Tegmark's mathematical universe hypothesis

[Sarkus]

Yes but this is where the error comes in, it seems to me. You can't build a mathematical model of something physical without first defining certain entities and their attributes, which you have to do in words. "An electron." "Energy." Momentum." etc.

None of these things can be defined by an equation without some words behind, to explain the physical concepts the equation relates together. This is where people can lose track of the physical nature of models in their worship of the maths.

Ultimately the issue may not be one of category error, but rather semantics. i.e. Tegmark may be defining things (I don't know if he is, I haven't examined his work that closely) such that their equivalence is assumed.
I also have no doubt he has an argument for asserting their equivalence (the model of the duck, and the duck etc), but also one must consider that if a "physical" object is so perfectly described by mathematics that one can simply conclude that the object thus is mathematics. The particles, the sub-atomic particles, are all perfectly described by mathematics, as are their interactions. Our experiences of something as "solid" or "wet" are then just interpretations of the mathematics, with meaning only in the conscious mind, which is itself simply a mathematical process / structure / whatever.
I would be interested to hear someone's summary of how he does argue their equivalence, ideally from someone who seems to name-drop Tegmark as if they actually understand this work of his, if just to save me time of wading through hours of videos to find such a thing.

 

[exchemist]

Ultimately the issue may not be one of category error, but rather semantics. i.e. Tegmark may be defining things (I don't know if he is, I haven't examined his work that closely) such that their equivalence is assumed.
I also have no doubt he has an argument for asserting their equivalence (the model of the duck, and the duck etc), but also one must consider that if a "physical" object is so perfectly described by mathematics that one can simply conclude that the object thus is mathematics. The particles, the sub-atomic particles, are all perfectly described by mathematics, as are their interactions. Our experiences of something as "solid" or "wet" are then just interpretations of the mathematics, with meaning only in the conscious mind, which is itself simply a mathematical process / structure / whatever.
I would be interested to hear someone's summary of how he does argue their equivalence, ideally from someone who seems to name-drop Tegmark as if they actually understand this work of his, if just to save me time of wading through hours of videos to find such a thing.

Yet it seems to me maths cannot describe a physical object. All it can do is describe the object and its properties in relation to others, which need definition by means other than maths. To give an example, what equation defines an electron? Or energy? There are no such equations. The maths relies on the concepts being defined first, and then tells you the relationships between these.

 

[James R]

We can always buy his book of course (available at most reputable bookstores...)

That will only encourage him.

 

[James R]

I think there is room for confusion concerned Tegmark's hypothesis and more general philosophical ideas.

The big philosophical problem is the question of what is the true nature of existence. In the context of the present discussion, there are two ideas that I think we should exclude upfront.

The first idea is the problem of hard solipcism. Solipcism is the claim that we cannot be sure that anything exists, apart from our own minds. Actually, you can't be sure that my mind exists, except as some notion in your mind. This means that there's no way to know whether ducks - or anything else normally considered external to your mind - actually exist separately from your mind.

It seems to me that solipcism is, by its nature, an unfalsifiable hypothesis. No conceivable test could ever show that it is false. Therefore, we should leave it to one side when we ask questions like "what is the ultimate nature of our universe?" Not discount it - because it can't be disproved - but just put it aside as something that we can't investigate further. The universe may be an illusion created by your mind, but to make any progress, we have to adopt as a working assumption that things other than your mind have some reality of their own.

The second idea is the "simulation hypothesis". This is the claim that the outside world that you are aware of is generated entirely by some external agency pumping sensations into your head, which you take as real. You might, for example, be a brain in a vat, fed sensory information directly into your neurons by some sort of computer. This idea is different from solipcism because it does not assume that your mind and everything else in the (apparent) universe are one. It contemplates the existence of other beings or entities ourself of yourself, which have their own, separate existence beyond your ability to perceive.

This, too, is an unfalsifiable hypothesis. There is nothing you can do to disprove that you are in a simulation. Therefore, this is another useless avenue for speculation (by us) about the nature of the universe we actually perceive.

We come, then, to Tegmark's claim that the universe is mathematics. One thing to note, before we go on, is that if the simulation hypothesis is correct, that doesn't support Tegmark's hypothesis. If you and are I just digital data in some kind of machine run by aliens, it still does not follow that we and our universe are "made of mathematics". A simulation would need to run on something - just something is inaccessible to our senses.

So, let's step away now from these unfalsifiable philosophical hypotheses and accept, for the sake of argument, that you really do exist separately from ducks (that they aren't just things in your head) and that, as far as we can tell, our universe is "real", in the sense that it will go on existing after you're no longer aware of it. Let us also agree that, even if we are in a simulation, there appear to be certain rules and regularities that we can investigate from inside the simulation, even if we can never look outside it. Let's do what we can do.

Now we're into the realm of observation and science. We observe that that there are two types of things in our world - physical objects and ideas. Put simply, physical objects are things that can be touched or otherwise sensed. They exist outside our minds which, for the sake of argument, we are accepting as separate from one another and from the universe at large. Ideas, on the other hand, are thoughts in our heads. They are information. We can communicate them to other people, to a certain extent using physical media, but they cannot be touched or otherwise sensed.

What is mathematics? Is it a physical object (or collection of physical objects) that we can touch or otherwise sense? I say: it is not. It is a collection of ideas. Tegmark, on the other hand, says that mathematics and physical objects are one and the same. He wants to abolish the distinction. In Tegmark's world, the number 3 is on the same ontological footing as a real-life duck. Tegmark says that mathematics is the ultimate reality: the duck is mathematics, along with every other thing that you and I would normally call a "physical object".

The main problem I have with Tegmark's hypothesis is that I think it's a dead end in terms of suggesting any useful programme of research to better understand the universe in which we find ourselves (simulated or otherwise, as the case may be). Worse, I think Tegmark has lost his grip on what for (most of) the rest of us is the common-sense appreciation that concepts are different from physical objects. We recognise that the idea of an apple is not an apple. But for Tegmark, both the idea of the apple and the apple itself are the same thing, in essence. That is, both the idea of the apple and the apple itself are, he claims, mathematics.

