"An unwillingness to admit the possibility that mankind can have any rivals in intellectual power occurs as much amongst intellectual people as amongst others: they have more to lose." - Alan Turing
Are We Living in the Matrix?
This page examines the theory that our universe is in fact a simulated universe which is running on a massively powerful computer programmed by some advanced civilisation. Though the world feels "real" to us, we might be merely logic states in an advanced computer. As improbable as this might sound, the theory has gained a lot of attention recently due to a similar idea in the film The Matrix, and the idea is even attracting the attention of several physicists.
However, as we shall now see, the particular situation depicted in The Matrix would seem to be a very unlikely description of our reality:
1) The "Brain-in-a-Vat" Scenario
The idea that we might be living in a simulated world is so fascinating because it is impossible to disprove the theory that we are living in a simulated universe. In order to see how difficult it is to disprove, consider the Brain-in-a-Vat Argument. The Brain-in-a-Vat Argument considers the situation whereby a person's brain has been removed from their body and is floating in a life-sustaining fluid. The brain is connected by wires to a computer which provides the brain with exactly the same impulses as the brain would normally receive, the computer effectively creating a "virtual reality". The person with the disembodied brain would continue to have perfectly normal conscious experiences without these being related to objects or events in the real world. It would be impossible for the person to discover the reality of their simulated world.
This is the basic premise behind the movie The Matrix in which Keanu Reeves's character was kept in a coma in a vat while the aliens' computer fed him false sensory information (fortunately for Keanu Reeves, the aliens did not remove his brain!). The simulated world created inside Reeves's head was called the Matrix, and for Reeves it was indistinguishable from normal reality.
While it might certainly be the case that the reality I feel is just a "dream state" and I am actually a brain-in-a-vat, I feel that would be very unlikely. I can think of no reason why a "Grand Simulator" would behave in that way. This is because the only person able to experience the excitement of the elaborate virtual reality world would be the person whose brain is in the vat: the simulator would not experience anything. So why bother to go to all the trouble of inputting an elaborate virtual reality world into the head of some poor unknowing person? What could possibly be your motive?
In the movie The Matrix the motive of the simulators was explained by claiming that the humans in the vat were being used as batteries (to power the aliens' machines). But if that was the case, why did the aliens need to go to all that trouble of creating that virtual reality world in the heads of their human captives? Couldn't the aliens simply just have kept their human captives in a drug-induced coma while extracting the energy from them? Why bother with creating the Matrix world?
2) The "Universe-in-a-Computer" Scenario
However, there is another model of our world as a computer simulation which does not require the confinement of some poor soul floating in a vat. Instead, the possible type of computer-simulated universe which will be suggested here is one in which our entire universe is contained within the computer of an advanced simulation (i.e., there is no need for our universe to have its own "Keanu Reeves" floating in a vat somewhere). In this case, the "particles" of our universe would be represented by "bits" inside the alien computer. This is now a similar scenario to the computer game The Sims in which all the simulated characters and the entire simulated world is contained within the simulating computer.
The motivation of the simulators in creating this simulated world is now much clearer: the world could be viewed and experienced on the computer for entertainment purposes, just as we currently enjoying playing so-called God games such as The Sims.
David Deutsch finds the simulated universe hypothesis highly distasteful: "It entails giving up on explanation in science. It is in the very nature of computational universality that if we and our world were composed of software, we should have no means of understanding the real physics - the physics underlying the hardware of the Great Simulator itself. Of course, no one can prove that we are not software. Like all conspiracy theories, this one is untestable. But if we are to adopt the methodology of believing such theories, we may as well save ourselves the trouble of all that algebra and all those experiments, and go back to explaining the world in terms of the sex lives of Greek gods." (quote taken from David Deutsch's paper It from Qubit). And many scientists have criticised the idea on that very basis that if it is untestable (unfalsifiable): if a theory can never be proved wrong then it should not be regarded as scientific. However, Brian Whitworth in his paper The Physical World as a Virtual Reality makes the point that the existing orthodox view of the physics establishment is equally unfalsifiable: "The theory that the world is is an objective reality is just as unprovable as the theory that it is a virtual reality. It is inconsistent to dismiss a new theory because it is unprovable when the accepted theory is in exactly the same boat."
To sum up, the simple truth is that if our universe was a computer simulation is some strange alien computer, we would never be able to detect it or prove that that was the case. We would never be able to tell.
The General Uncertainty Principle
So if we were living in a simulated universe we would never be able to detect it - there would always be an uncertainty as to whether our universe was real or not. A fundamental uncertainty. But does the uncertainty go deeper?
