If Neo Was Your Neighbour, Would You Notice It?

If you would have asked me 20 years ago whether I believe reality is a simulation, I would have been almost 100% sure it is not. However, today I’m not so sure anymore.

The reason for the change is simple: 20 years ago I would have based my answer on the level of technology available at that time. Now I understand that our current technological level is irrelevant in trying to figure out whether reality is a simulation or not.

We’ve Seen It In the Movies

Many of you’ve probably seen the movie/trilogy called Matrix. The main character, called Neo, learns that his life is not “real” but that he has been living his whole life in a simulated reality, made by a computer. Neo has a physical body and brains but his perception of the world around him is fed into his nervous system via a connector on his neck. Once freed, Neo learns about the real reality and finds out that the year in the real world is way ahead of that in the simulated reality, which he though was the real one.

There are many other examples of simulated reality in fiction (see http://en.wikipedia.org/wiki/Simulated_reality_in_fiction). The idea is not new. Plato played with the idea in his Allegory of the Cave text as early as 380BC. In a Chinese book Zhuangzi (from the 3rd century BC) is a story called The Butterfly Dream in which a man dreams of being a butterfly. When he wakes up, he is not sure whether he is really a man who dreamt of being a butterfly or a butterfly who now dreams of being a man.

Plato’s Allegory of The Cave, by Jan Saenredam, according to Cornelis van Haarlem, 1604, Albertina, Vienna

Simulations are not only fiction anymore. There is a huge number of computer simulations ran every day for different purposes. We simulate air masses to predict tomorrow’s weather forecast, we simulate transfer and scattering of photons inside human body in radiation therapy, we simulate small virtual worlds in realistic 3D computer games for entertainment and so on. I myself have written several computer programs during the past decades that can be considered to be simulations of some kind of reality. These programs include computer games, physics engines and particle simulations.

The fact that we have created simulations raises our awareness of the possibility of reality being a simulation but it does not, in my mind, provide any added certainty to the probability of reality being a simulation. Is there a way to estimate the probability for us living in a simulated reality? That’s what I try to find out in this blog post.

History As a Facade

Before trying to convince myself that simulated reality might be highly probably, let’s figure out what it would mean to create a simulated reality identical to the one we live in.

To us universe appears to be a pretty complex system. It also appears to contain a lot of “stuff”. Roger Penrose estimated that the number of baryons in the observable universe is about 10⁸⁰. If we assume a binary based computer system and make a grossly optimistic estimate that we would be able to represent each baryon with a single bit, it would require 1,25 * 10⁷⁹ bytes, or about 1,137 * 10⁶⁷ terabytes of storage to store the state of the universe, assuming no compression is used. In 2013 – according to some estimates – there was approximately 4 * 10²¹ bytes worth of data on the internet. Let’s double that to account for any storage outside the internet. We would then have about 8*10²¹ bytes available on our computers today. We would therefore need 1250000000 0000000000 0000000000 0000000000 0000000000 000000000 times more computer storage to satisfy the need for storing all baryons for the simulation. I don’t care to estimate the amount of physical space needed to have such an amount of bytes available but you get the idea: according to our standards, that’s a helluva lot of storage space.

However, if you take a solipsistic approach, you don’t need to simulate the entire universe. You only need to simulate the life of one person, namely yourself. Number of baryons observed by a single person is a lot less than the total number of baryons in the universe. You would save a considerable amount of storage space and computing power when you simulate the life of just one person. In addition, you don’t need to run the simulation from the beginning of time, but start instead, say from year 1967. You’ve already saved some 13798000000 – 47 years worth of computation time in the simulation. Even if you include all 7.2 billion humans into the simulation, you would get a saving of similar magnitude in the simulation storage size and computation time.

But wait, can we really skip the odd 13,7 billion years from the simulation and start from the modern times? Aren’t we clever mammals and learn more and more about our own and universe’s history all the time? Surely this information needs to be available in the simulation for us to explore it and learn about times long gone. I cannot say whether the reality simulation would require the total history of the universe as been simulated properly in order for the simulation to be coherent and plausible but I can offer a programmer’s point of view to this dilemma.

