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<blockquote data-quote="Conaill" data-source="post: 2097744" data-attributes="member: 1264"><p>Yes, time can be viewed as a 4th dimension, but it is not a *spatial* 4th dimension. There is some weird mixing going on between the time and spatial dimensions, but it's not as if you could do, for example, a rotation between a time and a spatial dimension.</p><p></p><p>What's we're talking about in this thread is a 4th spatial dimension. For a long time, this was just an abstract notion. Just as we - living in 3 dimensions - can imagine objects in 2 spatial dimensions (we can draw them on a piece of paper - heck, we can ieven imagine <em>life</em> in 2 dimensions, as in Abbott's 1884 book "<a href="http://www.geom.uiuc.edu/~banchoff/Flatland/" target="_blank">Flatland</a>"), we can imagine objects in more than three spatial dimensions. </p><p></p><p>It's really just algebra: 2 points define a line, 3 points define a plane, 4 points define a 3D space... 5 points define a 4D space! (And if those 5 points are equally far spaced apart, they outline a <em>pentatope</em>, the smallest 4D "die".) Just like we can algebraically define objects in 3D, nothing stops us from defining objects in any artbitrary number of dimensions, and analyzing properties of such objects. For convex polytopes, this is fairly easy, because you only need to define a set of points in N-dimensional space. The object formed by the convex hull of these points is the polytope. In 4 dimensions, that's called a (convex) polychoron.</p><p></p><p>Now, more recently advanced theories of the natural world such as string theory have postulated that there may very well be more that 3 spatial dimensions even in our seemingly 3D world! It is thought that those extra spatial dimensions are "rolled up" very tightly, so we don't actually observe them. Just like a clothesline looks 2-dimensional to us, but it would look distinctly 3-dimensional to an ant crawling on its surface.</p></blockquote><p></p>
[QUOTE="Conaill, post: 2097744, member: 1264"] Yes, time can be viewed as a 4th dimension, but it is not a *spatial* 4th dimension. There is some weird mixing going on between the time and spatial dimensions, but it's not as if you could do, for example, a rotation between a time and a spatial dimension. What's we're talking about in this thread is a 4th spatial dimension. For a long time, this was just an abstract notion. Just as we - living in 3 dimensions - can imagine objects in 2 spatial dimensions (we can draw them on a piece of paper - heck, we can ieven imagine [i]life[/i] in 2 dimensions, as in Abbott's 1884 book "[url=http://www.geom.uiuc.edu/~banchoff/Flatland/]Flatland[/url]"), we can imagine objects in more than three spatial dimensions. It's really just algebra: 2 points define a line, 3 points define a plane, 4 points define a 3D space... 5 points define a 4D space! (And if those 5 points are equally far spaced apart, they outline a [i]pentatope[/i], the smallest 4D "die".) Just like we can algebraically define objects in 3D, nothing stops us from defining objects in any artbitrary number of dimensions, and analyzing properties of such objects. For convex polytopes, this is fairly easy, because you only need to define a set of points in N-dimensional space. The object formed by the convex hull of these points is the polytope. In 4 dimensions, that's called a (convex) polychoron. Now, more recently advanced theories of the natural world such as string theory have postulated that there may very well be more that 3 spatial dimensions even in our seemingly 3D world! It is thought that those extra spatial dimensions are "rolled up" very tightly, so we don't actually observe them. Just like a clothesline looks 2-dimensional to us, but it would look distinctly 3-dimensional to an ant crawling on its surface. [/QUOTE]
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