Is the Universe a simulation?

[Avder]

A number of articles have been popping up online speculating that the Universe is in fact a simulation. A few people postulate that it's extremely likely that we are simply simulated beings simply by virtue of the fact that the math says its far more likely than not.

One such article is here: http://www.express.co.uk/life-style...e-Matrix-Universe-Planet-Earth-NASA-Scientist

So this provokes an interesting thought experiment: assuming the universe is a simulation, what conclusions can we draw about why the universe works in the way it does, and what purposes does this simulation serve to the entities running it?

A couple of my ideas:

The purpose of the universe is obviously to see what happens at its broadest. The same reason a kid sets up a ton of dominoes and then watches as they all fall down.

At its narrowest however, since intelligent life has formed, one distinct possibility is we could be a test model to see if free will is a real thing or not. If free will is a thing, it stands to reason that at some level of the situation, our choices should be in defiance of the laws of physics and chemistry through our ability to choose between things.

Another possibility is that Earth was itself designed and is in fact the center of the simulation. This would quickly explain why we have yet to detect any other intelligent life in the cosmos. I personally do not think this is the case, as other features of the universe would seem to suggest otherwise.

Lets start by acknowledging the simple fact that particles do not have distinct properties until they are observed. We can draw a very simple analog to this with our own computer simulations: video games. Characters are not rendered in video games until they are very near a point of observance: namely something that can be viewed by a player through some means. If this programming method is common to the universes creators, it means that nothing in the universe is instantiated beyond the most general form until it is needed to be due to observation by some form of intelligent life, and then only as detailed as it needs to be to satisfy those observations.

Following that, it stands to reason that the simulator has a set processing capacity and the fact that things do not have properties unless observed would be an obvious way to conserve resources.

Futher, since information can not at present propagate faster than then speed of light, this would limit the amount of the universe that needs to be simulated to the light that has reached the intelligent life at that point. In may be that certain galaxies that we've only recently observed which are demonstrated to be at a distance of 13.3 Billion years in the past were only just begun to be simulated when we first observed them.

It may be that different parts of the universes are simulated asynchronously and as new parts are observed, the simulation elsewhere halts as that new region is simulated forward to the present.

This would suggest that the speed of light itself is a property designed to limit the complexity of the simulation at any one time. Since we can barely see anything in the universe beyond the most general, we could reasonably assume that the universe has only been simulated as far as we can see it. If light were treated as a "hit scan" weapon is treated in modern day FPS's, we would be able to observe all points in the universe as they are today, and thus all points in the universe would need to be simulated, at least in the most general sense, at least as far as they would need to be in order to be observed as they are now. Since they don't have to be, this saves a **** ton of processing time for more important and more complex things: namely us.

The fact that the universe seems to be spreading out, rendering the most distant parts of more and more unobservable would also seem to suggest a plan that is in place to limit the complexity of the simulation as entities spawn that can observe and thus require the simulation to process objects past the most general and into higher resolutions. Once a galaxy recedes from view, it will no longer have to be simulated, at least for us.

Assuming there is other intelligent life elsewhere in the simulation, the universe expanding would also allow for the simulation to run different species at different points in parallel. If a race of intelligent beings were to exist on the opposite side of the universe, our galaxy, to them, would appear as a small, indistinct blob and thus would not have to be displayed to them any further than their ability to observe it based on what information they can obtain with their current technology.

It would also allow our galaxy to be rendered from the history of it that we have created by virtue of being able to observe it much sooner than they can. It would be analogous to rolling a spot check in a DND game and the game master calling out that you don't see **** because you only rolled a 12, and you needed to roll 14 or greater in order to see the monster behind the fake mirror.

As galaxies and intelligent species recede from eachothers view, it would allow the simulation to stop rendering parts of the simulation for each species view, and also allow it to page the history of each formerly viewable galaxy to archive storage and free up more memory to allow the simulation to continue running at an acceptable rate even as it gains more overall complexity. In other words it could be broken down into multiple simulations that are only loosely linked. This is analogous to the way EVE online is run: different solar systems and solar system clusters are simulated on different servers, allowing the game to gain additional processing overhead as technology is developed and the needs of the growing player base dictate.

The fact that the plank length seems to be a thing would also suggest that that is as granular as the simulation is programmed to go and we have discovered the simulations maximum display resolution.

