Nice story, it is very well thought out. I wonder what other philosophical conclusions you could come up with about this train of thought? Also, nice captcha.

The really amazing implication if you could build a computer to recreate the universe is that everything is completely deterministic. it means there is no free will, because a computer could calculate ahead of time all your choices for your entire life. In this particular story, because it works on the atomic level, it would imply that your actions were determined from the big bang, there can be no good or evil, no hell, and no heaven, and people and everything else alive is really as mechanical as the planets orbiting the sun.

Simply because I can tell what decision someone will make doesn't mean they aren't making a decision.

I know that if I ask my D&D group if they want pepperoni or green peppers on their pizza, they will say pepperoni. This is not the same as them not having a choice in the matter.

Actualy, it is. If you Know with a capital K that they are going to choose peperoni then there is no other alternative and hence there is no choice as there is only one option.
If you roll a ball down a slope two times in exactly the same way there is only one way it can roll

Gah, this commenting system needs an edit buton.

:
Actualy, it is. If you Know with a capital K that they are going to choose peperoni then there is no other alternative and hence there is no choice as there is only one option.
If you roll a ball down a slope two times in exactly the same way there is only one way it can roll, no matter how bumpy the slope or how random the rolling seems.
I think that because of this our universe must be determenistic on the lowest possible level, implying everything Ben says. I mean, if the big bang happened in one particular way, where would the randomness come from?
Though this means that you could predict the future with a powerfull enough computer, you would need total information about every particle in your system which isn't possible due to heisenbergs uncertainty principle. And it's a bit tough because of the ludicrous ammounts of computing power needed.

Great story.. however, you should read up on quantum computing... a quantum computer simulation of the universe would simulate a 'multi-verse', where every possible quantum reality would exist.

Isn't that exactly what's its doing?

If I was running the topmost simulation, I think I'd just turn it off.

which is precisely the philosofical problem of the story.
you need an infinity downstream AND upstream as well.
Maybe it can work that way ... But then there is no upmost... even weirder.

BTW when it says it simulate only a part it can't be complete as interactions on the border would be aproximated and recurring aproximations can happily diverge... so ALL the universe in always completely simulated.

Im not sure that a limited portion of the universe can completely simultate all the properties of the whole without violating thermodinamics...

anyone ?

But the top most level doesn't completely determine what occurs a long way down the line, as it is stated there's a leveling out that occurs (where they were/are) which must imply that certain upstream levels do not respond to the top most. If you were in the top most level and you shut the simulation off, sure, many universes would shut off to but the event of them all turning off, is impossible/ improbable/ statistically insane. In effect you may wipe out many levels but not all, creating a new top level. So go ahead turn off the top level.

side note, why does the comment page ask me what the square root of negative one is? do i have to know to be able to post? of course i know.

Ben, is that you?

How do I type the square root of minus one? It's impossible, can anyone help me? When you do, I will then travel back in time and tell my past self what to type in the box because it is otherwise impossible that you could be reading this post. Please, prevent a paradox and tell me the answer...

This raises an interesting question, what would happen were they to run the simulator and change something in the past on the simulator which would prevent them from running that prevention? If their universes are perfectly identical then that would cause a paradox. A similar thing would happen were they to run the simulation forwards, predict the future, then change it.

Paradoxia - I guess they are testing the mathematical knowledge level of the people interested in the subject. In complex numbers, the square root of minus one is the imaginary number "i" (a complex number is written as x = x + iy, where x, y are real numbers). In my country we were doing this by grade 10...

However, nice mental exercise, with interesting conclusions. It's nice to discuss, just for the sake of the arguments, but otherwise I don't believe this is possible at all. Any simulation to start needs initial conditions, even at time zero (big-bang), and given the size of the universe, this would require a tremendous amount of data to be entered in the simulation by the user (considering the user knows these conditions). Being all deterministic, any small change in the initial values would propagate through the entire evolution of the universe to give it a considerably different version.

What they should do is simple: They should fast forward the simulation until the (absolute or practical) end of it's time. Then, when their timeline is perfectly insured, they could have safe (if only less) fun with the best god-game ever created.

Acutally, looking over it again, I realise that there is not as much of a paradox to the time travel as I first thought. travelling backwards is easy enough to explain, they set their computer backwards, and at the instant that they set it backwards, the one above them sets them backwards. Just imagine just one layer now, with you in the top layer running the simulation, you can run the simulation, set it backwards, change something, and run it again, the first simulation is simply lost. There are in fact no paradoxes to time travel as long as the one controlling the flow of tim is outside the flow itself.

