I'm in the first week of a 5 week trip to Europe. I'm in England and will be visiting France, England again, Germany, and Poland (where I'll be attending the GR20 conference in Warsaw).
Expect posting to be light to nonexistent. However, if you leave comments, I'll try to eventually respond.
After writing about the death penalty recently, I was reflecting about the real meaning of Justice. It's tempting to think that Justice refers to the thing which happens (or should have happened) in Law Courts. And of course we hope that the laws and the "justice system" will work out in a way which is actually just. However, there is a sense in which the justice system is a million miles away from true Justice, if we define Justice as harmonious reciprocal relationships.
Even if the justice system worked perfectly on its own terms, it would be a mistake to think that this is Justice. The fact that crimes are committed (or else people are suing each other in civil courts) means that the harmonious relationships in society have already been disrupted. Our Law Courts are, at best, a means for correcting injustice, and even then they can only do so in limited respects: judges can restore property and restrain criminals, but they cannot change people's hearts to love each other again.
We call a hospital part of the "health-care system" not because lying in a hospital bed is Health, but because it is something we use to remedy sickness. The best sort of Health is not needing to go to the hospital in the first place.
Let's see what the Prophet Zechariah has to say about this. Someone came and asked him a question about what the (religious) law should be:
In the fourth year of King Darius, the word of the Lord came to Zechariah on the fourth day of the ninth month, the month of Kislev. The people of Bethel had sent Sharezer and Regem-Melek, together with their men, to entreat the Lord by asking the priests of the house of the Lord Almighty and the prophets, “Should I mourn and fast in the fifth month, as I have done for so many years?” (Zechariah 7:1-3, NIV)
Some context is important here. The Jews had formerly been captured and exiled to Babylon, as a divine punishment for their sins. Jerusalem and its Temple had been destroyed, and the fast in question commemorated that.
But now the Persians are in charge, and they have authorized the City and Temple to be rebuilt. So the Bethelites have a natural question. Do we have to still keep fasting or not? The fast has become part of their religious practices, and they want to know whether it still applies to them. What will Zechariah tell them?
Religious people naturally trend into thinking of religion as a certain set of rules which have to be kept, as if it were a secular legal code and they just have to stay on the right side of the law. They want to know which way God wants things to be—but in fact either Yes or No would be misleading, because God wants a different sort of thing entirely:
Then the word of the Lord Almighty came to me: “Ask all the people of the land and the priests, ‘When you fasted and mourned in the fifth and seventh months for the past seventy years, was it really for me that you fasted? And when you were eating and drinking, were you not just feasting for yourselves? (7:4-6)
Stop asking whether you should fast or feast—it's the wrong question. Instead ask why you were fasting, and why you were feasting. Was it really for God, or was it just to mourn your own sorrows and celebrate yourself?
And the word of the Lord came again to Zechariah: “This is what the Lord Almighty said: ‘Administer true justice; show mercy and compassion to one another. Do not oppress the widow or the fatherless, the foreigner or the poor. In your hearts do not think evil of each other.’ ” (7:8-10)
The Lord replaces the people's question with a different command—do justice, resuce the oppressed. THIS is the point of all of the religious rules, not which days are appropriate for fasting. This is reiterated later:
“These are the things you are to do: Speak the truth to each other, and render true and sound judgment in your courts; do not plot evil against each other, and do not love to swear falsely. I hate all this,” declares the Lord. (8:15-17)
There is indeed a role for Law Courts in this notion of Justice. Zechariah was speaking to a broken society which had lost its bearings, which needed legal stability and fair dealing in order for any reconstruction to occur. But the requirement of Justice goes deeper than just institutions. The Just person is not just characterized by legal justice but by honesty and integrity in all of his dealings.
The Law Courts are a means and not an end. What end it is a means towards may be seen in this beautiful passage:
This is what the Lord Almighty says: “Once again men and women of ripe old age will sit in the streets of Jerusalem, each of them with cane in hand because of their age. The city streets will be filled with boys and girls playing there.”
This is what the Lord Almighty says: “It may seem marvelous to the remnant of this people at that time, but will it seem marvelous to me?” declares the Lord Almighty. (8:4-6)
We have now nearly ascended the treacherous craggy slopes of Mount Justice. Peering into the misty summit, upon which the Earthly Paradise is located, what do we see? Children playing games with each other! And sentimental elders looking on and reminiscing.
