at 10-33cm? Do you think it is plausible that it is lower? Should we continue looking for it?
  • What do you think is the most promising area to look for quantum gravitational effects and why?
  • Do you think that gravity can be successfully quantized without paying attention to unification?
Lara and Gloria say hello and wish you a happy Easter :o)

Thursday, April 17, 2014

The Problem of Now

[Image Source]

Einstein’s greatest blunder wasn’t the cosmological constant, and neither was it his conviction that god doesn’t throw dice. No, his greatest blunder was to speak to a philosopher named Carnap about the Now, with a capital.

“The problem of Now”, Carnap wrote in 1963, “worried Einstein seriously. He explained that the experience of the Now means something special for men, something different from the past and the future, but that this important difference does not and cannot occur within physics”

I call it Einstein’s greatest blunder because, unlike the cosmological constant and indeterminism, philosophers, and some physicists too, are still confused about this alleged “Problem of Now”.

The problem is often presented like this. Most of us experience a present moment, which is a special moment in time, unlike the past and unlike the future. If you write down the equations governing the motion of some particle through space, then this particle is described, mathematically, by a function. In the simplest case this is a curve in space-time, meaning the function is a map from the real numbers to a four-dimensional manifold. The particle changes its location with time. But regardless of whether you use an external definition of time (some coordinate system) or an internal definition (such as the length of the curve), every single instant on that curve is just some point in space-time. Which one, then, is “now”?

You could argue rightfully that as long as there’s just one particle moving on a straight line, nothing is happening, and so it’s not very surprising that no notion of change appears in the mathematical description. If the particle would scatter on some other particle, or take a sudden turn, then these instances can be identified as events in space-time. Alas, that still doesn’t tell you whether they happen to the particle “now” or at some other time.

Now what?

The cause for this problem is often assigned to the timeless-ness of mathematics itself. Mathematics deals in its core with truth values and the very point of using math to describe nature is that these truths do not change. Lee Smolin has written a whole book about the problem with the timeless math, you can read my review here.

It may or may not be that mathematics is able to describe all of our reality, but to solve the problem of now, excuse the heresy, you do not need to abandon a mathematical description of physical law. All you have to do is realize that the human experience of now is subjective. It can perfectly well be described by math, it’s just that humans are not elementary particles.

The decisive ability that allows us to experience the present moment as being unlike other moments is that we have a memory. We have a memory of events in the past, an imperfect one, and we do not have memory of events in the future. Memory is not in and by itself tied to consciousness, it is tied to the increase of entropy, or the arrow of time if you wish. Many materials show memory; every system with a path dependence like eg hysteresis does. If you get a perm the molecule chains in your hair remember the bonds, not your brain.

Memory has nothing to do with consciousness in particular which is good because it makes it much easier to find the flaw in the argument leading to the problem of now.

If we want to describe systems with memory we need at the very least two time parameters: t to parameterize the location of the particle and τ to parameterize the strength of memory of other times depending on its present location. This means there is a function f(t,τ) that encodes how strong is the memory of time τ at moment t. You need, in other words, at the very least a two-point function, a plain particle trajectory will not do.

That we experience a “now” means that the strength of memory peaks when both time parameters are identical, ie t-τ = 0. That we do not have any memory of the future means that the function vanishes when τ > t. For the past it must decay somehow, but the details don’t matter. This construction is already sufficient to explain why we have the subjective experience of the present moment being special. And it wasn’t that difficult, was it?

The origin of the problem is not in the mathematics, but in the failure to distinguish subjective experience of physical existence from objective truth. Einstein spoke about “the experience of the Now [that] means something special for men”. Yes, it means something special for men. This does not mean however, and does not necessitate, that there is a present moment which is objectively special in the mathematical description. In the above construction all moments are special in the same way, but in every moment that very moment is perceived as special. This is perfectly compatible with both our experience and the block universe of general relativity. So Einstein should not have worried.

I have a more detailed explanation of this argument – including a cartoon! – in a post from 2008. I was reminded of this now because Mermin had a comment in the recent issue of Nature magazine about the problem of now.

In his piece, Mermin elaborates on qbism, a subjective interpretation of quantum mechanics. I was destined to dislike this just because it’s a waste of time and paper to write about non-existent problems. Amazingly however, Mermin uses the subjectiveness of qbism to arrive at the right conclusion, namely that the problem of the now does not exist because our experiences are by its very nature subjective. However, he fails to point out that you don’t need to buy into fancy interpretations of quantum mechanics for this. All you have to do is watch your hair recall sulphur bonds.

