Science is the search for and study of patterns and laws in the natural and physical worlds. Could that search become exhausted, like an over-worked coal vein, leaving nothing more to be found? Could science end? After briefly touching on several fairly obvious possible end-games for science, we explore how the vast Unknown could undermine - rather than underlie - the scientific enterprize. The possibility that science could end is linked to the reason that science is possible at all. The path we must climb in this essay is steep, but the (in)sight is worth it.
Science is the process of discovering unknowns, one of which is the extent of Nature's secrets. It is possible that the inventory of Nature's unknowns is finite or conceivably even nearly empty. However, a look at open problems in science, from astronomy to zoology, suggests that Nature's storehouse of surprises is still chock full. So, from this perspective, the answer to the question 'Could science end?' is conceivably 'Yes', but most probably 'No'.
Another possible 'Yes' answer is that science will end by reaching the limit of human cognitive capability. Nature's storehouse of surprises may never empty out, but the rate of our discoveries may gradually fall, reaching zero when scientists have figured out everything that humans are able to understand. Possible, but judging from the last 400 years, it seems that we've only begun to tap our mind's expansive capability.
Or perhaps science - a product of human civilization - will end due to historical or social forces. The simplest such scenario is that we blow ourselves to smithereens. Smithereens can't do science. Another more complicated scenario is Oswald Spengler's theory of cyclical history, whereby an advanced society - such as Western civilization - decays and disappears, science disappearing with it. So again a tentative 'Yes'. But this might only be an interruption of science if later civilizations resume the search.
We now explore the main mechanism by which science could become impossible. This will lead to deeper understanding of the delicate relation between knowledge and the Unknown and to why science is possible at all.
One axiom of science is that there exist stable and discoverable laws of nature. As the philosopher A.N. Whitehead wrote in 1925: "Apart from recurrence, knowledge would be impossible; for nothing could be referred to our past experience. Also, apart from some regularity of recurrence, measurement would be impossible." (Science and the Modern World, p.36). The stability of phenomena is what allows a scientist to repeat, study and build upon the work of other scientists. Without regular recurrence there would be no such thing as a discoverable law of nature.
However, as David Hume explained long ago in An Enquiry Concerning Human Understanding, one can never empirically prove that regular recurrence will hold in the future. By the time one tests the regularity of the future, that future has become the past. The future can never be tested, just as one can never step on the rolled up part of an endless rug unfurling always in front of you.
Suppose the axiom of Natural Law turns out to be wrong, or suppose Nature comes unstuck and its laws start "sliding around", changing. Science would end. If regularity, patterns, and laws no longer exist, then scientific pursuit of them becomes fruitless.
Or maybe not. Couldn't scientists search for the laws by which Nature "slides around"? Quantum mechanics seems to do just that. For instance, when a polarized photon impinges on a polarizing crystal, the photon will either be entirely absorbed or entirely transmitted, as Dirac explained. The photon's fate is not determined by any law of Nature (if you believe quantum mechanics). Nature is indeterminate in this situation. Nonetheless, quantum theory very accurately predicts the probability that the photon will be transmitted, and the probability that it will be absorbed. In other words, quantum mechanics establishes a deterministic law describing Nature's indeterminism.
Suppose Nature's indeterminism itself becomes lawless. Is that conceivable? Could Nature become so disorderly, so confused and uncertain, so "out of joint: O, cursed spite", that no law can "set it right"? The answer is conceivably 'Yes', and if this happens then scientists are all out of a job. To understand how this is conceivable, one must appreciate the Unknown at its most rambunctious.
Let's take stock. We can identify attributes of Nature that are necessary for science to be possible. The axiom of Natural Law is one necessary attribute. The successful history of science suggests that the axiom of Natural Law has held firmly in the past. But that does not determine what Nature will be in the future.
In order to understand how Natural Law could come unstuck, we need to understand how Natural Law works (today). When a projectile, say a baseball, is thrown from here to there, its progress at each point along its trajectory is described, scientifically, in terms of its current position, direction of motion, and attributes such as its shape, mass and surrounding medium. The Laws of Nature enable the calculation of the ball's progress by solving a mathematical equation whose starting point is the current state of the ball.
We can roughly describe most Laws of Nature as formulations of problems - e.g. mathematical equations - whose input is the current and past states of the system in question, and whose solution predicts an outcome: the next state of the system. What is law-like about this is that these problems - whose solution describes a progression, like the flight of a baseball - are constant over time. The scientist calculates the baseball's trajectory by solving the same problem over and over again (or all at once with a differential equation). Sometimes the problem is hard to solve, so scientists are good mathematicians, or they have big computers, (or both). But solvable they are.
Let's remember that Nature is not a scientist, and Nature does not solve a problem when things happen (like baseballs speeding to home plate). Nature just does it. The scientist's Law is a description of Nature, not Nature itself.
There are other Laws of Nature for which we must modify the previous description. In these cases, the Law of Nature is, as before, the formulation of a problem. Now, however, the solution of the problem not only predicts the next state of the system, but it also re-formulates the problem that must be solved at the next step. There is sort of a feedback: the next state of the system alters the rule by which subsequent progress is made. For instance, when an object falls towards earth from outer space, the law of nature that determines the motion of the object depends on the gravitational attraction. The gravitational attraction, in turn, increases as the object gets closer. Thus the problem to be solved changes as the object moves. Problems like these tend to be more difficult to solve, but that's the scientist's problem (or pleasure).
Now we can appreciate how Nature might become lawlessly unstuck. Let's consider the second type of Natural Law, where the problem - the Law itself - gets modified by the evolving event. Let's furthermore suppose that the problem is not simply difficult to solve, but that no solution can be obtained in a finite amount of time (mathematicians have lots of examples of problems like this). As before, Nature itself does not solve a problem; Nature just does it. But the scientist is now in the position that no prediction can be made, no trajectory can be calculated, no model or description of the phenomenon can be obtained. No explicit problem statement embodying a Natural Law exists. This is because the problem to be solved evolves continuously from previous solutions, and none of the sequence of problems can be solved. The scientist's profession will become frustrating, futile and fruitless.
Nature becomes lawlessly unstuck, and science ends, if all Laws of Nature become of the modified second type. The world itself will continue because Nature solves no problems, it just does its thing. But the way it does this is now so raw and unruly that no study of nature can get to first base.
Sound like science fiction (or nightmare)? Maybe. But as far as we know, the only thing between us and this new state of affairs is the axiom of Natural Law. Scientists assume that Laws exist and are stable because past experience, together with our psychological makeup (which itself is evolutionary past experience), very strongly suggests that regular recurrence can be relied upon. But if you think that the scientists can empirically prove that the future will continue to be lawful, like the past, recall that all experience is past experience. Recall the unfurling-rug metaphor (by the time we test the future it becomes the past), and make an appointment to see Mr Hume.
Is science likely to become fruitless or boring? No. Science thrives on an Unknown that is full of surprises. Science - the search for Natural Laws - thrives even though the existence of Natural Law can never be proven. Science thrives precisely because we can never know for sure that science will not someday end.