Sunday, December 02, 2007

Two Ships That Passed in the Night

Ships that pass in the night, and speak each other in passing,
Only a signal shown and a distant voice in the darkness;
So on the ocean of life we pass and speak one another,
Only a look and a voice, then darkness again and a silence.
-- Henry Wadsworth Longfellow,
"The Theologian's Tale: Elizabeth"

I've spent a total of 24 hours in Germany--I went to commemorate the wedding of two of my friends from college, who were married in Illinois while I was living in France. At their reception-diner, I had a very nice chat with a young German fellow, and afterward I found myself contemplating one-day friendships: Two paths cross, two people enjoy each others company for a time, and then they continue their separate ways. Was there a point to such brief encounters, I found myself asking, if they produced no lasting connection?

"If a thing is a pleasure, a hmân wants it again. ... But the pleasure he must be content only to remember?"
"That is like saying 'My food I must be content only to eat.' "
"I do not understand."
"A pleasure is full grown only when it is remembered. You are speaking, Hmân, as if the pleasure were one thing and the memory another. It is all one thing. ... What you call remembering is the last part of the pleasure, as the crah is the last part of a poem. When you and I met, the meeting was over very shortly, it was nothing. Now it is growing something as we remember it. But still we know very little about it. What it will be when I remember it as I lie down to die, what it makes in me all my days till then--that is the real meeting. The other is only the beginning of it. You say you have poets in your world. Do they not teach you this?"
-- C.S. Lewis, Out of the Silent Planet

Would it be reasonable for a ship to mourn the passing of another, saying "What good did the meeting accomplish? I would have been better off alone." Not at all. The encounter brings a little light, a little comfort, and a little memory to carry along on the journey. Instead of wasting energy regretting the brevity of a short meeting, better to enjoy the moment fully and cherish the memory as the friendship's final fruition.

Friday, November 23, 2007

After God's Own Heart: Love Your Enemies

He testified concerning him: "I have found David son of Jesse a man after my own heart." (Acts 13:22, cf. 1 Sam 13:14)
But I tell you: Love your enemies and pray for those who persecute you. (Mat 5:44)
As I was listening to Eric Whitacre's "When David Heard" again this afternoon, I was struck by David's capacity to love even those who would do him harm. Certainly it's well known that David refuses to retaliate against Saul, despite Saul's incessant attempts at David's life (e.g. 1 Sam 24, when David cuts off the corner of Saul's robe in his hiding cave), but this could flow not from love, but merely from a respect for Saul as God's anointed.

Absalom, on the other hand, is another matter altogether.

David's third son Absalom was envious of the royal throne and plotted to usurp David's place. For four years, he flattered courtly visitors and spread self-aggrandizing propaganda to "steal the hearts" of Israel. When the time was right, he gathered sympathizers to declare him king and marched into Jerusalem (2 Sam 15). When David hears that Absalom has died in the ensuing altercation, he is shaken to the core and cries out with profound grief, "O my son Absalom! My son, my son Absalom! If only I had died instead of you--O Absalom, my son, my son!" (2 Sam 18:33)

Unlike Saul, Absalom had not been granted a special status by God that would command David's respect. Moreover, Absalom was jealous and conspired to bring about David's downfall. And yet, although Absalom expressed contempt and hatred toward his father, David never lost sight of the fact that Absalom was still his son. He continued to love him and sought his welfare, even during the height of his rebellion (2 Sam 18:5).

If not for anything else, David manifests the heart of God in this. For, "God demonstrates His own love for us in this: While we were yet sinners, Christ died for us" (Rom 5:8). Despite our open rebellion, God looked beyond our contempt for Him, and treating us not as the enemies that we were but as His beloved creation, gave Himself up to pay the fatal penalty of our rebellion in our place so that we may enjoy a reconciled relationship with Him as His children.

And so, like David, like Jesus, let us, too, love those who hate us and would do us harm. For this is the heart of God.

Friday, October 12, 2007

Scratchpad: Motivations to Do Good

To like to do X implies that doing X provides a sense of enjoyment or pleasure. To want to do X because one likes to do X means that doing X is motivated by the joy or pleasure received by doing X. There are certainly many other kinds of motivations for doing something. One might engage in the activity in order to receive financial gain, increase security, inflict pain, achieve social standing, and so on.

Now, if one likes doing something, can one help being motivated to do it by the fact that one likes it? There may certainly be other additional motivations, but I don't think these will somehow "crowd out" the motivation of joy or pleasure, and one can certainly be motivated by a multitude of factors.

But what of doing good? I think one could justifiably say that one has an obligation to do good by definition. That is, a moral act is an act obligated by a moral code, and the moral code defines what is good, which is just another way of saying that the moral code obligates one to do good. To put it one more way, one is obligated to do good for its own sake. But, does this obligation preclude doing good for other additional reasons?