Let us imagine the universe of the "Grand Simulator", the universe which contains the computer which is simulating our universe. Would the Grand Simulator know if HIS universe was being simulated or not? The answer is clearly no. No matter how far you travel down the "simulation tree" you can never know if you have reached ultimate reality - there will always exist that uncertainty. Uncertainty seem to be fundamental, and any form of certainty is revealed as being just an illusion: you can never be certain of anything, the only certainty is uncertainty.
David Deutsch appeared well-aware of the drastic implication for science when he said: "From the point of view of science it's a catastrophic idea, the purpose of science is to understand reality. If we're living in a virtual reality we are forever barred from understanding nature." (quote taken from here). Well, maybe Deutsch is being too pessimistic. Maybe we just have to accept uncertainty as being part of science, and it is certainty which is just an illusion. As science and mathematics digs ever deeper, it is starting to reveal this uncertainty in principles such as Gödel's Theorem (described on the Mathematical Universe page), and the Heisenberg Uncertainty Principle from quantum mechanics (described on the Quantum Mechanics: An Introduction page). Physics has been able to incorporate the uncertainty of the Heisenberg Uncertainty Principle and made it part of science, not something to be feared.
The Simulation Argument
The Simulation Argument presented by Oxford University philosopher Nick Bostrom is ambitious in that it that it does not stop by merely suggesting that we might be living in a simulated universe, it argues that we probably are living in a simulated universe! The argument uses evidence gathered from the world around us (about the rapid growth of our computer technology) and solid scientific reasoning to show that a rational scientific person has to take seriously the possibility that we are already living in a computer simulation.
The basic principle behind this theory is that the human civilisation will one day have access to sufficient computing power capable of running simulations of their ancestors (us!). Maybe in a few thousand years in the future we might actually make a re-appearance (as Sims) in those advanced simulations. That doesn't sound too far-fetched, does it? But what if it is the case that human civilisation has, in fact, already reached that advanced state and is already running those simulations? That would mean we are living in a simulated world right now!
In fact, the future human race could easily create simulations containing astronomical numbers of simulated beings (this has the ring of truth to it: when you run The Sims there's only one of you, but the program contains thousands of Sims). There is therefore a possibility that the number of conscious, simulated humans will one day become very much larger than the number of real humans.
The Simulation Argument then goes one step further by stating that with the number of simulated humans inevitably outnumbering real humans, the computer simulation scenario is actually the most probable situation (unless you think the human race is going to become extinct pretty soon, or we're going to get bored with The Sims and start playing Tetris again - both of which seem quite unlikely).
To sum up, the Simulation Argument is a rigorously-presented argument which means that a rational, scientific person considering the extraordinary recent increase in computing power available to us, now has to treat seriously the possibility that we are already living in computer simulation.
The Monkey Universe (Revisited)
On the page entitled Is the Universe a Computer? we imagined how the universe could be created by a million monkeys randomly typing into a typewriter for ten hours a day. We concluded that the probability of a monkey typing the information which defines the universe would be infinitely small. However, if the same monkeys type onto a computer instead then there would be a much higher probability that one monkey might type the short computer program which could produce our universe (a short computer program can generate tremendously complex structures, such as intricate fractals).
However, if we now entertain the possibility that the universe could be generated by some intelligent entity (some "Grand Computer Programmer") then we find we can interpret this result differently. We had previously assumed that the short program which produced the universe was generated by a random process (a monkey). However, we can now consider an alternative scenario that the program is short because a simple, short program would be easier for our Grand Programmer to write, and would be a more compact and elegant solution for producing a complex universe. A short, elegant program would be the result of good software design.
John Barrow describes this well in his book "Impossibility": "Just as the most expert computer programmer is the one who can write the shortest program to effect a particular task, so we might expect the Architect of the ultimate program that we call the laws of nature to be elegantly economical on logic and raw materials. It is a common tendency to think that it would be a hallmark of the universe's profundity if it were unfathomably complicated, but this is a strange prejudice. This view is motivated by the idea that the Creator needs to be superhuman - and what better way to assert that superiority than by incomprehensibility? But why should that be so? Anyone can explain how to assemble a model aircraft in 500 pages of instructions; it is not so easy to do it in 10 lines. Profound simplicity is far more impressive than profound complexity."
But ... surely there's "nothing outside the universe"?