Another way to explain this is using the analogy of the map and the territory. The idea of an apple is like a map. It is what allows us to recognise physical apples when we encounter them. The physical apples themselves are the territory that the map describes. Similarly, Einstein's theory of general relativity is an idea - it describes the "territory" of the physical space and time that we experience. Einstein's theory is a set of ideas which can be expressed partly using mathematics, but it is a category error to mistake a description of spacetime for spacetime itself. It is a category error to mistake the idea of a duck for a duck.

Suppose we accept Tegmark's hypothesis, and hold that everything is mathematics - indeed, there is only mathematics. What follows? Having abolished the distinction between ideas and physical objects, it seems to me that we're in for a whole lot of problems. It might be okay to accept that the idea of an apple is not very different from an apple, at a stretch, but the idea of Godzilla appears to be very different from Godzilla, in an important way. Even when it comes to mathematics itself, we immediately run into difficulties. The idea of a tesseract is perfectly valid mathematics, but we observe no tesseracts in our physical world. Yet Tegmark would have to say that tesseracts are on an equal footing with apples (not to mention apples and Godzilla) when it comes to appreciating what is real in our world.

Tegmark's hypothesis also appears to be unfalsifiable. How could we test to find the difference between the idea of an apple and an apple? In Tegmark's universe, there can be no such test. Maybe the idea of an apple involves slightly different mathematics than the physical apple, but Tegmark would hold that both are mathematics none the less. Also: at what level of probing will a physical apple be seen to be nothing but mathematics? At what point does it become apparent that the physical things and the ideas have become one and the same? Because, from where I'm standing right now, those two things look very different.

None of this proves that Tegmark is wrong, of course. But I wonder whether Tegmark himself would concede that it's important to maintain a distinction between things and ideas, regardless of whether he believes, in the end, that they are one and the same. I don't think think I could take him seriously if he said that he wouldn't concede that.

To summarise: I just think that Tegmark's hypothesis makes a horrible mess of basic ontology and is practically useless in that it doesn't help to advance any actual knowledge that we have about our world. I also suspect that Tegmark hasn't really thought it through. I would suggest that maybe he should have taken a few classes in philosophy, alongside his physics.

 

[Pinball1970]

I posted Massimo's criticism of Tegmark/Shapiro in post 50. Peter Woit gives a thoroughly damning review of his ideas, as expresed in a recent book, here: https://www.math.columbia.edu/~woit/wordpress/?p=6551

I read the reviews and yes they are damning. More style than substance is the impression I am getting from Tegmark.
Very surprised he did not reference any note worthy mathematicians in this thesis, this is ultimately a book about the universe BEING mathematics!
Things have certainly moved on since 2014 and modern cosmology DOES favour some models of the universe that are infinite.
Interesting part regarding Gödel too, a universe with in built logical absurdities?
String theory too? 40 years with no results?
I want to check on Tegmark see what he is doing now. I will feedback.

 

[Pinball1970]

That will only encourage him.

I will not be getting the book, it is already ten years old and I do not read pop sci.
The reviews are enough to put me off such a book too.

 

[Sarkus]

The second idea is the "simulation hypothesis". This is the claim that the outside world that you are aware of is generated entirely by some external agency pumping sensations into your head, which you take as real. You might, for example, be a brain in a vat, fed sensory information directly into your neurons by some sort of computer. This idea is different from solipcism because it does not assume that your mind and everything else in the (apparent) universe are one. It contemplates the existence of other beings or entities ourself of yourself, which have their own, separate existence beyond your ability to perceive.

I'm afraid this is not entirely correct. The simulation hypothesis is not that we could be some brain in a vat, but rather that we are ourselves a simulation. Not some VR or other physical existence where only the inputs are simulated, but we ourselves are simulated. We ourselves are nothing but 1s and 0s.This is a very different proposition to being a brain ina a vat.
You're quite correct, though, in that it is not falsifiable, and I only raised it as an interesting aside that offers a different argument for at least our existence being "mathematical" in nature. But it is still worth correcting you on your understanding of it, so that one can appreciate the overlap of ideas with the MUH.

Anyhoo... Carry on.

 

[exchemist]

I read the reviews and yes they are damning. More style than substance is the impression I am getting from Tegmark.
Very surprised he did not reference any note worthy mathematicians in this thesis, this is ultimately a book about the universe BEING mathematics!
Things have certainly moved on since 2014 and modern cosmology DOES favour some models of the universe that are infinite.
Interesting part regarding Gödel too, a universe with in built logical absurdities?
String theory too? 40 years with no results?
I want to check on Tegmark see what he is doing now. I will feedback.

Yes, do that. I'd be interested, in particular whether he has addressed Pigliucci's suspicion that he is simply confusing the order displayed by nature, much of which* can be expressed by mathematics, with it actually being mathematics, and if so what he means by that.

*By the way, I am far from convinced that all of nature can be expressed by mathematics. Certainly it looks as though all of physics can, but there is more to nature than physics, provocative remarks by Lord Rutherford notwithstanding.

Over the years I have got the sense that Americans scientists, in particular, seem to have a great reverence for mathematics. It is commonplace on science forums for Americans to dismiss ideas by saying "show us the math[sic]" , or something equivalent. Maths seems to have been put on a pedestal, such that it is considered the apotheosis of scientific endeavour to reduce everything to maths. Tegmark looks like what happens when this process goes to completion.

With most ideas in which there is an element of truth, taking it to extremes tends to lead to silly results. I wonder if this is what we are seeing with the Tegmark/Shapiro phenomenon.

 

[James R]

I'm afraid this is not entirely correct. The simulation hypothesis is not that we could be some brain in a vat, but rather that we are ourselves a simulation. Not some VR or other physical existence where only the inputs are simulated, but we ourselves are simulated. We ourselves are nothing but 1s and 0s.This is a very different proposition to being a brain ina a vat.

