Wednesday, October 28, 2009

Fabric of the Cosmos, chapter 2.

Here is the next installment in our study this fall/winter on quantum physics and Biblical faith. Chapter one was primarily an introduction. Chapter two begins looking at historical developments in cosmology and how thought about these discoveries evolved over time.

Brian Greene
Fabric of the Cosmos
Chapter Two: The Universe and the Bucket
Is space a human abstraction or a physical entity?

It's not often that a bucket of water is the central character in a 300 years long debate. But a bucket that belonged to Sir Isaac Newton is no ordinary bucket, and a little experiment he described in 1689 has deeply influenced some of the world's greatest physicists ever since.

The experiment is this: take a bucket filled with water, hang it by a rope, twist the rope tightly so that it's ready to unwind, and let it go.

At first, the bucket starts to spin but the water inside remains fairly stationary - the surface of the stationary water stays nice and flat. [Then] the water starts to spin, too. As it does, the water's surface takes on a concave shape, higher at the rim and lower in the center...

...the bucket of spinning water is extremely puzzling. And coming to grips with it, as we have not yet done in over three centuries, ranks among the most important steps toward grasping the structure of the universe.

Early efforts and understanding the cosmos were geared heavily toward describing philosophically and mathematically how things move and what things (if any) are real. Movement we can now describe mathematically all the way to the edges of the universe down to the probable movements of the tiniest sub-atomic structures. But the "reality" question has not been so easy to pin down. Just because something can be described mathematically does not mean it has a real, independent existence. As was mentioned in the first chapter, mathematical equations can show time going backwards, but can it really? Time seems to be stuck in forward motion. Understanding motion, then, is a key to understanding time and space. Early philosophers understood this, though it may be lost on today's public school students.

It has been argued by Zeno, an ancient writer, that neither time nor motion themselves are real. If you take a moment - any moment - you can divide it in half. And that half can be divided in half, and so on - ad infinitum. Ditto for distance. Zeno argued that you can never reach any destination, because you travel half the distance to it, and then you travel half of the next half, and half of that half, and so on again - ad infinitum - meaning you never get where you're going. Motion is an illusion (and therefore so is time). This called Zeno's paradox. The math/motion/time entanglement influence Jewish thinking on the subject, too.

From the Jewish Virtual Library:
On the subject of time, Jewish medieval philosophers were divided into two broad camps: Those who subscribed basically to the Aristotelian concept of time, and those who favored a concept that goes back ultimately to Plotinus. Included among the former are Isaac Israeli, Saadiah Gaon, Abraham ibn Daud, Maimonides, and Levi b. Gershom, and among the latter are Ḥasdai Crescas and Joseph Albo. Maimonides may be taken as representative of the first group and Crescas of the second.

Maimonides, whose discussion of time appears in his Guide of the Perplexed (notably, 1:73), accepts the definition of time laid down by Aristotle as "the number of motion according to 'before' and 'after'" (Physics 4:11, 219b). Time, therefore, is neither an independent substance nor identical with motion, although it is totally dependent upon the latter and constitutes an accident of motion, which is itself an accident of body or corporeal substances. Time, consequently, possesses only a quasi-reality. Not only is it an accident of an accident, but it is composed of a past that is gone, a future that does not yet exist, and a present that serves only as a limit between the two. Accordingly, Maimonides rejects the concept of time proposed by the Mutakallimun (see*Kalām ) who, basing their thought generally on the atomism of Democritus, maintained that time is composed of time-atoms or instants, which are real entities.

Despite Maimonides' basic agreement with Aristotle on the definition of time, he rejects the latter's attempt to prove the eternity of the universe from the nature of time, and argues instead that time came into existence with the creation of the universe. Prior to creation, God existed alone in timeless eternity, for inasmuch as God is absolutely incorporeal, He has no relation to motion, and consequently none to time.

