I'll go over it in this comment very briefly — I'm trying to write a post for next week.

Firstly, we consider the global structure of the universe. We would like to have the overall dimensional structure to be the simplest structure required for propagation of matter through a completely locally similar universe. This means that any contraction in any dimension has to be balanced by expansion in another, and in a simple 3D universe, this axiom wouldn't be able to produce the results that we see in reality. Increases in density require fluidity, which requires discrete foreground particles moving past one another in background space. So we must have a perfectly consistently dense universe.

So the structure of a universe must be a symmetrical closed group containing one- and three-dimensional components, i.e. if we assume symmetry and a finite 3 + 1 universe, then having a universe like a Lie group (S1 x S3)² is minimal. This set is the product of two 3 + 1-dimensional components, one of which is very large compared to the scale of humans, and the other is very small.

So a local coordinate system would look like this: (w,x,y,z,W,X,Y,Z)

w-x-y-z is your classic 3 + 1 space, with w acting as a time-like dimension. These dimensions are very large.

W-X-Y-Z is a set of extremely small dimensions that act like the 3 + 1 space above, except that they are so small that propagations can easily resonate around them. It is the presence of these 'inner dimensions' that allows for the existence of matter, that is to say, the existence of mass. By travelling around the inner dimensions, a wave obeying $\square \psi =0$ ^[1] can be “at rest”, as far as larger-scale beings such as ourselves are aware.

“Perception” is a much neglected and much maligned term in the hard sciences. For the avoidance of doubt, perception, as we use the notion in this book, has nothing whatsoever to do with psychology, sense-data or mental interpretation. Perception is more fundamental than that: it falls into the domain of pure mathematics. The relevant fact is this: no entity can perceive a dimension in which it is symmetric. Why not? Because perception is based on distinctions between things — this object here rather than that object there — and an entity with symmetry in an inner dimension cannot, mathematically speaking, make any such distinction with regard to contents of that dimension. Nor, as a result, can the entity perceive the dimension itself: there is simply no physical mechanism by which the relevant data can enter the would-be perceiver.

A subject perceives an object only in those dimensions in which a) object, b) subject, and c) the relationship between them vary.

This theorem underpins much of the model, and a comprehensive understanding of it is a prerequisite for what follows. It has three facets. Firstly, a subject may fail to perceive an object, because the object has no variation. This is trivial. If there’s nothing to be perceived, as on a pitch dark night, then nothing is perceived.

Secondly, a subject may fail to perceive an object, because the subject has no variation. A single photoreceptor the size of a football field cannot track the movement of the football across the field. While this is obvious in analogy, it is not trivial in general, and is of paramount importance to understanding the nature of our physical reality.

Thirdly, a subject may fail to perceive an object, because subject and object have the same variation, as when both measuring ruler and measured object stretch by the same factor. No stretch is perceived. This is not trivial either.

What happens when matter (us) perceives matter (our surroundings)? Well, matter is constructed of waves travelling around the inner dimensions; this requires that matter waves resonate in the inner dimensions; in turn, this requires that matter waves have inner-dimensional symmetry. So, according to subject-symmetric imperceptibility, the inner dimensions must be imperceptible to any entity built of matter, whether it be a human being or a piece of laboratory equipment. Hence, while it may seem, at first glance, reasonable to question the whole affair, asking, “Why has no one ever seen these extra dimensions?”, the question itself is, in fact, a misunderstanding of the relevant mathematics. The very act of perception is, by definition, matter-based, so any dimension or dimensions that go symmetrically into the generation of the phenomenon “matter” are automatically imperceptible.

From here, we can attempt to find what is observable and what is not, and build up and understanding of the mechanisms behind the generation of higher-order concepts like matter & mass.

1. ^{^}

   This is the wave equation. Small disturbances Ψ in the substance of the universe obey the eight-dimensional wave equation $\square \psi =0$.

I very much understand your comments on metaphysics and its general circularity, or ability to only prove things which they take as axiomatic.

So, if this is such a stumbling block, then how about we start by just assuming the single-substance universe, and work up from there with the physics? Have you read my response to Mitchell_Porter? I'm extremely interested in getting into the meat of things, because as much as what I'm saying is ridiculous, I've really put together the maths and it does largely check out.

mathematical objects aren't real in the same way a tree is

I'd argue that this is largely meaningless, since if it is a purely mental concept, and all mental concepts have to supervene on physical reality (for it makes no sense to have a thought without something actually existing — this is not to say that I think that qualia doesn't exist) — then mathematical objects are real in the same way that a tree is, through our understanding of them.

exactly which flavor of metaphysical framing we adopt is mostly a matter of opinion, taste, and usefulness for our own thinking.

