One of the things I've been thinking about lately is my response to the question: how can I believe in both science and religion? I don't feel that the two are in as deep a conflict as some people obviously do, but I do see that there could be misunderstandings on both sides. Approaching the question as a scientist, I have come up with a few analogies for how scientists could view religious ideas.
Analogy one: limiting behavior.
Einstein's special relativity indicates that the classical form of the kinetic energy (for example) is incorrect. More precisely, it's the leading term in the series expansion for the correct (relativistic) kinetic energy. As long as velocities are small compared to the speed of light, the additional terms in the series are small, but as velocity gets large, the other terms are no longer negligible. In this example, the classical kinetic energy is a good approximation for the actual kinetic energy in the limit of low velocity. We don't notice the discrepancy under normal circumstances because the speed of light is very large compared to speeds we typically deal with, but we can conduct experiments with objects moving at relativistic speeds, and these experiments show that the relativistic world view is correct.
What if faith functions in our lives in a way similar to how velocity works in relativistic dynamics? Is it possible that the atheist world view is the approximation of our mortal experience in the limit of little faith? With reference to our own behavior and choices, this is certainly true; if you take an individual and remove faith from their decision making process, it will be (to them) as if God didn't exist. To be more objective, we need to ask what the difference is between a universe without God and a universe with God. Unfortunately, that's a hard question to attack. Those who believe in God are likely to say that a universe without Him is inconceivable, and those who don't are likely to say that a universe with Him would be intolerable. We don't have enough information to even really figure out what this question would entail. We don't have a provably rigorous theological system (analogous to mathematics) within which we can explore the ramifications of a change to the universe such as including or excluding divinity.
Let me set that one aside for a while and come back to it later. But, before I do, I just want to point out an additional wrinkle. In the scientific system, we have mathematics to explore the implications (and check the consistency) of theory. As noted, we don't have an analog in religion. In science, we also have standards for performing rigorous experiments: we have a theory of measurement, and feel confident that we can make measurements which are both repeatable and reproducible. We additionally have some sense of how to think about errors in our measurements, and some approaches we might take to mitigate them. In fact, most of the program of modern science centers on improving our ability to measure things. We lack this fundamental ability in religion.
Returning now to the current analogy, if the atheist world view is some sort of limiting case of a theist reality, we might have a hard time (a) understanding the difference between the two views and (b) detecting those differences we do manage to understand. Furthermore, we don't know if the amount of faith analogous to the speed of light in this example is large or small compared to the amount exhibited by an "average" religious person.
This is just a sketch. To fully round out this analogy, it would be necessary to work through some of the weirdness of relativity, and especially the fact that many of these things (paradoxes, and so on) are seemingly crazy if you take the classical view to be true. But I'm not sure how useful that would be as a project. All analogies break down at some point; their main utility lies in getting us to see things in a different way. I think the level of development I've reached with this first analogy meets that goal.
Analogy two: threshold effects (example: pair production).
When two particles collide (speaking semiclassically) there are a number of options. If the particles have enough energy, they can use some of that energy to create other particles. Since the lowest energy form of this involves producing an electron and a positron, this phenomenon is usually referred to as pair production. Before the 20th century, such a process would have been regarded as absurd. In fact, scientists talked about a law of conservation of mass, which seemed to be true. In fact, even in chemical reactions, it isn't true that mass is conserved, but the amount of mass converted to energy is small enough that the researchers at the time weren't able to measure it. This is another example of limiting cases, as described yesterday. It's only when we get to nuclear reactions (or processes like pair production) that the changes in mass are significant enough to easily measure. As with relativistic effects (corrections to kinetic energy, the velocity addition formula, and so on), the culprit here is again the speed of light; squared, it is the scale factor for converting mass into energy, and vice versa. Since c is a large number (300 million meters per second), very, very small amounts of mass convert to large amounts of energy, and so one needs very energetic reactions before the change in mass is noticeable.
In the case of pair production, however, this isn't just a case of making a process noticeable. The process actually cannot occur unless there is enough energy to account for the mass of both particles. Below that threshold, you have an energetic collision (and other things may take place), but no creation of new particles.
To make use of this analogy, I'm imagining that there may be religious processes which also operate on a threshold (e.g., "this kind goeth not out but by prayer and fasting"). Below a certain level of faith, or righteousness, or commitment, or preparation, the effects simply aren't observed. Since the people trying to test religious claims are often themselves not religious (they're seeking to debunk religion, as they see it), they wouldn't observe these effects in their own lives, and conclude (reasonably, I'll admit) that the effects are not real.
