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 Forum index » Archive » Archive: Perplex City » PXC: Questions/Meta
Four-dimensional Rubik's Cube
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The First Speaker
Boot


Joined: 18 May 2005
Posts: 55
Location: UK

I've just finished a module on General Relativity, so I should probably be able to answer your question. Are we trying to decide if a 4D object could distort 3D space-time?
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PostPosted: Mon May 23, 2005 6:45 pm
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thebruce
Dances With Wikis


Joined: 16 Aug 2004
Posts: 6899
Location: Kitchener, Ontario

interesting... re:gravity... I think if we apply physics that we know in our 3D world to a 4D world, the physics won't apply... I don't necessarily think a 4D object won't have any gravity - I think the concept of gravity won't apply to a 4D object in our 3D world... we just can't conceive of a 4D object, given our physics rely on 3D objects existing in theoretical 4 dimensions... so the 4D object would likely have similar effects - existing in 4 dimensions, with an effect in the 5th...


I don't think we'd even see a 2D object in a 3D world... the idea of paper-thin still requires a 3rd dimension. In order for us to see something, it must exist with some depth... a 2D object in a 3D world I don't believe would be visible in any way as long as our sight is defined within 3 dimensions... the 2D object may exist, but it would be invisible from any angle... our vision would need to be the same as the being in 2 dimensions - our eyes would need to exist in that 2D plane, and they would only be able to see along the plane...
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PostPosted: Mon May 23, 2005 6:47 pm
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hamatoyoshi
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Joined: 02 Aug 2004
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JebJoya wrote:
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?


I saw your point, but I think it's too difficult to answer.

Here, however, is a discussion of what you're asking scaling from three dimensions down to two-dimensions and using lasagna for an example. Very-unscientific, but the only discussion I could find on it.

weight = mass * gravity

Assuming we scaled down to a three dimensional object in the two-dimensional world (back to the hand again; only using this since it's easier to visualize), I don't think gravity would change at all.

I'm assuming it would work the other way too.

PostPosted: Mon May 23, 2005 6:50 pm
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JebJoya
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Joined: 13 Apr 2005
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Worryingly, I've done a course on Relativity (Special and General) and I'm still a bit confused on how to visualise this one! Essentially, as I remember, gravity is caused by the deformation of Space-Time in the 4th dimension by an object (eg the Earth). Now, if we were to imagine a 4 dimensional object being cross sectioned through our 3 dimensional space, presumably the laws of gravity would not hold, as the object will not be affected by any form of gravity in the 4th dimension? (This is assuming that there is no distortion of the 5th dimension by the 4 dimensional object, but can we leave that aside?)

I don't know, it's rather off topic, but an interesting thought to get your head around...

Jeb

EDIT: ahh, mass + energy... This will require more thought...
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PostPosted: Mon May 23, 2005 6:54 pm
Last edited by JebJoya on Mon May 23, 2005 6:58 pm; edited 1 time in total
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HitsHerMark
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Joined: 22 Aug 2004
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Can't you also discover the mass of an object by displacement? No wait... That's volume.

Never mind.
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PostPosted: Mon May 23, 2005 6:57 pm
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The First Speaker
Boot


Joined: 18 May 2005
Posts: 55
Location: UK

I feel exactly as you do jeb. 3 years at Uni and still stumped by a seemingly innocent question.

Surely, at a bare minimum though, the 3D projection of the object would create its own distortion in our 4D space-time? The extra effects though would probably be impossible for us to determine....an undeterminable mass!!! The cube!!
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PostPosted: Mon May 23, 2005 6:59 pm
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JebJoya
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That'll do, let's leave it at that!

Jeb
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PostPosted: Mon May 23, 2005 7:01 pm
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The First Speaker
Boot


Joined: 18 May 2005
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Location: UK

lol

Nice project to work on now exams are over though Smile
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PostPosted: Mon May 23, 2005 7:05 pm
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JebJoya
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Exams over? Pah, mine start Wednesday, 11 exams over 2 weeks, fun fun fun...

Jeb
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PostPosted: Mon May 23, 2005 7:06 pm
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hamatoyoshi
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The First Speaker wrote:
I feel exactly as you do jeb. 3 years at Uni and still stumped by a seemingly innocent question.


