Part 22: The Square Root
of Minus One
Dean was annoyed with the way Zak was acting around his mother. Zak
would spend most of the time staring at her, except if she addressed
him he would look down at his plate as he responded. So when Zak
threw him an appealing look Dean instead joined in on Fourier's line
Not that Dean wasn't often himself annoyed at Fourier. But his
mother was only human, after all, and if Fourier sometimes stayed
overnight, well, he preferred it was someone urbane and educated and
normally pleasant like Fourier, than, oh, say that young salopard at
the butcher shop who was always making eyes at her.
"The most famous equation in mathematics? Um, I would say , although
there are a few other candidates also," Dean said.
To Dean's satisfaction, Zak was now looking at him furiously.
"Precisely," Fourier said. "So, let's take logs of both sides. We
get that the log—we're referring to the natural log, of course—the
log of minus one is pi = 3.141592 etc. multiplied by i, the square
root of minus one. Remarkable, isn't it? You take the log of minus
one, and you get its square root multiplied by pi. But in any case,
that should settle the issue whether negative numbers have
"Is there a point to all this?" Zak asked.
Fourier looked at him in genuine surprise. "Why, yes. Aside from the
sheer beauty of mathematics, it illustrates that there was something
there all along, right in front of one's eyes so to speak, which
people chose not to see. First they pretended negative numbers
didn't exist. Then they pretended that imaginary numbers, ones
involving the square root of minus one, didn't exist, or were
absurd, or were meaningless. Space debris, as it were. Now, that is
exactly how it is today when it comes to the spiritual world, the
aliens, the things that go bump in the night, the hyper-dimensional
entities that intersect our space-time, cases of coincidence,
telepathy, teleportation. We pretend they are not there, or if
there, they are meaningless or absurd, or even if they are real,
well, so what, they are useless. But any engineer knows how useful i—or
j, as electrical engineers call the square root of minus one—really
is. The so-called imaginary numbers, or complex numbers (those
numbers having both a real and an imaginary part), are some of the
most useful in all of mathematics."
Dean saw Zak's face light up at this. "So," Zak said, "to understand
the aliens I need to study imaginary numbers? Or complex
"Well, I'm sure it would help," Fourier said, "but the simple point
I am making is that spiritual or hyper-dimensional phenomena are
imaginary." He paused and looked intently at Zak. "But they are
imaginary in the same way imaginary numbers are imaginary. They may
be imaginary, but they are very real, in some sense of physical
reality. They are built into the fabric of reality, and only a fool
Zak looked triumphantly at Dean. "So, what area of complex
mathematics would you recommend I start with?" he asked Fourier.
Fourier pondered the question seriously, as he consumed the last of
his canard à l'orange. Finally, as though after great difficulty, he
"Riemann's zeta function."
"Riemann's zeta function?"
"Otherwise known as the P.T. Barnum function," Dean interjected.
"There's a prime born every minute."
Dean began laughing as his own
joke. He stopped when he saw that both Fourier and Zak were looking
at him hostilely.
Dean's mother came to the rescue.
"We're having creme brulée for
dessert. Should I have it served now?"
I drove north. I had no destination. I drove more or less with the
same inattention I had driven out into the desert from Los Angeles.
Eventually I ended up on 395, still going north.
Later I would look at a map, trying to retrace my path. It wouldn't
compute. I had driven out into the desert into nowhere, and had
emerged from nowhere back into the ordinary world.
I was a fugitive, I guessed. At least until I sorted out what I
wanted to do about that butcher knife ending up in the belly of a
man on Oral Jerry Swagger's front lawn. Maybe it wasn't mine, but I
doubted that, after all that had happened. It had to be the two
ghouls, the two men in black—Little Olive and Big Pasty was the way
I thought of them. They had set me up good. First in the park, where
I had left my notebook. Oral Jerry Swagger's name prominent. Their
attack had led me to buy the butcher knife. Then . . . Then it
appears I left it in the hotel room and it ended up stuck in an OJS
employee on Swagger's lawn in Pasadena. Next there would undoubtedly
show up a link back to the Pasadena Hilton. Then my notebook would
mysteriously surface. Then . . .
I drove. Was this the way it had happened to Jack Parsons? He was
ready for a trip, a move to Mexico, to the 17th-century castle the
Mexican government was providing him—and then he got blown up in the
garage apartment he used as a laboratory while he was packing his
car for the trip. I was sure it was someone connected to the U.S.
government, trying to bury Parsons' technology—to maintain the
But, who knows? Before this Jack, with his magical workings, had
opened a crack and something had flown in. Maybe Little Oliver and
Big Pasty flew in from that direction also. I glanced at the other
end of the seat. The Louisville slugger was still with me. There are
a lot of things you can do with a baseball bat. Even play baseball.
Mt. Whitney loomed to my left, and I reached the turnoff to drive to
the base of the mountain. I was tempted, but continued on. One year
three other fools and I had tried to climb Mt. Whitney in the winter
time, while it was covered with snow. The first night we camped at
8000 feet. One of the guys stetched out his legs and stuck his
ice-covered boots right by the fire, to melt the ice off them. After
a time, someone smelled something burning. He had burned half-way
through the rubber sole of one boot, without even feeling the heat.
The next day we had continued on up the mountain. I was well ahead
of the others when we decided to turn back, because the guy's foot
was freezing—the guy with half a sole. In attempting to catch up
with those below, I noticed a nicely sloped, snow-filled, but
shallow ravine, and hopped in and went sliding down at a nice pace
on my rear end. Then abruptly I had to brake my slide, because there
was a sudden sharp drop-off of about 15 feet, right in front of me.
The ravine had by this time deepened considerably, and I fumbled
around trying to figure out how to climb out of it. The snow kept
getting deeper at the edge of the ravine, and I was in snow up to my
chest when it suddenly all went whoosh, and I fell into a crevice. I
had managed to wedge myself at the top, using my upper arms, with my
feet dangling. But there was no hand or foothold, because everything
was covered with ice. And when I finally got out of the crevice, I
was still faced with the original problem.
I jumped down 15 feet into a point beside where I saw a rock peeking
out of the snow below, and survived without hurting myself.
Being a fugitive wasn't so bad, I decided, since by all rights I
should have been dead years ago. When the four of us got off Mt.
Whitney that day, we drove to Death Valley and had a wiener roast.
We were looking for highs and lows, all in the same trip.
I drove on.