I don't see how this applies to most forms of idealism I am familiar with.

In terms of the multiplication of entities, I think you are mostly right. However, the argument generally goes that:

1. If the universe turns out to be fully broken down into discrete chunks (quanta), including discrete amounts of space and time, we have an issue. We have an issue because mathematics tells us we should be able to have continuous things, but instead we only have discrete things. Why would this be?

2. If the universe is a finite collection of discrete bits, then in theory you could simulate it. S(M) without infinite subdivisions of space and time could be simulated without an infinite amount of computation.

3. Simulation theory attempts to answer questions about the world that appear in physics to be brute facts. Why is there a limit on how fast objects can go? Why are objects not infinitely divisible? Why do we have a universe seemingly made up of small pixels, to use an analogy? Multiplying entities should be avoided, but in this case the multiplication is being invoked to answer a question that isn't currently answered. In this case, Ockham's Razor isn't being violated. Ockham's Razor does not entail that labeling everything as brute fact avoids multiplying entities. Indeed, each brute fact is its own ontological entity, and so simulation theory attempts to scoop up a bunch of these ontological primitives and explain them with one mechanism. A better critique might be that the claim is unfalsifiable and doesn't make any new predictions, but this is actually true of the entire field of quantum foundations so I'm not sure if it is fair to single out the simulation folks.

4. Not directly related, but S(M) might only have to model the experienced of all humans (maybe not even all of them, some could be "NPCs"). Since the amount of data in consciousness is vastly smaller than the amount in "actual" space-time, the size of the simulation might be able to be vastly, orders of magnitude, more simple than we think it is. The Matrix AI only has to render what we're looking at. And indeed, simulation theorists use the fact that many phenomena don't have values until we look at them as potential evidence of the simulation hypothesis.

In computer science it is known that it takes more computational power to simulate a computer system than the computer system itself has; typically, much more. — hypericin

Is this kind of like how computers used to be the size of a wall and now we wear them on our wrists?

Also,
You can't create a simulation on an average computer where the electricity works differently than it does in real life? Of course you can- it's a simulation!

For the record I do not believe reality is a simulation. More of a 'spiritual realms' guy myself. Now many people, for all intents and purposes, actually do live in man-made simulations, often of their own design- but that's another matter.

Or to make my point much simpler, the "brute facts of physics," the speed of light, the relative strengths and values of the fundemental forces, etc. are all irreducible ontological entities (maybe, some might be unified in the future).

Simulation theory is attempting to reduce these brute facts to a single cause, so they are swapping a great deal of entities for just one. Thier case might be the more parsimonious actually, but the problem remains, why should we believe this?

As for a simulation taking more information, that's aside the point for Ockham's. We're concerned about multiplying types of primitive things that can't be reduced not with there being a greater quantity of things.

This is why scientists want to unify the fundemental forces, as they have with electromagnetism and the weak force, because it means fewer entities, even if the amount of information stays the same.

By understanding that if a simulation is a world it is no longer a simulation. A simulation only makes sense in light of a world.

Is a map of the territory another "territory"? Just because the map does not represent itself on the map even though it is part of the territory does not mean that it is above and beyond the territory. It just means that it would be useless to do so. — Harry Hindu

Let's look at this from a human perspective. The possibilities are:

1. We're in a simulation, meaning there's the real world + the simulation we're a part of.

2. We're in the real world. This isn't a simulation.

Your point is that the simulation is part of the real world, whichever world that is, and that implies that I'm wrong (about the simulation hypothesis being a perfect Harry client for the novacula Occami :snicker: ).

Let's do the math.

From the simulator's point if view: Real world + The Simulation it creates = Real World (no issues).

