"I've read something of your work in models and simulations," I began.

"I call it Constructive Integrative Analysis," Callaghan interrupted, somewhat to my surprise at his affront to good manners.

"Ah, yes. It seems a novel approach to prediction," I went on, trying to inject a degree of sternness into my voice, "Although I'm not sure I appreciate the finer points."

Callaghan's eyes narrowed slightly, fixing me with a faintly disapproving look. He leaned forward in his chair.

"Well I'm sure I could tell you much about my methods," he said, "But you have seen my system of machines at work below. What can you tell me of their operation?"

I felt I was the one under examination here, as if my intellectual merits were being questioned. Suddenly I was back as a recalcitrant student under the jaundiced eye of a tutor at my Oxford college.

"I am impressed by the collection of Computational Engines you have amassed. You must be a man of some wealth" - Callaghan nodded politely in acknowledgement - "but it seems to me that all your machines are slightly different, even if they all seem to be running the same programme. I imagine you have been progressively improving your design, but why keep so many older ones?"

"The designs are neither old nor new," Callaghan said gravely, "They are merely variations on a theme. Individually, the Integrators consume data sets about a subject: histories, mainly, together with specific questions about future possibilities. In order to explore different parts of the Spaces of Probability, each machine gets the same data but, with each engine being different, they each might predict a different outcome. By analysing the outcome of all of the integrators taken together, I can with high reliability predict the future."

I was unconvinced, and said so.

"Are you suggesting that you can predict the results of games of chance?" I snorted.

"Of course not," Callaghan replied, looking displeased behind his polite smile, "If all such games were genuinely random, no machine could predict the outcome: the fall of a coin or the roll of a dice is genuinely indeterminate. But few games are pure chance, and fewer sports, and still fewer activities in the worlds of business and politics."

I sat back in the chair, intrigued despite myself by the assertions he was making.

"In the real world, previous success and surrounding circumstances and coupled changes all conspire to form the facets of the future," my host went on, waving his hand airily, "Of course, many are dimly aware that the past is a predictor of the future. Like the professional bookmaker who studies the racing form and offers odds for the field."

"So you can predict the results of horse races?" I demanded, "And make money by gambling?"

"Well that is certainly possible," he agreed, "But only up to a point. If I were to win too much or too frequently, then the bookmakers would refuse to accept my wagers."

"You know that for sure?"

"Of course!" he smiled briefly, wryly, "Cassandra has predicted it."

Part 1 Part 3