The Equations of Motion

by Aron Wall Posted on September 16, 2013

So far in my explanation of General Relativity, I've discussed the metric g_{ab}, from which one can calculate the curvature tensor R^{a}_{bcd} by way of the connection \Gamma^{a}_{bc}.

In practical astrophysical contexts:

  • The metric is related to the gravitational potential at a point, i.e. how much ``potential energy'' a unit mass will have sitting in the gravitational field.  But I haven't said anything about energy yet, so you're entitled to ignore this remark...
  • The connection (which involves a derivative of the metric) tells you the gravitational force at a point, i..e the amount by which freely-falling objects will accelerate in a given coordinate system.
  • Finally, the curvature (which involves a derivative of the connection) tells you the tidal forces at a point, i.e. a difference in the force acting on a nearby object.  Yes, the ocean tides happen because the moon's gravitational field has nonzero curvature at the Earth's location.  That's why it's called that.

So far this is just the kinematics of general relativity—that is, what kind of entities are involved, and the basic outline of their behavior.  For example, If I wanted to tell you the kinematics for basic Newtonian mechanics (what you learn in high school physics), I'd say that A) there are a bunch of objects which have masses and positions (and orientations if you want things to get complicated...), B) the position of an object can change with time, but its mass is ``conserved'' and therefore doesn't, and C) if you want to work out the ``force'' of an object, you can do so using F = ma.

OK, so I've told you all about Newtonian Mechanics, and now you can go use it to solve problems, right?  No, of course not!  You can recite "the time-derivative of the position is the velocity, the time-derivative of the velocity is the acceleration, and the acceleration equals the force over the mass" over and over again, but it's totally useless until I tell you what the forces actually are!  Without that, you can't make any predictions at all about what the objects are doing.

Unless you count boring predictions like "the object will be somewhere", you need to know something else.  This something else is called the dynamics, which means the rules for how things actually change with time.  (For example, if I told you that any two objects with mass m_1 and m_2 at a distance r are gravitationally attracted towards each other's positions, with a force that is proportional to F = Gm_1m_2/r^2, and if you know the initial positions and velocities, then you can work out their orbits!  At least, you can if you're clever at math, like Newton was.)

So we need to write down an equation which says how things can change with time.  We call this the equations of motion.  Ever since Newton wrote down F = m{\ddot x} (each dot being a time derivative, so that his archnemesis Leibnitz would have written F = m (d^2x/dt^2) to say the same thing) we've realized that these equations typically involve taking two derivatives.  So we shouldn't be surprised that the equation of motion for general relativity involves the curvature tensor R^{a}_{bcd}, since it's a double derivative of the metric, which is the basic field of General Relativity.

To write down the equations of motion, we need to massage the curvature tensor a little bit.  If you've forgotten the ground rules for tensors, click on the link.  We start with the the Riemann curvature tensor R^{a}_{bcd}.  Since each of the letters is a spacetime vector index with four possible values, it looks like this has 4 \times 4 \times 4 \times 4 = 256 components.  Fortunately there are a lot of symmetries and constraints, so there's actually only 20 independent components per spacetime point.  We can define the Ricci tensor R_{ab} by contracting the top index with the middle index on the bottom, like so:

R_{ab} = R^c_{acb};

Recall that the Einstein summation convention says that if you ever see the same letter as both a subscript and as a superscript, you've got to 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).  Since the Ricci tensor is symmetric (R_{ab} = R_{ba}), it only represents 10 out of the 20 curvature components.  If this is not enough simplification for you, we can go further by contracting again using the inverse metric:

R = R_{ab} g^{ab}.

R is called the Ricci scalar, because it has just one component.

Whew!  Without further ado, here's the equation of motion for General Relativity, called "the Einstein equation" after you know who:

R_{ab} - \tfrac{1}{2} g_{ab} R = 8\pi G T_{ab}.

Compact, beautiful, and probably completely incomprehensible since I haven't explained all of the symbols yet!

The 8 and the \pi are the same numbers which you learned about in school.  G is Newton's constant, which I sneakily introduced earlier in this post.  Note that the 8\pi isn't really just there for backwards compatibility with Newton's force law.  If Einstein's equation had been discovered first, we would have left out the 8\pi from it, and then we would have written the force law as F = G m_1 m_2/ 8\pi r^2.  But as it is, Newton got his G before Einstein did, so we're stuck with it.

But the really important symbol here is T_{ab}.  This is the energy-momentum tensor, or (because why should anything have only one name!) the stress-energy tensor.  It's a 4 \times 4 symmetric matrix which tells you how the energy and momentum of matter (stuff) are flowing through a given point.  Now if you are a true Israelite in whom there is no guile, you should be asking: "What on earth (or in the heavens) are energy and momentum!  You haven't explained that yet!"  No I haven't.  For now, let's just say it's a property of matter, but we will get to it in a later post.

