Shape of Infinite Space

[dwb001]

Is it possible for a circle to not have an edge?

Starr following a circle... when do you get to the end? Never said anything about an edge.

 

[sjastro]

Starr following a circle... when do you get to the end? Never said anything about an edge.

We mathematicians call it a closed loop which is the very definition of finiteness.
Extending it to three dimensions you have a closed universe which is not supported by evidence as illustrated in my previous post.

 

[dwb001]

We mathematicians call it a closed loop which is the very definition of finiteness.
Extending it to three dimensions you have a closed universe which is not supported by evidence as illustrated in my previous post.

So when do you get to the end of a circle. Not a loop but a circle.

 

[sjastro]

Ignoring the attempts of creationists to derail yet another thread, the current consensus is the entire universe (as opposed to the observable universe) is either very large or infinite in size as it is flat with a measured curvature of near zero.
This needs to be treated with caution however as there are other surfaces which are topologically flat but are finite sized such as a torus.

The curvature can calculated by measuring the hot and cold spots in the CMB (cosmic microwave background) by decomposing the signal from the CMB into various scales as explained in this post.
These hot and cold spots have an apparent size ~1⁰ in diameter and are produced by sound waves caused by plasma oscillations undergoing compression and rarefaction travelling through the hot ionized gas in the early universe at a known speed v = c/√3 where c is the speed of light for a known length of time (375,000 years).
The angular separation between the hot and cold spots caused by compression and rarefaction respectively corresponds to the wavelength of the sound wave which means the actual size of the hot and cold spots can be calculated.
When the universe cooled down and became transparent these hot and cold spots became permanent records in the CMB.

By comparing the apparent size of the spots to their known actual size, the curvature of the light path between the CMB and the observer and therefore the geometry of the universe can be determined.

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It is found from the light paths the apparent and actual diameters are based on triangulation where the angles add up to 180⁰ which is a property of flat space hence the evidence points to scenario (b) indicating a possibly infinitely large universe.

Here is a video I found which gives a non-technical explanation of the shape of the universe using the CMB as a source of evidence.

 

[sjastro]

So when do you get to the end of a circle. Not a loop but a circle.

Good grief man I SAID A CLOSED LOOP!!!

 

[dwb001]

Good grief man I SAID A CLOSED LOOP!!!

And I said a circle... no loops.

 

[sjastro]

And I said a circle... no loops.

A circle is a closed loop, you don't get to change the terminology to suit your ignorance.
To claim a circle is an example of infinity because there is no start or finish point is so ridiculously wrong.
If you arbitrarily started at a random point on the circumference and followed the circumference you will get back to that point in a finite distance.

A surface of sphere or 2-sphere can be considered an extension of a circle in 2D space where the same principle applies, it takes a finite distance to start and finish at the same point.

A closed universe is an example of a 3-sphere finite universe with a non zero positive curvature.
Observational evidence appears to rule this out as the measured curvature is near zero.

 

[Shemjaza]

So when do you get to the end of a circle. Not a loop but a circle.

Oh, easy, just turn 90 degrees and move alone the diameter to the other side.

If you're only talking about the edge, then for one you are talking about a loop, and for another you can easily move the entire length, you just don't run into any kind of barrier to continuing.

It's the same as saying how long a race track is, just because the finish line is the start of the next lap doesn't make it infinite.

 

[dwb001]

Oh, easy, just turn 90 degrees and move alone the diameter to the other side.

If you're only talking about the edge, then for one you are talking about a loop, and for another you can easily move the entire length, you just don't run into any kind of barrier to continuing.

It's the same as saying how long a race track is, just because the finish line is the start of the next lap doesn't make it infinite.

What finish line... just s circle. Start traveling along a circle... when is the end. No road marks, no signs, no arbitrary points along the way.

 

[Shemjaza]

What finish line... just s circle. Start traveling along a circle... when is the end. No road marks, no signs, no arbitrary points along the way.

The inability to see something doesn't mean it isn't there. There are still colours in a blind man's house even if no one ever comes in to see them.

You are describing moving in one dimension along the outer rim of a circle... that's a length of exactly Pi times the size of the circle.

 

[dwb001]

The inability to see something doesn't mean it isn't there. There are still colours in a blind man's house even if no one ever comes in to see them.

So there are colors in a blind man's mind?

You are describing moving in one dimension along the outer rim of a circle... that's a length of exactly Pi times the size of the circle.

I told you it isn't there... now when do you get to the end of a circle?
Not one dimension... do you not even get that?

That isnthe diameter... where is then end? You are speaking mathematical. Try philosophy.

