To the consternation of many legal experts, one of the issues now at stake in the double murder trial is the contents of the former American footballer's dreams. Did he, as one of his former friends claims, have dreams about killing his ex-wife, Nicole?
If so, can these - as prosecutors allege - seriously be considered evidence of a "fatal obsession" which eventually led him to stab her to death? Or are they no different from other people's dreams - a muddle of fantasies and snippets from reality which would land any of us in jail if we acted on them?
The evidence emerged when Ron Shipp, a former Los Angeles policeman and erstwhile friend of Simpson, appeared in the witness box. Simpson, he claimed, had invited him into his bedroom in his Los Angeles mansion on the night after the murders of his ex-wife, and Ronald Goldman, 25, a waiter. The two were alone. A conversation ensued in which Mr Simpson chuckled and said "to be honest, Shipp, I have had dreams of killing her. "
In other parts of the world, you might expect this testimony to be greeted by derisive sniggers from the jury. But this is California - seeding ground for the world's silliest cults. So there is a chance Simpson's mostly black, female jury will take his dreams seriously. The prosecution thinks so: "Walt Disney put it best," Marcia Clark told Judge Lance Ito yesterday (in a comment which reveals the blurred line between fact and fiction in this case), "A dream is a wish your heart makes . . ."
This raises a crucial issue. In most circumstances, it is illegal to introduce into a US court any evidence about lie detectors. Mr Shipp - who admitted yesterday that he had a drinking problem - has said OJ mentioned his dreams while explaining why he was reluctant to take a polygraph - a detail withheld from the jury. Some lawyers believe the judge's decision to allow the dream-related evidence out of context amounts to a blunder as it would be grounds for a successful appeal by Simpson if convicted. Mr Shipp's evidence could mean this trial is a waste of time.