The combination of curvatures R_{ab} - \tfrac{1}{2} g_{ab} R which appears on the left-hand-side is also known as the Einstein tensor.  It has the same 10 components as the Ricci tensor R_{ab}; they're just repackaged a bit differently.  So the Einstein equation is actually 10 equations.

So, if you know what the matter is doing, you can figure out something about the geometry of matter.  At least, you can figure out the 10 of the components of the curvature which correspond to the Ricci tensor R_{ab}.  Since the full Riemann tensor R_{abcd} has 20 components, there are 10 components left which are undetermined.  The remaining 10 components are called the Weyl tensor, and can be nonzero even in regions in which there is no matter.  That's why there can be tidal forces outside of the surface of the sun or moon, even though there isn't any solar or lunar matter there.  It's the Weyl tensor which does that.  Also, as I wrote in Geometry is a Field:

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.

It's also the Weyl tensor which allows for gravity waves.

Clever readers may notice that I never wrote down what the Weyl tensor actually is.  There's a clever formula where you start with R^a_{bcd}, and then cleverly suck out all of the information about R_{ab}, and end up with the Weyl tensor C^a_{bcd}.  But it's a bit complicated, so don't ask.  The important thing is even when all of the components of R_{ab} are zero, R^a_{bcd} doesn't have to be zero.

When we say that the Einstein equation is the ``equation of motion'' for General Relativity, we mean that you can use it to work out how the metric changes with time.   So, if you know the metric everywhere at some ``time'' which we will call $t = 0$ (think of this as being like the position of the gravitational field), and if you also know its first derivative \dot{g}_{ab} (think of this as being like the velocity), and if you know what the matter is doing, then the Einstein equation (which is like the force law) lets you work out the second derivative \ddot{g}_{ab}.  By continuing to apply the Einstein equation, you can work out the value of the metric for all time!

Well, not quite.  Remember that coordinates don't matter!  This means that we can't actually hope to totally determine the metric, since if we start with a metric which obeys the Einstein equation, and distort it by changing the coordinate system, we get an equally good solution to Einstein's equation.  So what we should really say, is that if you know the metric and its first derivative at t=0 (and you know how matter behaves so you can figure out T_{ab}), then you can determine the fields at t > 0 or t < 0 up to coordinate transformations.

So we can actually only need to figure out \ddot{g}_{ab} up to coordinate transformations.  There are 10 components of  g_{ab}, but there are also 4 spacetime coordinates (t,\,x,\,y,\,z) whose values can be freely determined.  As a result, we actually only need to use 10 - 4 = 6 of the Einstein equations in order to figure out how the metric changes with time.

The remaining 4 equations are called constraints, because they don't involve second derivatives of the metric.  Instead, they restrict which values of (g_{ab}(x,y,z),\,\dot{g}_{ab}(x,y,z)) you are allowed to start with.  These constraints are one of the most subtle features of General Relativity, because they ensure that the total energy and momentum of an object (like the sun) are encoded in the gravitational field coming out from it.  However, since I haven't yet explained what energy and momentum are, I should probably say something about that first, before going into this.

Posted in Physics | 6 Comments

Word-for-Word translations

by Aron Wall Posted on September 14, 2013

St. Rollin Weeks writes:

As an FMC member, I have attended two of your sessions.

I am interested in the prospect of time "before" the Big Bang, Time and Eternity, God's foreknowledge and man's free will, the Arrow of Time (Roger Penrose), Time Reborn (lee Smolin), and the books and papers on 'time' by William Craig Lane and J P Moreland of the Apologetics Dept. in Talbot Theol. Seminary at Biola.

But what I am really into right now is writing a paper on the King James Only (KJO) controversy. I have narrowed it down to 3 essential issues: (1 which are the best manuscripts (Greek, Hebrew, Aramaic) to use--the issue of Textual Criticism'? (2 if God preserved His Word perfectly throughout the ages, what mechanisms did He use, and where in the Scriptures do we find evidence that He would use these mechanisms?, and (3 how do we deal with the very intractable problem of translation from the original languages?

I have an MA in Linguistics, and I have done field work in Brazil with an indigenous tribal people. Some translation issues I have become aware of are:
~ ancient historical translations ((Coptic, Syriac, Septuigint) have used slightly different source texts. Were these the genuine Word of God?
~ Greek-to-English translation works fairly well, because both have highly developed vocabularies, but this is not the case when translating into a language with vastly different cultural emphases and interests, and
~ Greek and English are both members of the Indo-European Families. Ancient Hebrew to English is not so good a fit. When one gets into other wildly different languages, word for word translations become impossible.

I hope to join in again in one of your classes.

In Christ,
Rollin Weeks

Hi Rollin, I'm glad you enjoyed the classes.  That's a nice grab bag of issues you mention there, but since you highlight King-James-only-ism, I think I'll focus on that. I find it difficult to even take the KJO view seriously, for a variety of reasons.

