Sacred Algorithms:
Exchange Theory of Religious Claims

by William Sims Bainbridge

In a series of publications beginning in 1979, Rodney Stark and I analyzed religion, offering a definition that was simultaneously natural, interactive, constructive, and critical (Stark and Bainbridge 1979; 1980). To avoid personalizing this work as the "Stark-Bainbridge Theory," I prefer to call it the New Paradigm Theory of Religion (Warner 1993). Our aim was to provide a formal framework comparable to those in many branches of mathematics and the physical sciences, in which many theorists and researchers could develop explanatory models.

We defined religion as "systems of general compensators based on supernatural assumptions" (Stark and Bainbridge 1987:39). Compensators "are postulations of reward according to explanations that are not readily susceptible to unambiguous evaluation" (Stark and Bainbridge 1987:36). Many human beings postulate there is a supernatural realm consisting of "forces beyond or outside nature which can suspend, alter, or ignore physical forces" (Stark and Bainbridge 1987:39). These definitions require elucidation, and the best way to do that is by sketching the theoretical system of which they are parts. Specifically, I will place them in the context of evolutionary theory, suggesting how religious ideas are defined so that they are fit to survive.

One thing I should mention before we begin. The New Paradigm in the social science of religion is a general approach that contains within it various differences of opinion. Hopefully, these differences will develop into clear, testable hypotheses and be resolved through scientific research. But until that work is done, no one individual can speak for the entire New Paradigm. In some particulars, this essay does not represent the views of others who have worked either with me or in parallel to my efforts. My views differ from theirs in stressing the evolution of religion in a universe that does not in fact contain a supernatural realm or deities of any kind. My view is perhaps more ironic than other practitioners of the New Paradigm are entirely comfortable with: Religion is a necessary falsehood, and scientific examination has a tendency to debunk it.

In 1978, I wrote: "The sacred is a label for all those human dreams which cannot find fulfillment within conventional life. Religion is a hope and a demand: a hope that rapturous fantasies will be realized; a demand that others respect those fantasies" (Bainbridge 1978:79). The social science of religion is in a difficult position. It must respect religion, or there would seem no point in studying it. But it must not accept religion's assumptions, or scientific progress will halt at the barrier of faith.

Starting Points

One might want to begin a formal theory of religion with the very first sentence of the Bible. Conveniently enough, it is stated in axiomatic form:

In the beginning God created the heaven and the earth.

According to the General Social Survey, the most common image of God is that of creator (Davis and Smith 1996:129-131). However, as Pierre Simon de Laplace is reputed to have said to Napoleon, science has no need of that hypothesis (Newman 1956:1321). Indeed, the moment we postulate a supernatural deity who created the natural world and can intervene in it at will, our motivation to seek natural causes weakens. Prayer, rather than empirical hypothesis-testing, becomes the best method to gain knowledge, and we must face difficult questions about which of the many religions is true and why all the others are mistaken.

Progress in all of the sciences has been achieved by seeking natural causes. Science is like a game in which the object is to see how far we can go in explaining the features and dynamics of the world without deus ex machina recourse to supernatural assumptions. To be sure, it is possible to dispute the proposition that science is by its very nature secular. For example, some social historians argue that science was predicated on a fundamentally religious world view (Westfall 1958; Merton 1970).

People are unlikely to invest their energies in science unless they believe that natural laws exist for science to discover. Monotheistic religion postulates a single law giver who created a coherent, unified, and intelligible universe. Such a faith provides the cultural basis for the emergence of science. In the nineteenth century, a vast literature publicized scientific findings within the context of Protestant piety and read the book of nature as holy scripture (e.g. Miller 1858). However, a social phenomenon that arises out of religion can become independent of it (Weber 1904-1905). Thus, religion of a particular kind might have helped science get started historically, but this would not prevent science from evolving into an independent culture in later centuries.

