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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

Bin Laden’s Protectors in Pakistan

After a predictable wave of jingoistic euphoria, the death of Osama bin Laden has raised some troubling questions about Pakistan and discredited a lot of the previous conventional wisdom about his whereabouts. To summarize what we know:

  • Bin Laden was not constantly on the move, but had stayed in his final location for several years.
  • He was not in tribal areas near the Afghan border, but deep within Pakistan, not far from the capital.
  • He was in fact still operationally involved with al-Qaeda. He was by no means so preoccupied with evading detection that he could not continue to act as leader.

Regarding the U.S. operation against Bin Laden, it should be clear this was a “kill” mission from the beginning, as the original plan was to destroy the compound with a missile attack. It is hardly credible that trained SEALs would take a head shot to incapacitate an unarmed man if “capture” was a primary objective, rather than a contingency. The U.S. probably wants to minimize blowback by downplaying the cold-blooded nature of the assassination. Most noteworthy is how Obama’s bold disregard for Pakistani sovereignty (as promised in 2007) is praised even by liberals, as his predecessor Bush succeeded in raising American tolerance of overt imperial posturing. The world is our playground, so it seems.

What of the Pakistanis? It is clear by now that, contrary to Sec. Clinton’s initial attempt to emphasize the cooperation of Pakistan, this had been an exclusively American operation for almost a year. The Pakistanis had no knowledge of CIA surveillance in Abbottabad, and they were given no advance notice of the SEAL operation. In fact, the only reason they found out at all was because one of the helicopters crashed. Even then, the SEALs were on the way back to Afghanistan by the time planes were able to scramble. No magical radar-evading or radar-jamming technology was needed, as the helicopters were shaped to leave almost no radar image if they fly low enough, and they could not be sighted visually at night.

Bin Laden certainly had a support network in Pakistan, and it is credible that this included current or former members of the Pakistani military and intelligence service, which are known to contain radical Islamic sympathizers. Still, the high command is of more moderate, secular leanings, which means there was certainly a major intelligence failure on some level if the leadership was unaware of Bin Laden’s presence. The sometimes clumsy surveillance methods of Pakistani intelligence are well attested. Still, the required level of incompetence is not so great as one might think, considering that fortified compounds are commonplace in that part of Pakistan, and that the Americans entertained doubts about the compound for nine months before deciding there was enough evidence to act. The only reason they even found the compound was because they knew the identity and location of Bin Laden’s courier, who took great precaution not to leave an electronic trail to the hideout. Any official Pakistani support received must have been at a low level, judging from the negligible number of armed guards.

As for the civilian government, there is little reason to doubt that Zardari had no knowledge of any coverup, but he is a relatively weak leader in a country dominated by its military establishment. More than three years after the assassination of his wife lifted him to the leadership of his party on a surge of sympathy, the current president has sought to distance himself from his corrupt past, which earned him the nickname of “Mr. Ten Percent,” only to find a more dangerous situation in Pakistan, where top-level terrorists can operate with near impunity, under the noses of the military and security establishment. He is in the difficult situation of simultaneously claiming ignorance and competence.

The U.S., for its part, may be losing its propaganda touch, judging from its weak attempts to spin the released Bin Laden videos. “He dyed his beard and watched himself on television? How vain!” (Either that or he was trying to remove time indicators from his videos and learn what information the press had on him.) “He wore a blanket because he was cold? How frail!” If this is really the best they can do, then there is not much left of the American propaganda machine that Goebbels so admired. Still, even in their prime, Americans have had little of that Roman virtue of recognizing valor in an adversary (apart from the Civil War, where the enemies were Americans). If all our enemies must be cowardly and weak, it is remarkable that we expect to be praised for our victories.

Reflections on Egypt

As a rule, the masses will not revolt against even the worst government unless they are starving, and Egypt is no exception. Having endured the unpopular Mubarak regime for 30 years, Egyptians did not suddenly discover the internet or develop a stronger taste for democracy. What has happened in recent months is that food prices have escalated without an increase in government food subsidies, bringing an already impoverished society to its breaking point.

A nice graphical depiction of Egypt’s food and energy crisis can be found at The Oil Drum, showing how Egypt’s increased oil consumption is leading it to become an oil importing nation for the first time. Without the windfall of oil export revenues, the government can no longer subsidize its failed domestic economy to alleviate the cost of food and other necessities. Egyptians literally have nothing to lose by resisting a government that has denied them the means of subsistence.

Egypt’s problems are an extreme form of similar problems held throughout the Middle East, as global oil exports are down, and many Arab governments find themselves too cash-strapped to keep their populations fed by subsidies. Only in such extremes do we find genuinely spontaneous mass movements from the bottom up, which are not orchestrated by any political or military cadre. The success of the Egyptian revolution in a mere 18 days has removed the biggest obstacle to mass revolt, namely the fear that there is no chance of success.

Ironically, most of the Arab dictatorships came to power by leading populist movements that toppled Western-backed monarchs in the 1950s and 60s. Several of these regimes, facing the same economic problems as their predecessors, eventually became dependent on the US or the USSR for military aid in order to secure their rule. The nations with greater oil wealth could afford to deliver economic improvement to the lower classes, which was generally implemented through socialistic or statist programs. The inefficiencies of socialism led to attempts at privatization reforms, such as those enacted by Mubarak, but the implementation of these reforms reeked of cronyism and corruption, offering little tangible benefit to the lower classes.

The mass revolutions in Egypt and elsewhere have no discernible political program other than to get rid of the existing failed regime. It is by no means guaranteed that the long-term result of these revolutions will be parliamentary democracy. After all, that had been the intent of the 1952 revolution that resulted in Nasser taking charge of Egypt. The present Egyptian military has disavowed any intent to rule, but even civilian leadership in the Middle East often proves reluctant to relinquish power, once obtained. Whatever the form of the new government, it will face the same structural economic and social problems that brought down the previous regime, and free elections will not bring any miraculous solutions. Both the market economy and the social welfare state can bring their fair share of ills, as the wealthy nations of the West have recently learned or re-learned.

Much has been said of the role that so-called “social media” played in the Egyptian revolution. Such tools were undoubtedly helpful in coordinating mass revolts without the help of structured leadership, but they would have come to nought if there was not a broad determination among the people to persevere in their protests. The Egyptian government was astoundingly successful, from a technical perspective, in shutting down the Internet for five days, yet the protests persisted with even greater fervor and finally the government relented. Shortly after the revolution, Syria actually liberalized internet access, realizing that its suppression would only give the people one more occasion for discontent, as if you had cut off power or water or any other utility. The Internet does not create revolutions, but gives voice to discontent that is no less real if the nation is unplugged.