I started programming in 1983/1984 and have been programming ever since. During these years I’ve met a lot of talented programmers and seen a lot of code. It is safe to say that I know the mind of a programmer. If I was asked to create a computer simulation that would simulate our reality, I would say “No”. After been offered enough dark chocolate, red wine, marine plywood, epoxy and time to build my own wooden sailboat, I would agree to at least give it a try.

I am, like most programmers, lazy. But in a good way. I want to minimise the amount of code I need to write, with a few exceptions of infamous copy-pasting here and there. I would first try to set up a set of simple rules that would produce the multitude of complexity we seem to experience in our reality. These rules would need to be expressive enough to create things like stars, galaxies, planets, animals, plants and so on. If I would be able to find such a set of rules (which I seriously doubt), I would then run the simulation from the beginning of times until it reaches present time and check that it looks ok. Then I’d let the simulation continue to run on its own and start building the boat.

If I, however, was unable to find such rules or would not have time to run the simulation from the beginning of times, I would probably try to come up with a set of less expressive rules that would be enough to simulate our present time and then make some custom rules to account for the past, starting with more fine detailed rules for the history close to us and then proceeding to coarser and coarser rules for the events in the history further away from our present time. This way I wouldn’t have to run the simulation for the entire history but have a “fake” history governed by the custom rules and hope nobody notices the inevitable mismatches on the boundaries of my custom rules. History would be just a facade, simulated accurately enough to satisfy the curious mind of the clever mammals living inside the simulation at present time. Again, I seriously doubt I could manage to do this approach, either.

If, instead, they told me it is enough that I create some simulation that is interesting and intriguing enough but doesn’t have to be representing our reality, it would be fairly simple to do so. Depending on the complexity, I would choose either the “set of rules to simulate the entire universe” approach or the “history as a facade” approach and be done with it¹. Like I mentioned earlier, humans have already created thousands of simulations. They are no way near as complex as our reality appears to be, but they can be considered to be simulations of some realities.

We Can Be in a Very Simple Simulation, Even Though We Think Our World Is Complex

Let’s accept for the moment that, in principle, there is no difference between our reality and the simulations we already run on our computers. Although our reality is far more complex, vast and spans an enormous distance in time, the principle is the same: events happen, things interact with one another and there is a set of rules that govern how things proceed. The only difference is that reality is a bit more advanced simulation 🙂

Now I know some readers are not happy with this comparison. So I need to address some issues and explain why I think our reality can be compared to computer simulations. Depending on the reader, many things might spring to mind that are unique to our reality and do not exist in any simulation done so far. Such things might include consciousness, concept of life, free will, soul and quantum physics, among others.

I won’t be able to go through all of these in detail. The first four are similar and I will handle them as one group. The last one is a bit different but similar to the first group. I’ll try to explain why I don’t consider these to be a problem.

Many will say that there is something special we humans possess. Call it consciousness, free will or soul, it is something that separates us from other animals and makes us special. In addition, many think that these properties can be separate from our physical bodies and cannot ever be explained by laws of physics. I’ll talk about these subjects in my next post but for now I shall simply list the reasons why I think these properties are not anything special:

1. This kind of reasoning is so human-centric, it stinks. Looking back at our history, it can be seen that humans have always considered themselves as the centre of attention. Before Copernicus, we thought the earth was the centre of the solar system and other celestial objects revolved around our planet. Thinking that humans possess something other animals do not is a direct continuity in this line of thinking. I believe there is no meaningful distinction between humans and other animals. In fact, I believe there is no distinction between us and other entities in the world, including plants, rocks, matter and so on. There are only different levels of complexity, different levels of grey, so to speak, but we all of the same colour, nonetheless.
2. If consciousness, free will or soul would be separate from our physical bodies, how come it’s so easy to alter them with chemicals that interact with the brain? Drink a bottle of whiskey in one continuous sip and I dare you to make any conscious decisions that day 🙂
3. There is simply not a single evidence or proof available to support a statement that consciousness or soul can live outside a human body.

