Would it be easier to cut an apple in a 4 dimensional universe.

[KevinF]

ok try here. That one has the original illustrations. This one and this one don't have the illustrations but are good to have in case the other one goes down.

It's too bad that University of Minnesota site is down -- it had the entire story on one page which made for easier printing and reading.

 

[mrman3k]

I thought we live in a 4D world, Length, Width, Height, Time.

 

[rimshaker]

Interesting. Hard to explain. But i imagine it would be something like getting more than 2 pieces when you cut something in half.

 

[jurzdevil]

i hate to burst your instense and interesting discussion but i think apple slicing problems have been solved

 

[Walleye]

Well, in theoretical math, you can have unlimited dimensions. Personally, i havent found a use for any of those beyond 3 besides 6time.


and just for note, the 4th dimension of temperature, it would be more fitting to describe it as ambient energy concentration.

 

[silverpig]

Okay, many of you missed the point with the temperature model. It was just to show that every point in 3-space can have an infinite range of values in 4-space. I just used the temperature example to get people to picture a region of 3-space that was colourized due to temperature, and then once they had that picture, to apply the 2-D topographical map idea I had also outlined in order to imagine the colours as the "height" on the 4th dimensional axis. I wasn't saying that temperature is the 4th dimension or anything, but was just using it as a bridging example.

 

[Smilin]

I never had any idea this thread would last so long...I figured everyone would just think I was a tard. Just a few responses to the above:

Color/temperature make a great way to visualize an extra dimension...good call there I'm always looking for some way to 'visualize' additional dimensions and have had great difficulty. I usually just have to squash everything down a dimension to get it -- you know make a 3d object flat and then use a 3rd dimension to represent the 4th etc...

Stephen Hawkings "Universe in a Nutshell" ...great book but maybe not as good as his first.

 

[CaptainKahuna]

DarkLance, that reminds me of a paradox I heard of once:

If you were to create a time machine, and use it to go back in time and visit your grandfather when he was young. Suppose you pulled out a gun and shot him (kind of morbid I know). What would happen to you? Would you cease to exist? If so, how could you have shot your grandfather? If you didn't cease to exist, then your grandfather is dead, and where did you come from?

There's an excellent article in Popular Science that discusses time travel. I think it was like June or July.

 

[crumpet19]

see, this is what marijuana does to you, toker.

 

[Slatz]

Originally posted by: Cogman
according to Einstine, (ok, so I cant spell) There are 4 dimetions

Length, Width, Depth, Time (might also say Motion)

Of course, I guess if time did not exist it would be pretty hard to cut an apple, as you would not be moving

So in theory, you are saying that humans wouldn't exist, because without movement, one does not have sex.

 

[mobly99]

or you could just buy one of these, not worry about a 4th dimension and enjoy your apple

 

[Walleye]

im all for that idea.

 

[rbayer]

The mathematical concept behind "dimensions" is that it is the number of data points you need to describe one particular place. In 3 dimensions, you need x, y, and z. In four, you need to add in a w. Our minds think of the universe as being 3D because we only have direct control over 3 axes of motion. Anything beyond that just happens with or without our consent. Depending on who you ask, physics recognizes 11+ dimensions to the universe, claiming that you need 11 pieces of data to describe any point within it. As far as I know, nobody has given names to these higher dimensions nor has anyone really described what they "are." Saying that time is the fourth dimension is just another guess as it's not something we can control or observe. It's all hypothesis beyond 3D.

 

[Era]

The 4th dimension was Einstein's plot to confuse the Vogons.
Nothing more, nothing less.

Not all things have to be complicated.

 

[johnfreezz]

Originally posted by: crumpet19
see, this is what marijuana does to you, toker.

lmao...so true...if one could record and later observe the thought proccesses and ideas that occur when the brain state is altered...i bet we'd be much more scientifically enlightened

 

[bwanaaa]

The temperature example is interesting becuase it shows that to add another dimension, you need to measure another property. After all, the concept of a dimension is that you can change it without affecting any of the other dimensions. But what would a fourth spatial dimension be?how about polarity? time is not a 'dimension' - it describes motion of objects within a dimension

 

[Train]

you guys are way overanalyzing this.

the correct way to continue making perpendicular cuts in the apple is to take one of the 4 wedges, place it on one of its flat sides, and slice it perfectly in half though its center, not lengthwise like you are trying to do.


and to the people talking about temperature as a diff dimension, your also way off, temp is completely included in the dimensions of length, width and depth. Because temperature is only the SPEED at which molecules VIBRATE (faster vibrating molecules are hot, still molecules are at zero degrees kelvin, the temp at which everything is solid and not moving at all)

I'm surprised this thread was allowed to survive, the last time i was on this forum (over a year ago) i had a thread in here asking for someone to define the 5th dimension, the mods axed it saying it wasnt computer related. I guess the management has changed.

