Math Whizz

[Juliette]

Explain to me the concept of a transfinite symmetry group with 10 to the power of 19 dimensions.
Thank you!

[Ashu]

I'm not going to pretend i know that...

[RepliMagni]

Classical spacetime, where Newtonian mechanics reigns, appears totally unstructured and smooth with a very low dimensional symmetry group [1–6]. However, on close examination classical spacetime smoothness may be the expression of a manifold with a symmetry group of gigantic dimensions [2–5]. At an enormous order of say (10)19, the situation is similar to order going to chaos then ultra hyper chaos, that is to say, ergodicity looks orderly again at least when observed at a sufficiently large distance [6–11].

Hope that helps you understand it.....because it didn't help me!

[Juliette]

Basically, it says "What you see seems orderly, but it actually isn't. It is so damned chaotic that it looks orderly if you close your eyes just a little."

That's what I got from that. The numbers made little sense to me.





On closer examination, it does.
Normally when we describe spacetime (i.e. space - 3D, and time) it appears as though it is a very simple system; 4 dimensions isn't many, so to speak.
However, there are way more dimensions, and what the quote says is that there are in fact so incredibly many (they mention 10 quintillion) dimensions that the relative chaos appears as order.

Imagine this:

Each straight line is a chaotic dimension. There are about 10 to the 19th of such lines, forming what appears to be a perfect circle in the middle.
If you don't look at the lines, but at the circle, all you will see is a perfect circle (in your quote, this is the ultra hyper chaos appearing as order when "observed at sufficient distance"). Closely examined though, it is clearly not just a perfect circle, but a great many lines causing the appearance of a perfect circle.


That's how I read your quote, Mr. Repli. So I think it made sense to me. Thanks!

[Ashu]

Basically, it says "What you see seems orderly, but it actually isn't. It is so damned chaotic that it looks orderly if you close your eyes just a little."

That's what I got from that. The numbers made little sense to me.





On closer examination, it does.
Normally when we describe spacetime (i.e. space - 3D, and time) it appears as though it is a very simple system; 4 dimensions isn't many, so to speak.
However, there are way more dimensions, and what the quote says is that there are in fact so incredibly many (they mention 10 quintillion) dimensions that the relative chaos appears as order.

Imagine this:

Each straight line is a chaotic dimension. There are about 10 to the 19th of such lines, forming what appears to be a perfect circle in the middle.
If you don't look at the lines, but at the circle, all you will see is a perfect circle (in your quote, this is the ultra hyper chaos appearing as order when "observed at sufficient distance"). Closely examined though, it is clearly not just a perfect circle, but a great many lines causing the appearance of a perfect circle.


That's how I read your quote, Mr. Repli. So I think it made sense to me. Thanks!

I actually understood what you said...

[MajorLeeHurts]

its Beautiful isnt it

its unfortunate that we are so limited by our human bodies that we cant sensually experience this outside of an equation.

[Ashu]

You mean travel to other dimensions?

[MajorLeeHurts]

You mean travel to other dimensions?

by sensual I mean senses.

visual , and yes physically experience.

They are there , we just cant experience it with a interesting chemical cocktail and even then its subjective.

[Juliette]

You mean travel to other dimensions?

Are you sure you are not confusing the concept of 'dimension' with 'parallel universe', 'alternate universe' or 'another plane of existence'?

[RepliMagni]

Aye, that's kind of what I got from it.....but I'm curious what evidence there is for these other dimensions? Perhaps I'm being overly-dense at the moment, but I thought that all points in space were plottable across three dimensions, x, y, and z:

http://www.intmath.com/Vectors/235-3D.gif

So is this theory saying there are in fact millions of dimensions which essentially align to create these three basic dimensions, and that if we look hard enough we will be able to find them? The difference between looking at a rock with the naked eye, and then using a microscope?

[Ashu]

You mean travel to other dimensions?

Are you sure you are not confusing the concept of 'dimension' with 'parallel universe', 'alternate universe' or 'another plane of existence'?

Mno i was actually referring to a more physical comprehension of mathematics in particular, referring to it as a dimension.

[deni]

Aye, that's kind of what I got from it.....but I'm curious what evidence there is for these other dimensions? Perhaps I'm being overly-dense at the moment, but I thought that all points in space were plottable across three dimensions, x, y, and z:

http://www.intmath.com/Vectors/235-3D.gif

So is this theory saying there are in fact millions of dimensions which essentially align to create these three basic dimensions, and that if we look hard enough we will be able to find them? The difference between looking at a rock with the naked eye, and then using a microscope?

That's the case in the Euclidean space ... it has 3 dimensions and it is the space we live in.

There are other spaces as well, depending on the concepts behind them. While some of them are physical (for example the string theory uses 10 dimensional space and implies that we do not live in 3 but in 10 dimensions), others are purely mathematical concepts (for example the Hausdorff-dimensions) and thus independent from the simple 3D space we live in.


As for original question: I have no idea lol

[JolietJake]

oh, dear Lord, I feel like Col. O'Neill listening to Carter explaining something........although I probably would understand a bit more than he lets on that he does

[Bad Wolf]

Explain to me the concept of a transfinite symmetry group with 10 to the power of 19 dimensions.
Thank you!

Sick came up into my mouth, and I had to swallow it down...

Bad Wolf

The Man Who hates Maths

[RepliMagni]

That's the case in the Euclidean space ... it has 3 dimensions and it is the space we live in.

There are other spaces as well, depending on the concepts behind them. While some of them are physical (for example the string theory uses 10 dimensional space and implies that we do not live in 3 but in 10 dimensions), others are purely mathematical concepts (for example the Hausdorff-dimensions) and thus independent from the simple 3D space we live in.

*disclaimer: forgive my complete ignorance:

10 dimensions? How far is that an abstract concept that has not and cannot be proven? Or is there physical proof that more dimensions exist other than simple three dimensions and a time dimension?