In the Book of Mormon, there's a situation where the prophet Lehi shares a dream he had with his sons. The dream is full of symbolism, and it wasn't immediately clear to the sons what everything meant. Nephi asked the Lord for guidance, and was given a deeper understanding. Laman and Lemuel, his older brothers, did not. Nephi heard them discussing the dream and asked, "Have you enquired of the Lord?" Their response was no, but they additionally said that the Lord "maketh no such thing known unto us." They hadn't had success with that kind of activity in the past, so why bother trying now?
Under the threshold model, we compare this to a scientist looking at a picture from a bubble chamber. It's filled with traces of all kinds of exotic particles, seemingly coming out of nowhere. He shows this to his students, who have a hard time understanding. One of the students says to the others, "These are the results of particle collisions. We can make traces like this in our accelerator." The others shake their heads and say, "No, we've tried in the past, and haven't gotten anything resembling this." Afterward, the first student discovers that the others had been running their accelerator at just a few keV; energies too low for particle production to take place. When he tries to point this out, they won't listen. As far as they are concerned, they have tried the experiment, and it was a failure.
Analogy 3: duality (or, what you get is what you look for)
Prior to the 20th century, there was an ongoing debate about the nature of light. Is it made up of waves, or particles? Fundamental to this debate was the idea that light had to be one or the other; it couldn't be both (and the people involved hadn't considered the possibility that light might be made up of something completely different). The reason for this idea was the simple fact that particles and waves have a lot of exclusive properties: waves have properties that particles don't, and vice-versa.
For example, particles are well localized in space, and waves are not (even wave packets don't have really sharp edges, but particles, as classically conceived, do.) Particles have well defined trajectories, and waves do not (even though one can do ray tracing, there is the matter of interference to consider, which leads to...) Waves interfere with each other constructively and destructively, and particles do not. Waves are polarizable, and particles are not. And so on. The list is actually pretty long.
Christian Huygens came up with a wave theory of light, and it actually was pretty good. One can use Huygens' methods to get at refraction, ray tracing, and a whole host of other properties or techniques that are used to examine physical optics. Unfortunately, Huygens lived at the same time as Isaac Newton. Newton was a scientific juggernaut, and when he came out with his corpuscular theory of light (saying that light was made up of particles), it carried the day. Now, that's a slight oversimplification; Newton had good evidence and arguments for his theory, and it wasn't simply carried by his reputation, but the fact remains that there were a few details of light's behavior that couldn't be easily explained by Newton's theory (Birefringence being one of them).
Many years passed. Then Young did his famous double slit experiment, and the whole world view on light shifted. Young showed that light passing through a pair of very narrow, closely spaced slits made an interference pattern on a screen. This behavior isn't explainable by a particle theory of light, but it comes very naturally out of a wave theory. So, at that point, the question seemed settled. The wave model was correct.
Until Einstein. In 1905, Einstein published a paper about the photoelectric effect. When light shines on a metal, a current is produced. If that were the whole story, one might be able to explain it with a wave model, but some of the details of the effect make a wave explanation really difficult. For example, there is a cutoff in frequency below which current is not produced, regardless of the intensity of the light. Einstein solved the problem by saying that light was quantized into packets of energy called photons, and that the energy of the photon was related to the frequency of the light. In doing this, he drew on work that Max Planck had done earlier (work that Planck had thought of as a mathematical trick, rather than physical reality).
So, at this point, the picture became murkier. Light was still a wave (since it has a well defined frequency), but it's quantized into packets, like a particle. Further experimentation (via both thought experiments and physical experiments) showed that the behavior of light---whether it acts like a particle or a wave---depends on the circumstances or design of the experiment. In cases where the experiment is designed to measure wave properties, the light acts like a wave (Young's double slit experiment, for example) In other cases, where the experiment is designed to measure particle properties, the light acts like a particle. So, reality is complicated. Light isn't exactly a particle, nor is it exactly a wave. The classification system we had designed, which looked like it had clear boundaries between the two kinds of objects, was inadequate to describe physical reality. Later, we discovered that not only does light have this dual nature, but everything does. Electrons, protons, neutrons, and more massive objects can be made to act like waves if the experiment is set up correctly.
Now, to the interpretation of this analogy. Currently, to a lot of people, the religious view and the scientific view are like the wave picture and the particle picture (before Einstein). In this picture, the two world views have too many mutually incompatible features to be reconciled. What if reality is like light? What if looking at reality through the religious lens can give one kind of result, and looking at it through a scientific lens can give another kind of result? What if the actual nature of the universe is rich enough, or deep enough, to accommodate both views? What if both ways of looking at the world lead to approximations of a deeper fundamental truth?
Unlike the previous analogy, I don't have a scriptural example of this off the top of my head. The scriptures seem as focused on the religious view as the evangelical atheists are on the scientific view. I'm not sure how to bring the two together the way Einstein did with the wave and particle pictures of light. In all likelihood, I'm neither smart enough nor influential enough to pull something like that off. But I have confidence that someone, at some point in the future, will manage it.