Modern Rabbinic Judaism believes, however - based on Kabbalah - that God did move. In fact, God had to vacate an area, the void or womb of creation, in order to create. Until then, God's expanse filled all that is. After God "moved," there was the void - a place where God "was not." We can presume that after creation, God observes time, but is still not part of it. The Ain Sof is still outside the void, unaffected by space and time, which were both created. Creation set time and motion into their trajectories, or, as we might describe it, the Big Bang resulted in time having a certain forward momentum and the rules of physics were established that we perceive as motion began.

Relativity Before Einstein

Velocity - the speed and direction of an object's motion - is relative. Motion has meaning only in a relational sense. An object's velocity can be specified only in relation to that of another object.

Of course, there are circumstances under which your motion seems intrinsic, when you can feel it and you seem able to declare, without recourse to external comparisons, that you are definitely moving. This is the case with accelerated motion - motion in which your speed and/or your direction changes.

Even if your eyes are closed, you know you're moving, because you feel it. Thus, while you can't feel motion with constant speed that heads in an unchanging straight line trajectory - constant velocity motion, it's called - you can feel changes to your velocity.

What is it about changes in velocity that allows them to stand alone, to have intrinsic meaning? If velocity is something that makes sense only by comparisons - by saying that "this" is moving with respect to "that" - how is it that chages in velocity are somehow different, and don't also require comparisons to give them meaning? In fact, could it be that they actually do require a comparison to be made? Could it be that there is some implicit or hidden comparison that is actually at work every time we refer to or experience accelerated motion?

If velocity is not constant, with respect to what or from whose viewpoint is it not constant?

Newtons studied the Bible for years, and spent the latter portion of his life dissecting scripture for the "secret code" which he believed was contained in it that would explain all of creation. It is therefore worth noting here that Newton had a bias, a big one, in all his investigations into mathematics and physics - he believed in God, an outside observer. His conclusions were necessarily colored by his personal beliefs about God (as are all scientific and philosophical writings) - and his concept of God was the result of his childhood, his religious teachers, his personal understanding of scripture, and his personal religious philosophies on a variety of subjects. And the understanding of God held by persons of his era were colored by ideas such as the "watchmaker" and Calvinism - a very deterministic view which while understandable, is very likely completely wrong.

The Bucket

Newton was grappling with the very foundation of motion and was far from ready to accept that accelerated motion, such as spinning, is somehow beyond the need for external comparisons.*

*footnote: The terms centrifugal and centripetal force are sometimes used when describing motion. But they are merely labels. Our intent is to understand why spinning motion gives rise to force.

In totally empty space - no sun, no earth, no air, no doughnuts, no anything - what could possibly serve as the "something" with respect to which the bucket is spinning?

He answered by fixing on the ultimate container as the relevant frame of reference: space itself. He proposed that the transparent, empty arena in which we are all immersed and within which all motion takes place exists as a real, physical entity, which he called absolute space.

It's the "something" he proposed that provides the truest reference for describing motion. An object is truly at rest when it is at rest with respect to absolute space. And most important, Newton concluded, an object is truly accelerating when it is accelerating with respect to absolute space.

Space itself provides the true frame of reference for defining motion.

Newton, as someone who believed in God, believed in an impartial observer outside of space and time - but then, as now, you can't say that and still have "credibility" in the scientific community. The Enlightenment Era was all about throwing off the "oppression" of religion and embracing a rationalistic point of view - a scientific point of view which states only things which can be measured and observed and "proved." (Of course, we now know that getting data and reaching correct conclusions from it are two ENTIRELY different things - LOL.) But getting back to the point, Newton "needed" to maintain that the universe is "fixed" and that lack of a human observer or human reference points was no barrier to accurate measurement or experience. By substituting "space" for "God," Newton filled his need and retained credibility. He could not at that time have entertained the idea that God allows things to happen, that the future and all of creation is not "fixed" in concrete. His belief that God micro-manages and that everything is predetermined made him decide that space, as an aspect of time and motion (read "future events as described in prophecy and scripture"), must be predetermined down to the tiniest atom, also.