My mistake. You're right, of course.

Nevertheless, the simulation hypothesis still implies that our 1s and 0s are encoded in some physical substrate somewhere. The simulation must run on something. It also wouldn't make our universe mathematics.

The brain the vat is not very different. It just assumes that the relevant substrate for the simulation to run on is, in part, a physical human brain.

 

[Sarkus]

Nevertheless, the simulation hypothesis still implies that our 1s and 0s are encoded in some physical substrate somewhere. The simulation must run on something. It also wouldn't make our universe mathematics.

It's not as simple as that, though. If we are a simulation, then nothing in our universe is real, including ourselves. The substrate upon which those 1s and 0s reside does not exist in our universe. Our universe is entirely the 1s and 0s, and the relationships between them. I.e. mathematics. There is no need to even consider the substrate, as it is irrelevant to our universe (the simulated universe).

The brain the vat is not very different. It just assumes that the relevant substrate for the simulation to run on is, in part, a physical human brain.

No, it is very different, I think. The Brain in a Vat (BiaV) gedanken is merely about a change in the perceptions, from reality to a virtual reality. The processing and substrate still exist within the universe, in both universes (real and virtual). This makes it very different to the SH, where there is no such substrate that exists in the simulated universe.
There is/may be outside of that universe, but the MUH concludes that our universe is mathematical, and the SH would seem to conclude the same. So to dismiss it as casually as you do is to misunderstand it, I think, or at least its relevance to the MUH.

But, that said, I am not sure how either the SH or MUH are testable. They seem to be more metaphysical and philosophical than anything else.
Maybe Write4U can explain how the MUH is testable?

 

[Halc]

I've bailed on much of this discussion, especially the derailments, but am nevertheless trying to keep up.

What's the difference between declaring the universe a "physical structure" and declaring it a "mathematical structure"?

'Physicial' in this context seems to be a reference to the mathematical structure of which we are a part. We consider the primitives of that structure to be physical, and give them physical names like 'electron' and such. A simple mathematical structure (a given triangle say) doesn't seem meaningfully physical. It's just a geometric planar polygon. The words we use to describe one are tools of abstraction, but a triangular mathematical structure is just that simple thing. It isn't a graph or a picture or any other abstract representation, all of which are mental and physical concepts.

If the latter is completely disassociated from graphics or pictures, then "mathematical structure" might become radically different by consisting purely of technical description

Well, it's the thing in itself, not a description at all. The description is one of the things one needs to disassociate from it. A system of just a triangle has nothing capable of creation of a description of anything.
A tesseract is a 4D mathematical structure, and yet one that cannot be physical. It cannot be approximated in our universe, which lacks sufficient spatial dimensions..

But that's the point where few, if anybody, can fathom what mathematical realists (in general) are claiming with respect to their abstract entities being "real", or how they exist.

Unlike Tegmark, I'm not a mathematical realist, which is another word for mathematical Platonism. I perhaps can defend that the universe is a mathematical structure, but I would not go so far as to suggest it has (or needs) the property of being real. A triangle has 3 sides and 3 angles, no? Or does one have to first establish that it has this other property before it can the property of having 3 angles? A relational ontology makes more sense to me, and that seems somewhat irrelevant to MUH.

So one structure that often comes up is the Mandelbrot set, which is often approximately represented via a 2D image. The name we gave it is human. It is, in its fundamental form, nothing but a mathematical set of complex numbers that have a certain property, as being distinct from the rest of the complex numbers that do not have that one property..

We've not yet discovered the description of the nature of the mathematical object that is us. It would be something on the order of some wave function, and its evolution as per something resembling the Schrodinger equation. The actual written expression of these things is not required, only for us to abstract it. Like the tesseract, that structure has certain properties that are independent of some abstract entity actually considering it. So one of the properties of our structure is that it has observers capable of learning the nature of the structure itself. To deny that is to deny that mathematics alone can describable our universe, which so far doesn't seem to be the case. It also can be a denial of naturalism, but then the view is anti-science. Searle comes to mind as an example of this.

The MUH is philosophy, and apparently Tegmark, while an accomplished Physicist, is an unaccomplished metaphysician. He proposes all sorts of empirical tests for his view, none of which hold water. On the other hand, the view is quite open to logical and statistical analysis, and it is in these areas it needs to defend itself. In particular, I paraphrase Carroll, whose words regarding a somewhat unrelated topic seem nevertheless appropriate:
"The issue is not that the MUH hypothesis is ruled out by data, but that some MUH theories are cognitively unstable: they cannot simultaneously be true and justifiably believed."
That's a mix of his words (not speaking of MUH) and mine. Tegmark does not address this problem. The gist of the problem is that so many mathematical structures are uninteresting, to the point where it is far more likely that we're one of the uninteresting ones instead of the interesting one we posit. That's a painful criticism of MUH, one for which I have no easy reply.

Which seems to be an obscured way of mathematical realists claiming (without the directness) that the universe is a simulation.

Those that suggest that seem to not realize the difference between a mathematical structure and a simulation of one. By definition, our universe cannot be a simulation. It can be simulated (not by any classical means, but still...). And those that posit it often confuse a simulation with virtual reality, without knowing the difference between the two.

 

[Halc]

The big philosophical problem is the question of what is the true nature of existence. In the context of the present discussion, there are two ideas that I think we should exclude upfront.

Pretty much all of philosophy is unfalsifiable, at least the valid views. I agree with your list (both versions of solipsism) because indeed, both render empirical evidence meaningless. Perhaps MUH does as well, per my post just above. To you list I would add any kind of anthropocentrism. Both in your list are versions of it, and I name the more general case. Nothing can really be known about the nature of reality if reality is all about me.