Consider three hypothetical people: the first does good begrudgingly, because he has to but wishing he didn't; the second does good neutrally, without feeling anything for or against the act; the third does good enthusiastically and thus enjoys it (for, is it possible to have enthusiasm for something one doesn't enjoy?). It seems somewhat intuitive to say that the first is less praiseworthy than the other two, and the third more praiseworthy. So, one could say that it's better to like doing good than to do good without liking it. But, one usually wants to do what one likes, so it seems that doing good may also be motivated by the joy or pleasure received by performing the act. After all, "doing good is its own reward"---the reward being the joy received from doing good.

Now, some may recoil at the idea that doing good can be motivated by the pleasure received by performing the act; for, shouldn't good be done for its own sake? And yet, taking joy in doing good (doing good enthusiastically) is better than doing good begrudgingly or neutrally. These two ideas can be reconciled by taking into consideration that doing good can be an expression of love, or it can be motivated by other factors.

Just as in doing good, an enthusiastic loving act is more praiseworthy than one done neutrally or begrudgingly (if such an act could be called loving at all). Thus, one can (and should) take pleasure in loving acts, and one will therefore be motivated in some degree by the joy or pleasure obtained in performing the act. However, the loving act is not motivated solely by the pleasure received, but also by the love (affection, care, concern) one has for the recipient. As such, the motivation for the act is not merely inwardly focused, and thus the act is not selfish.

Similarly, if one does good merely for the pleasure received, without love, one could justifiably be held culpable of a morally reproachable inward focus. So, it isn't the pursuit of pleasure itself that denigrates an otherwise good act, but performing the act without outwardly focused love. As such, a good act may therefore (must therefore) be motivated of itself, by the joy or pleasure received in performing it, and with love for the recipient.

Now, what of other possible motivations? Since doing good ought to entail love, one could approach this question by determining whether loving acts may have additional motivations. Is an act any less loving if there are secondary motivations? My first inclination is to say yes, but the reason for this doesn't seem immediately obvious. Why should other motivations somehow decrease the genuine love expressed by an act? If this is the case, then performing good acts with self-interested motivations could be justifiable provided that the acts are also accompanied by a genuine love for the recipient and the additional desire to perform the acts for their own sake and for the joy or pleasure obtained by doing good.

Thursday, August 30, 2007

Calculating a Graduated Annuity

(Use the calculator to skip the math below.)

Calculating the future value of a savings program with fixed savings installments and a fixed interest rate (a simple annuity) is fairly straightforward with a geometric series:


T_1 = p ; T_2 = pr + p ; T_3 = pr^2 + pr + p ; T_n = pr^{n-1} + pr^{n-2} + pr^{n-3} + \dots + pr^2 + pr + p

To calculate the value after n periods, we multiply the last equation by r and subtract the result:

rT_n = pr^n + pr^{n-1} + pr^{n-2} + \dots + pr^3 + pr^2 + pr ; (r-1)T_n = pr^n - p ; T_n = p{r^n-1\over r-1}

So, saving $1,000/year for 10 years at 5% interest would give:

T_{10} = \$1,000{1.05^{10}-1\over 1.05-1} = \$12,577.89

And if we had the goal of saving $100,000 over 30 years with a 8%
interest rate, we could calculate the yearly deposit required:

p = T_n{r-1\over r^n-1} = \$100,000{1.08-1\over 1.08^{30}-1} = \$882.74


Now, since the real value of the periodic deposit degrades over time due to inflation, and since one's ability to save will hopefully increase over time due to increased income through cost-of-living increases and promotions, a real-life long-term savings plan will likely include deposits that increase over time (a graduated annuity). These, too, can be represented with a series:

T_1 = p ; T_2 = pr + pa ; T_3 & = pr^2 + par + pa^2 ; T_4 = pr^3 + par^2 + pa^2r + pa^3 ; T_n & = pr^{n-1} + par^{n-2} + pa^2r^{n-3} + \dots + pa^{n-3}r^2 + pa^{n-2}r + pa^{n-1}

where a is the geometric ratio describing the rate of increase (the graduation) of the deposits. This series is similar in form to the binomial series, except that the coefficients in this series are all the same. To solve for the sum, we multiply by a/r and subtract:

{a\over r}T_n = par^{n-2} + pa^2r^{n-2} + \dots + pa^{n-1} + p{a^n\over r} ; (1-{a\over r})T_n = p(r^{n-1} - {a^n\over r}) ; {r-a\over r}T_n = p{r^n-a^n\over r} ; T_n = p{r^n - a^n \over r-a}

Notice how this simplifies to the result for constant deposits, when a=1.

