so i mean this has quite a long history
in that at the end of the 19th century a
guy called edwin abbott wrote a very
famous book called flatland in which he
kind of explored a a flat universe it
was sort of social satire rather than
physics so he didn't go much into the
physics of the universe but subsequent
to that various people have looked at it
and most famously a guy called alexander
judy who's a computer scientist in
canada has gone through figuring out a
lot of the physics of what the
universe would look like if it actually
only had two dimensions whether you
could actually make it work or not
alexander judy wrote a book called the
plain universe in which he actually it's
a it's a story about some people who
accidentally start kind of communicating
with the two-dimensional universe and so
he kind of explores the communication
between universes and so on but there's
a load of technical appendices at the
end of the book about what the science
behind it was and actually i read it you
know in the mid-1980s just after it come
out somebody gave it to me for christmas
and i was fascinated by this it's one of
the things that sort of inspired me
about physics and actually one of the
things that just sort of made me think
the most when i started doing this was
it's something very trivial if you're a
two-dimensional being living on a flat
piece of paper so your little stick
figure living on a stacked flat piece of
paper and you try and lift one end of a
plank up you can't do it right because
there's nowhere for the air to rush in
you're kind of creating a vacuum by
lifting that into the plank because
you've got the plank resting on the
ground and then the u holding onto the
plank so there's no gap there for air to
come in the way there is from the sides
in three dimensions so you can't do it
you can't even pick up a plank and in
fact in this book he had his characters
having to kind of shuffle their feet up
and down to sort of let the air in as
they were lifting one end of things in
order for that to happen so it was just
that trivial example got me absolutely
fascinated with these things and there's
all sorts of stuff like if you start
trying to think about biology by
supposing you have a two-dimensional
being
if it had a digestive tract in other
words it has a mouth going all the way
down to the bottom then basically it
will fall in half right because there's
nothing holding the two halves together
in two dimensions
and so you have to come up with some
clever wave if you want your
two-dimensional beings to be able to eat
and not fall in half
and so judy came up with this idea of
basically a zipper you can because you
can have a zipper in two dimensions and
so these creatures are kind of zipped
together and that allows things to kind
of work their way down through their
bodies
so it's complicated world living in two
dimensions give you one more example
that one more good good thing so an
astronomical example astronomy in two
dimensions and space travel in two
dimensions turns out space travel in two
dimensions is quite tricky and that's
because the the concept of escape
velocity doesn't exist in in two
dimensions right actually it turns out
that so on in three dimensions the force
of gravity drops off like one over
distance squared which means as you go
you go twice as far away the force of
gravity is four times as weak if you go
down a dimension so it's only two
dimensions it turns out that only
gravity only drops off like one over
distance so when you're twice as far
away gravity is still weaker but only by
a factor of two rather than a factor of
four so that means gravity is a much
longer range force in two dimensions
than it is in three dimensions and so
that means that so in three dimensions
there's this concept of escape speed you
can actually fire a rocket fast enough
from the earth say and it can actually
escape entirely
in two dimensions because the force of
gravity is that much stronger that much
longer range no matter how fast you fire
your rocket up into space it will
eventually always turn around and come
back
and that means firstly that actually you
can't you know but deep space travel is
very difficult right because actually
you have to put huge amounts of energy
in to get far enough to actually get to
the next planet
but worse than that it means that
actually the universe is sort of doomed
because the entire universe can't
achieve escape velocity either so the
universe can't keep expanding forever
and will eventually collapse back on
itself and so there will always be a big
crunch in the two-dimensional
a lot of people are probably under the
belief that our universe is going to do
that so well life is complicated right
firstly in our universe in three
dimensions it doesn't have to happen in
our universe there's probably this thing
called a cosmological constant or dark
energy which is driving things apart
so actually when i started thinking
about this again for making this video i
started thinking couldn't you do the
same for a flat universe right if we
introduce this cosmological constant
would that actually allow the universe
to keep expanding forever so i talk to
my particle theory colleagues who are
much clever at these kinds of things it
turns out that actually general
relativity doesn't work in two spatial
dimensions that or at least you can make
it work but it's very limited in that
the concept of action at a distance goes
away in other words the pull of gravity
outside anybody is zero
so actually you can't even if you live
in a general relativistic universe you
can't even have gravitational
interactions between bodies the way we
do in our three-dimensional
three-spatial dimensional universe
so if you believe in general relativity
rather than newtonian gravity which is
what i was just talking about then
actually you can't build a universe at
all with gravity in it or at least not
gravity in any way that we recognize it
so why why bother to do this um
probably because it's kind of
fascinating and actually you know
if you like you can think of it as sort
of an exercise for scientists because
it's good to kind of think about things
in ways you don't usually think about
things and that's how you kind of try
and do new sciences trying to think
about things in new ways but it turns
out actually there are two-dimensional
things in the real universe and the most
current example is this stuff called
graphene
which is this sort of single layer
thickness of carbon new new type of
carbon that's been discovered and it
really does behave because it's only a
single layer of atoms thick the
electrons as they move around within
graphene are really moving in two
dimensions which means that the physics
of what's going on really is explained
in terms of two dimensions so there are
physical systems that are of real
current research interest where
understanding the physics of what goes
on in two dimensions is really important
it's really stuck with me the idea of
these
two dimensional beings trying to eat and
falling in half yes and these other
conundrums
if there are people who live in
four spatial dimensions
well they look at us and laugh in the
same way
are there things about us that we're
limited what are we limited
i think they probably would they would
how on earth can you exist in only three
dimensions it's so restrictive you know
the number of things you can do in three
dimensions here in four dimensions we
can do all sorts of clever things that
they can't do in three dimensions
another thing in if you start thinking
about two-dimensional three-dimensional
beings is the the connections in the
brain because um in three dimensions you
know it's quite easy to wire things up
and so you can actually wire all the
neurons together in two dimensions it's
actually a lot more complicated because
things have to cross over and you've got
to figure out how you can pass
information where wires cross over and
so on and so actually a
three-dimensional brain is probably
easier to design and probably can be
more efficient than the two-dimensional
brain now presumably if you went up into
four dimensions things would get even
more efficient because the number of
ways you can link things together gets
you know that much bigger and so
presumably you know a four-dimensional
brain could be an awful lot cleverer
than a three-dimensional brain and they
will presumably pity us for our
miserable three-dimensional thoughts
when they can have four-dimensional
thoughts
i can't imagine how a fourth spatial
dimension works
can no human imagine that or is that my
limitation well that's the i mean in
some ways that's the lovely thing about
thinking about two dimensions because
actually if you start thinking about
well how would a two-dimensional being
think about three dimensions
that at least gives you the beginning of
an insight of how can a
three-dimensional being start to think
about four spatial dimensions
but there is no fourth spatial dimension
well if you ask the particle theorists
they can tell you that sometimes you
have 11 spatial dimensions but most of
them are very small but now for
practical purposes there are three
spatial dimensions that we know of
uh following the earth around there used
to be lots of science fiction stories
about l3 it used to be a popular place
to put the anti-earth or you know if
you're an evil genius that's where you
put your hidden layer because it was
always hidden behind the sun as the two
kind of orbit around each other we've
now had enough satellites out there that
have actually looked at the other side
of the solar system to know actually
there isn't anything much at l3