Mathematical Monks and the Multiverse

I recently read a truly excellent SF novel by Neal Stephenson entitled Anathem. It's about an alternate universe that has monks whose interests are more on mathematics rather than theology; and they have an alternate philosophical history that parallels the real one. I highly recommend it to pretty much everyone (especially Elliot at CotC if he hasn't already read it).

Part of my motivation for bringing it up is that at one point the monks discuss the Anthropic Principle, and give an excellent account of it:

Paphlagon said, "The cosmogonic processes that lead to the creation of the stuff we are made of -- the creation of protons and other matter, their clumping together to make stars, and the resulting nucleosynthesis -- all seem to depend on the values of certain physical constants. The most familiar example is the speed of light, but there are several others -- about twenty in all. Theors used to spend a lot of time measuring their precise values, back when we were allowed to have the necessary equipment. If these numbers had different values, the cosmos as we know it would not have come into being; it would just be an infinite cloud of cold dark gas or one big black hole or something else quite simple and dull. If you think of these constants of nature as knobs on the control panel of a machine, well, the knobs all have to be set in just the right positions or --"

Again Paphlagon looked to Moyra, who seemed ready: "Suur Demula likened it to a safe with a combination lock, the combination being about twenty numbers long."

"That is right. If you dial twenty numbers at random you never get the safe open; it is nothing more to you than an inert cube of iron. Even if you dial nineteen numbers correctly and get the other one wrong -- nothing. You must get all of them correct. Then the door opens and out spills all of the complexity and beauty of the cosmos."

"Another analogy," Moyra continued, after a sip of water, "was developed by Saunt Conderline, who likened all of the sets of values of those twenty constants that don't produce complexity to an ocean a thousand miles wide and deep. The sets that do, are like an oil sheen, no wider than a leaf, floating on the top of that ocean: an exquisitely thin layer of possibilities that yield solid, stable matter suitable for making universes with living things in them."

However, to get around the theistic repercussions, Anathem appeals to the multiverse hypothesis. Stephenson does this very cleverly: any view that argues that the physical universe isn't all that exists is a sort of multiverse hypothesis. So the Platonic world of forms is positing a multiverse, in which one is a universe of pure forms (in the Anathem alt-history Plato = Protas and Platonist = Protist). Similarly, any theistic explanation of the Anthropic Principle is a multiverse hypothesis, since it holds that there is another world that has some effect in this one. Stephenson's monks conclude from this that, if we have to posit another world in order to account for this one, there can be no reason for limiting the number of other worlds to one.

"It is a legitimate move in metatheorics. You have to be continually asking yourself, 'why are things thus, and not some other way?' And if you apply that test to this diagram, you immediately run into a problem: there are exactly two worlds. Not one, not many, but two. One might draw such a diagram having only one world -- the Arbran Causal Domain -- and zero arrows. That would draw very few objections from metatheoricians (at least, those who are not Protists). One might, on the other hand, assert 'there are lots of worlds' and then set out to make a case for why that is plausible. But to say 'there are two worlds -- and only two!' seems no more supportable than to say 'there are exactly 173 worlds, and all those people who claim that there are only 172 of them are lunatics.'"

Of course, in this post I pointed out that there is a reason for limiting the number of worlds to two: Ockham's Razor. The more entities you have to posit, the less likely your theory is correct. The Anthropic Principle shows that we have to posit a world in addition to this one in order to account for the fact that this world has the very specific properties necessary for the existence of life. But unless we have a reason to posit a third or fourth or 173rd world, then to do so simply violates Ockham's Razor.

Ironically, part of Anathem's alternate history includes a parallel to Ockham's Razor, which is frequently referenced by the characters:

Gardan's Steelyard: A rule of thumb attributed to Fraa Gardan (-1110 to -1063), stating that, when one is comparing two hypotheses, they should be placed on the arms of a metaphorical steelyard (a kind of primitive scale, consisting of an arm free to pivot around a central fulcrum) and preference given to the one that "rises higher," presumably because it weighs less; the upshot being that simpler, more "lightweight" hypotheses are preferable to those that are "heavier," i.e., more complex. Also referred to as Saunt Gardan's Steelyard or simply the Steelyard.

So, basically, the multiverse hypothesis violates the Steelyard: the anthropic coincidences make it absurdly implausible that this world is the only one that exists; but unless it is absurdly implausible that only two worlds exist, it is invalid to think there are more than two. Anathem contains the refutation of one of its premises without realizing it.

However, I'm willing to give Stephenson some grace here, since such an acknowledgment would essentially destroy the premise of the entire book. Now go read it.

The Anthropic Principle for Misanthropes, part 4

(See also part 1, part 2, and part 3)

In this series I have left out a lot regarding the Anthropic Principle, because my focus is on its value as a teleological argument for the existence of God. So, for example, I have not gone over the several types of APs that have been proposed, i.e. the Weak (WAP), Strong (SAP), Participatory (PAP), and Final (FAP) -- the latter of which Martin Gardner cleverly called the Completely Ridiculous Anthropic Principle (CRAP).

Some people think that any teleological argument is invalid in light of Darwin. Such arguments are automatically excluded from consideration, since they also apply to arguments against biological evolution. If some teleological arguments from a particular field are invalid, why doesn't that give us grounds for rejecting those from other fields? My answer is fairly simple: because the arguments against evolution don't work and the arguments from the AP do. It doesn't matter who is presenting the argument or what their motivation is: if it's valid, it's valid; and if it's invalid, it's invalid.

