Profeor 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.”

Spacewarp

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

Profeor Sanuki's Soliloquy 211

The universe

is so

mysterious...

Since I came from

that universe, I

wi ask humans

to ponder its

mysteries so that

they may learn

ofthe universe

and the universe

may learn of

them.

Isn’t that right,

Mr. Sanuki?

That’s right. As a

wise man of earth,

it is my miion to

sk answers to

such questions.

Kaguya-hime did

not return to her

home planet, but

she continued to

live haily on Earth

while talking about

the universe with

this knowledgeable

viager.

Bravo...

Bravo!!

CLAP

CLAP

CLAP

CLAP

Your acting

was great,

Profeor!!!

Have you

ever acted

before?

Actuay, I was

in the drama

club in high

schl.

Wow. I

never

expected

that!

I was in various

plays, such as Alice in

Wonderland and Ae

of Grn Gables.

Wow! What part

did you play,

Profeor?

The leading

role, of

course!

Oh…

...

Huh?!

I thought you

would have bn

in the astronomy

club!

March hare?

Caterpiar?

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