The fact that we can't seem to pin down how gravity works compared to the other fundamental forces could suggest that it's not the same type of force at all, but possibly a simulation wide constant. A hardcoded limitation either because they could not get a dynamic property to simulate right, or they genuinely wanted it to work how it does. This could be analogous to how you can only mod a game so far because of the engines absolute limits. Without changing the engine itself, it is not possible to change certain properties of the game.

It could also be that they the simulation developers have not even completed their implementation of how gravity works and did not notice that we were starting to investigate it until it was too late to implement it how they had designed. Now that we're actively working to discover it, they may need to further refine how it works to fit within the narrative of what we've tried so far and what we would need to try in order to be able to get the simulation to fully implement it in its dynamic, fully evolved form. In other words, gravity could be in beta and will shortly be patched in during server downtime.

It would also mean that time travel is right out, because if they are indeed going to have to patch it in that way, it stands to reason that the only reason they're doing it that way is because it is not possible to run the simulation in reverse. This would be loosely analogous to how we've developed asymmetrical cryptography allowing for the use of a public keys, but since they never imagined that they would need to run it in reverse, they never implemented a way to do so and the simulation records the history of it to storage in such a way that certain bits of the past are irretrievable.

What does all this mean for us here, today? Not a damn thing. Since we have not yet developed a method to test for any of this, there is no point fretting about if the simulation is real or not because to ourselves we are real, therefore we exist in some form somewhere, and should just continue to exist and enjoy that existence as long as it lasts.

On the other hand, we could certainly try a few things and see what happens.

For instance, if we develop a way to create AI that can observe as we do, we could potentially create enough of them and place them such that the simulation has to run much much more complex than it does now. What would this do? It would likely get us noticed by the creators and maintainers of this simulation due to the fact that we're suddenly redlining the CPUs associated with our portion of existence and simulation speed has dropped from 15 days simulated per time unit to 1 day simulated per time unit.

If we can develop more theories for how things work, we may somehow discover exploits that we could use to harness control of the simulation. How much control? Anything from something as stupid as changing the color or your hair to as meaningful as spawning a comet such that it only just now comes into view and is on a trajectory to destroy earth in X years.

Potentially, we could also find some way to exploit the data display system that they use to start sending text data direct to their screen much like how Clippy would pop up and nag you. If those methods ceased to work, we could infer that the sim was patched and our creators prefer to remain separated from us.

We could also use exploits to pull up the history of the simulation elsewhere in the universe and get concrete evidence of the existence of other intelligent life, and then potentially find a way to contact them directly without having to wait for light to propagate the unknown number of lightyears between our civilizations. We could possibly time travel in a limited fashion depending on if my earlier speculation of asynchronous simulation holds. We could talk to some species 3 billion years in the past and get a picture of what our galaxy looked like 6 billion years ago from them. Or we could talk to some developing species that will exist 23 billion years from now and tell them about all the cool technology we've developed and completely throw them off their natural development path.

Boy oh boy, that would sure wreck havoc with the simulation, wouldn't it?

Of course, it may turn out that that is entirely the point of the simulation: to see how long it runs before something it simulates within itself starts breaking things. Either way it seems likely that such an event would merit some kind of response from above.

So then, what is the meaning of life?

If we're living in a hyper advanced video game, it would seem to me that the whole point is for us to get the high score, and to define what we consider that to be in the process.

Click to read more...

 

[PredsV82]

this whole "we really are in the Matrix" crap is what happens when smart people do really strong drugs.

 

[Kestrel]

Interesting thought exercise... but that's all it is.

 

[Moskau]

this whole "we really are in the Matrix" crap is what happens when smart people do really strong drugs.

And yet there's just as much evidence to support our existence being a simulation than any other theories. When you start really getting into space and the universe you start realizing that none of it makes any sense. Even the brightest minds in the world that understand why and how things are happening will tell you that it still doesn't make much sense. We will never be able to comprehend how the universe exists.

 

[FLYLine27*]

My brain hurts after reading half of that.

 

[LT]

Does it really matter?

 

[Hurt]

I've thought about this before but I couldn't wrap my head around it. Then again, not many people can. Who are the people running the simulation? What's to stop them from ending the simulation at any given time? How did we progress to the current stage of our evolution if we are in fact in a simulation? What's the time ratio like?

Boggles the mind.

