God and Evil

Back in the comments section of my post on Giving Thanks, an old college friend and I are discussing the age-old problem of why God permits suffering and other evils.  This is a serious problem; in my view the Argument from Evil is the only really formidable positive argument for Atheism.  (By a positive argument for Atheism, I mean something that provides specific evidence against God's existence, rather than merely making the negative claim that there isn't enough evidence for Theism to believe it.  In order to show that Christianity is plausible, both claims must be addressed.)

The conundrum is famous: If God is the All-Knowing, then he knows what things are evil, if he is the All-Powerful, he should be able to prevent them, and if he is the All-Loving, then he will want to prevent evil.  So why is there evil?

The only way to solve the problem is to postulate the existence of some good thing which cannot exist unless evil either exists, or is at least possible.  (Common "defences" might refer to putative goods such as free will, the opportunity for humans to exercise virtues, the orderliness of the universe, an afterlife of a sort that depends on people having had certain experiences, etc.)  If the good is such that it is logically impossible to get it without (possibly) getting the evil too, then the defence would be successful, since when we say that God can do anything, we don't mean that he can or would create a logical contradiction.  (As C.S. Lewis says in The Problem of Pain, "Nonsense remains nonsense even when we talk it about God.")  I'm not going to attempt a detailed defence here, but I do want to make some general points about the Argument from Evil.

My first point is that God's omniscience actually makes the Argument from Evil weaker, not stronger.  The reason is that we humans are not omniscient.  If we are ignorant, there's no particular reason to assume that we know what is the morally best way to run a world.  Suppose that you wrote down a list of all the things you regard as good (happiness, knowledge, beauty, whatever).  Suppose you figured out a way to weight all of these factors numerically—of course, there's no way we could ever agree on how to do this, and I'm not convinced it even makes sense, but let's run with it—so that you could assert that some possible kind of universe (call it U) is optimum: the best possible.

[Note for experts: my kinds of universes U here aren't exactly the same as the "possible worlds" discussed by analytic philosophers.  If the best possible kind of universe contains something like free will or nondeterminism, there will be multiple "possible worlds" W_1, W_2 \ldots consistent with the same overall plan U of the universe, some of which may be morally better or worse compared to the others.]

Now if God knows about even a single kind of goodness that we are ignorant of, or if he weights the various kinds of goodness differently than us in any way, then of course God will view some other kind of universe U^\prime as best.  It seems infinitely unlikely that U = U^\prime just by coincidence, so it seems to be almost certain that the universe will appear to us to contain evils that we can't explain.  One can argue about whether this is a sufficient explanation, but it's definitely something that has to be taken into account.  The idea that a superhuman entity which created the universe will see things exactly the way we do is absurd:

“For my thoughts are not your thoughts,
neither are your ways my ways,”
declares the Lord.
“As the heavens are higher than the earth,
so are my ways higher than your ways
and my thoughts than your thoughts.”
(Isaiah 55:8-9)

The second point I'd like to make, is that the Argument from Evil has emotional force as well as intellectual force.  Atheists tend to get annoyed when Theists suggest that Atheists don't believe in God because they resent him.  I've certainly seen plausible cases of this, but I don't want to speculate that all Atheists are this way, since I don't like making unfounded accusations about individual people's characters.  (Maybe that's why my Politics category only has one post in it so far.)

Nevertheless, leaving the Atheists aside for a moment, I think I can say from an examination of my own heart, and conversations with other people, that it's easy to carry an unconscious grudge against God for various real or imagined grievances in our lives, or the lives of those we care about.  Even if we have no grudge, there can be a deep sense of pain from all the kinds of grief that we don't understand.

So the Argument from Evil carries emotional force as well as intellectual force.  There's no necessary reason why an intellectually satisfying answer should be an emotionally satisfying answer, or vice versa.  One should bear this in mind when evaluating the intellectual arguments, since we may be asking from an argument something that no argument can do.

Finally, I believe that Christianity has resources for addressing the Argument from Evil which don't exist in generic-brand Theism, or indeed in any other religion.  It's much too simple to say that the existence of evil contradicts Christianity, when in fact the most basic doctrine of Christianity logically implies the existence of evil.

