Ok, but the simulation could easily have been written to include an adjunct professor at UBC’s much-less-well-known Okanagan campus who isn’t actually that great at Gödeling.
"We have demonstrated that it is impossible to describe all aspects of physical reality using a computational theory of quantum gravity," says Dr. Faizal. "Therefore, no physically complete and consistent theory of everything can be derived from computation alone. Rather, it requires a non-algorithmic understanding, which is more fundamental than the computational laws of quantum gravity and therefore more fundamental than spacetime itself."
Seems like quantum gravity theory might be missing something, no?
Ah, no. At best they prove that we can't simulate our own universe. They don't prove ours isn't simulated or that other, higher fidelity simulations can't simulate similar ones.
What's the difference between a simulation and a non-simulation? Nothing, except where the simulation can be broken.
Can we accurately simulate a smaller universe in this universe? If I understand correctly, according to this paper the answer is "no". Except how do we determine the simulation is inaccurate, without either knowing what is accurate (and thus having a correct simulation), or being unable to distinguish the inaccuracy from randomness (the simulation already won't perfectly predict a small part of the real universe due to such randomness, so you can't point to a discrepancy)? What does it mean for a simulation to be “inaccurate”?
Also, you don't need to simulate the entire universe to effectively simulate it for one person, e.g. put them in a VR world. From that person's perspective, both scenarios are the same.
As the simplest theory, my default position is the universe is computable and that everything in the universe is computable. Note that they are not the same thing.
Some intuition:
1. If the universe contains an uncomputable thing, then you could utilize this to build a super turing complete computer. This would only make CS more interesting.
2. If the universe extends beyond the observable universe, and it's infinite, and on some level it exists, and there is some way that we know it all moves forward (not necessarily time, as it's uneven), but that's an infinite amount of information, which can never be stepped forward at once (so it's not computable). The paper itself touches on this, requiring time not to break down. Though it may be the case, the universe does not "step" infinitely much information.
One quick side, this paper uses a proof with model theory. I stumbled upon this subfield of mathematics a few weeks ago, and I deeply regret not learning about it during my time studying formal systems/type theory. If you're interested in CS or math, make sure you know the compactness theorem.
At best, this proves the imperative paradigm of computation with any set of instructions close to what we currently use cannot adequately simulate a universe. I like this, lest we forget there are and there can be many more ways to compete, fundamentally different from what we currently consider the typical one.
Isn't there a deeper philosophical question on what it means to be a simulation?
Is the constraint of the "simulation" definition that the thing "simulating" the universe would be a computer less complex than the universe itself?
Consider a game world in a computer, we call it a simulation, and it is, but is it any less real than our reality, when thinking in terms of realities? In other words, we feel like our reality is more real because the game is less complex, we understand it fully and it is run using mechanisms we know and understand. So what would make us think it is a more real reality than our own?: If we didn't understand how it works? If its workings and rules are more complex than ours?
Taking a step back, are we as humans even capable of understanding a reality that isn't ours, even as a concept? Things like time, space, and fundamental logic are properties of a reality. I can't imagine a reality without them (at least time and space). We keep thinking in terms of "another place with time and space", how about a place with just one or neither? Imagine a computer program trying to understand a reality that isn't memory and clock rate. memory isn't space as in the space we know, it is capacity. clock rate isn't time as in the time we know, but it is very similar. In an SMP system you have "clock rate" spread across cores and processors so it is a concept different from our concept of linear time. If our reality is in an SMP, there would be multiple separate parallel but converging timelines, but then again is dejavu speculative/preemptive execution?
I know I'm all over the place with this post, but my goal is to question the entire concept of a "simulation". Is it simply a relativistic and human-centric way of expressing our perception of reality relative to other realities? When We dream, is that dream world any less real than ours? Certainly, for us it is no different than any unreality, but that's only for us.
I'm thinking the whole concept of "simulation" stops making sense if there are multiple realities (which I'm only talking about hypothetically, I don't actually believe that). In terms of a single reality within the same time-space and rules of physics and all that, what does it mean for the universe to be a simulation?
With multiple realities, you have to stop presuming things like time and space as we understand them, just the same as time and space in a dream, or in a video game (or any program). Is the world of bits, bytes, processor instructions and memory addresses any less real or more of of a simulation than ours would be in a multiple-reality scenario?
Consider the very basic assumption of causality, that things originate from somewhere and sometime, if the space-time assumption isn't a given, then the very concept of causality might not apply in some realities, and thus in the relationship between realities, and therefore the whole concept of our reality being a simulation depends on causality being a thing, because we're saying our reality is caused by another reality. For there to be a causal relationship, not only does space-time need to exist but it needs to be in the same space-time reference-frame for one to cause another. But again, we can't assume the rules of causality are the same or that there isn't some other fundamental element of reality that makes it all work when talking about inter-reality relationships.
I think we are too tethered to things like mass, energy, time, space. 1+1 resulting in two. What I would like to see explored more (by people smarter than me) is the fundamental element of reality that is information. Before all of those things (time,space,mass,energy, rules,etc...) there is information. Similar to the realities we create in our computers and how they need information to exist first and foremost, and then things can be done with that information and our own little primitive proto-reality is creat...