I don’t mean these things don’t exist. I simply mean they are an emerging result of yet unknown series of operations inside our brain and are merely labels or definitions we have given for these operations. I’m sure animals, plants and other entities in the universe possess these same qualities, depending only on the amount of liberty we allow for these labels or definitions. So, I’m not against consciousness, free will or soul. I’m simply saying they are not anything a simulation couldn’t reproduce. Concept of life is even a broader definition and purely semantics in my opinion.

About quantum physics. I love Feynman’s QED for its clarity and simplicity but I don’t claim to be an expert on the subject. QED gives us a well-defined way of calculating the probabilities for particle positions according to quantum mechanics but it does not predict where an individual particle will be at a given time. And as far as I have understood it, not only does it not predict individual particles, it is said that it is impossible, because of the uncertainty principle or to put it more profoundly: because nature does not work that way.

If there is something in the quantum phenomena that cannot be predicted or calculated, how could a simulation produce our reality? I don’t know. My intuition tells me quantum uncertainty is not something profound but it is something that can be predicted but we haven’t figured out how to do it yet. I might be wrong, of course. However, if probability distribution is all that is outside that which can be calculated, the simulation could simply include a random generator which serves as the unknown. I’d give it a go.

Finally I get to my point for this section. Think for a moment reality is a simulation. According to our standards, our universe is too complex for us to understand and we cannot see how we could simulate anything that complex. However, our standards are not significant. If our (simulated) reality has been created by a far more advanced entity, our seemingly complex universe would be child’s play for her. There is no reason to assume there cannot be vastly more advanced entities in the “real” reality and they could easily run a simulation such as our universe. One could wonder, why would they bother to run a simulation which is far simpler than their own reality. Wouldn’t they prefer running a simulation which more closely resembles their own reality? Maybe they don’t know how to, just as we don’t know how to simulate our reality. Instead we run thousands of simulations which are far simpler than our reality. Notice the analogy?

So, if you accept the possibility that there can be far more advanced entities in the “real” world, it is reasonable to accept the possibility that they can simulate a universe such as ours.

If You Accept It Could Be Done, Neo Most Likely Is Your Neighbour

So far I have reduced the possibility of living in a simulation to the possibility that they are more advanced entities in the “real” reality². Since there can be only one “real” reality³ and several simulated realities, the probability that we are in a simulation is greater than the probability for being in a “real” reality. If, for example, 1000 simulations have been created that are at least as advanced than our universe, there’s a 99,9000999001% change we are in a simulation and only 0,0999000999% change we are in a “real” reality.

So the question we should ask is: “how likely it is that there exists a reality far more advanced than ours?” Remember also that our universe might evolve to become such a reality in the far future. If you can imagine us evolving to a state where we would be able to simulate reality as it is in 2014, you need to accept the high possibility that we are inside a simulation already.

Could We Spot Neo?

As far as we are concerned, living in a simulation and not knowing it is identical to living in a real reality. If the creator of the simulation never lets the simulated know of the reality, entities in the simulation have no way of knowing and might as well be convinced theirs is a real one. For some individuals just the thought of simulated reality might be disturbing but majority couldn’t care less, since, for them, there seems to be no evidence to support the argument.

If some speculation is allowed, it might be possible to reveal the underlying simulation. Here’s how:

• First figure out all and complete set of rules that make up the universe. Physicists would call these complete laws of physics the theory of everything. Programmers would call this reverse-engineering the simulation source code. Piece of cake.
• Once the rules are known, we might be able to figure out what kind of “operating system” and “hardware” is used to run the simulation. Another small piece of cake.
• Then all that remains, is to figure out a way to somehow affect the underlying simulation hardware to verify the theory and ensure we are in fact in a simulation. A bit bigger piece of cake, but edible, nonetheless.

If we were able to convince ourselves that we are living in a simulation, this information would be devastating to many of us. Some would not be able to accept the fact that we are merely “bits or numbers” in a program of some sort and do not exist as real human beings. Some might be indifferent, claiming that their life is not affected by the fact. Many people would probably deny all evidence and continue to believe we are real physical beings and claim that the simulation theory is just a hoax.

