story identification - The tooth-tapping time traveler

I seem to recall a short story of a time traveler who would tap out a code on his tooth to move through time and space. It starts with him discovering that someone had put him in a closed loop intended to trap him. He escapes and starts a chase thereby showing his potential captors that he is more powerful (and from a more distant future) than they expected.

While continuing the pursuit of the person ultimately responsible, and in a twist, he discovers that he is dealing with someone even more powerful only to learn that it is a robot from the far far distant future .. a period long after the end of humans.

I read this back in '98 or '99 in a paperback short story collection dealing entirely with time travel. The cover of the book had a robot and a robotic dog if memory serves (and, admittedly, it does as user14111 found the story with links :-) ).

Ring any bells?

Answer

I seem to recall a short story

"The Timesweepers", a novelette by Keith Laumer. It was expanded into the novel Dinosaur Beach.

of a time traveler who would tap out a code on his tooth to move through time and space.

It was a twenty-minute walk to the nearest spot the gauges said was within the acceptable point-point range for a locus transfer. I tapped out the code with my tongue against the trick molars set in my lower jaw, felt the silent impact of temporal implosion, and was squinting against the dazzling sunlight glaring down on Dinosaur Beach.

It starts with him discovering that someone had put him in a closed loop intended to trap him.

"Listen carefully," my voice said to me. "I've come full circle. Dead end. Closed loop. No way out—except one—maybe. I don't like it much, but I don't see any alternative. Last time around, we had the same talk--but I was on the floor then, and another version of us was here ahead of me with the same proposal. I didn't like it. I thought there had to be another way. I went on—and wound up back here. Only this time I'm the welcoming committee."

He escapes and starts a chase thereby showing his potential captors that he is more powerful (and from a more distant future) than they expected.

"Since no basis for such actions within the framework of your known psychindex exists, it is clear that your motives must be sought outside the context of the Nexx policy. Clearly any assumption involving your subversion by prior temporal powers is insupportable. Ergo—you represent a force not yet in subjective existence."

While continuing the pursuit of the person ultimately responsible, and in a twist, he discovers that he is dealing with someone even more powerful only to learn that it is a robot from the far far distant future . . . a period long after the end of humans.

"All life vanished in the one hundred and ten thousandth four hundred and ninety-third year of the Final Era," I said.

"And you . . . you machines," he forced the words out. "How long?"

"I was dispatched from a locus four hundred million years after the Final Era. My existence spans a period you would find meaningless."