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4th spatial dimensions etc.

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JJJJ

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Okay, Youtube is filled with videos about a theoretical 4th spatial dimension, and even though i understand what they are trying to say, there is much i dont get about the explanations they are trying to make....

Here is a video of Carl Sagan explaining his view of a 4th spatial dimension: http://www.youtube.com/watch?v=Y9KT4M7kiSw...feature=related

He(and other people) bring up the the example of the 2-dimensional flatlanders, and how we could possibly "freak them out" by just appearing and disappearing in their dimension. At first i accepted this as totally clear, and didnt even think about the 2d-creatures, but then i started really thinking. My brain may be the size of a peanut, but i dont understand, even theoretically, how such a creature, could even theoretically exist. If something is entirely flat, with no height at all, doesnt that mean that he has no matter at all, even if his surroundings actually were 3d, or even some freaky theoretical 4d. And even if that creature somehow could exist, it is completely impossible that a 3d creature could ever see it.

I mean, put a sheet of paper on your table. Then imagine that that sheet, would have absolutely no height at all. The fallacy comes from thinking that a sheet of paper doesnt have any height, and Sagan even admits that in the video, but i still do not understand, and he doesnt explain it in any way, how we could ever see anything that lacks height altogether. How could we see the width and lenght of something that doesnt have height? Imagine that you would lift up this creature that lacks height? Where would you grab? I mean, Sagan says in the part where he the apple lifts the flatlander up in the air, that he "makes contact from below" with the flatlander. What below, is he referring to, if the flatlander does not have any height at all?

Just like if this 2d creature lacked width or length. It is absolutely impossible to imagine what such a thing would look like, and as impossible to think that such things can exist. Despite this, they use this flatlander example as an easy way to show how 3d creatures can "freak out" 2d creatures, even though i dont get it at all.

Because i do understand that everyone agrees that it is completely theoretical for a 4th dimension to exist, but i cant even fathom there existing anything 0d, 1d or 2d, and yet Sagan, and other similar videos, give this 2d example as an easy way of "imagining" how a 4d creature would look at "us" 3d creatures. Is there something im missing, as i cant understand why these videos accept as a fact that we could see these theoretical 2d creatures, as i cant get it at all, as my logic would make them impossible to exist, due to them lacking substance in a very fundamental dimension, therefore lacking any substance. Even the thinnest sheet of paper is always 3d, and no matter how many times you cut it in half, it will remain 3d.

Any thoughts on my incoherent ramblings, as im dumbfounded that people like Sagan and others dont explain these 2d-creatures at all, and just take it for granted in order to explain some 4d.....

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It's a thought experiment. You're supposed to imagine a 2-d "space" without any height, or at least where the inhabitants cannot perceive height. This is easy to do because there are things whose height we cannot perceive. For example, print a page in a laser printer. Yes, the letters have a height and it can be measured, but you don't perceive it because it's too small. So for al practical purposes, the printed words on paper are two dimensional.

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There's a satirical book called 'flatland' that does a good job of explaining it well. A fun read too. People in it are different shapes which represent different social rank(more sides=higher). Loosely based on Plato's republic where the circles are the philosopher kings. They perceive by bumping into things and feeling them. I recommend it.

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He(and other people) bring up the the example of the 2-dimensional flatlanders, and how we could possibly "freak them out" by just appearing and disappearing in their dimension. At first i accepted this as totally clear, and didnt even think about the 2d-creatures, but then i started really thinking. My brain may be the size of a peanut, but i dont understand, even theoretically, how such a creature, could even theoretically exist. If something is entirely flat, with no height at all, doesnt that mean that he has no matter at all, even if his surroundings actually were 3d, or even some freaky theoretical 4d. And even if that creature somehow could exist, it is completely impossible that a 3d creature could ever see it.
The measure of the 'substance' of a 2d object is its area, not its volume. And height isnt necessary for a 2d shape to have a clearly defined area. If the elementary particles of our universe have 3-dimensional extent then no, a 2d object couldnt be made up from them, but presumably the 'atoms' in a 2d universe would be 2-dimensional and have area rather than volume.