There is simply no such thing as a perfect translation.  Even from Greek to English, word-for-word translation is not always the most accurate or faithful way to translate. I assume you know that Greek is a case language, meaning that (unlike English) it is the endings of the words, rather than their position in the sentence, which determines their grammatical role in the sentence (subject, object, possessor, etc.).  Instead they used word order for purposes of emphasis.  The first and last words in a sentence are the ones which are being emphasized.

Another issue is particles.  In a normal Greek sentence, there are a few two or three letter words called "particles" which normally appear right after the first word. When you are first learning how to translate Greek, you simply leave these words out since they don't seem to affect the basic meaning.  For Greek experts (as I am not!) they show how the ideas in the sentence are connected to the ideas which have gone before.

There are various tricks which can be used to render these meanings into English, but they usually involve departing from the word-for-word ordering.  In these respects, "paraphrases" like the New Living Version or St. Phillips' translation can sometimes actually be more accurate than a more "literal" translation, since they have the freedom to signal emphasis and connection-between-ideas in other ways.

In the absence of a specific divine revelation, it is simply hubris to say that God specially favors one particular English translation, given the existence of numerous good translations both before and after the KJV. That being said, given the time and the lesser degree of scholarly knowledge, the KJV was a remarkably good translation, combining literalness with style in a skilled way (partly with the help of archaic English "particles" such as "lo!").  Another very nice feature is that when the original language is ambiguous, they tried to translate into English in a way which reflects that ambiguity, instead of just picking one possibility.

I said it was a good translation: since the meanings of many English words have changed over 400 years, and many passages now convey an incorrect meaning to modern readers.  To use the KJV today, especially with uneducated readers, is to guarantee that they walk away with wrong ideas about what the Bible says.

Regarding issues of Textual Criticism, the Textus Receptus differs from the accepted scholarly text in numerous places.  This has a lot to do with the fact that St. Erasmus's Greek text was based on only 7 relatively late Greek manuscripts, each including only parts of the New Testament, and all but one from a single textual tradition.  And we are supposed to believe that this is more accurate than all other more carefully compiled texts?  That God miraculously preserved his word through Erasmus, while allowing all other scholars everywhere else to fall into error? Because of his special desire for later English-speaking people (but apparently not people in other cultures) to have a perfect translation?  Ridiculous!

Regarding the Old Testament textual issues, you are right that the Septuagint seems to have been based on a somewhat different version of the Hebrew text than the Masoretic, which is used by almost all modern translations.  Which text is more accurate in a given place is anyone's guess, but the Dead Sea Scrolls are more similar to the Masoretic text.  There are many instances in which we know that the Septuagint was poorly translated (sometimes they even left out large chunks which they didn't know what to do with!), although in other cases we have to defer to them because the meaning of the Hebrew words is otherwise unknown, or in when the Masoretic text is corrupt (e.g. 1 Samuel 13:1, which in the Masoretic text says that Saul was one year old when he became king, and that he reigned for two years!)

I believe that God has promised this about his word:

For as the rain cometh down, and the snow from heaven, and returneth not thither, but watereth the earth, and maketh it bring forth and bud, that it may give seed to the sower, and bread to the eater:

So shall my word be that goeth forth out of my mouth: it shall not return unto me void, but it shall accomplish that which I please, and it shall prosper in the thing whereto I sent it. (Isaiah 55:10-11)

This, however, is not a promise about every word being preserved perfectly in some static sense.  It's a promise about God getting the results which he intended to get: namely a harvest of righteousness and justice in the lives of those who are transformed by God's word.

The belief that this transformation will somehow be inhibited if we don't have 100% certainty about every word (or even 100% certainty about which books should be in the Old Testament!) is a Fundamentalist notion which has little connection to actual progress in holiness.  Yes, God's word is fully inspired and should be treated with respect, down to the last "jot and title"—at least when we know what they are—but we can't lose sight of why he gave us his word.

I believe that God is very unscrupulous in how he reaches people.  His Spirit can sometimes even use translation mistakes to bring people closer to him (and in that sense, they may be God's word to that particular individual), but we should still do our best to avoid making them.

There's a very important word which is missing from this post so far.  That word is "Jesus".  Muslims believe that the highest revelation from God is a Holy Book, dictated to a prophet without any human contamination, and perfectly preserved from error through the centuries.   We also have a Holy Book, but we believe that God's final revelation is a Person.  That's why God chose to use the human personalities of the biblical authors as a means to communicate to us the personality of Jesus.

What we need is not a word-for-word translation onto paper, but a "Word-for-Word" translation onto our hearts and minds.  Remember what St. Paul says:

Do we begin again to commend ourselves? or need we, as some others, epistles of commendation to you, or letters of commendation from you?  Ye are our epistle written in our hearts, known and read of all men: Forasmuch as ye are manifestly declared to be the epistle of Christ ministered by us, written not with ink, but with the Spirit of the living God; not in tables of stone, but in fleshy tables of the heart. 