The first idea is the problem of hard solipcism. Solipcism is the claim that we cannot be sure that anything exists, apart from our own minds. Actually, you can't be sure that my mind exists, except as some notion in your mind. This means that there's no way to know whether ducks - or anything else normally considered external to your mind - actually exist separately from your mind.

We come, then, to Tegmark's claim that the universe is mathematics. One thing to note, before we go on, is that if the simulation hypothesis is correct, that doesn't support Tegmark's hypothesis.

What you described in your post is a VR hypothesis, a version of solipsism. Tegmark does not seem to suggest anything of the kind. He says mathematics is fundamental. Both the simulation and the VR thing posit a more fundamental reality on which our reality is being implemented. So no machine under the mathematics. Nobody seems to get that.

[/QUOTE]So, let's step away now from these unfalsifiable philosophical hypotheses and accept, for the sake of argument, that you really do exist separately from ducks (that they aren't just things in your head) and that, as far as we can tell, our universe is "real"[/QUOTE]The universe doesn't have to 'be real' in order for me to be separate from the duck, for the duck to not depend on me or any other observer to be a duck. I suppose it depends on humans to have the human name 'duck' attached to it, but that's about as far as it goes.

I find it more useful to define 'real' or 'exists' as a relation of A measures B. So the duck is real relative to anything that measures it, like say the water. The water is affected by the displacement of the duck, so the duck exists in relation to the water. That's seems a more useful definition, a relation instead of a property. But that's just me. Tegmark is pretty obviously a realist, and says the duck is part of the universal structure, and so are you, so there cannot be a duck without you since you're both part of the same thing. But the universe, being real, exists as much as any other mathematical structure. That's the level-4 multiverse thing going on. His assertions, not mine, but more mainstream (and also naive in my opinion).

in the sense that it will go on existing after you're no longer aware of it.

You seem to have a presentist definition of existence, that things stop existing after a time. Just something I notice. The MUH thing seems incompatible with presentism since it would entail the mathematical structure existing within time, making time more fundamental than the mathematics, a contradiction of the premises.

Let us also agree that, even if we are in a simulation, there appear to be certain rules and regularities that we can investigate from inside the simulation, even if we can never look outside it. Let's do what we can do.

Now we're into the realm of observation and science. We observe that that there are two types of things in our world - physical objects and ideas. Put simply, physical objects are things that can be touched or otherwise sensed. They exist outside our minds which, for the sake of argument, we are accepting as separate from one another and from the universe at large. Ideas, on the other hand, are thoughts in our heads. They are information. We can communicate them to other people, to a certain extent using physical media, but they cannot be touched or otherwise sensed.

This again is the VR idea, with artificial inputs to real minds. Dualism does indeed have empirical falsification tests, which nobody seems to pursue since I suspect the proponents fear the falsification. It becomes a matter of faith. All the arguments seem to be faith and incredulity based. If I am a real mind controlling a simulated avatar body, it is pretty easy to show that the decisions made by the avatar do not come from the avatar itself, but from outside.

What is mathematics? Is it a physical object (or collection of physical objects) that we can touch or otherwise sense? I say: it is not. It is a collection of ideas.

The mathematics in context of the MUH is not about ideas or abstractions. Once again, nobody seems to get that, and thus the incredulity. The hypothesis is not suggesting that the universe is the product of any abstracting entity, a sort of higher level universe implementing the lower one.

Tegmark, on the other hand, says that mathematics and physical objects are one and the same. He wants to abolish the distinction.

That's a misrepresentation of what he says. A tesseract for instance is not physical. To us, it is an abstraction, an idea, the map so to speak. An actual tesseract would be neither of these things. A physical approximation of a triangle could be made, but our physics does not support the creation of an actual physical triangle.

In Tegmark's world, the number 3 is on the same ontological footing as a real-life duck.

That's a begging statement since you're implying that the duck is real life and 3 is not. Attack the hypothesis on its own ground instead of adding your own premises. The duck is part of a mathematical structure, and 3 is a valid mathematical structure on its own, so perhaps in Tegmark's world, 3 is on somewhat more solid ontological footing than is the duck, a mere component of a far more complex structure. The duck is physical because anything that is part of our structure is considered 'physical' by other parts of that same structure. The word 'physical' is merely a means of self reference in that regard. I saw no suggestion that 3 was a physical thing.

The main problem I have with Tegmark's hypothesis is that I think it's a dead end in terms of suggesting any useful programme of research to better understand the universe in which we find ourselves (simulated or otherwise, as the case may be).

Agree there. It's philosophy, and almost all of philosophy has this problem. Research is for science. MUH is not science.

What follows? Having abolished the distinction between ideas and physical objects,

This distinction has never been abolished. The hypothesis is not about ideas at all. So much of your post here obviously assumes otherwise. You cannot critique the hypothesis if you don't get that.

 

[James R]

Sarkus:

It's not as simple as that, though. If we are a simulation, then nothing in our universe is real, including ourselves. The substrate upon which those 1s and 0s reside does not exist in our universe. Our universe is entirely the 1s and 0s, and the relationships between them. I.e. mathematics. There is no need to even consider the substrate, as it is irrelevant to our universe (the simulated universe).

This sort of response is why I took some time to explain why I didn't want to discuss the simulation hypothesis. It's a distraction from Tegmark's hypothesis.

Tegmark's hypothesis is, I assume, about our universe - the universe we perceive and have access to. Tegmark claims that our universe is mathematics. I say that, in our universe, there is an obvious and clear distinction between ideas and physical things, and that mathematics is firmly in the realm of ideas rather than physical things. Hence, physical things cannot be "made of mathematics". It's a category error to assume that they could be.

As for the simulation hypothesis, which as I pointed out is an unhelpful distraction from the topic we're supposedly discussing here, if there is a physical substrate on which those 1s and 0s are being stored and processed - necessarily a substrate that is not part of our measurable universe, as you said - then it is not true to say that our universe is mathematics, as a matter of fact.

