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Old 07-18-2003, 09:20 PM   #1 (permalink)
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4th dimensional objects

I read some parts of my friends book titled Hyperspace and I got to think about 4th dimensional objects. As 3rd dimensional beings we are unable to directly see a 4th dimensional beind/object. However, we have ways of detecting them such as seeing thier shadow. I've also read in other books such as A Brief History of Time by Hawking that most of the Universe is "dark matter." It seems to me that most of the Universe is made up of higher dimensional stuff. That theory has been debated by many scientists but it is generall accepted.
My questions are: Why would the universe be made up of mostly higher dimensional matter? Could it be possible that a small portion of that matter is an entire other Universe that is 4th dimensional, then another portion 5th dimensional and so on? And if thats the case is it possible that smaller portions of the universe are made up of 2 and/or 1 dimensional matter?

Another thing that tends to bother me when it comes to theories on higher dimensional matter is that most of the theories are based on the relationships between 2nd and 3rd dimensional matter. Such as a 3 dimensional cube can be unravelled into a 2 dimensional cross shape. This we can observe. However, it is then related to a 4th dimensional "cube" or "hyper cube" can be unravelled into a 3 dimensional cross shape. To me it doesn't make a whole lot of sense because the 3rd and 4th dimensions can have entirely different relationships to eachother. I base this off of the fact that some math equations only work under certain conditions such as piecewise functions. If math is unable to yeild proper answers some times then it is possible that the way different dimensions relate to eachother can be different.
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Old 07-18-2003, 09:46 PM   #2 (permalink)
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OK a few things that can be kind of confusing in those books seem to have messed with you.

1) Dark matter isn't particularly magical stuff. Its actually a pretty broad categories which includes anything thats not actively glowing (like say the earth, black holes and suns that have gone out) I have never heard any reference of dark matter being higher dimensional.

2) The theory as it goes (last I checked, it keeps on changing) is that our 4 dimensions (the three traditional ones and time) are large and open, and that there are either 6 or 7 more dimensions which are "curled up" very tight. To be perfectly honest I don't know what that means, but I have seen the phrase several times, and its how Hawking's explained it when he lectured at my university. (on an unrelated note Hawking's makes for a really creepy lecturer, my room mate worked sound for him, they didn't have to mike him, they just plugged the sound system into a little box on his wheelchair)

As to your complaints about relations between 4D and 3D being treated the same way as relations between 3d and 2d, well, its honestly all we have to work with. Humans have a lot of trouble grasping something that is 4d, but we can handle 2d quite well. Essentially what is done is we take what we understand 2d/3d and try to extrapolate general rules from that. The hypercube cross (did you catch that picture by Dali in the hyperspace book? its the one with Christ on the hypercube) makes sense if you think about it. just remember that its solid, and will make a hollow hypercube.

On a side note, if you liked A brief history of time and Hyperspace you might want to look into a book called "Godel, Echer, Bach... Eternal golden braid"
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Old 07-19-2003, 05:06 PM   #3 (permalink)
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Once in my linear algebra class my professor starting discussing an infinitely-dimentional object. I think I nearly had an aneurysm trying to imagine what it would look like.
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Old 07-19-2003, 09:35 PM   #4 (permalink)
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i have a confession to make: I was hung over during most of hte relativity lectures... made em easier to understand at the time, I swear! Of course, can't recall a lick of it, now :/
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Old 07-21-2003, 10:36 AM   #5 (permalink)
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just a plug. Golden Braid has been recommended to me my many a philosopher and mathematician AND musician (theorists mainly) and from the excerpts they have had me read (with explanations; the only way in this book) it is wonderful and interesting.
another thing, the 4th dimension debate is really annoying to me. Supposedly it is "time". that does not make sense it seems with the hyper cube theory. How can time give shape and (supposedly) mass? is this theory saying that there is another physical dimension or is it actually using time as that dimension? I am having such a hard time with analytical chem, i don't want to think about analytical or theoretical physics. sounds frightening.
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Old 07-21-2003, 02:53 PM   #6 (permalink)
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how i understand it all
4th demension: 3D but there is a plane that connects 2 other planes together WITHOUT intersecting the other plane.

hyperspace (program tutorial but intro to 4d)

pictures to help u understand:
klein bottle

see how this is just one big tube thingy. in 4d the "handle" simply connects to the bottom, but since we can only display 3d images it passes thru the side connecting to the bottom. the 4th dimension connects the handle and the bottom with out intersecting the side.

more pictures and some movies
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Old 07-21-2003, 03:18 PM   #7 (permalink)
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Originally posted by MacGnG
awesome, im starting to understand it now...

i just recently started "A Brief History of Time" by Hawkings, and im just getting into chapter 4, I cant read at my full speed, but its still a great read. I know in that book Hawkings refers to 4 dimensions as space-time, and probably describes this other take later on. I kinda wish i was reading this in school, because it almost requires someone to talk it over with.