 

[dlamberth]

Not anywhere close to being a mathematician and here in this thread the first time I've heard the term "loop" in that context, I went to ChatGPT and ask: What is loop in mathematics. Here is the response received:

In mathematics, the term "loop" can have multiple meanings depending on the context in which it is used. Here are a few different interpretations of "loop" in mathematics:

1. Graph Theory: In graph theory, a "loop" refers to an edge that connects a vertex to itself. In other words, it's an edge that starts and ends at the same vertex.
2. Topology: In topology, a "loop" typically refers to a closed curve or path within a topological space. A loop is a continuous mapping of a closed interval (usually the unit interval [0,1]) into a space, where the starting and ending points of the curve are the same.
3. Computer Programming: In computer programming, a "loop" is a control structure used to repeatedly execute a block of code. Common types of loops include "for loops," "while loops," and "do-while loops." Loops are used for tasks that need to be performed iteratively, such as iterating through a list of items or performing a set of instructions multiple times.
4. Knot Theory: In knot theory, a "loop" refers to a closed curve that is embedded in three-dimensional space without self-intersections.

The specific meaning of "loop" in mathematics can vary depending on the mathematical subfield or context in which it is used, so it's important to consider the context to determine its precise definition and significance.

 

[Shemjaza]

So there are colors in a blind man's mind?

I told you it isn't there... now when do you get to the end of a circle?
Not one dimension... do you not even get that?

That isnthe diameter... where is then end? You are speaking mathematical. Try philosophy.

Logic is a part of philosophy. and your entire thought experiment just describes a space that is not infinite, but would seem so. As I said much earlier in the thread finite, but unbounded.

 

[dwb001]

Logic is a part of philosophy. and your entire thought experiment just describes a space that is not infinite, but would seem so. As I said much earlier in the thread finite, but unbounded.

Not even part of my question.
Where is the end of the circle?

 

[sjastro]

Not anywhere close to being a mathematician and here in this thread the first time I've heard the term "loop" in that context, I went to ChatGPT and ask: What is loop in mathematics. Here is the response received:

In mathematics, the term "loop" can have multiple meanings depending on the context in which it is used. Here are a few different interpretations of "loop" in mathematics:

1. Graph Theory: In graph theory, a "loop" refers to an edge that connects a vertex to itself. In other words, it's an edge that starts and ends at the same vertex.
2. Topology: In topology, a "loop" typically refers to a closed curve or path within a topological space. A loop is a continuous mapping of a closed interval (usually the unit interval [0,1]) into a space, where the starting and ending points of the curve are the same.
3. Computer Programming: In computer programming, a "loop" is a control structure used to repeatedly execute a block of code. Common types of loops include "for loops," "while loops," and "do-while loops." Loops are used for tasks that need to be performed iteratively, such as iterating through a list of items or performing a set of instructions multiple times.
4. Knot Theory: In knot theory, a "loop" refers to a closed curve that is embedded in three-dimensional space without self-intersections.

The specific meaning of "loop" in mathematics can vary depending on the mathematical subfield or context in which it is used, so it's important to consider the context to determine its precise definition and significance.

Let's ask ChatGPT the question if a circle is an example of infinity as has been proposed in this thread.

A circle is not an example of infinity in the mathematical sense. A circle is a geometric shape defined by a set of points that are all equidistant from a central point. It is a finite and well-defined shape with a specific size and circumference. It is not infinite.

Infinity, in mathematics, is a concept that represents something unbounded or limitless. It is not a specific shape or object like a circle. Instead, it is used to describe the idea of a quantity or a process that goes on forever without a finite endpoint. For example, the set of all natural numbers (1, 2, 3, ...) is infinite because you can keep counting natural numbers indefinitely.

So, while a circle is a geometric shape with a finite and well-defined boundary, infinity is a mathematical concept used to describe the absence of a finite limit or endpoint. They are fundamentally different concepts.

The question of closed loops plays a very important role in physics, suppose you go from point A to point B and back to point A in a loop which can include a circle.

The forces involved in moving you may be either conservative or non conservative.

It makes absolutely no sense to think of circles (and closed loops) to represent infinity as force, work and energy cannot be defined.

 

[Aaron112]

Hello everyone,

I have been wondering about the shape of Infinite space. I still haven't figured it out. What's the shape of Infinite space?

Did you ever wonder what a jelly donut that grows inside a watermelon looks like ?

 

[Aaron112]

Not even part of my question.
Where is the end of the circle?

Right there, next to the beginning of the circle.

 

[dwb001]

Right there, next to the beginning of the circle.

And where is that?

 

[Aaron112]

And where is that?

Wherever you started the circle.

 

[dwb001]

Wherever you started the circle.

Yes... but WHERE IS THAT?

Philosophy not mathematics remember?