One thing that frustrated me about the AP when I first studied it, however, is that there seem to be examples of fine-tuning that don't serve any purpose. The example that particularly hit home with me was that our location with regards to the sun and the moon make it appear as if they just happen to be the same size in the sky. The AP shows that we have to have a moon a particular size and distance from us, and the earth has to be a particular distance from a particular kind of star during a particular burning phase; but it just seems weird to me that this results in the sun and moon appearing to be the same size in the sky. If someone rigged the game, it looks like they were rigging it to mislead us into thinking that they were the same size. Of course, the ancients were able to study the sun and the moon and determine that they're not even remotely close in terms of size. But it seems like a meaningless coincidence, and this made me suspicious that the examples of alleged fine-tuning that the AP demonstrates were similarly coincidental.

The resolution to this leads to a very interesting corollary to the AP. The surface of the earth is the only place in the solar system where an observer could see a total eclipse, in which one body blocks out the sun, but does so just barely, so that the sun's corona can be observed. For millennia, solar eclipses were one of the primary methods by which humankind could study the sun. Such study would only be possible if the sun and the moon appeared to be the same size in the sky. So the same characteristics that make life possible are also the characteristics that allow us to study and investigate the universe around us.

With the advent of the Mars Rovers, there has been a boon in the last several years on Mars studies. Below, on the left, is a series of pictures taken by one of the Rovers of Phobos, one of Mars' moons, crossing between Mars and the sun. The picture on the right is of Mars' other moon Deimos doing the same. Click here to see a very short video (a couple of seconds long) of it.



The point in showing these is that such "eclipses" (they're actually called transits or occultations) would not allow any observers to study the sun's corona.

Here's another example: the AP says that in order for life to be possible, the solar system must reside in a spiral galaxy, and lie in-between spiral arms. In the same way, we have to be between spiral arms in order to see anything beyond our own galaxy. In any other location in any other type of galaxy, the number of nearby stars and the light they produce would prevent us from seeing very far beyond them. So just as it looks like the universe and Earth have been arranged in order to support life, it looks like the universe and Earth have been arranged in order to allow for scientific discovery. Praise God.

An Interesting Reaction

One theistic argument is the moral argument (or axiological argument). It's the idea that in order to say that there are actual moral rights and wrongs, we have to presuppose a sort of metaphysical anchor or ground for these values that transcends individual cultures and epochs, something in fact which looks very much like the Judeo-Christian God. If we reject such a ground, then we are left with pure relativism, where nothing is actually right or wrong. This may be OK when the issue under discussion is whether you should be completely forthcoming on your taxes, but when we point to horrific atrocities, it becomes very difficult to say that there is simply nothing morally wrong going on.

However, rather than defend this argument, I want to point to an interesting reaction to it. Many atheists who hear the moral argument misunderstand it to mean that atheists cannot be moral people or upstanding citizens. If you need to believe in God in order to believe that rape is wrong, then you're essentially arguing that if you don't believe in God, then you must not believe that rape is really wrong. But of course, this isn't the argument. The point, rather, is that the moral judgment "rape is wrong" -- made by theist and atheist alike -- must have a metaphysical ground in order to be valid. Thus, according to the moral argument, the atheist is being inconsistent in affirming that rape is wrong while denying that God exists. But this does not mean that atheists don't know right from wrong.

Now part of the reason I find this reaction interesting is that I could present a parallel argument which almost certainly would not provoke the same reaction. Say, for example, I argued that in order for mathematics to be possible we have to posit a metaphysical foundation for numbers, a Platonic realm of forms, which is best understood as the mind of God (such arguments have been made). So in order to affirm that 2 + 2 = 4, we have to presuppose something like the Judeo-Christian God. How many people would misunderstand such an argument to mean that if you don't believe in God, you don't really believe that 2 + 2 = 4? I suspect very few, if any. Yet this argument is exactly parallel to the moral argument: in order to affirm X we have to presuppose a metaphysical foundation for it that is best understood as God.

So why are some people so liable to misunderstand the moral argument? Again, I suspect (although I could very easily be wrong) it's because our views on morality are inextricably bound up with our views of ourselves: what we do and what we think should be done says a great deal of what kind of person we are. So when someone tells an atheist that her worldview is inconsistent with believing that rape is wrong, she reacts. Instead of realizing that the moral argument is saying something about the relationship between her worldview and moral beliefs, she only sees it as saying something about her moral beliefs, and thus about herself: whether she is a good person.

The Anthropic Principle for Misanthropes, part 3

(See also part 1 and part 2)

In part 1 I explained what the Anthropic Principle is: in order for life to exist anywhere in the universe at any time in its history, multiple conditions must be met which make it virtually impossible that the universe would be hospitable to life if left to its own resources. Since the universe is hospitable to life, it follows that it was not left to its own resources: Something that exists independently of the universe made it so that it would be able to support life. In part 2, I dealt with several objections to this monotheistic conclusion. In this post I'm going to take a look at two more objections to it. I saved these two for their own post because they require a fuller response than the others.