From the simulated's point of view: The Simulation it's part of + The real world of the simulator > The Simulation it's part of.

and yet S(M) is always more complex than M, S(M) can always be discarded via Occam's Razor. — hypericin

You should check out Boltzmann brains, because according to that M is much more complex than S(M):

The Boltzmann brain thought experiment suggests that it might be more likely for a single brain to spontaneously form in a void (complete with a memory of having existed in our universe) rather than for the entire universe to come about in the manner cosmologists think it actually did.

...

In Boltzmann brain scenarios, the ratio of Boltzmann brains to "normal observers" is astronomically large. Almost any relevant subset of Boltzmann brains, such as "brains embedded within functioning bodies", "observers who believe they are perceiving 3 K microwave background radiation through telescopes", "observers who have a memory of coherent experiences", or "observers who have the same series of experiences as me", also vastly outnumber "normal observers". Therefore, under most models of consciousness, it is unclear that one can reliably conclude that oneself is not such a "Boltzmann observer", in a case where Boltzmann brains dominate the Universe. Even under "content externalism" models of consciousness, Boltzmann observers living in a consistent Earth-sized fluctuation over the course of the past several years outnumber the "normal observers" spawned before a Universe's "heat death".

As stated earlier, most Boltzmann brains have "abnormal" experiences; Feynman has pointed out that, if one knows oneself to be a typical Boltzmann brain, one does not expect "normal" observations to continue in the future. In other words, in a Boltzmann-dominated Universe, most Boltzmann brains have "abnormal" experiences, but most observers with only "normal" experiences are Boltzmann brains, due to the overwhelming vastness of the population of Boltzmann brains in such a Universe.

Is a map of the territory another "territory"? — Harry Hindu

It can be, e.g:

There is a Borges story, "On Exactitude in Science," about map makers who were so accurate that they would make 1:1 scale maps the same size of the territories they were mapping. Not only this, but they would carry forward enough detail that the two became indistinguishable.

Similarly, with "Funes the Memorious" there is a character whose memory is exact. He can relive entire days, but it takes him 24 hours to do so. He rejects objects. For example, referring to Carlos's dog is ridiculous, you should refer to Carlos's dog on January 19th at 8:32 AM, as that dog is totally different from the one on February 11th at 6:01 PM.

I thought they were clever little ways to poke fun at the way some metaphysics seems pretty arbitrary, grounded in human capabilities and nothing more.

Is a map of the territory another "territory"?
— Harry Hindu

It can be, e.g: — Michael

That's pretty cool. I can't imagine the the time that went into making that.

My point was that even the map is part of the territory depending on how much territory we're talking about. For instance, that map is part of the territory of the Earth that is taken to represent another part territory of the Earth, just on a smaller scale and with less detail. For instance the map you posted does not include the people of that territory. It can only represent so much being on a smaller scale than what it is representing. What parts of the real territory it represents and what parts it doesn't depends on the map-maker's intentions and goals.

Now that I think about it, a map can include itself on the map. When hiking nature trails, you will find a sign post that contains a map of the surrounding territory with a mark on the map labeled, "You are Here". It's not really where you are, it's where the map is because you move along on the trail but the map and it's mark of where "you" are doesn't move. So the mark is really where the map is, not where you are.

Let's look at this from a human perspective. The possibilities are:

1. We're in a simulation, meaning there's the real world + the simulation we're a part of.

2. We're in the real world. This isn't a simulation.

Your point is that the simulation is part of the real world, whichever world that is, and that implies that I'm wrong (about the simulation hypothesis being a perfect Harry client for the novacula Occami :snicker: ).

Let's do the math.

From the simulator's point if view: Real world + The Simulation it creates = Real World (no issues).

From the simulated's point of view: The Simulation it's part of + The real world of the simulator > The Simulation it's part of. — Agent Smith

I don't understand your point.

It's really simple. A simulation is part of reality in the same way that the Earth is part of reality and the same way the Andromeda galaxy is part of reality and the same way our universe is part of the multiverse (reality). It's not a mathematical relation. It's a spatial relation.

