# (1/3) “Man fears time…”

I have wondered if Imhotep had some hidden meaning in the pyramid. Little is recorded about him, but he lived during the Old Kingdom of Egypt under Djoser. He seems to have been born a commoner, and become renown as a great architect, sage, and perhaps the first physician in the world. His monument to King Djoser, the Step Pyramid, is the archetype for all pyramids that followed and the oldest stone structure in the world.

Pyramids are uniquely stable structures. They have survived many thousands of years and all the storms and earthquakes that time could bring. The mass at the peak of the pyramid we may say is in a high energy state. It is supported by progressively larger masses that reside at lower points of the gravitational potential. This is the thermodynamic analogy I mean to draw, and I speculate:

That Imhotep, born a commoner and working at a time when there may have still been living memory of an Egypt much less advanced, and therefore much less hierarchical. He may have understood on some deep level the changes in social structure that were necessary to make the pyramid possible. Because pyramids are built by slaves, and laborers, and craftsmen of many kinds. Hunters and gatherers cannot build them, and pastoral nomads can’t either. Only a culture with advanced agriculture and the division of labor agriculture makes possible can build structures like this.

The great works of the ancient world were not possible without slavery, and systems of exploitation and power rise to reflect the skyward structures themselves. Then, at the earliest years of that civilization, Imhotep may have understood in some way that Egypt had passed into a new thermodynamic mode of existence. A mode in which energy is drawn up through the roots of plants, and into the people who plant and harvest them and other resources, to flow up and be concentrated into progressively more privileged classes, to terminate finally in the vested power, privilege, and abundance of the King.

There is a clear connection here to the flows of energy in ecosystems. Apex predators eat and scavenge whatever they can. A lion will steal a kill from a hyena. The grazing animals are fed ultimately by the sun. People deny this similarity because they don’t want to know they are eating each other.

In a way, modern civilization seems to be an extension of an ecological structure that humans used to be embedded in, or maybe civilization has superseded that ecology completely. We were prey once. Then we became apex predators. We have advanced our civilization by replacing most of the world’s fauna with our own biomass in both livestock and human chattel. And the more developed a society tries to become, the more material must be put underneath in the base. Egypt and other ancient civilizations could only advance so far, but the modern western imperium extends across the entire globe, purchasing its privileges with sweatshops and child miners.

There are observations to make and questions to ask. I won’t have  a proper response to all of these. Among the most important:

• The poor don’t need the wealthy, but the wealthy do need the poor. The world is right-side up, not upside down as Ayn Rand would have it.
• Scientific discoveries are typically made by the upper classes.  They benefit everyone, but not uniformly. Most of the benefit reaches the upper classes first, or exclusively.
• People are interdependent, and though it’s not clear that the quality of life in post-agricultural civilization is better in absolute terms, most people today would not be alive without modern technology. Is it forbidden by the laws of physics to have this modernity without its gross inequality?
• Are there scaling principles at work such that the thermodynamics of current societies could be used to predict an upper limit to any society’s development, assuming the total flux of energy on the surface of the Earth bounds its base?
• There are limits on an empire’s geographic span which seem to determine how wide the base can become, and these limits are primarily technological, viz. communications technology may have played a dominant role in determining the size of social structures in each era of history. What effects are due to new technologies, not just in the size, but in the topology of society?
• If preagricultural societies exist in a “first” thermodynamic mode, and post-agricultural societies are in a second mode, does a third mode exist?  If I have anything worthwhile on this question it will wait until part 3 of these posts.

It has always bothered me that Americans never seem to understand their relationship to the rest of the world. It is the nature of privilege never to recognize itself, but it is absurd to see them so oblivious to how they in fact depend on the poverty in the greater part of the developing world and the working class in their own country.

I can’t go to the grocery store without being reminded of this. My hands aren’t the first to touch the onion and the tomatoes in the produce section. You see, it is apparently very hard to build a machine that can cut the stem of an onion and leave the bulb intact. It’s necessary to have people, sometimes children, do this by hand. They crawl through the field on their hands and knees under the summer sun and cut the stems with a knife. In the western United States of course, these people are mostly immigrants from Central and South America and their children.

