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We start with a point
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like the "point" we know from geometry
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it has no size, no dimension
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It's just an imaginary idea that
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indicates a position in the system
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a second point, then
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can be used to indicate
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a different position
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but it, too, is of indeterminate size
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To create the first dimension
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all we need is a line
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joining any two points.
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A first dimensional object has length only
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no width or depth
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If we now take our first dimensional
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line and draw a second line
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crossing the first
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we've entered the second dimension
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the object we're representing
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now has a length and width,
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but no depth
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to help us with imagining
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the higher dimensions
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we're going to represent
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our second dimensional object
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as being created using
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a second line
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which branches off from the first
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Now, let's imagine
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a race of two-dimensional
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creatures called "Flatlanders".
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What would it be like
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to be a Flatlander
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living in their
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two-dimensional world?
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A two-dimensional creature
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would have only length and width
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as if they were the royalty
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on an impossibly flat
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playing card.
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Picture this
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a Flatlander couldn't possibly
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have a digestive tract
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because the pipe from
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their mouth to their bottom
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would divide them into two pieces
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And a Flatlander trying
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to view our three-dimensional
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world
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would only be able
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to perceive shapes
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in two-dimensional
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cross-sections
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A balloon, for instance
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would start as a tiny dot
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become a hollow circle
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in which inexplicably
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grows to a certain size
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then shrinks back to
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a dot before popping
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out of existence
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And we three-dimensional
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human beings would seem
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very strange indeed
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to a Flatlander
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Imagining the third-dimension
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is the easiest for us
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because every moment of our lives
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that is what we're in
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A three dimensional object has
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length, width and height
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but here's another way to describe
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the third dimension
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If we imagine an ant
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walking across a newspaper
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which is lying on a table
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We can pretend that
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the ant is a Flatlander
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walking along on a flat
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two-dimensional
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newspaper world
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If that paper is now folded in the middle
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we create a way
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for our Flatlander ant
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to "magically" disappear from
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one position in his
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two-dimensional world
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and be instantly transported to another
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We can imagine
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that we did this
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by taking a two-dimensional object
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and folding it through
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the dimension above
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which is our third dimension
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Once again, it'll be more convenient
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for us as we imagine
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the higher dimensions
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if we can think of the third dimension
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in this way
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The third dimension is what
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you "fold through"
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to jump from one point
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to another in the
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dimension below
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The first three dimensions
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can be described
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with these words:
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length
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width
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and depth
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What word can we assign to
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the fourth dimension?
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One answer would be
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duration
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If we think of ourselves as
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we were one minute ago
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and then imagine ourselves
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as we are at this moment
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the line we could draw from
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the "one-minute-ago version"
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to the "right-now version"
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would be a line in the fourth dimension
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If you were to see your body
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in the fourth dimension
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You would be like a long
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undulating snake
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with your embryonic
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self at one end
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and your deceased self
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at the other
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But because we live from
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moment to moment
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in the third dimension
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we are like our second
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dimensional Flatlanders
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Just like that Flatlander
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who could only see
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two-dimensional cross-sections
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of objects from the dimension above
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we as three-dimensional creatures
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can only see three-dimensional
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cross-sections
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of our fourth dimensional self
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One of the most intriguing aspects
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of there being one dimension
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stacked on another
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is that down here in the dimensions below
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we can be unaware of our motion
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in the dimension above
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Here's a simple example:
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if we make a Mobius strip
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take a long strip of paper
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add one twist to it
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and tape the ends together
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and draw a line down the length of it
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Our line will eventually
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be on both sides of the paper
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before it meets back with itself
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It appears somewhat amazingly
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that the strip has only one side
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so it must be a representation
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of a two-dimensional object
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And this means that a two-dimensional
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Flatlander traveling down
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the line we just drew
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would end up back where
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they started without ever
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feeling like they had left
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the second dimension
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In reality
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they would be looping and twisting
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in the third dimension
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even though to them it felt like
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they were traveling
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in a straight line
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The fourth dimension
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time
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feels like a straight line to us
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moving from the past to the future
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But that straight line in
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the fourth dimension is
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like the Mobius strip
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actually twisting and turning in
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the dimension above
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so, the long undulating snake that is us
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will feel like it is moving in
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a straight
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line in the fourth dimension
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but there will actually be
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in the fifth dimension
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A multitude of paths
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that we could branch to
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at any given moment
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those branches will be influenced
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by our own choice
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chance, and the actions of others
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Quantum physics tells us that
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the subatomic particles
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that make up our world
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are collapsed from waves
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of probability simply by the act
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of observation
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In the picture we are drawing
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for ourselves here
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we can now start to see
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how each of us are collapsing
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the indeterminate wave of
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probable futures contained
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in the fifth dimension
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into the fourth dimensional line
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that we are experiencing as "time"
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What if you want to go back
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into your own childhood
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and visit yourself?