Even heaven and hell (if they were to exist) are part of reality with reality being the entirety of all causal relations. The events in our universe would have a causal relation with the events in heaven and hell with your actions here in this world determining whether you go to heaven or hell, and God - being in heaven - creating the universe. Heaven, hell and our universe would not be separate "realities". They are all part of one reality because they all interact with each other (Occam's Razor) and any boundaries between them would be arbitrary constructions of our mind.

I don't understand your point. — Harry Hindu

Not surprised.

You have a point monsieur - the simulation is part of the real world; you said the same thing about the notion of unnatural many suns ago if you recall.

The difference between unnatural and simulation is that yhe latter is a world and so deserves, how shall I put it?, equal respect as the real deal.

You have a point monsieur - the simulation is part of the real world; you said the same thing about the notion of unnatural many suns ago if you recall. — Agent Smith

What I said about the distinction between natural and unnatural (artificial) has nothing to do with the distinction between reality and simulation.

The difference between unnatural and simulation is that yhe latter is a world and so deserves, how shall I put it?, equal respect as the real deal. — Agent Smith

So you think that simulated people deserve the same rights as real people?

What I said about the distinction between natural and unnatural (artificial) has nothing to do with the distinction between reality and simulation. — Harry Hindu

That's an odd statement to make.

So you think that simulated people deserve the same rights as real people? — Harry Hindu

We could be simulations, in fact that's what follows if you think my argument based on the novacula Occami is flawed and you do. Do we deserve the same rights as our creator(s)?

We could be simulations, in fact that's what follows if you think my argument based on the novacula Occami is flawed and you do. Do we deserve the same rights as our creator(s)? — Agent Smith

No, we wouldn't. But I doubt we're simulations. Why would the creators create simulations that create simulations? What would be the point?

No, we wouldn't. But I doubt we're simulations. Why would the creators create simulations that create simulations? What would be the point? — Harry Hindu

I see. I'm sorry if you feel that way about the rights of simulated beings knowing full well that we ourselves could be them.

There are n number of reasons why someone capable of creating a simulation would do so - from play to research, and everything in betweeen.

Thier case might be the more parsimonious actually, — Count Timothy von Icarus

Not at all. It is only a superficial parsimony, as you subtracting some constants, while adding a whole additional universe. It is like theism, "because god wills it" is only superficially parsimonious, when in reality it adds a whole new class of entity to the universe that makes laws, rather than follows them. How does that work? Is there a whole new set of laws that govern god's behavior?

We have an issue because mathematics tells us we should be able to have continuous things, but instead we only have discrete things — Count Timothy von Icarus

Mathematics doesn't "tell us" this. Just because reality sometimes follows structures predicted in math doesn't mean that the existence of a mathematical construct is any kind of argument for it's instantiation in reality.

Help me understand, why should a brain spontaneously materializing be more likely than one evolving naturally?

Help me understand, why should a brain spontaneously materializing be more likely than one evolving naturally? — hypericin

This is what the Wikipedia article says:

The Boltzmann brain thought experiment suggests that it might be more likely for a single brain to spontaneously form in a void (complete with a memory of having existed in our universe) rather than for the entire universe to come about in the manner cosmologists think it actually did.

A brain evolving naturally requires a much larger ecosystem (a Star, a habitable planet, millions of years of reproduction and natural selection, etc., all of which have prior requirements of their own). That is far more complex than just a brain forming in a void.

Mathematics doesn't "tell us" this. Just because reality sometimes follows structures predicted in math doesn't mean that the existence of a mathematical construct is any kind of argument for it's instantiation in reality. — hypericin

Well that of course depends on your attitudes towards mathematical Platonism and the Quine-Putnam Indispensability Argument. Is math something we discovered, or something we invented? If math is the study of patterns, and most of the patterns we started with (e.g. Euclid's descriptions of 2D space) are continuous, what's up with that? How does our limited cognitive power offer up a finer grained (indeed, infinitely finer grained) reality than that which seems apparent?

