We start with a point.
like the point we know from geometry
it has no sice, no dimension
it just an imaginary idea
that indicates a position in a system
a second point then can be used to indicate a different position
but it too is of undetermined size
to create the first dimension
all we need is a line joining any two points
our first dimensional object has length only
no width or depth
if we now take our first dimensional like
and draw a second line
crossing the first
we invented the second dimension
the object we're presenting now has a length, a width
but no depth
to help us with imagining with the higher dimensions
we're going to represend our second dimensional object
as beeing creating a second line which branches off from the first
now lets imaging a race of two dimenstional cratures called flatlanders
what would it be like to be a flatlander living in their two dimensional world
a two dimensional creature
would only have length and width
as if they're the roaylty on a implossibly plain play card
picture this
a flatlander couldn't possibly have a digestive tract
because the pipe from the mouth to the bottom
would devide them into two peaces
and a flatlander trying to view our three dimensional world
would only be able to perceive shapes
in two dimensional crossections
a baloon fro instance
would start as a tiny dot
become a holow circle
which .... grows to a certain size
than shirnks back to a dot
before popping out of existence
an we three dimensional human beeings
would seem very strange indeed to a flatlander
imaginging the third dimenstion is the easiest for us
because for every moment of our lives this wat we're in
a three dimensional object has length, width and hight
but here is another way to describe the third dimension
if we imagine an ant walking across a newspaper
which is lying on a table
we can pretend that the ant is a flatlander
walking along in a flat two dimensional newspaper world
if that paper is now foldet in the middle
we create a way for our flatlander ant
to magically diappear from one position in his world
an be instantly tranported to another
we can image that we did this by taking a two dimensional object
and folding it through the dimension above
which is our third dimension
once again it would be more convinient for us
as we imagine the higher dimensions
if we can think of the third dimension in this way
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