On the Time and the Block Universe page we stated that there was "nothing outside the universe" (which was called the "first principle of cosmology" by Lee Smolin in his book Three Roads to Quantum Gravity). We then saw how this simple maxim led to important conclusions such as the principle of relativity. However, we now seem to be suggesting that our universe might be a simulation on a computer contained within an external, simulator universe. So in that case, there is something outside the universe. In fact, there's another universe outside our universe! So was it wrong to say that there's "nothing outside the universe"? Is our simple maxim wrong?
Well, we came to the conclusion that there's "nothing outside the universe" by examining the behaviour of the universe and realising that the universe behaves in a self-contained manner which needed no external axes of position or time. Hence, what we really should have concluded was that the universe needs nothing outside the universe - which is a different thing to saying that there is definitely nothing outside the universe.
This is an important distinction as it would be possible to create a simulated universe which, to its inhabitants, would appear to need nothing outside of that universe. David Deutsch realises this in his book The Fabric of Reality when he writes: "The rendered environment would also have to be such that no explanations of anything inside would ever require one to postulate an outside. The environment, in other words, would have to be self-contained as regards explanations." Indeed, this is probably the most likely form of simulated environment as it would deceive the inhabitants into thinking that their environment was not simulated. In other words, they would think there's "nothing outside the universe" when, in fact, there was a whole simulator universe outside of their universe!
The Big Brother Universe
But do we have any evidence that we are living in a computer simulation? Is it just a coincidence that our current popular pastimes - such as watching reality shows like Big Brother and playing God games such as The Sims or the latest astonishing game called Spore - are aimed at producing environments identical to the one in which we find ourselves? Why should that be? It doesn't have to be that way. We love to watch these participants carry out their (often boring!) daily activities, contained within a carefully controlled, closed environment.
There's no reason why these forms of entertainment should be so popular, but the fact of their popularity and their increasing sophistication does seem to provide circumstantial evidence that maybe 500 to 1,000 years from now we would ourselves be interested in creating simulations of the environment we now inhabit. And that, in turn, might be viewed as providing evidence-of-a-kind that we are, indeed, already participants that ultimate game of Big Brother.
Some tactics have been suggested to ensure we remain participants in any such universe simulation: "You should care less about others ... expect to and try more to participate in pivotal events, be more entertaining and praiseworthy" (see here) - surprisingly similar to the tactics likely to avoid eviction from the Big Brother house!
Russell Brand and me on Big Brother's Big Mouth.
Here are some insights about the Big Brother environment:
- If our universe is a simulation, then the Big Brother house would be a simulation within a simulation. On eviction from the house, the contestant returns to the higher-level simulation. Similarly, if you were woken (evicted) from a particularly vivid dream you would return to the higher-level reality. By analogy, if our universe really is a simulation then maybe when we are evicted (die) we move to the higher-level reality - maybe this could give some solace to those who believe in some form of existence after death! (See this thread on the Big Brother forum).
- Contestants on the show frequently behave unnaturally, aware that they are being watched. In physics we know you cannot make an observation without distorting the experiment. The only way to avoid this would be if the contestants were unaware they were being observed (in a recent reality show, Space Cadets, the participants were completely unaware they were on a show). This would provide an explanation for why we would not be informed if we inhabited a simulation.
- The UK version of the show has a concept of an "Evil" Big Brother who stirs things up within the house to increase the entertainment value. If our universe is simulated then maybe that would provide an explanation for natural disasters and other challenges - they're designed to increase the entertainment value for those viewing the simulation (see the illustration below!).
Maybe we should modify Edward R. Harrison's "natural selection" universe theory (described at the top of this page) in which only universes conducive to intelligent life would predominate. Instead we should say that only those universes which support intelligent life which is interested in creating Big Brother-style simulations would predominate.
Wouldn't it be ironic if now by taking a look at ourselves, and our own behaviour, we may indeed - as Stephen Hawking famously said - finally get to "know the mind of God"?
(Footnote: The "Space Cadets" experiment was due to be terminated if the participants figured-out the secret of the hoax. So maybe we shouldn't be trying too hard to uncover these secrets!)
Comments are now closed on this page.
where's the updates??? it's time for some major improvements around here!!! - jan, 3rd March 2007
Evidently, the simulation initially provides a gross shot of our surroundings, just enough to fool us into thinking everything is there. It only provides details when we focus on something.
This method saves huges amounts of processing time and memory.
The simulation need not keep track of things you are not presently engaged in. For example, Paris, or the wall behind you. It only needs to provide you with what you are seeing now.