1. "Maybe there are an infinite number of universes and this just happens to be the one with all the necessary conditions for life." This is known as the multiverse hypothesis (also called the "many worlds" or "world ensemble" hypothesis; Humphrey's been blogging on it lately), and it has some gynormous problems. The first is that it violates Ockham's Razor. This is the idea that the simpler explanation is more likely to be the correct one. Often, atheists misunderstand this to mean that a qualitatively simpler explanation is preferable, and then argue that an omniscient and omnipotent God would be the most complex explanation imaginable. Unfortunately, at least for their case, there are two difficulties with such an understanding. First, it just flies in the face of the doctrine of divine simplicity. This is the view that God is the least complex entity in existence, and was held by most of the Christian theologians and philosophers in history, although it's fallen on hard times recently. But even if we ignore that, this argument completely misunderstands what is meant by simplicity. It's not that the cause of an effect must be understood as ontologically simple; it's that it must be numerically simple: the more entities you have to posit, the less likely your theory is correct. In other words, Ockham's Razor is the claim that the quantitatively, not qualitatively, simpler explanation is more likely to be true.

To apply it to the case in point, the multiverse hypothesis has to posit an unfathomable or infinite number of universes in order to account for one universe having the necessary conditions for life. By contrast, Monotheism posits the existence of one causal agent who brought the universe into existence with the necessary conditions. Obviously, the latter is the simpler explanation, and so according to Ockham's Razor, we should prefer it to the multiverse hypothesis.

The second problem with the multiverse is as follows: if you watched someone flip a coin a million times and it came up heads each time, you could either conclude that it's fixed in some way (maybe it's a two-headed coin) or you could conclude that there are an infinite number of coins being flipped and you just happened to see the one that came up with a million heads in a row. The gambler takes the chance on the latter and so bets that the coin is due to come up tails on the next flip. But 1) even if it is an honest coin, it only ever has a 50-50 chance of coming up tails at any particular flip. It isn't "due." This is the gambler's fallacy. The multiverse hypothesis, however, does not commit the gambler's fallacy, it commits 2) the inverse gambler's fallacy. Basically, regardless of whether the gambler was right to think the coin is due to come up tails, his assumption that it's an honest coin would only be valid if he actually saw all the other infinite number of coins coming up with all their different results. When you have a sample of one, it is much more rational to conclude that the game is fixed. (This, incidentally, is a further response to the third objection in part 2, that we cannot draw any conclusions about probability because we only have the one universe to work with.) So the fact that we have a universe that appears rigged is best explained by the hypothesis that it is, in fact, rigged. The universe is the way it is because someone decided it should be.

Third, no one has been able to come up with a multiverse that does not itself have a beginning as well as numerous anthropic coincidences of its own. So it doesn't evade the question of why the universe can support life; it just forces us to ask it again with slightly different terminology.

Fourth, the supposition of other universes by itself does not evidently lead to a solution of the Anthropic Principle. As William Lane Craig writes,

even if we conceded that a multiple universe scenario is unobjectionable, would such a move succeed in rescuing us from teleology and a cosmic Designer? This is not at all obvious. The fundamental assumption behind the Anthropic philosopher's reasoning in this regard seems to be something along the lines of

8. If the Universe contains an exhaustively random and infinite number of universes, then anything that can occur with non-vanishing probability will occur somewhere.

But why should we think that the number of universes is actually infinite? This is by no means inevitable, not to mention the paradoxical nature of the existence of an actually infinite number of things. And why should we think that the multiple universes are exhaustively random? Again, this is not a necessary condition of many-worlds hypotheses. In order to elude the teleological argument, we are being asked to assume much more than the mere existence of multiple universes.

Finally, the multiverse hypothesis is just as metaphysical as the monothestic hypothesis. For those who don't like metaphysics in their science, the multiverse is no better than saying "God did it." So it's not a choice between one theory that's metaphysical and one that's not (or perhaps one that's less so); it's a choice between two equally metaphysical solutions, one of which commits fallacies and one which does not.

2. "These characteristics are just for life as we know it." Another way of stating this objection is that life accommodates itself to its surroundings. Observing how the universe just happens to meet the necessary criteria for life is like a puddle observing how the pot hole just happens to be shaped for the puddle to fit in it.

So let's clarify our terms. When we refer to life in this context we mean physical life, life that is composed of matter, i.e. atoms. Moreover, in order for something to be physically alive it must be capable of processing physical energy to perform work; when a living thing stops processing energy we call it death. Now of course, one may simply say that there may be non-physical life out there. Certainly. In fact, most religions maintain that there are entities that are not physical. They're called angels. Or one could say that non-living material entities are alive in some sense; perhaps each rock is conscious for example. But this would merely be ascribing an occult property (rather than a physical property) called "life" to physical objects; as such it would also be a form of non-physical life. And if one is willing to accept the existence of a non-physical realm in order to explain the Anthropic Principle, there can be no objection to the monotheistic explanation of it. In order to avoid such an explanation, therefore, this objection must say that the Anthropic Principle only applies to physical life as we know it.

In order for a physical entity to process energy, it must have complex molecules which are physically capable of such processes. Complex molecules are those that are based on atoms that are able to form a large number of bonds with other atoms. There are only three elements capable of forming complex molecules: silicon, boron and carbon. Silicon can only form about a hundred amino acids, which is insufficient for physical life. Boron is rare, and poisonous to life where it does exist in concentration; plus, wherever boron exists, carbon exists in much greater abundance, so it's not very likely to happen. Thus, when we discuss the necessary parameters for life, we refer to carbon-based life. One might think if the laws of nature were different it would change the situation. True. The Anthropic Principle shows that if the laws of nature were different, physical life could not exist at all.

