if two 2-spheres overlap, you get a circle where they overlap.
If two 3-spheres overlap, I think you would get a ball, in 3D space, for where the two touch.

I just wondered whether matter, or particles might be the interaction between two hyperspheres(3-spheres), ie the Universe,as one, and the smaller one that causes the particle...

I know electrons are thought of as probability clouds, but maybe the two 3-spheres could be thought of the same way.


I dunno, just a thought.

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If you have two sphere overlap then if you look at where the plane that can be drawn through the intersection of the two spheres then yes this area would be a circle but the same is true for a cube and sphere if they are aligned properly.

The actual intersection between two 2-spheres is not just a circle. It is still a 3 dimensional object.

As for the intersection of two 3-spheres I'll have to bow out to someone with the actual math to do this. Likewise two 3-spheres would still produce an intersection that is 4D.

What do you think your idea adds to the probability cloud?

Well, I was just saying that electrons aren't really balls, most of the time, are they? I'm not sure. When an electron is detected, does it collapse into a ball-like object?


And I'm not sure about what you said, a 2-sphere is a 2-dimensional object embedded in 3 dimensions, I think, so the intersection is 2 dimensional; is it not? Or is it a one dimensional circle, in a 2D world?

The intersection of two balls would be 3D, but that's not the same..

Oh, well. A bit more to think on.

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I think I'll nip over to Q&A and ask about the intersection thing.


eta: What would be the intersection between two 3-spheres?

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That's a very promising thought, go on..

Indeed, is there any thing like 3-balls in a even higher dimension Universe ? could those 3-balls expressed in a form of , say 4-balls, or 5-balls ? flatten ? how would 3-balls in a 5 or 6 dimensional universe, intersect ... means ?

If the observable universe is itself a 3 or 4 -ball, what would you say about the background, the wholesome Universe, would be ? a 4 or 5 ball ?

I like Prof Muller's term that the fundamental particles can be called "particle waves" They have properties of both particles and waves. How you measure them seem to determine how the wave function collapses.

Someone correct me if I'm wrong but a 2-sphere is just a sphere. a 3-sphere is a 4 dimensional equivialent to a sphere.
ie 1-sphere = circle
2-sphere = sphere
3-shpere = a 4 spatial demensional object whos has a surface where every point on that surface is the same distance from another point within that 4 spatial dimension world.

So a 2-sphere is a 3d object, a 1-sphere is a 2d object. n-sphere is a n+1 dimensional object.

The funny thing about physics today, at very root formulation, are dealing with equations (invariants) something like:
E^2 = (MoCC)^2 + P1^2 + p2^2 + .....
S^2 = (Tc)^2 - X^2 -Y^2 -....
etc.

In general Y1^2 + Y2^2 + Y3^2 + ... + Ym^2 = X1^2 + X2^2 + .... + Xn^2 ( Eq 1 )

Eq1 is in fact a funny form of 2 Equations combined i.e. [ when K1 = sqrt( K2^2) ]:
Y1^2 + Y2^2 + Y3^2 + ... + Ym^2 = K1^2 (Eq 2 )
X1^2 + X2^2 + X3^2 + ... + Xn^2 = K2^2 (Eq 3 )

Do they make any sense to you ?
Two b___s interaction ? ( fill in the blanks. )

that makes no sense to me, no.

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I agree.
They are just (m-1)-sphere and (n-1)-sphere, nothing more .... not everybody like math, my fault.

You agree that it makes no sense to me?

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Everybody is different, making sense or not is personal ..
If you said so. I can't help it .

.... second thought, is it better for me to:

I don't agree.
Following by something like a 5-square intersect with a 3-sphere in a 10d space , depends on their orientation, could be a circle, etc ?

Not sure about 5-squares....

topologically an n-square is the same as a n-sphere?; I don't know, do they even exist.

Wiki has a page on n-cubes.

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