The pyramid of Djoser is a reification of the Egyptian social structure in power and exploitation that was necessary to construct it. And like the pyramid, it may be that social structure is just as long lived, and reflects some underlying thermodynamic stability. There is an irony then in the old Arab Proverb,

Man fears time, but time fears the pyramids.

Do we really know how to build pyramids, or was that knowledge buried with Imhotep and hidden with his tomb? Have we learned the secrets hidden in our own societies? Do we know what is necessary for a long-lived, sustainable, self-sufficient society?

Does it bear repeating that the Step Pyramid is a tomb? And how long will it last, compared to the sand dunes that flow across the eons of the desert?

Some of these things I have understood, if dimly, since I was a 12 year old crawling through an onion field with a rusty knife in my hand. I don’t know if I’ve made much progress in my understanding. I was actually working on a post about Elon Musk’s Mars Colony, when I realized I hadn’t written this yet.

(2/3) The eugenics of a Mars Colony.

(3/3) In Extremis. (soon)

# Living in Avalon

…If you assume any rate of improvement at all, then the games will become indistinguishable from reality….given that we’re on a trajectory to have games that are indistinguishable from reality and those games could be played on a set up box or a pc or whatever, and there would probably billions of such computers or set top boxes…it would seem to follow that the odds that we’re in base reality is one in billions…tell me what’s wrong with that argument.

When I saw him answer the simulation question, I was immediately reminded of  the 2001 film, Avalon.

The simulation question has been talked about extensively in the last month or so, but I still haven’t seen any physicists chime in and it seems an argument from this perspective would be most appropriate for Musk (1). There was a response from a cognitive scientist and a philosopher here, but they seem to have missed the mark a bit, and they don’t seem to have understood what Musk may have meant by indistinguishable. I’m going to focus on this word, because it makes specific demands on the physics of the possible technologies involved.

Questions:

1. Is it possible to build a simulation “indistinguishable from reality?” Indistinguishable is critical here.
2. I expect the trajectory Musk describes will change. Where is the asymptote? I will have no chance of answering this one.
3. If it is possible to build such a simulation, does it matter?

Re: Question 1: Is it possible to build a simulation “indistinguishable from reality?”

[All Equivalent] I am going to assume, as Musk seems to, that by “reality” he means a world that operates with the same rules as ours appears to; that it has the same laws of physics. The distinction he is making is between “base” reality and simulated reality. They both behave exactly the same but one is an original. His argument seems to require all of the simulated realities operate under the same rules, so that our experiences here can carry implications about what’s possible in realities that simulate other realities.

[Computable] I think I have to assume further, also like Musk, that “reality” is computable. That all of the rules can be reduced to logically rigorous statements, also that there is nothing that doesn’t follow the rules, and therefore classical or quantum computations are sufficient to simulate reality (2).

It happens that our experiences here operate under quantum mechanical principles at the most fundamental level. We live in a universe that obeys Heisenberg Uncertainty, and there is a fundamental scale set by a constant of nature:

$\Delta x \Delta p\ge \dfrac{\hbar} {2}$

Any object we observe has a momentum ‘$p$‘ we associate with what Newton called a “quantity of motion”, and a position ‘$x$‘. This inequality is an assertion about the distributions of position and momentum. Roughly speaking, the uncertainty principle sets an absolute, fundamental limit on how well it is possible to know $x$ and $p$. This limit comes from the quantity $h$ – it is Planck’s constant. It is an incredibly small number measured in units of space and time we’re familiar with, but it is not zero, meaning it is impossible to know both the position and momentum of an object perfectly.

The less obvious consequence for our purpose: the uncertainty principle represents the limits in nature’s own detail. Once you know as much as uncertainty principle permits, there really is nothing else to know: nature itself carries no more information (3).

It shouldn’t seem plausible that a full fidelity (“indistinguishable”) simulation of a physical space could be housed in any volume less than or equal to that space, but I don’t know how to prove this. My intuition says the most parsimonious way to simulate a  physical space is to have that volume time evolve on its own. As Einstein put it, “God does not care about our mathematical difficulties. He integrates empirically.” There shouldn’t be any shortcuts, I think.

