Is the Universe a simulation?

[chicagoskycam]

The theory would explain why the laws of physics tend to break down in some instances. I prefer to believe there is so much we don't understand about the universe.

 

[Hippasus]

Literally the entire point of calculus is to look at the behavior of the series as it approaches an infinite length, not to actually calculate the series out. You don't need some mystical perception/apprehension to make those calculations. Humans don't have some mystical ability to understand how a series converges or what it converges to.



Mathematical analysis is a fundamentally different topic than calculus. The reason computers lag behind humans at the highs of the field are likely similar to the reasons computers lagged behind humans at Chess for so long and still do at Go. It's not simply about applying strict rules, but about recognizing the abstract patterns. That has nothing to do with infinity and everything to do with creativity, but that's an entirely different topic and has nothing to do with calculus.

I think I know what mathematical analysis is: infinite series, differential calculus, integral calculus, plus probably other things. Feel free to complete the list if you think I am missing important areas.

The idea of infinity implies the idea of direction. I wouldn't say that creativity has nothing to do with the infinite. What is a pattern without direction? One cannot say that creativity is all about any one given property, even if you came up with a good theory of structural analysis or some such thing. (Speaking of which, the opening post seems very creative.) Rules, signs, and synchronic representations are probably a small part of creativity. There is also the diachronic (not saying you didn't say this one), and metaphors. Perhaps also some sort of non-representation, nonsense, and-or noise. This is just a crass laundry list of things that might play a part in creativity for some. How could a single program encompass all these things? Perhaps there could be multiple programs, as suggested by the opening poster, but I would think they would still have to be unified by a single theory accommodating a formal system.

Regardless, even if I say you have proven me wrong on calculus and programs, there remains the other four factors. The four would be (a) the property of continuity on the part of some areas in mathematical analysis--namely the the infinitude, or lack thereof, of programs (b) Godel's Second Incompleteness Theorem (c) the Halting Problem (d) Hume's problem of the lack of knowledge of the existence of causation (e) creativity.

Regarding (a): I think continuity, and thus the infinitesimal, is implicit to ordinary experience / perception. If a single program has to be written to be able to generate the entire universe, indefinite complexity should not be precluded, which it seems to be by virtue of the Halting Problem. Do you not think the Halting Problem is relevant for One Blurred Eye's extension of the opening poster's premise for this thread? Or Godel's Second Incompleteness Theorem for that matter? This might be another one: how is any program supposed to decide if a given collection of numbers is the result of a function? Suppose it is. How could it decide if that sequence is an infinite series? Suppose it is. How could it decide that that series is countable or uncountable? Mathematics simply outruns the capabilities of a given program, or collection of programs by a single theory. This is an occasion for skepticism regarding the premise of the opening post if nothing else.

 

[hatterson]

I think I know what mathematical analysis is: infinite series, differential calculus, integral calculus, plus probably other things. Feel free to complete the list if you think I am missing important areas.

Mathematical analysis is the study of continual change. Yes, there's calculus involved, calculus is really the underpinning of it. If you want to look at it this way, mathematical analysis is the theory, calculus is the language. Computers are absolutely capable of performing calculus, just head over to Wolfram Alpha if you want a demonstration.

The idea of infinity implies the idea of direction.

Why?

Regarding (a): I think continuity, and thus the infinitesimal, is implicit to ordinary experience / perception.

Can you explain what you mean by this?

This might be another one: how is any program supposed to decide if a given collection of numbers is the result of a function? Suppose it is.

It is impossible to tell, given a set of numbers and no explanation as to how they appeared, if they were the result of a single function, multiple functions, or fully randomly generated (assuming true randomness even exists). That holds true for humans as well as computers.

It is possible (again for both humans and computers) to develop a potential algorithm which would generate said collection of numbers, but you cannot say if the numbers were or were not generated by that algorithm.

How could it decide if that sequence is an infinite series? Suppose it is.

Again, without a description of how the numbers were generated, it would be impossible for both humans and computers to tell if a sequence is infinite or simply larger than has been currently experienced.

How could it decide that that series is countable or uncountable?

By finding a 1:1 mapping between the natural numbers and the given set, or by proving that no such mapping exists. Again, computers would do this the same way humans would.

 

[Hippasus]

Mathematical analysis is the study of continual change. Yes, there's calculus involved, calculus is really the underpinning of it. If you want to look at it this way, mathematical analysis is the theory, calculus is the language. Computers are absolutely capable of performing calculus, just head over to Wolfram Alpha if you want a demonstration.