And such trust have we through Christ to God-ward: Not that we are sufficient of ourselves to think any thing as of ourselves; but our sufficiency is of God; Who also hath made us able ministers of the new testament; not of the letter, but of the spirit: for the letter killeth, but the spirit giveth life.  (2 Cor 3:1-6)

Posted in Theological Method | Leave a comment

Is it possible to be good without God?

by Aron Wall Posted on September 12, 2013

Is it possible to be good without God?  Well, it depends on what you mean...

In what follows, I will identify 11 different possible meanings to the question.  I have answered them with 5 Yeses and 6 Noes.  Of the six No answers, half apply equally to religious and nonreligious folk alike, while the other half distinguish those who believe from those who do not.

At the most basic metaphysical level, a Christian might start out with the following answers:

  1. No, because God is the Creator of all things.  Apart from God, nothing would exist.  Therefore, it would be impossible for there to be any good (or bad) human beings.
    .
  2. No, because God is the grounding of all morality.  He is Goodness itself.  All other things are good by participating in his goodness (or are bad by failing to do so in some respect).

Note, however, that although #1 and #2 are true in the real world, they are deductions from the Christian worldview.  They make sense, but are not strictly required given human existence.  Although in my view the evidence strongly supports Theism, it is not a logical contradiction to imagine that Atheism is true (in which case, the things which exist would obviously not depend on God).

Some Atheists, especially those of a scientistic bent, think it's obvious that morality is nothing more than a set of primate instinctual behaviors which have been refined by human cultures, that differences in evolution or culture could have produced quite different kinds of "ethics", and that there is no way to compare these as being better or worse in any kind of absolute way.  If so, there is no such thing as good and evil, objectively speaking.

Other Atheists may say that this doesn't do justice to our beliefs about right and wrong, and that there must exist some objectively defined notion of goodness, that Hitler must really be worse than Ghandi according to some rationally compelling measuring stick.  Such Atheists may differ in their account of what this consists of.

The first kind of Atheist might say to the second: "Wait, that's really weird!  If there's such a thing as an objective right and wrong, that's like saying that the universe cares whether you are good or bad.  But caring is the sort of thing that persons do.  So your view is suspiciously similar to Theism."  This is the Argument from Ethics, normally employed by Theists as an argument for the existence of God.  It says that if Ethics corresponds to an objectively real property in the world, then it must somehow be an aspect of the Ultimate Nature of Reality (whatever that is).  But if there is an Ultimate Reality which discriminates between good and evil, it's only a short hop-and-a-step from there to Theism.

However, this Argument from Ethics can only be a successful argument for Theism if Atheists have some valid reason to accept its premise (that ethics is objective).  So if Theists expect to deploy this argument, they are actually conceding the following point (which may superficially seem to contradict #2):

  1. Yes, in that there are reasons to believe that morality is objective, which can be known to an Atheist, prior to realizing that God exists.  Therefore an Atheist can believe in objective moral standards.

This, however, leads us to a completely different question.  Before we were asking whether Ethics depends on God actually existing.  This is completely different from asking if ethical behavior depends on some person believing in God's existence.  (In my experience, when a Theist and Atheist get into an argument about whether Ethics requires God, usually the Theist is talking about something like #2, while the Atheist often means something more like #5 below.)

Let's continue on the thread of this new question:

  1. Yes, in that God has placed in each human heart a conscience, which no one can completely ignore.  This is true for everyone, regardless of their philosophical beliefs about Ethics, and regardless of whether they know about the Bible, or have any other specific divine revelation.  This gives to all people an opportunity to do what is right.  As St. Paul says:

 God does not show favoritism.   All who sin apart from the law [i.e. pagans, who either don't know, or don't accept the "Torah" or Jewish Bible] will also perish apart from the law, and all who sin under the law [Jews who know about God's revelation] will be judged by the law.   For it is not those who hear the law who are righteous in God’s sight, but it is those who obey the law who will be declared righteous.

Indeed, when Gentiles [i.e. non-Jews], who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law.  They show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts sometimes accusing them and at other times even defending them.  (Romans 2:11-15)

           In this way, every kind of person can do what is good, at least sometimes.

  1. Yes, in that fear of divine punishment is not necessary to be virtuous.  Nor is it the best reason.  Many Atheists would argue that one should be ethical for its own sake, not because of fear.  And Christianity agrees.  "Perfect love casts out fear," says St. John, "because fear has to do with punishment, and whoever fears has not been perfected in love" (1 John 4:18).  Perfect means complete, so the meaning is that the most ethically advanced person does good out of love for others, not out of fear of being judged (either by men, or by God).
    .
    However, although obeying out of fear of divine judgment is a lower stage of moral development, I would argue that it still has some value.  "The fear of the Lord is the beginning of wisdom" (Prov. 9:10, Psalm 111:10).  And of course, deep reverence and awe for God and his commands is appropriate at every stage of moral development, in light of his holiness.
    .
    Note that hoping to be rewarded by God is not in the same category as fearing punishment.  It would be, if one were looking for an arbitrary incentive which has nothing to do with being virtuous.  But there also exists a natural reward for virtue, which is due to obtaining what one was seeking.