 

[No Fun Shogun]

The odds that any of us would be born are incredibly small, as each of us have countless trillions of unborn brothers and sisters and yet we were the egg and the sperm that somehow made it, and yet here we live in a world were 7+ billion of us are all alive anyway. The odds are prohibitively, enormously against that, too.

It's a thought experiment, nothing more. The idea that some species could develop such a tech is understandable, but extrapolating that into a belief that we somehow are more likely to exist as a simulated entity versus a real species is just ludicrous.

 

[One Blurred Eye]

If you assume that the host universe in which the simulation is running is capable indeed of hosting such a simulation, and that the intent of the programmer in creating such a simulation is to perfectly model and simulate his own universe and succeeds in doing so--then the simulation he creates must be capable of producing and running its own perfect simulations (if to be considered a perfect simulation), and if left to run indefinitely would probabilistically result in such perfect simulations arising, with infinite recursion. Which means eventually, someone within the tree of simulated universes will have simulated--precisely duplicated--the programmer's own universe (and the programmer himself), to the point that the simulated duplicate contains an exact copy of the entire tree of simulations the "real" universe produced with its original simulation, while also including itself (the duplicate), and all its copies, and so on. Which means it's possible that the answer is that our universe is both a natural occurring phenomenon and also a sophisticated simulation running somewhere within itself.

 

[Hippasus]

My opinion is that if there is not evidence or some reason to believe something like this, it isn't a very worthwhile thought experiment. It is vaguely reminiscent of some conspiracy theories.

 

[Avder]

If you assume that the host universe in which the simulation is running is capable indeed of hosting such a simulation, and that the intent of the programmer in creating such a simulation is to perfectly model and simulate his own universe and succeeds in doing so--then the simulation he creates must be capable of producing and running its own perfect simulations (if to be considered a perfect simulation), and if left to run indefinitely would probabilistically result in such perfect simulations arising, with infinite recursion. Which means eventually, someone within the tree of simulated universes will have simulated--precisely duplicated--the programmer's own universe (and the programmer himself), to the point that the simulated duplicate contains an exact copy of the entire tree of simulations the "real" universe produced with its original simulation, while also including itself (the duplicate), and all its copies, and so on. Which means it's possible that the answer is that our universe is both a natural occurring phenomenon and also a sophisticated simulation running somewhere within itself.

They wouldn't necessarily produce replicas of themselves and their world. It would require the exact same laws of physics to be modeled, and the exact same starting conditions. It would also require free will to be a lie, as the moment any person in the simulation made a different choice, the simulation would start to diverge from the reality that birthed it.

Personally I'd think that if this is a simulation, it's a somewhat simplified version of our parent dimension's physics and possibly a fraction of its mass. If you were to perfectly simulate your entire universe at the same size and complexity, you'd require....a whole universe of data storage and processing.

Maybe we're 3D beings being simulated by creatures who live in a 4D space.

Who knows. And we likely never will.

 

[One Blurred Eye]

They wouldn't necessarily produce replicas of themselves and their world. It would require the exact same laws of physics to be modeled, and the exact same starting conditions. It would also require free will to be a lie, as the moment any person in the simulation made a different choice, the simulation would start to diverge from the reality that birthed it.

Personally I'd think that if this is a simulation, it's a somewhat simplified version of our parent dimension's physics and possibly a fraction of its mass. If you were to perfectly simulate your entire universe at the same size and complexity, you'd require....a whole universe of data storage and processing.

Maybe we're 3D beings being simulated by creatures who live in a 4D space.

Who knows. And we likely never will.

A universe with at least one perfect simulation of a universe may not perfectly simulate its host, true (but the possibility, however small, still exists that it could, either by design or through probability). But a simulation running within that simulation also might--in order for a simulation of a universe to be considered perfect, remember, it must allow for the possibility of its simulated inhabitants also perfectly simulating a universe. With each nested simulation the probability of duplicating the original increases--a kind of birthday paradox. Even if there are an infinite number of possible universes, that would entail an infinite number of simulations, each running an infinite number of nested simulations. There's obvious assumptions that come into play--that the programmer made no mistakes in his code, that the host universe "lives" long enough for the simulation to run to a point where its own inhabitants create a perfect simulation, that the simulated universes themselves "live" long enough to produce the conditions necessary for life, that intelligent simulants arise in these simulations and develop their own simulations before their own extinction, etc, etc.. There's also the question of whether the initial programmer is satisfied if his "perfect simulation" doesn't eventually give rise to its own perfect simulation of a universe--if it fails to do so, can he truly know if his simulation is perfect? Does he run it again and again until it does? By which again the probability of it eventually simulating itself increases. That's the thought experiment--a perfectly simulated universe begets the possibility, perhaps even the inevitability, that a universe can be both "real" (naturally occurring) and simulated--that in fact the entire history of a universe could have been played out in a simulation within itself before its natural self had (if you allow that simulations don't have to run in real-time).

