Posted 4:40 PM by Robert

Relative Miracles

Lodged in rubble and narratives of the disasters now nearly a year old are events seen by Peggy Noonan and some others as possible miracles, such as the discovery of a cross formed from fallen girders, as well as many individual stories of apparently miraculous escapes and human bravery. And where people consider miracles they nearly always consider God, who Ms. Noonan also writes was brought "Back" to New York by the tragedies. In this sense, miracles - or possible miracles - bring people to God, like horses to water. Ms. Noonan notes, for example, that her teen age son thinks hilarious her thoughts of the miraculous.

A year later it is natural and appropriate to remember the events of last September 11 elegaically, at least if one does it as well as Peggy Noonan. But it is not the only way to remember. So while it is natural and appropriate to remember elegaically, I want to remember with some modest personal thoughts on what a miracle is or might be.

It's often convenient to start an analysis with a definition, if only as a sacred cow to pat as one passes by. Unsurprisingly, "miracle" has many definitions to pat. One could look to the Bible. ("Miracles are those acts that only God can perform; usually superseding natural laws. Baker's Dictionary of the Bible defines a miracle as 'an event in the external world brought about by the immediate agency or the simple volition of God.'") Similarly, St. Augustine (354-430) defined a miracle as anything that happens "contra quam est nota natura" (in defiance of natural laws known to us). One could consider "miracle" as a term employed to discuss a supposed competition of science and religion. ("Let us define a 'miracle' simply as an event which violates at least one law of nature. ...[I]t is sometimes additionally required that miracles be caused by a supernatural being. For our purposes and in the interest of economy, that further requirement can be dispensed with. Alternatively, a miracle is sometimes taken to be any extraordinary event, particularly one that provides someone with a great benefit.") One could consider definitions which in themselves prohibit the recognition of miracles. David Hume claimed that miracles were impossible events and therefore did not happen as there is no way to prove their existence

But a definition is a tool, and I want to my own tool, which I call "relative miracles." Starting with any set of logically consistent principles (say, some formulation of modern science), then a miracle relative to those principles is defined to be an event that is not determined (that is, predicted) by applying those principles to the state of the world prior to such event and could not be determined by application of any consistent extension of those principles to the state of the world prior to such event. Specifically, a miracle relative to modern scientific principles is an event not determined (or predicted) by applying modern science to the state of the world prior to such event - and which could not be determined by application of any consistent extension of modern science.

Miracles relative to scientific principles do not have to violate any such principle (remember, this is by definition). So they need not satisfy St. Augustine's requirement of "contra quam est nota natura." Instead, such a relative miracle merely has to be not determined (predicted) by those principles - so in this sense my definition is weaker that St. Augustine's. But a "relative" miracle must also not be predicted by any consistent extension of scientific principles, regardless of whether those principles have yet been discovered. In this sense, the "relative" definition may be stronger than St. Augustine's, for example, since he seems to have restricted his considerations to "natural laws known to us".

It may also be worth noting that merely because a given set of principles is consistent with the later occurrence of a particular event, it does not necessarily follow that one could consistently add a definite prediction of that event to the original principles. For example, suppose a particular event (say, a meteor landing) actually occurred east of the Mississippi, but prior to the event a given set of scientific principles predicted that the event had a 50% chance of occurring east of the Mississippi and a 50% chance of occurring west of the Mississippi. The definite assertion that the event would happen east of the Mississippi is not consistent with the original principles because adding such an assertion is inconsistent with the conclusion that there is a 50% chance the event would occur west of Mississippi. On the other hand, if the original principles did not address the event at all, then one could consistently add a definite prediction of that event including its location to the original principles. In this sense, the "relative' definition of the miraculous avoids the famous objections of David Hume. The reader is invited to compare other defintions of "miracle" with the relative definition.

I think the relative concept of a miracle is important because people do not start from a blank slate in assessing unusual events, and for several centuries now there has been a perceived displacement of the religious - especially the "miraculous" - by scientific principles. So it seems worth while to ask: are there events whose full explanation is necessarily denied to us even in principle once we accept modern science? As long ago as St. Augustine (in the Confessions, for example), serious religious thinkers have realized that no amount of reasoning could alone lead one to faith in God - reason's role was seen as limited to bringing one into a position for a separate and irrational "leap of faith." (This Augustinian realization was curiously rejected by St. Anselm's "ontological proof" of the existence of God. But that is another story.) For example, that acceptance of modern science may itself deny the possibility even in principle that certain events can be fully explained will not interest everybody, but it may intrigue a scientific skeptic who believes that “A miracle is nothing more than a natural law not discovered.”

Are "relative miracles" possible? They may be, at least relative to certain formulations of quantum mechanics. Albert Einstein famously exhaled in skepticism over the indeterminism of at least the so-called "Copenhagen interpretation" of quantum mechanics that "God does not play dice with the universe." He was reportedly hopeful that the probabilistic conclusions and theories of quantum mechanics might be completable by a (possibly deterministic) subquantum theory explaining individual measurement results. That is, Einstein was hoping for a "deterministic hidden-variables" theory, that is, one in which the value of the hidden variable uniquely determines the measurement result. It was not to be - at least relative to the Copenhagen interpretation, which is non-deterministic, if one also believes in the principle that the "hidden-variables" cannot transmit information instantaneously (hidden-variables conforming to this restriction are called "local"). The Irish physicist Bell demonstrated that all local hidden-variables theories - including those needed to provide a deterministic foundation - are incompatible with quantum mechanics.

The "Copenhagen formulation" has been the formulation favored by most textbooks. But other, even deterministic, versions of quantum mechanics exist, including an impressive formulation by Bohm. Many scientists also believe that any meaningful hidden variable theory must be "local," and and nonlocality has not been experimentally demonstrated.

Of course, quantum mechanics famously concerns the action of very small objects. However, it is not hard to imagine that events on a molecular level - especially if the molecule in question is DNA, RNA or the like - could have quite profound macroscopic consequences. Many a frisky young couple has discovered such things - or at least experienced the results of such things - for themselves. And more than one religion is based on the curious, particular qualities of a single baby.

Many topics related to the one discussed here are treated in the recent and beautiful book Quantum Mechanics: Scientific Perspectives on Divine Action.

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UPDATE: More elegaic, cold Noonan gold.