So, how can we explain the emergence of religion without assuming that the supernatural exists? All we need to show is that intelligent beings would not be satisfied with the natural world, and that religion would evolve through social interaction between such discontented mortals. For example, we could start with this axiom:

In an infinite universe, evolution by natural selection will produce intelligent life at least once.

If I were rewriting A Theory of Religion from scratch, I might well begin with this axiom. Darwin's "dangerous idea" of evolution by natural selection has been called the most profound insight of science, and Christian fundamentalists are right to consider it anathema to their faith (Dennett 1995:21). If Darwin is right, then human intelligence, morality, and even religious faith are merely the result of natural processes rooted in random variation, rather than God-given gifts.

The explanatory power of the principle of evolution by natural selection from random variation is potentially even greater than is generally assumed. Not only can it explain the emergence and diversification of biological organisms, but it can also extend far beyond the realm of biology. The physical sciences can employ a variant of natural selection to explain the regularities of physics, astronomy, and chemistry. The social sciences can likewise explain the emergence and development of societal institutions, including religion.

The best way to see the application of natural selection to the pre-biological world, without straying far from the theme of religion, is through the argument from design: God must exist, because without him the world could not be so orderly and beneficial. This argument notes the remarkable fact that the planet Earth is hospitable for human life. We can breathe the air, drink the waters from the streams, and eat the bountiful plant and animal foods of field, forest, and ocean. The parsimonious theological explanation for all this bounty is that God intentionally constructed the world as a home for humanity.

However, the suitability of the Earth for humans can also be explained without recourse to divinity. If we were on the planet Venus, we would not rejoyce in the benignity of the environment. The corrosive, acid-laced atmosphere would scorch our throats before we could complain that God had done a bad job in preparing that planet for us.

The hospitable nature of the Earth is a selection effect. Only on such a planet as ours would the human species evolve. Astronomers have already located about a hundred planets, and they have discovered that solar systems vary greatly in their characteristics. Probably, there are many trillions of planets in the universe, plus a vast range of other objects, both smaller and larger. Thus, it is not surprising that one planet is capable of sustaining human life. Which planet has these characteristics is pure accident, but our presence on it is explained by evolution.

Early in the previous century, biochemist and sociologist Lawrence Joseph Henderson (1913; 1917) wrote a pair of books arguing that the laws of physics and chemistry are improbably conducive to the evolution of life. Had the characteristics of the element carbon been different, for example, it could not have been the basis of the complex molecules that make life possible. Thus a theologian could argue that God designed the laws of nature, if not the exact details of the planet Earth, so that the universe could provide a home for humanity.

However, developments in cosmology toward the end of the twentieth century suggested a natural selection explanation for the laws of nature themselves (Carr and Rees 1979; Gale 1981; Leslie 1982; Barrow and Tipler 1986). Some laws can be deduced from others. For example, the inverse square law governing the declining intensity of light as one moves away from the source can be deduced directly from the principle of the conservation of energy and the formula for the area of a sphere. But a deductive system must begin somewhere, in this case with what we are calling the fundamental laws of nature. For natural selection to provide the answer, we must imagine that these laws vary widely, so that a suitable selection can be made from them. But the observed universe has uniform laws.

Twenty years ago, cosmologist Alan Guth (1981) suggested that in fact this uniformity is limited to small regions of the entire universe, and we can observe only one of a vast myriad of such regions. In particular, Guth postulated that everything we observe was in direct contact at the birth of the universe, and interactions between its components homogenized them. Other regions were not in direct contact with ours, and underwent their own homogenizing processes, arriving at different sets of natural parameters. The differences in the laws of separate regions would give them very different histories, as the universe expanded during an initial phase of rapid inflation.

The details of Guth's model and the extensive subsequent work related to his ideas need not concern us here. Some variants of the model imagine that existing universes give birth spontaneously to new universes that inherit some properties while undergoing mutations in other properties, analygous to the way that living organisms reproduce, inherit genetic characteristics, undergo random mutation, and evolve (Linde 1994). If these models are approximately correct, then the pre-biological universe provides ample scope for evolution by natural selection from random variation to operate, preparing the way for biological evolution (Carter 1983).