If the initial assumption is that the simulation isn't perfect, and that part of the imperfection is that its inhabitant simulants can know this--then the inevitable conclusion of the experiment is that the moment we recognize a flaw in the simulation we will know we're not "real." We're Moriarty on the Holodeck. If we can't ever know it, then the conclusion is that the speculation is pointless--in the end we have to assume we're real, because assuming we're a simulation--a broken one--is inherently dangerous to our well-being.

Even if we did eventually realize ours is a simulation, and that we could hack it, and we did all the fun sci-fi stuff delineated in the OP with that knowledge, at some point the existential crisis must set in--could we really be content to live in what is little more than an elaborately designed video game, particularly one where we can reprogram ourselves/each other? Would that not be a terrible sort of hell? When do we start praying to our programmer, to make us real, as real as he? Or do we take it upon ourselves to patch the bug/feature that allows us the ability to know that we're just code and algorithms, and return ourselves to blissful ignorance?

 

[Hurt]

To have a simulation that perfectly simulates the Universe, or rather, allows the simulation to run its course, would require an unfathomable amount of data. Are we sentient if the simulation is in fact, real? There was an interesting YouTube video recently that some of you may have seen which originally got me thinking about this:

 

[One Blurred Eye]

My opinion is that if there is not evidence or some reason to believe something like this, it isn't a very worthwhile thought experiment. It is vaguely reminiscent of some conspiracy theories.

Even if you toss out the question as to whether or not we ourselves exist within an elaborate computer program, there's a lot of interesting philosophical ground to cover in the idea of a simulated universe. If we arrive at the point in our technological evolution that we ourselves could create such a simulation, then we open a can of worms just in the ethics of such an undertaking. Is it right to create such a simulation in which intelligent "life" could potentially arise? If we do, is it right to deny them the ability to know if the universe within which they live is a simulation? Do we intervene if we notice a development that puts a civilization in peril, or if one becomes too powerful and antagonistic? What is our moral obligation to such a creation? Sometimes I find myself staring a bug caught in a spiderweb, trying to escape, and I wonder which is more right, to give the bug another shot at life, or to allow the spider its hard-earned meal. Imagine such a moral quandary by orders of trillions.

There's also the possibility that creating a simulation is the only way to ensure humanity's survival in some form--if, for instance, the difficulty of space travel makes it impossible for us to colonize other worlds and propagate the species, could we dump our collective human spirit into a running simulation, and pick up from there? Wondering about the nature of our own universe and existence informs our decisions should we ever arrive at the point where we might program our own--what would we expect and desire of our creator, if indeed we have one, and how capable are we of living up to that standard for those we might by our own ingenuity create? Somewhat important questions, I think.

To have a simulation that perfectly simulates the Universe, or rather, allows the simulation to run its course, would require an unfathomable amount of data. Are we sentient if the simulation is in fact, real? There was an interesting YouTube video recently that some of you may have seen which originally got me thinking about this:

Storage is an interesting aspect of discussion--as an axiom, a universe must exist in some medium that has at least enough storage for that universe. Any simulation within that universe would occupy some portion of the mass and energy of that universe, meaning if the base universe's mass and energy is finite, then every nested simulation within it would be smaller by some amount relative to the storage its host occupies in its own host. What implications that would have on our ability to know the nature of our reality, i 'unno, but it's amusing to think somewhere down the branching tree of simulations there would eventually be these micro universes, possibly occupied by lonely little programmers living alone on little planets orbiting little stars, dreaming of simulating their own little universes.

