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4d perspective lesson: Brief summary

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I dont know how many of you know about this, or how to manipulate its awesome powers in flash. But i'll teach you guys a brief despcription of The Fourth Demension. Try not to get to confused. I learned this when i was 13..last year biggrin.gif But seeing as i am a 1337 ninja it wasnt hard.. ninja.gif ninja.gif ninja.gif

 

To the Lessons!

 

Four-dimensional geometry is Euclidean geometry extended into one additional dimension. The prefix "hyper-" is usually used to refer to the four- (and higher-) dimensional analogs of three-dimensional objects, e.g. hypercube, hyperplane, hypersphere. n-dimensional polyhedra are called polytopes. The four-dimensional cases of general n-dimensional objects are often given special names, such as those summarized in the following table.

 

The surface area of a hypersphere in "n" dimensions is given by

S_n==(2pi^(n/2)R^(n-1))/(Gamma(1/2n)),

 

where Gamma(n) is the gamma function, giving the first few values as

S_1 = 2

S_2 = 2piR

S_3 = 4piR^2

S_4 = 2pi^2R^3,

 

with coefficients 2, 2, 4, 2, 8/3, 1, 16/15,

 

The volume is given by

V_n==(pi^(n/2)R^n)/(Gamma(1+1/2n)),

 

giving the first few values as

V_1 = 2R (7)

V_2 = piR^2 (8)

V_3 = 4/3R^3 (9)

V_4 = 1/2pi^2R^4, (10)

 

with coefficients 2, 1, 4/3, 1/2, 8/15, 1/6, 16/105, .

 

Thats my lesson this week. Stay tuned :P

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Is it correct, then, that a 4D cube would look like a smaller cube within a bigger cube, with lines connecting the corners of the 2 cubes? The 2 cubes (and the things that don't look like, but are, cubes formed by the connecting lines) would be the same size in actuality, but would look skewed/smaller, as they are back in the 4th dimension..

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What the funk? you learned thuis hen you were 13? None of it makes any sence to me.

 

Haha this made me laugh on the ebay item:

Platform: Sony PlayStation 2 Type: Playstation 3

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Is it correct, then, that a 4D cube would look like a smaller cube within a bigger cube, with lines connecting the corners of the 2 cubes? The 2 cubes (and the things that don't look like, but are, cubes formed by the connecting lines) would be the same size in actuality, but would look skewed/smaller, as they are back in the 4th dimension..

 

Well the net of a hypercube looks like this:

Tesseract2.png

 

Now you have to fold it up into the 4th dimension so that each outer face touches the others.

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Questions. 4D glasses & PS3

 

Q:This item sounds too intense for me. Can a 4D game hurt me or my family?

A:Yes. But it is the good pain.. the kind that installs discipline.

 

Q:Is the manufacturing of these glasses part of the reason for the Delay of the PS3?

A:Yes. To assure that fans get the Ultimate 4D Experience, Sony has dedicated over 2/3rds of its development process towards these plastic glasses alone.

 

Q:What happens if i plug the glasses into the PSP?

A:It would be like 4D you can play with outside.

 

Q:So will these glasses cause me harm? Seeing that I will be so Immursed into the game?

A:Sony aims to support 4D games that are extremely realistic as possible. So Yes. Very much so, in fact.

 

Q:The stunning quality of the graphics SOny showed in their PS3 videos at E3 last year were already beyond belief - can you give me an idea of how games are going to look on the PS3, complete with the 4D glasses enhancement?

A:Remember the Killzone 2 video shown? Imagine yourself being fully immersed in that... with Chuck Norris! Yeah... it's that awsome.

 

Q:What happens if i get lost in the fourth dimension and can't get out.

A:Sony promises to bring you an intense 4D experience Like No Other. Even if you were trapped, you'd probably never want to leave. Ever.

 

Q:How will the glasses' backwards compatibility work with the Toy Story quality graphics I am enjoying with my PS2? Will it make it look Madagascar quality, or just Toy Story 2 quality?

A:Better... Toy Story 3! .. in 4D!!

 

Q:Do these glasses come in different frame colors to match the PS3? (i.e. silver, white, etc)

A:Yes, White (pictured), Silver, Black and Flaming Fuschia Pink to be announced later next year.

 

Q:Can this glasse be use with the Xbox 360??

A:I'm afraid not. The Xbox 360 only supports 3D games, therefore, it is not truly next-gen system. Only with the PS3 will you experience true 4D next-gen gaming. In fact, attempting to use them on any non-Sony product may cause severe bleeding and excessive damage to one’s retinas.

 

Q:By looking through these glasses, will I be able to make anything 'live'? (ie can I raise the dead?)

A:Yes... but it's not recommended.