Some work on the limits of computation using uncertainty principle, general relativity  (GR) (and/or?)  the second law of thermodynamics has been done, producing theoretical limits regarding computation. This work is bit out of my depth but it seems GR is required for its limits on energy density (4). Anyway, these details should not interfere with reaching this implication: Because there are fundamental limits on computational power, and by [All Equivalent] these limits apply to a simulating reality, it is not possible to embed, as a subsystem, an indistinguishable simulation of a region within that region. There can’t physically be any substitute for proper reality.

Now, what about the plug-in Matrix kind, aka the dream or the video game? Maybe it is only necessary to fully simulate observed, or observable regions of space and time? And even then only to the limits of observational powers of the individual. I have been assuming that our “reality” fully obeys all the known laws of physics, even when we don’t directly test or observe them. I should just be able to say this kind can be rejected because it is solipsism – we are trying to use physics here and this would take all the bets off. But I think I can do better, especially since it was this kind Musk directly proposed, though I will have to offer inductive arguments.

1. This world is too shitty for too many people. Unless Musk somehow thinks this reality is his very own oyster and none of the rest of us are real, what reason would we have to simulate a reality like this with so much suffering?
2. All software has bugs. “Indistinguishable” is too strong a demand for any software to meet with, no matter how advanced its developer. Honestly I think bug-free software cannot exist. There would be dejavu’s and glitches.
3. This reality is definitely not a video game in its lack of lucidity. Why don’t we know it’s a simulation?
4. If we had this kind of computational power, we could do a lot better for a video game than this. It would literally make gods out of everyone. Just ask: are you living in the world you wish existed?

If an indistinguishable reality were possible, it would not be desirable. The truth is too hard. If people had unlimited power to create their own realities they would hide from base “reality” in ways that are more robust and complete than religion and technology  allow them currently.

I have one remaining physical argument. We know that some physical systems are described by models whose equations lead to algorithms that are “hard” in this sense: That the computation time needed to predict observables scales so greatly that the computer would effectively require the lifetime of a universe in base reality to integrate, violating our [computable] assumption (5). This argument is not without a certain subtle problem.

Re: Question 2: I expect the trajectory Musk describes will change. Where is the asymptote?

I should just give up on this one for now…I suspect the bound found by Seth Lloyd is too generous but I don’t know how to improve it:

$\text{Max Operations Per Second}$ $\sim \dfrac{mc^2}{h}$

The numerator is the most recognized formula in physics: the rest energy of Lloyd’s “ultimate laptop” from relativity. Planck’s constant has appeared again because this is a quantum computer, and the computation speed is limited by how quickly one state can “rotate” into another state that is sufficiently …distinguishable, again determined by Heisenberg uncertainty(6).

Re: Question 3: If it is possible to build such a simulation, does it matter?

When we ask for indistinguishability we are asking, by definition, for a reality that will never fail to satisfy any demand we might make of it. It is impossible to devise an experiment that would reveal that it is a simulation. I don’t know why Musk is unsatisfied with this (7). Again by definition, these doubts would persist for anyone living in base “reality.”

I think a minimal plea for sanity requires us to take our reality as it presents itself. Further, that we take it as simply as it presents itself, and imagine no hidden variables, mechanisms, Wizards of Oz, Dungeon Masters, Cartesian Demons, or code beyond nature’s capacity for information, i.e. its ability to distinguish.

It is a hardcore, base reality that what can’t be observed really isn’t there. A simulated reality and a base reality if indistinguishable must be one and the same. Nature itself can brook no hypotheses about the unobservable. We cannot allow ourselves superstition, or even agnosticism if we are going to move past barriers of imagination. We’ll have to be atheist. Nature is just too creative and extends too far beyond our ken to allow us any less.

Maybe we should be hopeful that we are living in a simulation…either we develop simulations that are indistinguishable from reality or civilization ceases to exist.