The simulation hypothesis is an unhelpful distraction because it merely bumps Tegmark's ideas up one metaphysical level, in effect, where they are found to be wrong for the same reasons.

No, it is very different, I think. The Brain in a Vat (BiaV) gedanken is merely about a change in the perceptions, from reality to a virtual reality. The processing and substrate still exist within the universe, in both universes (real and virtual). This makes it very different to the SH, where there is no such substrate that exists in the simulated universe.

It's not very different.

In the simulation hypothesis, you have universe A being a simulation run on a computer of some kind that has some physical existence in universe B. Universe B is, of course, completely unperceivable from inside universe A.

In the brain in a vat scenario, you have a computer and a human brain in universe B, which creates the perception of a simulated universe A in the brain. Again, the person experiencing simulated universe A has no effective access to universe B.

You are trying to teach me to suck eggs by telling me that the brain in a vat is fundamentally different from the simulation hypothesis. But from the point of view of the person perceiving universe A, it is really no different at all. In both cases, universe B is equally out of reach for the person who perceives universe A. When the person who perceives A tries to determine the ultimate nature of his reality, he is necessarily restricted because the only observations he can make occur within universe A. It doesn't matter whether A is a simulation in a biological brain or in some other kind of computer.

As for Tegmark - just to repeat - whether or not we're in a simulation, Tegmark's mathematical universe hypothesis still fails to distinguish between mathematics and physics - a clearly meaningful distinction in the only universe we can test - universe A.

 

[James R]

Halc:

What you described in your post is a VR hypothesis, a version of solipsism. Tegmark does not seem to suggest anything of the kind. He says mathematics is fundamental. Both the simulation and the VR thing posit a more fundamental reality on which our reality is being implemented. So no machine under the mathematics. Nobody seems to get that.

I get it. It was, in fact, precisely the point I was trying to make post #79. Perhaps I didn't express myself clearly enough. I have tried again in post #98, above.

The universe doesn't have to 'be real' in order for me to be separate from the duck, for the duck to not depend on me or any other observer to be a duck.

How could you not believe that the universe is real? (Are you thinking of a simulation? Does a simulation have no reality? I just don't know what you're talking about.)

I find it more useful to define 'real' or 'exists' as a relation of A measures B. So the duck is real relative to anything that measures it, like say the water.

So, while I sit here in Australia, is the Eiffel tower real? I'm not currently measuring it. Are you confident that something else is measuring it, to keep it real? What gives you that confidence?

I'm a little worried that your definition leads to the idea that reality is merely a matter of perception. It threatens to lead us down a slippery slope towards things being "real for me" and "not real for you", simultaneously, which I think is highly metaphysically problematic.

Tegmark is pretty obviously a realist, and says the duck is part of the universal structure, and so are you, so there cannot be a duck without you since you're both part of the same thing.

I don't think he says there can't be a duck without me. He says that a duck is mathematics, and I am a separate bit of mathematics, and we both exist in a universe that is entirely mathematics. But I don't think he would consider either myself or the duck to be a necessary part of that universe.

But the universe, being real, exists as much as any other mathematical structure.

Mathematical structures don't have the type of "existence" that I want from my universe.

I also think there are many mathematical structures that are not instantiated in any way in our physical universe, which seems like a problem for Tegmark's hypothesis. If our universe is mathematics, why just this mathematics, and not some other mathematics?

You seem to have a presentist definition of existence, that things stop existing after a time.

Maybe I do. In what sense would you say that things don't stop existing after a time? Is there some problem you think I need to correct?

The MUH thing seems incompatible with presentism since it would entail the mathematical structure existing within time, making time more fundamental than the mathematics, a contradiction of the premises.

In the MUH, surely time would just be more mathematics?

This again is the VR idea, with artificial inputs to real minds. Dualism does indeed have empirical falsification tests, which nobody seems to pursue since I suspect the proponents fear the falsification.

Can you give me an example of a test that falsifies (or could falsify) dualism?

If I am a real mind controlling a simulated avatar body, it is pretty easy to show that the decisions made by the avatar do not come from the avatar itself, but from outside.

How would you go about showing that? (Please read post #98, above, first.)

The mathematics in context of the MUH is not about ideas or abstractions. Once again, nobody seems to get that, and thus the incredulity. The hypothesis is not suggesting that the universe is the product of any abstracting entity, a sort of higher level universe implementing the lower one.

I agree. This is why talk of solipsism and simulation hypotheses are not relevant to the discussion of the MUH. It's why I wanted to take a little time to set those things to one side, because it seems to me that some people here think they are important for the MUH.

Unfortunately, I think I might have had the opposite effect. Now people seem more interested in talking about the peripheral matters than the ones that are actually relevant.

That's a begging statement since you're implying that the duck is real life and 3 is not.

That's exactly what I'm implying. It's my major objection to Tegmark's hypothesis. How can "3" make a duck?

Attack the hypothesis on its own ground instead of adding your own premises.

Which premises do you think I have added?

The duck is part of a mathematical structure...

That's Tegmark's claim. I think it is misguided, for reasons I have explained.

What do you think? Do you think that a duck is a mathematical structure?

..., and 3 is a valid mathematical structure on its own, so perhaps in Tegmark's world, 3 is on somewhat more solid ontological footing than is the duck, a mere component of a far more complex structure.

No. They are both mathematics, according to Tegmark, so are on an equal footing, like I said.

The duck is physical because anything that is part of our structure is considered 'physical' by other parts of that same structure. The word 'physical' is merely a means of self reference in that regard. I saw no suggestion that 3 was a physical thing.

As I said, I think that this idea abolishes the useful - not to mention common-sense - distinction between matter and ideas. It seems more obfuscatory than useful.

This distinction has never been abolished. The hypothesis is not about ideas at all. So much of your post here obviously assumes otherwise. You cannot critique the hypothesis if you don't get that.

Do you claim that mathematics is something other than conceptual?