The basic doctrine is that 1) we human beings are wicked and deserve punishment, and that 2) in order to forgive us, God became an innocent human being and allowed himself to be tortured to death by us, and that 3) this act provides us with spiritual healing now, as well as physical immortality for all eternity.  Now regardless of whether you like this idea, even if you find it implausible or downright incomprehensible, you must admit that it's an idea about how God relates to evil, and uses it for the sake of good.  If there were no such thing as innocent suffering, Christianity wouldn't even be possible.  If Christianity is true, then God has arranged things so that the most important thing that ever happened was a horrible but redemptive evil.  All other evils, we view in the light of the Cross.

Posted in Theology | 32 Comments

A Universe from Nothing?

Today I went to a talk by Lawrence Krauss entitled “A Universe from Nothing”, which had the following abstract:

The question, "Why is there something rather than nothing?" has been asked for millenia by people who speculate on the need for a creator of our Universe.  Today, exciting scientific advances provide new insight into this cosmological mystery: Not only can something arise from nothing, something will always arise from nothing.  Lawrence Krauss will present a mind-bending trip back to the beginning of the beginning and the end of the end, reviewing the remarkable developments in cosmology and particle physics over the past 20 years that have revolutionized our picture of the origin of the universe, and of its future, and which have literally revolutionized our understanding of both nothing, and something.  In the process, it has become clear that not only can our universe naturally arise from nothing, without supernatural shenanigans, but that it probably did.

In the first 45 minutes, he provided an animated and reasonably clear explanation of concordance cosmology, the current version of the Big Bang model, dating from the discovery in 1998 that the expansion of the universe is accelerating (rather than decelerating as one would expect from the attractive gravity of ordinary matter).  This is exciting but now well-established work, which I've heard about a hundred times before, but was probably new to many of the people in the audience.  It was peppered with occasional off-hand sneers at Republicans, Theology, and Young Earth Creationism, but for the most part it was a pretty valiant stab at popularizing an important set of 20th century discoveries.

The real reason I was there, of course, was to listen to his claims in the last 15 minutes that modern cosmology somehow points to the nonexistence of a Creator.  His claim was that there is evidence that the universe came from "Nothing" according to physical processes, and this apparently is supposed to undermine the religious view that God created the world supernaturally.  There were so many things wrong with this part of his talk, both a physics and a philosophical perspective, that I'm not entirely sure where to begin.  But let's try anyway.

His Slam on Theology.  Krauss said that Theology wasn't based on empirical evidence, so therefore he didn't believe it.  That was it.  He didn't seem to take any particular theological ideas seriously enough to even try to define them, let alone refute them.  There was no indication that Religion had any other origin besides a bunch of clueless dudes sitting around asking "Why is there Something rather than Nothing?"  (In the case of Christianity, I thought it had more to do with a guy claiming to be God, doing miracles, and dozens of people saying that they saw him alive after he was killed.  But what do I know?)

But let's get back to cosmology, since that was the subject of his talk.  It used to be that Christians believed that the world was created a finite time ago, out of Nothing.  Although some of them, like St. Thomas Aquinas, said that God could have created a universe with an infinitely long past.  Atheists had (and have) a diversity of opinions, but most of them thought that things would make more sense if the universe were around forever, since then maybe you wouldn't have to explain where it came from.  Then Big Bang cosmology came along, and it now seems—provisionally speaking—like the Universe really did have a beginning.  Now some atheists think they can refute the Christian view that God created the Universe from Nothing by arguing that the world did emerge from Nothing.  The role-reversal here is a little strange.

What Christians mean by creation ex nihilo is that God created the Universe, but that he didn't make it out of any pre-existing stuff that was lying around.  Thus, while the universe didn't come "out of" anything, it still comes from God.

What Krauss seems to mean is something quite different, namely that there's some specific entity we can talk about called "Nothing", which has suitable properties for generating our universe.

But the universe can only come from nothing if you define a certain kind of something as being "Nothing".  Duh, because any explanation by its very nature must explain one thing in terms of some other thing!  This other thing must be taken for granted for purposes of the explanation.  Now, Krauss actually referred to 3 different ideas which he called "Nothing #1, #2, and #3":

Nothing #1: an "empty" spacetime a.k.a. the vacuum.  In ordinary non-speculative quantum field theory (QFT), the "vacuum state" (the configuration of fields with the lowest energy) is actually filled with so-called virtual particles which can affect physics in various ways.  At least, that's what the popularized physics books say; if one actually studies quantum field theory rigorously, people tend to use somewhat different language since the notion of "virtual particle" can be difficult to define.  But let's spot him the terminology since he was talking to a popular audience.

