The Return of a Small Universe?
telescoper.blog
telescoper.blog
The author knows perfectly well that the observable universe is finite. So the question is about sensible models for what happens beyond.
Any such "models" would be philosophy.
As it stands right now there is an impenetrable barrier. All of our modern theories and technology for astrophysics and cosmology emerged recently. We haven't know about the big bang for 100 years even. I think it's highly likely that our views on these things will change. For all we know we could be inside a hyperbig black hole inside some much larger universe. We can make models that fit what we're able to see and then use those to extrapolate the things we cannot. But we cannot see what we cannot see.
By the way, to me, "unobservable is not unknowable", sounds pretty philosophy to me. All of the physics we cannot observe, we currently cannot explain. Maybe some day with some great minds leap nobody saw coming, maybe hundreds of those, but everything i not of that cannot be observed cannot be known certainly. There must be some interaction, whether we're seeing gravitational waves, light, high energy particles doesn't matter, they still all travel at the speed of light and will be outpaced by expansion at some point.
I think the distinction is way more blurry than you're acknowledging. For example, the way we "know" what atoms look like is by technology like x-ray crystallography or scanning tunneling microscopes. In these cases, we're in no sense directly observing the atoms, were looking at correlated electric or photonic signals and using mathematical equations to infer what the atoms look like.
In this case there truly is an "impenetrable barrier" to observation, instead of speed of light, it's wavelength of visible light.
The amount of physics we cannot directly observe is much larger than amount of physics we can, without even getting into quantum phenomenon which we also cannot observe even in principal.
(1) There are points of the universe that are currently unobservable, because their light hasn't hit us yes, but that will become observable in five minutes. I posit that they are already in the realm of science now, and not just in five minutes.
(2) Please read the article. The author directly addresses this point:
> Anyway, my point is that speculative ideas are all very well but they don’t mean much if you can’t test them. This one at least has the virtue of making testable predictions.
Edit:
Reading the paper they found correlations indicative of a non flat space but could be explained by other factors and noise. So it wasn’t conclusive but left open the door for curved space and a small universe.
The paper doesn't question the flatness of space. In fact it uses it as a constraint for its models, because there is extremely strong observational evidence that our universe is globally flat (which is actually its own mystery, since the universe contains energy and energy curves space). What the paper suggests is that if inflation (i.e. the first moments after the big bang) happened in a specific way that is consistent with current experimental data, the universe might be much smaller than previously thought. If it actually is finite and below a certain size, we could even detect it using upcoming observations from large scale structure surveys.
However, if as he asserts this can be studied and verified, have we really not done that?
A common general pattern in games is to not process that which is not seen or known not to have any interaction - e.g there's no point in making NPCs/enemies move or think in the last room of a level (or a far away planet) when the player is at the beginning of it, there's no point in rendering what's outside the frustum, etc... which kind of echoes the deep philosophical questions of "do unobserved things exist?" or "if a tree falls in a forest and no one is there to hear it, did it fall?", or quantum wave collapsing/Schrödinger's cat.
Is there any game engine that does such general lazy evaluation based on the observation effect or are they all using ad-hoc hardcoded laziness rules?
Many side scrolling platformers have ad-hoc rules based on where the virtual camera is looking on the 2d level that are pretty close to what a systematic rule would be.
E.g. Elite would bring ships into existence only when you entered a planetary system. If you then shot at police, it'd affect your reputation and impact others reaction to you even after ships have blipped out of existence. But the ships themselves retained no state.
Minecraft, on the other hand, maintains state of objects "too well": Once you visited an area, the landscape goes static once you leave: While mobs disappear and are reinstantiated, nothing will grow or decay while you're away.
If you want to make a realistic lazy simulation and you also want to minimise computation and storage, you could do this:
* For any entity, you assign a function that computes its change over time, including being able to give a result that is effectively "reconverged to base-state of the map at time t". * When a user re-enters a map location, you 1) generate the map as per that time, which might include whatever effects you want to cause change over time, 2) you apply the functions for any user-affected objects that were present, and let them be affected by map changes since last time-step, 3) you purge any user-affected changes that will have re-converged to the base state of the map.
E.g. clear an area of trees? If you come back soon, it'll still be clear; if you come back much later, it will have reverted to the freshly generated state of the biome affected by a time factor so it's not identical.
Leave your farm for a while? A bit later it'll be ready to harvest. Too long, and it'll have fallen into disrepair.