But can a nonreligious person be a good person in the sense of actually fulfilling their most basic moral duties?

  1. No, because according to Jesus, the first of the two most important commandments is "The Lord our God, the Lord is one.  Love the Lord your God with all your heart and with all your soul and with all your mind and with all your strength" (Deuteronomy 6:5; Mark 12:30).  If God exists, then there is a morally prescribed right relation to him, as well as to human beings.  Although there were monotheistic pagans, clearly it is impossible for an Atheist to obey this commandment.
    .
    Related to this, Christians regard holiness as an essential aspect of good character, but most Atheists aren't even trying to be holy.
    .
  2. Yes, in that Atheists can obey the second commandment singled out by Jesus: "Love your neighbor as yourself" (Leviticus 19:18, Mark 12:30).  Clearly it is possible for a nonreligious person to do particular things which are consonant with loving other people.  I'm not going to belabor this point, but only because I don't think it should be controversial.
    .
  3. No, in that Christians regard these two commandments as a unity, so that it is impossible to fully obey the one without obeying the other.  We cannot love God and hate men, nor do we understand what real love is until we know God's love.  As St. John says,

Dear friends, let us love one another, because love is from God, and everyone who loves has been born of God and knows God.  The one who does not love does not know God, because God is love.  God’s love was revealed among us in this way:  God sent his One and Only Son into the world so that we might live through him.   Love consists in this: not that we loved God, but that he loved us and sent his Son to be the propitiation [or atonement] for our sins.  Dear friends, if God loved us in this way, we also must love one another.  No one has ever seen God.  If we love one another, God remains in us and his love is perfected in us....

If anyone says, “I love God,” yet hates his brother, he is a liar.  For the person who does not love his brother he has seen cannot love the God he has not seen.  And we have this command from him: The one who loves God must also love his brother.  (1 John 4:7-12, 20)

  1. No, in that all human beings are sinners, so that no one—religious or not—in fact succeeds in being ethical.  For most of us, we fall short even of the standard which we rightly expect of other people.  How much more when judged by God's perfect standard!  In Genesis, even as God promises not to wipe out the human race, he kvetches that "every inclination of the human heart is evil from childhood" (Genesis 8:21).  And St. Paul, after making it clear that sin is a problem even for people who know God's law, gives us this montage of Old Testament passages about the human race:

“There is no one righteous, not even one;
     there is no one who understands;
there is no one who seeks God.
 All have turned away,
they have together become worthless;
there is no one who does good,
not even one.”
“Their throats are open graves;
their tongues practice deceit.”
“The poison of vipers is on their lips.”
     “Their mouths are full of cursing and bitterness.”
“Their feet are swift to shed blood;
ruin and misery mark their ways,
and the way of peace they do not know.”
“There is no fear of God before their eyes.” (Romans 3:10-18)

I was reminded of this passage when the scandal broke about Penn State coach Joe Paterno failing to report a child molestor.  People were amazed that such a righteous-seeming person screwed up that badly.  But if they really knew how to examine their own hearts and conduct, they shouldn't have been surprised.  He wasn't a hypocrite; his virtues were real, but they also weren't enough.   That is how God views even the best of us.  And apart from God's protection, each of us would be similarly unreliable in situations of power—I don't say that we would all make the exact same mistake he did (although many of us would have!) but that we are all capable of similar treachery against our own best ideals.

Fortunately, although we are all wicked, God has provided a way for us to be forgiven, cleansed, and healed through the death of Jesus.  This is the Atonement, one of the core doctrines of Christianity.  Through Jesus, God offers his grace to all of us.  His offer is to purify us from sin, not because we deserve it, but because we need it.  (And this is why, in accordance the canonization policy of this blog, I still ought to have said Saint Joe Paterno in the previous paragraph.)