A theologian could grant all of these speculations and still argue that God was necessary to bring the whole universe into existence so that these processes of natural selection could begin. However, since Einstein's work on general relativity nearly a century ago, it has been unnecessary to assume that the universe exists in relation to any external framework. Existence is a relationship between entities and forces within a physical system, thus no effort may have been required to create the system as a whole (Gott 1982). One way this could be true is if the sum total of all the constituents of the universe added up to zero, because for each of its units of mass and energy there was an equal and opposite unit.

Cosmologist John Archibald Wheeler (1980) has even suggested that our act of perceiving the universe is the only action required for it to exist. Thus, natural selection comes full circle. Given a conducive universe, intelligence evolves. That universe "exists" only because intelligence evolves in it, and by perceiving it gives it meaning.

A very different new realm for the theory of natural selection is human society, including religion itself. Several inflential works have examined how human biology and culture may have evolved in tandem (Dawkins 1976; Cavalli-Sforza and Feldman 1981; Lumsden and Wilson 1981). In earlier publications, I have suggested that religion can be analyzed from the perspective of cultural genetics, and that the laws governing human behavior are part of the same evolutionary system as the laws governing the behavior of the physical universe (Bainbridge 1985; 1997).

When Rodney Stark and I first published elements of the New Paradigm Theory, we made no attempt to trace the evolution of human society all the way back to its biological and chemical foundations. Rather, we began with seven general propositions that we called axioms, and outlined how religious phenomena could be derived from them. As we quickly sketch that deductive system in the following section, it is worth keeping in mind that ideally we would want to derive some of these axioms from even more fundamental principles, notably evolution by natural selection from random variation.

A Theory of Religion

The New Paradigm Theory sought to derive the main features of religion from seven axioms that did not mention religion in any way. Here is that list (Stark and Bainbridge 1987:27-32):

A1 Human perception and action take place through time, from the past into the future.

A2 Humans seek what they perceive to be rewards and avoid what they believe to be costs.

A3 Rewards vary in kind, value, and generality.

A4 Human action is directed by a complex but finite information-processing system [i.e. the mind] that functions to identity problems and identify solutions to them.

A5 Some desired rewards are limited in supply, including some that simply do not exist.

A6 Most rewards sought by humans are destroyed when they are used.

A7 Individual and social attributes which determine power are unequally distributed among persons and groups in any society.

We do not claim that these axioms are self-evident, nor that they are the best set that could ever be devised from which to derive religion. Rather, we view them as a provisional set of principles from which religion could be derived, open to revision on the basis either of logical analysis or empirical research. Indeed, we improved the axioms slightly from the journal article that first stated them in 1980, for the book that came along seven years later (Bainbridge and Stark 1984). In our view, developing a formal theory should be an iterative process, involving empirical discovery, logical explanation, and active imagination (Homans 1967; 1974; 1984).

Axiom A4 introduces the human mind, which is the set of human functions that directs the action of a person. It is roughly equivalent to the hardware of the brain plus the software of culture and the memory of personal experience. Alternatively, the human mind is the network of neural connections that processes information dynamically when the person makes a decision or a plan (Bainbridge 1995a; 1995b). Humans seek rewards and try to avoid costs, employing their minds to analyze their situation and identify the path to their goal. Put another way, humans solve problems by means of explanations, which are statements about why rewards may be obtained and costs are incurred.

Explanations that explicitly tell a person how to obtain a reward can be called algorithms. This term is commonly used in computer science for programs or segments of programs that accomplish a particular task. Daniel Dennett (1995:48) has pointed out that evolution by natural selection is an algorithm . Stated teleologically, from the standpoint of a computer programmer, an algorithm is a step by step procedure for solving some problem. But Dennet defines the term without reference to purpose, so that it can include any regular mechanical process: "An algorithm is a certain sort of formal process that can be counted on - logically - to yield a certain sort of result whenever it is 'run' or instantiated" (Dennett 1995:48).