Well, the thing is, most people in school at any level never get into multi-dimensional physics, so I don't really think it's such an innocent question.

I don't think we would have to worry about a problem of the sort anyway as it's probably 1) too difficult and speculative for the PMs to pose intelligently, and 2) too difficult and speculative for the players to answer intelligently.

Supposing they went ahead and played the multi-dimensional physics card anyway and were found to be wrong by an actual knowledgable player, it probably wouldn't be the first time, and it probably wouldn't matter to the game-playing experience.

PostPosted: Mon May 23, 2005 7:09 pm
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Leeravitz
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Joined: 14 May 2005
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Location: Stevenage, England

Oh, its at these post -Einsteinian times that I simply wish to retreat into the nearest copy of 'Flatland'...
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PostPosted: Mon May 23, 2005 7:10 pm
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yanka
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Joined: 06 Oct 2003
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JebJoya wrote:
Essentially, as I remember, gravity is caused by the deformation of Space-Time in the 4th dimension by an object (eg the Earth). Now, if we were to imagine a 4 dimensional object being cross sectioned through our 3 dimensional space, presumably the laws of gravity would not hold, as the object will not be affected by any form of gravity in the 4th dimension?


As far as I understand, gravity isn't caused by distortions in spacetime (they are caused by an object's mass) - it is that distortion itself. Essentialy, this is the crux of Einstein's general relativity - whereas Newton was able to relate the formula for gravity, nobody really knew what this magical force was, and just how it worked until Einstein came along.

Basically, the gravity of Earth is the "region" of spacetime distorted by Earth. It seems to me, then, that at least in those 3 dimensions where the fabric of spacetime is curved by Earth's mass, that 4D-object would still be affected by Earth's gravity (since said fabric is distorted, and it doesn't really care whether that object is there or not (not to be confused with the distortions caused by the mass of the object itself)).

What that would mean for the weight of the whole object, as opposed to its 3D slices that interact with with the respective 3D of the curved spacetime, I have no idea...
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PostPosted: Mon May 23, 2005 7:18 pm
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invfish
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Joined: 09 Oct 2003
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This is my idea on other dimensions =D

if we look at the 2nd dimension everything is x, y co-ords (length and height). Its mass is always 0. The 2nd dimension could be known as 'thought'.

The third dimension is x,y,z co-ords (length, height and width). Also its mass is greater than or equal to zero (equal if the co-ords are 0,0,0 but then they are the same co-ord which is then a little tricky).

The 4th Dimesion could include time and it could refer to x,y,z over a specific time period. So if the object moves slight to the left in 2 seconds the whole of it within that time frame would be the forth dimension.

I heard the 5th dimension is similar to the 3rd except what you do is you imagine a cube around you and you then turn the cube inside out.

The 6th could be the same as this except over a particular time frame.

Then you have things such as matter displacement and warping etc.. or seeing everything as one energy and change being the only constant. Then you have quantum mechanics where time doesn't seem to apply to the rules of time as we know it. Then you have different energys and so forth. It goes on and on and on.. well as far as the imagination can stretch Wink ..and then stretch your heart just as big =)

PostPosted: Mon May 23, 2005 7:51 pm
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Violet
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Joined: 08 Mar 2005
Posts: 217

thebruce wrote:
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...

As I understand it from a biological point of view, we see in 2D because our retinas are flat surfaces, but our brains convert to 3D by knowledge of depth through experience. That's why babies have less hand/eye coordination, and why some children have problems with motor skills, such as dyspraxia.

My understanding of a tesseract is the only way a hypercube can exist in 3 dimentions, ie unravelled, such as a cube unravels to a 2D net of a cube. I know some people use the term to refer to a hypercube itself, but I think it can be applied to both.

PostPosted: Tue May 24, 2005 8:30 am
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tangohead
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Joined: 27 Apr 2005
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Location: North West England (Wigan)

The First Speaker wrote:
The extra effects though would probably be impossible for us to determine....an undeterminable mass!!! The cube!!


just as the firebox catalogue says....

Firebox Catalogue wrote:
Metallic appearance indeterminate mass..


and a definition of indeterminate...

Dictonary.com wrote:
Not precisely determined, determinable, or established: e.g. a person of indeterminate age.


PostPosted: Tue May 24, 2005 10:06 am
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