This equation can be rearranged to the elegant form:

{T_n\over p}r - r^n = {T_n\over p}a - a^n, r \ne a

When asked to solve for either rate, Mathematica complained that this equation involves variables in "an essentially non-algebraic way," which I found a bit odd. Nevertheless, to determine the interest rate necessary to achieve a given sum with a set rate of deposit graduation (or vice versa), one can evaluate one side of the equation, move the resulting constant to the other side, and calculate the positive real roots of the n-th degree polynomial.

In any case, after 10 years, a savings program that begins at $1,000/year
and increases by 4% each year with 8% interest would give:

T_{10} =  \$1,000{1.08^{10}-1.04^{10}\over 1.08-1.04} = \$16,967.02


This equation is also useful for determining savings left after a series of increasing withdraws. If one starts with $500,000 in retirement savings invested at 5%, taking a 2% inflation-adjusted $30,000 annuity for 5 years would leave:

T_n = Ar^n - p{r^n - a^n \over r-a} = \$500,000\cdot1.05^5 - \$30,000{1.05^5-1.02^5\over1.05-1.02} = \$465,940.02


One can rearrange the formula to achieve a somewhat unwieldy but functional equation for the number of years before the retirement savings will run out:

0 = Ar^n-p{r^n-a^n\over r-a} ; {A(r-a)\over p}r^n = r^n - a^n ; a^n = [1-{A(r-a)\over p}]r^n ; n\log a = n\log r + \log[1-{A(r-a)\over p}] ; n(\log a - \log r) = \log[1-{A(r-a)\over p}] ; n = \log[1-{A(r-a)\over p}] \div \log {a\over r}

So, to find out how long the $500,000 investment from the previous example will last:

n = \log[1-{\$500,000(1.05-1.02)\over\$30,000}] \div \log{1.02\over1.05} = 23.9 years


All of these calculations assume that payments occur at the end of the year (an ordinary annuity). The calculations for payments at the beginning of the year (an annuity due) are equally straightforward, and yield:

T_n = pr{r^n-a^n\over r-a}

Wednesday, August 22, 2007

Because We Were Slaves

When you are harvesting in your field and you overlook a sheaf, do not go back to get it. Leave it for the alien the fatherless, and the widow, so that the Lord your God may bless you in all the work of your hands.

When you beat the olives from your trees, do not go over the branches a second time. Leave what remains for the alien, the fatherless, and the widow.

When you harvest the grapes in your vineyard, do not go over the vines again. Leave what remains for the alien, the fatherless, and the widow.

Remember that you were slaves in Egypt. That is why I command you to do this. (Deuteronomy 24:29-22)

What would people say if you were to ask them why they should give to the needy? "It's their human right to have adequate food, shelter, clothing, and education," some might say. "It's your social responsibility," perhaps. Or maybe, "What goes around comes around."

Do you think anyone would say, "Because we were slaves"?

I find it striking that God gave precisely this reason for his command of charity to the Israelites as they were poised to cross the Jordan into the Promised Land. Why, of all things, would God ground his command in their former slavery?

Some might suggest that God was calling the Israelites to recall their former meager estate in order to identify with the poor, and thus to give out of empathetic pity. And, while this certainly could be part of it, I think there's something much more to God's reasoning here.

Not only were all the riches the Israelites possessed--from the spoils of Egypt to the land they were soon to inherit and its abundant fruit--gifts directly from God, but the Israelites would be in no position to enjoy any of these material goods if not for God's mighty deliverance of them from the bondage of slavery in Egypt. In recalling for them their former slavery, God is saying, "Remember how it is you got the land for your fields and vineyards; remember why you are free to cultivate and harvest. The only reason you live in comfort is because I have saved you and given you all you have." God commanded the Israelites, therefore, to give of their goods (which were really God's to begin with) to the poor among them in thanksgiving to God for his provision and liberation, providing a kind of miniature liberation in turn for the poor from the bonds of poverty.

"Now that's all well and good for the Israelites," you might say, "but I worked hard for my own riches, and have been enslaved to no man." Not so fast. Whatever work you have done to earn your income you would not have accomplished without the gifts of God--even the gifts as basic as your latent abilities and drive for hard work. But more importantly, you, as well, were also a slave--a slave to sin and death. By trusting in Jesus Christ, you accept the gift of liberation from the bondage of the slavery to death. And in thanksgiving for this salvation, God calls you to share his gifts with the poor.

So, when asked why charity is important, you too can say, "Because we were slaves."


