I've started thinking lately that we're actually in the [math]\pi[/math]'th dimension and quantum theory is a result of us realizing those extra pieces of our fractal dimension. In the infinitely many other fractal dimensions on [math](3,4)[/math] the ratio of the circumference of a circle to its diameter would not be 3.1459265... and the limit [math]\lim_{x\to\infty} (1 + 1/n)^n[/math] would evaluate to something other than 2.7182818... but most likely [math]e^{i \pi} = -1[/math] would still hold for the new values of [math]e, \pi[/math].
>I've started thinking lately that we're actually in the ππ'th dimension Prove it or fuck off
Jordan Murphy
Reading this post will keep me a way from Veeky Forums for a while (thank god), because this is most fucking retarded thing I have ever read here.
Jackson Morgan
The very least we know is that we live in something that is well described by 4D spacetime, per experiment. This does not preclude the possibility that has more than 4 dimensions (some advanced physics theories require up to 11D), but if there are more than 4 dimensions it is not obvious how they manifest themselves.
Some physicist have considered universes with different numbers of spatial dimensions and time dimensions, and while some of the arguments are suspect, the case has been made that there aren't many other combinations besides 3 spatial dimensions and 1 time dimension that seem possible.
Personally, I think there is something about the mathematical structure of 3D and 4D space that is fundamentally unique amongst nD spaces, and is why we experience the universe as it seems. I don't have many examples (please, if any one else has some, share), but there are certain group structures and things like cross products that only really work 3D. I wonder if someday we will be able to prove the dimensionality of the universe could be nothing other than 4 for the logical consistency of physics.
Tyler Jones
>The dimension we are in affects our ability to do math involving any dimensions Everything else you said is stupider. This is funny.
Ian Hughes
>lim x->inf >uses n in the expression
Jesus christ, what a stupid fucking post.
Levi Carter
Put down the blunt son, also delete this shit.
Brody Watson
we don't know we're in any dimension at all, light is flat when reaches the eye, what is really happening to the nonvisible frequencies of matter can't seen
at least, not under normal conditions
DO DRUGS
ask a parent or guardian for help
Adrian Bennett
actually, some how you bring up a valid point in that the universe may be a hologram. No joke.
Matthew Hughes
DELET THIS
Nolan Foster
>cross products that only really work 3D This can be generalized to other dimensions. In n dimensions its [math] \star (v_1\wedge v_2 \cdots \wedge v_{n-1}) [/math]
David Nguyen
My understanding (which is nothing) is that you get different types of mathematical objects when you apply the wedge product in different dimensions, and only in 3 and maybe another dimensional space the result is a (psuedo)vector. I really don't know though because I have never studied generalizations of cross product.
Parker Lee
The formula I gave gives the standard cross product in 3 dimensions but generates an analogous object in any n dimensional exterior algebra. You input n-1 vectors and it gives you the signed hypervolume generated by the vectors in their mutually orthogonal direction.
>ITT: everyone shits on me for being speculative but provides no proof or argument for why our existence is in an integer dimension. question your assumptions some time plebs. this is food for thought, what would existence in the [math]pi[/math]'th dimension look like? have YOU seen the edge of the universe?
Euler asked why he shouldn't wear pants on his head, and look where that got him.
I'm not sure about 4D but in 3D and 7D the cross product has this property: [math] a x b = - b x a[/math] and in 3D the result is unique.
Either way you jerks are going to find out one day that Mandelbrot changed the world and you'll think back on your poor ol' OP.
Jackson Phillips
You're still in HS. Get off this board and learn instead of talking. It'll raise the intelligence of the board by a few IQ points
Ian Hughes
Dimensionality is related to the number of vectors in a basis of a space. Now tell me, how can you have 3.1415926535.... vectors?
> 3D and 7D the cross product That's what I was thinking of, though I don't anything about it. > look where that got him lol
That is one definition of dimension particular to linear algebra.
This guy was getting at the fact the fractal folks found out that you can meaningfully assign some mathematical objects fractional dimensions.
The concept isn't too hard to grasp.
Consider a 1D line segment. You can assign a measure to it saying that it has length [math]L=L^1[/math].
Consider a 2D square with sides of length L. You can assign a measure to it saying it has area [math]L^2[/math].
Consider a 3D cube with sides of length L. You can assign a measure to it saying it has volume [math]L^3[/math].
Consider a 4D hypercube with sides of length L. You can assign a measure to it saying it has hypervolume [math]L^4[/math].
etc.
The pattern the fractal folks picked up on was that one way to define dimension is how quickly does your measure grow when you increase your object's scale. People found most things we are familiar with work like how we'd expect, like your example of vectorspaces.
However some things act... weird. Take the serpenski triangle. When you define the above procedure rigorously, you find the triangle has (Hausdorff) ln(3)/ln(2).
Still, I've thought non-integer bases would be interesting, but it seems impossible to construct a positional number system with them, so I don't know how'd you'd write them down.
It's trivial to demonstrate the Universe is either, at a macroscopic level, a 2D+1 or a 3D+1
It is evident we are not a 1D +1 nor a 4D+1
Alexander Murphy
"Dimensions" are mathematical constructs we came up with, and we just happen to observe 3 orthogonal ones at human scale on Earth.
Brayden Carter
the dimensionality of geometric objects/patterns and the dimensional of a vector space don't directly translate when you start considering fractal dimensions. The Hausdorff dimension doesn't provide a prescription for writing down elements of a 2.43 dimensional vector space; it measures instead how much of the ambient space an object fills in compared to just the space of parameters required to map it out.
Justin Lewis
>too stupid to read the shit that's linked >hurr none of you provided proof
Tyler Clark
Your gif hurts my brain, make it stop.
Robert Ramirez
It will hurt your brain to hurt even more that the cube has to spin 720 degrees to get back to it's original state, just like electrons and any other spin 1/2 particle, and yet the belts never tangle or twist up...
If this isn't a meme please do yourself a favor and research Mandelbrot's contributions.
Isaac Green
No, it's not that the electron has to spin 4π radians to get back to its original position, it is a point particle. The whole system needs to rotate that 4π. Read up a little more before spouting out rubbish :)
Jeremiah Powell
What the shit did I just read
Nathaniel Johnson
I've never thought about it like that, I'm still trying to pick up the subject, and I don't have many good resources on it. I really need to pick up Sakurai.
Can you elaborate a little more to further the conversation rather than stopping short and just calling me ignorant?
Asher Reed
0, 1, 2, and 4+ dimensions are theoretical only. they make no god damn sense in the real world. there are 3 spatial dimensions. end of story.