Similarly, concepts need not be "filled in" until you spend time thinking about them. And when you do, the concepts you are then ignoring can be purged from memory. - Bob Sage, 17th March 2007
jr - John, 14th August 2007
While I agree that the laws of physics - the behaviour of objects - could be completely different inside the simulation, I am not convinced that the physical reality of the simulation is any different from the external simulating universe. This is because each atom in the simulated universe has to be represented by an atom in the simulating computer (which would be a bit "1" or "0"). So, from a physics point of view there is no problem here: the physical reality of both universes is actually the same. It doesn't matter if our universe is simulated or not. - Robert Puttnam, 5th June 2008
But what if you are **inside** the simulated universe, or, more to the point, what if we are **currently** inside a simulated universe? Does that pose a problem for physics inside the simulated universe? Could that physics ever represent the true reality of physics in the external simulating universe?
I think it does pose a complete problem for physics. I think physics would be fundamentally unable to reveal the truth of reality. Let's consider your example of an atom in the simulated universe. You state that an atom in the simulated universe has to be represented by an atom in the simulating computer, and so they are effectively the same object. However, this is not the case. The Grand Simulator is effectively omnipotent, and can make atoms appear and disappear at will inside the simulated universe. So clearly there is no direct link between an atom in the simulated universe and an atom in the simulating computer (as no atoms in the simulating computer could ever disappear like that).
So "reality" inside the simulated universe is completely different in every respect from the true reality of the external simulating universe. And that is why physics would be unable to reveal true reality. There would forever be complete uncertainty. - Andrew Thomas, 6th June 2008
I'll do a mini-review of the paper:
Starting with Section 3 of his paper, McCabe considers Frank Tipler's hypothesis that our universe could be a perfect computer simulation, a precise copy, such that every "particle" in our universe is represented by one "bit" in the simulating computer system. So there is a precise one-to-one correlation between elements in the simulated universe and elements in the simulating computer (this seems quite a likely scenario, as it would be an easy method to simulate complex universes (such as ours) using this method: just initiate a "Big Bang" and then let all the pieces fly). This is similar to a "cellular automata" universe such as the Game of Life (discussed on the "Mathematical Universe" page on this website).
McCabe claims that if we were living in a universe such as that (i.e., a Frank Tipler-style precise copy) then we would be able to tell if it was running on a digital computer or not by attempting to find non-computable functions in our universe (which would disprove the computer hypothesis). This seems fair enough, and I would certainly agree. But then McCabe has to admit that a variation of Tipler's theory by Nick Bostrom (in which there is no longer a requirement for that one-to-one correlation between elements in the simulated universe and the simulator computer) would be impossible to detect. This is because the experiences of the observers within the simulated universe could be faked in Bostrom's simulation. As McCabe admits: "The possibility of such illusions prevents Bostrom's computer simulation hypothesis from having empirically testable predictions". So any test you could perform to disprove Tipler's theory (by testing if the universe was not spatially compact, or a computer being unable to hold an infinite amount of information, as McCabe suggests) could be faked by Bostrom's theory. So you could never be certain of detecting if you were living in a computer simulation using McCabe's suggested methods.
In Section 4, McCabe takes a very peculiar tack and makes a rather bizarre claim that a digital computer cannot realise a discrete object (and hence could not simulate a tornado, in the example he provides). The basis for his claim is that all voltage levels in a digital computer are continuous, not discrete. But surely all voltage levels in a computer are thresholded to produce binary values? He then claims: "Successive runs of the same program will not produce exactly the same sequence of electronic states in computer memory". Eh? Of course it will. Run the same program twice, you get the same output, pretty obviously, no? He then proceeds: "This level of electrical noise prevents a contemporary digital computer from exactly realising anything, even discrete objects". Sorry, this is a desperately weak argument. And even if a computer didn't manage to produce a completely accurate copy of a tornado, say, the inhabitants of the simulation would never realise the minute discrepancy of the position of an air molecule.
The simple truth of the matter is that an advanced civilisation could certainly simulate a tornado using a particle system to generate the path of each air molecule: http://en.wikipedia.org/wiki/Particle_system using much the same approach which Hollywood used to simulate tornados so convincingly in the movie "Twister".
(continued ...) - Andrew Thomas, 14th October 2008
In Section 5, McCabe presents a more philosophical argument and, as with most vague philosophical arguments, things become a lot trickier and unclear here. He starts making claims with great certainty about subjects we do not fully understand, most notably the true nature of physical reality.
McCabe claims that the numbers within a computer are interpretation-dependent, so there is some form of transformation or mapping required to move from computer bits to physical reality. Without such a mapping, he claims, it can never be possible for computer to generate a reality which would appear "physical" to an occupant of a simulated universe.