Krauss claimed that if you start with an empty space which has no virtual particles in it, virtual particles will appear, and this is "something" coming from "nothing".  This is bosh, since strictly speaking, there's no such thing in QFT as a state with no virtual particles.  (If there were, it would be infinitely different from the vacuum state, and would therefore have an infinitely large energy.  That's not nothing at all!)  If anything can colloquially be called "Nothing" in QFT, it is the vacuum state.  But this state already has all those virtual particles in it.  And as time passes, this vacuum evolves to....wait for it....itself!  That's right, if you agree to call the vacuum state Nothing, then Nothing comes out of it.  (He seemed to think this story might change once you take gravity into account, due to negative energies, but I didn't really understand this suggestion so I won't comment on it.)

The QFT vacuum isn't nothing.  Of course, from a strict philosophical point of view, the vacuum state of QFT is not Nothing since it's filled with all those virtual particles, and even aside from that, there's the space and time geometry, which is not Nothing.  To fix this he started taking up a different kind of nothing:

Nothing #2: the absence of any space or time.  This actually connects to an interesting quantum gravity idea known as the "Hartle-Hawking state" or the "no-boundary boundary condition".   (Jim Hartle is on my floor at UCSB, by the way.)  The suggestion is that the laws of physics not only tell you how the universe at one time evolves to a later time, they also tell you what the initial state of the universe is.

In some sense, one can think of this state as emerging out of Nothing #2.  However, the sense in which this is true is subtle.  There's another sense in which the Hartle-Hawking state does not emerge from Nothing; rather it has existed for an infinite amount of time— the popular physics articles never mention this, for some reason!  This is an interesting and important idea, but I think it deserves to be in it's own post, after I've explained QFT better.  The important thing to know is the following:

The crucial physics here is totally speculative!  It was entirely based on speculative ideas about quantum gravity which anyone working in the field would admit are not proven.  This is because we currently have no experimentally testable theory of quantum gravity!  (Nor do we even know how to formulate a consistent theory of quantum gravity mathematically, except perhaps in some special situations that probably don't apply to the beginning of our universe)

I mentioned this in the Q&A afterwards.  My comment seemed to aggravate him a little, since he thought he'd been sufficiently clear about this.  But I discovered that at least one member of the audience was still unclear on which parts were speculative, and which weren't, at the end of the lecture.  In my experience, one has to be crystal clear about this sort of thing when speaking to a popular audience, or they tend to walk away thinking that "Science" has proven things when it hasn't.

Atheists such as Krauss scorn theology as being completely non-empirical.  They claim it is not based on evidence of any sort.  I find it extremely ironic when this sort of atheist thinks that speculative quantum gravity ideas are just the right thing to further bolster their atheism.  Suppose you think that Science is better than Religion because it is based on evidence, and suppose you also want to refute Religion by using Science.  Here's a little hint: consistency would suggest using a branch of Science that actually has some experimental data!

The universe has zero energy.  Krauss thinks that the universe coming out of Nothing has been made more plausible by cosmology.  To understand his terminology, you have to know that (roughly speaking) a closed universe means that space at one time is finite in volume, and shaped kind of like a sphere, so that if you travel around the universe far enough you come back to where you started.  On the other hand, in a flat universe, space at one moment of time is shaped like ordinary Euclidean geometry, and is infinitely large.  Current observations indicate that the universe is flat.  As far as I could tell, Krauss' argument can be translated into these terms:

  1. The total energy of a closed universe is zero.  (It's tricky to define energy in general relativity, but according to one commonly used definition, this is true.)
  2. Conservation of energy suggests that if the universe came from Nothing, it should have zero energy.
  3. If there was a period of extremely rapid expansion at the beginning of the universe (as evidence suggests there was—this is called inflation), then whether or not the universe started out closed, it should look flat today.
  4. But the universe does look flat,
  5. Therefore Science suggests that the universe was created out of Nothing,
  6. Therefore there is no need for God.

Perhaps I'm missing some crucial steps in his argument.  But there seem to be several enormous leaps of logic in there.

The Hartle-Hawking state isn't Nothing either.  Strictly speaking, even the Hartle-Hawking idea doesn't strictly get the universe out of Nothing, since it says that the initial state of the universe depends on the laws of physics.  Now the laws of physics aren't nothing.  So if, for example, you are wondering if there is any role left for the Creator, then one might say he picked the laws of nature.