We do not see here the perfect restoration of body at the Resurrection, but we see the highest vision of Justice between humans beings which any society here and now can attain. Doubtless the children sometimes accuse each other of cheating. But the ideal of neighborliness is there, which is indeed the point of the command to Love your Neighbor. This is Justice.
There is also a harmonious relation of the entire people to God:
This is what the Lord Almighty says: “I will save my people from the countries of the east and the west. I will bring them back to live in Jerusalem; they will be my people, and I will be faithful and righteous to them as their God.” (8:7-8)
This is Justice too. The establishment of a truly just earthly society (harmony between human beings) requires also a correct relation to the God who works justice and righteousness in the earth:
This is what the Lord Almighty says: “You who now hear these words spoken by the prophets who were there when the foundations were laid for the house of the Lord Almighty, let your hands be strong so that the Temple may be built. Before that time there were no wages for man or beast. No one could go about his buisness safely because of his enemy, for I had turned every man against his neighbor. But now I will not deal with the remnant of this people as I did in the past,” declares the Lord Almighty.
“The seed will grow well, the vine will yield its fruit, the ground will produce its crops, and the heavens will drop their dew. I will give all these things as an inheritance to the remnant of this people.” (8:9-12)
God, humans, animals, the environment; all harmoniously related. This is Justice.
Once the Temple is established (not just as a building but in our hearts) then there is a bond between neighbors which allows children to play safely in the streets. Humans and animals can be fed for their work, because they are treated fairly. Commerce is possible because people don't need to be afraid of aggressors (this is why the Law Courts aren't optional). Responsible cultivation of Nature is possible because the Temple trains us that things which belong to God are sacred.
Only then does the Prophet return to the question of fasting:
This is what the Lord Almighty says: “The fasts of the fourth, fifth, seventh and tenth months will become joyful and glad occasions and happy festivals for Judah. Therefore love truth and peace.”
This is what the Lord Almighty says: “Many peoples and the inhabitants of many cities will yet come, and the inhabitants of one city will go to another and say, ‘Let us go at once to entreat the Lord and seek the Lord Almighty. I myself am going.’ And many peoples and powerful nations will come to Jerusalem to seek the Lord Almighty and to entreat him.”
This is what the Lord Almighty says: “In those days ten people from all languages and nations will take firm hold of one Jew by the hem of his robe and say, ‘Let us go with you, because we have heard that God is with you’.” (8:18-23)
Real Justice is attractive, and causes celebration and emulation. It is no longer a question of rules, but of God's promises. Whether or not you abstain from anything else, abstain from injustice. Days for producing Justice are always festivals. Therefore, rejoice always whatever you do.
Suppose we have a field 
in a curved spacetime, and we want to know how fast it is changing as you move in some direction in space or time. Because there is more than one possible direction to move in, we have to select a vector 
which tells us which direction in the coordinate space 
to move in (remember, stands for a list of all 4 spacetime coordinates.) Then we can calculate it by taking a partial derivative. If your calculus is rusty, the partial derivative 
is defined by:
at two different points ( and 
). As 
gets smaller, these two points get closer and closer together, so the values of typically get more and more similar, but because we divide by we end up with a nonzero answer in the limit. I've written instead of 
because I'm lazy.
That was the formula for the partial derivative in a particular direction (which is itself a list of 4 numbers). If we want to have a list of all 4 possible partial derivatives at each point, we can just write 
without the . This is the partial derivative covector, where a covector is a thing which eats a vector (like 
) and spits out a number. That's almost the same thing as a vector, but not quite, which is why its index is downstairs instead of upstairs. (You can convert between covectors and vectors by using the metric, e.g. 
, where as usual we sum over all 4 possible values of the index.)
Now, was a scalar field, meaning that it didn't have any indices attached to it. What if we tried to do the same trick with some vector field (or a covector 
)? Well, nothing stops us from taking the partial derivative of a vector in the exact way:
with the "t" component of a vector at another point 
, because the definition of "t" is arbitrary. If you change the coordinate system at but not you'll get confused.