 

[Sarkus]

This sort of response is why I took some time to explain why I didn't want to discuss the simulation hypothesis. It's a distraction from Tegmark's hypothesis.

Then don't reply, James R. The more I think about it the more I find it is useful in this discussion, and not a distraction at all.

Tegmark's hypothesis is, I assume, about our universe - the universe we perceive and have access to. Tegmark claims that our universe is mathematics. I say that, in our universe, there is an obvious and clear distinction between ideas and physical things, and that mathematics is firmly in the realm of ideas rather than physical things. Hence, physical things cannot be "made of mathematics". It's a category error to assume that they could be.

It appears to be, given what I know of the MUH, but then I am not an expert in his arguments. I find comparing to the SH helps, though. What are his arguments for either ignoring or accepting what you perceive to be this category error? I assume you know, to be able to assert his hypothesis as being based on this error?

As for the simulation hypothesis, which as I pointed out is an unhelpful distraction from the topic we're supposedly discussing here,...

And which I'm pointing out is useful and not a distraction...

if there is a physical substrate on which those 1s and 0s are being stored and processed - necessarily a substrate that is not part of our measurable universe, as you said - then it is not true to say that our universe is mathematics, as a matter of fact.

???
Just above you refer to the MUH as being "about our universe - the universe we perceive and have access to". No disagreement there. But now here, with regard the SH, you're not giving the same benefit. Yet you say specifically that any substrate "is not part of our measurable universe". Both the MUH and the SH are about the universe that those within the universe experience. Therefore any substrate of the SH is an irrelevant consideration. All that is relevant is whether the universe under consideration is mathematical or not. The SH universe would seem to be - the abstract 1s and 0s and the maths that guides their interactions. All abstract. All maths.

The simulation hypothesis is an unhelpful distraction because it merely bumps Tegmark's ideas up one metaphysical level, in effect, where they are found to be wrong for the same reasons.

They are both in relation to this universe. The SH doesn't bump his ideas anywhere, as they are talking about the same thing. Whereas the SH specifies that it is a simulation, with the substrate being outside of the universe in question, the MUH is really just asserting that our universe is akin to the 1s, the 0s, and the relationships between them... in this universe.
So, no, to me at least, and perhaps to others, the SH is not an unhelpful distraction, but rather a parallel idea that can help people wrap their heads around what Tegmark might be trying to argue for, even if not entirely the same. That you don't find it helpful, sure, I get that. Then feel free to not reply to it. Don't let it distract you.

It's not very different.

Sure, whatever you say. This I actually do find to be an unhelpful distraction. Whether you understand the fundamental difference I'm trying to explain to you or not is actually irrelevant to the wider discussion. So I won't push it.

As for Tegmark - just to repeat - whether or not we're in a simulation, Tegmark's mathematical universe hypothesis still fails to distinguish between mathematics and physics - a clearly meaningful distinction in the only universe we can test - universe A.

I'll ask again: have you read and understood his MUH sufficiently to be able to assert this? Or do you mean that you are not aware of how he has distinguished it, if he has? I'm just trying to see whether you're saying you think the flaw is definitely with the MUH, or perhaps that you don't know enough about it, about his arguments, to understand how he has distinguished, if he has?

 

[Halc]

I say that, in our universe, there is an obvious and clear distinction between ideas and physical things, and that mathematics is firmly in the realm of ideas rather than physical things.

You see a distinction between the idea of an apple and an apple, the reference vs. the referent, map vs territory. You seem to accept this for most things, but then decide to treat mathematics differently by equating idea and the thing itself, equating reference to referent. This seems inconsistent to me. The distinction is clear to some of us, and the MUH presumes such a distinction, so I don't think it a valid criticism to be incapable of it.

What are physical things made of, anyway, in your opinion? What, say, composes an electron? They've never found any actual matter consuming actual volume no matter how close they look. The closer they look, the less it looks physical. That was one of the points Tegmark was trying to make in one of his replies to a suggestion that physical things are made of mathematics. I don't think Tegmark ever said physical things are made of mathematics. He said something else, that the universe is a (one) mathematical structure.

In the brain in a vat scenario, you have a computer and a human brain in universe B

BIV (the VR hypothesis) does not posit that there is a human brain. It just says mind. Sure, it is fed artificial input to make it believe it is human with a pink brain that sits in its head, but there's absolutely no evidence of that given the BIV scenario.

I get it. It was, in fact, precisely the point I was trying to make post #79. Perhaps I didn't express myself clearly enough. I have tried again in post #98, above.

I don't think you get it, because in post 98 (quoted just above), you assert that mathematics can only be an idea, denying that the idea is a mere referent to the actual mathematics, which is objective, independent of both mind and of this particular universe.

How could you not believe that the universe is real?

Being real is a relation to me. It has nothing to do with perception, but rather to do with cause and effect. Hence only the observable universe being real to me since anything outside that has no more causal effect on me than say some 5-dimensional universe with confused unicorns.

And no, I never support a simulation hypothesis, which seem a category mistake. It would be a simulation OF something, which doesn't change what the thing being simulated is. For the record, our universe cannot be classically simulated (here's a state, and now we compute the next state some short moment later). That just doesn't work with our physics.

So, while I sit here in Australia, is the Eiffel tower real?

It's been measured by you, so yes. You can't un-measure something.

I'm not currently measuring it.

You are actually. It has nothing to do with conscious measurement or 'looking at'. Stuff in Paris has a continuous effect on all particles in the planet, if nothing else, by its mass curving spacetime. It's why I used the water as the thing measuring the duck, something that doesn't do a conscious measurement.

Are you confident that something else is measuring it, to keep it real? What gives you that confidence?

It cannot cease to be. It can fall down, and be recycled into new stuff. Any of that would have an effect on you in Australia in probably under a second. To stop measuring it, you'd have to put it in a Schrodinger's box, something from which zero information can escape. Even then, the tower would exist, but its exact state (up, fallen say) might be in superposition. The largest object they've ever managed to isolate like that was barely visible to the naked eye, and even then, they only managed to keep it unmeasured for under a microsecond. Long enough to demonstrate the superposition state though.

