The Teacher

by Aron Wall Posted on October 26, 2013

But you are not to be called `Rabbi', for you have only one Master and you are all brothers.  And do not call anyone on earth `father', for you have one Father, and he is in heaven.  Nor are you to be called `teacher', for you have one teacher, the Christ.  The greatest among you will be your servant.  For whoever exalts himself will be humbled, but whoever humbles himself will be exalted.  (Matthew 23:8-12)

Only one teacher!—and he is Christ.  None of the rest of us can claim that status, which he reserves for himself.  Yet for that very reason, all instruction which is true instruction must find its origin in him.  Those of us who are earthly instructors must therefore recognize, that if there is any wisdom in what we say, it comes from the Son of God.  We are not the teacher, but we allow God to be the teacher.

In every form of knowledge, there is both a spiritual opportunity: seeing Jesus as your teacher, and a spiritual danger: idolatry.  Idolatry comes when we see ourselves or others as the teacher, and don't allow the knowledge to lead us onward to God.  In some ways, the more noble the pursuit, the greater the danger of idolatry.  When scientists are satisfied to learn about creation without learning about the Creator, Science becomes a mere distraction to occupy the mind.  Maybe this is the real reason why fewer scientists than ordinary folk believe in God.  Science is so interesting that one doesn't feel the need to investigate deeper questions . . . and so the opportunity for salvation slips by, unnoticed.

On the other hand, the spiritual opportunity is present no matter how "low" on the scale of spiritual values is the thing which is being taught.  So long as the thing contains within itself something that is good, whether physical or mental, aesthetic or practical, there is a spiritual lesson to be had in it.  Any craft demands that one humbly learn from some particular Reality what is the right way to approach it: the corollary is the need to repent of your bad habits and learn how to do the thing properly.  Different tasks demand different skills, but the skill of humility is always the same.

To the extent that any earthly teacher is worthy of the name, it is only because they are first and foremost a student of the Reality being studied.  Even Jesus is the Teacher only because he is the Student:

The Son can do nothing by himself; he can do only what he sees his Father doing, because whatever the Father does the Son also does.  For the Father loves the Son and shows him all he does" (John 5:19-20).

Within the Trinity, the Son receives everything he is from the Father.  (Indeed, the Father's identity consists entirely in his love, that is, in his breathing the Spirit into his Son.  As Christians, we must not think that our Father is anything more or other than the Father of Jesus Christ, or that the Father held back anything of himself when he gave his Son.)  The Son's divinity consists entirely of learning from the Father.

We also see this play out in the humility of his earthly life:

In the same way, Christ did not take on himself the glory of becoming a high priest. But God said to him,

“You are my Son;
today I have become your Father.” [Psalm 2:7]

And he says in another place,

“You are a priest forever,
in the order of Melchizedek.” [Psalm 110:4]

During the days of Jesus’ life on earth, he offered up prayers and petitions with fervent cries and tears to the one who could save him from death, and he was heard because of his reverent submission. Son though he was, he learned obedience from what he suffered and, once made perfect, he became the source of eternal salvation for all who obey him and was designated by God to be high priest in the order of Melchizedek. (Hebrews 5:5-10)

Now as our teacher, Jesus taught about the Kingdom of Heaven using stories taken from the crafts of his day.  After instructing his disciples in the meaning of his parables, he says this:

“Have you understood all these things?” Jesus asked.

“Yes,” they replied.

He said to them, “Therefore every teacher of the law who has become a disciple in the kingdom of heaven is like the owner of a house who brings out of his storeroom new treasures as well as old.” (Matthew 13:51-52)

If Jesus is your teacher, he will also teach you about the Kingdom using your own craft, whatever it is.  Not that your craft is God's Kingdom, but any time you have the bracing shock of really learning something, there is some way in which it is going to be similar to the Kingdom.

In college, I did some fencing.  Recently I decided to take it up again, since this August.    The game consists of trying to trick people into allowing themselves to be stabbed with a metal stick.  But to explain how this connects onto spirtual topics, I need to go a little further back.

In high school I briefly took instruction from a karate instructor named Rob, for high school credit.  (My mother and brother had much more extensive lessons though).  Now St. Rob is a Christian, and he said that learning martial arts was very informative for his spirituality.

