The idea that we have faith in everyday matters is not new. This secular faith is practiced by, well, everybody, since we rely on a sort of faith that our senses do not deceive us in perceiving the world around us. This sense of secular faith is no less apparent (and certainly no less important!) in the sciences. Indeed, we have some amount or other of faith in each step of the “process” for a given experiment, which we exercise quite unconsciously.
Faith in Theory
It’s been said before that a scientific theory is a sort of story which we tell ourselves to makes sense of some set of (presumably repeatable) data. Well and good. But what reason do we have to believe that our “story” describes reality—and especially, that it holds true anytime, anywhere? What reason do we have to believe that it really describes the natural world as it is?
It is worth noting here that a great many theories—at least in physics—begin with any number of assumptions. There is a joke that physics never works in real life because most objects aren’t spheres and very few of us actually live in a vacuum. We often, moreover, ignore any number of “small” interactions when deriving our formulas , which interactions may not actually be ignorable, and may play a large or a small part in any given interaction; these interactions may or may not be separable from the particular interaction or effect in which our theory takes some interest.
Lest we argue that these theories are validated by observation, it’s worth considering an observation of a different kind. In his Aquinas; A Beginner’s Guide, Professor Edward Feser notes that
“a serious problem with the idea that science is merely in the business of establishing regularities on the basis of observation is that the sort of regularities that the hard science tend to uncover are rarely observed, and in fact are in ordinary circumstances impossible to observe. Beginning students of physics quickly become acquainted with idealizations like the notion of a frictionless surface, and with the fact that laws like Newton’s law of gravitation strictly speaking describe the behavior of bodies only in the circumstance where no interfering forces are acting on them, a circumstance which never actually holds. Moreover, physicists do not in fact embrace a regularity as a law of nature only after many trials, after the fashion of popular presentations of inductive reasoning. Rather, they draw their conclusions from a few highly specialized experiments conducted under artificial conditions. None of this is consistent with the idea that science is concerned with cataloging observed regularities.”
I might include here a note about simulations—the other side of theory work—which are often used to help in the design of an experiment (on the one hand) and to “test” a theory (or, for that matter, to develop it). Simulations very often do a good job of predicting how an experiment will work out—that’s why we use them, of course—and allow us to test our theories in the “idealized” environments for which they are written.
On the other hand, the simulation  may or may not perform in the same way as reality. For one, we are left to assume that the algorithms used by the simulation actually are correct. Ok, there are ways of testing some of that assumption, but then we also are responsible for including any relevant interactions—some of which may be outside of the theory, and hence not included in the simulation, either. And of course, there is the simulation result; presumably, the simulation is being used to compute a number of parameters whose value we do not know; there is thus no way for us to be certain that the simulation results are correct save to actually conduct the experiment under the same conditions as in the simulation.
Faith in Experiment
This brings me to the experiment itself. Physics, at least, and the other sciences are supposed to follow a cycle which begins with observation, then builds a theory, which it then tests and modified and re-tests and modifies some more. The observation, and especially the “testing” is done via experiment. Of course, if this process is to begin at all—let alone be successfully continued—it must begin with some amount of faith in the ability of an observer to make good observations. As the late Fr Jaki notes in his Miracles and Physics,
Immediate and direct observation of things and the certainty of that observation (or at least the certainty with which it can be corrected or improved) is the rock bottom basis of not only philosophy but also of science as well…if it is impossible to start a march with the second step, concern about the laws of nature should give second place to concern man’s ability to register things and events with certainty. And since without that ability nothing can be known about the laws of nature, the chief intellectual concern should be not so much the possible violations of the laws of nature as about the actual violation, if not plain rape, of man’s mind whose natural function is to know reality with immediate certitude.
That is to say, without faith that our plain observations are actually correct, the whole project of “scientific investigation,” the whole foundation for science, comes undone. The French physicist Pierre Duhem explains this another way in his essay The Primacy of Common Sense:
When a sincere witness, sufficiently sober so as not to take the whims of his imagination for observation and familiar enough with the language to express his thought clearly, affirms to have registered a fact, the fact is certain. If I declare to you that on such a day, at such an hour, I saw a white horse, you must believe, unless you have reason to consider me a liar or a victim of hallucination that on that day, at that hour, in that street, there was a white horse….But…what the physicist states as the result of an experiment is not a recital of facts registered by him. It is rather an interpretation of these facts, it is their transposition into the abstract, symbolic world of theories which he considers to be well established.
Therefore, after the physicist’s testimony has been submitted to the rules which establish the degree of confidence due to the account of a witness, you have accomplished only a part, and the easier part, of the critique of his experiment.
In other words, in the sciences—and especially in the increasingly collaborative projects of modern science—we must often trust not only in our own observations, but in those of others; and moreover, since often we have only the interpretations of those observations to go by , we have to trust that these interpretations are correct; granted, we can offer some critique, or we can compare them with the theory—but if the whole point of the experiment is to test the current theory, then it would be begging the question in favor of said theory to reject our experimental findings solely because they conflicted with the theory.
Even when the data is our own, the task of interpretation is never an easy one. Theories often predict smooth curves (for a graph, that is) where data is jagged and discontinuous; there are frequent statistical fluctuations, and the conditions of two data runs (or, for that matter, two shots from a laser) are seldom if ever really identical. There are indeed some rather famous experiments whose outcome has come down to a judgment call on the part of the investigators.
All of which becomes a great illustration of G.K.Chesterton’s observation in Orthodoxy that
It is idle to talks always of the alternative of reason and faith. Reason is itself a matter of faith. It is an act of faith to assert that our thoughts have any relation to reality at all. If you are merely a sceptic, you must sooner or later ask yourself the question, “Why should anything go right; even observation and deduction? Why should not good logic be as misleading as bad logic? They are both movements in the brain of a bewildered ape?” The young sceptic says, “I have a right to think for myself.” But the old sceptic, the complete sceptic, says, “I have no right to think for myself. I have no right to think at all.”
Reason itself is, after all, based at least in part on our ability to take what we know  and apply it to a given situation or question. Thus, if we cannot have so much faith as to even believe in our senses, our interpretations of the information which we collect through those senses, or for that matter to believe the plain testimony of other eyewitnesses who collect the information firsthand, then we leave reason (to say nothing of science!) without a meaningful leg to stand upon. Granted, we can spend time (and money) in the lab verifying every finding which we make–we usually do this to some extent–and in turn every finding which our colleagues and competitors make (again, we sometimes do this), but more often than not, we place some amount of faith in our results: enough, that is, that we cannot claim to be skeptics. Indeed, a great many discoveries rely on our trusting that our senses do not deceive us at every turn, whatever our predictions say ought to have happened: scientific advances ultimately rely on so many “small” acts of scientific faith.
 So for example, any field which uses perturbation theory relies on the assumption that we can make a Taylor series expansion of one variable, which expansion requires that this variable be small if the expansion is to be useful. Among others, the field of nonlinear optics is especially reliant on this particular approach.
 Understand, of course, the simulation can be “checked” by calculating something easy first, that is it can be run against some standard theory or experiment the results of which are well-known. On the other hand, these results are “well-known” only because some previous experiment was conducted to get those results. Not to mention that it is a bit of a leap of faith to assume that when a simulation gets the physics right for a simple scenario, it will therefore get the physics right every time in a more difficult and complex scenario.
 Consider that there is a joke, which is not too far from the truth, that anything in a presentation or paper labelled “typical data” really means “the best set of data I have from all the thousands of trials I ran, the only shot which shows exactly what I wanted all this data to show.”
 Knowledge does, after all, come to us through the senses—and I don’t think we have to take St Thomas’ word for it.