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[The First Speaker]

Four-dimensional Rubik's Cube

[Anderian]

Heh. That's kind of cool - I've been using this list of movies also hosted on the same site as a list of movies to rent, and it turns out that it's the list of one of the cube's creators, Melinda something. Nifty. As for the cube itself, I could never manage the 3D one, I'll leave the 4D to you guys.

Nifty name, by the way.

[JebJoya]

Okay, this has got me thinking, what would the weight (note i say weight and not mass) of a 4 dimensional cube be, if we were to have one (say, for example, the receda cube is 4 dimensional, and we are seeing a 3 dimensional cross section of it in our universe). Assuming, for the moment, the Einstein theory of gravity, would the weight be determinable, or for that matter even relevant, and would it have an indeterminable mass in our space? I'm trying to imagine a 2d/3d version, and am having difficulty, maybe someone else can visualise it better?

Sorry for the off topicness here, it just made me think...

Jeb

[The First Speaker]

I think if we could see a 3D cross-section of the hypercube, we would be able to model it mathematically in 4D and using the measured mass of it in our world, could calculate its density in 3D and then extend this to the fourth dimension... or maybe I'm just talking nonsense

Cool Fourth dimension site[/url]

[Leeravitz]

Oooh, yeah. Now that'd be a trick. If Mind Candy had set it up so that we had to construct a 4D Cube within a three dimensional reality

You never know, maybe the mystery backers are some obscure conglomerate who have been beavering away to create it in a laboratory somewhere.

Although, then again...

[Violet]

aaaaah, u guys want the Cube to be a hypercube too - so wouldn't that mean it'd have to be a tesseract on earth, as we can't have 4 dimentions in a 3 dimentional world?

I can feel a big slimy fish coming towards me...

[yanka]

In my understanding, it wouldn't really be a tesseract in 3D: isn't a tesseract just a way of illustrating a hypercube in 3D space, specifically by "unfolding" it, like here?

[hamatoyoshi]

[thebruce]

technically we are viewing everything in 4D - we just can't take in the objects in their entirety, because our vision is also locked in this '4th dimension', so we only see snapshots of the first 3 dimensions as we travel through the 4th... that is if you consider time the 4th dimension rather than it being another physical plane of existence...

I guess an object that changes over time could be similar to that fist moving through the 2D plane... we can see a 3 dimensional object change over time, just as a 2D being could see their visage of the 3D object change as it moves through the plane...

I guess the theory of how a 4 physical dimension object would appear in a 3D world, or even if it would appear, is an ongoing debate... interesting to say the least

[hamatoyoshi]

Ignoring time as a possible fourth-dimension...

I didn't want to go into it in my first post, but our retinal image is only two dimensional, but we have different facilities, stereoscopic vision for one, that allow our minds to perceive depth.

Just Googled an interesting page concerning it.

Extending an analogy of ourselves to other dimensions, a two-dimensional being should only be able to see one-dimension, passing one's hand through its world should just make a line suddenly appear, though it may have facilities to allow its mind to perceive both dimensions.

Finally, a fourth-dimensional being (a Perplexian?), should be able to see an item (say a dumpster) from all directions at once, the outside, and the contents.

[thebruce]

but at the same time, I think the idea of not seeing a different dimension can be applicable going down the scale... in a 3D world, we can't perceive a 2D object. If we see an object that has no depth, then it must have some depth, even if microscopic, in order our vision to perceive it... can a 2D object exist in 3D space? Yet a 3D object may be perceived in a 2D world in a very limited way. Would a 4D person be able to perceive us in a 3D world?

[JebJoya]

I think my point has rather been missed, so I shall try to enforce it.

The point I had was what would the WEIGHT of a 4 dimensional object appear to be in our 3 dimensional world? Given Einstein's theory of gravity, it relies on a mass distorting Space-Time in the 4th dimension, but what would this result in in terms of weight of a 4 dimensional object in our world given that it has no gravity directly affecting it?

Jeb

[hamatoyoshi]

If we saw a strictly 2-dimensional object, for example a square, it'd be like looking at a rotating sheet of paper, except when you got to the "thin" end, you'd see nothing at all.

That said, I'm not sure how we could interact with a two dimensional object. I could see the possibility of collision if one walked into the "area", but if one walked into the "thin" end (which in fact doesn't exist), would it merely appear to bisect the individual?

[The First Speaker]

If there is no gravity acting on it it will have no weight. Weight is simply a measure of the force a mass is experiencing in a gravitational field.

Slap me if I'm being pedantic.

[JebJoya]