But what is absolute space, really?

Newton's next words have become famous. "Absolute space, in its own nature, without reference to anything external, remains always similar and unmovable." That is, absolute space just is, and is forever, period.

So Newton leaves us in a somewhat awkward position. He puts absolute space front and center in the description of the most basic and essential element of physics - motion - but he leaves its definition vague.

He had to, of course. He couldn't explain how time and motion could be fixed by God but not space, and didn't want to invoke God in his arguments - hence, the vagueness.

Space Jam

The struggle to come to grips with the meaning of space is an ancient one. Democritus, Epicurus, Lucretius, Pythagoras, Plato, Aristotle, and many of their followers through the ages wrestled in one way or another with the meaning of "space." Is there a difference between space and matter? Does space have an existence independent of the presence of material objects? Is there such a thing as empty space? Are space and matter mutually exclusive? Is space finite or infinite?

Should we ascribe an independent reality to space, as we do for other, more ordinary material objects...or should we think of space as merely a language for describing relationships between ordinary material objects?

Leibniz...firmly believed that space does not exist in any conventional sense. Talk of space, he claimed, is nothing more than an easy and convenient way of encoding where things are relative to one another.

According to Leibniz, if all objects were removed from space - if space were completely empty - it would be as meaningless as an alphabet that's missing its letters.

Ah, Leibniz. Those were his younger days. In 1676 he traveled to the Hague for one purpose: to meet the Heretic, Baruch de Spinoza.

From The Courtier and the Heretic, by Matthew Stewart:
Spinoza did not invent the modern world, but he was perhaps the first to observe it well. He was the first to attempt to answer the ancient questions of philosophy from a distinctly modern perspective. In his philosophical system, he offers a concept of God befitting the universe revealed by science - a universe ruled only by the cause and effect of natural laws, without purpose or design. He describes what it means to be human after our pretension to occupy a special place in nature has been shattered...

Leibniz, on the other hand, seems to have more in common with Newton after his meeting with Spinoza:

Analysis of his unpublished writings makes clear that a decisive change in the tone and substance of his reflections occurred within days of his visit with Spinoza...

In large part as a direct result of his meeting with Spinoza, Leibniz came to represent his own original and antithetical response to the challenges of the modern era. In his philosophical writings, he articulates a strategy for recovering something of the old ideas about God and man by means of an analysis of the limits of reason. He claims to discover the meaning and purpose of life in all that modernity fails to comprehend.

Leibniz, like all other philosophers and mathematicians and scientists the world over, let his preconceived ideas influence the outcome of his supposedly impartial scientific work. Spinoza was formally declared apikorus by a bet din and excommunicated from Judaism long before Leibniz met him. But somehow Leibniz came away from that meeting convinced Spinoza was wrong, and Newton had been more correct (if not actually right).

While all this is interesting, knowing the biases of various writers and thinkers for or against religion doesn't really help answer the nitty gritty bolts and nuts of cosmology. Greene continues:

What is the location of the universe within space? If the universe were to move as a whole - leaving all relative positions of material objects intact - ten feet to the left or right, how would we know? What is the speed of the entire universe through the substance of space? If we are fundamentally unable to detect space, or changes within space, how can we claim it actually exists?

Newton argued that the existence of absolute space does have consequences that are observable: accelerations, such as those at play in the rotating bucket, are accelerations with respect to absolute space. Thus, the concave shape of the water, according to Newton, is a consequence of the existence of absolute space.

In one clever stroke, Newton shifted the debate about space from philosophical ponderings to scientifically verifiable data. The effect was palpable. In due course, Liebniz was forced to admit, "I grant there is a difference between absolute true motion of a body and a mere relative change of its situation with respect to another body." This was not a capitulation to Newton's absolute space, but it was a strong blow to the firm relationist position.