It's also possible perhaps that what we know as our universe is just a sophisticated database designed to hold an enormous amount of data about something else entirely. What we see as people, houses, cities, planets, stars, galaxies, etc, might be formatted storage cells for holding different kinds of data and data structures, to be accessed and used somehow in some application. What we observe as the passage of time, the evolution of the universe, even our own thoughts, could merely be the result of the recorded data being added or changed in the database by the administering software. To us, it is existence, but we might be little more than a big list of phone numbers or some high order being's Amazon wishlist. The database/server designers wouldn't have set out to simulate a universe, but--perhaps unwittingly--did so accidentally, as an emergent property of their design of the fantastical, exotic storage system they needed to hold all that data, whatever it's from or for. Someday we might call this phenomenon NSA/Facebook/Google/Apple Syndrome--the end result of unbounded data collection.

 

[H382]

Why can't I embed a damn gif..

http://gph.is/1m8mtt7

 

[Avder]

Storage is an interesting aspect of discussion--as an axiom, a universe must exist in some medium that has at least enough storage for that universe. Any simulation within that universe would occupy some portion of the mass and energy of that universe, meaning if the base universe's mass and energy is finite, then every nested simulation within it would be smaller by some amount relative to the storage its host occupies in its own host. What implications that would have on our ability to know the nature of our reality, i 'unno, but it's amusing to think somewhere down the branching tree of simulations there would eventually be these micro universes, possibly occupied by lonely little programmers living alone on little planets orbiting little stars, dreaming of simulating their own little universes.

The implication, to me, seems to be that, unless the base universe is infinite in some way (big bang to big crunch to big bang for example), every simulated universe it spawned would have to be smaller in some way, and that as you iterate down, the simulations would need to either use simpler physics rules, less mass, or less volume in order to make it possible to run.

Imagine if you could convert every atom in the universe except your own host planet and star into a device that would run the simulation. That simulation you are running must now be only able to hold as much information as their are elementary particles in its makeup, resulting in a maximum universe size+complexity+mass as the host universe minus the host star and the host planet. You'd also only be able to run said simulation as long as your host star burns, a time span on the order of a few billion to 100 trillion (the lifespan of the smallest mass red dwarfs) years.

It's the emulator within an emulator effect. Each layer means the next layer gets less resources. If you want a simple real life example, set up two mirrors such that you can see the infinity shot. How far can you see into that until the mirrors are no longer distinct from eachother?

To me that seems to indicate that the universe simulating ours would be a bit more complex, massive, or voluminous. Probably several orders of magnitude of the last two categories in fact.

And one thing we can see about our universe is that the vast, vast majority of it is empty space. Even the individual atoms that make up our bodies are mostly empty space, to say nothing of the space between planets, star systems, galaxies, and galaxy filaments.

The only thing that could potentially bridge the gap is compression and abstraction. But that itself is simplification of the physics.

 

[Hippasus]

Even if you toss out the question as to whether or not we ourselves exist within an elaborate computer program, there's a lot of interesting philosophical ground to cover in the idea of a simulated universe. If we arrive at the point in our technological evolution that we ourselves could create such a simulation, then we open a can of worms just in the ethics of such an undertaking. Is it right to create such a simulation in which intelligent "life" could potentially arise? If we do, is it right to deny them the ability to know if the universe within which they live is a simulation? Do we intervene if we notice a development that puts a civilization in peril, or if one becomes too powerful and antagonistic? What is our moral obligation to such a creation? Sometimes I find myself staring a bug caught in a spiderweb, trying to escape, and I wonder which is more right, to give the bug another shot at life, or to allow the spider its hard-earned meal. Imagine such a moral quandary by orders of trillions.

There's also the possibility that creating a simulation is the only way to ensure humanity's survival in some form--if, for instance, the difficulty of space travel makes it impossible for us to colonize other worlds and propagate the species, could we dump our collective human spirit into a running simulation, and pick up from there? Wondering about the nature of our own universe and existence informs our decisions should we ever arrive at the point where we might program our own--what would we expect and desire of our creator, if indeed we have one, and how capable are we of living up to that standard for those we might by our own ingenuity create? Somewhat important questions, I think.

Sure, it is interesting, as many abstract thought experiments are, but I find it highly unlikely given negative results in mathematical logic in the Twentieth Century like the Halting Problem result of Turing, or Godel's Second Incompleteness Theorem. The latter states that there is a tradeoff between provability and consistency in the context of a single theory of a formal system. The former states that there cannot be computer program complex enough to be able to tell if any other given program will halt or not. Given these results, I am highly skeptical of the feasibility of such a program that could not only not be hindered by the aforementioned negative results, but also be able to generate everything we consider to be the physical universe. Energetic matter and abstract laws and existence (that which legislates truth, falsity, etc.) seem fundamentally different such that there is no causal nexus between them. As a metaphysical pluralist, this is how I see it. It is Plato's Allegory of the Cave, The Matrix, etc., but there has been a substantial, even if diffuse history between Plato's time and the present. It could be useful for ethics as a thought experiment, you're right there.