In pursuit of desired rewards, humans exchange rewards with other humans. Indeed, this is a fundamental human algorithm: "When in need, seek help." In order to get help, we often have to be willing to give something in return, either now or at some time in the future.

Humans seek many kinds of rewards, some of which cannot readily be obtained by any lone individual. Rewards like food or fun get used up, and must be sought again and again. Thus, we learn to seek particular rewards through exchanges with particular other individuals or categories of people. Someone who is a frequent source of rewards, and to whom we give rewards in return, is an exchange partner. When we need a reward of a particular kind, and cannot readily provide it for ourselves, we go to a valued exchange partner, especially one who has provided similar rewards in the past.

One very important kind of reward is information about how to obtain a desired reward. This is another way of saying that algorithms can be valuable, and humans often seek them. Frequently, the best source of information is another person. Thus we have the algorithm: "When in need of an algorithm, ask a valued exchange partner."

Tragedy enters human life through axiom A5, which notes that some rewards are limited in supply, and some do not exist at all. A limited supply means that not everyone can have as much of a reward as they desire. Powerful people, those with great control over the rewards they can obtain through exchanges, are able to get more than their equal share of some limited rewards, and this fact is a major dynamic of social inequality. Rewards that do not exist at all are unavailable even to powerful people. Both inequality and unavailability create frustration. However, it is impossible to know for certain that a given reward does not exist.

In the absence of a desired reward, people will often accept algorithms that explain how to get the reward in the distant future or in some other context that cannot be immediately verified. These algorithms are compensators, in that they compensate the individual psychologically for lack of the reward. Typically, they are promises that the reward can be obtained.

Rewards vary in terms of how specific or general they are. Correspondingly, some compensators are relatively specific, for example promising cure of a particular disease or providing compensatory status for low status in society. Other compensators are more general, such as the hope for eternal life. Stark and I found it useful to distinguish magic from religion in terms of the specificity of the compensators they provide.

Magic is defined as specific compensators that promise to provide desired rewards without regard for evidence concerning the designated means (Stark and Bainbridge 1987:105). As noted earlier, religions are systems of general compensators based on supernatural assumptions. Thus, the defining difference between magic and religion, in the New Paradigm Theory, is the generality of the compensators they offer. There is no categorical dividing line between the two, and they blend into each other. Indeed, one of the chief variations among religious movements and organizations is the degree of magic (specific compensators) they offer in addition to the general compensators that define their religiousness.

Interaction and Innovation

One of the first parts of the New Paradigm Theory to be published was a 1979 essay outlining three mutually compatible models of compensator generation: the psychopathology model, the entrepreneur model, and the subculture-evolution model (Bainbridge and Stark 1979). Although presented as three different ways in which new religious cults could emerge in the modern world, these models were really theories about religious innovation in general, including the original emergence of religion in human history. They are compatible because all three concern human interaction and because the actual formation of any new cult of any significance is likely to include all three. Indeed, the third is a kind of combination of the first two. They address the question of how individuals can confidently offer new compensators to their exchange partners, in lieu of the rewards they would prefer.

The psychopathology model states that religious innovations are invented by individuals suffering from certain forms of mental illness. During a psychotic episode, the individual will experience a vision, discovering a new package of compensators to meet his or her own needs. After the episode, the individual will return more-or-less to normal, and be able to communicate the vision to other people. If some of these people are themselves experiencing unresolved psychological strain, they may adopt the new package of compensators for their own use. If the society as a whole happens to be undergoing a significant crisis, there may be a large enough constituency for the religious innovations to catch hold, modifying the existing religious tradition or even establishing an entirely new tradition.