The summary, please forgive me, is that Einstein was wrong and Mermin is right, but for the wrong reaons. It is possible to describe the human experience of the present moment with the “timeless” mathematics that we presently use for physical laws, it isn’t even difficult and you don’t have to give up the standard interpretation of quantum mechanics for this. There is no problem of Now and there is no problem with Tegmark’s mathematical universe either.

And Lee Smolin, well, he is neither wrong nor right, he just has a shaky motivation for his cosmological philosophy. It is correct, as he argues, that mathematics doesn’t objectively describe a present moment. However, it’s a non sequitur that the current approach to physics has reached its limits because this timeless math doesn’t constitute a conflict with our experience. observation.

Most people get a general feeling of uneasiness when they first realize that the block universe implies all the past and all the future is equally real as the present moment, that even though we experience the present moment as special, it is only subjectively so. But if you can combat your uneasiness for long enough, you might come to see the beauty in eternal mathematical truths that transcend the passage of time. We always have been, and always will be, children of the universe.

Saturday, April 12, 2014

Book review: “The Theoretical Minimum – Quantum Mechanics” By Susskind and Friedman

Quantum Mechanics: The Theoretical Minimum
What You Need to Know to Start Doing Physics
By Leonard Susskind, Art Friedman
Basic Books (February 25, 2014)

This book is the second volume in a series that we can expect to be continued. The first part covered Classical Mechanics. You can read my review here.

The volume on quantum mechanics seems to have come into being much like the first, Leonard Susskind teamed up with Art Friedman, a data consultant whose role I envision being to say “Wait, wait, wait” whenever the professor’s pace gets too fast. The result is an introduction to quantum mechanics like I haven’t seen before.

The ‘Theoretical Minimum’ focuses, as its name promises, on the absolute minimum and aims at being accessible with no previous knowledge other than the first volume. The necessary math is provided along the way in separate interludes that can be skipped. The book begins with explaining state vectors and operators, the bra-ket notation, then moves on to measurements, entanglement and time-evolution. It uses the concrete example of spin-states and works its way up to Bell’s theorem, which however isn’t explicitly derived, just captured verbally. However, everybody who has made it through Susskind’s book should be able to then understand Bell’s theorem. It is only in the last chapters that the general wave-function for particles and the Schrödinger equation make an appearance. The uncertainty principle is derived and path integrals are very briefly introduced. The book ends with a discussion of the harmonic oscillator, clearly building up towards quantum field theory there.

I find the approach to quantum mechanics in this book valuable for several reasons. First, it gives a prominent role to entanglement and density matrices, pure and mixed states, Alice and Bob and traces over subspaces. The book thus provides you with the ‘minimal’ equipment you need to understand what all the fuzz with quantum optics, quantum computing, and black hole evaporation is about. Second, it doesn’t dismiss philosophical questions about the interpretation of quantum mechanics but also doesn’t give these very prominent space. They are acknowledged, but then it gets back to the physics. Third, the book is very careful in pointing out common misunderstandings or alternative notations, thus preventing much potential confusion.

The decision to go from classical mechanics straight to quantum mechanics has its disadvantages though. Normally the student encounters Electrodynamics and Special Relativity in between, but if you want to read Susskind’s lectures as self-contained introductions, the author now doesn’t have much to work with. This time-ordering problem means that every once in a while a reference to Electrodynamics or Special Relativity is bound to confuse the reader who really doesn’t know anything besides this lecture series.

It also must be said that the book, due to its emphasis on minimalism, will strike some readers as entirely disconnected from history and experiment. Not even the double-slit, the ultraviolet catastrophe, the hydrogen atom or the photoelectric effect made it into the book. This might not be for everybody. Again however, if you’ve made it through the book you are then in a good position to read up on these topics elsewhere. My only real complaint is that Ehrenfest’s name doesn’t appear together with his theorem.

The book isn’t written like your typical textbook. It has fairly long passages that offer a lot of explanation around the equations, and the chapters are introduced with brief dialogues between fictitious characters. I don’t find these dialogues particularly witty, but at least the humor isn’t as nauseating as that in Goldberg’s book.

All together, the “Theoretical Minimum” achieves what it promises. If you want to make the step from popular science literature to textbooks and the general scientific literature, then this book series is a must-read. If you can’t make your way through abstract mathematical discussions and prefer a close connection to example and history, you might however find it hard to get through this book.

I am certainly looking forward to the next volume.

(Disclaimer: Free review copy.)

Monday, April 07, 2014

Will the social sciences ever become hard sciences?