However, the offer requires that we accept it, trusting him for this forgiveness.  And this is where faith comes in:

  1. No, in that in order to receive this forgiveness from Jesus, you must put your trust in Jesus as the Savior sent by God.  Now obviously it's hard to do that if you don't believe in God at all.  For "without faith it is impossible to please God, because anyone who comes to him must believe that he exists, and that he rewards those who earnestly seek him" (Hebrews 11:6).
    .
    Leaving aside the apparent unfairness for a moment, this is just common sense—if you don't believe in God, you don't have any incentive to hand your life over to him, and so you probably won't.  Of course, it's not enough to believe in God, since you can perfectly well think he exists without deciding to trust him.  As Jesus' brother said: " You believe that there is one God. You do well.  Even the demons believe—and tremble!" (James 2:19).  So Theism isn't enough.  No, you have to believe that it's worth your while to trust him, that he "rewards those who earnestly seek him".  That requires faith.
    .
    This isn't something completely different from the rest of life.  If you can't enter the water without panicking about drowning, you'll never learn how to swim.  If you don't trust anyone enough to say "I do", you will never be married.  It's just how things are.
    .
    I was just at the dentist to get my teeth cleaned.  This is essential for good hygiene, because no matter how well one might think one has brushed and flossed, there are always places that one misses.  Plus, once cavities start to develop, there's no way to fill them on your own.  If you "try to be good on your own, apart from God", then your teeth will rot away and fall out.  Metaphorically speaking, that is.
    .
    Only a tiny fraction of our mind is accessible to our conscious inspection at any one time.  And even in that small conscious part, we find that we are frequently unable to completely control our own passions, desires, and will.  We need someone else to cleanse us, someone who knows us inside and outside, and can reach into the parts of ourselves that we can't.  The good news is that God has offered to do this for us, for free, if we will trust ourselves entirely to him.  Only a fool would decline this offer—if they know about it, that is.
    .
  2. Yes, in that God will judge the world with perfect justice: "He will judge the world in righteousness and the peoples with equity" (Psalm 98:9).  This means actual justice, not some religious-affiliation test which has nothing to do with reality.  Therefore, if an Atheist is truly seeking what is good and true, and disbelieves in God through no fault of his own, then it must necessarily be that God will not condemn him in the Final Judgment.  If.  I do not make any judgment about how common this situation is.
    .
    Some caveats are called for here.  First, no one really does seek truth with their whole heart, see #9.  But God knows about about human nature, "for he knows how we are formed, he remembers that we are dust" (Psalm 103:14), nor has he "forgotten to be merciful" (Psalm 77:9).  If religious people cannot earn their salvation through works, then neither can the nonreligious.  Everyone who is saved is saved by God's grace, given through the Spirit by the work of Jesus.
    .
    Secondly, no one is saved apart from a relationship with Jesus.  But it may be that certain people can welcome Jesus without explicilty knowing that this is what they are doing.  The Parable of the Sheep and Goats seems to suggest this, anyway.  Alternatively, one could imagine people coming to faith after death, as suggested by St. Peter in a highly controversial passage, which is frequently mistranslated, because most theologians don't agree with what it really says!

In any case my hope is that you, Dear Reader, will come to know the inexpressible riches of God's salvation in this life, and that he will make you holy all the way through, so that you may love others sacrificially, just as he first loved us.

Posted in Theology | 26 Comments

Natural and Supernatural II

by Aron Wall Posted on September 4, 2013

Last time, I ended with a question: what are the Jews famous for?

The answer, of course, is Monotheism.  The Jews are famous for either bringing into the world, or else preserving, the doctrine that there is just one God.

It's important to realize that this is not just a matter of counting, as though Monotheism were the golden mean between Polytheism and Atheism.  It's not just about having the right number of gods.  It's a matter of what kind of gods you believe in.

Polytheists believe in gods which were born at particular times and places, and have limited spheres of influence.  In other words, their gods are just like you and me, except for being a lot more powerful.  In Greek or Norse mythology, most of the gods don't seem to have a moral advantage over human beings either.  They just get their way more often—except when they are quarreling with each other.

Monotheists, on the other hand, believe that God is the fundamental entity in existence, that he has no external limitations, that he is perfectly good and wise, that he is eternal, and that he created everything besides himself.  This, obviously, is a completely different kind of entity than the polytheistic divinities.  And, equally obviously, there cannot be more than one of these.  Logic says that there cannot be two rival Deities, each of which created everything else, including the other one.

Thus on the Monotheistic conception there can be only one God, and following the usual grammatical convention of capitalizing titles like "President" or "Dad" which single out a particular entity, one normally capitalizes the G.  But as a convenience, since in the rest of the post I will be talking about the Monotheistic God side by side with Polytheistic gods, in the rest of this post I will always use the captial letter to distinguish the two, so I don't have to keep using adjectives to keep them apart. (*)

A certain sort of Atheist likes to say, "What makes Jehovah any different than Zeus, Thor, Athena, or Allah?  Once you realize why you disbelieve in any of those gods, you'll know why I disbelieve in yours."  But this completely misses the point.  Thor and Athena are polytheistic gods, and they can both exist at the same time without contradiction.  Whereas "Allah" is not a different God from the God of the Jews or Christian, it's a name for the same concept of an ethical Ultimate Reality who created everything.  Monotheistic religions may disagree about how we should think about God, about what he is like, but we do not disagree about which God exists, since the basic concept is similar enough.  That's why Arabic speaking Christians also refer to God by the name Allah!