Thank you for sharing. It reminds me of Dedekind's paper "Continuity and irrational numbers". Cuts are the elements on the real number line and needed to be posited for continuity on account of the gaps by the rational numbers seen as constituting the abstract number line, in order to realize a full line.

Why?

The idea of infinity implies the idea of direction in the sense of mathematical series. The idea of the infinitesimal to realize continuity, is given in relation to its forming a set of numbers greater and a set of numbers less than. This implies directionality.

Can you explain what you mean by this?

I think continuity, and thus the infinitesimal, is implicit to ordinary experience / perception because we if we don't think of two discrete time events, say marked by a sort of self-consciousness in the present at two different moments, but rather a being in the zone or awareness of duration, then that is the sort of flow to time that implies a sort of continuity not wholly unlike that of Dedekind's cuts. Or, even better, one can take a moment of self-consciousness as being akin to a cut.

It is impossible to tell, given a set of numbers and no explanation as to how they appeared, if they were the result of a single function, multiple functions, or fully randomly generated (assuming true randomness even exists). That holds true for humans as well as computers.

It is possible (again for both humans and computers) to develop a potential algorithm which would generate said collection of numbers, but you cannot say if the numbers were or were not generated by that algorithm.



Again, without a description of how the numbers were generated, it would be impossible for both humans and computers to tell if a sequence is infinite or simply larger than has been currently experienced.

Fair enough. A lot of what you're saying sounds either constructivist or finitist.

By finding a 1:1 mapping between the natural numbers and the given set, or by proving that no such mapping exists. Again, computers would do this the same way humans would.

Re: your suggestion that we look for a one-one correspondence and see if we get it or not, is that the set of reals between any two numbers on the real number line, as well as naturals and rational numbers I suppose, is that ellipses (". . .") needs to be conceptually / relationally filled-in so to speak by our abstract thought / attunement as individuals. This requires a sort of self-consciousness, for instance, seeing how the context of a proof is formulated as being something we are looking to demonstrate in thought. Otherwise there is no way of knowing that uncontability has been demonstrated for the real numbers. There is a sort of intentionality to the act that is simply not present in Turing Machines / computers. So, I think you were correct in suspecting that self-consciousness or the ability to think is a crucial difference between calculus for us and for computers, like you said earlier in our discussion.

 

[Led Zappa]

The fault in your reasoning is assuming that a problem we have with our computers and our math is a problem that those who run the simulation would have. We really have no way of knowing what the capacities of the system running the simulation are unless those who created it confirm its existence by informing us of it. Like I speculated earlier, the rules that govern our existence could be a stripped down and simplified version of the rules that govern theirs.

The computer system running this damned thing could somehow be analog for all we know. It could also be a 4 dimensional object. We really have no way of knowing unless they tell us OR we come across a fault in reality that we can use to gain access ourselves. Of course by coming across this fault, it's quite possible we may just corrupt our own existence to the point of it being unrecoverable and thus be our own doom, but thems the breaks when you cause the biggest bluescreen of all time.

We should probably make sure we trigger the equivalent of File->Save first. Otherwise some weird alien blob could lose 14 billion years of work.

I really, really, really like this post.

 

[Bluelines]

What if our universe is just an atom in a giants body?

 

[Led Zappa]

I liked the MIT paper put out on the same subject years ago and posited that we could be a teenagers school project and whenever something like WWII happened it was because he fell asleep during a crucial juncture.

 

[kurt]

I'm far too lazy to read all the comments in this thread, but is it just me or is this not at all a new theory? Also I'm not even sure I understand how it even applies to any scientific or religious belief in how the universe is created, as one could argue that any explanation of creation could itself could be viewed as the initiation of a process with the application of certain rules, with or without any sort of intervention at given points.

All it really is, is using a new term, "simulation", to talk about something we have pondered for as long as we have have existed.

 

[hatterson]

Fair enough. A lot of what you're saying sounds either constructivist or finitist.

I suppose I make a break between conceptual arguments and practical arguments. Conceptually, the infinite and the infinitesimal are completely valid. As far as our physical universe, I'm not sure I'd say they don't as much as I don't think it matters.

I don't think true continuity is needed for how we experience the universe. Planck length and Planck time are so much smaller than anything we can experience or measure that I'm not at all convinced a system based on them as a foundation would have any discernible difference to us than a system with true continuity.

Note: I'm not arguing our universe is based on Planck scale, I'm arguing that if it was we wouldn't be able to tell the difference and thus any arguments about infinite/infinitesimal being required to simulate it don't hold water for me.

