okay everybody today I'm going to be
showing you what a ball would look like
in a fourth spatial dimension a four D
ball so I'm going to be showing you what
a sphere would look like if there were a
fourth spatial dimension and then what
would it look like if there was some
four D being that was going to move that
sphere through the fourth dimension what
would it look like in our 3d space and
what other cool stuff could they do if
they move stuff around and 4d what would
it look like in our three dimensions so
we live in a universe that has three
spatial dimensions that means you can go
this way you can go this way and you can
go up and down for example I have this
cube here in three dimensions but what
would it mean if I were only to look at
this cube in two dimensions well because
we only have two dimensions it means we
can only go this way and this way but
not up and down so it's the equivalent
of taking a slice of this cube so
instead of having a cube now I take a
slice of it so now this is just called a
plane it has the X and the y axis so it
has these spatial dimensions but it has
no up-and-down so that means when you
look at it sideways all you see is a
line so now we have a world that's only
two dimensions
what would a sphere look like in this
two dimensions well because everything
in two dimensions is just a slice of
three dimensions instead of a sphere
that has up and down to it you would
only get a slice of that sphere so a
sphere would now look like a circle
so the first thing I want you to notice
about this two-dimensional circle is
that for me in three dimensions looking
at this two-dimensional plane I can see
the entire circle at one time I see
everything the inside of it the outside
of it everything all at once but for
somebody living in this 2-dimensional
world they don't see a circle but they
see a line you can see what I mean is I
start from above I can see the entire
circle but as I come on to the plane
that circle shrinks down and gets
flatter and flatter and flatter until
eventually it just becomes a flat line
so if these two dimensional beings live
only on this flat plane all they see is
lines so what would a sphere look like
to this 2-dimensional person well
remember that that 2-dimensional person
can only see a slice through the sphere
and they would only see it if it's in
their plane anything outside of it they
can't see they only see what's in this
plane here so in order to see this I
would have to move it into the plane but
what it would look like from their point
of view it would look like a circle just
suddenly appears and then gets bigger
and then smaller and then disappears and
so me is a three dimensional being
moving this 3d object through their
two-dimensional plane would seem quite
mystical it would seem like things
suddenly appear then disappear appear
then disappear and with that in mind now
we can start to understand what it would
be like for a four-dimensional being to
move a four-dimensional object through
our three-dimensional space so I'm going
to show you what it would look like if a
four-dimensional being was to move a 4d
sphere through our 3-dimensional space
it would be similar to the
two-dimensional circle starting small
getting bigger and then going small
again but it would be in three
dimensions
so it looks something like this okay so
here's my four-dimensional ball and what
you're actually seeing is the very tip
of the four-dimensional ball this is the
small circle but because we're in 3d
mentions its the small sphere at the tip
of the fourth dimensional ball and I can
move it around and do anything that I
want with it but watch what happens when
I summon the powers of a fourth
dimensional being to move the ball
through the fourth dimension and through
our 3d space well it would look
something like this okay they're moving
it through the fourth dimension and as
he's moving it it's getting bigger and
bigger and bigger and stop so now you
can see as it got moved through the
fourth dimension the size changed in our
three dimension here so now we have a
larger sphere but we're not quite to the
center of the four dimensional spheroid
so let's set it down and have the fourth
dimensional beam move it through the
largest diameter that shows up in our
three dimensions okay and go so now it's
moving moving through the fourth
dimension which making which is making
the sphere get bigger and bigger and
bigger and our three dimensions until
finally we end up with this so now the
four dimensional sphere oeid is at its
largest diameter and our three
dimensional Plex space and so now I have
a very large sphere so we know that a
four dimensional being could suddenly
appear then disappear in our three
dimensional space could make objects
randomly appear disappear change shape
altogether and it would seem quite
mystical but here's an even weirder
thing that fourth dimensional being
could do they can turn you into your own
mirror image of yourself let me show you
what I mean
so going back to our analogy in two
dimensions here's our two dimensional
guy so now suppose in this two
dimensional world he's looking at this
object there's also a mirror behind it
so this line represents a mirror so
looking in that mirror the mirror image
looks like this but no matter what he
does in this two-dimensional world he
cannot get this object to look like it's
mirror image other than just looking in
the
but me as a three-dimensional being I
can come in and I can take it out of
this two-dimensional world flip it and
now it becomes a mirror image of itself
so because I was a three-dimensional
being and I was able to take it out of
this two-dimensional world and flip it
in my three-dimensional world now this
is permanently the mirror image of
itself for this two-dimensional person
now
so the same can be said in three
dimensions to four dimensions that means
that this fourth dimensional being could
take this pretzel bag flip it in the
fourth dimension and now it would be
permanently a mirror image of itself in
our three-dimensional world in fact you
would never be able to hide anything in
our three-dimensional world from a
fourth dimensional being everything
would be present at the same time they'd
immediately be able to see what is
inside this box similar to how I can
instantly see what's inside this box but
this two-dimensional person wouldn't be
able to see it because it's being
blocked by the outside so it would be
quite amazing to see some fourth
dimensional thing moving through our
three dimensions and making things
reappear change shapes do all sorts of
different things even making mirror
images of things but is there a fourth
dimension of space well actually there
could be string theory actually suggests
that there's 11 spatial dimensions but
only three of them are big enough to
notice so we have three spatial
dimensions that are big enough to see
any changes but the other dimensions
aren't big enough to notice any
difference with movement hey everybody
thanks for watching another episode of
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