Avalon, the legendary land
The isle of apple-trees and mist
Avalon is the land of elves
Where the hero comes today

Avalon, the legendary land
The hero set out there

Avalon is the land of elves
Avalon is the heavenly isle of shadows
Enchanted isle
The ship set out to an unknown voyage
Avalon…

1. There are reasons for a good physicist (not me) to stay out of this discussion. The primary one I’m thinking of being that this notion is, at least at face, untestable. Please take all of the physics presented here with a grain of salt.
2. One thing I’m definitely not sure of: would this reality simulation require a theory of everything, so that all of the physical laws would have to be known?
3. It might be argued that nature does know more, but simply behaves in a way that prevents us from knowing or observing any more. I think all hypotheses of this kind can be equated to a “hidden variables” description of quantum mechanics, and I believe all such theories have been excluded by Bell’s Theorem and its experimental verification(here, and here).
4. There’s a whole literature on this that I won’t be able to go into. I neglect distinctions  made between limits on memory capacity, the longevity of a record, and what research in this area may imply about time itself, and any relationships between gravity and thermodynamics. In due time, I think the research on quantum computing will reveal much more about these questions.
5. Most of the research in this area is for Classical computation – where the states of computer are strictly binary, 1 or 0. The situation for quantum complexity is less clear, as this field is still fairly new and many quantum algorithms are still being developed.
6. There is an energy and time relation analogous to the one for momentum and position, though its interpretation is a bit more subtle.
7. Really I think he didn’t mean the full quantum mechanical notion of indistinguishable, but I needed an excuse to write this post.

# The math is real.

All details of the analysis have a physical meaning and should be interpretable for the physicist.

If there was some detail in a mathematical expression – any factor, any exponentiation, addition or whatever, that detail has a specific physical meaning. If it didn’t matter, there wouldn’t be any reason for it to be there, and you are using an analysis with superfluous detail. If it has to be there to get the answer that matches experiment, then it has meaning…

Sometimes I will hear that one thing or another is “just a mathematical thing”, but that is clearly not so. I think sometimes we give up on doing physics and just start doing math, but if we really are physicists we can’t give up on understanding our equations. Shankar has already said very similar things.

# Entropy, etc.

I don’t have anything useful to post here. I’ve alluded to these issues before but have nothing to add.

I have this strange feeling that the problems of the interpretation of quantum mechanics, dark energy, the big bang, and quantum gravity will all necessarily be solved simultaneously, all involving the same concepts.

What I know about the history of advancements in theoretical physics suggests our problem is very rarely a lack of mathematical tools, or an understanding of the present state of physical concepts. Mathematicians have been out ahead for about 100 years now, developing mathematics that have no apparent use in physics. The tools almost certainly exist already for tomorrow’s theories. The problem has to do with the concepts themselves and our imagination; as Haldane put it, “the Universe is not only queerer than we suppose, but queerer than we can suppose.

It seems we need experimental evidence not just to suggest absurd things, as with Lorentz (4), but unambiguously require them for theory to remain consistent before we can accept them. In this way our “common sense” is very often an obstacle.

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1. Someone better trained than I am described a problem I actually think has something to do with why “you can’t have nothing isn’t.” http://physics.stackexchange.com/questions/65177/is-the-preferred-basis-problem-solved
3. Zurek: http://www.nature.com/nphys/journal/v5/n3/full/nphys1202.html, http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.75.715
4. A Mechanical Universe Episode, includes the history of Special Relativity. http://www.dailymotion.com/video/x2z75hb

# My suspicion that space and time are not fundamental.

When we are doing science we have to start by making assumptions we are confident in: nothing can come from nothing, and nothing just disappears (energy/mass conservation). One even more basic assumption, which I think is where science really has to begin, can be stated this way:

[MP] That which is not observable does not exist.

I call this the materialistic principle, and it is similar to Newton’s Rule 1 for reasoning in philosophy: “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.” I have articulated the MP in this way in part because I’m not sure I understand causality. I also want something simple and almost tautological. What I mean is that if anything whatsoever is not observable, and not measurable, then really for no physical model or theory should we pretend it to be there; it would be supernatural, miraculous, magical.

Now, in particle physics and statistical mechanics there exists a principle called indistinguishability. It asserts that there is no way to tell the difference, for example, between one electron and another, or between two photons. That all Helium-3’s are exactly the same, and if I have understood correctly it demands something further: That it is physically impossible to devise any experiment that can distinguish between any two such particles.

