Portals and (imaginary or negitive?) space

[alan2here]

I made a thread with general exploration of the concept of portals before but now I want to just explore this scenario. I was wondering where to put this but I think that it needs to be explored mathematically to be solved although I would be grateful if explanation would be given as well as mathematics.

 

For this thread what I will be calling portals are 2D areas of space in a 3D environment, they behave physically like an other very thin thing would. They can't bend and are rectangular. They are one sided and the back side is solid, things cannot pass though the solid parts. There are thin edges around the front side much like the frame of a picture, they are also solid. The functional part of the portal is therefore in most of the middle of the front. There are two portals and one of them has the solid parts colored red and the other has the solid parts colored blue.

 

They are linked to one another such that stuff which passes though one seamlessly moves out of the other with momentum and other properties conserved. An observer therefore looking at the two portals with an item half way though one (therefore by definition it would be half way though both of the portals) would see two items. There are many interesting possibilities mathematically such of both were put at 45 degrees from horizontal facing each other and a ball was thrown though one what angle, position and power would it have to be to form a continuous loop.

 

 

My scenario involves the red portal being moved though the blue one. For the first part we move it only some of the way though, lets say 10%. Certain combinations of the two size dimensions and orientations of the interfitting portals make the portals not fit or get stuck later on and certain combinations work quite well.

 

What would you see through the red portal? Think about it before reading the answer. The answer is you would see the small end of the red framed portal going towards you and the larger end going away from you.

 

You can continue in your mind adding more iterations but it gets complicated. Bear in mind that we are only bending space that exists, there are only two portals there. It is a bit like looking into a mirror.

 

What happens when the red portal goes 40% though the blue portal. The solution potentially becomes more complicated, you will see why if you try and imagine it. Read on until the end before you try this as this is where I ran out of mental power and had to go write a thread about it.

 

Now try 60%. Here we have a problem, in our mental model we seem to be using space that doesn't exist anywhere. As the title suggests names could be imaginary or negative space?

 

EDIT: I would quite like to know if my explanation is no good, the problem is uninteresting, the problem is too hard or you are all still thinking about it. Obviously chaining the size of ether portal or rotating them differently makes the solution much harder and in some cases also opens up more questions.

Edited July 18, 2008 by alan2here
multiple post merged

[scmatema]

You said anything that goes through one portal comes out through the other one.Terefore, one would, theoretically speaking, be unable to put 60% of the red portal through the blue one, as it would have to come out through itself.

[alan2here]

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