- Jan 2, 2024
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I am continuing to show how Hypersphere Topology solves many of the problems in Cosmology using English & Logic without posting reams of AI.
First, we need to look at what flatness means. The curved surface of a cylinder is regarded as flat in topology because if we cut the cylinder, we can lay it out flat, i.e. by a simple process, we can see that the angles of a triangle add to 180 degrees; therefore, the surface of a cylinder is flat.
So, how can the surface of a 3-ball be measured flat (?) Or, perhaps more accurately, how can a curved surface be thought to be flat? The answer concerns the nature of time. In a flat universe, time is arbitrarily considered to be an arrow; the process of 'now' moving to the future is regarded as a fourth dimension (a direction at 90 degrees to 3D space).
In the Hyperspace model (HET), Time is the increase in the radius of the hypersphere. Time is radial and points in every direction available in the 5-dimensional embedding space of the hypersphere. Time, then, is not the fourth dimension as suggested in the flat space sense.
So, how do we mistake the curved 3D space of the Hypersphere for flat space? We use a similar method as used to flatten a cylinder. We rotate all space to orient the direction of time as if it were a unidirectional arrow, thereby matching most astronomers' assumption of the nature of time. This process flattens space because the whole surface map can be laid flat. However, it is clear that the resulting surface is not continuous, even though flat. This suggests that the flat assumption of using a unidirectional arrow of time is the wrong model and that time should be considered as radial.
The use of emergent radial time avoids the need to 'add time on' for no particular reason except to simulate reality. The Hyperspace model incorporates time within geometry and explains its function (or its mechanism as a monitor of spatial expansion of the 3D hypersphere).
I have an improved description generated here to improve readability:
John, your framing already offers a strong conceptual bridge between geometry, perception, and the role of time in cosmology. Here’s a refined version that aims to preserve your insights while enhancing clarity, flow, and accessibility to readers unfamiliar with higher-dimensional geometry:
---
**Reframing the Flatness Problem Through Hyperspace and Emergent Time**
How can a curved space—like the 3D surface of a 4D sphere (a “3-ball”)—appear flat? More importantly, *why* do we so often treat it as flat in cosmology?
Traditionally, flatness is defined through our assumptions about time. In standard cosmology, time is considered a straight arrow moving from past to future, treated as a fourth dimension, orthogonal to the three spatial ones. This “arrow of time” acts as a frame for interpreting a 4D spacetime continuum.
But in the **Hyperspace model**, time emerges from something quite different: the *radial expansion* of a hypersphere. Rather than being a separate added-on axis, time is the increase in the radius of 3D space, embedded within a higher (5D) space. Here, time isn't linear—it's **radial**, pointing outward from every location in space like the spokes of a wheel.
So why do we perceive space as flat? The trick lies in how we **project** this curved reality onto the framework we’re used to. Like how a cylinder’s curved surface can be unwrapped into a flat sheet, we *rotate* or align our coordinate system so that time looks like a straight arrow. This reorientation makes it possible to “flatten” the space, even if it’s fundamentally curved. However, this projection comes at a cost—it introduces discontinuities that reveal the model’s artificiality.
By adopting **radial emergent time**, the Hyperspace model naturally incorporates time into the fabric of geometry itself. It removes the need to “bolt on” a separate time axis just to simulate reality. Instead, it provides a deeper explanation for cosmic expansion: space grows radially, and what we call time is our experience of that expansion.
First, we need to look at what flatness means. The curved surface of a cylinder is regarded as flat in topology because if we cut the cylinder, we can lay it out flat, i.e. by a simple process, we can see that the angles of a triangle add to 180 degrees; therefore, the surface of a cylinder is flat.
So, how can the surface of a 3-ball be measured flat (?) Or, perhaps more accurately, how can a curved surface be thought to be flat? The answer concerns the nature of time. In a flat universe, time is arbitrarily considered to be an arrow; the process of 'now' moving to the future is regarded as a fourth dimension (a direction at 90 degrees to 3D space).
In the Hyperspace model (HET), Time is the increase in the radius of the hypersphere. Time is radial and points in every direction available in the 5-dimensional embedding space of the hypersphere. Time, then, is not the fourth dimension as suggested in the flat space sense.
So, how do we mistake the curved 3D space of the Hypersphere for flat space? We use a similar method as used to flatten a cylinder. We rotate all space to orient the direction of time as if it were a unidirectional arrow, thereby matching most astronomers' assumption of the nature of time. This process flattens space because the whole surface map can be laid flat. However, it is clear that the resulting surface is not continuous, even though flat. This suggests that the flat assumption of using a unidirectional arrow of time is the wrong model and that time should be considered as radial.
The use of emergent radial time avoids the need to 'add time on' for no particular reason except to simulate reality. The Hyperspace model incorporates time within geometry and explains its function (or its mechanism as a monitor of spatial expansion of the 3D hypersphere).
I have an improved description generated here to improve readability:
John, your framing already offers a strong conceptual bridge between geometry, perception, and the role of time in cosmology. Here’s a refined version that aims to preserve your insights while enhancing clarity, flow, and accessibility to readers unfamiliar with higher-dimensional geometry:
---
**Reframing the Flatness Problem Through Hyperspace and Emergent Time**
How can a curved space—like the 3D surface of a 4D sphere (a “3-ball”)—appear flat? More importantly, *why* do we so often treat it as flat in cosmology?
Traditionally, flatness is defined through our assumptions about time. In standard cosmology, time is considered a straight arrow moving from past to future, treated as a fourth dimension, orthogonal to the three spatial ones. This “arrow of time” acts as a frame for interpreting a 4D spacetime continuum.
But in the **Hyperspace model**, time emerges from something quite different: the *radial expansion* of a hypersphere. Rather than being a separate added-on axis, time is the increase in the radius of 3D space, embedded within a higher (5D) space. Here, time isn't linear—it's **radial**, pointing outward from every location in space like the spokes of a wheel.
So why do we perceive space as flat? The trick lies in how we **project** this curved reality onto the framework we’re used to. Like how a cylinder’s curved surface can be unwrapped into a flat sheet, we *rotate* or align our coordinate system so that time looks like a straight arrow. This reorientation makes it possible to “flatten” the space, even if it’s fundamentally curved. However, this projection comes at a cost—it introduces discontinuities that reveal the model’s artificiality.
By adopting **radial emergent time**, the Hyperspace model naturally incorporates time into the fabric of geometry itself. It removes the need to “bolt on” a separate time axis just to simulate reality. Instead, it provides a deeper explanation for cosmic expansion: space grows radially, and what we call time is our experience of that expansion.
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