# 4th dimension is extension of 3rd dimension. A world within worlds

That is where we disagree.

The mathematics ar expressed through physical interaction. But the concept of Universal mathematical constants describes the very essence of a geometric spacetime.
Physics is what it is

We tame physics down to our level of understanding through the language of mathematics

Write4U said:
That is where we disagree.

The mathematics ar expressed through physical interaction. But the concept of Universal mathematical constants describes the very essence of a geometric spacetime.

Physics is what it is

We tame physics down to our level of understanding through the language of mathematics

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True .

Meanwhile the Physical Universe continues . Regardless of wether there is a intelligent life contemplating mathematics or not .

How do you get geometry without anything physically existing ?
The Universe is a mathematical geometry. It has a name, it is a mathematical pattern that has duration and can be described in mathematical terms as a " manifold".

Shape of the universe
The shape of the universe, in physical cosmology, is the local and global geometry of the universe. The local features of the geometry of the universe are primarily described by its curvature, whereas the topology of the universe describes general global properties of its shape as of a continuous object.
The spatial curvature is related to general relativity, which describes how spacetime is curved and bent by mass and energy, while the spatial topology cannot be determined from its curvature; locally indistinguishable spaces with different topologies exist mathematically.
Moreover, so that calculus can be applied, the universe is typically assumed to be a differentiable manifold. A mathematical object that possesses all these properties, compact without boundary and differentiable, is termed a closed manifold. The 3-sphere and 3-torus are both closed manifolds.....more
https://en.wikipedia.org/wiki/Shape_of_the_universe

I like the genus 1 (2 dimensional) torus. It's simple and mathematically perfectly suited for self-formation. Throw a rock in a lake and watch the spreading wave function naturally form a circular wave action in 2 dimensions. Anything more complicated runs into Occam's razor.

Torus
It is a compact 2-manifold of genus 1. The ring torus is one way to embed this space into Euclidean space, but another way to do this is the Cartesian product of the embedding of S1 in the plane with itself. This produces a geometric object called the Clifford torus, a surface in 4-space.

As the distance from the axis of revolution decreases, the ring torus becomes a horn torus, then a spindle torus, and finally degenerates into a sphere.

https://en.wikipedia.org/wiki/Torus#:~:text=It is a compact 2,a surface in 4-space.

This is how the wave function becomes expressed on a torus surface.

Wave dynamics on toroidal surface
Abstract
Wave dynamics on curved surfaces has attracted growing attention due to its close resemblance to the warped space time governed by general relativity. It also opens up opportunities for designing functional optical devices such as geodesic lenses. In this work we study the wave dynamics on the surface of a torus, a shape of considerable interest due to its nontrivial topology.
Governed by the conservation of angular momentum, light propagates on the torus in two different types of modes: one is able to twist around and sweep through the whole surface of the torus; the other is confined within a certain angular range along the torus latitude direction.
The confined mode exhibits an interesting self focusing or imaging behavior, which, similar to a geometric lens, shows no dependence of wavelength and thus suffers no chromatic aberration. By changing the geometric parameters of the torus, both the focusing point and the focusing distance can be controlled. Our work provides a new approach to manipulation of light propagation on a curved surface under the conservation of angular momentum.

Fig. 1 (a) Schematic of torus coordinates with usual parametrization. The energy density of (b) reflected wave on a 2D torus. (c) free wave on 2D torus. (d) reflected wave on 3D space torus. (e) free wave on 3D space torus. The geometric parameters used in calculating the effective permittivity and permeability are R1 = 3 m and R2 = 3/2 m, the corresponding frequency is 10GHz.
Download Full Size | PPT Slide | PDF

https://www.osapublishing.org/oe/abstract.cfm?uri=oe-26-14-17820#Abstract

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True .
Meanwhile the Physical Universe continues . Regardless of wether there is a intelligent life contemplating mathematics or not .
Also true and it continues to function in a mathematical manner, regardless if there is an intelligent living thing contemplating the observable and symbolized "relative values" and "mathematical functions".

How do you get geometry without anything physically existing ?
How do you get anything without anything physically existing.

Don't forget, physical patterns (including humans) are formed from elementary "values" and are an expression of mathematically evolved simpler patterns. The physics involved are always of a mathematical nature in that they have inherent values and must function in accordance with mathematical permissions and limitations.

How do you get anything without anything physically existing.

Don't forget, physical patterns (including humans) are formed from elementary "values" and are an expression of mathematically evolved simpler patterns. The physics involved are always of a mathematical nature in that they have inherent values and must function in accordance with mathematical permissions and limitations.

And have no relation to reality , at all .

Also true and it continues to function in a mathematical manner, regardless if there is an intelligent living thing contemplating the observable and symbolized "relative values" and "mathematical functions".

Define " it " .

Based on real physical objects , in any state .

Michael 345 said: Physics is what it is.

We tame physics down to our level of understanding through the language of mathematics.

Which proves the mathematical nature of physics. That is the very definition of "proof".

Physics is not a natural phenomenon. It is a scientific discipline for studying naturally forming mathematical patterns and interactive functions.
Physics consists of modeling Universal constants with human mathematics by measuring the physical expression of universal mathematical patterns and functions from prevailing relative physical values and mathematical functions.

