Profeor Sanuki's Soliloquy 209
Professor Sanuki's Soliloquy
Everyone has probably heard how the universe was born with the Big Bang. However, what
does it mean for the universe to be born?
The universe that we recognize is three-dimensional, and it can be represented by three
coordinate axes for length, width, and height. Of course, we cannot escape the bounds of it.
For us, this is everything we know.
However, space with four (or more!) dimensions is called hyperspace, and from the
perspective of hyperspace, a three-dimensional space is just a single, closed system. (By the
way, the four-dimensional space I’m talking about here is space represented by four coordi-
nate axes, not three-dimensional space plus time).
Since we cannot make an image of such a four-dimensional space, let’s consider a
model by looking at two dimensions from a three-dimensional perspective.
I have a balloon here, and its surface is two-dimensional. It is spatially curved and
forms a three-dimensional sphere.
In the same way, the three- dimensional space in which we live could be four-
dimensionally curved.
Since this hypothetical four-dimensional rocket simply passes beyond the edge of the
three-dimensional universe, from its view point (that is, if we look at our three-dimensional
universe from four dimensions), the edge of the universe is everywhere. This is what
I meant earlier when I said, “The edge of the universe is right here.”
Return to the original location
Two-dimensional rocket
If the two-dimensional rocket aims for the edge of the balloon, it will return to its original location.
210 Chapter 4 What Is It Like at the Edge of the Universe?
Incidentally, suppose that we had a spaceship with some sort of “warp drive” that
allowed us to move by entering four-dimensional space and then re-entering three-dimen-
sional space at a different location. To people observing us, our ship would appear to just
vanish through a “warp” in space and then appear suddenly elsewhere.
Well, then, what is the shape of three-dimensional space?
Although I will omit the difficult explanation here, according to mathematical calcula-
tions, it is like one of the following three models.
In the first model, where the curvature of space is zero, space continues to extend no
matter where you go. When illustrated in two dimensions, space is a plane that goes on for-
ever. Although the figure appears to have an edge, since the plane actually continues in all
directions, you absolutely cannot reach the edge of the universe as long as you move within
three dimensions.
In the second model, where the curvature is positive, space is a spherical surface like
that of a globe when it is represented as a two-dimensional model.
In the third model, where curvature is negative, space is “saddle shaped”—it curves up
and it curves down.
If we consider the spherical surface with positive curvature as the model of our uni-
verse, a spaceship that travels in three dimensions while aiming for the edge of the universe
will eventually return to its original location.
If we could build a spaceship that could travel faster than the speed of light, it might
be able to reach hyperspace at the edge of the universe through a space warp. However, as
long as we are in three-dimensional space, travel faster than the speed of light cannot occur
because of the constraint of the theory of relativity. In other words, no matter how far we
travel, we cannot get to the edge of the universe and, at best, will only return to our original
point of departure.
2-D Universe Model 1 2-D Universe Model 2 2-D Universe Model 3
Profeor Sanuki's Soliloquy 211
The universe
is so
Since I came from
that universe, I
wi ask humans
to ponder its
mysteries so that
they may learn
ofthe universe
and the universe
may learn of
Isn’t that right,
Mr. Sanuki?
That’s right. As a
wise man of earth,
it is my miion to
sk answers to
such questions.
Kaguya-hime did
not return to her
home planet, but
she continued to
live haily on Earth
while talking about
the universe with
this knowledgeable
Your acting
was great,
Have you
ever acted
Actuay, I was
in the drama
club in high
Wow. I
I was in various
plays, such as Alice in
Wonderland and Ae
of Grn Gables.
Wow! What part
did you play,
The leading
role, of
I thought you
would have bn
in the astronomy
March hare?

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