I think McCabe misunderstands physical reality and, for this reason, no interpretative step or mapping is required to produce reality from a computer. He does not appear to understand how difficult it is to produce a clear definition of physical reality. The key is that our reality is **relative**, not absolute. If our reality was absolute (i.e., we could devise a form of objective reality test to determine "this object is real") then, yes, we would need some form of mapping or interpretative step. But our reality is relative: we define real objects in terms of other objects which we already consider to be real, or tangible. For example: "I know the apple is real because I can hold it in my hand". That's the best definition of physical reality we can ever possess, a rather circular definition. We can never have an objective "reality test".
It is this relative nature of reality which means there is no need for an interpretative mapping. Because where does that interpretation come from in our current physical world? It comes from humans! Humans who would be nothing more than patterns of numbers in a simulation ourselves! All there is is the numbers (which would be the computer bits). With nothing objective, all that remains is the relationships, relationships between "physical objects" and other "physical objects" (which are defined in terms of each other), or relationships between computer data and other computer data. Objects in a simulated universe would feel tangible to the occupants as the objects would have precisely the same ontological status as the "humans".
This is actually the idea behind Max Tegmark's Mathematical Universe Hypothesis (MUH). Whereas the customary terminology in physics textbooks is that the external reality is **described** by mathematics (as McCabe suggests, we would need an additional interpretative step to generate reality in that case), the MUH states that reality IS mathematics. Tegmark describes the inside view of an observer living inside the generated universe which is called the "frog" view in his Mathematical Universe: http://www.ipod.org.uk/reality/reality_mathematical_universe.asp Other mathematical structures in that universe would appear physically real to that frog, so no additional interpretative step is required. In fact, Tegmark specifically says that no interpretive "human baggage" is required, which McCabe seems to feel is essential.
Thanks very much for your question, David. - Andrew Thomas, 14th October 2008
The simulated universe experienced by the simulated being is **completely independent** of the type of computer performing the simulation. It doesn't matter if it's running on a slow Mac or a new PC, as long as the resultant rendered image is the same then the experience will be the same. So the external laws of physics also do not affect the experience.
Considering your example of the speed of light, it is actually possible to move things around at **infinite** speed within the simulation just by making them disappear at one moment in time and then making them reappear some arbitrarily large distance away (100 million light years?) at the next moment in time. That's effectively infinite speed within the simulation, but it does not involve any extra processing power.
David Deutsch agrees with this in his book "The Fabric of Reality" when he considers the related problem of creating virtual reality environments: "A flight simulator can give the user a wide range of piloting experiences, including some that no real aircraft could: the simulated aircraft could have performance characteristics that violate the laws of physics: it could, for example, fly through mountains, **faster than the speed of light**, or without fuel." - Andrew Thomas, 2nd February 2009
You say that the external laws of physics do not affect the experience, and "It doesn't matter if it's running on a slow Mac or a new PC, the experience will be the same". But surely if the simulated environment takes a long time to render on a "slow Mac" then the simulated beings will notice time slowing down? So there IS a dependence on the external environment. - Robert Puttnam, 4th February 2009
Everything inside the simulated universe is defined in terms of other objects inside the simulated universe. For example, the simulated beings would measure time using clocks (these would be simulated clocks, of course). So if the simulated world is generated more slowly (on a "slow Mac") then the rate at which the clocks move also slows down at precisely the same rate. Even the functioning of the simulated beings' brains would slow down at precisely the same rate. So the simulated beings would feel like nothing had changed: time would feel the same in their brains, and their clocks would give the same readings.
(For more on this idea of time being defined by relationships, see page 11 of Carlo Rovelli's paper "Quantum spacetime: what do we know": http://arxiv.org/abs/gr-qc/9903045 which considers the relationship between a clock and a moving pendulum).
David Deutsch also makes this point on pages 124-125 of his book "The Fabric of Reality" when he considers the similar situation of a user wired-up to a virtual reality machine. He wonders how an extremely complicated scene could be rendered quickly enough: "The computer causes the brain to slow down (or, if necessary, to stop) until the calculation of what should happen next is complete; it then restores the brain's normal speed. What would this feel like to the user? By definition, like nothing. The user would experience only the environment specified in the program, without any slowing down, stopping, or restarting."