Monotheists criticize Polytheists, not because they have too many gods, but because to us they don't have any!  They are idolators, worshipping things which do not deserve to be worshipped.   Worship is an act of total submission and reverence, holding nothing back.  The polytheistic gods are not worthy of that.  They are mere creatures like us.  Polytheism is a form of Atheism.

In fact, the concepts of God and "gods" are so distinct, that one could even believe in the existence of both!  We Christians believe in the existence of many "supernatural" beings (angels and demons) who are much more powerful than we are.  But we don't worship them, because they aren't God; like us they are limited creations.  As St. Paul says:

We know that an idol is nothing at all in the world and that there is no God but one.  For even if there are so-called gods, whether in heaven or on earth (as indeed there are many “gods” and many “lords”), yet for us there is but one God, the Father, from whom all things came and for whom we live; and there is but one Lord, Jesus Christ, through whom all things came and through whom we live.  (1 Corinthians 8:4-6).

It's important not to get confused, as St. John is near the end of the Book of Revelation:

I, John, am the one who heard and saw these things. And when I had heard and seen them, I fell down to worship at the feet of the angel who had been showing them to me.  But he said to me, “Do not do it! I am a fellow servant with you and with your brothers the prophets and with all who keep the words of this book. Worship God!” (Revelation 22:8-9)

The flip side of this coin is that even worshipping just one god doesn't necessary square you with the Monotheistic worldview.  To make a silly example, suppose that the Internet became a sentient being and that some former Atheists started worshipping it as the most powerful and wise being in existence.  It would still be a polytheistic-type "god", even though there was just one of it.

Zeus is a particularly interesting case.  Most people are familiar with Greek mythology, in which Zeus is simply the most powerful of the many gods.  But many educated Greeks knew full well that mythology was just lies made up by poets, and used "Zeus" as the name for the monotheistic-type God.  One Greek text, a sky altas quoted by St. Paul in his sermon to the Athenians, illustrates this confusion well.  Aratus' Phaenomena begins by invoking Zeus as though he were the Absolute Creator who dwells in all things:

From Zeus let us begin; him do we mortals never leave unnamed; full of Zeus are all the streets and all the market-places of men; full is the sea and the havens thereof; always we all have need of Zeus. For we are also his offspring; and he in his kindness unto men giveth favourable signs and wakeneth the people to work, reminding them of livelihood. He tells what time the soil is best for the labour of the ox and for the mattock, and what time the seasons are favourable both for the planting of trees and for casting all manner of seeds.  For himself it was who set the signs in heaven, and marked out the constellations, and for the year devised what stars chiefly should give to men right signs of the seasons, to the end that all things might grow unfailingly. Wherefore him do men ever worship first and last.

and then in the middle inconsistently recounts the origin of Zeus as a deity who was born at a particular time and place, with the world already in existence:

If, indeed, the tale be true, from Crete they by the will of mighty Zeus entered up into heaven, for that when in olden days he played as a child in fragrant Dicton, near the hill of Ida, they set him in a cave and nurtured him for the space of a year, what time the Dictaean Curetes were deceiving Cronus.

We see here that Greek religion and Greek mythology were not the same thing.  Even more striking is the Stoic philosopher Cleanthes' Hymn to Zeus, written in the 3rd century B.C.  Go ahead, click on the link.  I wager you'll be a shocked at how Christian his poem sounds, if you read "God" for "Zeus".

To Monotheists, it is blasphemous to think of God as being the same as any created thing.  He is more superior to an archangel, than the archangel is to a slug.  Neither angels, nor souls, nor the heavenly realms, not even the entire universe, have any intrinsic religious significance to us at all.  We desire God alone.  As one modern Christian song says:

We are a moment, You are forever
Lord of the Ages, God before time
We are a vapor, You are eternal
Love everlasting, reigning on high

Only one is Holy, only one is Good.  He is the Supernatural.  Everything else is a limited, finite being, subject to laws set by the Almighty.  They are natural.  We don't always know their laws, but that doesn't change the fact that they part of a definite Nature, which originates from, and is circumscribed by, God's will.  God is the Unlimited, in whose bosom all of these limited things exist.

Forget heliocentrism and geocentrism!  In Christianity, everything revolves around God.

UPDATE: Edited post in response to some criticism.  The paragraph marked with a (*) used to read: "Thus there can be only one God, and following the usual grammatical convention of capitalizing unique titles, we capitalize the G."

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Natural and Supernatural I

by Aron Wall Posted on August 31, 2013

In a recent post I described a list of things and events which we Christians believe in.  For obvious reasons, I didn't belabor the existence of pandas and hurricanes, which are not in dispute for most people.  Thus, while I mentioned the existence of the physical universe (something which not all religious traditions believe in, by the way), I wanted to focus on the things that nonreligious people of a skeptical bent don't accept.  These things are normally called supernatural, because they are not a part of the world of "Nature".  That is, they are not among the "visible" things; they cannot be seen by our senses or deduced through ordinary scientific research.  They are therefore above, or additional to, the things which Naturalists believe in.  The latin word for above is super, and thus we get the word "supernatural".