 

Q:Are these glasses backwards compatible with 3D and 2D applications?

A:Yes, backwards compatibility is activated by covering the yellow and green sections of the glasses with the palm of your hands.

 

Q:Will these glasses allow me to know discipline?

A:Of [email protected] Nothing less than strict and painful discipline in our children and adults! Everyone will know discipline!

 

Q:Will these glasses also allow me to see through time?

A:Most Certainly, Yes. In many cases, you'll be able to turn time from Spring to an ''Early November'' almost instantly!

A:Yes, backwards compatibility is activated by covering the yellow and green sections of the glasses with the palm of your hands.

 

Q:Will these glasses allow me to know discipline?

A: Of [email protected] Nothing less than strict and painful discipline in our children and adults! Everyone will know discipline!

 

 

Q:Will these glasses also allow me to see through time?

A:Most Certainly, Yes. In many cases, you'll be able to turn time from Spring to an ''Early November'' almost instantly!

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This is odd, i was always under the impression that the 4th dimension was Time?

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You faff on about 4D all you want, in the end there are only three actual physical dimensions that we can interact with. I also don't trust something which has spent the last couple of weeks screeching around the Gamespot PS3 forums from someone calleing themselves "noob". Don't ask why. I've just got this gut feeling.

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Is this thread just designed to confuse people? It seems it.

There seems to be a lot of throwing down of information without any real attempt to explain what people are talking about.

Firstly you have to accept the idea that other than the 6 directions we have in 3-d space (imagine the 4 compass points and add 'up and down' to them). There is another space direction that is at 90 degrees to all of these (in the same way that North is at 90 degrees to both 'up/down' and 'east/west').

This can't be achieved in 3-d so we add another dimension, call it 'in/out'. Note how we haven't mentioned time yet, we are talking about 4-d space not 4-d space-time.

The easiest thing is to start with a circle. In 2-d space a circle is all the points (x,y) that are a fixed distance from the centre. Let that representation sink in.

A sphere is all the points that are the same distance away from a central point in 3-d space. Imagine a fly tethered to a fixed pea in space by an invisible string. As the fly, well, flies, it stayed the same distance away from the pea. This is a sphere, the set of points (x,y,z) in 3-d space that are the smae distance from a central point. Let this idea settle.

Now imagine a sort of ghost-fly tied to the same pea. It can't escape it's bonds but it can escape 3-d space by fading out. The 'distance' it can fade out is the same as the length of the string. It is moving 'in' and 'out'

All the points that the ghost-fly can reach are the same distance away from the central point in 4-d space (x,y,z,w). This is a hypersphere.

that's the best i can do.

A good book to look at about this sort of stuff is 'the knot book' by colin c adams.

But it is pretty high-level maths and I only touched upon it briefly in a 3rd year and 4th year uni course in maths.

The hypercube can be projected into 3-d spcae where it's shadow looks like a pair of cubes with every corner on cube 1 joined to a corner on cube 2.

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This is odd, i was always under the impression that the 4th dimension was Time?

 

That's a common misconception; time is a fourth dimension, not the fourth dimension.

 

And KingJoe, have you ever tried painting a hypersphere?- you end up trapped in a sphere of paint. (Not that that's relevant, just interesting).

 

Good books to read on dimensions are Flatland, by Edwin Abbot Abbot, and Flatterland, by Ian Stewart.

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Just to say I don't believe you learned this when you were 13, and that 4D is just a concept and can't be percieved by us (even with does drawings), just like a 2D being can't percieve a 3D object.

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Just to say I don't believe you learned this when you were 13, and that 4D is just a concept and can't be percieved by us (even with does drawings), just like a 2D being can't percieve a 3D object.

 

I wouldn't be suprised if he did; I easily understood the theory of dimensions at that age. And yes, it doesn't make sense to a 3D brain, but being able to understand it is realises this and working from there.

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Good books to read on dimensions are Flatland, by Edwin Abbot Abbot, and Flatterland, by Ian Stewart.

 

flatland is available here.

 

This topic has awakened my dormant interest in higher dimensional and non-euclidean geometries. Well done!

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parallel universes, please! if time were to be the 4th dimension, and a 4d creature were able to view all moments in the same instance, then the ability to see all possible moments must be the next dimension up..?

 

Meh.

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flatland is available here.

 

This topic has awakened my dormant interest in higher dimensional and non-euclidean geometries. Well done!

 

Flatterland is a tribute to flatland, but its more complicated and much more physics based, despite being written by a mathematician.

 

You might find some of it a bit simple though; e.g. it has a whole chapter explaining i and how you can use it to make mandelbrots. It's also childish, although I think that's fairly tounge-in-cheek.

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