Build a house? Leave long enough, and there will be damage to it, and cobwebs etc. Leave for really long and it might be ruins when you return.
Dug out a tunnel? Wait too long, and things might have fallen and started blocking them.
Put another way: A good enough simulation could potentially short-circuit a lot of the need to retain state and simulate what has happened by applying pure function of time decay. You don't need to simulate the process of a house decaying, just the outcome at time t unless it's being observed at a given time.
Incidentally, when people don't know/remember the details of something we've done, we're great at just making up the details - we know this from split brain experiments - so even if you instantiate simulations of people in this kind of scenario you could likely work your way around inconsistencies just by decay memories as well and letting people fill in the gaps in a way consistent with the effects they see.
I fully agree with you that it won't always be worth it vs. just simulating the full detail in the first place, but I also think you can at least get far closer to realistic even with aggressively pruning what you actually fully simulate. To what extent you can get close enough is another question, and something that's fascinating to think about.
Consider a hypothetical game like No Man's Sky. A tree falling on a neighbouring planet has zero impact on the current one the player is standing on.
> something where if if not simulated while nobody was around, the simulation would need to catch up on if an observer ever came near.
That's the wave collapsing part: probabilities become reality.
> this eventually amounts to processing work that is equal or even worse compared to just simulating it in full detail in the first place.
Collapsing treefall probabilities for the small area of a planet the player is due to observe when coming near the area is orders of magnitude less than simulating every single treefall on every planet in real time.
This principle could be equally applied to NPCs, e.g a NPC having a probability to be at this or that place, taking into account a lightcone of causality so that they don't warp from one place to the other.
I think you are taking us far too serious, we are not that important...
In other words, maybe you're the only subject. Or maybe I am. Or maybe all that exists are isolated "snapshots" and that we only assume time passes because we process a single momentary "image" of memories that includes the sensation of it passing.
The problem, of course, is that we can not possible ever know. And so we mostly discard this notion because absent someone pulling us through a door and letting us observe it from the outside, we're stuck inside a room and trying to infer the outside shape of the building without having any idea how much of the interior we have access to.
My use of programming terms to describe this is both a nod to 'gosh this game engine has great memory management and algorithmic efficiency' but also me thinking about the relationship between the fundamentals of programming and the fundamental nature of information.
When programming we understand that time is simply a matter of cycles of information processing, and that space in a rendered 3d game is not real, but a representation of relationships between data structures, and it's interesting to think about what computers - machines built in this universe from the stuff of this universe - are revealing about the nature of this universe.
I know that it is easy to mock computer metaphors as the next iteration of the universe is a clockwork, but the people who thought the universe was a clockwork were not wrong, they were taking a small step forward. They had a new metaphor which gave them additional insight that they had not had before - a model built in this universe from the stuff of this universe that shed new light on the nature of the stuff of the universe. This is what a computer is, it is an object built of the stuff of this universe that has given us new insight in the nature of the stuff of this universe.
Like some programs escape a virtual machine by escalating priviledges.
I read that the computer game Eve online (never played it) slows down when there are big battles with many players. Sounds a lot like black holes. Time slows there down too - too many calculations? Planck time is the tick rate of the universe? Can pauses happen?
As I said in a different comment, even if the stars in the Milky Way suddenly rearranged themselves to spell out »You are in a simulation.« on the night sky, you could not tell for sure whether this is a message from the simulators in the outer universe or whether this is just some weird behavior arising from the laws of physics in a real universe.
This of course proves nothing, and I'm absolutely not suggesting it's evidence of anything. But it's fascinating when possible design tradeoffs for a simulation might fairly neatly line up with how things actually work in our universe. (At least from a science fiction POV; I have a couple of story ideas I intend to write that makes use of that notion)
I do share your thought that it's harder and harder to dismiss some variant of the simulation argument - especially as the original one is far too constrained (which made sense in as much as you want to cut away as much as possible that might make people casually dismiss it)
Imagine we have a really close look at space and discover that it is made out of small voxels. Simulated universe! No! Who said that real universes are not made out of small voxels? It could be the other way around, the real universe could be made out of voxels but a voxel-based simulation does not fit into memory, so they assigned a real position vector to every object in order to approximate the real voxel universe. In that case it would be wrong to conclude that our universe is real because it is continuous and a flawed analogy with our own computer simulations suggests that simulations must be discretized in some way. [1]
So no matter what you observe in our universe, you have no idea if it is indicative of a real or simulated universe. Maybe if the stars in the Milky Way would suddenly rearrange themselves and spell out »You are in a simulation.« on the night sky, that could be a good hint that we are indeed in a simulation. But even then, maybe that is just how real universes behave, spelling out messages on the night sky from time to time might just be part of the laws of physics. Admittedly, if that actually ever happened, I would also consider the simulation hypothesis the better explanation.
