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 □ψ=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.
I am curious but very skeptical…
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 □ψ=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.
This is the wave equation. Small disturbances Ψ in the substance of the universe obey the eight-dimensional wave equation □ψ=0.