Love Story: In The Web of Life (35 page)

"Me too."

We both sipped our champagne and dried our
eyes.

After a long pause, when I could again speak, I
said. "We should get married?"

Tina put down her glass, took mine, and then
took both my hands in hers and said, "I think we just
did."

We celebrated everything that night.

****

A month later, after a round of celebratory
receptions and parties thrown by our associates and friends, Tina,
Elise, and I flew to Sacramento, rented a car and drove to Steve
and Georgia's. Tina and I stayed in the guest cottage. The next
morning we all drove a few miles away to a site on the top of a
hill. A Native American medicine wheel, a large circle of large
stones containing a smaller circle of smaller stones was sculpted
on the ground. A flat–topped darkly–speckled granite boulder was in
the center. Four radial lines of stones aligned with the four
compass directions joined the center and the circles.

Steve took his place in the center while we
waited outside the wheel. Tina and Elise on the South side, Georgia
and I on the North. Steve stood on a round, and did a short magic
ritual opening the circle with the spirits of the four directions.
Then, Elise and Georgia escorted us to the center.

Tina and I both noticed an intense spark of
light coming from one of the crystals of mica in the boulder under
Steve. Tina pointed at it and glanced at me questioningly and then
smiled. I replied with a nod.

After a brief ceremony in which we exchanged
rings, Steve pronounced us Husband and Wife.

We walked to the shade of a nearby tree, and
Georgia produced a bottle of champagne for teary-eyed toasts and
hugs. After a while, Tina said, "Was that spark of light on the
boulder Uriel?"

With delight I said, "You heard and saw him!
That's fantastic. Did anyone else see or hear Uriel?'

Only Tina replied, "I didn't exactly hear him.
I felt an amazing feeling of love, happiness, and congratulations,
all mixed up together. I also had the feeling he, or they, were
laughing about something. A leg? There was something about
touch."

I hugged her with delight. "The leg thing is
reference to a bad joke I'll tell you later. Uriel was saying, 'We
will be in touch.'"

We went back to celebrating with our dear
friends. After a few minutes, Tina led me away from the others and
made me stand on the granite boulder at the center of the
circle.

"One more thing," she said, "Read what I had
engraved inside your ring."

I took my wedding ring off and read the
inscription:

Pour le Me'rite.

****

Appendix:

CANDICE'S EIGHT-DIMENSIONAL MOVIE

(Including Equations)

Film: Cast: Narrator and historical and
contemporary characters.

The show opens with a real person, a
commentator who is a well known physics professor (having appeared
in PBS scientific programs) who sets up the idea that we will learn
how to calculate distances in spacetime and explore other concepts
of space and time.

In the first scene we have an animated
character, Pythagoras who is a Greek, in a toga, being asked by a
Nero-looking character to calculate the distance (d) from the
entrance in a Greek temple to the farthest corner. He measures the
distance from the door of the temple to the back wall (x) and then
measures the distance from there to the corner (y) and then the
animation shows him calculating the hypotenuse of the triangle,
mumbling his famous formula, 'the square of the hypotenuse is the
sum of the squares of the two sides.' He scratches out a formula in
the dirt on the ground:

(d)
²
=
(x)
²
+
(y)
²
and continues mumbling to
himself."

Then, he decides to calculate the distance from
the door to the top of the wall in the far corner. He scratches his
head, and then he measures the distance up the wall (z) and then
adds it to his formula,

(d)
²
=
(x)
²
+
(y)
²
+
(z)
²

and then dances around in delight.

Another character who has modern dress, a baggy
sweater, tennis shoes and wild hair comes in. It is Einstein. He
tells Pythagoras that if we put the temple on a big chariot
traveling at a speed of (v), we can calculate the distance from the
door now the upper corner where it will be (t) later. All we have
to do is add one more term to Pythagoras' formula:

(d)
²
=
(x)
²
+
(y)
²
+
(z)
²
+
(vt)
²
.

Cut to the temple sitting on a giant chariot.
Einstein hits the horse on the rump and it charges off. We see a
line connecting the door of the temple before it started moving
stretching to the corner of the moving temple as it moves
away.

Pythagoras says, "That is interesting, but who
would ever do anything with that?"

Einstein is seen scratching his head as the
scene fades.

The commentator then adds:

"That is about how far we can go visualizing
spacetime. There was no evolutionary advantage for our species to
evolve with the ability to visualize more dimensions than we can
see. Quite a bit after the time of Pythagoras, mathematicians
decided their equations didn't have to limited by what they could
see. They can have equations that describe any number of dimensions
and geometries. Einstein's mathematics teacher at his college,
Herman Minkowski, liked to play around with a higher number of
dimensions than four. One of his sets of higher dimensions is now
called complex eight-dimensional Minkowski space, which we will
call eight-space for short. Mathematicians like to name things
after their originators. Pythagoras's theorem is named after Mr.
Pythagoras, for instance.