Now some might suggest that I'm simply not taking the concept of "life as we know it" far enough. I'm still working in terms of atoms, and perhaps if we look into the subatomic realm, we would find ways for different types of atoms to form into different types of molecules that could then form living creatures. The problem here is that the ability of atoms to form bonds is directly related to the configuration and properties of its electrons. So the capacity for something to be alive in a physical sense is based on the basic properties of atoms, and thus of matter. Now the question arises: would it be possible to alter the basic properties of electrons or other subatomic particles in such a way that they would still be able to form into complex molecules capable of processing energy to perform work? To the best of my knowledge, the answer is no. The properties of electrons, protons, and neutrons as well as their interaction are some of the most dramatic examples of anthropic coincidences. Their masses must be precisely what they are, their decay processes must be precisely what they are, their ratios to each other must be precisely what they are, etc. in order for life to exist. For example, the ratio of electrons to protons that were created in the Big Bang must be exactly the same number to within one part in 10³⁷ in order for their charges to balance out. Otherwise, the electromagnetic force would have dominated gravity and prevented the formation of planets, stars, and galaxies.

One might still object, though, that if completely different subatomic particles were created in the Big Bang which then formed completely different atoms and molecules, it would be possible to have a different type of life. But as soon as we're positing a completely different type of matter, it becomes difficult to continue calling it matter. In other words, this would (again) be just as metaphysical a solution as the monotheistic one. Moreover, at this point, we're positing different universes in order to explain the Anthropic Principle, so for this suggestion to have any force it must be wedded to the multiverse hypothesis with all of its failings. Thus, the monotheistic solution to the Anthropic Principle is preferable.

There's one more installment to go. Stay tuned.

Arguments and Authority

One of my pet peeves is when people confuse the fallacy of authority with the argument from authority. The former is better called the fallacy of irrelevant authority, since it's when you use the views of someone who is an authority in a particular subject to justify positions outside of that subject. It's the irrelevant part that makes it a fallacy, not the authority part. For example, I often see letters to the editor, editorials, and essays where the writer uses his status as an academic to promote his political views, even though his academic standing is in a field completely unrelated to political science. Such a person's political views carry no more weight than yours or mine or anyone else's.

By contrast the argument from authority is a perfectly valid form of argumentation in informal logic. It takes as its premise that an authority on a subject is more likely correct about that subject than not. In my opinion the most it can do is shift the burden of proof to one who is denying or arguing against the authority's position. Also, in order to have any strength, I think it has to be an argument from the consensus of authorities on a subject, since you can always find some authority in some discipline willing to make outrageous claims.

In formal logic, however, arguments from authority are invalid. This is because the validity of a syllogism is completely distinct from the person presenting it. However, again, some people think this means that any appeal to authority is invalid, regardless of whether it falls into formal or informal logic. For example, I've actually had discussions with people who think Jesus never existed, and when I mention that their view contradicts those of virtually all historians who have written on the subject, they yell, "Appeal to authority! Invalid!" Of course it's not invalid at all. It's perfectly appropriate to look to those who have devoted their lives to the study of the subject under debate to see how they have assessed the evidence. Again, I think it only goes so far -- it's a weak argument -- but it's still a valid argument, as long as you're working outside of formal logic.

The Anthropic Principle for Misanthropes, part 2

(See also part 1)

In part 1 I explained what the Anthropic Principle is and gave some examples to illustrate it. Basically, the idea is that certain conditions must be met in order for life to be possible anywhere in the universe at any time in its history. These conditions are so numerous and so unlikely that, when added together, they make it virtually impossible for there to be a planet capable of supporting life -- at least advanced life -- anywhere in the universe if left to chance. Since there is a planet capable of supporting life (Earth in case you were wondering) it suggests that it wasn't left to chance, that someone intended that the universe would be hospitable to life.

However, while the basic facts are not disputed by scientists in the relevant disciplines, the theistic conclusion is a matter of controversy; some scientists accept it, others don't (here's an interesting sample). In this post I'll go over some of the most common objections made against this inference. I'm saving two objections that require lengthier responses for the next post.

1. "We would not be here to observe the universe unless the very unlikely did happen, so of course we're going to notice how the universe 'just happens' to have the necessary conditions for life." This was my first thought when I heard about the Anthropic Principle for the first time. However, it really doesn't hold any water if you think about it for more than a few seconds. The fact that we are here of course proves that the necessary conditions for life's existence have been met, regardless of how unlikely it is; but the question is not whether these conditions have been met but how they've been met. And the fact that they are unlikely to the point of being impossible shows that they were not met by chance.

The common analogy I've seen in the philosophical literature is the firing squad. If a man were sent to be executed by a hundred sharpshooters and he survives the experience, he could draw two conclusions: they all missed by chance, or they intended him to live (by missing on purpose or filling the guns with blanks for instance). But he would not take the fact that he was alive as evidence that it happened by chance. He would not say, "I wouldn't be here to observe the fact that I'm alive unless I survived -- therefore they must have missed accidentally." In fact the more unlikely his "being alive" was, the more rational it would be for him to conclude that someone decided he should live. In the same way the rational conclusion to draw from the incredible degree of fine-tuning we find in the universe is that someone decided we should live.

2. "We don't have enough information to warrant drawing any conclusions, much less theistic ones." There is certainly some truth to this; the Anthropic Principle is a relatively young field of study, and we should bear this in mind. However, it should also be borne in mind that all of the research has consistently pointed in the same direction: that the prerequisites for life's existence are very specific. Perhaps future scientific discoveries will overturn this evidence, but this could be said of virtually any scientific claim (although it's less implausible for younger fields of study than older ones). At any rate, this isn't really an objection to the theistic conclusion, but to the data itself, and virtually all scientists in the relevant disciplines acknowledge the data.