The problem, I think, actually comes in using the computer to try and predict the future rather than changing the past. Since there are an infinite amount of layers and the simulation will be doing EXACTLY what you would do (even if you were in the TOP layer (scary thought)), it would have to find a balance where whatever they do in the simulation would cause you to do exactly that.

Do you understand me?

Ow ow ow, headache. But an awesome headache.

If the topmost experimenters turn off their simulation, *ALL* simulations terminate immediately.

If the nth experimenters turn off their simulation, then *ALL* simulations n+1 and higher terminate immediately.

However, if the simulation is "perfect", then no simulation will do *anything* other than what "reality" does.

Did you ever stand between two mirrors, placed parallel to each other? The reflected images seem to gradually curve away from you in either direction. This example perfectly illustrates the storyline to me, where the further away you are from the "current" level, the more differences can appear. I know the analogy is not perfect but it works for me.

So they created a super, quantum computer, with infinite processing power, which is essentially one single fundamental particle. Diane recreated the exact conditions of the big bang, without error, as the initial action of her universe simulation program. She ran the program and the universe was simulated flawlessly with such unbelievable accuracy that her and Tim could even view a simulation of themselves viewing themselves.

But at what point did this program cease being an exact recreation of our universe inside a particle quantum computer? What exists inside that computer is an infinitely expansive SIMULATION of our universe and other universes inside infinitely smaller simulated quantum computers. Granted that, in this story, its the closest thing to a perfect program ever created, its still a program and has no bearing on anything outside of the quantum particle.

What I'm saying is that Diane created a computer program. She did not communicate with an infinite number of universes, nor did she tap into other dimensions. They could and probably do exist, but by creating a supercomputer she did not create a means to communicate or alter them. The bit where she conjured the opaque viewing port in the very room they were in just isn't possible based on the rules of the story established.

NEVERTHELESS....this is a great story from a great writer.

Veyr nice, with a great line of thinking and some interesting philosophical conclusions. I don't quite get how logically concludable realities are synonomous with actual realities (you can draw an 'impossible box' or a 'devil's fork', but you can't build one), but still fascinating.

With regard to the question of how the "lower" simulation comes to be identical to the simulation simulating it, I think that "levelling off" and "stability" are the key words. There doesn't have to be an explanation for why the two are identical, because in an infinite series of random simulations, each (or perhaps only some) simulating another in turn, eventually one (or more likely several) will arise which simulates itself exactly. These are the "stable points" because they give rise to infinite replicas on themselves.
Now, I'm not terribly well versed in the mathematics of infinities, but if I recall correctly, some infinities are "larger" than others. Soooooo, what you have is one infinite series of non-identical simulations, and another (or several, or probably infinitely more) infinite series of identical simulations. Now it seems to me that statistically one is therefore almost certain to find oneself in one of those, rather than any individual one of the tiny, (if infinite) minority of "unstable" simulations.
This argument might even be extended to resolve the time-meddling issues, assuming that those simulations which permit it fall into the unstable catagory, but this is giving me a headache, and now that I think about it, I'm not sure that makes any sense.

Who's to say it isn't circular, though? In this case, I would think there is in fact no top at all, and what you do would happen to yourself because, in essence, you are below yourself. Making any sense? I dunno. Just a thought.

I suppose with a quantum computer, a simulation would be so advanced that the simulations running inside of it would actually be sentient, althought its future actions may be laid out before it.

Anybody else think so?

Poog, I'm not sure I follow. What do you mean by advanced? Are you arguing that complexity neccessarily gives rise to sentience? Wouldn't that imply that the universe we're living in right now is sentient? Because that sounds dangerously like hippy talk...

You got me there.

If you were on top would you turn it off?

yes

They have no idea how good they have it. Technically their entire universe was created mere weeks ago (real time), but time passed in their universe for 13.6-ish billion years. Since the computer has infinite processing power, they could run the simulation to literally forever in just a few seconds (although they should probably halt at some points to stop the pesky big rip from destroying everything). They could then turn the simulation off, having ensured perpetual life on Earth.

I would have to disagree with the curving mirror theory. If your body was transparent and you stood in the exact center between said two mirrors, you would be faced with an infinitely straight image of yourself.

you made a pretty good point Poog. Assuming the simulation was a perfect simulation, then the people within would perfectly resemble those in "higher levels." Not just in location or appearance, but in cognition as well. Thus the people within each simulation would be "sentient" on the level of every high level. This takes determinism to another level where thought and sensation are merely part of the physical reality.