The definition of Physics doesn't say anything about the nature of the universe. Mathematics do!
Physics (from Ancient Greek: φυσική (ἐπιστήμη), romanized: physikḗ (epistḗmē), lit. 'knowledge of nature', from φύσιςphýsis 'nature')[1][2][3] is the natural science that studies matter,[a] its motion and behavior through space and time, and the related entities of energy and force.[5] Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.
https://en.wikipedia.org/wiki/Physics

And we found that the universe behaves in a mathematical manner which can be symbolized with human mathematics.

Which proves the mathematical nature of physics. That is the very definition of "proof".

Physics is not a natural phenomenon. It is a scientific discipline for studying naturally forming mathematical patterns and interactive functions.
Physics consists of modeling Universal constants with human mathematics by measuring the physical expression of universal mathematical patterns and functions from prevailing relative physical values and mathematical functions.

The definition of Physics doesn't say anything about the nature of the universe. Mathematics do!
https://en.wikipedia.org/wiki/Physics

And we found that the universe behaves in a mathematical manner which can be symbolized with human mathematics.

But doesn't explain the physical reality , of reality .

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But doesn't explain the physical reality , of reality .
Physical reality is only observable as mathematical patterns. It is the density of the pattern, the inherent values and potentials, that makes an individual or a collection of mathematical objects observable. Can we see the air we breathe to stay alive? Yes, when its cold enough for the H2O content to form a "mist" (a mathematically ordered physical function).

But if we did not have actual recording instruments our observation of anything would be reduced to a mental "best guess" by the brain.
Schematic depiction of a function described metaphorically as a "machine" or "black box" that for each input yields a corresponding output.

https://en.wikipedia.org/wiki/Function_(mathematics)

Established , but incomplete .
.
Every man and his dog know our accepted theory of the evolution of the universe, the BB/Inflationary model is incomplete, but it is still the best by far that we have.
And even when we finally aquire an observational valaidated QGT, it will certainly most likely contain the BB, much as GR gives the same answers as Newtonian in sufficiently accurate applications.
But that's 21st century cosmology river, something you obviously are totally ignorant of.

Physical reality is only observable as mathematical patterns.
Not disagreeing with your take and the articles in answer to river's well know nonsensical ignorant and usual claims, but simply put, mathematics is the language of physics, and physics describes the universe [or reality] around us and the principals [described by maths] of the physical world/universe.
And that totally puts pay to his silly gobbledygook claims.

Physical reality is only observable as mathematical patterns. It is the density of the pattern, the inherent values and potentials, that makes an individual or a collection of mathematical objects observable. Can we see the air we breathe to stay alive? Yes, when its cold enough for the H2O content to form a "mist" (a mathematically ordered physical function).

But if we did not have actual recording instruments our observation of anything would be reduced to a mental "best guess" by the brain.
Schematic depiction of a function described metaphorically as a "machine" or "black box" that for each input yields a corresponding output.

https://en.wikipedia.org/wiki/Function_(mathematics)

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Table of Elements and the like , true .

And those patterns are physical , before any mathematics .

And those patterns are physical , before any mathematics
No, mathematics form the patterns. Patterns are not physical constructs, they are mathematicl constructs.
A triangle is not a physical thing. It is a mathematical thing.

river said:
And those patterns are physical , before any mathematics

No, mathematics form the patterns. Patterns are not physical constructs, they are mathematicl constructs.
A triangle is not a physical thing. It is a mathematical thing.

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Based on physical things .

Put another way , how would mathematics explain real existence , physically ; without any thought given to the physical as the foundation of the mathematics ?

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Based on physical things .

Put another way , how would mathematics explain real existence , physically ; without any thought given to the physical as the foundation of the mathematics ?
"Probability density" of the values contained in the mathematical patterns .

What Does Quantum Theory Actually Tell Us about Reality?
Nearly a century after its founding, physicists and philosophers still don’t know—but they’re working on it.
Note the density patterns.
Mathematically speaking, however, what goes through both slits is not a physical particle or a physical wave but something called a wave function—an abstract mathematical function that represents the photon’s state (in this case its position). The wave function behaves like a wave.
It hits the two slits, and new waves emanate from each slit on the other side, spread and eventually interfere with each other. The combined wave function can be used to work out the probabilities of where one might find the photon.
The photon has a high probability of being found where the two wave functions constructively interfere and is unlikely to be found in regions of destructive interference. The measurement—in this case the interaction of the wave function with the photographic plate—is said to “collapse” the wave function. It goes from being spread out before measurement to peaking at one of those places where the photon materializes upon measurement.

Based on physical things
No, mathematics are not based on physical things. They hold in the abstract as well. Mathematics is an abstract property (potential) of spacetime and has non-conscious, but "quasi intelligent Agency"......

river said:
Based on physical things

No, mathematics are not based on physical things. They hold in the abstract as well. Mathematics is an abstract property (potential) of spacetime and has non-conscious, but "quasi intelligent Agency"......

Write4U said:
No, mathematics are not based on physical things. They hold in the abstract as well. Mathematics is an abstract property (potential) of spacetime and has non-conscious, but "quasi intelligent Agency"......

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Fundamentally mathematics is .

What is the foundation of the abstract .

What is the foundation of the abstract .
Logic.

But you're posing the wrong question. Mathematics is not a result of physical interaction. Physical interaction is the result of pre-existing mathematical functions. The way things work.