The divine "madness" of psychopathology contrasts with the practical rationality of the entrepreneur model. New beliefs about the supernatural are probably very difficult to establish, and a single charismatic individual seems to have been key to many of the historical cases we know about. However, some individuals appear to have consciously constructed new compensator packages, the way a craftsman might create a work of art or a piece of furniture, without experiencing any unusual psychological states. These compensators are manufactured and sold by entrepreneurs, who treat religion as their business, although typically cloaking it in supernatural mystifications. Like those in other businesses, they are motivated by the desire for profit, which they can gain by exchanging compensators for rewards.

The entrepreneur model seems to imply that compensator creators are devious liars, and one might therefore be tempted to define religion as the holy lie. Entrepreneurs may be liars, but they need not be. Years ago I completed an extensive interview study of a man who had devised his own complex new religion, essentially from scratch. I decided not to publish at any length, because to do so would inevitably subject him to the ridicule of his business associates. He was very cautious in selling his new religion, and it would be impossible to hide his identity in any detailed presentation of his accomplishments. His regular occupation was selling insurance, and the parallels between religion and insurance have been noted by sociologists (Zelizer 1978). With great enthusiasm he explained to me the steps he had gone through to develop his majestic speculations about the nature of reality and human fate, often expressing momentary doubts, then getting swept along again by his sales pitch. All salesmen exaggerate, but they often honestly imagine themselves to be benefactors of humanity.

The subculture-evolution model notes that profound innovations can occur in a large number of small steps. Individually, these steps may be like tiny examples of psychopathology and entrepreneurship. We all have mental lapses, and we all exaggerate from time to time. In a social system, such as a family, tribe, or small group, there is an active exchange of hopes and demands, rewards and suggestions about how to obtain rewards. In the absence of a desired reward, sometimes rumors can grow about algorithms to obtain it. Some of those algorithms can readily be tested and found valuless. Some others, including those that rest upon supernatural assumptions, are harder to test and will not fail so obviously. These rumors will remain in the culture, unless of course somone finds an algorithm that is really effective in obtaining the desired reward.

Primary and Secondary Compensation

The survival of supernaturally-based compensators, when more testable compensators are disproven, is a good example of natural selection. In a series of computer simuations, I showed how people could generate hypotheses about how unattainable rewards might be achieved (Bainbridge 1987; 1995b). The computer programs used a general approach called neural networks or agent-based modeling to simulate human thought.

In particular, the simulated people tried to imagine which categories of other people might provide eternal life. Then they interacted with each other, exchanging other rewards and learning that none of their exchange partners could really give them immortality. However, they were able to imagine supernatural persons who could not be directly encountered within the rules of the simulation. As the simulation progressed, the computer models of human minds came to realize that other beings like themselves could not provide the desired reward, and they developed the hope that the reward could be obtained from supernatural beings. Thus, in evolutionary terms, false beliefs that other humans could provide the reward became extinct, but the untestable idea that it could be gotten from a deity survived.

The evolution of a new set of compensators begins when a group of persons commits itself to the attainment of certain rewards. In working to obtain these rewards, members begin exchanging other rewards as well. This part of the model is a straightforward application of the classic small group theory of George Homans, focusing on the fact that human social life is a mechanism for obtaining rewards that individuals cannot get for themselves (Homans 1950). But social life becomes elaborated as the members exchange rewards of increasingly diverse kinds, and as they develop obligations to provide each other with rewards that are empirically difficult to find. As they progressively come to experience failure in achieving some important goals, they will gradually generate and exchange compensators as well. To the extent that these compensators are specific, the group will create magic. But as the compensators expand to become general, the progressive innovation process becomes fundamentally religious.

Here it is worth drawing a distinction that was not explicit in the original publications of the New Paradigm Theory, that between primary and secondary compensation (Bainbridge 2002). Primary compensation is when a person accepts a compensator in lieu of a reward that the individual personally seeks. Secondary compensation is when a person offers a compensator in lieu of a reward that the person is obligated to provide to another person. The article that introduced these concepts illustrated them with incidents from the life of my great-grandmother, Lucy Seaman Bainbridge, a prominent missionary who lived from 1842 through 1928 (Bainbridge 1924; McKinney 1932).

