Speculation with portals
I've watched that, and while it's an interesting thought exercise, it doesn't provide a convincing argument for time actually being the "fourth" dimension.
Consider a point traveling along vector x. The point experiences this travel as a passage through time. It has no control over the rate at which it travels, but it knows that it travels. It decides that the dimension above it, 1st, must be Time.
We as observers of a higher dimension, however, see that this point actually belongs to a set of points (a line) that are not, in fact, moving with relation to each other. This line lies along vector y. This line, y, is in its entirety, moving along vector x.
Through the magic of hypothesis and anthropmorphization, we communicate to our point that the line (1st dimension) in which it resides is not, in fact, Time. It is baffled, claiming that since Time is the only dimension it is aware of, it must be the next higher order. We grant it the ability to communicate with its neighbors, and all of the points in line y gradually become aware of each other and discover that there is indeed a dimension between them and Time.
Quickly, they conclude that Time must be the second dimension.
While it is true that this line is moving along vector x, upon closer examination we see that it is part of a collection of an infinite number of other lines, all of which exist on plane yz. All of these lines are fixed in relation to each other. This entire plane is moving at a fixed rate along vector x.
Our community in line y is willing to consider this now, when we tell them. They claim that their experience of Time, and our revelation of lines and planes, adds up to three dimensions. Therefore time must be the third dimension.
We know, however, because we have been observing and discussing the situation, that this plane yz is not moving at all in relation to us. Calmly, and with great pride in our wisdom, we tell them that because we can experience length, width, height, and time, Time must be the fourth dimension.
Immediately after that, great bulbous things grow from nothingness to the size of basketballs in the air around us, close in, and with a strange sensation rip us from our cozy collection of lines and planes.
Nicely written, Shmitz.
Just to reiterate, guys, Portal is a puzzle game where you manipulate geometry/topology in order to play, so we should probably stick to discussing geometrical dimensions only in these hypotheticals.
Not to put too fine a point on it, the people who keep trying to bring time and string theory into it are really deeply missing the point. Thinkers in those fields find it useful to refer to certain phenomena as "the nth dimension" in order to explain things to their students, to have a shorthand for discussing matters with colleagues, or sometimes simply to sell books.
Just because they are saying the same words -- "fourth dimension!" -- doesn't mean that they are referring to the same thing that a topologist or a Portal player designates by that term. Context matters. Our context is strictly geometrical. Can we please give the interruptions about time a rest?
UNLESS... unless anyone wants to give their thoughts on how portals would behave when traveling at near-light speed? I'm pretty sure time (or spacetime) would come into that question. I ain't fer sure, but I reckon so.
Let's clear up the fourth dimension.
Myself, a physicist, see the first four dimensions as altitude, latitude, longitude plus a timeline. This way one can explain the non-Euclidean space-time used in Einstein's theories of special relativity and general relativity.
Others who refer to theoretical mathematics, see the fourth dimension as an addition to the three already established spacial dimensions and use it as an asset to describe an objects position, shape and size in a system, rather then it's change when exposed to duration.
As such, the fourth dimension can be one of two things, depending on the profession one is discussing. In this case, we are arguing from different professions and therefore have hit several roadblocks along the way. One can say we have been arguing with ourselves.
Yes, I totally agree.
My point, which I maybe didn't make clear, is that it's the physicist/cosmologist types who are clouding the issue. Time is completely innocuous in Portal. Time does not affect the behavior of portals; Portals do not affect the flow of time. On the other hand, the whole game is about manipulating multidimensional manifolds.
So, my feeling is it's obvious we should talk about what's interesting about the game without confusing everyone by introducing theories from unrelated disciplines.
That's another great thing about taking the topological approach: It's abstract, but it's not pure theory. You can figure out a lot about 5- and 6-space manifolds just reasoning by analogy on your own before you run into anything really wonky or controversial. Not so with metaphysics.
It does actually. Portals do not support the fourth dimension (as in physics (time)) and will bream down and close immediately when exposed to duration. The reason this is true is because any portal on any moving surface will close, and for any surface to move or shift in any way, the fourth dimension (again; physics) must be present.
However, I would like you to explain your theory of portals in 4-space in a simpler manner, so that I can understand it. 
I would have to disagree at this point. Everything is moving through time, including the portals and the surfaces the portals are applied to. If this wasn't the case then no portal could last longer than an infinitely small duration and as such be useless.
What I think we're seeing in game is that as long as two portals are on surfaces that are stationary relatively to eachother they will stay connected. But as soon as one of the surfaces starts diverging from the other (relatively speaking) it closes. (Which is illogical imo; both should close since neither should be able to detect which of the other is actually moving, but that's a side issue.)
So -- in theory, something easily disproven by Hammer use -- if we construct two pistons that move in exact tandem and thus always have the same distance to eachother, with portable surfaces on, it should be possible to attach portals to them and have them stick. My gut feeling is that that's definately not how the game will work though, since the game actually has a "world space coordinate system", something that doesn't really exist in the real world, but is an easy approximation for game developers to cling on to 
Aaaaaanyways...
I wonder if one could posit a theory linking material validity to portals closing on movement. Why will a portal stick to concrete, but not metal/glass/etc? It seems at least possible to me that the reason may be very similar to the reason a portal collapses when its supporting surface moves.
It's a good point actually. It's either connected to the fact that portals can't support moving surfaces, as you say, or if not then it must be connected the actual underlying properties of the material.
I don't really see the connection to moving surfaces though, so I'm inclined to think that it's the latter that's the case. But if so, what then is it that a portal requires of the material of the surface it's attached to?
It might be that the portal projectile has to be able to "stick" to create the portal connection, which would explain why it won't work on surfaces that are too hard (metal would simply bounce the projectile off, whereas concrete would allow a fast travelling solid projectile to stick). But if that's the case why don't the projectiles leave bullet holes after the portal has gone away again?
And this doesn't explain the fact that you can shoot a portal at a patch of concrete that's too small to actually hold a portal, which will have the same effect (ie. the projectile simply bounces off). Some of this might be explainable if you accept that portal the game is simply an approximation of the actual portal stuff, but meh, that's sort of far fetched.
Imo when a projectile hits a surface that is too small to hold a portal, but otherwise of valid material, we should see an animation of aportal beginning to form, but then collapsing when it can't expand to it's full size.
I 
this thread so hard.
Fuckin' A right on both points, IMO.
You are semi-purposely conflating movement and time to prove your point. What you say is true, that for portals to react to movement at all (relative or otherwise) must mean they experience time. What you imply is that a change in position/movement is equivalent to a change in time, therefore the portals close because they "do not support the fourth dimension, [time]."
This is invalid reasoning. You have not shown that the reason they close is due purely and only to time. You cannot rule out that it is the movement, relative or otherwise, that causes the portals to close, and that the portals experience unperturbed time while these changes occur.
True, movement involves time, in the same way a fire involves heat, but you cannot say that movement is time or fire is heat. It is just not so.
Furthermore, I fucking beg you to stop referring to time as "the fourth dimension" even if qualified by (physics). It's just confusing. Just call time "time." There will be no confusion. I also liked your "when exposed to duration" phrasing. That's very clearly stated.
Can do. Gimme a couple hours to come up with a good explanation. Just to be sure what you're asking: You want a more intuitive way to start understanding portals as a purely spatial phenomenon in four dimensions / a 4D manifold / 4-space (these three terms are equivalent). Right?
Alright then. 
And yes, they are equivalent, and yes, thet's what I'm asking.