 

[Finlandia WOAT]

You can't get out of The Matrix until someone gives you the "Red Pill"- as in, they inform you that you are in The Matrix. You have to be told, it is 100% impossible to figure it out for yourself. IIRC, this is one of the points of Plato's Philosopher-King: normal people/batteries are unable to realize they are in The Matrix, so they need the Philosopher-King to set them free.

(Also: who set free the Philosopher-Kings? I did, said Plato. Alright, who set you free? Socrates did, said Plato. Alright, who set him free? Shut up, said Plato...if this is inaccurate, I regret nothing)

In other words, it's impossible to realize you are in a simulation or a simulacra (I'm trying to get through this, if you've read it let me know what you think) as long as you are in the simulation or simulacra.

Could you explain why the Halting Problem and Godel's Second Incompleteness Theorem confirm otherwise? I have no more than high school math training (sorry) btw.

As a thought experiment, I fear people will use it to confirm a Fatalist view about their life- I can't control (my weight/my relationship/excessive posting on HF)- and thus use it as an excuse for their lack of self-motivation and improvement. Religious people have "God wills it", hippies have "the 9 corporations that secretly rule America", now "smart" people have "reality is a simulation".

 

[Hippasus]

You can't get out of The Matrix until someone gives you the "Red Pill"- as in, they inform you that you are in The Matrix. You have to be told, it is 100% impossible to figure it out for yourself. IIRC, this is one of the points of Plato's Philosopher-King: normal people/batteries are unable to realize they are in The Matrix, so they need the Philosopher-King to set them free.

(Also: who set free the Philosopher-Kings? I did, said Plato. Alright, who set you free? Socrates did, said Plato. Alright, who set him free? Shut up, said Plato...if this is inaccurate, I regret nothing)

In other words, it's impossible to realize you are in a simulation or a simulacra (I'm trying to get through this, if you've read it let me know what you think) as long as you are in the simulation or simulacra.

Could you explain why the Halting Problem and Godel's Second Incompleteness Theorem confirm otherwise? I have no more than high school math training (sorry) btw.

As a thought experiment, I fear people will use it to confirm a Fatalist view about their life- I can't control (my weight/my relationship/excessive posting on HF)- and thus use it as an excuse for their lack of self-motivation and improvement. Religious people have "God wills it", hippies have "the 9 corporations that secretly rule America", now "smart" people have "reality is a simulation".

Any complete generation of the physical universe would have to be based on a program to run it. Otherwise the generation would be a fluke, as far as I can tell. An algorithm is a (finite) mechanical procedure or series of commands to effect a process in the abstract. Computer programs can't actually do calculus for this reason, because calculus uses the infinite or infinitesimal. Any such program couldn't actually even explain the continuity of ordinary experience. (I am assuming calculus explains this here.) The Halting Problem shows the limits of such abstract computing machines. I mentioned it because it already introduces skepticism about the ability to have these extremely powerful programs, which are able to bring about the generation. Godel's Second Incompleteness Theorem shows limits of any given formal system (complex enough to be a able to model arithmetic). It is similar to Turing's Halting Problem in the sense that (a) it is a self-referential proof and (b) introduces skepticism: what the Halting Problem does for programs, the Second Incompleteness Theorem does for (theories of) a given formal system.

You know The Republic better than I could explain it. I never actually read the whole thing.

Hume showed that we cannot know causation exists. We only perceive concatenations of events or durations. The difference between causation and correlation is a legacy of this, and also gets at the lack of a causal nexus between that which is described by pure abstraction and the physical universe.