[1] This is just an illustrative example, whether this is realistic or even possible is besides the point.
The best we could hope for would be someone popping their metaphorical head in and telling us there's an outside and then show us, but that just gives rise to the question of whether that "outer universe" is simulated or not, so infinite regress here we come.
Ultimately we just have to accept that we can never conclusively prove whether we're in the "outermost layer", and we can only prove we're not if we somehow "escape" and can look in on our own universe from the outside and for what we know we're in an unexploitable simulation, so the lack of evidence of either certainly does not prove the other and we're left wildly speculating and it's not very useful.
But that doesn't make the mechanisms less interesting to explore, and for me it's mostly a series of fun thought experiments, and your voxel example to me is a good illustration of what an interesting rabbit hole it is even if it doesn't lead to anything practical.
For me it was an interesting one because the simulation argument is really a rehashed variant of Berkeley's philosophical idealism, and the same conflict with materialism exists for the simulation argument as with respect to Berkeley: We can speculate about it, but since we can't prove it, day to day we need to act on the assumption we live in a material world. If someone pops their head in to inform us we're in a simulation, then sure, then we can reasses.
Until then it's an entertaining diversion.
EDIT: I'll add one caveat, though: You're right in as much as talking about what we can say about a simulation by looking at our universe, but the core of the original simulation argument is much more pared back. It's an argument that if we can run simulations and eventually do, then statistically we are more likely to be in a simulation. Or to pare it back further: If there are 3 or more "realities" and 2 of them are simulation, then we are more likely to be in one of the simulated ones than the single "real" world. What that boils down to, then, is how realistic you think it is that someone will simulate this time period, and we can assert some limited things about that if we get to the point of running our own realistic simulations. But until/unless we get there, we can't really assess the odds, and even if we can show that such simulations are common, you're of course still right that it won't prove whether we are in one or not.
To address the actual trilemma, I think the solution is that there are or will be no simulations. Generally the most compact representation of a thing is the thing itself. If you want to simulate something faithfully, then the simulator will need more resources than what you simulate. You are not going to build an electron simulator that needs less than one electron to simulate one electron. You are not going to simulate a computer with a gigabyte of memory on a computer with a gigabyte of memory. That might work under special conditions, when the simulated memory is mostly zeros and you can compress it, but it will not work in general.
You can simulate the weather on earth well enough for the whether forecast to be useful if you throw away enough details, but you are not going to simulate it in full detail with a computer much smaller than earth's atmosphere. Simulating a cubic meter of universe faithfully will generally require at least a cubic meter of computer. I do not see us building galaxy-size computers. The other option would be to go the way of the weather forecast, make the simulation as simple as possible, simulate entire humans but not cells or atoms to make the problem tractable. That seems much more plausible.
In both cases it seems unlikely to me that you could deeply nest simulations. If you have a faithful simulation and simulating a cubic meter of universe requires two cubic meters of computer, then you could at best simulate a universe half the size of the real universe if you turned the entire universe into a computer. The people in that simulated universe could at best build a simulation half the size of their universe and so on. The simulated volume would exponentially approach zero with increasing nesting level.
If you go the other way, if you simulate entire humans and not cells or atoms, then it is not even clear how the simulated people would go about creating their own simulator as simulating arbitrary machines is not part of the simulation. So you are forced to move towards a more faithful simulation mechanism if you want to enable nested simulations which, as said, will probably shrink the simulation volume rather quickly.
There's no reason to believe this, and (I would argue that) any civilization creating ancestor simulations has, in fact, likely reached a post-scarcity economy where it's entirely possible that the "programmers" are doing it for the love of programming, the love of simulation, the love of understanding, etc. Or that they are trying a very large number of simulations with different setups at one time. And the Higgs boson fits perfectly well into any or all of that.
There’s not actually any proof for multiverses, that’s a hypothetical, related to the whole sims theory.
Not saying that could not be true but there’s more proof that this isn’t the first or the last universe than there are other universes.
Why would there have to be an "into"? It seems like the most parsimonious expansion is that there isn't one.