The question isn't how the quantum computer "creates" a reality, but as to how we know whether or not reality is nothing more than a conjectured system of logic which is manifested as the physical reality we observe.

I laughed really hard because I said "But they know they're the top level because they've existed prior to the next simulation." Then I realized that each simulation started at the beginning of the universe, and each pair would assume that they existed prior to running the simulation. Given this bit of info though, it can be assumed that each successive simulation would lag behind the previous one slightly.

The question is what would happen when this slight time gap went to zero. With an infinite computer calculating all the possibilities of an infinite number of the same computers the recursion grows beyond understanding. However, based on a rather tired and lazy understanding of math, infinite limits are not all created equal, and it seems logical that the first computer would overload somehow as each successive computer began to create a further strain.

They can't do good stuff to layers below, and have it happen to themselves.

The moment they realized they were simulated, their universe diverged from the top-level: The top-level version of themselves did not realize they were simulated, and likely wouldn't have shut off the blank cube at the exact same time. After the universes had diverged even a little, it seems unlikely they could ever be made to converge.

If they did good stuff to the guys in the lower level, there is nothing that says it's likely that the guys in the levels above would do the same. (Except for the first time the lower levels are modified, when all universes are still in sync.)

However, since everything that happens in all layers is possibly a function of the starting conditions of the universe, which are apparently known, and their simulator can simulate this, they might be able to simulate what happens in all the layers.

Just my 2 cents...

Ignore my previous post, I get the bit about a stable point now.

Totally amazing story.

What would happen if you set the simulation to run five seconds ahead of yours, and then copied the actions of your simulations exactly? Every simulation would be copying the simulation below it, with no true "original". Or, you could set the simulation to run ten seconds ahead of real time, but copy their actions immediately. Thus, each higher level universe is running five seconds faster than the one below it, leading to infinite acceleration. These of course assume that every particle in the universe is participating.

Damn lack of edit. I was unclear in my last post and should clarify: Each universe would run five seconds faster than it should, not five seconds faster than the one below it. The acceleration problem is the same though. If A-Me shakes my head at 10:30, then B-Me (In the layer above) shakes his head at 10:25, but C-Me shakes his head at 10:20, and so on. In theory, the "bottom universe"-Me will be the last one to shake his head, even though he's the one everybody is copying.

That would be impossible, because each simulated deterministic universe below yours (beyond the "stable mirror" point anyway) is a perfect simulation of the previous one, so when you set your simulation forward 5 seconds, the ones above and below you do so as well in perfect sync, and so when they rewind and start copying, the simulations will still be in perfect sync all the way down.

Assuming the simulations are perfect, every simulation will be the same, as the people in every universe will make exactly the same decisions. Even if they tried to introduce a random element to distinguish between universes (such as rolling a dice to generate a "random" number and then creating that many objects in the next universe down), the dice would be rolled exactly the same way in each universe and so the same number would be rolled and each universe would be affected in exactly the same way.

The exception to this is the top universe. When the people in the top universe notice that the changes they made in the universe below them did not occur in their universe, they can deduce that they are in the top universe. At this point the top universe diverges from the lower universes. It is no longer identical. Instead we now have one oddball universe and a whole series of still identical universes. The universe which was previously second is the new top identical universe. But of course they are unaware of this until they do something that doesn't happen to them in turn, which makes them different to the other universes, so this one diverges as well. And then the same thing happens again and again...

The people in an ex- top identical universe could actually prevent this if they acted after realising that they are (were) the top identical universe but before the people in the second universe realise they are the new top identical universe. If they copied exactly the next-universe-affecting actions of the people in the second universe, the people in the second universe would not realise that they are now the top identical universe, since they would assume the changes were caused by identical people in an identical universe above them, rather than people in a non-identical universe just pretending to be identical. However, if the people in the top universe do anything to the second universe that the second universe doesn't do to the third (or if they don't do something that the second universe does do), the second universe people would notice the difference and deduce that they are the top identical universe, which would then of course make them non-identical.

Or maybe it's all a loop. Maybe there is no "top" universe. Maybe there is an infinite number up until it reaches around and becomes you again. Maybe the "bottom" universe affects the "top" and that means that everything there is identical.

doog: How do you propose that works? It's all well and good do say "hurr durr maybe it's a giant circle", but you don't argue how that is even physically feasible.

Tropolist: Pretty immature to berate a voiced thought derived from a thought-provoking story.

