Searching for the Sword of the Cherubim

So he drove out the man; and he placed at the east of the garden of Eden Cherubims,
and a flaming sword which turned every way, to keep the way of the tree of life. - Genesis 3:24

So concludes the brief story of humans in Paradise as related in Genesis. The rest of the Bible is concerned with human history and redemption in a fallen world. Cherubim do reappear as artwork on the Ark of the Covenant, and as angelic creatures in Ezekiel, but the flaming sword is not mentioned again, although it is implied to be present so long as this world endures.

In an age which has seen expeditions searching for the remains of Noah's Ark, one might expect that someone would have sought some manifestation of this flaming sword as a clue to this story of Paradise. However, if such an effort has been made, it has not been covered extensively enough to leave a public impression.

On the other hand, this does not mean that such a structure does not exist. It is the premise of this essay that within the last century that we have indeed become aware of something fitting the sword's description in Genesis. However it is so grand in scope, and so omnipresent, that the similarities have been overlooked. Yet, it not only has the properties suggested in Genesis, but it has additional traits which could be said to render this world less than Paradise. Furthermore, it may suggest ways in which the story of Genesis can be reconciled with the world described by modern science.

The Light Cone

Following Einstein's development of the Special Theory of Relativity in 1905, Herman Minkowski demonstrated that the theory could be pictured in a particularly elegant way by considering space and time as a unified, four-dimensional structure. Time is added to the common three dimensions of our everyday spatial experience, and the resulting four-dimensional spacetime is now viewed as the fundamental container of our reality, or our world.

In this four-dimensional structure, there exists at every point, a structure now known to physicists as the light cone. According to physics, all electromagnetic radiation emitted at a point will pass along the forward cone into the future. All such radiation received at a point passes into the point from the past along the backward cone. Heat and light (flame) are forms of electromagnetic radiation. In a very real sense, the cone's surface flames. Furthermore, as pictured in our three-dimensional space, the radiation leaving an open flash at a point is emitted in every direction, and so it turns every way. As already noted, in the broader four-dimensional view, the cone is also present at every point, or everywhere in our universe.

But what about keeping the way? Today, almost everyone will have heard of how Einstein's theory prevents travel faster than light. In terms of the light cone, this is equivalent to saying that any line inside the light cone which describes the possible motion of a physical object must always remain inside that object's light cone. No such trajectory can pass through the wall of its cone, and reach the region outside that cone (although a line for a separate object can pass through the walls of my cone, it cannot pass through the walls of its own cone). The wall of the cone really does represent a physical barrier that we cannot breach. That barrier also divides our experience into regions which must be in the future from those that must be in the past, and both of those regions are separated from an additional spacetime region which we can never reach. That last item even affects our notions of cause and effect in that we say we cannot affect events in that exterior region, nor can our point be affected by them. Equally important is the fact that we cannot twist a line around in four dimensions to travel first to the future, and then back to the past. To do that we would have to pass through the impenetrable walls of the cone, which we cannot do. Thus, we cannot warn the past about events in the future. In a very real sense, the light cone even defines our notion of time itself, and our concepts of cause and effect. It also leaves us vulnerable to the unexpected in the future¹.

Beyond restricting our motions in this world, it is worth noting that the light cone spans the entire known universe. It is a magnificent structure embracing all of the billions of galaxies with their billions of stars. It defines some of the most fundamental attributes of this universe. In its scope, it is truly an entity grand enough to be worthy of the Hand of God.

The Fall

If the light cone were to be identified with the sword of Genesis, then the narrative of Genesis suggests it was not always present². In order for any sense to be made of this, we would assume that "time" in the first few sections of Genesis is something quite different (perhaps some sort of hypertime) from time in the universe as we know it, because time as we know it is closely related to the light cone. Furthermore, cause and effect would not necessarily be perceived in the same manner either, without the light cone.

These points raise the image of the universe as we now know it as being some sort of exile realm, perhaps more akin to the walls of Plato's cave than as the fundamental seat of existence. Time as we now experience it, as well as cause and effect, would be like shadows of the world of the pre Fall realm. In this sense then, the models of our universe as conceived by science could be accurate within their own framework without being inconsistent with the narrative of Genesis. Our measure of time, and our perception of causes need not be the same as those of Genesis, without there being any contradiction.