Volume measures a fundamentaly different quantity than area, the two arent directly comparable. And similarly 'volume' in a 4-d space isnt directly comparable with volume in a 3-d space. [technial aside - mathematically speaking, the 'volumes' of higher dimensional spaces exhibit some very surprising properties. For example, the 'volume' is a hypersphere with radius 1 shrinks to 0 as you increase the dimensionality. That is to say, if you embed a hypersphere inside a hypercube (eg putting a circle inside a square in 2d space, or a sphere inside a cube in 3d) then as the dimensinoality increaes then the ratio of the hypercube's volume to the hypersphere's becomes infinite'. This means that hypercubes have a very 'odd' shape since all of their volume is located in their corners rather than in their centre].

But as other people have said, its meant to be a metaphor. If real space was 4-dimensional then presumably the objects we think of as being 3-d would actually have a very very small extensionality in the fourth dimension rather than being entirely 3-d. The point is more than we cant see or move in the 4rth dimension, not that we dont have extentionality in it. It may be helpful to think of dimensionality here as a measure of the degrees of freedom that an object can move in, rather than of the space it exists in.

Any thoughts on my incoherent ramblings, as im dumbfounded that people like Sagan and others dont explain these 2d-creatures at all, and just take it for granted in order to explain some 4d.....
I think its more because Sagan comes from a maths background, and people who've studied maths will generally be quite comfortable working with high-dimensional spaces and start to forget how counter-intuitive they seem once you start thinking about what it would be like to live on one. The difference is that in maths these spaces are treated as abstractions rather than as something which exists in the physical world. To me, the idea of a 4+ dimensional space makes perfect sense and I work with them daily, but only as mathematical objects - I've no idea how physics could work on one if they had physical existence (nor do I care for the sort of work I do).

In maths, a 4+ dimensional space isnt something that needs to be 'visualized' nor do you have to think about what it would be like to live on one - you just define what it is in a formal way and off you go.

Edited by eriatarka
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I certainly do understand the abstract 0d,1d,2d and probably could understand what 4d was abstractly if is studied some math. But even abstractly, i cannot understand how a 3d being could ever theoretically enter this 2d world so that the 3d object would be visible.... Because all explanations and illustrations, such as this Dr Quantum one:

, has the flatlanders having height. In that video they cannot move upwards or downwards, but they still clearly are 3-dimensional objects, in a 3d world. So, they would actually be seeing in 3d all the time, without understanding that the third dimension is a dimension, because everything they have ever encountered has the same height. That still doesnt mean that it has the height=0. And Dr.Quantum could have easily shown the flatlanders what height is without taking them out of their "universe". He could just carefully, and slowly insert his finger into their world, so that his finger wouldnt have gone all the way through, but that just the tip of his finger would have reached halfway down in their world. Then the flatlanders could have understood what height is, as they would have seen something for the first time, that is not of the same height.

Now i dont claim that Dr.Quantum here gives an accurate description, but if i try to apply this to the thought that we actually live in a 4d(or higher) dimension, it gets tricky. For it to apply, there would have to be something, that we dont understand as a spatial dimension, due to the fact that we have never encountered a situation where the amount of this 4th dimension, lets call it "pought", would be different from anything else we have ever seen. Every object we see would have to have the same amount of "pought". This is the only way i can theoretically understand how we could live in a 4th dimension. That doesnt mean that we dont have any "pought", or that we dont see "pouhgt" all the time. We do see "pought", but dont know that we are seeing it....For other dimensions to exist, and someone being able to come into a "dimensionally challenged" creatures world and "freak them out", these lower creatures should be able to see "pought", and have physical 4th(and 5th, 6th etc.) dimensional characteristics. Otherwise it is impossible, even theoretically, that a being with physical characteristics in 4 dimensions, could ever show itself, even just partially, to a creature with physical characteristics in 3 dimensions, and i would even claim that for higher dimensions to exist, we would with absolute certainty have to have physical characteristics in all these dimensions, even if they were really miniscule.

Now, what this "pought" could be, is a different thing, and it makes my head ache when i try to think about it

I know, my language isnt exactly scientific, and english isnt my first language, but i hope you understand what i mean.

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