"Like many things in mathematics, the idea of
eight-space lay around unused for years. After the turn of this
century, a mathematician found eight-space could be used to explain
many mysteries in physics and expand the field to explain some
no-no topics such as ESP. Until this new explanation came along,
most physicists would write you off as crank if you even mentioned
ESP, because there was no scientific explanation for it. All
psychic phenomena were considered the product of ignorance,
superstition, and unscientific thinking. Few credible scientists
would touch the subject for fear of being ostracized by their
peers.

"Knowledge of eight-space may change the way we
think about many things, so lets explore it further. We have to
first address the idea of the word 'complex' in eight space, the
idea of complex numbers. If you went to k-12 school in the last
decade, you know all about complex numbers. However, chances are
your parents and surely your grandparents don't know about them In
1545 an Italian mathematician, Geroiamo Cardano was trying to solve
an equation but nothing worked. Lets let Geroiamo
explain."

Switch to another animation. Our character,
Geroiamo, is dressed like the men we see in Shakespearian plays,
wearing puffy sleeved shirts, pantaloons, tight pants, pointed toe
shoes.

Geroiamo is sitting at a table scribbling away
on equations. He keeps muttering and swearing, wadding up his paper
and throwing it on the floor, starting over. His cleaning lady
comes in to clean up and asks him why he is making this mess. He
explains that he is trying to solve this equation, and he keeps
ending with an impossible number, the square root of minus
one.

The cleaning lady picks up a piece of paper,
unwads it and stares at it for a minute. "You mean this number
here, minus one that looks as though it is under a table or
awning?"

"Yes,'" says Geroiamo. "There can be no number
that, if multiplied by itself, can make a minus one. A minus times
a minus is always a plus."

The cleaning lady looks at the paper and says,
"But the number is right here. Why don't you simply call it a
number and stop making such a mess."

We see Geroiamo showing his equations to
friends. They all laugh derisively and ridicule him for only being
able to solve the equation with a fictitious or imaginary numbers.
They say, "Who will ever do anything with that?"

The commentator returns and says:

"As Geroiamo found the imaginary numbers
convenient to solve problems, other mathematicians found it
convenient to use them. After a while, certainly by the start of
the nineteenth century, nobody thought anything bad about using
imaginary numbers. Engineers used them in designing and analyzing
bridges.

This brings us to Einstein in the early
twentieth century:"

In the animation, we see a child Einstein
working on a formula. Old Pythagoras is looking over his shoulder.
He says, "You are only twelve years old, do you think you can prove
my theorem in a new way?" Einstein hands Pythagoras the paper and
Pythagoras reads it a while, and then dances around joyfully
saying,

"He did it! He did it! It has been a thousand
years since anyone did anything original to prove my theorem. But
who will ever do anything with that?"

The commentator returns and says, "In 1901
Einstein submitted his doctoral dissertation, an early paper on his
theory of relativity. Here, we see what happened."

A young Einstein, recognizable by his not-yet
wild grey hair, walks, in a dejected slumping mode, into a room
where there is a professor, identifiable by his academic
robe.

"Why so glum?" asks the professor.

"Professor Minkowski, my doctoral dissertation
on the theory of relativity was rejected because it was too far
out. Those old fossils want me to write a paper on old stuff that
they will be comfortable with."

Minkowski says, "I read your paper and thought
it was quite good. I think you should make
time
an imaginary number so your theory will fit
with other new stuff going on physics."

Then, we see Geroiamo walk in saying, "Good
suggestion, imaginary numbers can be used to solve all kinds of
problems."

Einstein replies, "In all due respect, I don't
like imaginary numbers. I don't know how to visualize them, and
particularly imaginary
time
,
and that is how I think."

Minkowski adds, "That's one of the differences
between working in math and physics. Mathematics doesn't need to
relate to anything you can see. Physics, especially among the old
guys on your dissertation committee, has to relate to something you
can measure. Your relativity theory doesn't have any experiments to
go with it. Why don't you dust off that old paper you did about the
size of atoms."

Einstein replies, "That paper has a great
amount of measurement data. That should satisfy the old
goats."

The commentator returns:

"In 1905, Einstein was awarded his doctorate.
Around that time, he was working on a paper about mass and
energy:"

We see Einstein in a baggy sweatshirt and
tennis shoes with his wild uncombed hair. He is scribbling on
paper, scratching his head, pulling his hair, getting up and
walking around in a circle.

Pythagoras in is toga walks in and asks, "What
is the problem?"

Einstein says, "I am working on a paper about
inertia, mass, and energy, and can't get the right
formula."

"Why don't you use my old one that you proved
as a kid?" advised Pythagoras. He goes to the blackboard and
writes:

(d)
²
=
(x)
²
+
(y)
²

Einstein says, "Yes, but I think I will use the
one with the four dimensions plus a time dimension.

He goes to the blackboard and writes one more
term:

(d)
²
=
(x)
²
+
(y)
²
+
(z)
²
+
(vt)
²

Einstein scratches his head and says, "If I
replace dimensions x, y, z with symbols that mean momentum, mumble,
mumble, mumble."

Einstein fills the blackboard with symbols,
erases, writes again and finally steps back.

(E/c)
²
=
(Mc)
²
+
(p
₁
)
²
+
(p
₂
)
²
+
(p
₃
)
²