Ok, I'd say that this particular definition of the world as a monistic thing is extremely useful, and the proofs that you can get with regards to physics retroactively justify the world being a monistic thing.

Dualism makes no sense because if you agree that the two things interact through some sort of bridging concept, then surely, the concept as a whole must be continuous, and therefore one thing. Sure, I can say that yesterday and today are two different things, but I understand how they interact with one another. Yesterday becomes today via a process called a calendar, which explains both yesterday and today. Yesterday and today are just second-order concepts to the first-order concept of the calendar. (And I suppose the zeroth-order concept of time...)

Plus: Occam's Razor! I know it's a lazy, incomplete argument to rely on, but I really think that this sort of monistic metaphysics solves literally every problem. Argument? You're both one. Debate? You came from the same place. Physics? That's for my future LW posts!

Your second paragraph reads to me in this way: We can create functions between anything that exists, as long as it exists. (ie. the empty category is simply non-existence) — I hope I'm right in reading that, since that argument is exactly what I'm trying to get at.

According to that statement, it is logically impossible to have a flat discontinuity between X and Y that could not be trivially bridged by a function — ∴ such a function Z could not not exist, which then proves that every X-Y pair can be bridged, which means that B) in my previous argument cannot be the case, then A) has to be the case, and therefore we arrive at a logical monism.

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I'd also say that if things do not interact, but then are bridged, then they interact by virtue of that bridging. Assigning a function which bridges two disparate, non-interlinked concepts makes them linked. For example, I could merely state that a rock on an extremely distant planet and my computer are not linked (by virtue of their being too far apart to ever possibly interact) — but even by linking them in this trivial fashion, they are linked. In fact, how would I know about this rock, and link with it, if they were too far apart to interact?

I would go one step further and say that I can even trivially link with things that don't actually exist. The only thing I'd say that you are unable to create a bridging function to is, as you said, the empty category.

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Also, can I just say thanks for taking the time to read through this. I've been lurking for a while on LW and the response I've gotten for writing this post has been lovely. Cheers.

With regards to the bridge-based dualism that you discuss here, and indeed every single flavour of pluralism, I would argue that if you're making a gradual distinction between X and Y through a bridge Z, then it is not logical to say that either X, Y, or Z has an implicit existence outside of the whole {X,Y,Z} set, which could be inferred as a monism. All flavours of pluralism fall into this format, in which people pick certain world-qualities and claim they are different to one another (which is true) but then do not understand that by fact of their having-to-interact, this means that they have to share at least some gradient-similarity.

Here's another formulation of that:

A) If there are differences of type between X and Y that are expressible in a gradient, then there's a function that can explain this, which would have to explain both X and Y, and could be regarded as an X-Y monism.

B) And if there is a flat discontinuity between X and Y, then how can they interact? There would be no bridging function Z(X,Y), and there would be no possibility of them having any sort of linked existence.

So either A) is true and {X,Y} is explicable by monism, or B) is true and X and Y cannot interact, and therefore cannot both exist.

∴ A) has to be true.

I would argue that my arguments put forth here do prove a monism of sorts, but merely a logical one. We actually have to use this logic (which I have done partially in another comment, but I'm rate-limited right now...) in order to move towards an explanation of a physical monism.

And as for the exploration of metaphysical questions, I'd say that this point of looking at things "from the inside" is an incredibly interesting one. If we know we are looking at something from the inside at all? If we know we are inside something, then can we infer the existence of an 'outside' from this concept? These are all very complex questions and I think we'd be able to argue for days on them.

Variance does not have to necessarily entail the existence of a separation of 'background' and 'foreground' substance. It is possible to have a single substance, which, due to dimensionally-symmetrical disturbances (which keep space at a local constant density) can cause higher level representations of those disturbances (ie. particles) to appear to 'move'.

A perception of time does not foreclose on monism either. Time is a measure of when, not a physical thing that can be stretched or compressed. Hence, there is no disagreement with the axiom when we say that time is not made of substance.

It could be argued that this is part of the original axiom, but honestly, you are correct in saying that it is not insinuated by my original claim. So I'll say that this is maybe a secondary axiom, but conceptually linked to the main one.