Re: your suggestion that we look for a one-one correspondence and see if we get it or not, is that the set of reals between any two numbers on the real number line, as well as naturals and rational numbers I suppose, is that ellipses (". . .") needs to be conceptually / relationally filled-in so to speak by our abstract thought / attunement as individuals. This requires a sort of self-consciousness, for instance, seeing how the context of a proof is formulated as being something we are looking to demonstrate in thought. Otherwise there is no way of knowing that uncontability has been demonstrated for the real numbers. There is a sort of intentionality to the act that is simply not present in Turing Machines / computers. So, I think you were correct in suspecting that self-consciousness or the ability to think is a crucial difference between calculus for us and for computers, like you said earlier in our discussion.

Cantor's diagonal argument doesn't use infinity, or the concept of infinity, directly. It uses the concept of a finite, but arbitrarily large, list and proof by contradiction.

 

[Hippasus]

I suppose I make a break between conceptual arguments and practical arguments. Conceptually, the infinite and the infinitesimal are completely valid. As far as our physical universe, I'm not sure I'd say they don't as much as I don't think it matters.

I don't think true continuity is needed for how we experience the universe. Planck length and Planck time are so much smaller than anything we can experience or measure that I'm not at all convinced a system based on them as a foundation would have any discernible difference to us than a system with true continuity.

Note: I'm not arguing our universe is based on Planck scale, I'm arguing that if it was we wouldn't be able to tell the difference and thus any arguments about infinite/infinitesimal being required to simulate it don't hold water for me.



Cantor's diagonal argument doesn't use infinity, or the concept of infinity, directly. It uses the concept of a finite, but arbitrarily large, list and proof by contradiction.

On the possibility of a Planck scale interpretation, fair enough. Perhaps my interpretation is a bit Kantian in supposing an abstract category to be informing that sort of ordinary experience.

On Cantor's diagonal argument, for all intents and purposes arbitrary large = infinite. My point is a program would never be able to tell the difference between a countably infinite sequence and uncountably infinite sequence unless it was filling in the ellipses in its conceptualization of that which is to be demonstrated. The program would have to "understand" the proof by contradiction in a way it is unable to do, by its very nature. One-one correspondences work for countably infinite sequences only. In order for the realization to occur that a sequence of real numbers is uncountable it is necessary one supposes the list to be complete (countably infinite), but then conducts an operation in which a new number not on the list is generated by diagonally manipulating the digits (uncountably infinite). The Turing Machine wouldn't be able to get to the point in the thought process where a decision on the countability or uncountability of a sequence could be made.

 

[EmeticDonut]

I don't see how us being in a simulated reality would really change anything. Life is as meaningful or meaningless as you make it. I guess it would cause some existential crisis among many, but would it really matter?

 

[bombers15]

If you see design in the universe, maybe an alternative explanation is.....God?

*runs from thread as a dozen people quote my post and yell at me*

 

[LT]

Honestly, what does it matter?

 

[Led Zappa]

Honestly, what does it matter?

Nothing really matters ♪ ♫ ...

 

[Nordic*]

To be a 100% fail safe simulation, there can be absolutely no bugs, errors or mishaps - or the subjects would realize that it in fact IS a simulation.

Even if there were a computer or an intelligence powerful enough to pull this off, I find it unlikely that it has run for hundreds of billions of years without the slightest hick-up.

Or is the idea that distant history never really took place, but is just memories baked into the simulation?

Dinosaurs never really existed, the simulation simply added bones buried across the globe, to make us think they actually existed at one point?

If I ran a simulation and realized that something didn't fully work or was believable, I would simply shut down, improve and reboot.

Reboot = Big Bang?

 

[LT]

To be a 100% fail safe simulation, there can be absolutely no bugs, errors or mishaps - or the subjects would realize that it in fact IS a simulation.

Even if there were a computer or an intelligence powerful enough to pull this off, I find it unlikely that it has run for hundreds of billions of years without the slightest hick-up.

Or is the idea that distant history never really took place, but is just memories baked into the simulation?

Dinosaurs never really existed, the simulation simply added bones buried across the globe, to make us think they actually existed at one point?

If I ran a simulation and realized that something didn't fully work or was believable, I would simply shut down, improve and reboot.

Reboot = Big Bang?

Or you simply program the subjects to view any bugs in a certain way. Provide us with science, for instance, to explain everything that we're unsure of.