That particles actually are indistinguishable I think holds from experimental evidence. The entropy is used extensively to predict the properties of systems of particles. The entropy is related to the number of ways the system can be configured(1). If there were unknown properties that caused the particles to differ from each other, those properties would entail extra degrees of freedom and therefore some contribution to the entropy (2). The accuracy of predictions about the system that require indistinguishability implies that we have completely described the system and its particles.

What are we to do with this? By [MP], I am lead to the hypothesis: Things that are by all observable properties exactly the same, are the same things…

The reason we can’t tell photons apart is because they are, in fact, all the same particle (singular!). That goes for electrons, protons, neutrons, etc.

If I stand in front of a three-way mirror, and you cannot see me directly, but only through my reflections, are there three of me, or only one? Does it depend on how you think about it, and the extent of our experience and expectation? What if all you ever saw were the mirror images, and never actually saw me directly? What would you make of the images?

There are some immediate problems with this, and a lot of confusion, but I am going to struggle through this despite having no resolution for a bit longer because there is an accompanying use of [MP] that will confound and clarify things further. Consider this question:

Is it possible to observe the passage of time without some increase in entropy, or dissipation of some kind occurring somewhere in the system that measures it?

These days there are some very accurate atomic clocks in use. Did you know that a quantum mechanical pendulum really will swing forever, assuming it can be kept from entangling with the exterior environment (read: dissipation, of a sort?). Somehow ‘entropy always increases’ does not apply to quantum mechanics proper. The second law of thermodynamics has to grow out of the quantum mechanical regime in some way that I think is to this day not yet fully described, but is intimately related to problems of coherence (3). The point is that even with a quantum mechanical clock, the device that counts its ticking is necessarily classical and requires some ΔS (entropy increase) of its own.

It follows, and again by [MP], that whenever the system has suffered no increase in entropy, no time can be observed to pass and therefore no time has actually passed.

I can’t go much further than this. I imagine that perhaps the Bing Bang did not occur, or is not located some ‘long time ago’ the way we feebly conceptualize it. I think in a sense we are still inside the singularity, or locked in some (mathematical?) structure that can be described without any recourse to notions of space and time, and in fact from which spacetime can be seen to emerge and give rise to the world of appearances (and mirror images?).

a. In such a Universe, what is causality and how does it arise?

b. We think of entropy as increasing with time, but if entropy is fundamental and time is its consequence, what is the arrow time? How is the apparent passage of time reproduced?

Obviously there are a lot of problems, but there are some things that are easier to swallow, and some problems may become tractable in a description of the universe without space and time as inherent components:

When two particles are in an entangled state and separated by a great distance, and a measurement is performed on one, why does the wave function collapse at the other?

What is the apparent energy which is constant in all space and time, accelerating the galaxies from each other that we call dark energy?

What does the universe look like to a photon?

This last question I have heard was the one that brought Einstein to relativity in the first place, and even now I’m not sure he ever got his answer. If you’ve looked at the equations and studied relativity, you know that lengths will contract for an observer moving at constant speed, and that the equations suffer a singularity when the full velocity of light is reached, i.e, the equations predict that the universe around you, as you approach speed c, will become infinitely squeezed into a plane perpendicular to travel (4). For anything with mass to reach c is forbidden, but what the photon itself sees at c I don’t know, but notice it also predicts that approaching c, time will stop.

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1. Notice I am not using entropy in the way that is typical in popular science writing, nor am I making explicit reference to any formula. Here I just mean a quantity that is proportional to the logarithm of the number of ways a system can be configured (or might be measured). Here’s a nice video that gives an explanation beyond “order/disorder” without getting too math heavy: http://www.youtube.com/watch?v=vSgPRj207uE
2. What if it just so happens that all of the experiments that have been done have never occurred in a regime that allows the particles to access these degrees of freedom? The evidence is not sufficient in that case to show all of the properties are accounted for.
3. Coherence, decoherence, entanglement and how the classical world arises from the quantum are all things I am studying and can’t into depth here. I will not linger on this tangent.
4. It would take an infinite amount of energy to accelerate anything with mass to the speed of light. It is forbidden for any massless particle (only photons AFAIK, maybe some theoretical ones) to move at any speed other than the speed of light.