I have a couple more questions about this that i will formulate later.
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Old 07-22-2003, 10:16 AM   #8 (permalink)
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Trust me, if you are like me you will read all of these books about 4 times each and understand about half of it. It will make your head hurt thinking about it and will only bring on more questions about what we are and what else is out there.

The more you learn, the more you realize you hardly know anything.
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Old 07-22-2003, 12:11 PM   #9 (permalink)
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Great post, any more interesting pics/links? Took me a while to get my head round it, but wow, this is interesting stuff..
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Old 07-22-2003, 01:01 PM   #10 (permalink)
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The Eletgant Universe is also a great read on the subject of superstrings and extra-dimensional space-time. I think that it was written by Brian Green.
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Old 07-23-2003, 07:50 AM   #11 (permalink)
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Cool pic Mac GnG really helped explain that concept to me, thanks!
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Old 07-23-2003, 08:34 AM   #12 (permalink)
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Unfortunately you are not going to understand the arguments for multi-deminsional universes (at least not by reading books such as . You might be able to grasp the general ideas (where books like "The Elegant Universe" and "A Brief History of Time" shine) , but the basis for most multi-dimensional theories are on advanced mathmatics. The reason 11 (I think that is the current prefered amount of dimensions) is favored is that is what works with some of the math. Unfortunately, the math is so complex and the ideas so hard to wrap ones brain around, that scientists studying this have really only begun to scratch the service and without a major breakthrough will likely keep scratching away... We need a new Einstein to explain this all to us.

Which brings me to the more accepted and slightly easier to understand concept of the "Fourth Dimension", time. The pictures and ideas like the Klein bottle are purely dealing with four spacial dimensions. Time is its own unique dimension, though there is no reason to rule out there being two or more time dimensions, most theories favor there being only one. Maybe because the idea of multiple time dimensions is even harder to understand than more than three spacial dimensions. Where time gets wrapped up into the dimension business is with Einstein's Relativity. For example, the equations state that if you move in one dimension, either three spacial dimensions or the one time dimension, you move slower in the others. Therefore if you travel the speed of light (the fastest anything can move according to relativity) in one direction you will not be moving through time at all...

Well, that is the way I remember it anyway...
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Old 07-23-2003, 08:43 AM   #13 (permalink)
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AAIGGH!!! my brain is going to explode...

great topic... love the discourse so far. 4D objects are really neat to conceptualize and visualize...
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Old 07-23-2003, 10:02 AM   #14 (permalink)
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You also might try Flatland by Edwin A. Abbot (A. Square). Here it is on the web.
And I think there's a sequel to it as well.
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Old 07-23-2003, 07:50 PM   #15 (permalink)
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Elegant universe is a great book. String theory for dummies.

We currently live and interact in four dimensions - 3 spatial, and one temporal. String theory requires additional dimensions to work, and the math comes out to either ten dimensions or 24 (don't ask me how, I have no idea). The four we currently understand, and then (supposedly) six more that we pass through without knowing.

Owwww....my brain.....
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Old 07-23-2003, 11:14 PM   #16 (permalink)
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another good book is "The fourth Dimmension" by rudy rucker. Good intro to the theories and whatnot, and discusses the idea of different types of fourth dimmensions.
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Old 07-23-2003, 11:37 PM   #17 (permalink)
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Quote:
Originally posted by teflonian
For example, the equations state that if you move in one dimension, either three spacial dimensions or the one time dimension, you move slower in the others. Therefore if you travel the speed of light (the fastest anything can move according to relativity) in one direction you will not be moving through time at all...

Well, that is the way I remember it anyway...
I have never heard it stated that way but that makes sense. I wish I had heard that while I was still taking physics.
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Old 07-24-2003, 03:54 AM   #18 (permalink)
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Whoa I missed a lot. I was away on a vacation of sorts.
Anyway, I like the discussion so far. While I was in the car I re-read part of Universe in a Nutshell especially the part about multiple dimensions. I somewhat better understand the mathematical reason for higher dimensions, but what still bothers me is why are they there. (Aside from the above stated reason, math.) They must have another purpose aside from answering an equation that WE created. I suppose no one will really know that at all.
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Old 07-25-2003, 09:39 PM   #19 (permalink)
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Thanks for all the simplified explanations. I realised last year that I shouldn't think about other dimensions because it is impossible for us to interact with objects in a different spacial dimension so I won't ever need to know what they might look like.
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Old 07-25-2003, 10:05 PM   #20 (permalink)
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supersix2, but that would assume that there is a need for a purpose. If they exist, then we can obviously exist with them existing, and may even require their existence for our existence (that would be a tautological argument if I have ever heard one, and a confusing one at that). If they do exist we might be able to find ways to exploit the nature of multi-dimensions like we have exploited the consequences of quantum mechanics, relativity, Newtonian physics, and every other advancement in our theories.
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Old 07-29-2003, 02:27 AM   #21 (permalink)
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Has anyone else read a thing called line-land? its all about interpretation of 1st and 2nd dimensions, i found it interesting.