 

[Nordic*]

Or you simply program the subjects to view any bugs in a certain way. Provide us with science, for instance, to explain everything that we're unsure of.

Even more rational, bake religion into the equation to make people never question anything at all.

 

[LT]

Even more rational, bake religion ibto the equation to make people never question anything at all.

Exactly.

 

[PanthersHockey1]

I'd rather talk about really existential questions with a scientific tinge.

I think it is more interesting to speculate whether there could be multiple universes. And the answer, scientifically at least is a definite maybe.

Imagine two helium balloons side by side. We and everything we know that compromises our universe are in one balloon with the inability to see anything outside said balloon while someone else is in their balloon universe with the inability to see us.

 

[Finlandia WOAT]

To be a 100% fail safe simulation, there can be absolutely no bugs, errors or mishaps - or the subjects would realize that it in fact IS a simulation.

No, you would only realize that if you could see outside the simulation.

If the "real" world were exactly the same as our simulation, save that there is a bug in the simulation that has caused some lions and zebra to merge into a completely original being called a "tiger", then the programs in the simulation would never realize that this is faulty or incorrect because that knowledge is predicated on knowledge of the "real" world. They would merely presume that it is "real", unless they learned the fact that they were in a simulation beforehand.

Mr. Anderson/Neo/"God" Himself did not realize the Matrix for what it was. He had to be informed of its general existence. Morpheus himself says this- "I can't tell you the Matrix exists- you have to see it for yourself".

 

[Knave]

Or you simply program the subjects to view any bugs in a certain way. Provide us with science, for instance, to explain everything that we're unsure of.

"It's not a bug, it's a feature!".

As for simulation - I think it's a little crazy. Interesting but crazy. The multiverse is also interesting and I think slightly more plausible but still a little crazy to really believe in all this stuff without some evidence.

 

[Nordic*]

Potentially I am successful in one of these universes.

That thought is both pleasing and depressing.

 

[Hippasus]

Honestly, what does it matter?

Being skeptical about the entire universe in its entirety being a simulation gets at why one thinks existence is true / objects are real. I think this is a valuable question for its own sake.

Also, during the course of my trying to debunk the extreme version of this thought experiment, I came to realize that Dedekind's theory of continuity (for real numbers) may bridge the gap between the continuity of ordinary perception ("being in the zone") with a Planck scale interpretation of time along the lines suggested by hatterson. Dedekind's theory of continuity in terms of discrete elements, as a theory, perhaps bridges discrete numbers with the continuous as a type of ordinary experience. This was when I was trying to point out fundamental limitations of programs (for the purpose of generating the universe as simulation).

 

[Avder]

To be a 100% fail safe simulation, there can be absolutely no bugs, errors or mishaps - or the subjects would realize that it in fact IS a simulation.

Even if there were a computer or an intelligence powerful enough to pull this off, I find it unlikely that it has run for hundreds of billions of years without the slightest hick-up.

Or is the idea that distant history never really took place, but is just memories baked into the simulation?

Dinosaurs never really existed, the simulation simply added bones buried across the globe, to make us think they actually existed at one point?

If I ran a simulation and realized that something didn't fully work or was believable, I would simply shut down, improve and reboot.

Reboot = Big Bang?

If I were to engage in more speculating as I did in the OP, I would guess that the simulation would probably be able to run time compressed. Re-read my OP for stuff about being simulated only when it's observed. Doubtful it's running at a 1:1 time rate in both the "real" world and our "simulated" world. That would probably preclude it being useful for large scale scientific study. Unless of course the beings running it live for a very, very, very long time.

Plus things can be re-programmed on the fly. So if it did **** up, they'd probably have some mechanism in place to de-bug it. One possiblity is they're using some kind of savestate system like gamers use when playing old console games on modern emulators. Auto-save every X years (whatever is statistically significant to that region, for example a stellar nebula might be saved every 100,000 years, but our world might be backed up daily due to the complexity), and when something goes boom, freeze program, debug, and restore from last save point.

As for the "manufactured history" speculation, I would doubt that quite a bit. For it to be a true simulation of a universe, it would probably have been given a mass and a set of rules and started with a big bang.

Perhaps you are right that the sim may have been restarted a number of times. Perhaps nothing interesting happened in those (no intelligent life by the end of stelliferous era for example) and they had to tweak some constants and adjust the laws governing the fundamental forces until intelligent life started developing.

So here we are. And for us, that's the important part.

 

[Nordic*]

If it is a simulatoon, what happens to "life" when someone passes away?

Does that energy move on to another vessel?