One example here will suffice to illustrate the differences between rewards, primary compensators, and secondary compensators. In the early 1860s, Lucy's older brother George fell victim to typhoid fever, a disease that often brings great pain and a lingering death. Their mother, Cleora Augusta Seaman, was a medical doctor, but the medicine of the day could not offer a reliable cure, which was the reward George desired. Members of the Baptist church, the Seaman family was forced to rely upon religious compensators instead. Lucy sang hymns and comforted George as best she could, until he died. For George, the prayers of his family were primary compensators, to some degree giving him hope that he would live again. For his physician mother and nurse sister, they were secondary compensators, allowing them to feel they were fulfilling their obligation to save George, even though they lacked the power to do so.

In the absence of a desired reward, primary compensation is the best that a person can have, even if it represents wishful thinking. Secondary compensation is more subtle. By offering compensators to an exchange partner, a person attempts to maintain the exchange relationship despite the failure to deliver the required reward. In a sense, secondary compensation is a confidence game or an instance of bad faith. However, if those who give and receive the compensators do so within a shared religious culture, they will define the compensators as rewards, and avoid defining them as lies.

An unresolved scientific question of great importance concerns how important each kind of compensator is to the maintainence of religion. Clearly, if nobody ever accepted religious beliefs as primary compensators, it would be impossible to offer them as secondary compensators. But it is possible that, for example, George Seaman felt only slightly better because Lucy sang Baptist hymns, and their chief value was as secondary compensators for Lucy. He died in agony, but she could feel that she did all she could in the context of her culture. Thus it is possible that secondary compensators are more effective in building and sustaining religious organizations.

An empirical test of this proposition might be achieved by observing the future course of religious institutions in western European welfare states. Perhaps the hallmark of the welfare state is that it takes on the obligation of dealing with many of the problems that afflict its citizens. It may not do an especially good job, so it does not remove the need for primary religious compensators. However, it does relieve people of many of their private obligations to take care of each other. If secondary compensation is the main support for religion, than we would expect religious institutions to weaken, which is exactly what we do see in western Europe. Other explanations for European secularization exist, so serious scientific research is needed before we can confidently say whether the welfare state erodes religion by supplanting secondary compensators.

Natural Selection

In the realm of religion, natural selection operates through interactions between human beings, in which compensators are defined as more or less valuable and more or less supernatural. That is, evolution takes place in the interplay of promises and hopes, fantasies and arguments, definitions and redefinitions. Obeying the meta-algorithm of natural selection, religious algorithms compete with natural algorithms and with other religious algorithms. Survival of the fittest religion means increased faith by individuals and respect by social groups.

However, by analogy with the biological world, we would not expect one, single religion to triumph over all others. Although humans and eagles soar high above other creatures, slugs and slime molds continue to prosper. Indeed, a proper scientific understanding of religious evolution demands an ecological perspective, in which different kinds of church, sect and cult adapt to different niches in the environment, sometimes becoming symbiotes rather than competitors of each other.

Ecologies are dynamic, and A Theory of Religion explicitly identified three areas where evolution could be observed in the religious environment: gods, magic, and religious movements. The third chapter of the book, titled "Evolution of the Gods," sought to explain why the gods worshipped by societies of the past tended to grow in scope and to decline in number over the centuries (Stark and Bainbridge 1987:55-87). In part, this reflects the increasing complexity of human culture as it evolves, the increasing occupational specialization that early on leads to the emergence of a professional priesthood, and the emergence of coherent religious organizations that seek a monopoly over religious compensators. This chapter of the theory book addresses the scientific question of why there seems to have been an historical evolution away from polytheism toward monotheism, without as yet resulting in the complete disappearance of the former or universality of the latter.

