# Dimensions beyond 4 **URL:** \ **Category:** Factual Questions\ **Created:** [June 21, 2003, 4:03am UTC](https://boards.straightdope.com/t/dimensions-beyond-4/183360 "2003-06-21T04:03:56Z")\ **Posts on this page:** 12\ **Page:** 3
**Author:** ![moriah](https://avatars.discourse-cdn.com/v4/letter/m/b2d939/32.png) [@moriah](https://boards.straightdope.com/u/moriah)\ **Post date:** [February 15, 2013, 8:11am UTC](https://boards.straightdope.com/t/dimensions-beyond-4/183360/41 "2013-02-15T08:11:31Z")
> [@SayTwo](#): > > Help me understand this. Would this mean something like…where you are (your X, Y, and Z coordinates), when you are there, what color you are while you’re there, what mood you are in, how old you are at the time, and so on? That would be a description of a field, not extra spatial dimensions. > **[Classical field theory](https://en.wikipedia.org/wiki/Classical_field_theory)** > > A classical field theory is a physical theory that predicts how one or more fields in physics interact with matter through field equations, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum field theories. In most contexts, 'classical field theory' is specifically intended to describe electromagnetism and gravitation, two of the fundamental forces of nature. > A physical field can be thought of as the assignment of a physical quantity at ea... ---
**Author:** ![SayTwo](https://avatars.discourse-cdn.com/v4/letter/s/e56c9b/32.png) [@SayTwo](https://boards.straightdope.com/u/SayTwo)\ **Post date:** [February 15, 2013, 8:23am UTC](https://boards.straightdope.com/t/dimensions-beyond-4/183360/42 "2013-02-15T08:23:08Z")
Or, that would be describing extra “spatial dimensions,” not a field. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 15, 2013, 2:43pm UTC](https://boards.straightdope.com/t/dimensions-beyond-4/183360/43 "2013-02-15T14:43:49Z")
No, those wouldn’t be spatial dimensions, because you couldn’t have two different people in the same place but in different moods. ---
**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\ **Post date:** [February 15, 2013, 2:48pm UTC](https://boards.straightdope.com/t/dimensions-beyond-4/183360/44 "2013-02-15T14:48:35Z")
[quote=“Gary “Wombat” Robson, post:37, topic:183360”] My first reaction was, who creates a website with a couple of paragraphs per page and no navigation system except for linear reading? [/QUOTE] Adolph Webmaster? ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [February 15, 2013, 5:55pm UTC](https://boards.straightdope.com/t/dimensions-beyond-4/183360/45 "2013-02-15T17:55:42Z")
The kind of explanation of higher dimensions posted by **JanH** seems to be popular in popular science circles. There’s a video on YouTube called \*Imaging the Tenth Dimension[/i[ that has over two million views and is in very much the same vein as Jan’s website. Unfortunately these are purely hand-waving, never really go beyond the obvious and can be misleading. Quantum mechanics uses state spaces of uncountably infinite (Hamel) dimension, though the requirement that they are separable means that their orthonormal dimension will be countable. Quantum field theory uses state spaces that have arguably uncountable orthnormal dimension. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [February 15, 2013, 6:16pm UTC](https://boards.straightdope.com/t/dimensions-beyond-4/183360/46 "2013-02-15T18:16:30Z")
> [@Asympotically\_fat](#): > > The kind of explanation of higher dimensions posted by **JanH** seems to be popular in popular science circles. There’s a video on YouTube called \*Imaging the Tenth Dimension[/i[ that has over two million views and is in very much the same vein as Jan’s website. Unfortunately these are purely hand-waving, never really go beyond the obvious and can be misleading. I think of “popular science” as something that is as accurate as possible written for the lay public by scientists or knowledgeable writers. Something like “Imaging the Tenth Dimension” is crankery or New Age philosophy or just bull. It is not popular science in any way. What I’m saying, ironically enough, is that popular science is a term that has a real and specific definition and shouldn’t be abused to include any old nonsense that claims to talk about science. ---
**Author:** ![Folly](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/folly/32/3219_2.png) [@Folly](https://boards.straightdope.com/u/Folly)\ **Post date:** [February 15, 2013, 7:01pm UTC](https://boards.straightdope.com/t/dimensions-beyond-4/183360/47 "2013-02-15T19:01:48Z")
> [@Chronos](#): > > No, those wouldn’t be spatial dimensions, because you couldn’t have two different people in the same place but in different moods. Yeah, they’d both be _pissed_! ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [February 15, 2013, 8:15pm UTC](https://boards.straightdope.com/t/dimensions-beyond-4/183360/48 "2013-02-15T20:15:52Z")
> [@Chronos](#): > > No, those wouldn’t be spatial dimensions, because you couldn’t have two different people in the same place but in different moods. Yes you can, but not at the same time. I know this because I’m married. ---