The term “hard science” as opposed to “soft science” has no clear definition. But roughly speaking, the less the predictive power and the smaller the statistical significance, the softer the science. Physics, without doubt, is the hard core of the sciences, followed by the other natural sciences and the life sciences. The higher the complexity of the systems a research area is dealing with, the softer it tends to be. The social sciences are at the soft end of the spectrum.

To me the very purpose of research is making science increasingly harder. If you don’t want to improve on predictive power, what’s the point of science to begin with? The social sciences are soft mainly because data that quantifies the behavior of social, political, and economic systems is hard to come by: it’s huge amounts, difficult to obtain and even more difficult to handle. Historically, these research areas therefore worked with narratives relating plausible causal relations. Needless to say, as computing power skyrockets, increasingly larger data sets can be handled. So the social sciences are finally on the track to become useful. Or so you’d think if you’re a physicist.

But interestingly, there is a large opposition to this trend of hardening the social sciences, and this opposition is particularly pronounced towards physicists who take their knowledge to work on data about social systems. You can see this opposition in the comment section to every popular science article on the topic. “Social engineering!” they will yell accusingly.

It isn’t so surprising that social scientists themselves are unhappy because the boat of inadequate skills is sinking in the data sea and physics envy won’t keep it afloat. More interesting than the paddling social scientists is the public opposition to the idea that the behavior of social systems can be modeled, understood, and predicted. This opposition is an echo of the desperate belief in free will that ignores all evidence to the contrary. The desperation in both cases is based on unfounded fears, but unfortunately it results in a forward defense.

And so the world is full with people who argue that they must have free will because they believe they have free will, the ultimate confirmation bias. And when it comes to social systems they’ll snort at the physicists “People are not elementary particles”. That worries me, worries me more than their clinging to the belief in free will, because the only way we can solve the problems that mankind faces today – the global problems in highly connected and multi-layered political, social, economic and ecological networks – is to better understand and learn how to improve the systems that govern our lives.

That people are not elementary particles is not a particularly deep insight, but it collects several valid points of criticism:

  1. People are too difficult. You can’t predict them.

    Humans are made of a many elementary particles and even though you don’t have to know the exact motion of every single one of these particles, a person still has an awful lot of degrees of freedom and needs to be described by a lot of parameters. That’s a complicated way of saying people can do more things than electrons, and it isn’t always clear exactly why they do what they do.

    That is correct of course, but this objection fails to take into account that not all possible courses of action are always relevant. If it was true that people have too many possible ways to act to gather any useful knowledge about their behavior our world would be entirely dysfunctional. Our societies work only because people are to a large degree predictable.

    If you go shopping you expect certain behaviors of other people. You expect them to be dressed, you expect them to walk forwards, you expect them to read labels and put things into a cart. There, I’ve made a prediction about human behavior! Yawn, you say, I could have told you that. Sure you could, because making predictions about other people’s behavior is pretty much what we do all day. Modeling social systems is just a scientific version of this.

    This objection that people are just too complicated is also weak because, as a matter of fact, humans can and have been modeled with quite simple systems. This is particularly effective in situations when intuitive reaction trumps conscious deliberation. Existing examples are traffic flows or the density of crowds when they have to pass through narrow passages.

    So, yes, people are difficult and they can do strange things, more things than any model can presently capture. But modeling a system is always an oversimplification. The only way to find out whether that simplification works is to actually test it with data.

  2. People have free will. You cannot predict what they will do.

    To begin with it is highly questionable that people have free will. But leaving this aside for a moment, this objection confuses the predictability of individual behavior with the statistical trend of large numbers of people. Maybe you don’t feel like going to work tomorrow, but most people will go. Maybe you like to take walks in the pouring rain, but most people don’t. The existence of free will is in no conflict with discovering correlations between certain types of behavior or preferences in groups. It’s the same difference that doesn’t allow you to tell when your children will speak the first word or make the first step, but that almost certainly by the age of three they’ll have mastered it.

  3. People can understand the models and this knowledge makes predictions useless.

    This objection always stuns me. If that was true, why then isn’t obesity cured by telling people it will remain a problem? Why are the highways still clogged at 5pm if I predict they will be clogged? Why will people drink more beer if it’s free even though they know it’s free to make them drink more? Because the fact that a prediction exists in most cases doesn’t constitute any good reason to change behavior. I can predict that you will almost certainly still be alive when you finish reading this blogpost because I know this prediction is exceedingly unlikely to make you want to prove it wrong.

