On that topic, this is a very common misconception about how that proof works. Multiplying all the primes and adding one does not have to be a prime (just try 2 x 3 x … x 13 + 1) - the point is it’s not divisible by any of the supposedly finite number of primes, so it must have some other prime divisor.
Your original proof is correct. Yes the number may not actually be prime, but given the assumption that you have finitely many primes it follows that the number you have constructed is prime, since it has no divisors.
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.
This is a confusing way to present this argument. We can’t say, by assumption we used up all the primes, so the new number must be a new prime - this doesn’t make sense. And you might as well say the new number has some new prime divisors (could be the number itself, could be new primes smaller than the number), which is at least slightly more correct.
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.
> We can’t say, by assumption we used up all the primes, so the new number must be a new prime - this doesn’t make sense.
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.
> Stating "N has non-zero remainder when divided by each prime less than N" is equivalent to stating "N is prime."
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 isn't that the newly formed integer is a prime!
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.
A proof by contradiction works by assuming something incorrect, and using it to prove various incorrect things until finally we manage to prove both p and not p for some proposition p. Being able to prove such an absurdity shows that the assumptions must be wrong.
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).
Ok I see what you’re getting at. Maybe a better way to construct this version of the argument is
- 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.
There are many alternative definitions of the rational numbers.
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.
You can’t logically prove anything about anything unless it follows from the premises. Do you mean to suggest that all consequences of the premises are in some way part of the definition of said premises? That’s not irrational, but I don’t think it’s particularly illuminating either.
Suggesting that proving the universe is infinite isn't any different than proving anything else is infinite. And you shouldn't be surprised it's impossible.
We can’t actually prove much at all about the universe beyond that it exists (cogito ergo sum). Basically everything else is talking about some model and not the actual universe. The map still isn’t the territory no matter how much we might wish it were.
You're right, but: I think we could imagine finding something like "if the universe is infinite we can describe it with this simple set of laws, otherwise we need to use this much more complex set of laws." That would at least be suggestive.
Even with infinite time on your hands you'd never even be able to reach the edge of the currently-observable universe, because the rate of the expansion of the universe is increasing, and objects are already receding from us too quickly, even for a traveler moving at the speed of light.
I think it is a statement when philosophy draws its tongue and starts making faces.
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.
I'd say that the Universe is effectively unbounded if it's flat for, say, 1 GLY around us. We will not observe any difference for a billion years, and that's enough time for us to improve our science and technology and find a way to "look" further.
That blog feels like it's from a small universe -- a narrow ribbon of text, surrounded by great voids. It would be fine, I suppose, even praiseworthy, if we were still reading on paper, as it would provide ample space for any marvelous proofs we might contrive. But on a blog page? Why?!
I felt like the blog post got cut off. It felt like it was leading up to some statement, as they outlined how a small curved universe would be identified through patterns etc etc, even link a paper they wrote on it…… then…… nothing. Did I miss something crucial in the reading?
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.
>Reading the paper they found correlations indicative of a non flat space but could be explained by other factors and noise.
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.
Inflation "smooths out" the curves in space-time by stretching space out in an exponential manner. So any curves get flattened until the universe is effectively flat. An inflation-like theory that doesn't stretch space out that much leads to its own mysteries.
This is by no means a trivial task. Studying these far away structures takes powerful telescopes operating over decades. Things like the JWST have barely begun taking data.
I wouldn't worry about it. The heat death of the universe isn't the end. The Second Law is a statistical, not an absolute, law. So, even after heat death, structures of all sizes will randomly emerge on large enough timescales. (Read: effectively infinite timescales -- timescales large enough to make Graham's Number look like a small number.) Wait long enough, and you'll get Boltzmann Brains, Boltzmann planets, and even Boltzmann galaxies. All sorts of things. In many respects, the universe after heat death is more interesting than the universe before heat death --- it's an unbound infinite probability space.
I agree about the second law, but aren't there also other reasons to expect gloom and doom? Like an ever decreasing energy/mass density as everything drifts away into infinity? I dont think thats a question of probabilities but rather something that must happen based on the equations of motion?
Entropy is a measure of the number of possible states.
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.
From a layman that enjoys scifi, I always thought universe appears to be infinite because we are in a lower dimension. Gravity is a product of interaction between parallel 3D universes. And dark matter is just matter from other universes. Is there any basis to this theory or am I over simplifying it.
> 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'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.
> And dark matter is just matter from other universes.
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.
That matter from the other universes seem to pretty well line up with galaxies in our own universe which makes this theory a bit sus. I'd expect at least some of them to be scattered at random places, whose gravitational lensing effect we should be able to observe.
The matter is not in a different universe, but in our universe. Just a different spatial plane of it. Much like a 3D structure intersected by the plane of a 2D universe is surrounded "by itself" in the third spatial dimension. In such a case, the extradimensional matter lines up quite well with the observable.
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.