One learns about original sin—prior to being instructed, your instincts about what to do are pretty much always going to be wrong.  Your stance is wrong, your posture is wrong, and your motions are wrong.  The first thing you have to do is accept this as a fact, swallowing your wounded pride, and trust your teacher to correct you.

Then you have to actually do what the teacher says, without sliding back into what seems "natural"—until what is correct becomes second nature.  (I'm pretty sure there's something about a second nature in the New Testament somewhere or other.)  Rob also liked to say "practice doesn't make perfect, practicing perfect makes perfect".

Progress in holiness doesn't come about from "gradual improvement".  Rather, it comes from being "perfect, just as your father in heaven is perfect" (Matthew 5:48).  (By the way, in Greek the word "perfect" means complete, not flawless.) Of course, you can't do it.  So the teacher comes alongside of you and moves you into the right shape.  Jesus, the same personality who lived, died, and rose again, is there beside you showing you what to do.  That's what we believe.

Then you become perfect—forgiving your enemies and loving the unlovable—for about five minutes, perhaps, before relapsing again.  But at any time you can come back again.

The spiritual journey is more like continually being recalled back to what we ought to be, than like walking down a road to a destination.  Getting into shape may take years, but getting into the right posture only takes seconds.  In the same way, you can be who God wants you to be in a matter of seconds, if you really choose.  Sanctification involves making that choice over and over again.

This may sound like hard work, but it isn't salvation by works.  There's no nonsense about merit or deserving here.  "It is not the healthy who need a doctor, but the sick" (Mark 2:17).  And when corrected, you don't have to waste time agonizing about it.  That's just pride.  Just allow yourself to be corrected, and then think of the next thing.

Posted in Theology | 1 Comment

Does the Atonement make ethical sense?

by Aron Wall Posted on October 22, 2013

...and so, the Judge sentenced the murderer to go to the electric chair.  But just then, the Judge's only Son piped up.  "Please punish me instead!  That way, he won't have to die."  Out of his compassion for the criminal, the Judge agreed.  The Judge's Son was executed, and the criminal went free.  Tears pouring down his face, the killer vowed to be a new man from that day forward...

This parable is found nowhere in the Bible, but I'm pretty sure I've heard some version of it preached from the pulpit once or twice, as an analogy for what Jesus did for us on the Cross.  Here's the problem: the story is ethically outrageous.  How could punishing an innocent person instead of a guilty person possibly be just?  In the story, the Son volunteers to die; it's not as though the judge just ordered the execution of some random person.  But how could the guilt of punishment possibly be "transferred" from one person to another?  The basic responsibility of the Judge to judge correctly is violated:

Acquitting the guilty and condemning the innocent—
the Lord detests them both.   (Prov 17:15)

Admittedly, the story I began with was just meant to be an illustration, not the actuality.  There are many different metaphors in the Bible to describe the Atonement, and most of them don't have to do with the justice system.  The Bible talks about ransoming slaves, healing diseases, growing new life, being adopted as sons, and so on.  But the criminal justice metaphor is one of the most common analogies in Western Christianity, so let's try to run with it for a moment.

Metaphors do not need to accord with the reality in every single way.  It is even possible to illustrate righteous behavior by means of a person who, in the fictional story, behaves immorally.  (For example, in Jesus' parable of the Dishonest Steward, the steward's clever way of enriching his master's debtors by fraud, to get special treatment from them later, is an analogy for how Christians should give away their "worldly" possessions to the poor in order to gain something more valuable.  One is a sin and the other isn't, but Jesus' point is that they are similarly clever.)

However, in the (nonbiblical) story of the Judge's Son, the ethics of the story is so anomalous that it seems to render suspect any meaning which can reasonably be obtained from the story.  The motivations of the characters don't make any sense, either from an altruistic or a selfish perspective, so it's unclear how we should react, other than with horror at the perversion of justice.

But now let's change the setting a little bit.  We'll replace the criminal trial with a civil trial, and the death penalty with a fine:

A man breaks his neighbor's window.  The neighbor sues, and the Judge orders the man to pay $200 to repair the broken window.  However, the man is unable to pay, due to his poverty.  So his friend kindly agrees to pay the fine instead.   The friend pays $200 to the neighbor, and the windowbreaker goes free.

