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Why Understanding Space Is So Hard

nautil.us

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Re: Why Understanding Space Is So Hard

#11

Post by sdenton4 »

donutz wrote: post #9
gobbo wrote: post #6

Earlier quoted context omitted.

Doesn't need to be, but observations constrain extra spacial dimensions to be compact and under ~1mm in size.

Does anyone have a good way of explaining to a layman how a dimension can be small?

Imagine a cylinder. It has one flat direction, which goes on forever, and a curved direction which can have a very short circumference.

Re: Why Understanding Space Is So Hard

#12

Post by aardvark179 »

donutz wrote: post #9
gobbo wrote: post #6

Earlier quoted context omitted.

Doesn't need to be, but observations constrain extra spacial dimensions to be compact and under ~1mm in size.

Does anyone have a good way of explaining to a layman how a dimension can be small?

Consider the outside of a straw. The surface is a curved two-dimensional space which is bounded in one direction only by the length of the straw, but is quite small in the other (the circumference of the straw). If the straw is very long and very thin then it may appear to be essentially 1-dimensional, but the surface is still two dimensional.

Re: Why Understanding Space Is So Hard

#13

Post by fennecfoxen »

xyzzy4 wrote: post #10
gobbo wrote: post #6

Earlier quoted context omitted.

Doesn't need to be, but observations constrain extra spacial dimensions to be compact and under ~1mm in size.

How can a dimension be under a size? The four regular dimensions (3d and time) can go infinitely in any direction.

Well, how can you go on forever without falling off the edge of the Earth? The surface of the Earth two-dimensional, and approximately flat... but there's small positive curvature, so you're continuously wrapping around to a different part of the space. The surface of the Earth can be meaningfully understood as a two-dimensional surface that possesses finite dimension.

A three-dimensional space can be close to flat but have positive curvature as well (or negative curvature, for that matter). Some proposals give our universe positive curvature, rendering its space finite, though still stupidly-big. (I'm not aware of there being a final word on the subject, though). And if different dimensions can have different curvatures, some of them could be much smaller than others.

Re: Why Understanding Space Is So Hard

#14

Post by gobbo »

xyzzy4 wrote: post #10
gobbo wrote: post #6

Earlier quoted context omitted.

Doesn't need to be, but observations constrain extra spacial dimensions to be compact and under ~1mm in size.

How can a dimension be under a size? The four regular dimensions (3d and time) can go infinitely in any direction.

Infinite is a big word :) . As explained above, the extra spacial dimensions would need to be compact, which implies them being finite in size. Perhaps the simplest example of compact manifold is the circle: you can imagine one extra dimension to be closed on itself. Going around the circular dimension one circumference length, you will find yourself where you started. The size of the dimension then refers to the characteristic size of the circle, i.e. the circumference.

Re: Why Understanding Space Is So Hard

#16

Post by aardvark179 »

T-A wrote: post #15
amelius wrote: post #5

I'm still wondering why space is 3-dimensional.

Here is a fun attempt to answer that: http://arxiv.org/abs/gr-qc/9702052

Anthropic arguments such as this are good for examining reasons why spacetime with a different number of dimensions might not support interesting universes, but they fail to ask answer the question why we have a spacetime with 3 dimensions.

Some non-string theory attempts at formulating quantum gravity have started without an assumption of space-time and attempted to make it an emergent property, and given 3-dimensional space's quite unique properties that feels like it might ultimately be a better course of reasoning.

Re: Why Understanding Space Is So Hard

#17

Post by donum »

donutz wrote: post #9
gobbo wrote: post #6

Earlier quoted context omitted.

Doesn't need to be, but observations constrain extra spacial dimensions to be compact and under ~1mm in size.

Does anyone have a good way of explaining to a layman how a dimension can be small?

Funnily enough, the same question is currently at the top of /r/AskScience:

http://www.reddit.com/r/askscience/comments/42u57e/how_can_a...

Re: Why Understanding Space Is So Hard

#19

Post by ashark »

abecedarius wrote: post #8

Julian Barbour's The Discovery of Dynamics goes into great detail on absolute vs. relative pre-Einstein. His The End of Time reviews the ideas at a more popular level and continues the story into the 20th C.

Do you have the paperback? If so, is it well-constructed? I'm interested, but with so many pages I'm wary of the format. I'd usually buy something like this in hardcover but the paperback's not cheap and the hardcover's far more expensive, and seemingly out of print.

Re: Why Understanding Space Is So Hard

#20

Post by spacehome »

aardvark179 wrote: post #16
T-A wrote: post #15

Earlier quoted context omitted.

Here is a fun attempt to answer that: http://arxiv.org/abs/gr-qc/9702052

Anthropic arguments such as this are good for examining reasons why spacetime with a different number of dimensions might not support interesting universes, but they fail to ask answer the question why we have a spacetime with 3 dimensions. Some non-string theory attempts at formulating quantum gravity have started without an assumption of space-time and attempted to make it an emergent property, and given 3-dimensio…

Couple that with Max Tegmark's ideas about multiverses. The idea is that all possible combinations of dimensions exist as a universe. We see 3+1 dimensions because this is the one combination that's most likely to develop life.

http://arxiv.org/abs/0704.0646

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