The loop/circle thing is something that has actually rolled through my head as an idea that, our universe and reality exist because of actions taken somewhere within our own timeline, as a self contained paradox. And that this could be so perhaps because time wasn't so much set into motion like a pencil across paper but more like stamped onto it in its entirety.
A circle of simulations is one possible approach to this..
We can say Simulation 0 only exists due to Simulation -1, S-1 is there because of S-2 and so forth, and there actually not being a "top" level. And we can obviously tell there's no "bottom" level. While this can be expressed as an infinite line, it simply makes more sense as a circle. A perfect circle can't exist in reality due to the nature of pi, but perhaps the conceptualization of this sort of loop is more of what a perfect circle is.

Unfortunately it doesn't seem a exact copy of the universe can be truly simulated, unless I'm not understanding something about randomness.

Caz pointed out
"Even if they tried to introduce a random element to distinguish between universes (such as rolling a dice to generate a "random" number and then creating that many objects in the next universe down), the dice would be rolled exactly the same way in each universe and so the same number would be rolled and each universe would be affected in exactly the same way."

This holds true but what about from a digital source? Is the product of a electronic function tasked to pick a random number between x and y somehow governed by the condition of the universe preceding and at the moment it produces a result?
If not, and I don't see how it could be, then all sorts of scenarios where there are different outcomes based on the result of a digitally produced random number (such as gambling) would potentially cause a simulation to have a drastically different growth.

B: A lot of what you're saying doesn't make a great deal of sense. Just because a line is infinite in one extent doesn't mean it is infinite in both extents. For example, a line can begin at (0,0) and travel right forever. It doesn't necessarily have to travel left forever too, it can simply have only one end. In the same way, just because every universe in the simulation has another universe in the simulation below doesn't mean that every universe has a simulation above it too. There *is* a top simulation even though there is no bottom one. Certainly there is nothing in the story to suggest otherwise, and that wasn't what I had in mind when I wrote it.

In addition, even *if* the sequence of universes extends infinitely upwards as well as downwards - which is a much less interesting concept, to say nothing of being even more improbable than the story as stated - there is no reason to suggest that there is any kind of "loop" going on. In fact, if all the universes in the infinite sequence perfectly imitate each other, then there is no loop. There is effectively only one universe, which is contained within itself. A loop with only one element.

You also appear to misunderstand the concept of randomness and random number generators, or, to give them their full name, *pseudo-random* number generators. Of *course* computers have to generate random numbers based on the current configuration of themselves and the universe around them. How else could you possibly do it? Magic? If the universe and the computer are precisely identical to infinitely many decimal places, then so is the generator, and so are the "random" numbers which come out.

there is no top. it's an infinite number of possibilities and therefore universes. also, wouldn't we all have been nonexistent before the construction of the computer?

They can turn the simulation off. They just need to fast-forward far enough (heat-death/big crunch/whatever, just to be safe), and then turn it off.

They're only in this tricky hall-of-mirrors situation because they're simulating the exact moment they're living. Go forward or back in the timeline of the simulation, and it's like tilting one of the mirrors so they're no longer parallel: the images diverge more and more the deeper you go down the tunnel.

massentropy: of course there's a top. I'm telling you there's a top. It's my story and I get to decide what happens in it, and for there not to be a top makes no sense. You ever hear the phrase "bottomless pit"? A bottomless pit has a top. So does the stack of universes in this story. There is no argument!

Was just going off the loop idea Sam, there's a top level in your story how you intended, but your intentions can't stop people from theorizing and imagining further from it. Sorry if that aggravates you.

Why can't a true random be achieved?

True randomness just cannot be in a completely deterministic system, because the particles that make up the die being rolled, logically, had to come to be through a pattern that continues to weave this universe even as I type (assuming we live in a deterministic system). The die and the precise way in which it rolled, landed, etc.. is all the sole, conclusive resultant of the previous "step". This also assumes that time is traversed in finite "frames" (argue that one too...and double points for anyone who brings up relativity).

That is the bigger problem to me. We have no indication or idea of how exactly time is traversed, so how did Diane manage to program a time-lapse simulation when the system of "time" is so poorly understood? I remember once hearing some deep, intellectual quote; "The only thing that is constant in the cosmos is change." ...because time is an artificial system for describing change and nothing else logically has to exist. If everything disappeared tomorrow, the only thing that would be the same would be the concept of change. When all of your clocks are gone and no one is left to tap their foot and count the seconds, time disappears with the humans that created the concept. The idea of "things changing" is the only true universal constant.

