But when I went back, I realized I had trivialized my subject again. It wasn't just that the tone of voice was flippant; it was the glibness with which I tossed off references to tragedy. My Lai, for example—what did I know about the My Lai massacre except that a lot of Vietnamese civilians were killed? I could research and find more details, but that wasn't the point. I had used the name My Lai for its immediate guts'n'gore familiarity, not out of genuine feeling for the victims. The same for all the other ghosts—I had used them to give the story color, nothing more. They were only empty names. They were just body count.

I stared at the computer screen for a long time, wondering what to write…wondering if there was anything I could write that wasn't just exploiting someone else's pain.

Nothing came to mind.

A mathematical singularity is a place where a function, a formula, breaks down. Often the breakdown happens because the function "goes to infinity" at that point; for example, the formula for the function may try to divide by zero.

In the heart of a Kerr-Newman black hole there is a singularity in a function called R, the Riemannian scalar curvature, a measurement of gravity. R goes to infinity. It cannot be measured.

For a long time, physicists wondered if the singularity was genuine. Maybe it was simply a result of their choice of coordinates: the way they wrote out the formula for R With the right choice of coordinates, one can extend the black hole model past the singularity into the white hole beyond. Perhaps with another choice of coordinates the singularity in the middle would go away. Perhaps it was only the ruler that broke down, not the universe that the ruler measured.

In the late 1960s, mathematicians proved that the singularity existed in all coordinates. All possible rulers broke at the same point. At the heart of the black hole's darkness, physicists could only throw away their rulers and stand back in blank contemplation.

Days and weeks passed. I kept thinking. Nothing more, just thinking. I didn't see the dead students in my dreams. To tell the truth, if I wanted to remember their faces I had to go back and look at their photos in the book.

Kent State didn't haunt me. It niggled at me.

The library books came due. I wrote the names of the books in my files and took them back. I also recorded the names:

Allison Krause

Jeff Miller

Sandy Lee Scheuer

Bill Schroeder

Those names hadn't appeared anywhere in my three story attempts. I had to write them down separately so I would remember them. Otherwise I'd lose the names and be left with three uncompleted story-scribbles that all missed the point.

Now and then I would open my "ideas" notebook and see my original jottings about Kent State. Time travel. Ghosts. But I couldn't travel backward in time. I couldn't summon ghosts or lay them to rest. I could stuff my stories into the empty spaces surrounding the tragedy, but the stories themselves walled off the reality, put it out of reach.

The situation reminded me of a white hole. A white hole floods its universe with light; but you can never touch it.

And so I began thinking of white holes, black holes, and a mathematics thesis whose math had leaked away, leaving behind only metaphors. The result wasn't a story about Kent State. But at least it was my story to tell.

Imagine an object falling into a black hole: something small like the body of a young man or woman, or perhaps something large like the campus of a university.

Imagine an outside observer, a distant spectator far removed from the immediate pull of the black hole. He shines a light toward the falling object—the object casts no light of its own, so if the observer wants to see it he must provide his own illumination. He waits for the light to strike the object, then return to his eye.

There are several possibilities for what happens next.

The light may strike the object as it falls through the ergosphere, a region where places become moments and moments become places. That close to the black hole itself, the returning light particles may take years to climb back out of the gravity well and reach the observer. But someday the light will return.

Or the light may not reach the falling object until the object has crossed the event horizon. If the object is inside the hole, the light may strike the object and bounce, but it cannot reach the observer outside. The light will only bounce deeper into the blackness. The observer will never see it.

Or perhaps, if the cosmos deigns to conform itself to mathematics, there is a third alternative. The falling object plunges through the heart of the black hole and out a white hole on the other side. By the time the observer's light enters the black hole, the object is gone. The light finds nothing but blackness. There is no contact. To the observer, the object has fallen into an impenetrable dark; but in another universe, perhaps the object tranquilly sails on.

The outside observer waits for his light to return. He wonders if the object has fallen so far he will never truly see it. There is no way to tell until the light actually comes back. If it ever does.

Other observers have given up and gone home.

The outside observer waits.

Withered Gold, the Night, the Day

The vampire Rogasz had taken to carrying a knife when he walked the streets on his hunt. It was not for protection; it was to slash the faces of his victims as they lay drained of blood, to cut them for being so stupid. "Stupid, stupid, stupid!" he screamed at them…and sometimes witnesses heard his cries, drunks hidden under piles of trash or street kids waiting to turn tricks in darkened doorways. The witnesses sold their accounts to impatient Eyewitness News teams and so the story spread throughout the city, "STUPID, STUPID, STUPID!" ran the headlines, and in the coffee shops, reporters from all the media brainstormed what they would call this latest novelty. The Stupid Slasher? No. Not menacing enough. And menace was what sold newspapers.

Meanwhile, Rogasz stalked through the city like a jaded library goer who can't find any books he wants to read. Some rainy nights he would just stake out a territory, attacking anyone who violated the space: striking them down, cutting them with his knife, throwing them off his land without even drinking their blood. He couldn't bring himself to feed on such meager feasts; they would taste the same as all the others, back through the centuries. Besides, he hardly needed to drink these days—the city air was so full of blood and desperation, it seeped into his pores by osmosis. In a more lucid moment, he wrote in his notebook,

I have the feeling I do not drink blood, but rather karma—the personal richness of a human soul. This explains the poignant flavor of a virgin as opposed to sluts…and yet, in this bleak age, the difference is nearly imperceptible. The best wine is but a hairs-breadth from vinegar. The world has lost its saints.

There came a steamy summer night when the city smelled of garbage—garbage rotting in Dumpsters as hot as ovens, garbage thrown into the streets by children whose mothers said, "Get this stink out of the house, I don't care what you do with it." Long ago, no one heaved decaying food onto someone else's sidewalk, nor did people sit in front of overloud TVs, too desensitized to realize they were bored. Rogasz prowled past fortress apartment buildings and screamed at the flickering television light reflected in every window. "Poisons, poisons, poisons!"

(Lately, he had taken to saying things three times. He knew he did it; he couldn't stop.)

On he walked, words pouring from his mouth and tears streaming from his eyes, until he reached a corner bus shelter, its glass thick with obscenities written in faded black marker. A man leaned against the doorway of the shelter; and as Rogasz drew nearer, he recognized the man as the Adversary—the Fallen One, the Lost One, the Morning Star Eclipsed.