If there was a way to communicate with our creator(s), things would become interesting. We would be able to learn about the real reality and would most likely get answers to questions that have wondered the human race for ages:

• Why do we exist? Why were we created?
• What’s the purpose of (our) life?
• Who created us?

Getting answers to those questions would be a big deal. It is of course possible and even probable that if we are in a simulation, those who created us are also in a simulation, only in one that is a bit more advanced than ours. Their answers might sound awesome to us, but in reality they would be as “shallow” as our reasons for creating simulations we have already created and are running on computers today. With a communication link to our creators, however, we might be able to convince them into altering the simulation to meet our wishes. That would be a true genie in a bottle -metaphor in practice.

Since there is one real reality, eternal questions still hold and might never be answered to the inhabitants of that reality. Which destiny do you think is better: that we are living in a simulated reality and therefore might be entitled to answers of those eternal questions or that we are living in a real reality and will probably never know why we are here and how we got here?

Epilogue

I just have to say this. There’s about 99.9% chance that any given computer program has a bug. I believe this to be true for advanced simulations, as well. If we are indeed living inside a simulation, shouldn’t we be seeing something that doesn’t seem to work properly or clearly doesn’t make any sense? I’d say commercials in tv, radio and web pages are a strong candidate.

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¹To be honest, I would be tempted to try a third approach, one which would be cybernetic: code that would alter itself. Just to make things more interesting.

²Not conclusively, but roughly that’s what I have been trying to do.

³One might argue that there can be several “real” realities, as proposed by Everett in his many worlds interpretation of quantum mechanics. That shouldn’t have an effect on the probability, assuming these worlds are more or less as advanced and capable of running similar simulations.

Is Occam’s Razor Dull?

You’ve probably heard of Occam’s Razor. It’s a scientific principle that prefers simple explanations over complex ones. The “father” of this principle was an English Franciscan friar and scholastic philosopher William of Ockham (c. 1287 – 1347). Ockham stated the principle in various ways, but the most popular version “entities must not be multiplied beyond necessity” was written by John Punch from Cork in 1639.

William of Ockham, from stained glass window at a church in Surrey

You might also have heard of Hume’s Scale. Scottish philosopher, David Hume, considered miracles in his book called “An Enquiry Concerning Human Understanding”. Hume discussed everyday belief as often resulted from probability, where we believe an event that has occurred most often as being most likely, but that we also subtract the weighting of the less common event from that of the more common event. In the context of miracles, this means that a miraculous event should be labelled a miracle only where it would be even more unbelievable (by principles of probability) for it not to be. In other words, a novel idea is most likely true, if disproving it requires a greater leap of faith than the novel idea itself does. 

Albert Einstein was also fond of simplicity. However, being smart, he didn’t go to such extremes as preferring the simplest solution. Instead, he has been quoted to say “It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience” or “Make things as simple as possible, but not simpler.”

Why Should We Opt for Simplicity?

It is in our nature to opt for simplicity. It just makes things easier to understand and cope with. Our fore-fathers would have starved to death if they would have considered all possible scenarios for finding food. Instead, they hunted where it would be most likely for them to find prey, relying on common knowledge accumulated over past generations. Acting on the most probably choice makes sense, since it is – by definition – most likely to succeed.

We simplify things all the time, even without noticing it. We categorise people based on stereotypes and past knowledge of other individuals. We take sides in conflicts without knowing all relevant information. We sometimes accept an argument if it sounds simple over a more complex one, just because it makes our brain “click” in a right way and we feel a sense of understanding, even if the simpler argument would be false. This is most likely (pun intended) due to our survival instinct. Making approximate decisions quickly is more beneficial than considering all possible aspects to find out the absolute truth.

Since opting for simplicity is so built into our dna, we do that in science as well.

But does it work? If we are looking for the absolute truth (which in my mind is one of the main goals of science), does simplifying or opting for the simplest explanation actually help us in finding the right answer? Or can it even be that using simplification will prevent us from finding the right answer and steer us away from the absolute truth?