In a curved spacetime, you can only compare vectors at different points if you select a specific path to go between the two points. You can then drag (or if you prefer, parallel transport) the vector along this path, but if you choose a different path you might get a different answer.
Well here, because the points are really close, there's an obvious path to pick. Since spacetime looks flat when you zoom up really close, you can just parallel transport along the very short straight line connecting the two points. This allows you to relate the coordinate system at the starting point to the destination point . Thus, when we take the derivative, we want to compare 
not to the same coordinate component of 
, but to the parallel translated component of the vector. When we do this, we get the covariant derivative, defined as follows: 
:
direction and drag it a little bit in the 
direction, then 
says how much your vector ends up shifting in the 
direction, relative to your system of coordinates. It turns out that the bottom two indices are symmetric: 
.
Similarly, if you want to define the covariant derivative of a covector, you just have to attach the indices a little bit differently:
for each of the indices. How tedious! But, in the case of a scalar field , we get off scot free: the covariant and partial derivative are just the same.
If your spacetime is flat and you use Minkowski coordinates, then 
. But even in flat spacetime you can have 
if you use a weird coordinate system, like polar coordinates.
All of this is a little bit circular so far, since I haven't actually told you how to calculate yet. It's just some thing with the right number of indices to do what it does. In fact, you could choose to think of the connection as a fundamental field in its own right, in which case there would be no need to define it in terms of anything else. But that is NOT what people normally do in general relativity. Instead they define the connection in terms of the metric 
, because it turns out there is a slick way to do it.
We want to find a way to use the metric to compare things at two different points. In other words, the metric is a sort of standard measuring stick we want to use to see how other things change. But obviously the metric cannot change relative to itself. (If you define a yard as the length of a yardstick, then other things can change in size, but the stick will always be 1 yard by definition.) Therefore, the covariant derivative of the metric itself is zero: 
. But if we write out the correction terms we get:
in terms of the metric. To do this, we just switch around the roles of the , , and indices to get 
directly as 
. You get this by writing the metric out as a matrix and inverting it. (Technically we write 
where 
is a very boring tensor which is always 1 if and are the same index, and 0 if they are different.)
So then, the connection (which allows us to transport vectors from place to place) can be written in terms of the first derivative of the metric. We'll need to take a second derivative of the metric to get the curvature 
, but that will be the subject of another post.
In the previous post I mentioned that I support the death penalty, without providing any details. Commenter Darryl asks:
Aron, (and other commenters, too!) I wonder if I might probe your notions on the death penalty. Given that in the US alone at least 120 (a fairly conservative estimate depending on which sources one consults) persons on death row have been exonorated by DNA evidence, what are your thoughts on this quote I came across the other day: "So, as long as the death penalty is in place, you are pretty much guaranteed to occasionally execute an innocent person."
I agree with the quote at the end of Darryl's comment. However, I would add that "So long as imprisonment is in place, you are pretty much guaranteed to occasionally imprison an innocent person," and "So long as fines are in place..." etc. Any human system of justice, no matter how careful, risks punishing the innocent. And the more cautious the system is to protect the innocent, the more often the guilty will remain unpunished.
In this respect, the only thing that is different about the death penalty is that once you do it, it cannot be reversed. However, this is a relative rather than an absolute distinction. If you sentence someone to 25 years and then the person is exonerated 20 years later, you can give back the 5 years but you cannot give back the 20 years. (In politically unstable countries, the reversibility of imprisonment may even be an argument for the death penalty, if one is worried e.g. that the genocidal dictator's old faction will retake power and set him free.)
I also do not think that the death penalty is really even an order of magnitude worse than life imprisonment. If I were unjustly accused of a crime, I would prefer A) 50% chance of being released to rejoin my family and my career; 50% chance executed, over B) 100% chance of life imprisonment w/o possibility of parole. Remember all those Revolutionary War slogans about liberty being more important than life!—do we still believe that?
Obviously, whenever an innocent person is executed this is a travesty of justice, a very bad outcome. We live in a modern, first-world nation in which long-term humane imprisonment is possible. Therefore, if there is no particular good to be had from executions rather than imprisonment, then it is our moral duty to abolish the death penalty. But is that really true?
