Category: Religion

When Mathematics Fails as Theology

It is fitting that the failed California doomsday prophet should have his formal education in engineering rather than theology, since his contorted interpretation of the Bible relied on a hermeneutic that would make mathematics theologically informative. While it is easy to ridicule his particular belief, the mentality that created it is quite widespread, and can be found even among the most eminent scientists who profess no religious faith. By this mentality I mean the fallacy that mathematics can determine ultimate questions of reality.

Camping’s unwavering certainty in his prediction (“The Bible guarantees it”) was grounded in the appearance of remarkable mathematical coincidences that pointed to May 21, 2011 as a Biblically significant date. Given the premise that the Bible is absolutely true, and the additional premise that his inferences are mathematically certain, we can appreciate why Camping would present his particular interpretation of Scripture to be as authoritative as Scripture itself. Mathematics allows no room for interpretation, so it seems, as the numbers speak for themselves.

This mathematical absolutism disregards the role that subjective choices play in developing a mathematical model. Just because our model accounts for all the data, that does not mean we could not have constructed another model that works equally well. In general, it is impossible to prove theoretical uniqueness. Camping, for example, found it astounding that the same date that was seven thousand years after the Flood was also after the Crucifixion by a number of days equaling the square of the product of three numbers with significance in Hebrew Gematria. He ignored the fact that his dating of the Noachic Flood in 4990 BC was highly idiosyncratic, as well as the more obvious fact that any number of arithmetic operations could have been chosen. Further, why must the end date be determined by the square of the product rather than the cube? In short, he made some deliberate subjective decisions, consciously or unconsciously, which led to the desired result that the Rapture would occur in his lifetime.

Lest we think that such mathematical idolatry is confined to elderly fundamentalist preachers, let us take a look at the opposite end of the spectrum. The famed physicist Stephen Hawking has recently proffered his view that it can be proven – through abstract mathematical theorizing, of course – that heaven does not exist and God is unnecessary. The basis of this claim is his construction of a theoretical model whereby the universe “creates” particles with mass, and the universe is self-enclosed with respect to temporal causality. As with Camping, this model is cleverly constructed to confirm a priori convictions Hawking has held for decades. He already suggested in A Brief History of Time that the need for a beginning of creation might be elimintated by “rounding off” the light cone so there is no causally “first” event. “What need then for a creator?” Such a manipulation was highly tortured, as it would contradict a plain interpretation of general relativity by allowing effectively superphotonic expansion, and generalizes the notion of temporal causality to the point that it is no longer an effective constraint on physical theorizing. Such liberties are part and parcel of the “anything goes” approach to modeling the early universe.

The point is that Hawking had many options available to him, but he did not take the most “obvious” option (in light of relativity’s causality postulate and observed expansion from a single point). Just as Camping wants the Rapture to occur in his lifetime, Hawking wants the universe not to rely upon a transcendent God. He ignores the significant role that his own subjectivity has played in the formation of his mathematical model.

Even if Hawking’s recently proposed theory should someday prove to be an accurate mathematical model of physical reality, it would not accomplish the theological aims he intends for it. The universe does not create massive particles out of nothing, but (theoretically) from a vacuum field or some other construct with definite quantifiable properties. However you want to characterize such an entity, it certainly is not “nothing” in a strict philosophical sense. Modern physicists play fast and loose with philosophical concepts in order to make their mathematical models appear to sanction their metaphysical predilections.

A universe that is self-enclosed with respect to temporal causality does not thereby find itself without need for a creator. To take a simple example, take a universe with one particle that has two states, A and B, where the event of being A causes the event of being B and the event of being B causes the event of being A. (I assume the physicist’s error that events cause events.) In this chicken-and-egg universe, our one particle goes back and forth between being A and B. Does it follow that it needs no creator? Not at all, for there is still no logical necessity that such a universe should exist at all, and we should have to ask ourselves why this particular universe with its causal structure and laws is actually existent, while some other equally mathematically valid universe is not. No natural order is absolutely necessary, in which case we must appeal to some higher cause to account for the natural order as a whole.