That is, anyhow, the rationale within which simulation theorists tend to put forth conclusions. I don't find it terribly convincing, for one because space-time seems like an entity ready to get torn up and replaced; it's in the sort of rough shape that Newtonian space was in the late 19th century. So, I honestly think we have no idea what we'll find in terms of things matching up with mathematics at a basic level.

Second, I think you're right that lurking behind any simulation is a another set of metaphysical questions about the nature of the simulator.

Some "simulationesque" formulations don't have this problem. The "Holographic Universe," doesn't propose God-like alien simulators, but rather follows the natural conclusion of the observation that the information content of a thing is determined by its 2D surface area and that information only exchanges across 2D surfaces. In this related argument, 3D space and time are illusory, a sort of hologram created by 2D information theoretic structures.

The other simulation-like model is the idea that our brains essentially hallucinate/simulate a reality. The information content our bodies are exposed to is orders of magnitude greater than the information our sensory organs take in (this has to be the case or we'd succumb to entropy). The actual data our sensory organs take in is orders of magnitude greater than what makes it to consciousness. Each step along the way from incoming sense data to consciousness involves massive amounts of data compression, as well as computation to shape the data into something useful. The systems we inherit aren't selected for on the basis of how well they actually represent reality, but only how well they allow genes or other informational units to replicate. Donald Hoffman's "The Case Against Reality," has a good summation of this set of ideas.

In that sense, the world around us is a simulation. 3D space-time might actually be an error compressing code that evolution hit upon, an effective means of encoding fitness information, rather than the structure of reality.

These similar types of arguments I find more plausible, even if they make metaphysics more difficult. The long history of arguments over objects, their related universals or tropes, if they posses a pure substratum of haecceity, etc. might all be simply an artifact of how our cognition is optimized to sort out patterns and define things as discrete "objects."

That all said, I still don't think the size of said simulation works against simulation theories. Reason being that a simulator would only need to simulate the areas you're currently looking at, not the entire universe. It could be analogous to video games, which render the world around them based on the players' line of sight.

Is math something we discovered, or something we invented? — Count Timothy von Icarus

But this is a different question than whether the math is instantiated in the world. For instance, I believe the Mandelbrot set was discovered: after all, it has an endless capacity to surprise. But it is not instantiated in the world. At best, tiny fragments are echoed in computer programs. Similarly, numbers like 10^100000000000000000000 are numbers, but we needn't believe that magnitudes of this scale exist in reality.

How does our limited cognitive power offer up a finer grained (indeed, infinitely finer grained) reality than that which seems apparent? — Count Timothy von Icarus

It seems straightforward to me. From our perspective, reality is so fine grained it appears to be continuous. Real numbers are a mathematical abstraction of the seemingly continuous quantities that present themselves to us. Whether or not reality itself is continuous at its fundamental level is an entirely different question.

In this related argument, 3D space and time are illusory, a sort of hologram created by 2D information theoretic structures. — Count Timothy von Icarus

3D space and time are the built in models our brains build from the 2D perceptions it receives. Does it follow that the model is wrong? It is hard to see it's survival value if so.

3D space-time might actually be an error compressing code that evolution hit upon, an effective means of encoding fitness information, rather than the structure of reality. — Count Timothy von Icarus

This seems tangential to the original argument. This is not S(M), rather it is suggesting suggesting an alternate, unspecified M to 3D space and time.

Reason being that a simulator would only need to simulate the areas you're currently looking at, not the entire universe. It could be analogous to video games, which render the world around them based on the players' line of sight. — Count Timothy von Icarus

Even here it is not obvious to me. Simulations of the caliber of our actual waking lives are so far beyond us, we might never achieve them, even if technological progression continues uninterrupted for a million years. It may be beyond our universe's capacity to compute that much. Or beyond our intellect to create them. So already, this presupposes beings of godlike technological prowess, and a whole other unrelated real universe to house them, on top of all the apparent laws and objects in the simulated world. This is my basic intuition, that S(M) is never a good theory, in the absence of extraordinary evidence.