In particular, the current debate over the accuracy of the Theory of Evolution may be misguided. The scientist may indeed accurately measure items that point to a planet Earth that is 4.5 billion years old in the time of this universe, as well as detect a long history of evolving life forms. Not only need these not be inconsistent with Genesis, but the entire concept of, "Survival of the fittest," can be viewed as an affirmation of the fallen state of this universe, and its separation from God. The believer need only contrast that law of nature with the injunction from both the 37th Psalm and the Beatitudes that, "Blessed are the meek; for they shall inherit the earth." In that verse, the faithful accept the fact that this world is not so structured as it stands now, and they look forward to a restoration of that higher law in a new Paradise.

¹In contrast, Genesis states that Adam and Eve were clearly warned of consequences to be expected from their actions.

²Interestingly enough, it is possible to form a consistent theory of electromagnetism without a light cone.

No endorsement of this essay by any websites referenced within is implied.

Interview with Schoenborn

Beliefnet has an interview with Cardinal Schoenborn in which he further discusses his controversial op-ed piece.

Comments from Pope Benedict

Wednesday, Pope Benedict commented on the controversy concerning design or its absence in the universe. This appears to represent yet another step by the Vatican to participate in this debate. Earlier comments by Cardinal Schoenborn are noted in a previous post in this blog.

New Orleans

The past few days have stirred up memories of visits to New Orleans. I remember Mardi Gras, 1965, and a summer visit in 1966. I drove near there on Interstates 10 and 12 as recently as December, 2001, but didn't go into the city.

It's a beautiful, graceful city. My heart goes out to its people in this time, and to the people in Mississippi, Alabama, and other states who have also been devastated.

This disaster brings to mind a post by a friend last winter, after the Tsunami. He was quoting a friend of his who came upon the following lines from Habakkuk after 9/11:

"Though the fig tree does not bud
and there are no grapes on the vines,
though the olive crop fails
and the fields produce no food,
though there are no sheep in the pen
and no cattle in the stalls,
yet I will rejoice in the Lord,
I will be joyful in God my Savior."

Habakkuk 3:17 - 3:18

Sadly, his thoughts also seem to apply now, in this tragedy.

Free Will and Randomness

Since the concept of fundamental randomness arose in the previous post, I'd like to discuss a related concept, the notion that "free will" is somehow denied in a universe lacking randomness. The basic idea seems to be that if there is no randomness, then strict determinism will remove the possibility of free will, and reduce all consciousness to preprogrammed automatons. Indeed, it is my understanding that this view has been expressed by more than one theologian ever since the time of Newton. Some theologians seem to have welcomed the rise of the orthodox interpretation of quantum mechanics because they felt it somehow reintroduced a possibility for free will in the world. (I can't find any specific references right now).

I feel any such fear of "determinism" is misguided. To me, the flaw arises from assuming that some utterly separate higher law or power must be behind a universe that is deterministic, and that this amounts to a denial of any free will to the occupants of that world. But I don't agree with that underlying assumption.

Instead, I visualize the souls that inhabit the universe as being an integral part of the higher power and laws behind the universe. As such, they are part of the "determining" spirit, and thus freely participate in the determination of the resulting creation. By this process, they retain free will. Furthermore, I perceive this as an organic four dimensional process (time as the fourth dimension), not one limited to the three dimensions of space at separate instants in time. Thus, even if the future were to be revealed as "definite" (by physical law, or even "fate" and prophecy), that "definiteness" was achieved with the cooperation and input of the souls involved, still acting "freely" across the spacetime continuum. I suppose this viewpoint again involves the idea that time itself may be in some way an illusion. It may also be more feasible in a continuous field model of nature, as opposed to a discrete particle model.

I hope that all makes sense. I had to wrestle with those issues when I first studied physics, and heard the objections that determinism removes free will. The above is my own response, and arose because I personally disliked the orthodox interpretation of quantum mechanics, but I believed in free will. To reconcile those viewpoints, I contemplated the above "organic" outlook on free will and determinism.

The other side of the coin is that fundamental randomness in nature is often no longer described so much as justifying free will as it is used to picture creation as mindless, and even pointless. I think that was always the trap lurking in an attempt to defend free will via a belief in fundamental randomness in nature.