**Author:** ![Learjeff](https://avatars.discourse-cdn.com/v4/letter/l/94ad74/32.png) [@Learjeff](https://boards.straightdope.com/u/Learjeff)\ **Post date:** [February 15, 2013, 9:42pm UTC](https://boards.straightdope.com/t/dimensions-beyond-4/183360/49 "2013-02-15T21:42:02Z")
> [@Ben](#): > > That’s easy enough to do. Suppose you have a point with the following coordinates in your illusory, 3-dimensional space, earthman: > > x=0.125724… > y=0.5678957… > z=0.30145… > > Reading the digits off downwards, the single coordinate in linear quozrog space is: > > q=0.153260571… > > (This is the crux of Cantor’s proof that the number of points in a surface or volume is the same as the number on a line.) This might prove that the cardinality is the same despite the number of dimensions. However, the fact that you can make a 1-to-1 and onto relation between two sets does not mean that the sets are equally useful for describing the world or doing the math. As shown above, this mapping makes the results useless, from any practical perspective. Correspondence is not equality, it’s just equality of cardinality. That said, it’s conceiveable that physical reality _could_ be described in some manner in one dimension. String theorists seem to be working the opposite way, though. I’m skeptical that the 1-dimensional approach would ever be illumunating. > [@Sqwert](#): > > So for this three-in-one dimension theory you’d have to throw away any and all traditional mathematics from addition on up. Does Cantor talk about this at all in his proof? He didn’t need to, he was only addressing cardinality, and more shouldn’t be read into it. > [@](#): > > I also have a big logic problem with this statement. If said line lies in said plane, then they can not have same number of points. For all the points in the line are in the plane, but there are plenty of other points in the plane not in the line. Sure, there are an infinite number in each, BUT all infinities are not equal. Mathematics even has a way (L’Hopital’s rule) to compare infinities. Your argument has intuitive force, which proves that intuition isn’t terribly helpful when dealing with infinites. Consider the very well accepted fact that the cardinatily the set of of whole numbers is exactly equal to the cardinality of the set of even numbers, even though the one completely contains the other, and includes members not found in the other. The method is very simple; you can define a mapping so that for every whole number you can find a corresponding even number, and vice versa. Thus the two sets map 1-to-1 and onto, and have the same cardinality. (Likewise, the number of fractions and whole numbers is the same.) Here’s my favorite infinity conundrum. At 10 minutes to midnight, you put 10 pieces of paper numbered 1 to 10, and take out a random one from the hat. At 5 minutes to midnight, you put in 11 to 20 and take out a random one (from the remaning 1-20). Do this every time the clock gets halfway to midnight. At midnight, how many pieces of paper are in the hat? An infinite number (aleph null, of course), because infinity divided by 10 is infinity. But since you’re not tired yet, let’s do another experiment, similar to the above, but each time you don’t take out a random paper, but you take out the next in sequence. So, the first time you take out #1, the next time you take out #2. At midnight, how many pieces do you have left? Zero. This is easier to prove than the result above: name any number, and I can tell you precisely when you removed it from the hat. Therefore, there are no pieces in the hat. Having fun yet? ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [February 15, 2013, 10:40pm UTC](https://boards.straightdope.com/t/dimensions-beyond-4/183360/50 "2013-02-15T22:40:37Z")
What you’re saying is true enough, but since neither Sqwert nor Ben has posted here since 2003 I don’t think they’re going to learn much from it. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 16, 2013, 1:58am UTC](https://boards.straightdope.com/t/dimensions-beyond-4/183360/51 "2013-02-16T01:58:39Z")
There are actually some stringy models where the true Universe only has two spatial dimensions, and what we perceive as three dimensions are actually just a holographic projection. And in principle, you could similarly extend the idea to a single spatial dimension. Unfortunately, I’m pretty sure that these models have now been ruled out by the experimental data. But you can at least get a universe that looks an awful lot like ours, that way. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 16, 2013, 2:01am UTC](https://boards.straightdope.com/t/dimensions-beyond-4/183360/52 "2013-02-16T02:01:30Z")
Oh, and **Learjeff** , with regard to your thought experiment with the infinite pieces of paper, the answer is not well-defined, since you’ve only specified the state of the system at times prior to midnight, not at midnight. One can say “just take the limit”, but there’s a non-removable discontinuity there, so that different ways of taking the limit can lead to different results. One might, for instance, also end up with an infinite number of pieces of paper in the hat, but without a number on any of them. [Previous page](https://boards.straightdope.com/t/dimensions-beyond-4/183360.md?page=2)