It’s All or Nothing

Before I try to answer my own questions, I want to explain why I think everything must be connected to everything.

Our universe is a complex thing. We don’t have a clue how it was made, whether it was even made, how it works and how, if ever, it will end. I know there are some people who claim to understand some of these things but trust me on this: they don’t have a clue. No one has.

But there are some things we can say about our universe and we should be fairly certain of their certainty. For example, all things in the universe are connected to one another or they are not.

Let’s consider first the latter case, that they are things in our universe that are disconnected from other things in our universe. (You may have noticed that I use a rather un-scientific term “things in our universe” to make my point. I do this for simplicity’s sake (another pun intended) with a full understanding that it does not weaken my argument). In order for a “thing” to be completely disconnected from other things in our universe, other things must not know anything about it: must not see, hear, feel it in any way or interact with it in any way. Such a thing would thus be non-existing from our universe’s point of view and therefore not part of our universe.

We are then left with things that are connected¹ to some other things in the universe. Does this automatically imply that everything must be connected to everything? Let’s consider three things and call them A, B and C. Let’s try to make a system where there exists a thing that is not affecting some other thing. Since all things must be connected to at least one other thing, there are 4 possible scenarios:

Four possible ways three things can be connected to each other.

The last case is clear: A, B and C are all connected to one another. The first 3 cases are different since there exists a pair of things that are not connected to one another. They are, however, all connected to one another indirectly via a third thing. In terms of “being connected” this is the same as being directly connected since, e.g. in the leftmost picture, A affects B which in turn affects C, resulting in A affecting C. Thus in the case of three things, all things are connected to one another, meaning all things affect all other things.

What happens if we increase the number of things? It should be relatively easy to prove that there are more than three things in our universe. Depending on what you consider to be a “thing”, there are billions and billions of things in our universe interacting with each other. Regardless of number of things, I have demonstrated that every single thing needs to be connected to at least one other thing. This results in all things affecting all other things. If this was not the case, there would exist a thing that is not connected to any other thing and this would be in violation with the previous argument I made that such a thing cannot exist in our universe. One way of putting it is to say that universe is one. In order to understand it, you need to consider it as a whole.

I have made an assumption. I have described our universe as something that is made of “things” and that there are interactions between these “things”. Universe does not need to be constructed that way. Universe could be just a big lump of stuff, with no way to separate individual things in it. But for the sake of argument I’m trying to make, dividing universe into separate things only makes it harder for me to make my point so this assumption is not detrimental.

If All Things Need to Be Taken Into Account, Can Simple Rules Exist?

Hopefully I have been able to convince you that in order to understand the universe, all things in it need to be taken into account. If you disagree with me, leave a comment below and we’ll see if either one is willing to change his or her mind.

But even though all things in the universe need to be taken into account in understanding it, it is still possible that it is made of simple rules and simple elements. If this is the case, Occam’s Razor would be a good tool in finding these rules and elements. Before trying to argue against this idea, I want to show an example of a complicated thing made with simple rules, namely the Mandelbrot set.

Benoît B. Mandelbrot was a French mathematician who was interested in fractal geometry (I shall never forgive myself for not knocking on his door in 1991 when I visited the IBM research centre in New York and saw his name and room number on the lobby’s directory). He became famous in the 1980’s for his fractal image, called the Mandelbrot set:

The Mandelbrot set

The image itself is intriguing and to some viewers, even beautiful. But the amazing part of the story is that the rules that create the image are extremely simple and every part of the Mandelbrot set is unique. Even though similar forms and patterns repeat themselves in the image, every local portion of the image is different from other parts of the image. The formula for creating the Mandelbrot set is often written using complex numbers:

Z_n+1 = Z_n²+c

This formula is written in the way mathematicians like to write formulas and it emphasises the simplicity of the Mandelbrot set but for most people it is too vague and the mention of “complex numbers” casts a veil of mystery over the formula. I prefer writing the formula using “normal” numbers and in a more pragmatic (i.e. programmer-friendly) way:

function colourForPixel(cx, cy) {
⋅⋅⋅⋅x = 0;
⋅⋅⋅⋅y = 0;
⋅⋅⋅⋅for(iteration = 0; iteration < iterationMax; ++iteration) {
⋅⋅⋅⋅⋅⋅⋅⋅xx = x * x – y * y + cx;
⋅⋅⋅⋅⋅⋅⋅⋅y = 2 * x * y + cy;
⋅⋅⋅⋅⋅⋅⋅⋅x = xx;
⋅⋅⋅⋅⋅⋅⋅⋅if((x * x + y * y) > threshold) {
⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅return iteration;
⋅⋅⋅⋅⋅⋅⋅⋅}
⋅⋅⋅⋅}
⋅⋅⋅⋅return iterationMax;
}

What the formula means is that the colour of pixel (cx, cy) in the image is determined by repeatably calculating a new value for x and y and checking whether the distance of point (x,y) from origin remains within a predetermined threshold. If the point “escapes” from the origin, it is not part of the Mandelbrot set (colourful areas in the image) and if it does not escape, it is part of the Mandelbrot set (black areas in the image). The colour of the pixel is based on the number of iterations it took for the pixel to escape.

The important part is that there are only four normal multiplications and three subtractions or additions in the formula. Using these seven primitive arithmetic operations we are able to produce an image that is unique and detailed and never repeats itself. Here are some closeup images of the Mandelbrot set:

Close-ups of the Mandelbrot set

This is an example of a complex outcome from simple set of rules. It is possible to produce seemingly complex systems using very simple rules. It is therefore also possible that our universe is produced by a set of simple rules and Occam’s Razor would in deed be sharp. But is there a way of estimating the probability of our universe being created by simple rules or not?

Universe Is

If one believes in simplicity, one needs to be prepared to go all the way. One could argue that in order to save energy (or for some other allegedly “obvious” reason), universe is based on simple rules. If maximal simplicity was the main design principle of our universe then the simplest universe would be an empty one. The fact that we exist should alone be enough to convince us that universe is not based on maximal simplicity. There must be some reasons why universe is not the simplest possible.

At the other end of the spectrum is a universe that cannot be described in any other way than by including the entire universe in the description. No rules would exist that would explain even small parts of the universe or how they are organised. For some reason, this sounds to me like the only plausible alternative. Let’s call this the Unique Universe alternative.

The logical opposite of the Unique Universe alternative is that there is at least one rule that explains at least some part of the universe. It is also required that this rule completely explains the part in question (otherwise it wouldn’t be much of a rule, now would it). Previously I have showed that all parts or “things” in the universe are connected, either directly or indirectly. If a rule tries to explain part of the universe, it needs to be compatible with the entire universe, since other parts of the universe will have an effect on the part the rule is trying to explain. Does this requirement for compatibility mean that the rule must explain the entire universe? If it does, one rule is enough to explain the whole universe. In order to be compatible with the entire universe, the rule must be able to explain all effects caused by the entire universe on the given part. As it happens, this is equivalent to the rule explaining the entire universe².

It looks like there are two possibilities: either the universe cannot be explained by any rule or there exists one rule that explains it all. If universe cannot be explained by any rule, Occam’s Razor is useless. We are left with the mystery of one rule that explains the entire universe in determining whether Occam’s Razor is dull.

What do you think? If there is one rule that completely explains the entire universe, is this rule simple or complicated?

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¹ I made an assumption that connections between things are two-directional. Meaning that if A and B are connected, A has an effect on B and B has an effect on A. Logically, our universe could also be made of one-directional connections. A could have an effect on B but not vice versa. From A’s point of view, B would not exist. If we allow such connections to exist, the final result might change. Intuition tells me connections cannot be one-directional but I can’t prove it now. I’ll try to address this issue in another post.

² I’m cutting some corners here, to be honest. It is logically possible that some parts of the universe would be completely static throughout the duration of the universe and it would be possible to explain those parts with rules that need to explain the rest of the universe. If, however, we exclude those kind of parts, we are left with parts that in my opinion require knowledge of the entire universe to be explained completely. Again, this is something I cannot prove now.