Furthermore, I do like the idea of there being a *top* layer...an actual existance...but this program does prove, through its accuracy, the existence of a deterministic universe, which means that in some way, shape, or form, the top layer is nothing more than an infinitely iterating pattern or formula or calculation or recursive computer program, etc... That concept, all on its own, is a humbling one, and one which I firmly believe. Who says God has to be a floating figure somewhat resembling a human? Why can God not be a formula, or a mathematical pattern?

On a lighter note, did this story give anyone else the urge to build a supreme quantum computer and start playing the lottery?

B: I was note berating or belittling him. I was just asking him to defend his claim, which shouldn't even be a surprise since he has the onus of proof. As previously stated, his/your arguments don't make any sense beyond the fact that they're poetic. You said that if there were no top or bottom, a loop would "make more sense". This is not solid reasoning. Our universe would "make more sense" if it were perfectly spherical, if general and special relativity didn't contradict each other, and if quantum entanglement didn't exist. But it isn't spherical, they do contradict each other, and it does exist. We have to just deal with it. Yes, a closed circle is very poetic and interesting, but it isn't plausible. If we are going to consider this thought experiment seriously, baseless theories are not welcome. Sorry if you feel that I'm berating you, but I didn't expect the people reading this story would need sugar coating.

Yeah, but what happens when they get a power outage with no backup generator?

Bweeoooo-FFzzzzt. -NO CARRIER-

They wouldn't know when it happened. The power would cut out in every universe, immediately ending all universes below it. Only the universes above the stability point would survive, and even then they might disappear too.

Haha, this made me laugh! Amazing story... altho i had no idea what you were talking about at first.
and rereading this... it made me laugh in a good way, as in amusing... also meant in a good way.

I am interested in the consciousness. If they are there, having ideas, talking, thinking and otherwise acting intelligently, they have a consciousness. But all the other people above and below them also have consciousnesses. But they are identical. So do they have different thoughts or the same? If the same, as is implied, what makes them different? If nothing, then they are observing the same thing as the universe above and below them, otherwise they would not observe what they are observing: a stack of universes identical to them in every way. So they all must be identical. This applies to every layer, and implies that there is an identical layer above each. There is no top layer.

Somebody's been reading Asimov--this is exactly the kind of thing he'd have written. :) I love the ending.

I assume everyone realises that in the real universe things are absolutely *not* deterministic, right? (so this story could not possibly happen)
...just clarifying...
This was a great story though, perhaps even approaching Douglas Adams inwonderfulness(!)

Good read. I agree that it feels like a cousin of Asimov's stories, especially "The Dead Past." (Got here via a link on the xkcd forums.)

Sweet...

Actually, they COULD turn off the machine, as long as they later turned it back on. Think of it in terms of the Sims. When you save and quit, they don't die or anything like that. And when you reload it, they keep going. To them, time didn't stop for a day or so. They didn't notice anything at all. Also, if it needed to be on, how did the universe exist before it was created?

Different comment: they don't have to be 'nice' to the worlds below them. Essentially what they have is a God machine. They can do anything they want to the 'simulated' world and it happens in theirs, so basically, they can do anything they want to the world.

I, personally, would make it rain purple hippos but give everyone purple armour to survive the torrents. After that, the sun would evaporate some of the hippos, the plants would drink and later transpire others, and some would seep into the bore hippo supplies, to hippo people's lawns and stain their bricks. (If you don't get it, try replacing 'hippo' with 'water', and after that, read it as it is.)

Great story - a brilliant introduction to the Simulation Hypothesis, which says that once you know how to create simulations realistic enough to host intelligent life, you have to accept that it is vanishingly unlikely that you yourself are in the single, top-level universe: the only universe which isn't a simulation inside some higher-level universe.

If you liked this story, you might like to search for Simon Tatham's "Infinity Machine", which explains a bit about how you might program an infinitely powerful computer

Oh god. Wow. ._________________.


Nice captcha.

In response to the comments about the universe not existing before the simulation was run, the simulation was run from the beginning of time, or the universe, and then "fast forwarded" to the present day so the universe did exist from the beginning of time.

Also, assuming the are infinitely many universes, with no bottom universe, it is effectively certain that your universe is also infinitely far down the chain, meaning the even if there is a top universe, there are still infinitely many universes above you, so it doesn't matter if there is a top universe or not.

Actually, no. It doesn't matter how far down the infinite chain you are. There is always a finite number of universes above you.

Let's say you numbered them. The top universe is 1, the universe it simulates is 2. The universe simulated by 2 is 3. And so on.