My limited understanding of the math is also that that's what the math says.
The universe being small and it’s expansion just a mirage is one attempt to square the data and theory.
I’m not an expert so I don’t have any answers or anything. I just went into this rabbit hole recently when I got sick recently.
The universe doesn't appear to be infinite. The observable universe has a very definite size.
We can't really say much about what comes beyond. But the paper the linked article talks about tries.
> Gravity is a product of interaction between parallel 3D universes.
You might like https://en.wikipedia.org/wiki/Holographic_principle
> The holographic principle is a property of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region — such as a light-like boundary like a gravitational horizon.[1][2] First proposed by Gerard 't Hooft, it was given a precise string theoretic interpretation by Leonard Susskind,[3] who combined his ideas with previous ones of 't Hooft and Charles Thorn.[3][4] Leonard Susskind said, “The three-dimensional world of ordinary experience––the universe filled with galaxies, stars, planets, houses, boulders, and people––is a hologram, an image of reality coded on a distant two-dimensional surface."[5] As pointed out by Raphael Bousso,[6] Thorn observed in 1978 that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. The prime example of holography is the AdS/CFT correspondence.
So basically the opposite of what you are describing: gravity emerges because we are in a higher dimension.
> And dark matter is just matter from other universes.
Dark matter can be seen as the label we give to a bunch of experimental findings / problems. https://en.wikipedia.org/wiki/Dark_matter says:
> [Dark matter's] existence is implied by various astrophysical observations which cannot be explained by general relativity unless more matter is present than can be seen. Evidence for dark matter comes from many different angles, such as galaxy dynamics and formation,[2] gravitational lensing,[3] and the cosmic microwave background, along with astronomical observations of the observable universe's current structure, the formation and evolution of galaxies, mass location during galactic collisions,[4] and the motion of galaxies within galaxy clusters.
Positing matter that has gravity but doesn't otherwise interact (much) with the rest of the universe can explain those observations. But other observations are also possible. Eg some people like to fiddle with the laws of gravity to explain why the galaxies don't fly apart.
This is a fun idea. You can illustrate it by drawing your classic 2D universe on a piece of paper, sprinkle metal dust around, and move it with magnets held above or below the paper. To the 2D creature, matter in their universe seems to be affected by forces from entirely invisible objects, but 3D creatures can observe exactly what's happening. Likewise our "dark matter" would simply be matter on different planes in the same >3D universe as us. We neither see it nor collide with it, but we observe its gravitational pull.
Mind you, I'm not a physicist, and I'm not (necessarily) proposing this as a serious model. Just an internet commenter riffing on a fun idea.
In unbounded/infinite time, all states will be cycled through. However diffuse, all particles in space will be akin to H2O molecules in an ocean of water: they will move freely, interacting with each other, each assuming any number of positions. In an idealized ocean in boundless time, every H2O molecule will occupy every possible position, and then every possible configuration will repeat.
Post heat-death, the number of possible states that describe maximally (or near-maximally) disordered and diffuse systems is almost -- but not quite -- infinitely larger than the number of possible states which describe structures of some sort, indeed of any possible sort, emerging. That "not quite" does a lot of work, in view of unending time. So, in boundless space, in boundless time, should protons and other elementary particles not decay, very interesting things will still come into existence with some degree of statistical regularity.
That's only true if there are finitely many states.
An example in Python:
import itertools
for limit in itertools.count():
for i in range(limit):
print(i)If there are finite, multiply them all and add one. This number is prime. QED
2 x 3 x … x 13 + 1 isn't prime but that's because that's just a subset of the primes, not all of them. And the argument relies on using all of them.
The actual proof is by contradiction, and goes something like this:
1) Let’s assume there’s a finite number of primes
2) Multiply them all and add one
3) Since we assumed 1), the result in 2) must have a divisor that’s one of those finite number of primes
4) But that’s not the case since we always get a remainder of one
3) and 4) is a contradiction, therefore 1 is false. At no point it follows that the number in 2) is a prime.
The misconception also often causes people to assume that any first N primes + 1 is a prime itself, which is not correct. Someone will use this to make an insecure cryptographic system eventually :) Just kidding, but you see my point how it’s not just a technical detail.
I'm not sure what you mean. Are you simply pointing out that it's a contradiction? Because, indeed, it is a contradiction, and that's the point. It's a proof by contradiction!