Now, there's all sorts of difficult philosophical issues involved in what's called the Cosmological Argument for the existence of God.  But it's hard to get into them with someone like Krauss who is so dismissive of Philosophy.  The trouble with people like that is that it isn't possible to just find things out using Science instead of Philosophy.  That's because you have to do Philosophy to know what is or is not implied by Science.  People who dismiss Philosophy still end up doing it; they just do it badly, without a critical examination of their premises.

Nothing #3: the string theory multiverse.  Krauss acknowledges that the laws of phyiscs themselves might seem to call  for an explanation.  Especially since the various constants of Nature seem to be "fine-tuned" to allow the existence of life (I'll go into this in much more depth later).  On the face of it, this seems to be at least some mild evidence for the existence of God, but Krauss would never admit such a thing.

He suggests that we can explain this fine-tuning if string theory turns out to be true.  That's because string theory has an enormous number of different possible configurations, that look like universes with different laws of physics.  Some people have suggested that if there's a gazillion different universes (known as the "multiverse"), each with its own laws of physics, that it's not surprising that one of those universes should support life.  Krauss admitted that there was some dispute as to whether this idea counts as "Science", what with it being totally speculative and arguably untestable.  But what I want to know is, why the $@#& would we ever refer to an infinite number of universes, governed by the principles of string theory, as a Nothing?

I should say that this review is based entirely on Krauss' talk.  I have not read his book, but I have read this negative review by philosopher St. Feser.

[Update 7/21/20: added two paragraphs to the text, beginning "What Christians mean..." to make the argument a little clearer.]

Posted in Reviews | 18 Comments

Pillar of Science VI: Community Examination

Scientific Results are Examined Collaboratively.

Scientists do not work alone, but in a particular kind of community.  The last stage of a research project is publishing and explaining the results.  Assuming these results get noticed, this begins the process of further review, critique, confirmation and rebuttal by other scientists.  No one person is smart enough to see things from all angles.  We need help from others to look in a clearer, less fragmented way.  Perhaps one could call this undivided looking?

Science is not just a set of facts, or an abstract procedure for testing ideas.  It is an ethical, truth-seeking community.  The love of truth is embodied in the alliance of particular, fallible humans, united by a common geeky interest in finding something out.  Together we create a public deposit of information which can be used to find new things out.

Because the community as a whole is truth-seeking, in the long run it reduces the need to trust the competency and ethics of the original researchers.  If someone fakes an experiment (or else just makes an innocent mistake), other people will be unable to replicate the result, and eventually the truth will come out.

Healthy scientific collaboration encourages reasonable dissent.   Otherwise group-think can insulate the community from effective criticism of accepted ideas.  Some people say that scientists should proportion their beliefs to the evidence.  However, there's also some value in diversity of opinion, because it permits subgroups to work on unpopular hypotheses.  I suppose things work best when the scientific community taken as a whole proportions its research work to the evidence.

One might argue that collaboration is not strictly necessary to Science.  Imagine a solo scientist doing careful experiments in secret, and drawing the correct conclusions from them.  (Even in this case the scientist would be drawing on public ideas which had gone before, "standing on the shoulders of giants", as the saying goes.)  But in practice, the benefits of discussion are so great that it's hard to imagine a successful modern scientist working completely alone.  Hence the symbiosis of Science with the Academy.

Individuals who think they can revolutionize Science all by themselves are almost always crackpots, the sort of crazy person I described one pillar ago.  If you want to see clearly, you have to expose yourself to the light.

Posted in Scientific Method | 1 Comment

Geometry is a Field

In Time as the Fourth Dimension?, I explained how to calculate the distance (or duration) squared between any two points of spacetime, using a spin-off of the Pythagorean theorem:

s^2= (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 - (\Delta t)^2.

Then I explained the Ten Symmetries of Spacetime, i.e. ways to shift or rotate the coordinate system (t,\,x,\,y,\,z) that don't change the formula for s^2.

Well, it turns out that I lied.  The formula isn't actually true, except in the special case that there is nothing in the universe.  A significant reservation, I know.  Instead, what's true is that the geometry of space is a field, meaning that it varies from place to place, depending on where you are!  However, if you zoom in really close at any particular point, it looks similar to the formula I told you.

The field that says what geometry is like at any given place and time is called (brace yourself) the gravitational field.  In order to describe it, we use something called the metric, which indicates what the geometry of spacetime looks like at any given point.  The way this works is, suppose we have two points p and q which are very close to each other.  Suppose we want to know the distance between these points.