Another section of the theory book examines the relative fitness of religion versus magic, in the context of a discussion of the subculture-evolution model (Stark and Bainbridge 1987:184-187). Imagine a group of people who have committed themselves to achieving unattainable goals. Among the examples we have offered are new religious movements like Scientology, the Process, and Transcendental Meditation, that claim to possess techniques that can increase a person's mental and spiritual capabilities (Stark and Bainbridge 1985). Magic provides specific compensators for specific rewards, and it risks empirical disconfirmation when it fails to provide those palpable benefits. Because religious compensators substitute for more general rewards, they tend also to be more valued and thus allow priests to garner greater rewards from their clients, than magicians are capable of doing. Thus, other things being equal, religious compensators are more likely to survive and to grow in popularity, than any given set of magical compensators. Because religious culture tends to be more fit than magical culture, a group or society that begins exchanging specific (magical) compensators, will evolve into one that exchanges general (religious) compensators.

The eighth chapter of A Theory of Religion, titled "Evolution of Religious Movements," formalizes our understanding of the ecology of churches, sects, and cults, which is the same thing as the dynamic interplay between secularization, revivial, and innovation (Stark and Bainbridge 1987:239-278). The tendency of well-established religious institutions to avoid containing much magic, whose claims could be disproven thus discrediting the religion, is one of the pressures driving the form of evolution we call secularization. But in secularizing, a religious organization loses some of its most needy members, those who lack many of the rewards possessed by other members and who thus are more open to specific compensators.

This leads to schism and the eruption of revivalist sects that place a higher priority on specific compensators. This is equivalent to the biological process of speciation, in which a new species arises from an earlier one without necessarily supplanting it. High levels of secularization encourage the evolution of radically different innovative groups, which are sometimes called cults. This is the religious equivalent of the evolution of new genera, families, orders, or classes - taxonomic categories that are more different from each other than adjacent species typically are.

In his acclaimed book, The Rise of Christianity, Stark (1996) argues that Christianity was objectively better for people than the pre-existing pagan religions of the classical world. This is equivalent to saying that Christianity was better adapted to the environment in which it arose, more evolutionarily fit than its competitors. Stark even links this better cultural adaptation to biological superiority, because he says Christianity caused believers to have a higher rate of fertility, and lower mortality, compared with non-believers.

In contrast, James J. O'Donnell (1977) has argued that Christianity won because it was more particularistic than paganism was, refusing to tolerate other faiths while they were more likely to tolerate it. Demographer Nathan Keyfitz (1987) has argued that Islam is better adapted today than Christianity is, because its resistance to secularism and suppression of women gives it higher biological fertility. We do not have to decide among these various arguments here, but they are good examples of the ways in which one religion may be more adaptive than others.

Conclusion: True Lies

As Pilate asks in John 18:38, "What is truth?" In Latin: "Quid est veritas?" The anagram of Pilate's question, "est vir qui adest," suggests that the answer is Jesus. That is, the answer may be a man, a god, or a transcendental faith rather than a declarative statement written in the words of any human language and susceptible to empirical disconfirmation.

The word true can mean loyal. An instrumental definition of truth could be stated: I shall consider true those words which when spoken to another person serve my interests. Those words are true because they are loyal to me or, for example, to my religious creed. This is almost the definition of a lie, but not quite, because it leaves open the possibility that the person does not know whether or not the words are true according to other definitions that might be framed. This is the typical situation with respect to religious communications.

In general, it is very difficult to tell when a person is sincerely expressing firmly-held religious beliefs, because the norms of many social groups encourage people to say one thing while permitting them to act as if they believed something very different. You may tell me that you have personally spoken with God, yet if I have not had the same private experience myself, I can reasonably accuse you of being mistaken, lying, or merely interpreting momentary personal feelings in terms of the prevailing but arbitrary cultural definitions. Keeping faith means being loyal.