Suddenly, most of the ethical problems seem to evaporate.  Most of us would have no problem with a Judge allowing this.  In certain cases, we might feel like it is was a little unfair for a perpetrator to get off scott-free, because someone else paid the fine.  But here, the windowbreaker couldn't pay.  In light of the circumstances, the resolution of the case seems reasonable.  What is the difference?

Part of it, presumably, is that we are more used to thinking of money as fungible than life.  The concept of transferring debts is in accordance with our culture's common sense, while paying an innocent life for a guilty life is not (and rightly so)!

But I think the bigger issue here is the question of what the punishment is expected to accomplish.  In the case of the fine, the main issue is that the window is broken!  The fact that the windowbreaker is guilty comes in only secondarily.  Given that the new window needs to be paid for, it seems fair to assign the liability to the man who—whether accidentally, or in a fit of rage—broke the first one.  But if someone else wants to repair the window, that solves the problem: (1) The neighbor is compensated for the damage to his building, so he has no right to object, (2) The friend is allowed to do whatever he likes with his own money, and (3) the windowbreaker is enabled to pay the fine.  No more problem!

Things are quite different in the case of a murderer, who pushes someone out the window and breaks their skull instead of the glass.  The main problem is not the same.

One might be tempted to say that the main problem in the criminal case is that the victim is dead.  But that isn't so!  The death of the victim is the most tragic part of the situation, but it is not what the criminal trial is there to fix!  Sentencing murders to death does not bring back their victims.   Last I checked, not even a sentence of life-without-possibility-of-parole does that.  No, in the criminal trial, punishing the criminal is the entire point of the proceedings (although there are multiple goals which this punishment might accomplish).

Another way to see this, is to compare to a situation where the victim dies accidentally.  In this case, the death of the victim part is exactly the same.  That they were murdered is the crucial difference.  This fact is not located in the victim (who may not have known whether or not the fall was an accident), rather it is located in the mind and heart of the murderer.  The murderer kills the body of the victim, but it is their own soul which they are doing violence to.  If you murder someone, in the next moment you become the sort of person who would murder someone.

So then, this is the stain which the criminal punishment is supposed to fix.  As Socrates says in the Gorgias, having wickedness in the soul is the worst thing that can possibly happen to you, and the guilty who are punished are benefited by it, since the punishment is a medicine for their wickedness.

It then becomes clear why it is impossible for an innocent person to justly take on the punishment of a murderer.  Because it would not in fact fix the problem.  In the criminal case, it is the murderer who is the broken window.  Punishing the guilty party through the judicial system is our (usually very inadequate) way of trying to restore the window: to patch over the cracks with tape, or at least to sweep up the broken glass by taking away their power to hurt anyone else.  Punishing an innocent person does no good at all.  Unless...

Unless things were so arranged, so that the death of the innocent person actually did fix the broken window—or to drop the analogy, what if Jesus' death actually causes the stain in the murder's soul to be cleansed and purified?  Suppose that, by accepting Jesus' death, the soul of the murderer is put to death (Romans 6:6-11) and then restored, so that the person who once hated his victim is now is full of love and compassion.  In that case, justice would be done (but in a way invisible to the justice system, and perhaps even to society).  The murderer would be simultaneously punished and forgiven by one and the same act of God.

How is that even possible?  Well, I assume it has something to do with the divinity of Jesus; that when God assumed a human nature, this affected his relationship with every human being who ever lived.  I suppose it has something to do with the Holy Spirit tampering with the neural network of our brain, after we give him permission to do so.  I believe it has something to do with the omnipotent Father wanting to express his forgiveness through a tangible, observable event taking place in spacetime history.

But now we are asking a different question: does the Atonement make metaphysical sense?  That is, is it the sort of thing which could happen in the real world, given the most basic structure of existence (whatever that is).  The original question was whether the Atonement makes ethical sense.  That is, supposing it to be possible, would it be desirable?

Assuming it is possible, it seems clear that offering the possibility of moral redemption to every person on Earth, no matter how wicked, is a very great benefit.  One might still ask (if one is inclined to second-guess the Creator) whether we really need such a desperate remedy, and why God did not provide forgiveness in some less bloody way.  This does not change the fact that it works.