New York Times Op-Ed Piece on Evolution

Last week, Christoph Schoenborn, the Roman Catholic cardinal archbishop of Vienna, wrote a New York Times op-ed article discussing the views of Pope John Paul II on evolution and intelligent design. This article triggered an immediate follow-up news story in the New York Times the following day discussing the ramifications of Cardinal Schoenborn's op-ed article.

The key thought in the op-ed article seems to be summarized in the statements, "Evolution in the sense of common ancestry might be true, but evolution in the neo-Darwinian sense - an unguided, unplanned process of random variation and natural selection - is not. Any system of thought that denies or seeks to explain away the overwhelming evidence for design in biology is ideology, not science." This is reexpressed in several similar statements in the op-ed piece. To me, the word "random" is a key factor in these thoughts, so I'd like to dwell on that term, and the idea that randomness is somehow fundamental in scientific explanations.

This assumes first of all that any fundamental randomness in biological processes requires an irreducible element of randomness in the underlying physics. Conversely, if the laws of physics exclude fundamental randomness, then the appearance of randomness in biology presumably becomes dependent upon some fundamental inability to apply the laws of physics to biological systems. While chaos theory may take some stands on this, I will assume here that fundamental randomness in physics is required to have fundamental randomness in biology.

Now in fact, mainstream modern physics does embed randomness at a fundamental level in its explanations of microscopic events. Almost from its inception, quantum mechanics has claimed an irreducible element of probability in its laws via the orthodox, Copenhagen interpretation of the equations. This stipulates that the equations can only predict the probabilities of outcomes, and that no deeper theory is possible which eliminates this uncertainty.

Yet some of the best minds of the twentieth century rejected this school of thought, men like Einstein and Schroedinger, both among the founders of quantum theory. Einstein's comment, "God does not throw dice with men," is famous. And Schroedinger, the inventor of wave mechanics, sided with Einstein after an initial period of hesitation. Neither man ever gave up their convictions on this.

In Einstein's case, his criticism was twofold. First he attacked the orthodox view by pointing out the bizarre consequences of its predictions. When so called "entangled" particles are measured after substantial separation, orthodox quantum mechanics predicts a "spooky" action at a distance phenomenon that he thought was unacceptable. Ironically, recent experimental work validates this spookiness. The apparently bizarre results have been detected.

But in his own approach to physics, Einstein incorporated a much deeper rejection of the orthodox view. Instead of postulating the existence of particles, he insisted that the fundamental objects in his theories must be smooth, fluid-like fields, including even the distributions of charge and mass. He attempted to derive the discrete or particle-like properties of matter from such a theory, and hoped that a property of his equations called nonlinearity would help produce those properties. His fellow scientist Schroedinger pursued an almost identical path and hope. In both cases, the theories would presumably leave open the possibility that the field-like entities would actually be able to physically participate directly in entanglement by virtue of their smeared out distributions prior to measurements on them. Probabilities are not involved because the item requiring the probabilities, for example the "particle" location, may not even exist in a well-defined state prior to the nonlinearity introduced by the measurement. This effectively drops the concept of local realism as it exists in the classical mechanics of particles. Fundamental randomness then once again would vanish from physics, which becomes a physics of pure fields.

Neither man was able to demonstrate real success from their theories, and their approach was largely abandoned after Einstein's death. Yet, the effort that went into such theories without significant success was actually quite small by today's standards, perhaps less than a hundred man-years total. Who is to say if the approach is truly as barren as mid twentieth century physics assumed? At any rate, the point to note is that a belief in fundamental randomness in physical law still comes down to one's approach, and more than one approach still seems to be allowed. The well documented successes of quantum theory are successes of a set of equations, not necessarily the additional philosophy or interpretation which is normally attached to those equations. The claim of irreducible randomness is an element of the interpretation. To say that science has proven this existence of irreducible randomness is to confuse the accuracy of the mathematics with that of the philosophy surrounding it, and as we see with Einstein and Schroedinger, philosophy is still a matter of one's faith!