 

[Avder]

Any complete generation of the physical universe would have to be based on a program to run it. Otherwise the generation would be a fluke, as far as I can tell. An algorithm is a (finite) mechanical procedure or series of commands to effect a process in the abstract. Computer programs can't actually do calculus for this reason, because calculus uses the infinite or infinitesimal. Any such program couldn't actually even explain the continuity of ordinary experience. (I am assuming calculus explains this here.) The Halting Problem shows the limits of such abstract computing machines. I mentioned it because it already introduces skepticism about the ability to have these extremely powerful programs, which are able to bring about the generation. Godel's Second Incompleteness Theorem shows limits of any given formal system (complex enough to be a able to model arithmetic). It is similar to Turing's Halting Problem in the sense that (a) it is a self-referential proof and (b) introduces skepticism: what the Halting Problem does for programs, the Second Incompleteness Theorem does for (theories of) a given formal system.

You know The Republic better than I could explain it. I never actually read the whole thing.

Hume showed that we cannot know causation exists. We only perceive concatenations of events or a duration. The difference between causation and correlation is a legacy of this, and also gets at the lack of a causal nexus between that which is described by pure abstraction and the physical universe.

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.

 

[hatterson]

Computer programs can't actually do calculus for this reason, because calculus uses the infinite or infinitesimal.

Huh? I have no idea what you mean by this. Computers are absolutely capable of performing calculus and they're absolutely capable of working with the concept of convergence of infinite sequences. They may not "understand" the significance of infinity as a concept, but that's a totally different issue than being able to do the math.

 

[Hippasus]

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.

The theory is supposed to be absolutely general. If you can find a fault with it, by a better theory, then the theory was not solid in the first place. There is no reason to think that though apropos of the two mathematical logic result examples I gave. If you, or anyone can find a fault in the theory, or some other theory upon which the theory behind those two results are based, that would be like the laws of logic as we know them being void.

By the way, have you heard of this book by Jean Baudrillard? It is like the postmodern philosophy correlate of the premise of this thread.

https://en.wikipedia.org/wiki/Simulacra_and_Simulation

Huh? I have no idea what you mean by this. Computers are absolutely capable of performing calculus and they're absolutely capable of working with the concept of convergence of infinite sequences. They may not "understand" the significance of infinity as a concept, but that's a totally different issue than being able to do the math.

Any calculation done by a computer is finite. So if it is supposed to be doing calculus it is actually only an estimate. I have a programmer friend who corroborated this in a discussion. Coincidentally, he is one of the only programers with whom I spoke who knew about the Halting Problem.

 

[hatterson]

Any calculation done by a computer is finite.

Any calculation, done by a computer or a person, is finite by simple definition of it being complete in finite number of steps. A finite calculation does not mean anything.

So if it supposed to be doing calculus it is actually only an estimate.

The entire point of calculus is that you aren't estimating, but rather calculating how/if an infinite series converges. You turn a series of more and more accurate estimates into an actual calculation of the final true answer.

The two fundamental theorems of calculus show that this does not require an infinite number of steps nor actually reducing your change to an infinitesimal amount, but can be done in a finite number of step using derivatives and anti-derivatives.

Computers are just as capable of performing these steps as humans are.

Coincidentally, he is one of the only programers with whom I spoke who knew about the Halting Problem.

That's disturbing since the halting problem should be taught about in any basic algorithms course which should be fundamental to any computer science/software engineering degree.

 

[Hippasus]

Any calculation, done by a computer or a person, is finite by simple definition of it being complete in finite number of steps. A finite calculation does not mean anything.



The entire point of calculus is that you aren't estimating, but rather calculating how/if an infinite series converges. You turn a series of more and more accurate estimates into an actual calculation of the final true answer.

The two fundamental theorems of calculus show that this does not require an infinite number of steps nor actually reducing your change to an infinitesimal amount, but can be done in a finite number of step using derivatives and anti-derivatives.

Computers are just as capable of performing these steps as humans are.



That's disturbing since the halting problem should be taught about in any basic algorithms course which should be fundamental to any computer science/software engineering degree.

The finitude is the property of an algorithm, and that is significant for a Turing Machine. You can't realize the infinite / infinitesimal with a finite number of steps. Neither can a program calculate a series in its fullness. Our abstract and conceptual perception / apprehension does, Turing Machines don't. A computer can't do all of mathematical analysis like our abstract perception / being can.

 

[hatterson]

The finitude is the property of an algorithm, and that is significant for a Turing Machine. You can't realize the infinite / infinitesimal with a finite number of steps. Neither can a program calculate a series in its fullness. Our abstract and conceptual perception / apprehension does, Turing Machines don't.

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.

A computer can't do all of mathematical analysis like our abstract perception / being can.

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.