Since the points are really close to each other, we call the distance between them ds, where the d is just a reminder that we're using Calculus to study infinitesimal quantities.  If you don't know Calculus, just pretend these are really small numbers.  We want to figure out what ds is, if we know the infinitesimal coordinate differences (dx,\, dy,\,dz,\,dt).  The way we do this is by generalizing the heck out of the Pythagorean theorem.  I'll write it down, and then explain what it means:

(ds)^2 = g_{xx}\,(dx)^2 + g_{yy}\,(dy)^2 + g_{zz}\,(dz)^2 + g_{tt} \,(dt)^2 + \\ 2[ g_{xy}\,dx\,dy + g_{xz}\,dx\,dz + g_{xt}\,dx\,dt + g_{yz}\,dy\,dz + g_{yt}\,dy\,dt + g_{zt}\,dz\,dt].

The right-hand side of the equation consists of every possible way of multiplying two of the coordinate distances (dx,\, dy,\,dz,\,dt).  There are 4 different ways to pick the first (dx,\, dy,\,dz,\,dt), and 4 different ways to pick the second, which gives 4 \times 4 = 16 possible combinations in all.  However, multiplication is commutative so e.g. dx\,dy = dy\,dx.  So I added terms like that together; that's where the factor of 2 came from.  Taking that into account, there's 10 terms in all.

The funny g things with subscripts are just functions of spacetime, i.e. they are just numbers that depend on where you are, i.e. they are fields.  In the special case where we pick these numbers to be g_{xx} = g_{yy} = g_{zz} = +1,\,g_{tt} = -1 and the rest zero, we get the geometry I told you about, which goes by the aliases "Minkowski space", "flat spacetime", and "Special Relativity".  In all other cases we have what is colloquially called "curved spacetime" which is the province of "General Relativity".

The formula above looks kind of ugly, but we can prettify it by choosing good notation.  We collectively refer to all ten of these gravitational fields as the metric, denoted g_{ab}, where subscripts like a and b can refer to any of the four coordinate labels.  (People often call these labels (0,\,1,\,2,\,3) instead of (x,\,y,\,z,\,t) to avoid confusion, since the metric itself says which of the coordinate directions behave more like space, and which behave more like time, and this can vary from place to place!)  Then we write the four coordinate differences (dx,\, dy,\,dz,\,dt) collectively as dx^a, where the superscript says which of the four it is.  Finally, we make up a rule called the Einstein summation convention, that if we ever see the same letter as both a subscript and as a superscript, we add up all of the four possible ways for them to be the same (i.e. both 0, both 1, both 2, or both 3).  These are just changes in how we write things, not substantive changes, but they let us rewrite that long ugly equation like this:

ds^2 = g_{ab}\,dx^a\,dx^b.

There, isn't that much prettier?

Suppose we want to find the distance (or duration) between two points which are NOT infinitesimally close to each other.  In that case, we have to choose a path between the two points, since the amount of distance (or duration) depends on which path you choose, and in a curved spacetime there's not necessarily one "best" path.  This shouldn't seem that strange, since even in everyday life we know perfectly well that the distance between San Francisco and L.A. depends on which highway you take, and the distance between Tokyo and New York depends on which way around the globe you fly.  (It's totally intuitive for distances, but when the duration depends on the route you take through spacetime, people call it the Twin Paradox and act all shocked!)

So this is the first main idea of General Relativity: the geometry of spacetime is a field which varies from place to place.  This field affects matter by determining the paths that things take through space and time, but it also is affected by matter—we call this gravity.  The second main idea is that coordinates are an arbitrary choice; I'll tell you about this later.  The third main idea is the Einstein equation which says how matter affects the metric.  I haven't told you anything about this equation yet, but once I do, you would in principle be able to calculate everything about the gravitational field from that one equation.

There can also be distortions of the spacetime geometry which exist independently of matter.  These gravity waves are to gravity what light is to electromagnetism, ripples in the field which travel through empty space, and can be emitted and absorbed.  The propagation of these waves is also determined by the Einstein equation.  Since gravity comes from massive objects, gravity waves are emitted when extremely large masses oscillate, for example when two neutron stars orbit each other.  We know gravity waves are there, but we haven't detected them directly.  However, we hope to detect them soon with the LIGO experiment.

UPDATE: I realized that I never said how you would calculate the distance between two points, once you choose a path.  The answer is that you chop the path into lots of tiny little line segments, and find the length of each line segment using the metric.  Then you add them all up.  If you know Calculus, this can be done using an integral.

Posted in Physics | 6 Comments

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