I'm a little worried that your definition leads to the idea that reality is merely a matter of perception.

Never about that. I'm not an idealist. A rock does not perceive, but it very much is affected by its environment and thus it measures.

It threatens to lead us down a slippery slope towards things being "real for me" and "not real for you", simultaneously, which I think is highly metaphysically problematic.

You and I measure each other, and thus cannot have a significantly different list of what is real. If you and I were separated by a trillion light years, then yes, we'd have a completely different list, and neither of us would be real to the other. Again, this would be unrelated to us being conscious things. All this seems somewhat irrelevant to MUH. It's just how I define 'is real' since I find the usual (property) definition somewhat useless. Does a unicorn have a horn? How would you answer that? How might an idealist answer it? I would simply say yes.

I don't think he says there can't be a duck without me.

He doesn't talk about the duck of course, but the universe in question has a worldline of you in it, and a worldline of the duck, and these two interact. There is no 'present moment' in such a universe, so a universe that contains your worldline also has the duck worldline, else they could never have interacted. But you speak of after your death, like the universe somehow doesn't contain your worldline in that case, but it does. Only under presentism are you actually no longer part of the universe after your death, and MUH is not a presentist interpretation.

He says that a duck is mathematics, and I am a separate bit of mathematics, and we both exist in a universe that is entirely mathematics.

Maybe he says that. I read the book, a library copy. Don't have it. I don't know if he actually says a particular thing (duck) is mathematics, rather than being simply part of a mathematical structure. If the criticism revolves around that particular wording, I'd have to see the context because I would not have said that the duck is somehow some kind of separate mathematics on its own. Physics for one defines no concept of identity. The grouping of atoms into an 'object' upon which the label 'duck' is applied is strictly a conscious construct. The duck does not operate independently of the mathematics of the universe. Saying it is separate seems wrong.

But I don't think he would consider either myself or the duck to be a necessary part of that universe.

Our universe contains both, so without both, it would be a different mathematical structure, a different universe. This is similar to noting that there are other worlds (MWI worlds) that contain neither you nor the duck in question, but contain other people and ducks. There are also worlds where Earth has no life at all. But all those worlds are still part of our particular mathematical structure, and that structure contains you and the duck, in many but not most worlds. And yes, Tegmark is a big MWI fan. I am not due to my issues with realism.

 

[Halc]

Mathematical structures don't have the type of "existence" that I want from my universe.

You are of course under no obligation to accept MUH. I have problems with it myself. Tegmark was stupid enough to suggest tests, all of which are fallacious. I thought they degraded the impact of his proposal.

I also think there are many mathematical structures that are not instantiated in any way in our physical universe, which seems like a problem for Tegmark's hypothesis. If our universe is mathematics, why just this mathematics, and not some other mathematics?

I don't get this comment. Why should other mathematical structures be instantiated in other ones? Why is the lack of that (e.g. there are no circles in a triangle) be a problem for the hypothesis?

Maybe I do. In what sense would you say that things don't stop existing after a time? Is there some problem you think I need to correct?

To critique some hypothesis, you can't assume different premises and then find contradiction with your new premise. That's a begging fallacy. If our universe is a mathematical structure, time is part of that structure (block view). The structure does not exist within time (presentist view), which would make time more fundamental than the mathematical structure, a contradiction with the MUH premises.
So a universe that contains your worldline cannot also not contain your worldline, hence this structure contains you. The phrase 'stops existing after a time' is meaningless outside of presentism. Your worldline is bounded by time, going from year X to Y, but that worldline is part of the block and there is no present time at which that worldline is not meaningfully part of the block.

In the MUH, surely time would just be more mathematics?

Well it is of course. The block view regards time as a dimension. In a view where the structure is contained by time, one is saddled with the additional task of explaining what initiates the evolving mathematical structure, and how time can be meaningful in the absence of that structure, and if other structures are also contained by that same time.

Can you give me an example of a test that falsifies (or could falsify) dualism?

Dualism asserts that your choices are not the product of physics, so one needs to identify some construct somewhere in the causal chain leading to an action that has no physical cause. A human for instance needs to violate physics for it to work, and yet no such violation has been found, and those suggesting it decline to look for it, despite it being a very solid evidence for their stance.
Lara Croft raises her arm. Does her brain cause her to do that? No, she doesn't even have a brain. Clearly her action are not the product of internal brain activity, but come from outside. The limbs are controlled directly. Clearly a case of dualism. I hope you get the Lara reference.
Talk of this concerns the VR hypothesis, and seems pretty irrelevant to this topic.

Disproving presentism is like proving the afterlife. There's a test, but the results of the test cannot be published. The test is fatal.

because it seems to me that some people here think they are important for the MUH.

I agree that VR and simulation hypothesis are not important to MUH discussion. Both posit a higher reality, and MUH does not.

How can "3" make a duck?

I said 3 was on equal ontology as our universe. I didn't say 3 made a duck. 3 is a trivial mathematical structure, and our universe appears quite complex, sufficient complexity to contain internal states that glean the nature of the structure itself.

Which premises do you think I have added?

That 3 is only an abstraction without a distinct referent. You were quite explicit about this in several posts. See top of this post.

What do you think? Do you think that a duck is a mathematical structure?