At the Cross, we see God's solidarity with human beings.  He suffers with the innocent, and for the guilty (and we have all been both at times).  The Cross shows up the depths of human depravity, and reveals that the primary victim of our sin has always been God.  But it is also the triumph of God's mercy, because it shows us that no matter what suffering we cause to ourselves and others, God is there accepting the pain, refusing to retaliate and offering continual forgiveness.  I cannot imagine any more graphic way for God to show this, than the way he did.

Posted in Theology | 5 Comments

What actually happened with Galileo

by Aron Wall Posted on October 17, 2013

This finished a bit too late to get into the previous collection of Random Stuff, so it gets to be its own post.  A long but fascinating saga by St. Michael Flynn on the topic of what actually went down with Galileo, and the many competing astronomical models of his time:

The Great Ptolemaic Smackdown

I also very much enjoyed his book Eifelheim, about aliens landing in medieval Europe.  It gives a much better impression of how medievals actually thought, compared to the usual fare.  (Although I thought the frame story, set in the near-future, was a little weak.)

I've been travelling a bit recently, to Princeton and to the Perimeter Institute (which is in Waterloo, Ontario), but I hope to be able to get back to blogging soon.  But this week, I have a visiting collaborator, and potentially jury duty (which for the record, I am not trying to evade.)

Posted in History, Links, Reviews | Leave a comment

More Random Stuff

by Aron Wall Posted on October 1, 2013
  • I've always thought there was something silly about the librarian festival "banned books week", and this post by St. Darwin explains why.
  • However, there's no need to buy games on the web.  If you can afford index cards, and a pencil, then you can start playing The Card Game, a self-modifying card game invented by yours truly.
  • From St. William G. Witts' blog, an essay on A Hermeneutic of Discontinuity, a take-down some supposedly "Christian" theologians, who actually don't really believe much of anything.  I was particularly interested in the following passage because of my recent posts on Metaphors in Theology:

The primary criterion by which Borg decides whether an event mentioned in the Bible is historical or metaphorical seems to be whether it is miraculous, or mentions what Borg refers to as an “intervention” of God. As with many authors in our narrative of the “hermeneutics of discontinuity,” Borg is clear that contemporary people cannot believe that miracles happen, so any biblical story that contains such an event must be interpreted as a metaphor. For example, Borg writes that the biblical description of Jesus as the Son of God who died for our sins and rose from the dead “no longer works for millions of people.” Also, he writes, “there are many parts of the gospels that they can’t take literally. When literalized, the story of Jesus becomes literally incredible.”  Of course, that millions of contemporary people do take the miraculous events of the gospel “literally” belies Borg’s claim. For those who believe, the story of Jesus is literally credible. That is what the word “belief” means.

The approach here is entirely circular and question begging. Borg nowhere makes an argument that miracles are metaphysically impossible, or that the God who created the world could not become incarnate, or that if Jesus were the Son of God that he could not forgive sins or rise from the dead. Nor does he engage in a careful textual study to show that the biblical texts themselves distinguish between non-miraculous “historical events” and miraculous “metaphorical” events. The distinction between a “literal” and a “metaphorical” reading is assumed in approaching the text and then imposed on it.

Moreover, Borg’s is an odd use of the word “metaphor,” which normally means “figurative,” not miraculous. Presumably, a secular account of undisputed and non-miraculous historical events could use highly metaphorical language, and might have a great deal of contemporary significance or “meaning,” for example, a biography of Abraham Lincoln or Martin Luther King, Jr. At the same time, an account of an entirely fantastic and fictional event could use non-metaphorical and prosaic language. For example, tall tales about Paul Bunyan often derive their humor from describing highly exaggerated and impossible stories in prosaic language. It is not clear why Borg wants to use the expression “metaphorical” to describe certain events in the Bible except to say that “they did not happen.”

People have a bad habit of using the word "metaphorical" to mean "just kidding".  But that's just not what it means.  Nor does "literal" mean factual.  For example, when reading a novel we understand that "Mr. Jones went out the door" can be a literal statement, while "Mrs. Jones' heart was broken" is a metaphor.  The Literal vs. Metaphorical axis lies at right angles to the Factual vs. Fictional axis; all four combinations are allowed.

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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