 

[alankool]

oops wrong thread diregard this post

 

[Smilin]

Originally posted by: Train
you guys are way overanalyzing this.

the correct way to continue making perpendicular cuts in the apple is to take one of the 4 wedges, place it on one of its flat sides, and slice it perfectly in half though its center, not lengthwise like you are trying to do.

That's not really the point. In that case you are simply utilizing one of the three dimensions at your disposal to make the easy cut. I'm saying if I want to continue to make SLICES, not chunks.

and to the people talking about temperature as a diff dimension, your also way off, temp is completely included in the dimensions of length, width and depth. Because temperature is only the SPEED at which molecules VIBRATE (faster vibrating molecules are hot, still molecules are at zero degrees kelvin, the temp at which everything is solid and not moving at all)

No one is using temperature as a different dimension, it's just a tool to help you visualize such a thing. You can visualize up, down, left, right, forward, back but you CAN'T visualize say, "inside out to the left" so picturing a color or temperature gradient can be used to visualize extra dimensions. It's like if you have a 3d isometric graph on your computer screen...you are able to represent 3 variables: The "Tallness" of something at a particular X,Y location. If you add color to the graph you can then represent the "Tallness" and the "inside out to the leftness" of a particular X,Y location.

I'm surprised this thread was allowed to survive, the last time i was on this forum (over a year ago) i had a thread in here asking for someone to define the 5th dimension, the mods axed it saying it wasnt computer related. I guess the management has changed.

Perhaps for the better. I find quite a few intelligent discussions here that are non-computer related and I think as a paying subscriber I'm getting my money's worth.

 

[Soybomb]

If you're interested in extra dimensions check out some of Michio Kaku's books.

His book Hyperspace is an excellent start.

 

[Creedyou]

Smilin, your inquiry inspired me to research more into 4-D. From what I read....0 dimension = a point, 1st dimension = a line, 2nd dimension = a square, 3rd dimension = a cube, 4th dimension = a hypercube. In our 3-D world, we can see the whole square at once and place our finger inside of it without touching the sides. In a 4-D world, you would be able to see the whole cube from one perspective and place your finger inside of it without touching the walls.

 

[Shazam]

Hmm, well, since apples only exist in 3 physical dimensions as far as we know, then you can only manipulate it in 3 dimensions. Even if you were a fourth dimensional creature, the results of your actions on a 3 dimensional object must follow the laws of this universe. However, how you get to the results is the interesting part.

 

[Eteq]

First thing: Time is NOT "the 4th dimension" - Time is not another dimension of space - it's actually a PART of space - think back to any math or physics classes you may have had. When you want to trace the path of a particle in three dimensions, you don't make a 4-dimensional coordinate system with x, y, z, and t axis, you use three parametric equations that are all functions of t - x(t), y(t), and z(t).
Granted, when you are working with 2 dimensions, you sometimes use x, y, and t, but that is NOT three spatial dimensions - you are simply de-parametricizing (that's a word, but I'm not sure of the spelling ) an x(t), y(t) graph.

That's not really the point. In that case you are simply utilizing one of the three dimensions at your disposal to make the easy cut. I'm saying if I want to continue to make SLICES, not chunks.

Then you're asking the wrong question - if you take a circle (the two-dimensional equivalent of a circle), you can cut it into four "slices" - your definition of "slices" means that you're only accepting two dimensions of cutting - to properly show what the fourth dimension will do using the right-angles concept, you'd need to allow us to make the third slice to cut your apple into chunks.

So in other words, using your definition of "slice," a 4-dimensional apple would be no easier to cut - you're only allowing us to cut in two dimensions.




-A Undergrad Physics Major (well, that's not that impressive, but at least I can say I will one day know for sure if I'm telling the truth or not here)

 

[kdb003]

But what is the value of fourth dimension of an apple. What if it is 0. Then it would have no 4d equivilant of volume. Then you wouldn't be able to cut it in the fourth dimension anyway, so it would not be any easier.

1d has length
2d has area
3d has volume
4d has ??

If you assume the value of the fourth dimension of an apple is something is other than zero, then you definetly would have more places to cut it, but would that make it any easier.

 

[BFG10K]

If time is the fourth dimension then the fourth dimension is simply the state of the apple at any given time. That is if you cut the apple at 4 PM, you could go to the same Apple at 3 PM and cut it again. And if you could be at two different times at once you could cut the same apple twice.