So the generation of the simulation is truly implementation-independent as far as the simulated beings are concerned: it really doesn't matter if it's running on a "slow Mac" or a "fast PC", processor speed is unimportant. As David Deutsch again says in his book "The Fabric of Reality": "This method allows us to specify in advance **an arbitrarily complicated environment** whose simulation requires any finite amount of computation". So it would even be possible to simulate our existing universe on a basic PC - the processor speed would be sufficient, though it would take an incredibly long time! (And you might need to install a considerable amount of additional RAM!!) - Andrew Thomas, 4th February 2009
mol - Mol Smith, 28th June 2009
The answer I like to imagine as best fit is: at the centre of each galaxy (hub) is a 'black hole'. Here, all data is broken down into its raw parts and sucked out through the 'ports' into the super-real reality to be made use of.
We see 'black-holes' but I see the gateways which somehow fit the function of my hardware i am using to write this note.
- Mol Smith, 28th June 2009
So here are a few tothink about. i call them 'cracks in reality'.
1) World War II saw the desruction of bricks and mortar on a fantastic scale. London, Hiroshama, Nagasaki, Coventry, Dresden, Hamburg, Stalingrad, suffered poundings which obliterated billions of tons of physical structures.
Th twin towers in the USA took over 2 years to clear the debris: a tiny thing compared to the cities I just mentioned. Where have you read or seen a documentary on the colossal work of removing the debris from these cities. More... the engineering and manpower task of removing the waste and rebuilding these massive cities would have been so costly at a time when the world was bankrupt and focused almost 100% on destructive industries that the task would have taken decades.
Where in the world today is the accounts/accounts of this enormous set of projects?
2) In the UK, the 1950's saw the ris of nuclear power stations, 4 years after the second world war. I was born in 1950. I am now 58 years old. In 58 years, I have never witnessed the construction of electricity pylons and their wiring. They dont rot. You may see a guy here and there paintng one, but I just cant see how they all got there. In fact, as a child they must have been going up like blazes with all these incredible vehicles lifting tons of cables above my head to get over all the housing estates etc., but I never saw them. Ask everyone you ever meet now or knew in the past, they will tell you the same answer: they never saw one goingup nor any of this work either!
I kid you not.
There are cracks in reality in the everyday things. The big stuff is probably covered but the devil is always in the fine details. The illusion is never achieved by the big view but the lesser one. Each person should examine their own reality, or journey and see what facts they can agree on. Ask a friend his recollection of accounts on a small thing at school in the past or at at a job or any event which sticks in your mind that you both shared. Your accounts will differ greatly. Is this a product of your observations, your memories, or the event itself?
- Mol Smith, 28th June 2009
I've wondered about that question of reconstruction after the second world war myself. I think it's especially amazing when you consider how Germany was totally destroyed in the war but was leading the world by the 60s & 70s with great cities. It's interesting, I searched for "post-war reconstruction" on Google Images and there wasn't a single image of the reconstruction process - not a mechanical digger or a workman in sight.
I also think it's interesting when you boil a saucepan of water and you get huge bubbles of air bubbling up endlessly. We are told that that air is just dissolved in the water, but when you consider the volume of air released it seems like its 10-20 times larger than the volume of water it came from. Seems to me like a programming bug!
Anyway, great fun. Good luck with your book, Mol. - Andrew Thomas, 28th June 2009
The required processing power (of the Matrix) would be considerably less than one would imagine. If you didn't see it, it didn't happen and wouldn't be computed. - johnny, 6th July 2009
However, I think this shows a general lack of understanding over what "non-computability" entails. I explain it well on my "Is The Universe A Computer?" page:
Basically, for a particular, specified mathematical axiomatic system (i.e., a particular group of axioms) then there will always be a theorem which is true but you cannot prove (from those particular axioms). So the particular theorems which are undecidable will depend on the particular set of axioms you select. There is no such thing as an **absolute** undecidable theorem.
So a computer can basically do anything a human mind can as long as it starts from the correct axioms (i.e., as long as it is given the correct starting axioms in its programming). This is described about half-way down this review of "The Emperor's New Mind" by John McCarthy:
Here is the important quote from that review: "One mistaken intuition behind the widespread belief that a program can't do mathematics on a human level is the assumption that a machine must necessarily do mathematics within a single axiomatic system with a predefined interpretation."
The way I look at it, whenever we try to prove a theorem, or work out anything, in our minds then we clearly follow a step-by-step process (we could basically say what we are thinking, and the steps we are making). And any computer could make exactly the same steps. So as long as the computer is given exactly the same "basic knowledge" as a human (basically, the same initial axioms) then it could perform exactly the same steps as a human mind. So there is essentially nothing absolutely non-computable for a computer.