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We can imagine folding
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the fourth dimension through
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the fifth
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jumping back through time
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and space to get there
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But what if you wanted to
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get to the world where
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for example
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you had created a great
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invention as a child
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that by now had made you famous and rich?
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We can imagine our fourth-dimensional
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selves branching out from
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our current moment into
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the fifth dimension
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But no matter where you go from here
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the "great child inventor" timeline
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is not one of the available options
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in your current version
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of time
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you can't get there from here
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no matter how much choice, chance,
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and the actions of others
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become involved
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There are only two ways
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you could get to that world
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one would be to travel back in time
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somehow trigger the events
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that caused you to come up
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with your invention
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then travel forward in the fifth
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dimension to see one of the
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possible new worlds that
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might have resulted
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but that would be taking the long way
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the shortcut we could take
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would involve us folding
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the fifth dimension through
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the sixth dimension
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which allows us to instantly
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jump from our current position
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to a different fifth dimensional line
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In our description of the fourth dimension
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we imagined taking the dimension
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below and conceiving of
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it as a single point
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the fourth dimension is a line
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which can join the universe
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as it was one minute ago
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to the universe as it is right now
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Or in the biggest picture possible
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we could say that the fourth dimension
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is a line which joins
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the big bang
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to one of the possible endings
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of our universe
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Now, as we enter the seventh dimension
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we are about to imagine a line
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which treats the entire sixth
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dimension as if it were
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a single point
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to do that, we have to imagine
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all of the possible time lines
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which could have started from our big bang
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joined to all of the possible endings
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for our universe
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a concept which we often
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refer to as infinity
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and treat them all as a single point
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So, for us, a point in the seventh
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dimension would be infinity
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all possible time lines which
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could have or will have occurred
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from our big bang
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When we describe infinity
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as being a "point"
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in the seventh dimension
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we are only imagine part of the picture
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if we're drawing a seventh
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dimensional line
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we need to be able to imagine
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what a different "point" in
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the seventh dimension is going to be
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because that's what our line is
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going to be joined to
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But how can there be
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anything more than infinity?
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The answer is
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there can be other completely
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different infinities created
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through initial conditions
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which are different from
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our own big bang
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Different initial conditions
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will create different universes
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where the basic physical laws
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such as gravity or the speed
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of light are not the same as ours
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and the resulting branching time
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lines from that universe's
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beginning to all of it's possible
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endings
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will create an infinity
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which is completely separate
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from the one which is associated
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with our own universe
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so the line we draw in
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the seventh dimension
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will join one of those infinities
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to another
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and as boggling as the magnitude
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of what we are exploring
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here might be
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if we were to branch off
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from that seventh dimensional
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line
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to draw a line to yet
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another infinity
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we would then be entering
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the eight dimension
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As we've explored already
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we can jump from one point in
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any dimension to another
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simply by folding it through
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the dimension above
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If our ant on the newspaper were
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a two-dimensional Flatlander
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then folding his two-dimensional
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world through the third dimension
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would allow him to magically
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disappear from one
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location and appear in a
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different one
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As we're now imagining
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the ninth dimension
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the same rules would apply
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If we were to be able
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to instantaneously jump
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from one eighth dimensional
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line to another
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it would be because
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we were able to fold
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through the ninth dimension
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Before we discussed the first dimension
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we could say that we first
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started out with dimension
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zero
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which is the geometrical
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concept of the "point"
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A point indicates a location in a system
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and each point is of indeterminate size
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The first dimension then
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takes two of these "points" and
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joints them with a line
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When we imagine the fourth dimension
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it was as if we were treating
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the entirety of three-dimensional
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space in a particular state
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as a single point
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and drawing a fourth-dimensional
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line to another point
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representing space as
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it is in a different state
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We often refer to the line
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we have just drawn as "time"
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Then in the seventh dimension
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we treated all of the possible time
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lines which could be
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generated from our big bang
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as if this were a single point
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and imagine drawing a line
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to a point representing
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all of the possible time lines
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for a completely different universe
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Now, as we enter the tenth dimension
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we have to imagine all
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of the possible branches
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for all the possible time lines
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of all the possible universes
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and treat that as a single point
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in the tenth dimension
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Ah! So far, so good
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but this is where we hit a roadblock
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if we're going to imagine
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the tenth dimension
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as continuing the cycle
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and being a line
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then we're going to have
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to imagine a different point
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that we can draw that line to
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but there's no place left to go!
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By the time we have imagined
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all possible time lines
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for all possible universes
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as being a single point
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in the tenth dimension
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It appears that our journey is done
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In string theory
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physicists tell us
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that Superstrings vibrating
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in the tenth dimension
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are what create
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the subatomic particles
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which make up our universe
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and all of the other possible
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universes as well
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In other words
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all possibilities are contained
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within the tenth dimension
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which would appear to be
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the concept we have
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just built for ourselves
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as we imagined the ten dimensions
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built one upon another