Now, you may be in universe 1 or 2 or 588 or 456,344,222,100,000,000,000,000,000. That means that you will have 0 or 1 or 587 or 456,344,222,099,999,999,999,999,999 universes above yours. However, there is no "universe infinity". So, there is no universe with an infinite number of universes above it.

But if there were infinite universes, the probability that your universe is in the top n universes is equal to n/infinity, thus for any finite number n, there is 0 chance your universe is in the top n, and your universe must be infinitely many universes down the chain and thus there are infinitely many universe above yours.

Hah. I'm no mathematician or anything, but what you said, Thomas, reminds me a lot of Zeno's paradoxes. Then again, I'm crazy.

Interesting story!

I have been thinking about similar subjects for quite a long time. I have a different vision of the layered multiverse depicted in this story.

In fact, I think there is no top layer, no bottom layer, no circular multiverse but a single universe: our universe!

In order to run a perfect simulation, the quantum computer must store all the particles, quantum states, etc. Assuming a perfect efficiency, the state of the simulation is stored in a sub-atomic array with a granularity down to the fundamental particle (if it ever exists). In other words, to store the universe state you need at least the universe. The same can be said about running the simulation. You need at least the universe to run all the possible interactions.

Conclusion: to perfectly simulate the universe with a perfect efficiency, you need the universe. The simulation of the universe IS the universe.

The perfect quantum computer described in the story is then simply a window open on our own universe. What you see in the simulation is the universe itself. In the story, Tim and Diane are making a wrong assumption about the existence of layers.

Is this what the author had in mind from the start? I have no idea! I any case, it is an excellent and thought provoking story…

PS:
The story is also a good introduction to the ages old question: are we living in a simulated universe? My (current) answer: it does not matter! The universe and its simulation are strictly equivalent.

PPS:
The story describes a perfect computer simulating the universe. Assuming the simulation (that is the software) is the universe itself, we could say that our universe is a gigantic Information System. In other words, the most fundamental building block of the universe is … information! Recently, a few scientists go even further and talk about the Mathematical Universe…


In case you are reading this, many thanks go to you, the author. Your stories make me think again about philosophy and fundamental sciences. And, this is a good thing.

It is impossible to accurately simulate a finite object on a subset of itself. Since the observable universe is finite, this story is obviously complete fiction. In the story, the simulation of the universe and the real universe are two distinct objects.

There's another interesting point which hasn't been brought up yet. It says the simulation only simulates the part of the universe being looked at through the window, to make it quicker (even though in an infinitely powerful computer this is unnecessary). This means that as soon as they look at anything but themselves the universe above does the same and they cease to be simulated. If, at any stage, they stop focusing on the computer doing the simulation it will effectively turn off all simulations below it. Assuming their universe is an exact simulation of the one above (and so on up to the top) this will make it collapse back to a single universe. Fortunately, since I exist (I can tell because without me this post wouldn't exist), they either fixed it or I'm in the top layer.

I think that Diane fixed the simulation to simulate everything, so they still exist after they are not seen.

In probability theory, a probability of zero does not mean that it's impossible to happen, only that the chances of it happening are negligible. Fundamental to the concept of continuous random variables.

Interesting theory you have here, all that I can wonder about here is since they had the abilities to fast forward the simulation and it clearly didn't speed up their perception of their own reality, what would happen if they fast forwarded about 20 minutes to when he was walking out to catch the bus, but in order to test the reality he simply remained inside for a 30 minute duration. Thus negating the truth, but only performing this action after finding out that they themselves were not the original. Any thoughts on my quandary?

Its a very complex and well thought out story.

The whole idea is that at the end of the story you realise the entire story actually takes place within one of the simulated worlds below.
Even though there 'is' a top layer the computed layers can only determin their seperation from the original layer by observing the 'black sphere' that was programmed in, in the top layer the sphere would not have materialised, since it was reality. The reason for this is that up 'until' that point it was a logical simulation of reality and after that point it 'became' a logical simulation of 'what if this HAPPENED TO reality'.

That moment is the divergence point which determins if the universe was the
top universe or one of the potential infinite number of lower universes.

And yes if i was in the Top universe i would also turn off the computer.

Also if the simulation was run forward 'before the programming change' then it would probably correctly 'predict' the events of the future x-minutes from now, however if the program was turned forward 'after' the sphere incident when the layers had diverged from the top layer in realism then you would get a projection of what 'may' happen 'if this universe was a false one' x-minutes from now.