Anyone that has had a really vivid dream will tell you the brain needs no help in creating a simulation.
The idea that no computer or system could possibly be powerful enough for the complexities of a simulation is a very trivial way of looking at things and isn’t thinking of something that is readily available.
I have long held the theory the brain is very capable of filling in all the complex details required for a simulation.
Another thing to think about: if we are here, and assuming we experience things - that is we are not biological robots - and if the universe is indeed a simulation, then how are our conciousnesses any different from the ones that exist in the parent universe?
The simulation hypothesis runs in the Exponential Resource Problem:
To simulate a system with N states/particles with full fidelity, the simulator needs resources that scale with N (or worse, exponentially with N for quantum systems).
This creates a hierarchy problem:
- Level 0 (base reality): has X computational resources
- Level 1 (first sim): needs X resources to simulate Level 0, but exists within Level 0, so can only access some fraction of X
- Level 2: would need even more resources than Level 1 has available.
Every simulation layer must have fewer resources than the layer above it (since it is contained within it), but needs more resources to simulate that layer. This is mathematically impossible for high-fidelity simulations.
This means either:
a) we're in base reality - there's no way to create a full-fidelity simulation without having more computational power than the universe you're simulating contains
b) simulations must be extremely "lossy" - using shortcuts, approximations, rendering only what's observed (like a video game), etc. But then you must answer: why do unobserved quantum experiments still produce consistent results? Why does the universe render distant galaxies we will never visit?
c) the simultation uses physics we don't understand - perhaps the base reality operates on completely different principles that are vastly more computationally efficient. But this is unfalsifiable speculation.
This is also known as the "substrate problem"; you can't create something more complex thatn youself only using your own resources.
Even more devastating is the CASCADING COMPUTATION PROBLEM.
Issue: it is not just that you need resources proportional to the simulate system's complexity, you need resources to compute every state transition.
The cascade:
a) simulated universe at Time T: has N particles / states
b) to compute time T+1: the simulator must process all N states according to physics laws
c) that computation itself has states: the simulator's computation involves memory states, processor states, energy flows. Let's call that M computational states
d) but M > N: the simulator needs additional machinery beyond just representing the simulated states. It needs the computational apparatus to calculate state transitions, store intermediate values, handle the simulation logic itself.
The TIME PROBLEM
There's also a temporal dimension:
- one "tick" of simulated time requires many ticks of simulator time (to compute all the physics)
- if the simulator is itself simulated, its ticks require even more meta-simulator ticks
- time dilates exponentially down the simulation stack
So either:
a) we're in base reality, or
b) we're in a very shallow simulateion (maybe 1 - 2 levels deep max), or
c) the sim uses radical shortcuts that should be observable
17 comments
[ 4.7 ms ] story [ 55.2 ms ] threadSeems like quantum gravity theory might be missing something, no?
The same may apply to "intelligence" --- aka AGI.
As far as I know, there is no proof that AGI can be produced or simulated by a binary logic algorithm running on a finite computer.
Hence, some people support the idea of "emergence" --- aka alchemy, aka PFM --- Pure Friggin Magic.
https://arxiv.org/abs/0708.1362
https://www.tandfonline.com/doi/abs/10.4169/amer.math.monthl...
Can we accurately simulate a smaller universe in this universe? If I understand correctly, according to this paper the answer is "no". Except how do we determine the simulation is inaccurate, without either knowing what is accurate (and thus having a correct simulation), or being unable to distinguish the inaccuracy from randomness (the simulation already won't perfectly predict a small part of the real universe due to such randomness, so you can't point to a discrepancy)? What does it mean for a simulation to be “inaccurate”?
Also, you don't need to simulate the entire universe to effectively simulate it for one person, e.g. put them in a VR world. From that person's perspective, both scenarios are the same.
Some intuition:
1. If the universe contains an uncomputable thing, then you could utilize this to build a super turing complete computer. This would only make CS more interesting.
2. If the universe extends beyond the observable universe, and it's infinite, and on some level it exists, and there is some way that we know it all moves forward (not necessarily time, as it's uneven), but that's an infinite amount of information, which can never be stepped forward at once (so it's not computable). The paper itself touches on this, requiring time not to break down. Though it may be the case, the universe does not "step" infinitely much information.
One quick side, this paper uses a proof with model theory. I stumbled upon this subfield of mathematics a few weeks ago, and I deeply regret not learning about it during my time studying formal systems/type theory. If you're interested in CS or math, make sure you know the compactness theorem.
Paper direct:
https://jhap.du.ac.ir/article_488.html
I enjoyed some commentary here:
https://www.reddit.com/r/badmathematics/comments/1om3u47/pub...
See also:
https://en.wikipedia.org/wiki/Mathematical_universe_hypothes...
Then it was spirit
Then it was geometry
Then it was a machine
Then it was an equation
Then it was a network
Now it’s a simulation
They always remake the universe to the fashionable transcendent thing of the era,
Human mortality obfuscates this a little but if you were around for it, you’d see this clear repeating pattern of humanity
Is the constraint of the "simulation" definition that the thing "simulating" the universe would be a computer less complex than the universe itself?