I also have to say I find it interesting that when scientific discoveries can be seen as going against belief in God, this objection is rarely given. It's only when science seems to point to God that people start suggesting that we can't really draw any conclusions.

3. "We don't have any other universes to compare this one with, so we can't say how likely or unlikely it is for these conditions to be what they are." In the first post I stated that there are two levels to the Anthropic Principle: the conditions that have to be met within the universe, and the conditions that have to be met in the universe as a whole. The conditions that fall into the latter category are initial conditions that are simply given in the Big Bang itself. Since they are initial conditions, there are no prior physical conditions that force them to be the way they are, by definition. There are only two possible conclusions from this: first, that these initial conditions could have been different. Or second, that there were non-physical conditions forcing the universe's physical conditions to be what they are. The first leads to the problem the Anthropic Principle poses: that the universe simply shouldn't be able to support life if left to its own resources, and yet it does. The second leads to the conclusion that there is some non-physical reality, external to the universe, that is able to exert some degree of power over the universe. Thus, both of these conclusions have theistic repercussions.

As for the the conditions that have to be met within the universe, some of them are indeed speculative. For example, while we have no reason to think that planets inherently form with exactly the same surface gravity or axial tilt as Earth, we have not discovered enough extra-solar planets to test it directly. However, many of these conditions are not speculative, but are easily calculable. For example, in order for a planet to be able to support life it must be in a certain type of galaxy, in a certain part of the galaxy, orbiting a certain type of star, etc. It is easily observable and demonstrable how common these conditions are.

Moreover, the fact that we have a sample size of one actually supports the theistic conclusion. This will be demonstrated in the response to one of the objections in the next post.

4. "Chance and intent are not the only two explanations possible. There's also natural law. If there's a law which makes the universe and planets capable of supporting life, the odds of there being other possible life-sites in the universe would be very likely." Well, as pointed out above, the conditions necessary for the universe as a whole are initial conditions. As such, there is no preceding natural law forcing them to be they way they are by definition. The necessary conditions within the universe could, theoretically, be shown to be the result of as-yet-undiscovered natural laws. But in the absence of any evidence for such laws, this suggestion is completely ad hoc, since virtually anything could be explained as the result of some natural law we just haven't discovered yet. Besides, this would only push the problem back to the level of the universe as a whole: any law that makes the universe hospitable to life would have to be exactly what it is in order to ensure that the specific properties necessary for the existence of life are met. The universe would still be fine-tuned for the existence of life, and we'd still need an explanation for why this is the case.

5. "If you change one physical constant it may throw everything off-kilter, but then you can change the other physical constants to compensate for it, and bring it back to being a universe hospitable to life." Incredibly enough, scientists already thought of that. The obvious problem is that changing the other constants does not merely compensate for changing the first one; it would also have dramatic effects which would require us to change more constants, which would have their own effects requiring further changes, etc. There are a few cases where you could do this and end up with a life-permitting universe, but they would be extremely rare. It's like taking a medication that has significant side effects. You then have to take other medications to regulate these side effects, but then these medications also have side effects, so you need to take more medications...

Of course, this analogy only goes so far: taking more medications may actually bring some degree of health to the body. With the universe's physical constants, however, it is almost impossible to alter them and still end up with a life-permitting universe.

6. "Someone wins the lottery, and it would be irrational for that person to think that the extreme improbabilities involved in her winning would demonstrate that someone set it up for her to win. Similarly, life is the result of this universe. This doesn't allow us to think it was set up intentionally to be this way." To illustrate this objection, say you had, for some ungodly reason, billions of ping pong balls and inscribed each one with someone's name until you had one for every person in the world. Also say you had a big enough basket to hold all of them. You then mix them all up and pull one out while blindfolded. Obviously someone's name will be drawn, even though the odds were one in several billion that you would select that particular ball. Similarly, the fact that we have a universe with the specific properties it has may have been improbable, but that does not allow us to draw any conclusions about whether it was "arranged."

But this is a bad analogy. A better one would be if, every time you tweak the universe's properties, you paint a ping pong ball black if it permits the existence of life, and just leave it white if it does not. What you would end up with is an ocean of white ping pong balls with only a handful of black ones scattered throughout. Now of course the odds that you would pull any particular ping pong ball out is equally improbable; but the odds that you would pull out a white ping pong ball is enormously more probable than the odds that you would pull out a black one. Similarly, the odds that the universe would be life-prohibiting is vastly more probable than for it to be life-permitting -- unless someone decided to make it hospitable to life.

This objection seems to be suggesting that life -- the result of this universe -- is arbitrary. Any other universe would have had results too. The problem with this is that all the other possible universes would have had essentially the same result: just matter and energy in motion, and often not even the motion. Ours has something on a whole different level, and the universe must be balanced on a razor's edge in order for it to be that way.

Man on Fire

Denzel Washington's movies have increasingly had religious, and specifically Christian, elements in them. A few years ago, I saw Man on Fire, and it demonstrated this point well. Washington stars as a former assassin named Creasy. At the beginning, he asks an old friend (also a former assassin, played by Christopher Walken) if he thinks God could ever forgive them for what they’ve done. Walken says no, and Creasy agrees.