The trouble with most debates about the death penalty is that the begin in the middle (quibbling about statistics) rather than at the beginning, which is to ask why one might have the death penalty at all. Until you first ask what the purpose of the death penalty is, you cannot know whether the trade-off is worth it.
Here are some possible motivations for punishing the guilty:
In our system of justice, we make a clear distinction between civil proceedings (which exist to compensate the wronged) and criminal proceedings (which exist to vindicate the state's abstract interest in justice). I think that this is a good distinction, and that therefore #1 is irrelevant to the current question.
With respect to #2 and #3, life imprisonment and executions are probably about equally good. In principle, if execution is worse, people ought to be motivated more strongly to avoid it. But I'm not sure it works out that way in practice, given criminal psychology, and the remoteness of the punishment from the crime. (However, there is an important exception in the case of inmates who murder prison guards or other prisoners—in this case locking them up obviously doesn't prevent the crime, and if they already have a life sentence, the death penalty seems necessary as escalation.)
With respect to #4, the death penalty may well be better than life imprisonment. True, life imprisonment provides more time to repent. But the death penalty provides better circumstances. If the prospect of one's own immanent death—due to one's own crimes, no less—does not cause someone to reconsider their way of life, it is hard to see what would. Here the nonreligious and Christian might part ways. The former is likely to feel that it doesn't matter much if a person repents, if you have to kill them to get it. While for those like myself who believe in an eternal divine judgment following death, it is a matter of the greatest importance.
But I think the core issue at stake is actually #5: does anyone deserve to die? Is it possible for someone (such as the mass murderers described in my last post) to be so polluted by guilt, that it is a travesty of justice for them NOT to be executed? I think so, and it is for this reason that I support the death penalty.
For example, a while back there were two Judges in Pennsylvania who accepted bribes from a privately-run juvenile jail, in order to send the kids that appeared before them to jail, regardless of the nature of the circumstances. These men betrayed their position of power and deliberately perverted justice in a way likely to corrupt and destroy the innocent. Words cannot express how reprehensible their crime was. Actions are better. They ought not to have been allowed to go on breathing. (Instead they received 28 and 17.5 years.)
I said earlier that the death penalty didn't seem that much worse to me practically than life imprisonment, which is permanent exile, slavery, and confinement all wrapped up in one package. But there is one other respect in which "death is different", namely that it is psychologically horrible (and fascinating).
Ironically, I think the controversy over the death penalty itself illustrates this psychological response. Passions are stirred; zealous anti-death advocates hasten to show that the person was convicted unjustly. Those 120 people who were exonerated due to DNA tests were probably lucky to be on death row—if not, their cases would probably have been neglected, and they would still be in jail.
Death is numinous. In that post I wrote concerning the concept of atonement for guilt:
This is a numinous problem, not just an ethical problem. So it needs a numinous solution.
As the Bible says in a chilling passage:
“Whoever sheds man’s blood,
By man his blood shall be shed;
For in the image of God
He made man.” (Genesis 9:6)
Unless there is such a thing as real guilt, there is also no such thing as real forgiveness. Thank God that we have the "sprinkled blood that speaks a better word than the blood of Abel" (Heb. 12:24), which is sufficient to atone for all of our sins!
Now, how much evidence should we have before we execute someone? I can see nothing wrong with the standard implicitly required by the U.S. Constitution, namely beyond a reasonable doubt. If it is unreasonable to doubt whether the person did the crime, then it is unreasonable to take into account the possibility of their innocence when sentencing them.
In this country, no one is executed unless either (a) 12 citizens unanimously agree that they are guilty beyond a reasonable doubt, or (b) the accused waives his right to a jury trial. After that there are usually 5 different levels of appeals courts empowered to inspect the case for procedural flaws.
It may well be that juries fail to apply beyond a reasonable doubt to the cases that come before them, and as a result some innocent people are found guilty. But this has nothing per se to do with the death penalty. If you are not found guilty beyond a reasonable doubt, the correct judgment is an acquittal—not life imprisonment. Not even a $20 criminal fine can be imposed in this case. If our current justice procedure is unreliable, this is a problem for all cases, not just capital ones.