(what is the 5th dimension? i believe its when something is bigger inside than out?)
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Old 07-31-2003, 05:16 AM   #22 (permalink)
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Lineland???? Is that about a the lives of geometrical shapes in 2D and a visitor from a 3D world comes and visits one of the scientist shapes?
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Old 07-31-2003, 05:50 AM   #23 (permalink)
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No, that'd be Flatland, which I referenced above.
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Old 07-31-2003, 02:16 PM   #24 (permalink)
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Quote:
Originally posted by bobbles
Has anyone else read a thing called line-land? its all about interpretation of 1st and 2nd dimensions, i found it interesting.

(what is the 5th dimension? i believe its when something is bigger inside than out?)
nope. Its just another spacial dimension. even more difficult to visualise than four!
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Old 07-31-2003, 08:27 PM   #25 (permalink)
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All objects can be considered 4D in a very real sense. A dimension, mathematically, is simply an independent parameter required to describe something. An object is described by its shape in 3D space. Add to that that the shape can change over time. 3 "spatial parameters" and one temporal one are required to describe the object, so it has 4 dimensions.

There is nothing odd or new about this view. Galileo or Newton could easily have stated it, but it wasn't a terribly useful construction/visualization since time was considered universal back then. Special relativity came along to say that time was different to different people. One person's time axis could be rotated with respect to someone else's. This led to the 4D interpretation being a useful way to think about things.

"Higher dimensional matter" does not make any sense. Matter is stuff contained in space(-time). That stuff is represented (sort of) as having some energy/momentum distribution in spacetime: E=E(x,y,z,t), p=p(x,y,z,t). The "dimension" of the matter has to be the dimension of the space, or it makes no sense.

There are some differences in 2D->3D vs. 3D->4D. Physics is not done the way popular books sometimes imply. It is mathematics (logic), not picture drawing. Various types of spaces with arbitrary numbers of dimensions are defined by the mathematicians as abstract things that obey some list of logical rules. There is nothing intrinsically "real" about any of them. What physics has done is to say the universe as we think we know it obeys one of these sets of rules. These are simple things like saying that there exists a well-defined distance between any two points. Everything else is formally derived from these very primitive observations.
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Old 07-31-2003, 08:30 PM   #26 (permalink)
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Geez . . . reading the above is doing my head in . . . I need to get out of here before my head explo . . . . . . .
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Old 07-31-2003, 09:12 PM   #27 (permalink)
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Off topic but... Some guy coded a version of tetris using 4 spatial dimensions, projected onto a 3d model (which is then displayed on a 2d screen). I could only play for about 2-3 minutes before my brain just started malfunctioning. I had nightmares about being unable to stand in 4d space because I was 3 dimensional and in one dimension I was infinitely thin, and that's damned hard to balance on.

I'm not well versed in the pure mathmatics of higher dimensional physics, but it's damned fun to think about. On that topic, Greg Egan's Dispora is a pretty entertaining novel with lots of higher dimensional stuff to wrap your head around...
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Old 07-31-2003, 10:19 PM   #28 (permalink)
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human, you win the confusing award :S
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Old 07-31-2003, 10:31 PM   #29 (permalink)
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Quote:
Originally posted by MacGnG
how i understand it all
4th demension: 3D but there is a plane that connects 2 other planes together WITHOUT intersecting the other plane.

hyperspace (program tutorial but intro to 4d)

pictures to help u understand:
klein bottle

see how this is just one big tube thingy. in 4d the "handle" simply connects to the bottom, but since we can only display 3d images it passes thru the side connecting to the bottom. the 4th dimension connects the handle and the bottom with out intersecting the side.

more pictures and some movies
Cool. That figure only has one surface! Reminds me of the Mobius Strip. That doesn't really have any relevance to this topic, so I'll spare you a picture

I thought the 4th dimension was arbitrary? Such as... you can define an object by its length, width, height, and color. Or its length, width, height, and time at which it was created. Or it's texture... the third definition of the word "dimension" at http://www.dictionary.com/ states that a dimension can be an "aspect; element", which in my mind equates to "property". Is color not a property? Is texture not a property? I don't really know what I'm talking about. Sorry
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Old 07-31-2003, 11:01 PM   #30 (permalink)
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You can define as many dimensions as you want with color or whatever, but its only a useful definition if there's some useful geometry relating all the dimensions. Normally, color and position are unrelated, so its not useful. I guess its possible to dream up a very specialized situation where it could work though.
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