Consider a game world in a computer, we call it a simulation, and it is, but is it any less real than our reality, when thinking in terms of realities? In other words, we feel like our reality is more real because the game is less complex, we understand it fully and it is run using mechanisms we know and understand. So what would make us think it is a more real reality than our own?: If we didn't understand how it works? If its workings and rules are more complex than ours?
Taking a step back, are we as humans even capable of understanding a reality that isn't ours, even as a concept? Things like time, space, and fundamental logic are properties of a reality. I can't imagine a reality without them (at least time and space). We keep thinking in terms of "another place with time and space", how about a place with just one or neither? Imagine a computer program trying to understand a reality that isn't memory and clock rate. memory isn't space as in the space we know, it is capacity. clock rate isn't time as in the time we know, but it is very similar. In an SMP system you have "clock rate" spread across cores and processors so it is a concept different from our concept of linear time. If our reality is in an SMP, there would be multiple separate parallel but converging timelines, but then again is dejavu speculative/preemptive execution?
I know I'm all over the place with this post, but my goal is to question the entire concept of a "simulation". Is it simply a relativistic and human-centric way of expressing our perception of reality relative to other realities? When We dream, is that dream world any less real than ours? Certainly, for us it is no different than any unreality, but that's only for us.
I'm thinking the whole concept of "simulation" stops making sense if there are multiple realities (which I'm only talking about hypothetically, I don't actually believe that). In terms of a single reality within the same time-space and rules of physics and all that, what does it mean for the universe to be a simulation?
With multiple realities, you have to stop presuming things like time and space as we understand them, just the same as time and space in a dream, or in a video game (or any program). Is the world of bits, bytes, processor instructions and memory addresses any less real or more of of a simulation than ours would be in a multiple-reality scenario?
Consider the very basic assumption of causality, that things originate from somewhere and sometime, if the space-time assumption isn't a given, then the very concept of causality might not apply in some realities, and thus in the relationship between realities, and therefore the whole concept of our reality being a simulation depends on causality being a thing, because we're saying our reality is caused by another reality. For there to be a causal relationship, not only does space-time need to exist but it needs to be in the same space-time reference-frame for one to cause another. But again, we can't assume the rules of causality are the same or that there isn't some other fundamental element of reality that makes it all work when talking about inter-reality relationships.
I think we are too tethered to things like mass, energy, time, space. 1+1 resulting in two. What I would like to see explored more (by people smarter than me) is the fundamental element of reality that is information. Before all of those things (time,space,mass,energy, rules,etc...) there is information. Similar to the realities we create in our computers and how they need information to exist first and foremost, and then things can be done with that information and our own little primitive proto-reality is creat...
The idea that no computer or system could possibly be powerful enough for the complexities of a simulation is a very trivial way of looking at things and isn’t thinking of something that is readily available.
I have long held the theory the brain is very capable of filling in all the complex details required for a simulation.
To simulate a system with N states/particles with full fidelity, the simulator needs resources that scale with N (or worse, exponentially with N for quantum systems).
This creates a hierarchy problem:
- Level 0 (base reality): has X computational resources
- Level 1 (first sim): needs X resources to simulate Level 0, but exists within Level 0, so can only access some fraction of X
- Level 2: would need even more resources than Level 1 has available.
Every simulation layer must have fewer resources than the layer above it (since it is contained within it), but needs more resources to simulate that layer. This is mathematically impossible for high-fidelity simulations.
This means either:
a) we're in base reality - there's no way to create a full-fidelity simulation without having more computational power than the universe you're simulating contains
b) simulations must be extremely "lossy" - using shortcuts, approximations, rendering only what's observed (like a video game), etc. But then you must answer: why do unobserved quantum experiments still produce consistent results? Why does the universe render distant galaxies we will never visit?
c) the simultation uses physics we don't understand - perhaps the base reality operates on completely different principles that are vastly more computationally efficient. But this is unfalsifiable speculation.
This is also known as the "substrate problem"; you can't create something more complex thatn youself only using your own resources.
Even more devastating is the CASCADING COMPUTATION PROBLEM.
Issue: it is not just that you need resources proportional to the simulate system's complexity, you need resources to compute every state transition.
The cascade:
a) simulated universe at Time T: has N particles / states
b) to compute time T+1: the simulator must process all N states according to physics laws
c) that computation itself has states: the simulator's computation involves memory states, processor states, energy flows. Let's call that M computational states
d) but M > N: the simulator needs additional machinery beyond just representing the simulated states. It needs the computational apparatus to calculate state transitions, store intermediate values, handle the simulation logic itself.
The TIME PROBLEM
There's also a temporal dimension:
- one "tick" of simulated time requires many ticks of simulator time (to compute all the physics)
- if the simulator is itself simulated, its ticks require even more meta-simulator ticks
- time dilates exponentially down the simulation stack
So either:
a) we're in base reality, or
b) we're in a very shallow simulateion (maybe 1 - 2 levels deep max), or
c) the sim uses radical shortcuts that should be observable