I have been staring at this image for ages. It is a representation of the cross sectional image that a six dimensional object would leave if it intersected our space. I'm trying to get my head around that and failing. Hence the staring.
Higher dimensional objects can look like anything at all in lower dimensional spaces, it's lower dimensional objects that are restricted in higher dimensions, not the other way round!
The most disturbing thing about viewing higher dimensional objects is that things which look like different objects in a lower space may turn out be all one object when viewed from a higher space.
Imagine pushing your fingers into a two-dimensional plane to get the effect!
Therein lies the mind bending challenge. I believe that this is a highly symmetrical object in 6 dimensions - a 6D sphere or cube analogue. I have been trying to figure out which could produce a 3d cross section like this. Blind men looking at elephants have nothing on this.
(I think it is a symmetric cross section 6d cube - hyper hyper hyper cube - near to a vertex)
Thing is, I don't see the point in trying to define a 6D sphere. A sphere is a three dimensional object.
I'm assuming that a "6D sphere" is some sort of shape where the entire exterior surface is equidistant from the centre of the object in all six dimensions? But it isn't a sphere to me.
One could describe a sphere as a hyper-circle, but it would be silly! :)
Yes, circles, spheres and their higher dimensional analogues for which we don't have convenient names are defined as an locus equidistant in all available dimensions from a single point. The commonality is the form of a mathematical formula which can be generalised to any number of dimensions. The point is to see how that formula manifests as you go to higher dimensions. I guess you have to be a maths nerd to appreciate it but it does have applicability in 6D for brane theory which is one of the universe models which have come out of string theory.
If you can get your mind to 'see' in six dimensions, I have a dog I'd like to sell you who can read the newspaper. And if the above object is a cross-section, I need to rethink much of my cartography ... although I suspect my brain is much more mundane than I'd like it to be.
If I stare at it any longer I will need that dog as a guide dog. I have to resort to the maths a lot because like most people I can't actually visualise in 6D. Only, my maths isn't really up to it anymore. It used to be once - or that may just be that my memory isn't up to it either.
It is a cross section ... of sorts. The usual type is a 2D slice across a 3D object. This is a 3D slice of a 6D object.
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branchandroot
no subject
Date: 2007-02-13 06:00 am (UTC)no subject
Date: 2007-02-13 06:13 am (UTC)no subject
Date: 2007-02-13 06:26 am (UTC)Higher dimensional objects can look like anything at all in lower dimensional spaces, it's lower dimensional objects that are restricted in higher dimensions, not the other way round!
The most disturbing thing about viewing higher dimensional objects is that things which look like different objects in a lower space may turn out be all one object when viewed from a higher space.
Imagine pushing your fingers into a two-dimensional plane to get the effect!
:)
no subject
Date: 2007-02-13 06:42 am (UTC)(I think it is a symmetric cross section 6d cube - hyper hyper hyper cube - near to a vertex)
no subject
Date: 2007-02-13 06:51 am (UTC)no subject
Date: 2007-02-13 07:04 am (UTC)I'm assuming that a "6D sphere" is some sort of shape where the entire exterior surface is equidistant from the centre of the object in all six dimensions? But it isn't a sphere to me.
One could describe a sphere as a hyper-circle, but it would be silly!
:)
no subject
Date: 2007-02-13 07:13 am (UTC)no subject
Date: 2007-02-14 09:13 am (UTC)no subject
Date: 2007-02-14 09:24 am (UTC)It is a cross section ... of sorts. The usual type is a 2D slice across a 3D object. This is a 3D slice of a 6D object.