Walken gets him a job as a bodyguard for a little girl named Pita (played by Dakota Fanning). She’s a complete charmer, but Creasy resists for fear of caring for someone. Further events with religious or spiritual aspects take place: he describes himself to the mother superior at Pita’s school as the "sheep who got lost". Pita’s mother walks into Creasy’s room and sees an open Bible. "You read the Bible?" "Yeah, sometimes". "Does it help?" Yeah, sometimes". He tries to commit suicide, but the bullet has some flaw and doesn’t go off. Divine intervention?

Eventually, Pita wins Creasy over and shows him "it’s all right to live again" as Walken’s character puts it. Not long after, as he reaches for his nightly bottle of Jack Daniels, he pauses, puts it back, and then opens his Bible instead.

If it had ended here, it would have been an uplifting story about how none of us are beyond the pale, beyond the hope of redemption. It also would have been an after school special instead of a Hollywood action movie. Spiritual growth is boring.

Of course you already know what happens. They never have characters like Pita in movies unless they are put in mortal danger in order to tweak our emotions. The truly good person, the one who doesn’t deserve to suffer, suffers. The little girl is kidnapped. So Creasy goes back into assassination mode and starts torturing and killing -- in very artistic ways as Walken’s character again puts it -- everybody involved in the kidnapping.

Revenge movies like this usually employ a sense of divine justice -- that is, the protagonist has suffered at the hands of others, and so wreaks his wrath upon them mightily. The bad guys have exerted their wills against the good guy: "If you love your son/daughter/ husband/wife/mother/father/whatever, you’ll do what I say". But then the good guy exerts his will against the bad guys, so they get what’s coming to them. Thus you have the miracle of payback.

Ultimately this type of movie is about people exerting power over others. But nobody can actually live this way. As long as we encounter other people, we are faced with other egos who have as much free will, as much value and worth, and as much right to live as we do. It may make you sound tough to say that you will never give an inch, and that nothing and no one can stop you. But it’s false. This is why Sartre said that "Hell is other people". This is why Nietzsche wrote that his philosophy was more aesthetically pleasing than the "traditional" ideas of love and respect.

This is also why movies such as Terminator are so popular, especially with guys. Arnie played the ultimate male fantasy: he gets whatever he wants, he can’t be stopped, and anyone who gets in his way is eliminated without any remorse. Did you catch that? Not only does he kill anyone for any reason, he is free from any sense of recognizing others as individuals, as sacred, as having any existential value. It’s why Brad Pitt said in Fight Club "It’s only after you’ve lost everything" (i.e. your sense of self-worth and value) "that you’re free to do anything" (i.e. reject the worth and value of others as well). Once you reject the value of other people, you are no longer enslaved by the idea that you should take them into account as you live your life. You're free to live life on your own terms.

But again, this is all an illusion. As long as there are other beings in existence -- and you have to figure that the odds for that are at least 2 to 1 -- their rights, their needs, their wants and desires have to be taken into account. The only alternative to this is psychopathy.

The Anthropic Principle for Misanthropes, part 1

One of the ways in which contemporary science has appeared to undergird religious belief is the Anthropic Principle. This is the investigation of the necessary conditions for the existence of life. It's an entire field of study, so obviously my treatment here is not even remotely exhaustive. There could easily be a blog entirely devoted to this subject reporting on new discoveries and studies on an almost daily basis.

The Anthropic Principle has its origins in the 1960s with scientists trying to determine the likelihood of other possible life-sites in the universe. It was thought at the time that the universe is so huge, there must be plenty of habitable planets, potentially with life and advanced civilizations already present.

What they have discovered is that the number of conditions that have to be met in order for a planet to be capable of supporting life are so numerous and so unlikely that, even when factoring the size of the universe into the equation, the odds of there being any planet anywhere in the universe that would meet all of the necessary conditions by chance is essentially zero. But this raised an obvious problem: there is a planet that meets all of these conditions. You're sitting on it. Since the Anthropic Principle demonstrates that it's improbable to the point of being impossible for this to have come about by chance, it suggests that these conditions are the way they are because someone intended that Earth should be able to support life.

There is debate as to whether the Anthropic Principle applies to all life or only to complex life. Many scientists argue that simple, unicellular life might be able to survive outside of the severe parameters necessary for advanced life, and could even be widespread. Probably the most popular book arguing this point is Rare Earth: Why Complex Life Is Uncommon in the Universe by Peter Ward and Donald Brownlee. If we grant this for the sake of argument, we're still left with a universe in which advanced life simply shouldn't exist, if left to its own resources. And yet, as you may have noticed, it does.

There are really two levels to the Anthropic Principle. The first is what has already been mentioned: the necessary conditions that must be met within the universe. For example, the planet must be in a particular part of a particular type of galaxy -- in a spiral galaxy and in between spiral arms. It must also have a particular interstellar history, such as nearby white dwarf binary stars that have lost some of their surface material to interstellar space in order to provide flourine. It must orbit a particular type of star with particular types of outer planets. The planet must have a particular axial tilt, a particular magnetic field, have a moon of a particular size and distance, etc., ad infinitum. Again, it's not an issue of individual criteria being met -- the universe is so big that there will be other places that meet even extremely improbable conditions. The point is that it has to meet them all, and when the conditions are combined it shows, even given the unfathomable size of the universe, that the odds are absurdly improbable that there would be a place that would be able to support life.

One of the properties on this level that has impressed me the most involves the Kuiper Belt. This is an asteroid belt outside the orbit of Neptune. A few years ago, scientists decided (ex cathedra) that Pluto isn't actually a planet, but is just a fairly large and fairly close Kuiper Belt Object.