As an additional example of this, physicist J. S. Bell conducted one of the most detailed analyses of the spooky consequences of "entanglement" in orthodox quantum theory. Bell himself advocated another alternative to orthodox quantum theory called the Bohm interpretation. Moreover, when he tackled the problem of the "collapse of the wavefunction" which orthodox theory postulates occurs during a measurement, he speculated on the possibility of a more satisfactory theory of this. Rather than merely postulate wavefunction collapse in the emergence of a well-defined value in an experiment, he asked (in Speakable and Unspeakable in Quantum Mechanics) if the collapse could be incorporated into the equations of wavefunction evolution. This is an important point because without it, orthodox quantum theory largely simply postulates the existence and emergence of this "particle state" (the state which Einstein had sought to explicitly derive). Bell's comments are interesting. While no current theory is really successful at incorporating wavefunction collapse into the equations of motion, he speculated that nonlinear wave equations might have the best hope of success at this. But nonlinearity is precisely what Einstein hoped would help produce his particle states. Is there really that much difference between Bell's hope, and Einstein's approach? I don't think so, although they advocated very different models of reality overall.

In the end then, I say the question of irreducible randomness in physical law is still open, and still a matter of philosophy and faith. To say otherwise currently is to confuse philosophy and mathematics. Insofar as he rejects randomness as a factor in evolution, Cardinal Schoenborn is within his rights to follow his faith on that. Beyond that, we can all hope that further progress in physics will clarify this issue.

---Postscript: The more I read about this controversy over evolution, the more I suspect the "real answer" involves the nature of time itself. Is time itself some simple, fundamental, inescapable aspect of Creation? Or is it less than what it seems? Is it possible it is a very persuasive illusion, and that our secular "cause and effect" (or "random mutations and effect") are likewise illusions?

The Duration of "Eternity"

This topic stems primarily from a nonscientific moral issue that surfaces repeatedly in discussions and criticisms of the Judeo-Christian framework, the threat of eternal damnation and torment.

One of the most difficult things I had to deal with as a Christian in the early days of my experience was that concept of eternal damnation. If this has never bothered you, then I think either you don't take it seriously, or you don't take much of the New Testament seriously, such as, "Blessed are the merciful: for they shall obtain mercy."

Let me emphasize, we're not talking about simple justice, or punishment for bad deeds. We're talking about the idea of endless torture being heaped upon the heads of the damned. I could visualize plenty of reasons for pulling down evildoers, removing them from power, and administering justice. If there were absolutely no other possible course open, I could even visualize ending their existence completely to spare the next world their corruption. But I could never accept the concept of deliberately torturing any living soul after its fall for a never ending time period. That was, and is, non-saintly overkill to me.

So how do I still call myself a Christian? Of course, some might ask, how do people who unquestioningly accept the idea of applying such torture call themselves Christians? It's a real problem I think any serious Christian has to wrestle with at some point.

Let's ignore the possibility for the moment that "condemned" souls might freely choose a life separate from God, in a state that those who achieve Paradise might view as eternal torture, but which might be at least somewhat welcome to the condemned. I don't exclude this lightly, because I suspect it might have an element of truth to it, but there are other possibilities I wish to focus on here.

Let's also ignore for the moment those Christian sects that solve this issue by believing that essentially all souls eventually are saved. This too is worth discussing, but it is also not the main point that I wish to examine here. I wish to focus on some alterations to the concept of eternity made possible by modern geometry and physics.

Christian theology invokes "eternity" in several roles. We read of eternal paradise in the New Heaven and the New Earth. We read of this eternal torment for those who suffer the "second death". What do we mean by these statements? Do we really understand what we are referring to when we speak of these items? Perhaps not.

The honest answer is that we don't know if these terms imply some truly endless, euclidian, flat time, or whether at least some of them refer to non-euclidian paths, such as great circles on a sphere, which at least in some sense are finite in length. Non-euclidian geometry opens new possibilities for the concept of eternity itself.

More specifically, before the development of non-euclidian geometry, followed by general relativity, our notions of straight lines and distances were dictated by Euclid's geometry. A straight line could go on without end, and be infinite in length. We assumed there was one and only one line parallel to a given line passing through a point external to the line. And, time was considered to be an endless progression of instants along a simple euclidian straight line. Thus, eternity was an endless forever.

After general relativity, we learned of strangely finite times which appear infinite to others, particulary in the vicinity of black holes or "pits" in space which in some sense appear bottomless. And we learn that time may have an origin at the Big Bang, and could even end at a Big Crunch, although the Big Crunch now seems less likely, since recent observations have shown an accelerating expansion of our universe.

