Well, Roger Ebert thought the film was brilliant, which isn't that surprising, given that he gushed over Dark City, another SF film directed by Alex Proyas (I thought that one was kind of interesting, but also a bit silly).
Anyway, Ebert blogged about Knowing, and right off the bat he brings up one of the sillier moments of the film:
Is the universe deterministic, or random? Not the first question you'd expect to hear in a thriller, even a great one. But to hear this question posed soon after the opening sequence of "Knowing" gave me a particular thrill. Nicolas Cage plays Koestler, a professor of astrophysics at MIT, and as he toys with a model of the solar system, he asks that question of his students. Deterministic means that if you have a complete understanding of the laws of physics, you can predict with certainty everything that will happen after (for example) the universe is created in the Big Bang. Random means you can't predict anything. "What do you think?" a student asks Koestler, who says, "I think...shit just happens."
No, no, no, no, no.
Both the film and apparently Ebert are making a huge mistake here, confusing what we can know (epistemology) with the way things really are (ontology).
The limits of our ability to find out something about the world is directly relevant to us, and obviously important, but does not necessarily reflect the way things really are. Take a simple example: a machine holds a pair of fair dice in a shaker. Every thirty seconds, the machine shakes the dice, rolls them onto a felt surface, records the results, and scoops them back up again.
Are the actions of this system random or deterministic? That is, if before a particular roll of the dice, we knew their exact position, all the physical properties of the shaker, the algorithm the machine used, air pressure in the room, etc., would we be able to predict the outcome of the roll (e.g. 4-3). Sure we would. But that information is extremely difficult to come by, even in a small, controlled situation. Our knowledge about the outcome is limited by variables that are difficult to measure, so we use probability to describe what we can know about the outcome (e.g. there's a 1:6 chance of rolling a particular number on each die, and we can figure out distributions of outcomes when we roll both dice, and for successive trials).
So, we can't predict the outcome of this system, at least not to the precision of saying exactly what the outcome will be. We can approximate the outcome by saying which events are likelier than others. Does our knowledge about the system reflect the way the system actually is? Are the dice actually random? Of course not. They and the machine are behaving according to physical laws.
To recap: determinism does not equal predictability, and randomness does not equal unpredictability. Determinism means that what happens could not have happened any other way, whether we are able to predict it or not. Randomness means that there are things in the universe that behave probabilistically rather than behaving lawfully, e.g., a rock might sometimes drift up rather than fall in the presence of earth's gravity. If there are elements of the universe that are truly random, then it is truly impossible for us or anyone else to predict the outcomes of those systems, even in principle. But the definition of each term rests on the way things are, not our ability to measure them.