That is far more complex than just a brain forming in a void. — Michael

But I never proposed that complexity be the sole criterion for choosing a theory. That leads to absurdities like this.

Interestingly, the article cited a calculation that a Boltzmann Brain should be expected to appear once every 10^500 years. Truly an unfathomable duration, if any stock is to be placed in calculations like this. And still hard for me to believe this should happen with even that frequency. I wonder how often say a molecule of water is expected to appear.

But I never proposed that complexity be the sole criterion for choosing a theory. — hypericin

You said: "Since S(M) never possesses any explanatory power above M, and yet S(M) is always more complex than M, S(M) can always be discarded via Occam's Razor."

Replace S(M) with common sense life and M with Boltzmann brain.

Replace S(M) with common sense life and M with Boltzmann brain. — Michael

But here S(M) does possess explanatory power above M. With M we wonder how this extraordinarily unlikely event happened.

That is what I was asking you earlier, I don't fully understand the thrust of the theory. Boltzmann brians are phenomenally unlikely, so why is that a viable theory?

But here S(M) does possess explanatory power above M. With M we wonder how this extraordinarily unlikely event happened. — hypericin

The same with S(M). As the article says, "the Boltzmann brain thought experiment suggests that it might be more likely for a single brain to spontaneously form in a void (complete with a memory of having existed in our universe) rather than for the entire universe to come about in the manner cosmologists think it actually did."

So both M (Boltzmann brains) and S(M) (common sense life) are extraordinarily unlikely, but given that S(M) is less likely than M, what greater explanatory power does it have?

So both M (Boltzmann brains) and S(M) (common sense life) are extraordinarily unlikely, but given that S(M) is less likely than M, what greater explanatory power does it have? — Michael

I looked through it again, this is the argument I was looking for: "In a single de Sitter Universe with a cosmological constant, and starting from any finite spatial slice, the number of "normal" observers is finite and bounded by the heat death of the Universe. If the Universe lasts forever, the number of nucleated Boltzmann brains is, in most models, infinite; "

This is not a problem specific to my post, it is a problem for everything! It sounds silly, but I don't know how to counterargue without insisting on specific physics that rule it out. Assuming the above conditions, how can we be confident we are not Boltzmann brains?

Assuming the above conditions, how can we be confident we are not Boltzmann brains? — hypericin

We can't be, that's the problem.

We can't be, that's the problem. — Michael

And yet, if for every passing year a god were to count one atom in the (observable) universe (there are between 10^78 and 10^82 of them), by the time it had counted all of them it wouldn't have made the slightest perceptible dent in its waiting time for a single Boltzmann brain to appear. If for every atom, it begins anew the entire yearly enumeration of every atom, still, not the slightest sliver of progress, it's waiting would have not even begun.

If,
for every atom, it starts the process of,
for every atom, it starts the process of,
for every atom, it starts the process of,
for every atom, it starts the process of,
for every atom, it starts the process of,
for every atom, it starts the process of,
counting one atom every year,

Then, great! That's progress!
It just has to do that thing about another 100,000,000,000,000,000,000 (hundred quadrillion) times, and by that time it can expect one to have appeared!

Infinity is a hell of a thing.

It just has to do that thing about another 100,000,000,000,000,000,000 (hundred quadrillion) times, and by that time it can expect one to have appeared! — hypericin

Oh dear, I misread. Boltzmann brains are not expected to appear every 10^500 years. Nope, that's not even scratching the surface of scratching the surface. They are expected to appear every 10^10^50 years, which is quite another matter.

Our poor god hasn't even begun, after all. I don't even know how to do this one. It is a quantity of time that is not just beyond conception, it is beyond description at all.