Thanks for your great question, Gorav.
- Andrew Thomas, 16th July 2009
As to your question of how non-computability in the simulated universe would relate to non-computability in the Grand Simulator's universe - that's a very tricky and interesting question and it hadn't occurred to me. I would imagine the axioms generating the simulated universe would have to be equal to (or a subset of) the axioms of the external simulator universe (after all, it's just a program running in the simulator universe), and so it would not be possible to prove a theorem in the simulated universe if you couldn't prove it in the simulator universe.
So if you are the Grand Simulator and you find a theorem you can't solve, you wouldn't be able to make a shortcut by creating a simulated universe and hoping the simulated beings prove the theory for you!
I have just discovered that David Deutsch considers this idea of the mathematical limitations within a computer simulation in his book "The Fabric of Reality". He says: "A type of experience which certainly cannot be artificially rendered is a *logically impossible* one. I have said that a flight simulator can create the experience of a physically impossible flight through a mountain. But nothing can create the experience of factorizing the number 181, because that is logically impossible: 181 is a prime number."
Very interesting - thanks a lot. - Andrew Thomas, 17th July 2009
However, it might reveal some interesting facts about the structure of the Grand Simulator's simulating algorithm!
As to your USB theory, well, USB is bi-directional but black holes are pretty much uni-directional. So I'm not a fan of that theory. I actually think any Grand Simulator would be virtually omnipotent and would not be limited to sending information only through black holes - they would basically have complete control of the simulation. I would imagine they could traverse the simulation in the same way as we can when we play "The Sims". - Andrew Thomas, 17th July 2009
If we had a different universe with non-Euclidean space, or more than three spatial dimensions, then geometry (a branch of mathematics) would look very different. Even arithmetic could be different (see the section "Arithmetic in different universes" on my Mathematical Universe page). So when you say mathematics is the same in every universe, it is not necessarily the case. It all depends on the axioms. We have chosen a system of mathematics which closely follows the physics of our universe, and so is most useful. But we were at liberty to choose a completely different set of axioms.
The whole system of mathematics developed by the inhabitants of another universe could be different to the system of mathematics we have developed in our universe because it would be based on different fundamental axioms. Those axioms would be based on the physical axioms of their universe, but those physical axioms are different from our universe. But those different axioms would seem completely normal and "obviously correct" to the simulated beings, just as our axioms seem "obviously correct" to us!
I would recommend you have a read of my Mathematical Universe page for more on this. Things aren't as obvious as we might think they are at first glance - Andrew Thomas, 17th July 2009
The fundamental problem with Bostrom's premise is that, the way it is framed, *IT SHOULD HAVE BEEN JUST AS "PROBABLE" FOR THE ORIGINAL, REAL, NON-SIMULATED HUMANS TO THEMSELVES HAVE BEEN SIMULATIONS*.
There's some seriously flawed logic here that renders the entire premise unconvincing, regardless of how "rigorously" it is presented.
Is it not conceivable that in the original, "real", non-simulated universe, the humans who would one day build the simulation in which we "probably" exist, had a Nick Bostrom amongst themselves who reached exactly the same conclusion about his own REAL universe, convincing other REAL humans that their REAL universe was "probably" a simulation and who, incidentally, must have been flat-out wrong? Funny, that.
His assumption regarding probability is inherently flawed as well. Using his logic it seems easy to conclude the following; Since the majority of all humans living and breathing in the world today were born and live in Asia, the most probable case is that you yourself were born and live in Asia. If the only piece of information I knew about you was that you were neither born in nor live in Asia, I can then conclude that you are probably not a living, breathing human.....right?
The problem is that he creating a false equivalency between an unknown, hypothetical variable (the number of simulated humans presumed to exist in some future time) and real humans who do exist and have already in fact been born.
That simulated humans capable of sufficient complexity and depth of thought equivalent to you and I will someday exist is a prediction and extrapolation based on our own current technology, it is NOT an extant fact.
That, even given the assumption that simulated humans will one day be created, they will simultaneously exist in extremely large numbers is too large a leap of logic since he is imposing his own basic assumptions about the usefulness of such simulations to future societies which don't even exist yet. Historically, predictions about the needs, desires, and knowledge of future societies have consistently and embarrassingly fallen flat on their face (I'd bet such predictions will continue to fall flat).
As I've said, since his argument rests too much on assumptions about the specific desires and interests of future beings whose knowledge and intellectual abilities presumably surpass his own, those assumptions are essentially baseless as far as I'm concerned.