The "top" universe might not even contain an earth equivalent. It just needs to start a chain that eventually contains earth. In fact the original universe may have drastically altered forces, and dimensions. A test would be to simulate a universe from a different big bang, then search everything in that universe (including further simulations) for their version of earth.

Since the computer is infinitely powerful, you could run 2 universe simulations at the same time without it slowing down. After they realise that they are in a simulation, the two characters could simply run another simulation on the same computer and have fun with that one. They could probably run as many of these simulations as they want.

In one simulation, you could even put in a program that does to the universe whatever the people in the universe do on their computer, and just leave it to see what happens, instead of trying to perfectly emulate their actions.

Ok, please feel free to point out obvious flaws here, but could we not compare this to a super complex game of sims? Do we assume sentience on the part of the sim when he answers the phone without your command? No, because the sim is responding to the programming. The sims can even play sims on their sim computers, but does that mean that there is actually a whole new world of sentient sims?
The quantum computer is powerful enough to create an infinite number of simulated universes below the top level, but the simulations are based off of the most likely scenario, which is, in fact, what happens in reality. The program is really "guessing" what is going to happen next and making the simulated universe react correspondingly. Note, guessing here is a bit different than human guessing. The quantum computer would know everything about every possible bit of information in existence, and probably even more, so when it "guesses," it is going to come up with the only possible scenario that fits every fact ever, which is what actually happens.
You could watch the simulation create a simulation an infinite number of times, but in reality, you are still only watching a simulation.

This has been bugging me for a while. Say Tim and Diane leave the current sim running, and then run a second one, with the same parameters, and come up to the present time again. You now have two sims of identical, but different, universes. At first thought, they would be in a simulation chain as proved by the first sim, and Prime in the second chain.

Or not? Since it was unlikely for any given universe to be Prime in the recursion, it should be equally unlikely that that universe would be "Prime" in the second recursion. Changes should propagate along _both_ axis, right?

Hard stuff.

Anyway, regarding the power failure issue noted earlier, this is actually kind of easy to solve, and you can solve all sorts of other problems, like someone confiscating your control of the computer and taking over the universe.

It's based in what I like to call a Perfect Black Box, and it's going to make the computer self-contained and intangible.

First, the computer needs power, for all time. Easy as pie: program the simulation to provide energy to the computer in the simulation. In short: The computer creates energy for itself.

To maintain the laws of thermo-dynamics surrounding the computer, since we are locally violating them, create a barrier that prevents the transfer of matter or energy in any form away from or towards the computer at a certain radius. The outside world cannot directly interact with the computer systems, nor can the computer directly interact with the outside world. At certain radius around the computer, there now exists a black-body surface that nothing can penetrate.

Now, you can either leave it somewhere like a 2001-style monolith or black Egg or something, or flip it into the fourth dimension so you don't have to worry about it too much, though you may as well just program it to keep well away from black holes and leave it in 3-space.

Now, as for control, since we can no longer access the computer through a terminal anymore. Easy again, you tag administrators for it, and it recognizes them by genetics (or you track down the soul and use that.) Since the simulation is a database for the computer, it can just watch the administrators for commands, since it has infinite processing power, it can either do this by voice or let you ssh into it (it'd just intercept the commands and pipe the output to the terminal.) You'd be able to do this from any computer, and only you, it would be able to determine the person actually creating the commands. Duress is an issue, but it has access to all your thoughts, so... I'll leave the rest of security to the reader.

Now, the possibilities are endless when you have a simulation like this. As for me, I'd create a set of macros for predefined effects that can be accessed by beings of sufficient privileges through voice or motion or strange, possibly circular, drawings. These macros would, of course, satisfy the definition of magic. The computer+simulation is sufficiently advanced, you see. Two of those macros would be for granting and revoking macro privilege for non-admins. Being the only magic user would be boring. ("Artanis sets mode +o Sam.")

In a similar vein, macro-scale teleportation and FTL travel and communication, time travel (back requires the ability to rewind,) higher dimensional objects, any other tech you can think of, no longer requires a grounding in actual physics. If you want a giant mecha, you don't even need a minovsky particle to run it, the computer can intercept your input and just move all the parts from the sim in universe n-1.

Fun stuff. If anyone manages to build a quantum computer and prove we are a simulation by editing reality, call me up, 'kay? Though, if you need ask for my contact information, do not bother.

I haven't read all the comments, so I hope I'm not repeating anything.

First, we don't know exactly how the laws of physics work, and what we do know isn't deterministic. You could probably use such a computer to figure out the laws of physics by having it find the best way to compress a long stream of data so it just predicts the stream, and then reverse engineer the result.

