The Noblest Experiment in the Galaxy (1970) SF

Zeno Zenobius, head computer programmer for Intra-Galactic Investigations, Inc., was having a peaceful, uneventful life. Then he awoke to find himself a citizen of Wooten Dorset in England - a most unusual little town. Along with Victorian elegance, were hovercrafts, electric lights, and Zeno's own computer.

And then things got stranger.

There were two of him: Zeno I and Zeno II. And Zeno I's job was to find out what Zeno II was doing in Wooten Dorset.