For all we know, simulations of the scale that Bostrom conceives of may be totally unnecessary by the time the technology exists to create them, and superior, more efficient methods to acquire the same information will be developed and used instead. - Bostrom's argument is based on a false premise, 5th October 2009
Yes, you might well be right. But Bostrom's two assumptions do not in any way seem unreasonable to me.
Yes, the original "real" non-simulated universe WOULD have had its own Nick Bostrom convincing other REAL humans that their REAL universe was "probably" a simulation. And it that case, yes, that particular Nick Bostrom would have been wrong. But there would be many more simulated universes simulating other universes, so the probability that OUR Nick Bostrom is actually wrong and we are living in a real universe becomes vanishingly small.
This "Matrix" idea is a real possibility which is hard for a scientific argument to easily dismiss. It does seem to follow from only two reasonable assumptions.
- Andrew Thomas, 6th October 2009
I don't want to be a pain, bringing the speed of light subject back...
You really are right about the program being able to instantly teleport things around.
But I have written a couple of 3D games myself, and usualy that's not how we do all the movings.
3D elements are usualy moved by applying forces to them, not by direct manipulation of their positions.
Of course, I am talking about how programming is done in our own world :)
But to me that would also make sense in the simulated world.
There are a number of good reasons to do it that way.
First, it is a high level approach, highly object-oriented; it frees the "main program" from having to move objects around, specially if you (the simulated universe) has some kind of accelerated physics - like Ageya PhysX, in our world.
Then, there is the collision detection problem.
Collision detection is handled in many ways one would not expect.
If we are talking about a *multiplayer* simulation, then effective collision detection is usually handled by prediction, instead of actually detecting the collisions when they happen.
This saves a lot of processing power.
It works like this: particle A is moving by Va, while particle B is moving by Vb.
Will they collide? When will that happen?
We (and I would assume any programmer that uses a similar kind of logic, no matter what world he/she lives in) would project both speed vectors and see where they touch each other.
In order to achieve this, the program would deal with positions and velocity vectors.
This dramatically increases performance, at the cost of computing movements by using a set of equations and, invariably, a set of parameters that determine the limits for the simulation.
That's how physics engines work in our world - which does not mean that's how they would work in the "real world".
But as far as I can tell, that's how I would doit - and that's how it is made in ODE, Tokamak, Havok, PhysX... you name it.
So, in short, I am not trying to stick to some idea, I am just offering an explanation of why I believe limits like speed of light are required for the bread-and-butter physics of that simulated universe.
BUT - that would not keep the main program to apply "infinite speed" when it is needed. Those would be special "game objects". The rest of us, the core objects, the great majority of the simulated particles would still be moved around by the physics engine, still using object oriented approaches and still subject to the equations and the limits that are implemented by the classes they inherit their functionalities from.
That speed limit would then be easily explained, I guess... but I may be wrong and I would love to hear what you guys think about this.
- Rui Barbosa Jr., 11th October 2009
Yes, I am definitely in favour of the speed of light being a design decision rather than being due to any limit in processing speed (which, as I explained, isn't really a limitation anyway - we can still make things move at infinite speed). I actually think the reason why there is an absolute limit is to stop objects being able to move "backwards in time". Considering Einstein's theory of relativity, we see that time slows down for objects that move close to the speed of light: http://en.wikipedia.org/wiki/Time_dilation And if an object could ever move faster than the speed of light it would effectively be travelling backwards in time. See:
Why faster than light implies back in time
This would introduce all sorts of inconsistencies into your simulation, such as the ability to kill your own grandfather (see the section "The Need For Constraints" further up this page). So I think an upper limit on the speed of light could be a design decision to stop these inconsistencies (which would appear as an infinite loop in your computer program).
Thanks a lot, Rui. - Andrew Thomas, 12th October 2009
It makes perfect sense, it is elegant - and it is simple.
If I had to offer another explanation, I would say that it would have something to do with time granularity, or how small a time-slice can be.
Time granularity is critical when one needs to integrate velocities to get displacements.
Now that I think of it, this would make sense, too.
Moving objects by applying forces to them, rather than directly manipulating their space coordinates, would result in displacements, which are always relative, rather than absolute.
Why would we need to define the size of the smallest possible time-slice? I am not sure.
Maybe it has something to do with the way information is stored.
Maybe speed vectors are coded using time^-1 notation (how many time-slices are needed to move 1 space-unit). I don't see why one would do that, thou.
He... I don't think we can find another answer without analyzing the actual data structures that is being used.
Rui - Rui Barbosa Jr., 13th October 2009