Hawking’s physical theories, like all mathematical models of physics, contain determinate assumptions that are not tautological. Since they are not logically necessary, and mathematical principles have no power qua mathematical principles to actualize themselves as physical reality, it follows that we need something beyond physics to account for why this particular natural order was granted reality rather than another. Most physicists overlook the need for metaphysics because they unconsciously ascribe to mathematical principles an almost mystical power to result in physical actualization. This poorly thought out Platonism is rarely formally declared, but is implied in the way physicists speak of their theoretical constructs, particularly when dealing with the early universe or attempts at “theories of everything”.

We might try to make the natural order logically necessary by declaring that every mathematically valid possibility comes into existence. This make nonsense of Occam’s Razor, as it postulates an unfathomable infinity of universes just to account for this one. Further, it does not solve the problem of logical necessity, as it is not logically necessary that every possibility should become actual.

Lastly, one could decide that the natural order needs no cause, and is just a brute fact to be accepted without explanation. This is irrational in the true sense of the word, as it declares everything to be without a reason. It is also profoundly inconsistent to insist that everything that happens within the universe, no matter how insignificant, must have a reason or cause, yet the entire universe with its natural order can come into being and be sustained in being (physicists generally ignore this metaphysical problem) for no reason whatsoever. Logical cogency ultimately requires grounding in a metaphysically necessary Being, and none of our physical theories, by virtue of their mathematical contingency, can meet this requirement.

To the philosophically literate, it is no surprise that mathematics is incapable of serving as natural theology. In our society, however, mathematical ability has become practically synonymous with intelligence, since it is most easily quantified (naturally), and it is positively correlated with other mental abilities. It is a mistake, nonetheless, to make mathematical ability the defining characteristic of human rationality, since computation and spatial reasoning are easily replicated by computers that have no subjective thought processes. Although Professor Hawking and Brother Camping have both done their math correctly, that is no substitute for authentic wisdom and understanding, which requires a more subtle grasp of concepts and an awareness of one’s own subjective assumptions.

See also: Causality and Physical Laws

A Behavioral Approach to Social Disease

Criticism of Pope Benedict’s recent remark on the effectiveness of prophylactics fails to distinguish between the moral and physical aspects of using such devices. As the supreme teaching authority of the Catholic Church, the Roman pontiff is concerned mainly with the moral aspect of venereal disease transmission. Condom usage fails to address the moral cause of sexually transmitted disease – namely, promiscuity – and indeed may encourage it by creating a false sense of security. In this sense, prophylactics are not a solution to the problem, but may even exacerbate the problem.

Many commentators have misconstrued the Pope’s statement as making the untenable assertion that condoms are physically ineffective. While it is unquestionable that prophylactic devices significantly reduce the chance of infection, there are sound statistical reasons for doubting their ability to contain epidemics. We will examine these reasons briefly, to show that condoms, to some extent, fail as a solution to the STD problem even in a physical sense.

According to the FDA, when condoms are used properly and consistently, the rate of pregancy in one year is 3%. Based on actual use, with human error and negligence, the pregnancy rate with condoms is 14% in one year. Without protection, the pregancy rate is 85%, so the figures cited reflect condom failures in 3.5% of optimal users and 16% of actual users in a given year. However, we must also consider that those who became pregnant likely had multiple failures in that year, since it is difficult to become pregnant on the first attempt. Even with optimal fertility (25%) it typically takes 4 months, so those who became pregnant likely had 4 or more failures per year. Assuming a Poisson distribution of failures, this means there’s an average of 1.25 failures per year with optimal usage, or 2.25 failures per year based on actual usage.

Again using Poisson statistics, I compute from the above that the chance of one or more failures per year is over 70% based on optimal usage, and nearly 90% based on actual usage. Based on the U.S. average of 58 acts of intercourse per year, there is a 2% failure rate per act with optimal usage, and a nearly 4% failure rate with actual usage. These results are consistent with other studies showing that condoms slip off completely 1-5% of the time.

In a society where the prevalence of STD is low, the failure rate of prophylactics is low enough to provide adequate protection, since it is improbable that a failure will occur while with an infected partner. However, in many African countries, the prevalence of AIDS and other STDs is in the range of 10-20%. This makes it a statistical near-certainty that a person will acquire that disease in a decade or so, if partners are changed constantly, even if condoms are used properly and consistently. Thus condoms are not an effective solution to the STD problem in high-prevalence areas like Sub-Saharan Africa.

