Are we stuck in three-dimensional thinking because the forth dimension must be time?

The fourth dimension you mention is, Time.  It is a dynamic dimension whereas the spatial dimensions are static.  Space moves as would an expanding ocean: the center remains fixed, as it were, creating more water.  But it gets weirder.

The number of spatial dimensions increases with the decrease in density of the space it inhabits.

The math is a little on the weird side of bizarre, but it really does work.

To grossly oversimplify, think of the density of three substances in a jar: oil, water, and air.  Water is densest of the three in this "closed" space."  Next is the salad oil.  Atop the mess sits air. 

So, what happens when we heat it?  The densest fluid (having the greatest specific heat) changes state: steam.  The oil (less specific heat) expands, but does not change state.  The air (the least specific heat) merely increases pressure but does not change state.

Do you begin to see where we're going?

Now, let's look at adiabatic heating.  It causes everything to expand or increase temperature (sometimes both).

Now, what happens when we increase the pressure and reduce the volume?  The mass remained constant, did it not. 

Now, let's increase the pressure just a wee tiny little tad bit more -- to that of a singularity.

We were talking about time, were we not? 

You remember, time? 

It's an answer about time. 

We measure time by the rate it causes things to slow down: the heavier a chunk of matter is, the slower it oscillates.  Now, let's increase the mass of that jar by an infinity.

It seems to have stopped.  Or did it?  It pushes harder than a compacted galaxy would push, but it moves so slowly that we call it, "Stasis."

When we talk about that sort of density, we collapse the matter in it a full dimension.  Instead of a lump (XYZT dimensions present) we have lost a spatial dimension.  It is now absolutely flat (no X dimension) but still has its original mass and YZT dimensions.  It is a sheet of infinite density, but radiation would pass through it as though it were not there.

So, if one infinity is not enough to give you a headache, infinity times infinity will give you a migraine.  Let's say that star has lost the Y-dimension, and now exists as a two-dimensional "fibril."  It has all its originating mass, but is compressed down so tightly that it is now a "String." 

AHA! Now we know where the precursor of P-theory and then M-theory came from.  String theory gave us the notion of compacting dimensions, did it not?

But wait, folks.  We're not done stuffing matter down to small enough spaces yet.  It still has ZT dimensions.  But before we go just that least little infinity tighter, let's pack it down until that mass has no space at all.  Just the T dimension.

Nasty squeeze, huh?

What keeps it that tight? 

Space.  Space has a nonzero mass, as Guth and Hawking proved.  It is enough to stuff exotic matter down to four dimensions from its previous five -- or a billion.  Or for all we know, infinite.

Ponder why loose matter is much colder than 0 degrees Kelvin.  And ponder how much colder it is outside our cracking hot universe that scorches away at 2.67 degrees Kelvin -- far too hot for Electronium and Positronium -- among the entire periodic table of light exotics (and at the opposite extreme, heavy exotics) we have already deduced.

http://en.wikipedia.org/wiki/QCD_matter

Science ( Rocmike3, Guth, Hawkin etc.) is forced to use a nonzero mass space. I am waiting for the idea, nonzero mass space becomes a medium, though we finally have a logic to the thoughts of waves. Nothing really can move in space (or in further spatial dimensions) without appearing and disappearing in a line of space positions just like a wave. The elasticity brings waves forward in speed of light. I guess, it is easy to explain also the standard model. Of course, using energy states stronger as the elasticity of  the medium causes appearing or disappearing of dimensions. This but needs a reference in a multi dimensional universe (+ time), Though spatial dimensions will come to existence as Rocmike3 it depictured. But never forget: to come in existence does not mean dimensions are new created, they are all there but in this new state of energy (Big Bang) they can’t be find, waiting for the appropriate state for referencing them self.

Electromagnetic waves or everything of SPIN 1 are „in“ spatial dimensions (XYZ in our environment).They don’t have to be 3D, they could be polarized to 2 or 1 dimensions.
If dimensions compete, then not only 2 by 2 but all by all.

The best way to ponder about dimensions is, to assume, there is a multi dimensional universe, time is only a phenomena caused by the lack of omni consciousness ( 3D-thought). I’m sure, science will soon need to explain more and more with multi dimensional effects.

String theory suggests 10 dimensions and supergravity suggests an 11th.  Each with it's own membrane,  or brane,  and P-branes.

Fre, you are starting to get it.  But let's retreat in a dead panic from compressive to dimensional physics.

Pity that this processor won't support math.

Z is our static spatial dimension, T is our DYNAMICAL dimension.  Go ahead and put the little arrow over the top of the T.  Then put the little X between them.

We arrive at Fx [x=!] (X,T),(Z,T), xtZT (T!,t,T).

Fx = analytical function
x=lateral
y=parallel
z=vertical
t=time
!=inverse function

We see that time retains its dynamical function regardless the compression of matter inside x,y,z dimensions.  XYZ, and X,Y,Z dimensions differ in congruency: taken as expansive/compressive, matter contained in these dimensions may reach infinite density as it loses a dimension to compression, and develops infinite heat due to adiabatic heating, presuming a "closed" thermodynamic system.

When compressed a further dimension, we encounter a multiple infinity of density,(8^8) infinity raised to the infinite power.  Time retains its dynamical constant, accounting for mass density.

In short, pack matter down a bit, and it slows down a bit.  Pack it down a full dimension and time suddenly appears to play tricks on us: where we continue to move forward through time, when compacted, the compact matter slows enough so that time APPEARS to move in reverse. 

Similarly, in "lighter" space than we have, more dimensions are present, time moves infinitely faster and will support far lighter particles than our dense space/time will support (tachyons, exotics, etc).  Regardless, time retains its dynamical nature.

We can see a hint about it here:

http://en.wikipedia.org/wiki/Shapiro_time_delay

I do believe Gunter's got it!

Particle spin is not part of dimensional mechanics.  But it becomes a necessary part of quantum and particle physics.  Spin-0 fields, of course, can react with virtually any other field, resulting in the vexing hassles we get with W+/-, and Z bosons.  With these little miseries ripping nuclei apart, my job gets tougher by the day (and that much more secure). 

Pack a chunk of baryonic matter down a full dimension, and it becomes 1/compact matter.  Pack it down 2 dimensions, and it becomes 2/compact (2/C for short).  -1C matter has expanded a full dimension, and is so light that our space crushes it like a Kenworth over a potato chip.

You have it, Gunter!  I am proud!

Thanks for your comment, Griffin.

String theory suggests 10 dimensions and supergravity suggests an 11th.  Each with it's own membrane,  or brane,  and P-branes.

Actually, M-theory and P-theory both suggest multiple dimensions but neither goes far enough into compact matter.  "Intersecting branes" answers SOME dilemmas, but sadly, it raises more.  It is a very exciting time to get into physics.

One dilemma is that we need to revise fundamental laws now and then: observations can be faulty as seen with the Voyager sapcecraft.  Either I am correct (space has a nonzero mass) or the Pioneer spacecraft have fuel leaks -- that are so close as to be negligible! 

As these birds fly faster, they reach a significant percentage of C.  Miracle of miracles, they accrete mass (converting kinetic energy to matter, a particle or two at a time).  Smack into enough W+/- bosons along the way, and something will interact, adding mass where if space had zero mass, the spacecraft would have a known trajectory.

Let's hope Compton and Einstein were correct.  If not, expect a lot of gray hair to litter the floor, because I can see a whole bunch of sexigenerian physics nerds ripping it out because they have to retract papers that it took them years to write.

http://en.wikipedia.org/wiki/Pioneer_anomaly