Technologies in Minority Report "Minority Report" were handled by Jeff Boortz of Concrete Pictures, who said "the whole idea, from a script point of view, was that the advertisements would recognize you -- not only recognize you, but recognize your state of mind. It's the kind of stuff that's going on now with digital set-top boxes and the Internet." Nokia designed the phones used by the characters, and Lexus paid the producers $5 million for the rights to design the futuristic "Mag-Lev" cars. All told money raised through product placement accounted for $25 million of the film's $102 million production budget. Spielberg described his
Directed set Directed set In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set "A" together with a reflexive and transitive binary relation ≤ (that is, a preorder), with the additional property that every pair of elements has an upper bound. In other words, for any "a" and "b" in "A" there must exist "c" in "A" with "a" ≤ "c" and "b" ≤ "c". The notion defined above is sometimes called an upward directed set. A downward directed set is defined analogously, meaning when every pair of elements is bounded below. Some authors (and