For more Biblical insights on poverty, I commend to you the sermon series on poverty given at Blanchard Alliance Church, in Wheaton, Illinois:
The Dignity of Potato Eaters, 1/7/2007
Stopping Our Oppression of the Poor, 1/14/2007
Living on Less to Share with Others, 1/21/2007
Helping the Poor Regain the Dignity of Self Support, 1/28/2007

Friday, June 22, 2007

Universal Suffrage Includes the Mentaly Ill

Rhode Island, along with other states, is struggling with whether or not to grant suffrage to people who have been declared insane:

"I just think if you are declared insane you should not be allowed to vote, period," said Joseph DeLorenzo, chairman of the Cranston Board of Canvassers. "Some people are taking these two clowns and calling them disabled persons. Is insanity a disability? I have an answer to that: no. You're insane; you're nuts."
I believe, by definition, that Mr. DeLorenzo is incorrect in his assessment that the insane are not disabled. A disability is a limitation of physical or mental capacities, and the insane, most would agree, have severely limited mental faculties. But, Mr. DeLorenzo's prejudice against these people seems to be evident in his use of the slur clown.

Rhode Island state law currently prohibits people with serious psychiatric impairments from voting, which, in my view, is a serious misstep. We fought for years in this nation to eliminate discrimination in voting rights based on race (Fifteenth Amendment), gender (Nineteenth Amendment), and class (Twenty-fourth Amendment). Even after Reconstruction, many states and localities attempted to bar Blacks from voting with dubiously enforced literacy tests, which were finally banned by the National Voting Rights Act of 1965. We should by no means allow any backward motion in granting universal suffrage for full citizens.

What do opponents to suffrage for insane adult citizens fear? That the mentally ill might be too easily swayed to vote one way or another? There are plenty (far too many, I'm sure) sane people who are just as gullible--would they like to institute a test of mental fortitude in order to participate in democracy? And what would happen if the mentally ill actually did swing an election? If ever the insane gather enough votes to elect one of their own into office, our nation will have a much greater problem than the electoral process (namely, the state of the population's mental health).

Rather, limiting the voting rights of the mentally ill opens the door for even more oppression; for, who is to say that any sane person is actually fit to decide who should rule? What if they haven't thought through all the issues, or read widely enough, or can reason soundly enough? The National Voting Rights Act says that
No voting qualification or prerequisite to voting or standard, practice, or procedure shall be imposed or applied by any State or political subdivision in a manner which results in a denial or abridgement of the right of any citizen of the United States to vote on account of race or color . . .
Perhaps the time is right to extend this Act to secure suffrage for all citizens of our nation.

Tuesday, June 12, 2007

Strikes in France: Enough's Enough!

The educators at France's first juvenile penitentiary (établissement pénitentiaire pour mineur, AMOTMJ - English, pamphlet), in Lavaur, began a strike yesterday, the facility's first day of operation (Le Monde - English, La Dépeche du Midi - English, La Croix - English). The facility is the first of seven to be opened beginning this year in accordance with a criminal reform law creating a separate space for juvenile offenders in an effort to synthesize sanction and education (La Loi d'Orientation et de Programmation pour la Justice du 9 septembre 2002). Currently, France's 700 offending minors are held in adult facilities.

The educators' principal demand is to meet with with the facility's director to discuss their complaints regarding personnel, remuneration, and security. The Confédération Générale du Travail, who supports the workers, claims that the 24 recruited employees plus support staff are insufficient to handle the facility's detainees, since the original plans called for 36, even though the facility has temporarily lowered its maximum capacity from 60 to 40 to accommodate the lack of personnel. Twelve adolescents were transfered to the facility Monday, and another twelve are scheduled to arrive next week.

Now, please note that what I'm about to say does not come from any anti-French sentiment: I love the French--I lived and worked there for a year and would love to go back. But, give me a break! This attitude that you should exercise your right to strike on every occasion has gone too far. To say that the facility is understaffed when the pupil-to-adult ratio is better than one-to-one (or even two-to-one as would be the case at full capacity) is, frankly, utterly absurd. The staff may have a legitimate desire for personal alarm equipment, but a strike at the facility's opening is hardly the appropriate means of expressing their views, especially when the facility is operating at a drastically reduced capacity. This facility has been in the planning stages for four years--the personnel should have known what they were getting into when they signed up--and if they had any objections, raising them before the adolescents were scheduled to arrive would have been the appropriate action.

Union strikes may be useful in cases where the power imbalance puts workers at a significant disadvantage and working conditions are disgraceful, but I simply don't see how that could be the case here. My guess is that the personnel at this facility are decently well-educated and have a fair degree of social capital. Their working conditions, though perhaps improvable (what isn't?), are far from inhumane or unbearable. Furthermore, strikes in the public sector usually do nothing but create a lot of noise and inconvenience innocent third-parties (such as school children or people who rely on public transportation), unlike in the private sector where the interruption of production decreases profits and directly hurts the managers against whom the workers have a complaint. Refusing to play and pouting in the corner because you don't like the rules is childish--end this foolishness and have a mature, reasonable negotiation like adults.