We don’t assume it’s infinite, we assume it’s expanding. That’s the reason why there is supposed to be an end to the universe, I.e: the Big Bang and the Big Crunch
As for physical distance, that’s very large. Relativity is about time not space.
It's not actually clear that the Big Bang was the absolute beginning. There could have been things before. These days, I hear much more talk about 'inflation' than about the big bang.
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.
We don't assume either. We assume the universe is homogeneous and isotropic and that GR describes the world. Expansion follows from that and some observations. Finiteness is currently undetermined. It could be infinite, but it could also just be finite and really really big.
My money is on living in a simulation with lazy evaluation and constraints like maximum speed to prevent us from consuming too many resources. Intelligent species seem to love making simulations, so what are the chances we happen to be the first one outside of any?
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?
Well, depends on how you draw the line between systematic and ad-hoc.
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.
those things are not particularly similar. the tree that nobody can hear while it's falling still has a real and measurable impact on its environment in various ways, something where if if not simulated while nobody was around, the simulation would need to catch up on if an observer ever came near. this eventually amounts to processing work that is equal or even worse compared to just simulating it in full detail in the first place.
An idea I had a long time ago (I think I posted about it on Slashdot back when that was the hot place to be rather than a shadow of its former self) which I'm sure was not original, was that where many games pop things in and out of existence and (re)generate them purely based on a statically seeded pseudo-random number generator or similar, and then maintain some minimal state, if you take time and decay into account you can do much better.
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.
> those things are not particularly similar. the tree that nobody can hear while it's falling still has a real and measurable impact on its environment in various ways,
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.
You can rephrase that to an assumption that maybe everything other than those entities being simulated has no existence at all other than the bare minimum required for the observation. Whether or not the person you're responding to then exists at all as a subject of the simulation or are just another lazily instantiated entity that only exists to the point you interact with them is then an open question.
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.
Yeah you can take this antrophocentric view to an egocentric extreme where I am nothing but a lazily evaluated interaction with you which is, btw, the reason this reply came so late... The engine didn't get around to it earlier :)
I assume there is no double slit diffraction pattern until it is observed, and when that observation occurs - the universe has no information on which slit the photon or electron went through - it was not observed - it went through neither/both.
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.
My theory is that it will turn out that a) everything about Physics will be consistent with it being a simulation and b) it won't be possible to determine if it is or isn't. Put another way: reality will always appear to be the result of a simulation and that's just how things are.
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?
No. Because you have never seen a universe of which you are sure that it was a real universe, so you do not know how a real universe behaves, so you can not determine whether our universe behaves differently than a real universe. You are just postulating without justification that in a real universe time progresses uniformly and then conclude that our universe is not real because time does not progress uniformly.
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.
Or to stick with the software metaphor, you do not have a specification for real universe, so you can not tell whether the implementation is correct or has bugs. What you consider a potential bug might as well be a feature, impossible to tell without the specification.
My favourite thought on this is that if I wanted to build a large scale simulation of a universe, then one reasonable way of approaching it if with the assumption it'd need to be distributed without running into massive synchronisation issues is to impose a computational budget on every entity per time step of the simulation. If moving through space then involves computation to e.g. check for interactions with other entities in the simulation, then the amount of computation will be affected by velocity, and hence subjective time will be affected by velocity as an inherent property of the simulation.
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)
Any reasoning you do about the simulation hypothesis has one gigantic problem - the only thing you know anything about is the universe we observe. You have never seen a real universe and you have never seen a simulated universe, so you have nothing to compare our universe against in order to decide whether ours is real or simulated.
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.
As I said, it proves nothing, and I just made the same argument that we can't really know because we're stuck inside in another comment. So let me violently agree with your comment.
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.
Yes, the recent popularity stems from Bostrom's simulation argument trilemma. But everyone always jumps over that, takes it as granted that we live in a simulation, and proposes some wild ideas how we could find evidence or what might be hints of the simulation. This is what I wanted to address, that this is a relatively hopeless endeavour and I do have the impression that most people talking about living in a simulation are not aware of this. Despite, as you point out, it being a variation of solipsism about which people have pondered for centuries.
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.
I used to feel that way until they found the Higgs boson. No one would implement that. Too much effort and risk compared to just hardcoding the relevant masses. Ancestor simulation programmers have deadlines.
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.
Unobservable is not the same as unknowable. For example, the form of the universe beyond what can be observed could correlate with a testable hypothesis in the observed universe.
I think the idea is that it could but it would be impossible to know that. It can be fun to speculate but by definition it is impossible to know. It's not just that light can't get in at us, it's that literally the idea of causality cannot travel fast enoigh to reach us. I believe our light cone will keep expanding slightly before accelerated expansion takes over and starts reducing it but that timescale will far far outlive us humans.
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.
> It can be fun to speculate but by definition it is impossible to know.
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.
119 comments
[ 3.5 ms ] story [ 236 ms ] threadIf 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...
https://archive.ph/m7qjz
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.
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?
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:
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.
https://www.goodreads.com/ne/book/show/433567.Flatland
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?
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.
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.