Yes, in due course, Leibniz had to backtrack a bit. If he had held to his earlier course, he would have found himself in the same camp as Spinoza - and he wasn't, upon reflection, ready or willing to completely toss God out of the picture. And we should not be, either. Not to get ahead of ourselves, but quantum physics makes more scientific room for God than any previous paradigm of space and time before it.

Mach and the Meaning of Space

According to Newton, while you are certainly free to contemplate the world from any perspective you choose, the different vantage points are by no means on an equal footing.

Our perspective of anything is necessarily not 100% correct or true. "Radical subjectivity" is the position that the human mind is simply not capable of seeing things 100% accurately. In Greene's text, the example of an ant's perspective versus a person's perspective is discussed. But many secular humanists today claim that "scientists" by definition have some sort of superior perspective to persons of religious faith. As we saw in the example of Leibniz above, and the example of the hundreds of organic biologists, physicists, and other "scientists" who maintain their belief in God, all persons are subject to biases - and those who have a vested interest in "getting rid" of God often rely on feelings rather than facts. They "feel" that they don't want to obey God, therefore they look for justification to not have to. That's not science, that's adolescence.

And the idea that things are fixed in concrete is also somewhat adolescent, as teens often don't think of the long term affects of what they're doing. They are now young, healthy, and carefree and therefore always will be in their minds. And their simplistic and idealistic views of the world are, to them, crystal clear and obviously correct. But eventually, they learn - often in the school of hard knocks - that things are not black and white, nor set in concrete. So also did the adolescent age of science where everything was black and white give way to a less fixed, less absolute idea of the universe.

Accepting Newton's absolute space meant accepting an absolute conception of acceleration, and in particular, accepting an absolute answer regarding who or what is really spinning.

Why wouldn't relative acceleration, like relative velocity, be the only thing that's relevant when considering motion at velocity that isn't constant? The existence of absolute space decreed otherwise, but...this seemed thoroughly peculiar.

Beyond the intuitive sense that no perspective should be "more right" than any other, and beyond the eminently reasonable proposal of Leibniz that only relative motion between material objects has meaning, the concept of absolute space left many wondering how absolute space can allow us to identify true accelerated motion, as with the bucket, while it cannot provide a way to identify true constant velocity motion. After all, if absolute space really exists, it should prove a benchmark for all motion, not just accelerated motion. If absolute space really exists, why doesn't it provide a way of identifying where we are located in an absolute sense, one that need not use our position relative to other material objects as a reference point? And, if absolute space really exists, how come it can affect us (causing our arms to splay if we spin, for example) while we apparently have no way to affect it?

In other words, how can God affect us but we cannot affect God? It's so inequitable that it should not be. And if it should not be, then it must not be. And if it must not be, then it isn't. Right?

[In] the mid 1800s, the Austrian physicists and philosopher Ernst Mach came on the scene.

Might Newton have kicked the bucket aside with such ease that he skipped too quickly over the relative motion we are apt to invoke in real life, such as between the water and the laboratory, or the water and the earth, or the water and the fixed stars in the sky? Might it be that such relative motion can account for the shape of the water's surface, eliminating the need to introduce the concept of absolute space? That was the line of questioning raised by Mach in the 1870s.

Imagine now that you are immersed in the blackness of completely empty space: no starts, no galaxies, no planets, no air, nothing but total blackness (a real existential moment). This time, if you start spinning, will you feel it? Will your arms and legs feel pulled outward? Our experience in day to day life lead us to answer yes: anytime we change from not spinning (a state in which we feel nothing) to spinning, we feel the difference as our appendages are pulled outward.

But the current example is unlike anything any of us has ever experienced. In the universe as we know it, there are always other material objects either nearby, or at the very least, far away (such as the distant stars), that can serve as a reference for our various states of motion. In this example, however, there is absolutely no way for you to distinguish "not spinning" from "spinning" by comparisons with other material objects - there aren't any other material objects.