The gravitational effects from the Kuiper Belt stabilize Neptune's orbit. If the Kuiper Belt's mass were any different (either less or greater), it would start a domino effect, throwing off Neptune's orbit, which would in turn throw off Uranus', then Saturn's, and then Jupiter's. Then the orbits of the inner planets, including Earth, would be disrupted to the extent that none of them would have an orbit stable enough to permit life. It just blows me away that life on Earth is dependent on an asteroid belt outside the orbit of Neptune.

Recently, astronomers have found that our dependence on the Kuiper Belt is even greater than was previously thought (see here, here, and here). Using computer modeling of our solar system's development, they discovered that early on, Uranus and Neptune were much closer to the sun (as was the Kuiper Belt) and possessed much more eccentric orbits. The gravitational effects between the Kuiper Belt Objects and Neptune and Uranus had to be very specific in order for all of them to drift further away from the Sun and then establish the stable orbits they have today.

The second level of the Anthropic Principle is the universe as a whole. Scientists have formed mathematical models with the laws of nature slightly tweaked, and used this to investigate what must be necessary for the existence of life. What they've discovered is that if most of the laws were different by very slight amounts -- if gravity was slightly weaker or stronger for example -- it would prevent any kind of life from existing anywhere in the entire history of the universe. This implies, again, that whatever Agency brought the universe into existence did so in such a way that it could support the existence of life.

The best examples of this are the universe's mass density and its space-energy density (or "dark energy"). The former essentially refers to how much matter the universe contains. As the universe expanded outward from the Big Bang, the amount of matter affected the speed, since the more mass there was, the greater gravity would slow it down. If the mass density was any greater by even a tiny amount, it would have been the proverbial straw that broke the camel's back, causing the universe to collapse back on itself. If it was any weaker, then the expansion would overwhelm gravity enough that galaxies would never form, and without galaxies you don't have enough nearby stars to provide the heavier elements on which life depends. Specifically, the mass density has to be exactly what it is to within one part in 10⁶⁰ in order for life to exist in the universe.

The second factor mentioned above is dark energy. This refers to the "stretchiness" of the space-time fabric. This concept has its origins in Einstein's cosmological constant (symbolized by the Greek letter lambda), a force that counteracts gravity which he posited in order to escape the Big Bang singularity. He suggested that the further away two objects were, the more they would repel each other. However, no such force could be detected, much less at the strength required for Einstein's scenario. In the past several years however, scientists have managed to detect this force. It's far, far too weak to be used in the way Einstein intended -- to avoid a beginning of the universe -- but it does have a positive value. This force accounts for a very unusual phenomenon: that as the universe expands, it actually seems to be speeding up. The further the universe stretches, the more quickly it stretches. The reason this is called "stretching" is because it's not just a matter of stars and galaxies moving away from each other: the fabric of space-time is actually stretching out further. You yourself are getting slightly bigger each year as the universe expands. And you thought it was the donuts.

If the properties of dark energy were slightly different, it would affect the rate at which the universe expands, and this leads to the same problem as the mass density: either the universe would collapse upon itself (if it wasn't stretchy enough) or it would not form stars and galaxies and the heavier elements upon which life depends would not be available (if it was too stretchy). In fact, dark energy has to be fine-tuned to an even greater degree than the mass density is. It has to be exact to within one part in 10¹²⁰.

As far as I know, the fact that the universe is balanced on a knife's edge -- that if dozens of its properties were different in the slightest degrees, life (or at least advanced life) could never exist at any time and any place in its history -- is recognized by all scientists in the relevant disciplines. Accounting for this is a different matter. As I've suggested above, many scientists have thought that the fine-tuning of the universe demonstrates that, in Fred Hoyle's terms, "a superintellect monkeyed with physics, as well as with chemistry and biology." But of course there have been many objections made against this inference. I'll deal with a few of the more common ones in future installments.

The Tale of a Comet

It is well-known that people who lived before the Enlightenment were hopelessly superstitious. They believed, for example, that "odd" occurrences in the sky were omens signifying that odd occurrences would soon happen down here on Earth. The most blatant example of this took place when Halley's Comet appeared in 1456. While it was still visible, the siege of Belgrade by the Turks began; thus it was feared that this portent in the heavens had some relevance to the battle. Halley's Comet so upset Pope Callistus III that he resorted to drastic measures: he excommunicated it.

For years, this story was repeated as an example of how absurd and superstitious religion is, especially when contrasted with science. Carl Sagan referred to it in his book on comets. But of course, you know where I'm going with this: it didn't really happen. The story appears to have been popularized by Pierre-Simon Laplace at the end of the 18th century; Laplace, in turn, apparently got it from Vitæ Pontificum, a 15th century work, by Bartolomeo Platina. The Catholic Encyclopedia article on Platina dutifully translates the relevant text as follows:

A maned and fiery comet appearing for several days, while scientists were predicting a great plague, dearness of food, or some great disaster, Callistus decreed that supplicatory prayers be held for some days to avert the anger of God, so that, if any calamity threatened mankind, it might be entirely diverted against the Turks, the foes of the Christian name. He likewise ordered that the bells be rung at midday as a signal to all the faithful to move God with assiduous petitions and to assist with their prayers those engaged in constant warfare with the Turks.

Now there are a couple of things to note right away. First, there is no mention here of the Pope excommunicating the comet. Second, while the Pope had indeed issued a papal bull calling upon people to pray, and while Halley's Comet did appear in the sky at about the same time, there was simply no perceived link between the two. The bull doesn't even mention the comet. Platina just tied two events together that had no connection.