    Yes, there are cases when people’s knowledge of a prediction changes their behavior – self-fulfilling prophecies are the best-known examples of this. But this is the exception rather than the rule. In an earlier blogpost, I referred to this as societal fixed points. These are configurations in which the backreaction of the model into the system does not change the prediction. The simplest example is a model whose predictions few people know or care about.

  4. Effects don’t scale and don’t transfer.

    This objection is the most subtle one. It posits that the social sciences aren’t really sciences until you can do and reproduce the outcome of “experiments”, which may be designed or naturally occurring. The typical social experiment that lends itself to analysis will be in relatively small and well-controlled communities (say, testing the implementation of a new policy). But then you have to extrapolate from this how the results will be in larger and potentially very different communities. Increasing the size of the system might bring in entirely new effects that you didn’t even know of (doesn’t scale), and there are a lot of cultural variables that your experimental outcome might have depended on that you didn’t know of and thus cannot adjust for (doesn’t transfer). As a consequence, repeating the experiment elsewhere will not reproduce the outcome.

    Indeed, this is likely to happen and I think it is the major challenge in this type of research. For complex relations it will take a long time to identify the relevant environmental parameters and to learn how to account for their variation. The more parameters there are and the more relevant they are, the less the predictive value of a model will be. If there are too many parameters that have to be accounted for it basically means doing experiments is the only thing we can ever do. It seems plausible to me, even likely, that there are types of social behavior that fall into this category, and that will leave us with questions that we just cannot answer.

    However, whether or not a certain trend can or cannot be modeled we will only know by trying. We know that there are cases where it can be done. Geoffry West’s city theory I find a beautiful example where quite simple laws can be found in the midst of all these cultural and contextual differences.
In summary.

The social sciences will never be as “hard” as the natural sciences because there is much more variation among people than among particles and among cities than among molecules. But the social sciences have become harder already and there is no reason why this trend shouldn’t continue. I certainly hope it will continue because we need this knowledge to collectively solve the problems we have collectively created.

Tuesday, April 01, 2014

Do we live in a hologram? Really??

Physicists fly high on the idea that our three-dimensional world is actually two-dimensional, that we live in a hologram, and that we’re all projections on the boundary of space. Or something like this you’ve probably read somewhere. It’s been all over the pop science news ever since string theorists sang the Maldacena. Two weeks ago Scientific American produced this “Instant Egghead” video which is a condensed mashup of all the articles I’ve endured on the topic:

The second most confusing thing about this video is the hook “Many physicist now believe that reality is not, in fact, 3-dimensional.”

To begin with, physicists haven’t believed this since Minkowski doomed space and time to “fade away into mere shadows”. Moyer in his video apparently refers only to space when he says “reality.” That’s forgiveable. I am more disturbed by the word “reality” that always creeps up in this context. Last year I was at a workshop that mixed physicists with philosophers. Inevitably, upon mentioning the gauge-gravity duality, some philosopher would ask, well, how many dimensions then do we really live in? Really? I have some explanations for you about what this really means.

Q: Do we really live in a hologram?

A: What is “real” anyway?

Q: Having a bad day, yes?

A: Yes. How am I supposed to answer a question when I don’t know what it means?

Q: Let me be more precise then. Do we live in a hologram as really as, say, we live on planet Earth?

A: Thank you, much better. The holographic principle is a conjecture. It has zero experimental evidence. String theorists believe in it because their theory supports a specific version of holography, and in some interpretations black hole thermodynamics hints at it too. Be that as it may, we don’t know whether it is the correct description of nature.

Q: So if the holographic principle was the correct description of nature, would we live in a hologram as really as we live on planet Earth?

A: The holographic principle is a mathematical statement about the theories that describe nature. There’s a several thousand years long debate about whether or not math is as real as that apple tree in your back yard. This isn’t a question about holography in particular, you could also ask that question also in general relativity: Do we really live in a metric manifold of dimension four and Lorentzian signature?

Q: Well, do we?

A: On most days I think of the math of our theories as machinery that allows us to describe nature but is not itself nature. On the remaining days I’m not sure what reality is and have a lot of sympathy for Platonism. Make your pick.

Q: So if the holographic principle was true, would we live in a hologram as really as we previously thought we live in the space-time of Einstein’s theory of General Relativity?

A: A hologram is an image on a 2-dimensional surface that allows one to reconstruct a 3-dimensional image. One shouldn’t take the nomenclature “holographic principle” too seriously. To begin with actual holograms are never 2-dimensional in the mathematical sense; they have a finite width. After all they’re made of atoms and stuff. They also do not perfectly recreate the 3-dimensional image because they have a resolution limit which comes from the wavelength of the light used to take (and reconstruct) the image. A hologram is basically a Fourier transformation. If that doesn’t tell you anything, suffices to say this isn’t the same mathematics as that behind the holographic principle.