Mach took this observation to heart and extended it one giant step further. He suggested that in this case there might also be no way to feel a difference between various states of spinning. More precisely, Mach argued that in an otherwise empty universe there is no distinction between spinning and not spinning - there is no conception of motion or acceleration if there are no benchmarks for comparison - and so spinning and not spinning are the same.

This is, of course, far before the space age of rockets, zero-g training, and moon visits. We now know that our inner ear and nervous system are hard wired to respond to gravity and the first thing you would feel in a truly empty space is the urge to throw up and a splitting headache. We bio-physically NEED a point of reference or our wiring goes haywire. In the time of these thinkers, however, these practical things were unknown. It doesn't necessarily make the example worthless, but it does mean an effective argument would need a different example - or a non-human participant.

If you spun around in an otherwise empty universe, your arms and legs would not splay outward, and the fluid in our ears would be unaffected. You'd feel nothing.

This presumes, of course, that the universe is all there is, and there is nothing outside the universe that could exert any influence upon you. The Sages would, of course, vehemently deny such a possibility. God in the essence of the Ain Sof may be motionless, but there is no denying that motion (action) occurred and that it links us back to God.

From the Jewish Virtual Library:
...The link between God and the created world is, according to Philo, the *logos. Beginning its existence as part of the essence of God, the logos was given by God an existence of its own. As this separate, incorporeal existence the logos contains within itself, and is the mind of, the intelligible world and the ideas which constitute the intelligible world... [Later,] Maimonides...rejects the neoplatonic accounts of creation (Guide, 2:21). On the other hand, he argues that neither Aristotle nor his Muslim followers have succeeded in demonstrating the eternity of the universe. Hence, the issue cannot be decided on philosophical grounds alone. For Maimonides, however, it must be decided, since to adopt the eternity hypothesis is to give up belief in miracles; for the eternity hypothesis is tantamount to the claim that the universe and its laws necessarily emanate from God...

[Even later,] According to Levi b. Gershom, Aristotelian physics implies creation, even if it is the case that Aristotle did not recognize it. For Aristotle's system is teleological: it ascribes ends and purposes to nature (Aristotle, Physics, 2). A teleological conception of nature, however, implies a creator who fashions the universe according to specified ends (Levi b. Gershom, Milḥamot Adonai, 6:1, 7). Moreover, Aristotle's laws of dynamics are falsified if the eternity hypothesis is accepted...

Crescas' doctrine of creation exhibits a different use of the term "creation" and displays an ambivalence on the issue of the eternity or temporal beginning of the universe...Yet he claims that the traditional biblical view is that the universe had a temporal beginning. Perhaps the solution to this apparent inconsistency is to be found in his sympathy for the doctrine of eternal re-creation of many universes, a view that is found in rabbinic literature...

And, of course, still has many proponents in the scientific community today, although the latest mathematics seems to indicate that the universe lacks sufficient matter to retract back to a new Big Bang beginning.

Even so, there are none now who argue that this universe is eternal - the Big Bang theory is well established and entrenched. The philosophers up to and including Mach, influence by Enlightenment teachings, embraced the idea of an eternal universe and therefore reached philosophical conclusions that cannot now be substantiated.

But the idea that motion, time and space require some sort of something to provide a benchmark both for completely objective measurements and for our own sense of perception is one that continually plagues this era of thinkers. The idea of a theoretical place with absolutely no matter led to thought experiments such as Mach's. Greene continues:

This [idea that you'd feel nothing in a perfect vaccum of matterless space] is a deep and subtle suggestion. Without such benchmarks, Mach argued, the very concepts of motion and acceleration cease to have meaning. It's not just that you won't feel anything if you spin, it's more basic. In an otherwise empty universe, standing perfectly motionless and spinning uniformly are indistinguishable.