The contradiction you state in step 4 is precisely equivalent to the contradiction "the new number must be a new prime." Stating "N has non-zero remainder when divided by each prime less than N" is equivalent to stating "N is prime." However this is not equivalent to the statement "any first N primary + 1 is prime" which is indeed a misconception.
This confuses N, the bound on the largest prime, and the number (call it M) that’s the product of the all primes < N plus one. M is much larger than N. So what you’re really saying is:
> Stating "M has non-zero remainder when divided by each prime less than N" is equivalent to stating "M is prime."
This makes it clear where the error is, the correct statement should be:
> Stating "M has non-zero remainder when divided by each prime less than N" is equivalent to stating "M is either a prime or a product A x B where A is a prime > N”
The argument is that the newly formed integer has a divisor which is none of the primes in the original set that was multiplied together.
It's not any of those primes, because none of those primes divide it.
Therefore that divisor must be a prime which is not in that set, contradicting the assumption that the set is complete.
Since the argument works for any finite set of primes, it shows that no finite set of primes can contain all the primes. Thus there are always more primes.
There are times when that product + 1 will be that divisor (i.e. that number is prime). Not always though.
One such example is if we claim that the only primes which exists are 2, 3 and 5. 2 x 3 x 5 + 1 = 31. 31 is not divisible by 2, 3 or 5, leaving a remainder of 1, so we know it has a divisor that is a prime, and that is not one of those. It so happens that that divisor is 31 itself, since 31 is prime. With some other sets of primes, that won't be the case.
An example where the product plus one is not prime is the product of the primes 2 .. 13. That product is 30031, which is a composite number factorizing to 59 and 509. Because 30031 is not divisible by 2, 3, 5, 7, 11 or 13, we know that it has at least one prime factor which isn't any of those. It has two such factors: 59 and 509.
In this case we can prove that the constructed number both is prime (it's not divided by ANY prime hence it's prime) and isn't prime (it's not in the list hence it's not prime).
- every integer > 1 is either a prime or a product of primes (this is easy to show by induction)
- assume there’s a finite number of primes
- then the product of all primes + 1 must be either a prime or a product of primes
- but we know that it’s _neither_ (can’t be divided by any of the primes in the list, and not itself in the list), which is a contradiction - it had to be one or the other.
We can accurately predict many things with these definitions of infinity. They are useful, unlike... whatever this is.
I am sure you can come up with one that includes infinity in their clauses. But there are other definitions where that is a logical conclusion instead.
https://www.cantorsparadise.com/this-may-seem-more-irrationa...
But it broke down with singularities, violated symmetries, required special arbitrary numbers, didn’t conserve information, etc, …
Unless the universe was infinite, …
Then with great respect for Occam’s Razor, we could dispense with those unnecessary complications, and safely assume the universe was infinite, …
Until we saw the back of our heads!
Occams’s Razor is the scientific principle that lets you accept a seemingly perfect theory without forever watching (for) your back. O_o
It’s the final back stop.
Technically you cannot prove anything about the universe, because you need some presumptions to start any proof. Like you need to believe your senses for example.
Nevertheless we are confident in a lot of things in the universe, because we have some means to distinguish true statements about the universe from false ones. These methods go beyond rules of pure logic and they use a lot of presumtions (oftentimes in an implicit manner), and I'm not sure there are anything true these methods cannot prove. I mean I cannot prove or disprove such a statement. (I always wondered about "I think, therefore I am": how can we talk about "I" before we proved that "I" exists? Maybe it was not Descartes who thought "his" thoughts? Maybe they were induced by aliens? So you need to accept very complex presumptions just to be able to start thinking.)
Some downvoted comment above suggested Occam's razor: if we have 2 theories of the universe and the one assuming the universe to be infinite is simplier, then we should believe the universe is infinite.
Maybe it doesn't seem as a proof, but if the theory explains all known phenomena, then we have no reason to doubt it. Like with our senses: they work in practice therefore we accept them as a source of truth.
I can get to a point from a different direction. If we assume the universe to be infinite, and come with a falsifiable prediction from this assumption, and test it, then it could convince us that universe is infinite. No one can think of such a prediction today, but it doesn't mean that no one will think of one tomorrow.
As for physical distance, that’s very large. Relativity is about time not space.
The Big Crunch is currently seen as unlikely: the (observable) universe doesn't have enough matter to slow expansion and pull back together, expansion even seems to be accelerating.
> Relativity is about time not space.
Isn't it about both?