People can minimize their risk even in high-prevalence areas by remaining monogamous with a partner who is known to be uninfected. In this scenario, multiple prophylactic failures pose little or no additional STD risk. A promiscuous person, by contrast, is exposed to the full risk of the high prevalence rate in the general population. This risk can be reduced by having one’s partner tested in advance, but the clandestine and spontaneous nature of promiscuous encounters operates against the likelihood of such precaution.

These theoretical expectations are corroborated to an extent by the actual epidemiology of STDs. In the United States, more than 50% of AIDS cases are among homosexual males, a tiny subgroup (3% of men or 1.5% of adults) where extreme promiscuity is common, and having as many as 100 partners per year is not rare. More than half of all syphilis cases in the U.S. are in the South, particularly among blacks, where promiscuity among the youth is rampant, and 48% of black women aged 14-19 have an STD. Still, in most cases, the prevalence of disease is low enough for prophylactic use to contain its spread. Such is not the case in Africa, where adultery and prostitution are practiced with much greater frequency than in the West, enabling AIDS to become an epidemic in the heterosexual population.

The relationship between behavior and epidemiology is not always straightforward. For example, in the United States there was an eightfold increase in genital warts in females from the early 1950s to the late 1970s (rising from 13 to 106 per 100,000). Gonorrhea incidence rose to epidemic proportions in the 1970s and 1980s. These changes are generally attributed to the liberalization of sexual attitudes, leading to greater promiscuity. However, an infectious disease is caused by an organism, so it may be influenced by biological factors, as seems to be the case with the gradual decline of gonorrhea in Europe and Israel since 1970, as well as its resurgence in the late 1990s.

Still, the ability to contain STD transmission through the usual means of prophylactics seems ineffective in the long run when not accompanied by more fundamental changes in behavior. In the U.S., where condoms and sex education have been ubiquitous for decades, 65 million people have viral STDs. (American Social Health Association (1998), “Sexually transmitted diseases in America: How many cases and at what cost?”) Over 50 million of these have genital herpes (Fleming DT et al. (1997), “Herpes simplex virus type 2 in the United States, 1976–1994,” New England Journal of Medicine, 337, 1105–1111. NIAID estimates range from 45-60 million.) Considering the entire U.S. population aged 14 and over is 242.9 million (in 2006), this means about 27% of the postpubescent population has a viral STD, and 21% has herpes. If this is success, what does failure look like? Faced with these facts, only the hardhearted could deny that even a highly developed “safe sex” public policy is unable to contain STDs in the long run.

Indeed, with the prevalence of herpes exceeding 20% in the U.S., condoms can no longer serve as an effective means for containing the epidemic, because their failure rate is not low enough to stop the spread of the disease among promiscuous people. With an average of at least 1-2 failures per year even when used properly, it is only a matter of time before someone with multiple partners in an exposed community becomes infected. This is not to say that condoms are altogether ineffective, but they can only slow the epidemic, not stop its spread.

Emphasis on condom use rather than reforming behavior is predicated on the assumption that it is difficult or undesirable to get people to change their sexual behavior. However, the entire enterprise of promoting prophylactic use involves getting people to do precisely that. There is no reason in principle why the same educational effort could be applied to encouraging people to at least limit their number of partners, if they cannot be absolutely monogamous. When sexual disease is highly prevalent, it is utterly misleading to claim that promiscuous behavior is “safe sex” when condoms are used. Risk is best minimized by knowing one’s partner well, and limiting changes in partners as much as possible. While this should be obvious, it has not received due emphasis in public health education. This reticence may be grounded more in the liberal sexual morality of policy makers and educators than in sound reasoning.

It has been known for ages that promiscuity is at the root of “social diseases.” Historically, these diseases had been marginalized in Europe and her colonies, confined mainly to the indecent practitioners of prostitution, adultery and fornication. With the destigmatization of these practices, sexual disease has gone into the mainstream, and will likely remain there as long as people fail to maintain a salutary monogamy, or at least a very limited polygamy. Long-term monogamy or limited polygamy has been the dominant paradigm of most human cultures for good reason, and has survived the test of experience. It is bad policy not to discourage foolish behavior, and even worse to tacitly encourage it, by claiming that it can be made safe.

