I thought about this myself some time ago but I took a different approach.

How do we represent a 3D object in a 2D world (e.g. 3D games)? In essense, we take the x and y cordinates and divide them by the z coordinate. The result: As the object moves across the (non-existant) z axis, the 2D object gets smaller and bigger.

Extend this to 4 dimensions, representing in 3 dimensions. Take x, y and z, divide by the 4th spatial dimension of w and what do you get? A 3D object that gets bigger and smaller as you move it on the w axis.

I am now working on a device that alows me to push a loaf of gold along the negative w axis to make me infathomably rich [grin]

Quote:Original post by Oxyd
IIRC the time does not exist! I think, it was Einstein, who discovered this. Time is only set of presences stored in our memory. Thus - it's human-devised conception. The time is only inside us.

Oxyd

nah, time exists, if only as a construct of space. Einstein discovered time is relative to velocity, but that very discovery insures the existence of time. however, in simple linear geometry time and space can be interchanged so long as velocity is constant.

(swept spheres)

Quote:Original post by Oxyd
IIRC the time does not exist! I think, it was Einstein, who discovered this. Time is only set of presences stored in our memory. Thus - it's human-devised conception. The time is only inside us.

Oxyd

I always thought time was an illusion-- but if I say that around normal people, I just get called lazy. [grin]

Quote:Original post by Yann L
Crispy: there is one very important point you should consider when talking about "spatial" dimensions: the definition of the term "spatial". Spatial refers to dimensional coordinates perceived as space extends. There are only three of them, there can't be a fourth, simply because we wouldn't perceive it as a spatial extend. Basically, in your example, Daphne doesn't have an additional spatial dimension to Larry, because Larry lacks the ability to perceive it as a spatial extend. However, Daphne could extend it's 3rd dimension within the time dimension of Larry.

And that's the whole trick with projections: Larry would see Daphne as a projection of his 2D surface space along his time dimension, not along a 3rd spatial one.

In that case, it's only a matter of wording and perception, which both are irrelevant since there is absolutely no way of telling what that extra dimension is actually like.

What you're saying would very well support the hypothesis that time travel is more than possible. Furthermore, String theory claims there are 11 dimensions. We, commonly, only know of four. Taking this idea a step further, for instance, gravitons are known to interact with these extra dimensions - while that doesn't suggest that matter could, it does provide a potential means of transmitting data between these dimensions (as suggested by the Elegant Universe).

What's the current scientific stance towards interdimensional travel? That is, could something like a human being, theoretically, be dragged into a, say, 6D environment or are we forever glued to this boring 3D world?

All in all, the more I invest my brain cells in this, the faster they seem to be burning up and the more often I need to check if I can still touch my nose with my index finger. This is fun.

Quote:Original post by Crispy

Quote:Original post by Yann L
And that's the whole trick with projections: Larry would see Daphne as a projection of his 2D surface space along his time dimension, not along a 3rd spatial one.

In that case, it's only a matter of wording and perception, which both are irrelevant since there is absolutely no way of telling what that extra dimension is actually like.

More about perception that about wording. We perceive the fourth dimension as time. The behaviour of this dimension is clearly different than the one of the three spatial dimensions. But from the point of view of string theory, it's "just another dimension". The big question is why we perceive it as linear time. It might be that our three spatial dimensions are just drifting along the fourth dimension at a more or less constant rate, a little like we are drifting along the spacetime curvature (expanding universe). It might even be that time is nothing other that an expansion movement. It would be interesting to know if time "decays", ie. if time becomes slower over time. But since you cannot analyze the variation of a quantity over itself, we will never explicitely know (unless we had an observer outside of our time frame). Perceiving this expansion as the constant rate at which things happen might very well simply be the way we deal with this additional dimensionality.

Quote:Original post by Crispy
What you're saying would very well support the hypothesis that time travel is more than possible.

Depends. If we take the hypothesis that the time dimension is fundamentally equivalent to other dimensions, then yes, it would be possible. We know we can both accelerate and reduce the speed of time movement (relative to another frame), if we play around with very high speeds and gravitational fields. Forward time travel is definitely possible through gravimetric fields, that's a fact. Backwards time travel would be possible, if the time dimension is symmetric, we would just have to push ourselves backwards. This would theoretically be possible by exposing ourselves to an anti-gravitational field. We'd need negative mass matter ("exotic matter") to generate such a field. According to quantum mechanics, such exotic matter is definitely consistent with physical laws, and could therefore exist. We just have to find it...

For some years, many scientists believed in the so called "cosmic censorship principle", whereas the universe would simply disallow things that could possibly hurt causality. But this principle has partially been disproved by Saul Teukolsky, who derived a fully consistent computer model of a naked singularity without an event horizon - which would totally break causality.

Quote:Original post by Crispy
Furthermore, String theory claims there are 11 dimensions. We, commonly, only know of four.

Five, if you count curvature in. The other ones are highly abstract, and partially curled up.

Quote:
Taking this idea a step further, for instance, gravitons are known to interact with these extra dimensions - while that doesn't suggest that matter could, it does provide a potential means of transmitting data between these dimensions (as suggested by the Elegant Universe).

That's right, data is constantly transfered through these dimensions. If a large mass, say earth, moves around the sun, it both influences time and curvature. That is a way of information transmission.

Quote:
What's the current scientific stance towards interdimensional travel? That is, could something like a human being, theoretically, be dragged into a, say, 6D environment or are we forever glued to this boring 3D world?

We already live within those higher dimensions, we just don't perceive them directly. "Normal" matter (ie. not exotic matter, not strange matter) that make up you and me (ie. classical fermions) is bound to exist within 3 spatial dimensions. Period. There is no way for it to suddendly expand to 6D. But if you ask about whether we can "tunnel" 3D matter through a higher dimensional coridor, then it depends. Energy can, matter might. See wormholes - but those could theoretically only serve as a passage to classical matter if stabilized by negative mass exotic matter.