Whether or not this word is useful depends on what use we want to put it to.  An apt choice of word can illuminate a subject, while the wrong word can lump things together which ought to be kept separate.  Arguably, the word "supernatural" as defined above tells us more about what Naturalists think is important, than what Christians believe.  If we want to do a compare-and-contrast of the different worldviews, then it may be a useful word.  But if you want to explain what Christians think, the word is highly misleading.

Here's why.  Everything we Christians believe in, is supported by one of these two kinds of evidence:

  1. It has causally influenced the physical world at one time or another, and therefore made an observable difference to the actual sense experiences of some human beings.  If the human being is someone other than us, then we normally learn about this event, not through the scientific method but through the equally empirical historical method.  In other words, some one writes it down in a book, we decide that their testimony is credible, and decide to believe it.
  2. God (who falls into the first class due to his interactions with the world) has communicated to us, directly or through intermediaries, that something is in fact the case.

In the case of God, there is also a set of philosophical arguments for Theism which people can accept without necessarily being Christians.  Some of these arguments are even supported by things we have learned from Science!

If it really is true that supernatural entities are known to exist by these means, it isn't all that different from the way we know about most other things in life.  We all rely on sense experience, history, and authority in everyday life.  You don't have a separate name for things I know because my Aunt Rose told me, as though that by itself set it apart into a different category.  Well, you might if Aunt Rose was a notorious liar, but if you think Aunt Rose is a truth-teller, then they are just facts.  For some purposes, we may want to distinguish between historical facts and scientific facts, but it isn't as though there were a clear-cut distinction between those two things.

So we shouldn't really distingush between the natural and supernatural on the basis of how we know.  Could we distinguish them on the basis of how frequently they interact with our world?

I've said that Heaven (in the theological sense) and Earth are like two separate universes.  However, they aren't watertight compartments, since things can sometimes go back and forth between them.  If we try to define the supernatural as things which seldom interact with the world we live in, it would seem that gravitons would also be a supernatural concept since, even though they are predicted by our scientific theories, they interact so weakly with everything else that it is hopeless to ever observe an individual graviton.  That clearly isn't right.

Can we distinguish them on the basis of what kinds of things they are?  Well, we know something about what ordinary matter is made out of.  If there are supernatural entities out there, and if any of them have parts, they would presumably have to be made out of something else.

Of course, even here on Earth, some things are made out of different building blocks than others.  Light is composed of photons, elephants are made of atoms.  But the two interact with each other.  Physicists like myself—er, excuse me, I guess this should actually be physicists unlike myself—have studied the interactions between different kinds of matter, and figured out how they all work.

We have succeeded to the extent that we can write down a set of general equations which describe all of the experimentally known forms of matter.  Except, uh, for dark matter, which is 5 times as abundant as ordinary matter, and which we only know about through its gravitational effects.  And perhaps dark energy (although that can be explained with a simple modification to Einstein's equation of general relativity, which Einstein originally proposed to make the universe unchanging with time, thus missing out on the chance to predict that the universe is expanding).  And several different kinds of fields which may or may not be needed to describe physics shortly after the Big Bang.  And we have no idea how to treat gravity quantum mechanically.  But besides all that, we've got a pretty good handle on a precise description of the "fundamental" laws of physics, even if they're really just an approximation to something we don't have yet.

These equations have a certain amount of mathematical beauty and coherence.  Although they don't reduce everything down to one basic principle, they do reduce it to a medium- sized number of particles / fields which interact via four forces: gravity, electromagentism, and the strong and weak forces.  Although these four forces are not the same, there is a certain similarity in the way that each of them is handled.  (They also interact via the Higgs boson, but nobody ever calls this a fifth force, because it is not really very much like the others.)

But again, it seems provincial to define supernatural simply as things we can't describe with mathematical precision.  For all we know, if we could do experiments on angels, we would find that they also conform to an elegant set of mathematical equations.  (Although, considering that it took us thousands of years to find the right equations for the physical universe, which we interact with every minute of our lives, I wouldn't advise that you hold your breath.)  Besides, would we really want to say that until the time of Galileo, a ball falling to the ground was a supernatural event?  Once again, the concept which we thought was a description of the thing, turns out to be a fact about its relation to us, like the word foreign.

However, in Christian theology, there does turn out to be a distinction which is grand enough to justify a portentious word such as supernatural.  There actually is a way to divide the universe into two classes of entities, such that one really is "super" to the other, not just with respect to the limitations of our own knowledge, but in reality.  More on this next time.  But if you can't wait for the next post, ask yourself this question: what exactly is it again that the Jews are famous for?

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