Newton, of course, would have disagreed. He claimed that even completely empty space still has space. And although space is not tangible or directly graspable, Newton argued that it still provides a "something" with respect to which material objects can be said to move.

Mach strongly challenged the key assumption. He argued that what happens in the laboratory is not what would happen in completely empty space.

Without invoking absolute space - if absolute space is not a something - how would Mach explain the water's shape? The answer emerges from thinking about a simple objection to Mach's reasoning.

The unasked question here, of course, is that if you cannot distinguish movement, does that mean it's not "really" happening? Even if there is not an outside observer such as God, can such sweeping theoretical pronouncements even be made without such huge unstated assumptions as to render them senseless? It's the big question that science dances around but cannot answer: Is only the measurable real? And even without God, isn't our own intuition adequate to tell? Mach says yes, but it's not due to space or an outside observer. Instead, it's just due to matter - gravity, to be more exact.

Mach, Motion and the Stars

If you can feel spinning motion in a universe with merely a few distant start, perhaps that means Mach's idea is just wrong - perhaps, as assumed by Newton, in any empty universe you would still feel the sensation of spinning. Mach offered an answer to this objection. In an empty universe, according to Mach, you feel nothing if you spin (more precisely, there is not even a concept of spinning vs nonspinning). That is, the force you [do] feel is proportional to the amount of matter in the universe. In this approach, the force you feel from acceleration arises as a collective effect, a collective influence of all the other matter in the universe.

Again, the proposal holds for all kinds of accelerated motion, not just spinning. The force you feel represents the combined influence of all the other matter making up the universe. If there were more matter, you would feel greater force. If there were less matter, you would feel less force. And if there were no matter, you wouldn't feel anything at all. So in Mach's way of thinking, only relative motion and relative acceleration matter.

For many physicists, this is one of the most seductive proposals about the cosmos put forward during the last century and a half. Generations of physicists have found it deeply unsettling to imagine that the untouchable, ungraspable, unclutchable fabric of space is really a something - a something substantial enough to provide the ultimate, absolute benchmark for motion.

Space, in Mach's view, is very much as Leibniz imagined - it's the language for expressing the relationship between one object's position and another's.

We know, of course, that space is not empty. It is filled with particles - particles of dust and dirt, matter, energy, light, and radiations of all kinds. We know that the universe started as a dot and expanded - grew - and therefore at least at the beginning had finite edges. It still, technically, "contains" all this matter, dark and light, dust, dirt and various waves and particles. They can't go "outside" the universe, though it is so large as to be practically infinite. And as mentioned above, many scientists think it will shrink back down and a new Big Bang will occur. But none of this can answer the one question everybody wants to know the answer to: what was "here" before the universe was, and is God out there, outside of it? By postulating a truly infinite universe with no beginning and no end, early thinkers could write God out of the picture. Modern math, however, has let God squeeze back in.

Mach vs. Newton

Is Mach right? If his ideas were right, how do the distant stars and the house next door controbute to your feeling that you are spinning when you spin around. Without specifying a physical mechanism to realize his proposal, it was hard to investigate Mach's ideas with any precision.

From our modern vantage point, a reasonable guess is that gravity might have something to do with the influences involved in Mach's suggestion.

When the dust of relativity has finally settled, the question of whether space is a something - of whether the absolutist or relationist view of space is correct - was transformed in a manner that shattered all previous ways of looking at the universe.

The unasked question, of course, is: what if the universe is absolutist AND relationist? If quantum physics tells us there are only probabilities, not things set in concrete until AFTER they are observed, then only that which has been observed is absolutist - everything else is relationist. And there's a lot of room for free will and expansion of the universe in that relationist space, isn't there?


SJ said...

Ahava interesting stuff. Keep it coming. XD

>> Just because something can be described mathematically does not mean it has a real, independent existence.

Perhaps if there were bigger correlations than the simple number of 12, there would be a much stronger case.