If there are people on death row whose cases were never proven beyond a reasonable doubt, they should be released! That is not a good reason to commute the sentences of those criminals who were proven guilty beyond a reasonable doubt.
If you're wondering about the lack of posts recently: for the last 2½ weeks I've been travelling on a research trip to Boston and Canada (to Waterloo, Montreal, and Vancouver). The sashimi in Vancouver is out of this world, by the way.
Mostly I've been cramming my head with physics, but I did spare some time to read reports about the horrible news regarding the Boston marathon bombing, which killed 3 spectators and injured many more. This was after I had already left, so don't press me for eyewitness accounts of traumatized civilians.
I also read the news regarding the lack of news covering Kermit Gosnell's "abortion" "clinic", in which poorly trained and unlicensed "doctors" murdered hundreds of babies (i.e. viable infants outside of their mothers) and allowed women to die due to malpractice and unsanitary conditions, which the Pennsylvania government received complaints about for decades but failed to stop. This, apparently, is not news so far as the mainstream national media is concerned, but due to the untiring efforts of St. Mollie at GetReligion, at least the media's failure to cover it is now news.
Apparently the journalists are worried that anti-abortion* activists will make hay out of this story, and so therefore advocacy of "women's rights" must, paradoxically, include suppressing stories in which—even from the pro-abortion* viewpoint—the rights of women to safe health care were most certainly violated.
One has to tread cautiously when making accusations of media bias, since it's so easy to be biased oneself in making those accusations. As a moderate Republican who lives and works among academics in California, I would normally feel rather embarrassed to complain about this, since people would look at me as though I were one of those conservatives, who thinks that Fox News is a straight news source but everyone else is commie pinkos.
(Even though my political opinions are not the same as those around me, I worry sometimes about whether they have been influenced by the desire to look reasonable to other people when I explain them. Compared to the historical range of opinion, any given time in America there is only a narrow range of acceptable opinions, and this range is even narrower in academia. There's much less incredulity when my position is some sort of libertarianish compromise...)
Nevertheless, the fact that Fox News is tilted to the right doesn't change the fact that the mainstream newsmedia is clearly left-leaning on certain particular cultural issues, as I think GetReligion has abundantly demonstrated. I think the media tries to be fair when covering presidential election politics, but it wears its opinions on its sleeve when covering hotbutton social issues.
One also has to be careful in defining what one means by bias. There is nothing inherently wrong with: 1) media reporting issues which are more likely to be of interest to their constituents (e.g. spending more time on one party's primary election), or 2) straight-up advocacy or editorializing for ones preferred position.
These should be distinguished from 1') concealing relevant facts which ought to be of interest in order to give a partisan slant on reality, and 2') advocacy pieces which pretend to be straight news coverage, but are not.
In this case the news media has been caught out in a clear example of (1'). The sooner they correct their mistake, the quicker they can get to a world where conservative complaints of media bias really are crankish.
In the meantime, let us pray for those who died in these atrocities, for their families and friends, and for the twisted souls of the those who murdered them—that they would receive their rightful justice, and that God would grant them repentance, "so that they might be judged according to men in regard to the body, but live according to God in regard to the spirit" (1 Peter 4:6).
(*) Footnote: I refuse to use the terms pro-life and pro-choice on this blog, since I regard both of them as mealy-mouthed euphemisms. There was once a time when real men and women were willing to state their opinions plainly, even if it meant they had to be "anti-" something, or actually mention the name of the thing they are supporting/opposing. (I can respect the term "pro-life" when it is used as a catch-all term for "anti-abortion, anti-euthanasia, and anti-death-penalty", since in this case an abstraction is useful. Although I do support the death penalty myself.)
The term "pro-choice" is even more Orwellian, since it completely sweeps under the rug the nature of the choice being made, using a term so vague that it could just as well apply to e.g. school vouchers. Every decision to do anything can be characterized as a choice; the term avoids grappling with the fact that this choice involves killing one's own flesh and blood. The usual argument against the term "pro-abortion" is that the proponents do not advocate that all women terminate their pregnancies. But that's silly, because almost nobody wants that. Imagine if people who supported the death penalty refused the label because "we don't believe that everyone should be executed, so we prefer the term "pro-justice". Clarity is sacrificed in order to gain cheap points.
