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