Analogy 4: tolerating incompatibility, or, models of an unknown deeper truth.
Two of the models of modern physics, General Relativity and the Standard Model, are fundamentally incompatible. This is sort of a wave-particle duality redux, since the disagreements are of similar character (continuous vs. discrete), but so far nobody has been able to bridge the gap between them. Some very smart people, including Einstein, have tried for many, many years to do so, but haven't gotten very far. The prevailing hope is that advanced experiments such as what is going on at the LHC will help to bridge the gap eventually, but that is by no means certain.
String theory is the current theoretical frontrunner, but it has a number of problems (which I'm not well informed enough to really comment on; I just know they exist). As far as I can tell, the main issue is that it doesn't actually make any testable predictions, which makes validating it difficult. So we don't, at this point, have a way of knowing how to proceed.
The answer, for most physicists, is to simply put the issue on the shelf. We have confidence that one day it will be resolved, but even if it isn't, general relativity is successful enough at describing the things it describes that we can't throw it away, and the standard model fits into the same category. So, the wait and see approach is the only one that makes sense.
Returning now to the original question, when someone asks me how I can be both scientific and religious, I feel like referencing one of these (or more than one) analogies. For certain questions, I think the idea of limiting behaviors is appropriate. In other situations, I'm sure there are threshold effects at work. In still other cases, there may be the kind of dualism that is present in the wave-particle duality, and finally, there are questions for which I simply don't have answers yet, but am confident that they will be resolved eventually.
Some examples: On the question of the creation of the world, whether the Bible or the cosmologists and geologists have the right explanation, I would say the principle of limiting cases is at work. If one were to try to communicate our present understanding of the origins of the world to someone like the historical Moses (educated in Egypt, employed as a shepherd in the desert; probably literate, but not at all numerate by today's standards) I imagine the outcome would look something like what is found in the book of Genesis. That's just the level of precision that would have been available for explaining Earth's origins to someone in those circumstances. Trying to make things more accurate (or precise, for that matter) would only have confused the issue.
On the origin of man, it's possible that again limiting cases is the most useful principle, but there may be a dose of dualism or wait-and-see involved as well. I do believe that God was involved in our creation, and I do believe that we are His children. But, I also believe the fossil record, which has modern humans on the earth for about 100,000 years. These two statements seem to be in conflict, but I think that the conflict only really comes into play if one takes a very literal reading of the Bible (which I don't, especially the book of Genesis).
Another question, the efficacy of prayer, seems to be a mixture of thresholds, limiting cases, and duality. I believe that Joseph Smith (among others) was given visions in response to prayer. I have never had a vision. Having a vision or not is a binary thing; and it makes sense to me that there is some sort of threshold at work. I don't know exactly what the threshold is. It could be faith, or fervency, or need, or something entirely different, but the fact remains that I don't view the fact that I haven't seen any visions as evidence against Joseph's having seen visions. Our circumstances are different. Furthermore, though the efficacy of prayer has been subjected to some scientific tests, I can imagine a set of circumstances in which (analogous to the double slit experiment) trying to study the effects of prayers interferes with those effects. In the case of light, trying to determine which slit a photon passes through destroys the interference pattern.
Those are the big three. Questions of what happens after we die are fundamentally unresolvable in this life, so I don't think they're worth discussing in the context of science.
I consider myself to be a scientist. I also consider myself to be a religious person. Not only do I not feel that there is a conflict between these two statements, I feel that being a scientist helps me explore, understand, and live my religion better, and I feel that my religious perspective gives me new and different ways to think about scientific principles, and helps me to have a certain degree of wonder and respect for the natural world. Some people say that to be both requires a high degree of compartmentalization, but I think that doing so would cost me something valuable in both sides of my life and work.
Are there things I don't understand? Of course. But that is true of both my scientific experience and my religious experience. If I understood everything, life would be pretty boring; there wouldn't be anything left to struggle to figure out.
My views on science and religion are probably not unique, but they are certainly not universal, either among scientists or among religious people. There is, however, within my own religious tradition, a scriptural justification for them. In a revelation that Joseph Smith referred to as "An olive leaf, plucked from the tree of paradise", he wrote:
And as all have not faith, seek ye diligently and teach one another words of wisdom; yea, seek ye out of the best books words of wisdom; seek learning, even by study and also by faith.
For me, faith and reason both occupy trusted spots in my toolbox. I don't apply both to every problem, and there are certainly situations in which each is more useful. There may even be situations in which one or the other, wrongfully applied, can do us harm. But I would be hard pressed to do without either one of them.