Thank you for responding, I am to quick to think there will be no reply, Its the Latin nature of my Avatar I suppose take all the time you want.

I will add a few more bits-


If we line up the zero points of the two series



Have we got a field where what I referred to as functions can be compared?





Up and down times/divide; side to side plus/minus.


Now what about when we multiply the top series by zero?

Is the result not a series of zeros?



Thank you for your help I will by the next time try to get a bit of the terminology right.

(July 12, 2012 at 8:10 am)jonb Wrote: Thank you for your help I will by the next time try to get a bit of the terminology right.

No biggie. It's the way things work that's important, not the jargon. I'll try to throw up a more detailed response later, but right now it looks like the best characterization of your stuff is projective transformations. Being an artist, you'll probably enjoy/get a kick out of projective geometry anyways (this stuff works in higher dimensions too!).

Thanks for your help, but before we move into other dimensional use’s of this form. I think it would be nice to examine a possibility if this graph stands.



We seem to have a range of zeros or a stretched zero which is not a point, but that has length.
And although the value does not change we can see a definite progression along the line.

Is this a problem for theories such as those of Grigori Perelman. As a flow around an object will not necessarily be able to categorise what the shape is as, a distance of zero could contain enough differences to produce an inconsistent result..

My thinking is this way; I have a tours. I press the middle until it is almost connected, but is not actually connected. The central hole exists, but it occupies Zero space. If I categorise the shape by the flow over it, it will fulfil all the criteria of being a sphere, however if I categorise the same shape by the internal side of this zero space skin, it is in all effect a torus. We can do the same the other way round.
Now how could you examine a shape to find holes of zero size and get any meaningful result? So is it not so that Grigori Perelman’s theorem is only proof to a given resolution and not an absolute?

Shiite, what sexual orientation are your functions?



“I see it, but I don't believe it.”

— Richard Dedekind on Cantor's proof that the points in the unit interval were in one-to-one correspondence with points in the unit square.

(July 16, 2012 at 8:30 am)jonb Wrote: Thanks for your help, but before we move into other dimensional use’s of this form. I think it would be nice to examine a possibility if this graph stands.



We seem to have a range of zeros or a stretched zero which is not a point, but that has length.
And although the value does not change we can see a definite progression along the line.

Is this a problem for theories such as those of Grigori Perelman. As a flow around an object will not necessarily be able to categorise what the shape is as, a distance of zero could contain enough differences to produce an inconsistent result..

My thinking is this way; I have a tours. I press the middle until it is almost connected, but is not actually connected. The central hole exists, but it occupies Zero space. If I categorise the shape by the flow over it, it will fulfil all the criteria of being a sphere, however if I categorise the same shape by the internal side of this zero space skin, it is in all effect a torus. We can do the same the other way round.
Now how could you examine a shape to find holes of zero size and get any meaningful result? So is it not so that Grigori Perelman’s theorem is only proof to a given resolution and not an absolute?

The torus would be topologically distinguishable from a sphere--any loop enclosing the hole could not be shrunk to a point while remaining on the torus, whereas every loop on a sphere can be shrunk to a point.

If they're topologically distinguishable, then they will be geometrically distinguishable (since geometric manifolds incorporate topological manifolds).

(July 16, 2012 at 2:14 pm)CliveStaples Wrote: The torus would be topologically distinguishable from a sphere--any loop enclosing the hole could not be shrunk to a point while remaining on the torus, whereas every loop on a sphere can be shrunk to a point.

If they're topologically distinguishable, then they will be geometrically distinguishable (since geometric manifolds incorporate topological manifolds).

Is the same true for a sphere enclosing a sphere? At what point does the surface of the object become the object?

(July 16, 2012 at 2:06 pm)apophenia Wrote:


Shiite, what sexual orientation are your functions?



“I see it, but I don't believe it.”

— Richard Dedekind on Cantor's proof that the points in the unit interval were in one-to-one correspondence with points in the unit square.

Did you see it? What did the kid in the dunces cap make of his reflection in the ceiling?

(July 16, 2012 at 2:37 pm)jonb Wrote:

(July 16, 2012 at 2:14 pm)CliveStaples Wrote: The torus would be topologically distinguishable from a sphere--any loop enclosing the hole could not be shrunk to a point while remaining on the torus, whereas every loop on a sphere can be shrunk to a point.

If they're topologically distinguishable, then they will be geometrically distinguishable (since geometric manifolds incorporate topological manifolds).

Is the same true for a sphere enclosing a sphere? At what point does the surface of the object become the object?

I'm not sure what you mean by "a sphere enclosing a sphere." Suppose that S1 is a sphere of radius r1, and S2 a sphere of radius r2. If r2>r1, and S1 and S2 share the same center, then S2 encloses S1. This doesn't change S1's topology or S2's topology.

Or do you mean the surface enclosing the region 'between' the spheres?

(July 16, 2012 at 6:47 pm)CliveStaples Wrote:

(July 16, 2012 at 2:37 pm)jonb Wrote: Is the same true for a sphere enclosing a sphere? At what point does the surface of the object become the object?

I'm not sure what you mean by "a sphere enclosing a sphere." Suppose that S1 is a sphere of radius r1, and S2 a sphere of radius r2. If r2>r1, and S1 and S2 share the same center, then S2 encloses S1. This doesn't change S1's topology or S2's topology.

Or do you mean the surface enclosing the region 'between' the spheres?

A space of zero is enclosed by shell with no or one hole in it of zero size that shell is a sphere, the same shell with two holes is a tours since the holes are of zero magnitude how would you detect them?
I have a space of zero size what shape is it?

(July 16, 2012 at 7:00 pm)jonb Wrote: A space of zero is enclosed by shell with no or one hole in it of zero size that shell is a sphere, the same shell with two holes is a tours since the holes are of zero magnitude how would you detect them?
I have a space of zero size what shape is it?

I don't know what you mean by "a space of zero". Do you mean something like "a disc with one point, located at the center, removed"?