An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend in one single formula the motions of the largest bodies as well as of the lightest atoms in the world, provided that its intellect were sufficiently powerful to subject all data to analysis; to it nothing would be uncertain, the future as well as the past would be present to its eyes.
However, as physicist John Barrow has noted, British philosopher Roger Boscovich had essentially the same idea in 1758 [Barrow2007, pg. 63].
Now, if the law of forces were known, and the position, velocity and direction of all the points at any given instant, it would be possible for a mind of this type to forsee all the necessary subsequent motions and states, and to predict all the phenomena that necessarily followed from them.
These notions prevailed until the twentieth century, when two developments spelled their doom. The first was the discovery and development of quantum mechanics. One of the principles of this theory is that any physical system is described by an abstract wave function, and the probability that it will be in a certain position or exhibit a certain behavior is given by the squared amplitude of the wave function. In other words, nature, at its fundamental level, is probabilistic in a certain precise sense. Another well-known way in which this probabilistic nature is exhibited is Heisenberg's "uncertainty principle." This principle states that the uncertainty (in a certain precise sense) in the position of an object times the uncertainty (in a certain precise sense) in the momentum of an object (momentum = mass times velocity) must always exceed a certain minimal value. For example, if the position of an electron is given to high precision, then its momentum cannot be known to high precision, and vice versa.
Such notions were very hard to swallow, and numerous prominent physicists were reluctant to embrace the full scope of quantum mechanics for many years. One who could not accept the theory was none other than Albert Einstein, who famously quipped, "God does not play dice with the universe" [Einstein1971]. Sadly for Einstein and others, the principles of quantum mechanics have been very convincingly confirmed in numerous exacting experiments.
The other development that spelled the doom of the clockwork universe was the rise of chaos theory -- the realization that the governing mathematical equations for many, if not most, physical systems exhibit chaotic behavior -- if very tiny changes to the current state of the system, then after a moderate amount of time the system exhibits completely different behavior. This is often called the "butterfly" principle, namely that if a butterfly flaps its wings, then this tiny change to the atmosphere is likely to lead to completely different weather behavior a few weeks down the road -- i.e., the earth's weather is one of the systems that exhibits chaotic behavior.
This point was made quite vividly by British physicist-theologian John Polkinghorne in 1990. He suggested that we visualize a billiard-ball model of air molecules buzzing around in a container. Suppose, for ease of analysis, that each molecule is perfectly spherical. It is easy to show that the subsequent motion of two balls after collision depends very sensitively on exactly what angle they collide. Polkinghorne then says that, according to his calculations (subsequently affirmed by others), if one neglects to take into account the gravitational attraction of a single electron on the other side of the observable universe, then after just 10^(-10) seconds (i.e., a tenth of a nanosecond), which is time enough for roughly 50 collisions on average per molecule, the calculated positions of particles would be completely different than if one did correctly account for that electron [Polkinghorne1990].
In short, the very precise initial conditions that the clockwork universe requires are prohibited by quantum mechanics, and thus, because of chaos theory, the future of any particular physical system, or even the universe as a whole, is fundamentally unpredictable. As noted physicist Leonard Susskind explains, "It is as though Einstein's God had made sure that no one could ever know enough to predict the future." [Susskind2008, pg. 93].
Physicist-astronomer John Barrow describes the consequences in these terms [Barrow2007, pg. 66]:
The ubiquity of chaotic phenomena raises a further problem for our dreams of omniscience through the medium of a Theory of Everything. Even if we can overcome the problem of initial conditions to determine the most natural or uniquely consistent starting state, we may have to face the reality that there is inevitable uncertainty surrounding the prescription of the initial state which makes the prediction of the exact future state of the Universe impossible. Only statistical statements will be possible.
These facts have not been lost on observers in the area of science and religion. John Polkinghorne, for instance, has written [Polkinghorne1998, pg. 75]:
The dead hand of the Laplacean calculator, totally in control of the sterile history of his mechanical universe, has been relaxed. In its place is a more open picture, capable of sustaining motivated conjectures that can accommodate human agency and divine action within the same overall account. Modern science, properly understood, in no way condemns God, at best, to the role of a Deistic Absentee Landlord, but it allows us to conceive of the Creator's continuing providential activity and costly loving care for creation.
In summary, it is certainly worth taking note that modern science refutes the long-held deterministic worldview that we humans (as well as the rest of creation) are mere robots acting out a predetermined script. However, it is not clear whether this is reason to celebrate. Is the fact that the future is fundamentally "random" that comforting? As with all aspects of the science-religion discussion, one should read with interest but keep an open mind, not locked into any particular worldview that may have to be changed as new information comes forth.