William James (1907:86) offered a pragmatic definition of truth: "the expedient in the way of our thinking." This definition contains an ambiguity, the word our which could mean my (in the sense of the royal or editorial "we"), yours and mine (in the sense of the dual form of early Greek verbs, between singular and plural), belonging to my group, or belonging to all humanity. What is expedient for me to think, may not be expedient for you to think. Furthermore, what is expedient for me to think may not be expedient for me to say to you. Deception enters when I try to get you to think things that serve my interests rather than yours, as in the case of secondary compensation. If I have no cure to offer you when you are sick, I may pray for you instead, and try to convince you that by doing so I fulfill my obligation to help you. In one sense, this is good faith, but in another sense, it is very bad faith indeed.

It is possible that the tenets of religion are false in the senses that they ignore scientific models of reality, contradict empirical evidence, and lack direct support from the personal experience of many people. Yet it can be expedient to hold these beliefs, if to do so benefits the individual or the community. Many positive functions have been attributed to religion, including strengthening morality, improving mental health of believers, boosting fertility in competition with other populations, and emboldening warriors. Talcott Parsons (1964) even claimed that religion was one of the fundamental evolutionary universals upon which all of human society was based.

A striking example is what I call the Stark effect, because it was discovered by my colleague, Rodney Stark (Bainbridge 1997:277; Stark et al. 1980; Stark et al. 1982; Stark and Bainbridge 1996). Religion can deter juvenile delinquency in American communities with high rates of church membership, but not in communities with low rates of church membership. That is, the religious faith of an individual teenager is impotent to steer that individual's behavior, unless it is supported by social control, but social control is strengthened by religious faith. This is evidence of the power of religion, but also of its falsity.

If the typically Christian faith of religious teenagers in America were literally true, individual faith in God would mean a direct connection to the diety, sometimes described as having Jesus in your heart. But this idea is contradicted by the fact that individual faith does not deter delinquency unless socially supported by the community. The juvenile may pray to God for help obeying the law, but Gods fails to comply.

Sometimes, faith is good but false. Religion can be defined as the social institution based on explanations that are simultaneously true and untrue. This is the paradox of a true lie.

From an evolutionary perspective, or from the perspective of New Paradigm Theory, all this makes perfect sense. Human beings are not philosophers, existing somehow above mundane existence and spinning abstract theories without reference to their utility. Rather, the human mind evolved through natural selection because it conferred survival or reproductive advantages upon our ancestors. It allowed us to devise and communicate complex algorithms about how to gain rewards and avoid costs. But not all successful algorithms actually provided the desired rewards. Some algorithms accomplished other benefits, that might be called incidental, such as reducing useless anxiety and assisting in the raising of children. This was probably the case for many kinds of religious belief. Some religious algorithms may have survived not because they benefitted human beings, but simply because they could not be disproven as easily as other algorithms that promised the same rewards.

Religion may be a system of sacred algorithms, but to science nothing is sacred. The truth or falsity of religion, however these might be defined, are open to scientific inquiry. Only the desire to protect the true lies of religion prevents us from subjecting them to formal theoretical analysis and rigorous empirical research. To the extent that religious beliefs imply any observable effects in the natural world, they are susceptible to empirical evaluation. To the extent that religious beliefs do not imply any observable effects, they have little capacity to provide effective primary compensation. That is, if people did not believe their prayers could be answered in this life, they would pray only very seldom.

To define religion as "systems of general compensators based on supernatural assumptions" is to acknowledge the complex psychological motivations, social interactions, and cultural institutions that construct and sustain faith. People seek rewards, often in exchange with each other, and when they lack a reward desired by their exchange partners, they frequently offer compensators instead. By invoking supernatural assumptions, people prevent their exchange partners from empirically evaluating these secondary compensators.

One of the standard definitions of algorithms includes the requirement that they solve the given problem in a finite series of steps, that is, within the empirical world. Thus, a sacred algorithm is a logical contradition that cannot itself contribute to scientific progress. But religion can validly be the subject of research in the social and behavioral sciences, because it reveals much about how humans collectively construct their cultural world.

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