Laplace took Platina's account and suggested that Callistus sought to exorcize Halley's Comet -- and I can't help but wonder if he intended this as a metaphor. Regardless, subsequent writers took it literally, and replaced "exorcize" with "excommunicate" since all those religious terms mean the same thing anyway. The final paragraph of the afore-mentioned article summarizes this development well.

Of course, no doubt there were people who thought Halley's Comet had something to do with the siege of Belgrade. That's the kernel of truth in this story. For that matter, it may very well be true that people in the 15th century were in general more superstitious than people today tend to be. But we still have astrology. Most newspapers print the horoscope every day.

What interests me is how people who hold themselves up as skeptics were taken in by such a ridiculous story as this. Carl Sagan was, by any account, a brilliant man. Yet he uncritically repeats an urban legend in order to show how other people are gullible. What this shows, I think, is that there are no true skeptics. People are only skeptical of things that they want to be skeptical about.

For example, in his book My Life Without God, William Murray describes how his mother Madalyn Murray O'Hair would tell groups of atheists that religious people were so stupid that nobody realized sex led to pregnancy until the 19th century. This is difficult to write without chuckling, but her throng of skeptics bought it. O'Hair herself attended seances, and believed she could talk with dead people. Murray wrote that, as far as he knew, his mother never tried to reconcile this with her belief that there is no afterlife. The skepticism with which she and her fans approached religion was obviously not consistently applied.

The point of all this is that we should be skeptical of our skepticism. The reason why an intelligent person like Carl Sagan could be taken in by such a silly story as a Pope excommunicating a comet is because it fit with his views on the nature of science, the nature of religion, and the relationship between the two. Madalyn Murray O'Hair and her followers were completely contemptuous of religion and religious believers, so any claim that justified this attitude, no matter how insane, was plausible to them.

I have different biases: I am skeptical of the claim that science and religion are opposed to each other. This makes me prone to accept stories that seem to affirm this bias without showing them the same level of critical analysis that I would show to a story that contradicts it. I have to examine myself to determine, as far as possible, what my biases are, and how they might be influencing my beliefs.

Islam, Christianity, and Euthyphro

Euthyphro is one of Plato's dialogues which presents us with a meta-ethical dilemma that has been addressed throughout philosophical and theological history (meta-ethics being the study of the ground or foundation of ethics). In this debate, Socrates asks Euthyphro why God assigned the particular moral laws he did, such as to not commit murder or adultery. The problem this creates is that if God assigned these laws because they are good in and of themselves, then there is a "higher" reality than God, and God commands them because he must align himself with this reality just as much as we do. God, in other words, is not absolute; neither the ground of morality nor of reality. But if we say that these laws are not good in and of themselves, then these laws are simply arbitrary, and God could have made them differently. The "good" would have been to commit murder and adultery if God said so. In this case, God is not intrinsically good because the appellation of "good" is entirely arbitrary (this is the position that Euthyphro takes in the debate).

Traditionally, Christianity has split the horns of this dilemma. Moral laws are intrinsically good, not arbitrary. But their goodness is not derived from something outside of God; rather, they are derived from God's own intrinsically good nature. The ground of morality, in other words, is identical to the ground of reality. The error of the Euthyphro dilemma is that it tries to put the two concepts -- the goodness of certain acts and God's command of them -- into a cause-and-effect relationship with each other. If the goodness of these acts is what causes God to command them, then they are higher than he. But if his command of them is what makes them good, they are arbitrary. Neither, however, is the case: these two concepts are both effects from a common cause, namely, God's own nature.

Now, as far as I can tell, this option would be available to any general theistic position. But in my (admittedly limited) knowledge of Islam, Muslim theologians have not availed themselves of this resolution. A core doctrine of Islam is that God is completely transcendent; that is, he transcends even our moral and rational categories. God may give moral commandments, but ultimately, they are not expressions of his nature -- if they were, then he would not transcend them. Since they have their origin in his command of them, but not in his nature, they could have been different, and are therefore arbitrary, as Euthyphro thought.

Thus, in the Qur'an, God is represented as capricious. For example in the battle of Badr, God had told Muhammad (indirectly -- since God is completely transcendent there is no direct communication between him and humanity in Islam) that he would outnumber his enemies. When Muhammad's army got there, they found to the contrary that the enemy outnumbered them; but there was no way to avoid the battle at that point, and the Muslims ended up winning anyway. Later, when Muhammad asked why God told him that they would outnumber the enemy at Badr when they didn't, the response in the Sura of the Spoils of War is essentially, "If God had told you the truth, you wouldn't have gone".

Or take the Qur'an's explanation of Jesus' crucifixion, which Muslims deny: God made it seem that Jesus was crucified, but he really wasn't. Islamic tradition explains this by claiming that God put the image of Jesus on someone else (sometimes thought to be Judas Iscariot), and this person was crucified instead of Jesus. In any case, God made things appear differently than they really are in order to accomplish his objectives. So it seems that Islam has pitched its tent with Euthyphro, by accepting that the moral laws are good because God commands them, and that they are thus arbitrary.

In contrast to this, the God of the Bible cannot lie; not that he merely does not or will not, but he cannot. Unlike Islam, in Christianity morality and rationality are two things that put us in touch with God, because of their origin in his nature. God does not transcend morality and rationality, he is their very ground. That's part of what it means to say that we are created in his image -- there is a connection between humanity and God, even after the fall. We are created in his image because we have the capacity for morality and rationality. There's more to it than that of course, but that's at least some of it.