Perhaps there would be a stronger case if science can one day establish that the 12 dimensions were for the same things as the 12 sephirot.

As it is, I doubt that electromagnetism and general relativity has much to do with 12 sephirot.

>> Newtons studied the Bible for years, and spent the latter portion of his life dissecting scripture for the "secret code" which he believed was contained in it that would explain all of creation.

I watched the History Channel's Nostradamus Effect episode on Issac Newton.

In general, the Nostradamus Effect is terribly lacking in skeptic opinions. It said that Issac Newton used numbers in the book of Daniel to try to calculate when the end of the world would happen (the end of the book itself says to not even bother cause noone will ever get it right) and it picked one particular date that Newton flirted with without saying how many dates Newton flirted with ... and then calling it prophecy.

On a similar vein there was rumors that an astrologer predicted 9/11 but the astrologer wrote that lots of dates were flirted with that just something bad could happen. Oooooooh so prophetic.

And I say that when the United States and China goes into a nuke-off over Taiwan everything is going to be screwed up, and when it happens 10,000 years from now or 500,000 years from now, I'm gonna be a prophet. XD The prophet SJ. XD

Also the Nostradamus Effect said that Newton was speculating on how the world would end and he was thinking that it would happen when the Jews would build the third temple and then certain people are gonna be all pissed off. Wooooooooooooooooooooooooow you really need to have 10 PHDs in International Relations to figure that one out; and be a prophet of the Lord. XD

>> The Enlightenment Era was all about throwing off the "oppression" of religion and embracing a rationalistic point of view

Not entirely accurate. Rene Descartes was a famous enlightment philosopher and he beefed up the ontological argument for God's existence as well as coming up with the Cartesian coordinate system for math.

As for the rest of installment #2, I'm suprised Ahava that you didn't find a way to mention the Heisenberg Uncertanty principle which states that position and momentum of a subatomic particle can't be simultaneously known (location of electrons can't be pinpointed that kinda stuff); and also the Cosmological Argument which attempts to infer God's existence with the supposed impossibleness of an infinite regress.

They kinda go in the direction of your post.

Ahavah Gayle said...

Don't worry - Heisenberg's coming up. I particularly like the way the core (nucleus) and the properties of the shell (outcome, if you will) are fixed, but the interior "cloud" of atoms are a mess of whizzing orbits that can't be pinned down. To me, that's analogous with creation and the outcome (as much as we know of it from prophecy, that is) being fixed while the paths we take to get there are completely subject to free will and ordinary cause-and-effects of our own actions and inactions and natural phenomenon such as weather and natural disasters (which of course have their own cause-and-effect cycles). Does God intervene? Not normally. We call it a miracle when God does something to counteract cause-and-effect because it doesn't happen very often. Usually God lets us stew in our own screw-ups, and lets nature happen as it will. We are our own worst enemies. We think (badly), therefore we are (stupid).

Descartes arguments actually have come under fire as of late - and it's a question as to whether or not he believed in God or whether he simply wanted to avoid offending the then-current PTB. In the early 1600s you could still get in a bit of trouble for having non-PC views, some places more than others.

I have a friend who had such a vivid and terrifying dream of China nuking the west coast that she packed up, sold her house at a greatly reduced price, and moved back here where her sister still lives. (This was before the real estate market in CA began to crash - it must have been summer of '05 or so, I think). She really believes God sent her this dream. I don't know if she's been watching too many disaster movies on TV or really did receive an angelic message, but she believes she did. Since it hasn't happened yet, all I can say is they gave her plenty of time to move - but the possibility obviously can't be ruled out completely that China would nuke the US. In fact, the more I know of China's plans to make deals with the Middle Eastern Countries and non-OPEC oil producers to ensure their continual industrialization, the more I think it could really happen. It wouldn't have to be about Taiwan (though that is also possible), it could very well be about oil.

Did you pick up a copy of Greene's book? I'm curious if you're reading along.