Q: I keep hearing that the holographic principle says the information of a volume can be encoded on the boundary. What’s the big deal with that? If I get a parcel with a customs declaration, information about the volume is also encoded on the boundary.

A: That statement about the encoding of information is sloppy wording. You have to take into account the resolution that you want to achieve. You are right of course in that there’s no problem in writing down the information about some volume and printing it on some surface (or a string for that matter). The point is that the larger the volume the smaller you’ll have to print.

Here’s an example. Take a square made out of N2 smaller squares and think of each of them as one bit. They’re either black or white. There are 2N2 different patterns of black and white. In analogy, the square is a box full of matter in our universe and the colors are information about the particles in the inside.

Now you want to encode the information about the pattern of that square on the boundary using pieces of the same length as the sidelength of the smaller squares. See image below for N=3. On the left is the division of the square and the boundary, on the right is one way these could encode information.

There’s 4N of these boundary pieces and 24N different patterns for them. If N is larger than 4, there are more ways the square can be colored than you have different patterns for the boundary. This means you cannot uniquely encode the information about the volume on the boundary.

The holographic principle says that this isn’t so. It says yes, you can always encode the volume on the boundary. Now this means, basically, that some of the patterns for the squares can’t happen.

Q: That’s pretty disturbing. Does this mean I can’t pack a parcel in as many ways as I want to?

A: In principle, yes. In practice the things we deal with, even the smallest ones we can presently handle in laboratories, are still far above the resolution limit. They are very large chunks compared to the little squares I have drawn above. There is thus no problem encoding all that we can do to them on the boundary.

Q: What then is the typical size of these pieces?

A: They’re thought to be at the Planck scale, that’s about 10-33 cm. You should not however take the example with the box too seriously. That is just an illustration to explain the scaling of the number of different configurations with the system size. The theory on the surface looks entirely different than the theory in the volume.

Q: Can you reach this resolution limit with an actual hologram?

A: No you can’t. If you’d use photons with a sufficiently high energy, you’d just blast away the sample of whatever image you wanted to take. However, if you loosely interpret the result of such a high energy blast as a hologram, albeit one that’s very difficult to reconstruct, you would eventually notice these limitations and be able to test the underlying theory.

Q: Let me come back to my question then, do we live in the volume or on the boundary?

A: Well, the holographic principle is quite a vague idea. It has a concrete realization in the gauge-gravity correspondence that was discovered in string theory. In this case one knows very well how the volume is related to the boundary and has theories that describe each. These both descriptions are identical. They are said to be “dual” and both equally “real” if you wish. They are just different ways of describing the same thing. In fact, depending on what system you describe, we are living on the boundary of a higher-dimensional space rather than in a volume with a lower dimensional surface.

Q: If they’re the same why then do we think we live in 3 dimensions and not in 2? Or 4?

A: Depends on what you mean with dimension. One way to measure the dimensionality is, roughly speaking, to count the number of ways a particle can get lost if it moves randomly away from a point. The result then depends on what particle you use for the measurement. The particles we deal with will move in 3 dimensions, at least on the distance scales that we typically measure. That’s why we think, feel, and move like we live in 3 dimensions, and nothing wrong with that. The type of particles (or fields) you would have in the dual theories do not correspond to the ones we are used to. And if you ask a string theorist, we live in 11 dimensions one way or the other.

Q: I can see then why it is confusing to vaguely ask what dimension “reality” has. But what is the most confusing thing about Moyer’s video?

A: The reflection on his glasses.

Q: Still having a bad day?

A: It’s this time of the month.

Q: Okay, then let me summarize what I think I learned here. The holographic principle is an unproved conjecture supported by string theory and black hole physics. It has a concrete theoretical formalization in the gauge-gravity correspondence. There, it identifies a theory in a volume with a theory on the boundary of that volume in a mathematically rigorous way. These theories are both equally real. How “real” that is depends on how real you believe math to be to begin with. It is only surprising that information can always be encoded on the boundary of a volum if you request to maintain the resolution, but then it is quite a mindboggling idea indeed. If one defines the number of dimensions in a suitable way that matches our intuition, we live in 3 spatial dimensions as we always thought we do, though experimental tests in extreme regimes may one day reveal that fundamentally our theories can be rewritten to spaces with different numbers of dimensions. Did I get that right?

A: You’re so awesomely attentive.

Q: Any plans on getting a dog?

A: No, I have interesting conversations with my plants.