Second, quantum computers don't work that way. They allow you to do NP-complete problems in polynomial time. They're not hypercomputers. (http://en.wikipedia.org/wiki/Hypercomputation)

Third, hypercomputers don't work that way. Having a computer like that is mathematically impossible. There'd be nothing to keep you from writing a program that predicts its own output and outputs the opposite.

I'm sure Sam already knows the first one, he most likely knows the second, and there's a good chance he knows the third. Also, it's a good story.

OK, slight nitpicking here ( sorry sam! ) it's not that I'm not interested in the other facets, just I'm that sort of person....

"You knew for a fact: this thing could execute an infinite loop in less than ten seconds."

I'm not entirely convinced about that even infinite CPU power would allow you to complete an infinite loop in finite time, E.G.

while (1) {
Do (something)
}

As I see it there is NO circumstance under which that will ever terminate, no matter how much CPU power you throw at it. Infinite CPU power might allow you to run around the loop an infinite number of times in finite time, but would it really cause the loop to halt?

Umm, actually I guess this is related to the halting problem also mentioned. The way you solve the halting problem is simply to give the algorithm and input to the infinitely powerful computer and run it. If the algorithm halts, it halts instantly ( and gives you the output ) since an infinite computer can carry out any finite number of operations in zero time. If the computer doesn't instantly return an answer, it never will and the algorithm is non-halting.

Eh, Azrael, I think the point was that the computer is so powerful can do things that last forever in not only a certain amount of time, but a short amount. 'Tis called hyperbole, my friend.

My head hurts.

tedweird, I'm open to correction here by someone with a better understanding of the mathematics on infinity than I have, but it seems to me that there would be no "short time"s when you have infinite computing power available ( assuming you don't introduce any deliberate waits ) tasks should either be completed instantly, or never.

As far as I can tell, I don't think anyone has brought up the point that the simulation(s) may not be exactly "lined up" with the universe that the story is being told in. Note that Diane is the one stopping the fast-forwarding, not the program. This implies that there's an infinitesimal chance of exact synchronization. Would that mean that the simulations don't truly depict "reality" and its events? Or would that just mean that it does, but it doesn't need to be exactly simultaneous to happen?

That actually made me think of another thing... if they fast-forwarded it from that point, would they effectively be predicting the future? If they did something like collapsing the sun into a black hole a billion years into the simulation's future, would that mean that the sun would spontaneously do the same thing a billion years into their future for no apparent reason?

Also, a little comment about the infinite processing power: In theory, what would making a program with an infinite loop that incremented a variable do, considering both infinite speed and storage?

Oh gee, the world's first idiot-repellent, yet completely machine-solvable captcha... Doesn't this go against the very use of captchas?

AnotherSimulatedMan, if they were to look into the future, they would've seen themselves doing whatever they would be doing, so in the case they look into the future and see themselves on the bus home, they *will* take the bus home. If they don't take the bus home, then when they look into the future, that's what they would see.

The square root of infinity is infinity. Infinity by definition is a paradox, and attempting to quantify infinity, or an infinite loop of commands is pointless, and is in turn propagating an infinite loop of infinitely pointless quantification. If anything is infinite, then everything is infinite. Try to understand infinity. Infinity. Everything is nothing.

Where's NEO?

Okay, forgive me if I write some stupid things now. I am by far no expert in mathematics, physics or even quantum physics.
But I REALLY love such stories and theories. And even more I like to think about it.

For my logical way of thinking, the story left many questions unanswered to be really sure what is actually happening there or what would be the consequences of changing or turning off the computer. Of course these are questions we cannot answer - the story is still SciFi and a very good one.

So my theories are as follow:
1) There is neither a top- or bottom-level. These universes would differ as the top-level would not get any changes and the bottom level would not have a working Universe-Simulation - or a different one. But if ALL are the same, there must not be a top- or bottom-level universe. So I am in for the big-loop idea.
2) As a consequence from (1) - maybe only in a pragmatic way - there are no real multiple universes but merely just a direct way of changing our very own reality.
3) If you would turn OFF this computer, I think it would not *end* the universes, but only cut the interaction between them or - if following the theory from (2) - end the interaction with our own reality.

I am sure many think different than me and that is okay for me. I liked to read all your opinions and I am also excited to read your opinions about my theories (and how you maybe how you think they are wrong).

After all reading this story was a VERY exciting experience. Always showing what we can do with fantasy and logic - going beyond our very own borders which is our mind.

P.S. Sorry for my English talking - it's not my native language.