If we understand natural science as an attempt to formulate predictive laws through the study of natural, observable processes, then we are left with events that are not subject to predictive laws, these are random events.
If we want to be metaphysical, we can claim events are not truly random, we simply lack sufficient knowledge to be able to predict them. In fact, there are two specifically metaphysical approaches to viewing random events, one naturalistic, one super-naturalistic. The naturalistic viewpoint is to claim that there are no random events in nature: God does not play dice with the universe, per Einstein. The supernaturalist viewpoint is to claim that there are random events in nature, that is to say, things happen that are not predictable based on observable regularities in nature. At the same time, it is not to deny that these events do not have a cause, but that the cause is not intelligible based on merely a study of observable and natural regularities. The patterns might be revealed to the mind, but not derived from the empirical world (in fact, the patterns might formulate the basis for conceptualizing an empirical world).
Physics, to some extent, is the enemy of God, because the physicist seeks to explain everything that happens in the world with reference to mathematical laws derived from the observation of natural regularities. I believe Stephen Hawking is not so much opposed to the existence of God, as he is to the existence of natural phenomenon that scientists can't explain. If a power above the observable world acts on the observable world for its own purposes, then natural phenomenon must be, to some extent, random. Even more sinister, it might be that the empirical regularities turn out to be more a reflection of will than of "nature". For example, if you imagine a legal system with a penal code that is enacted by a justice system with regularity, you can speak of "law" in a positive sense. But this law exists only because there is an existing system of power, or order, which makes it so. One can positively describe and predict the operations of the system of law, procedural and otherwise, but there is nothing "natural" about the system. Likewise, random events suggest--or at least leave open the possibility--that there are no true natural laws, there are invisible powers acting on a material world. This would blow up the grand vision of "Science", without of course negating its utility.
The physicists are correct in a sense: there is an actual world, and if the features of the actual world in part include random phenomena, then the world is not defined by the laws of physics. If a power can be defined by its material effects, then it is a material power. (Heat, gravity, etc.) If there are material effects that cannot be explained by material powers (e.g. random events), then they can only be explained by supernatural powers. If the world is intelligible, then events have true causes, e.g. they are caused by a power. The cause of the world would therefore have to be supernatural, if the world is to be intelligible. If the world is unintelligible, then one can question how it could have an order at all, if only a random one. How could the regularities of nature be anything other than random coincidences? After all, a random sequence can contain *random* *illusory* order within the sequence, but an ordered sequence cannot contain any randomness. We are left with either an ordered universe, ordered by a supernatural power beyond our scientific comprehension, or a random universe with no true order upon which we project illusory patterns. No wonder the physicists are seeking possible worlds and multiverses to try and eliminate randomness. Otherwise, you are left with an all-powerful God establishing natural laws or an omnipresent Chaos creating the false appearance of patterns. But the problem is, even if there are infinite multiverses all running along the same laws of physics, our own experience of an actual world is random. Why am I running along in this universe and not another? What gives me my identity (or non-identity) across possible worlds? Physics cannot say, because it would define the ultimate container (consisting of an infinite batch of hermetically sealed containers), and would partially define what happens within a hermetically sealed container, but it would not address the motion/kinetics of things/individuals between the containers. If there are millions of identical organisms to myself in an ginormous number of universes, why do I only experience what I experience? What locates me here and not there? Why am I me, and not the famous rock star that a biologically similar organism with a biologically similar origin is in another universe? I would submit that these attempts to rid the world of randomness fail ultimately, because they simply shift the conceptual problem, rather than solve it. By trying to make randomness not actual, they succeed in making actuality random. (And a physical explanation that does explain an actual physical universe is worth what?)
I would submit there are two possible views of the universe: that it is in fact a universe, that is, a unified plurality that manifests a unified order, or that it is merely a random exercise in chaos. In the first, we can view physics as a limited, imperfect attempt to understand the order of things. In the second, physics is an illusion, the finding of an illusory order in a random scheme of events. These views are ultimately interpretations. The apparent universe is the only one we can observe, and its apparent patterns and regularities are the only one's that we are going to get. I think that the interpretation that views the Universe as providentially ordered is the superior interpretation, because it makes sense of the existing data. The second interpretation is inferior, because it basically discounts the data. Moreover, the deist viewpoint, denying miracles and the like, emerged as a result of Newtonian mechanics, which appeared determinant. (Newton's laws would not determine the angle of deflection and velocity resulting from a direct collision of two objects of equal mass and velocity.) If you give random phenomenon a fundamental role, such as in quantum mechanics, you have all the more reason to embrace the old-fashioned Providential understanding of the universe.
If we embrace the first view, then we can look at random events while not being explainable in terms of natural laws, we can view them as manifestations of a higher order, which shows patterns, intelligibility, without being capable of scientific explanation. Thus, the higher order can be revealed in history despite the fact that it defies scientific explanation.
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