Modern Western medicine has become notoriously negligent in addressing the behavioral causes of disease (e.g., nutrition, exercise, sleep), and instead increasingly emphasizes the use of expensive drugs and devices to address maladies after the fact. We see the same approach with sexual diseases: the solution is in a device that can be bought and sold, rather than in correcting behavior, which costs nothing, but requires patience and a modest amount of discipline.

None of this implies that prophylactics play no role in solving the STD problem, for they do indeed reduce the rate of transmission. For this reason, many contend that it is injurious for religious organizations like the Catholic Church to oppose the use of contraceptives, and effectively encourage the spread of disease. However, the same religions that oppose contraceptives also condemn adultery, fornication, and prostitution in even harsher terms. It is hard to believe that there are people who would have no qualms about committing the major offenses of adultery, fornication or prostitution, yet scrupulously heed their church’s strict teaching against contraception while committing those acts. Those who flout their church’s teaching on marital fidelity will almost certainly have no scruples about using contraceptives.

This appears to be borne out by religious statistics: only 20% of nominal Catholics in the U.S. (1999) accept official Church teaching against contraception, which is consistently the least popular of any doctrine surveyed (even less so among youth), being held only by the most scrupulously orthodox. By contrast, 68% accept that a Catholic must have his marriage sanctioned by the Church. The idea that religious teaching against contraceptives encourages STDs rests on the fallacy of divorcing such injunctions from the context of their full sexual ethic. I have yet to hear of any Catholics who heed Humanae Vitae yet live promiscuously (if such a thing were possible), so I must dismiss this as a straw man.

The fallacious argument above is made possible by a stubborn refusal to acknowledge the association between promiscuity and venereal disease.
This is evident in educational propaganda, where even monogamous intercourse is depicted as unsafe if lacking a condom, while promiscuous acts with a condom are safe. This completely inverts the actual degree of statistical correlation, and is therefore antithetical to the facts. How will a monogamous person magically acquire an STD? If the spouse is covertly unfaithful, any disease contracted through adultery will be passed on anyway when the couple tries to conceive. Many health educators not only neglect, but studiously avoid making a correlation between promiscuity and STD. By giving the false assurance that condoms are effective protection for a promiscuous person when disease prevalence is high, such educators are effectively prescribing the disease that it is their duty to prevent, by encouraging the behavior that is at its root.

Sharia and the Weberian State

The brouhaha raised in Britain over the Archbishop of Canterbury’s suggestion that sharia law be partially legitimized has exposed the statism at the core of secularism and the fragility of the truce that traditional cultures have made with one another through liberalism. Secularist peace comes at the price of ethnic and religious identity; man is freed from his church and neighbor only to be enslaved by the state, which claims unlimited jurisdiction over civil society.

Several forces combined to create the excessive reaction to Archbishop Rowan Williams’ comments. First, sharia itself is popularly demonized as being brutal or barbaric, in the sense of endorsing draconian violence and not respecting liberal ideals regarding gender equality, apparently forgetting that these are less than a century old, and we can hardly expect all rational people to share our arbitrary mores. This line of criticism ignores the fact that Dr. Williams only proposed applying sharia in the way that Jewish courts are applied to financial and marital contracts, as a civil arbitration agreed to by both parties, so there is no question of coercion. Further, as Dr. Williams points out, sharia is not a monolithic system of law, but a method of jurisprudence applicable only to Muslims who voluntarily submit to the law, so it is not incompatible with pluralism.

Another point of criticism is found in the Archbishop’s astonishing statement that for citizens “to be under the rule of the uniform law of a sovereign state” with all other commitments being private in character “is a very unsatisfactory account of political reality in modern societies.” He attacks the heart of liberal political theory, which takes pride in equality before the law, without regard for personality. Before the so-called Enlightenment, political philosophy was more sophisticated on this point, recognizing that laws ought to be tailored to local circumstances and customs, and that there is no one-size-fits-all system of government or law. This political wisdom was retained in the federal system of the United States in the nineteenth century, though this was gradually undermined in favor of a European model of increased centralization. The centralized state had expanded at the expense of local government and civil society long before the French Revolution; indeed, the revolutionaries simply inherited the marvelous administrative apparatus of the ancien regime. As liberal democracy spread, clerical and aristocratic privileges were abolished, so all political power was consolidated in the state. In the process, the state acquired powers historically foreign to it, including the regulation of marriage and private financial matters.