The first case arises for an object falling into a black hole (this example uses the Schwarzschild case). Outside observers will see this infall occur such that the object never quite reaches the event horizon, but instead gradually fades from view as its light becomes ever more red shifted as it appears to approach that horizon. That fade out appears to the outside observers to go on forever, but the infalling observers see no such barrier at the horizon. Instead they experience their infall in a simple finite time, and if the black hole is large enough, they will not even notice as they pass the event horizon. Of course, for the classical black holes such as a Schwarzschild hole, they will eventually approach a singularity, and be destroyed by tidal forces, but all that occurs in a finite time. If such holes turn out to be wormholes to other regions, the infalling observers -- like Dante and Virgil at the end of The Inferno -- may eventually even emerge elsewhere (but quite possibly in a shredded, primal state of matter and energy). The analogies with the "bottomless pit" of the Bible are interesting enough to consider, and the time scales actually experienced by those that transit such a pit are finite, while appearing endless outside.

Is such a device really a factor in those scenes from Revelations of "eternal torment?" Could that be a valid description, yet the experience still be finite for the "fallen?" I suggest it's worth considering. It's even worth considering if some spiritual rebirth is possible for those that take that path -- like the symbolic rebirth Dante and Virgil trace out as they ascend through the bitter bottom of Hell up to Purgatory.

We should remember that the Bible speaks of the end of time and the world, leaving us after all with a rather abbreviated "eternity" in this world, at least. We believe that the only endless (and perhaps timeless) world is the New Heavens and the New Earth. We should not assume a priori that any other "time" is really endless for its participants, not even in the bottomless pit, or perhaps especially not there.

Those who would quote the Bible to reject these possibilities should stop to consider a profound paradox found in Revelations. After we read chapter after chapter in which the "kings of the earth" are the servants of evil, and are overcome by the Lamb at the Second Coming, we reach the final verses of the Bible describing the new Paradise, and read in Revelations 21, verse 24,

"And the nations of them which are saved shall walk in the light of it: and the kings of the earth do bring their glory and honour into it."

The kings of the earth are evidently ultimately redeemed after all that drama of the earlier chapters. This is a beautiful mystery indeed!

Adam's "Rib"

Was a "rib" actually removed from Adam to create Eve? Seems ridiculous doesn't it? After all, males and females have the same number of ribs.

Or do they?

Females have 46 full blown chromosomes, including 2 X chromosomes, but males have 45, including 1 X chromosome, plus that shrunken little structure called a Y chromosome to bring their total to 46.

Is that Y chromosome the remnant of Adam's "rib"?

Before any females get too incensed by this idea, consider one of its implications. It would imply that before the removal of that "rib", Adam himself was what we would now call genetically female. Food for thought ...

Genesis 2:21-22
And the LORD God caused a deep sleep to fall upon Adam, and he slept: and he took one of his ribs, and closed up the flesh instead thereof;
And the rib, which the LORD God had taken from man, made he a woman, and brought her unto the man.

Theology for Physicists

The journal First Things has an interesting book review by Stephen M. Barr of a recent work by John Polkinghorne. I have used the title of the review as the title of this post.

Living in a "Simulation"?

While reading some of the reader comments on an MSNBC article on the possible future of human evolution, I ran across a link to an article by Nick Bostrom of Oxford University. Bostrom's paper includes many additional references, including one to an article by John Barrow.

Both of these last two articles raise interesting points about the consequences of sufficiently advanced cultures being able to simulate conscious creatures in simulated universes. The parallels with the world models of theology are noted. But there are also those who argue that such an ability to simulate consciousness in computers may never be developed. A summary of some counterarguments is discussed in a thread on Google.

To me, the issue becomes just what one means by the word "simulation". Since it is not clear just what "computer" could actually produce the above simulations, if any, we may be unfairly biasing the argument in advance to even use the word "simulation". In a sense, the shadows on the wall of Plato's Cave noted in a previous post might be called a simulation embedded in a higher reality. This brings us to a generalized concept of a simulation as being a "reality" which is not at the most basic level of reality possible. In other words, it is in some sense an image or a "world" created by a higher level of reality. I think that this concept of a simulation might include the world described by Christianity as the world we now live in, but in order to conclude that, I've stripped the word "simulation" of the mechanistic overtones we may normally associate with it.