I am attracted to MUH, but it has problems which I have pointed out, not in much detail. And no, I don't think a duck is a mathematical structure. It is only part of a much larger structure. A duck being a separate thing seem not emergent from any physics, and is essentially a mental construct. Sure, there is a referent. Other minds perceive and similarly label the same duck as an object, but physics doesn't seem to recognize any system as an object, distinct from 'the state of particles in a given volume' or some such.
To illustrate what I mean, physics allows the state of location 'x' to change from a missile to a bowl of petunias. All one has to do is consider some inertial frame where that volume is occupied by the missile at time x and the same volume is occupied by petunias a second later. There's no identity in physics, so a protest that the missile still exists elsewhere presumes the state of the EM field to somehow constitute the identity of 'missile', and that the similar state elsewhere is now where 'the missile' is. But physics assigns no such identity, and we defined the identity in this case to be simply the state of a certain volume over time, in a specific frame. Sorry if the example is hard to explain, and only somewhat relevant. I'm just trying to illustrate that 'duck' as an identity isn't part of physics but more of a mental designation.

I think that this idea abolishes the useful - not to mention common-sense - distinction between matter and ideas.

Appealing to common sense would have much of the last century of physics abandoned. Is the hypothesis useful? Only from a philosophical standpoint since it solves many of the issues with other explanations for the universe. As for matter and ideas, not all referents of ideas are material, so that is unfair. God is an idea. Is the idea wrong because the referent isn't matter? Is that a valid falsification of a god hypothesis?

Do you claim that mathematics is something other than conceptual?

That I very much do claim. When asked what we can know for sure, I immediately balk at 'cogito ergo sum', but I have a hard time denying that the sum of 2 and 3 is 5, even in the absence of a mind to conceive of it.

 

[Yazata]

My guess is that W4U is arguing (perhaps without realizing it) for a currently popular idea in the philosophy of science called Structural Realism.

https://plato.stanford.edu/entries/structural-realism

The SEP says,

"Scientific realism requires belief in the unobservable entities posited by our most successful scientific theories. It is widely held that the most powerful argument in favour of scientific realism is the no-miracles argument, according to which the success of science would be miraculous if scientific theories were not at least approximately true descriptions of the world...

...arguably the most powerful arguments against scientific realism are based on the history of radical theory change in science. The best-known of these arguments, although perhaps not the most compelling of them, is the pessimistic meta-induction, according to which reflection on the abandonment of theories in the history of science supports the expectation that our best current scientific theories will themselves be abandoned...

...Structural realism was introduced into current philosophy of science by John Worrall in 1989 as a way to break the impasse that results from taking both arguments seriously, and have “the best of both worlds” in the debate about scientific realism. With respect to the case of the transition in nineteenth-century optics from Fresnel’s elastic solid ether theory to Maxwell’s theory of the electromagnetic field, Worrall argues that:

'There was an important element of continuity in the shift from Fresnel to Maxwell—and this was much more than a simple question of carrying over the successful empirical content into the new theory. At the same time it was rather less than a carrying over of the full theoretical content or full theoretical mechanisms (even in “approximate” form) … There was continuity or accumulation in the shift, but the continuity is one of form or structure, not of content.' (1989: 117)

According to Worrall, we should not accept standard scientific realism, which asserts that the nature of the unobservable objects that cause the phenomena we observe is correctly described by our best theories. However, neither should we be antirealists about science. Rather, we should adopt structural realism and epistemically commit ourselves to the mathematical or structural content of our theories. Since there is (says Worrall) retention of structure across theory change, structural realism both (a) avoids the force of the pessimistic meta-induction (by not committing us to belief in the theory’s description of the furniture of the world) and (b) does not make the success of science (especially the novel predictions of mature physical theories) seem miraculous..."

And I take Tegmark as basically publishing a publicly accessable version of a rather Platonic (and Kantian?) sort of idea that is known in the literature as Ontic Structural Realism.

The SEP again:

"Some philosophers of physics had already more explicitly signalled a significant departure from traditional realist metaphysics. For example, Howard Stein says:

'[O]ur science comes closest to comprehending “the real”, not in its account of “substances” and their kinds, but in its account of the “Forms” which phenomena “imitate” (for “Forms” read “theoretical structures”, for “imitate”, “are represented by”).' (1989: 57)

Michael Redhead (1999: 34) says: “the best candidate for what is ‘true’ about a physical theory is the abstract structural aspect”. Accordingly, Ladyman (1998) argues that structural realism ought to be developed as a metaphysical position according to which, since the continuity in scientific change is of “form or structure”, the success of science should be accounted for in terms of the representation of modal relations among phenomena, not in terms of continuity of reference to objects and properties."

My own view is that this kind of idea might arguably be a reasonably plausible way of conceptualizing theoretical physics with its penchant for filling chalkboards full of mathematical squiggles describing relationships between variables, but it's less so for sciences like biology who damnedly persist in thinking that the objects of their sciences physically exist and can't be reduced without remainder to mathematical relationships between observations.

 

[Pinball1970]

My guess is that W4U is arguing (perhaps without realizing it) for a currently popular idea in the philosophy of science called Structural Realism.



My own view is that this kind of idea might arguably be a reasonably plausible way of conceptualizing theoretical physics with its penchant for filling chalkboards full of mathematical squiggles describing relationships between variables, but it's less so for sciences like biology who damnedly persist in thinking that the objects of their sciences physically exist and can't be reduced without remainder to mathematical relationships between observations.

Those objects do exists, DNA, chemical messengers, organelles, cells , tissues organs organism and populations. There is no point learning about organisms or cells in terms of quarks.

 

[James R]

While much of what Write4U has just posted is as irrelevant as usual, the article from the SEP on the structure of scientific theories is interesting. At a glance, the one that comes closest to my own view is what they call the "Pragmatic View":

Finally, for the Pragmatic View, scientific theory is internally and externally complex. Mathematical components, while often present, are neither necessary nor sufficient for characterizing the core structure of scientific theories. Theory also consists of a rich variety of nonformal components (e.g., analogies and natural kinds). Thus, the Pragmatic View argues, a proper analysis of the grammar (syntax) and meaning (semantics) of theory must pay heed to scientific theory complexity, as well as to the multifarious assumptions, purposes, values, and practices informing theory.​

Apparently, all that Write4U took away from that article (which I assume he didn't read or understand) was that "a structure is a mathematical object". There's a bit more in there than that.