These historical developments have led to a profoundly statist European culture that views any attempt by businesses, churches, or other institutions to assert their legal independence as cause for alarm. In the case of churches, a panic over theocracy arises whenever a church refuses to submit to the generic morality of the state. Such fears are thoroughly irrational, as the state, being far more powerful than any church, is a far greater threat to liberty than any ecclesiastical bogeymen. The masses flee the supposed tyranny of traditional institutions to labor under the much heavier yoke of modern government, which levies higher taxes than any ancient tyrant ever dared, and claims unlimited jurisdiction over all human affairs. This idolatrous concept of the state, circumscribed by neither natural nor divine law, was candidly described by Max Weber as the monopolization of the legitimate use of force, and of lawmaking. Today, the Weberian state so jealously guards its monopoly over violence, that it would pretend to have authority to decide whether parents may spank their children. Where one stands on such an issue is only of secondary importance; what matters is that the state actually claims the right to decide the issue, as for all human affairs. The state alone can coerce; the state alone can demand obedience, while other institutions only meekly request it of their members.

In the United States and much of the Americas, statist tendencies are checked by a robust cultural heritage of limited government, but in most of Western Europe, including Britain, statism is conventional wisdom. Indeed, the more stridently secularist parties tend to have the firmest conviction that the state ought to have plenary jurisdiction over civil society. The fatal mistake of statist liberalism is to mistake democracy as the basis of liberty, when the real basis of liberty is limited government. A state with absolute sovereignty is just as tyrannical whether it is monarchically or democratically constituted.

Rowan Williams has touched a sore nerve by pointing out that liberal democracy contradicts its promise of tolerance and multiculturalism by insisting on a uniform rule of law, without regard for what is reasonable in specific cultural contexts. By doing so, liberal governments deny many groups “the right to speak in their own voice”, as when they pass laws and rulings that admit no exception for religious conscience, defining their secularist views (often a minority opinion!) as the basis for what is reasonable, coherent and acceptable. It would seem they do not despise tyranny so much as they prefer their own sort of tyranny.

Archbishop Williams did not dare to suggest that the state’s sovereignty be circumscribed, but only proposed that people may voluntarily submit to other sources of authority. He is not ready to abandon the Weberian state, but even the concession that there should be any human authority besides the state is too much for many secularists to bear, even though in fact Britain already allows civil arbitration by religious courts. Hatred of religion is strong enough in some to make them forget their contempt of bureaucrats and strenuously endorse the monopoly of the state.

Just as the Romans subverted all local cultures and religions by including foreign gods in the Roman pantheon and requiring only that Caesar be worshipped universally, so too does liberalism undermine the freedom of local culture, as witnessed by the devastation of French and Italian rural cultures, replacing them with an increasingly amorphous, bland consumerism. The great paradox of the Enlightenment is that supposed political liberty has led to cultural homogenization, masked by a bewildering diversity of consumer goods. This is because the only social mores that are enforceable are those of the state. With the magnitude of modern states, an individual’s vote counts for practically nothing, and in fact he can do little to alter the bureaucratic system in which he is enmeshed. He is nominally a citizen, but practically a subject, and if he calls himself an atheist, he should be humbled to learn he is no less a slave of Caesar than the most superstitious pagan.

In addition to the issues raised by Dr. Williams, sharia presents a special challenge to the West in that it does not recognize a neat distinction between religious and civil law (a medieval European development), much less a Weberian concept of the state and civil society. In Islam, society is an integrated whole. One does not need to share this holistic view of society to present a stumbling block to the liberal model; one only needs social principles at odds with those of the liberal state. The social peace of liberalism is a sort of devil’s peace where all one’s enemies are dead or enslaved, as all institutions are silent before the overwhelming force of the state (or more realistically, the state and its friends in the private sector). The Weberian state can make life materially pleasant, but woe to the one who conscientiously prefers a distinct set of social principles, not to be relegated to the ghetto of “private” activity.