In terms of Christian theology, Christianity promises us wholesale proof of the nature of our world in its prediction of the Second Coming. That event is to become the interface to the higher plane of reality of the New Heavens and the New Earth. Or as Paul states in First Corinthians 13, verse 12:

For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known.

Opening the Gates

A little over a year ago, a prison chaplain was a guest minister at a church I attended. He gave his prison sermon, about the harrowing of Hell on Black Saturday, as Christ breaks open the gates, and leads out all the captive saints. They were prisoners, and the parallels with prison inmates, and the emotional appeal to them, were obvious. He used lines from the Psalms to animate his description of angels celebrating Jesus smashing open the Gates of Hell:

Psalms 24:7-10
Lift up your heads, O ye gates; and be ye lift up, ye everlasting doors; and the King of glory shall come in.
Who is this King of glory? The LORD strong and mighty, the LORD mighty in battle.
Lift up your heads, O ye gates; even lift them up, ye everlasting doors; and the King of glory shall come in.
Who is this King of glory? The LORD of hosts, he is the King of glory.

When I first heard this sermon, I felt it it suffered from overstatement and hype. But in fact, his imagery was in the same tradition as the "cave" imagery of a previous post. Christian theology may in fact picture us all as "cave" prisoners in this world, with God as our only hope of escape. The Second Coming is all about the finalizing of that escape. This is the, "Patience and the faith of the Saints." The striking thing about Christianity is that it juxtaposes that hope of a return to Paradise over against the "primordial catastrophe" that separated us from God through the Fall. The imagery used by that minister was actually quite appropriate for a picture of the freeing of the souls of the faithful from this fallen world.

Evolution

The number one reported conflict between faith and science today is probably the (overly) sensationalized conflict over the Theory of Evolution.

There's a brief post on the Internet that suggests one possible road to resolving this conflict. Readers can view it for themselves. It may take a little background study for those unfamiliar with some of the scientific concepts, and in the end, it suggests the outlines of a model that may not please the "fundamentalists" on either side. But it may appeal to some of those who feel there is truth in both camps.

To me, this model suggests that both camps can be right in their basic points. The analogy is made to Plato's Cave, a situation in which the everyday "reality" is a mere shadow of a much higher reality. This suggests that good, careful science can be consistent and accurate in terms of its own framework, and yet the spiritual description of Paradise -- as is found in the first part of Genesis -- can also be true and consistent on its plane just as it is described.

On the other hand, this introduces the concept of a higher plane, something I'd guess many scientists will criticize as unnecessary and unscientific. And it also proposes that in the everyday plane of our existence that the Earth really is some 4.5 billion years old, something I'd guess many fundamentalists won't accept. Perhaps I shouldn't assume either of those reactions, but based on the debate in prior years, those are my best guesses.

However, the view of this world as a shadow of a higher realm is one with a long history in theology. As recently as last December, such a model was invoked in an article by David Hart in the Wall Street Journal on the tsunami, and the theology of a world where such events occur. A friend has included portions of that article in his blog, including the line, "Perhaps no doctrine is more insufferably fabulous to non-Christians than the claim that we exist in the long melancholy aftermath of a primordial catastrophe, that this is a broken and wounded world, that cosmic time is the shadow of true time, and that the universe languishes in bondage to "powers" and "principalities"--spiritual and terrestrial--alien to God." This is a direct reference to such a shadow world.

The Meeting of the Ways

The hope of this blog is to contribute to the dialogue and reconciliation of science and Christianity. There is a Bible verse that symbolizes this to me, in the story of Christ's entry into Jerusalem on Palm Sunday:

Mark 11:4 - And they went their way, and found the colt tied by the door without in a place where two ways met; and they loose him.

We who believe in both these pathways of human civilization are in many ways like this colt, tied in a place where, "two ways met". We hope to be loosed under God's guidance to proceed with scientific understanding into the Holy City of God.

This is not a course without disagreements and strife. In yet another Bible verse, we find similar symbolism, in the story of Paul's shipwreck:

Acts 27:41 And falling into a place where two seas met, they ran the ship aground; and the forepart stuck fast, and remained unmoveable, but the hinder part was broken with the violence of the waves.

And so we too may encounter stormy seas in this quest, and find our ship at risk from, "the violence of the waves." ...