Offering of Indulgences: A Game Theory An Operations Research Approach.

Or: what happens when a math major ponders theology.

A few weeks ago, Fr. Robert gave a homily on the topic of indulgences: how to obtain them, the difference between partial and plenary, and offering them for the faithfully departed. And me being me, I began to wonder: what is the optimal way to offer indulgences to maximize grace through one's life?

First, let's define an indulgence. According to the Catechism of the Catholic Church, "an indulgence is a remission before God of the temporal punishment due to sins whose guilt has already been forgiven, which the faithful Christian who is duly disposed gains under certain prescribed conditions through the action of the Church which, as the minister of redemption, dispenses and applies with authority the treasury of the satisfactions of Christ and the saints."

It continues, distinguishing between partial and plenary, "an indulgence is partial or plenary according as it removes either part or all of the temporal punishment due to sin."

Lastly, the Catechism specifies, "the faithful can gain indulgences for themselves or apply them to the dead." (CCC 1471)

This last statement is what I would like to focus on, for the purpose of this discussion.

Why offer them for the dead?

The Catechism addresses the practice of offering an indulgence for the faithfully departed in paragraph 1479: "Since the faithful departed now being purified are also members of the same communion of saints, one way we can help them is to obtain indulgences for them, so that the temporal punishments due for their sins may be remitted."

And again, in 1032, "From the beginning the Church has honored the memory of the dead and offered prayers in suffrage for them, above all the Eucharistic sacrifice, so that, thus purified, they may attain the beatific vision of God. The Church also commends almsgiving, indulgences, and works of penance undertaken on behalf of the dead:

"Let us help and commemorate them. If Job's sons were purified by their father's sacrifice, why would we doubt that our offerings for the dead bring them some consolation? Let us not hesitate to help those who have died and to offer our prayers for them."

Lastly, in paragraph 1475, it is explained how the benefits of the holiness of one member of the church can benefit another: "In the communion of saints, 'a perennial link of charity exists between the faithful who have already reached their heavenly home, those who are expiating their sins in purgatory and those who are still pilgrims on earth. between them there is, too, an abundant exchange of all good things.' In this wonderful exchange, the holiness of one profits others, well beyond the harm that the sin of one could cause others. Thus recourse to the communion of saints lets the contrite sinner be more promptly and efficaciously purified of the punishments for sin."

So the teaching here is that by offering indulgences for the Church Suffering, we can help them to obtain their final glory, and there is the hope that, once they have achieved perfect unity with God, there holiness can then benefit us here on Earth (the reality, not the planet).

During the sermon, Fr. Robert mentioned that, since we cannot know who is in purgatory, he always offers the indulgences he earns for his closest relative that is in purgatory, and lets God sort out who that is. This brought to mind my method of offering indulgences: to offer them for the soul with the longest sentence. The idea here was that if I got a soul who would otherwise have a long temporal punishment out of purgatory, that soul would be more thankful, and thus be more likely to use his spiritual goods for my benefit here on Earth. But then I began to wonder. Is this really the best way to achieve optimal grace and spiritual benefit?

Assumptions (no, not August 15ths).

Let us began by making certain assumptions about indulgences and the Church Triumphant.

Firstly, let us assume that upon helping a soul obtain the beatific vision, that soul will be grateful and offer his share of the Church's Treasury (CCC 1476-1477) for our benefit. This will give us some spiritual benefit, B. Secondly, let us assume that B can vary depending on the length of time, T, of the soul's temporal punishment. That is, a soul who was to remain in purgatory for a very long time, who we help out, will be more grateful to us, and thus offer us a bigger portion of his spiritual goods than a soul who was not to serve for very long. If true, this would mean that B would be greater for helping a soul with a longer sentence. Now let us examine three possible cases for how B can vary between souls with different lengths of their temporal punishment.

1) Logarithmic or no change.

In this first case, a soul who has a long sentence would either not be any more grateful upon being helped out of purgatory by our good works, or his gratefulness would increase logarithmically in relation to his increased sentence. Since we are assuming a direct correlation between sentence length, gratefulness, and spiritual benefit, this would imply that B does not change, or increases logarithmically between souls with differing sentence lengths.

We could express B as:

B = c ln T, for the logarithmic case, or

B = c, for the constant case.

2) Linear.

In this second case, a soul's gratefulness for being helped from purgatory increases linearly with respect to the amount of time he was to spend in purgatory. That is, B increases linearly with respect to the length of time which we, through our indulgence-earning actions here on earth, remit from the soul's time in purgatory.

In this case, we would write

B = cT

3) Geometric or exponential.

In this last case, a soul's gratefulness, and thus our spiritual benefit, increases at a geometric rate or an exponential rate with respect to the amount of time by which we reduce the soul's temporal punishment.

In other words,

B = kT^c, i.e., B increases geometrically with respect to the temporal punishment of the soul, or

B = c^kT, or B increases exponentially with respect to time.

(For c, k positive.)

So the purpose of this exercise is to determine, for a given assumption about the relation between spiritual benefit and temporal punishment, what is the best strategy to maximize B with respect to indulgences earned during one's life? Essentially, we are balancing getting many less-grateful souls out of purgatory against getting fewer extremely-grateful souls.

Plenary vs. Partial.

A plenary indulgence, according to the Catechism, removes "all of the temporal punishment" due to sin. Basically, a plenary indulgence acts as a "get out of purgatory free" card, that will automatically attain the beatific vision for a given soul. In this context, it is clear that, for all but the most trivial case (that is, where there is no difference in B between souls with short or long sentences), it is most advantageous to offer indulgences to souls who have the longest temporal punishment. For this reason, we will instead focus our study on how best to offer partial indulgences.

Let us assume that a partial indulgence remits a constant, finite amount from a soul's temporal punishment, where the amount remitted is dependent upon the act that earned the indulgence. We will call the amount of remission R.

The Trivial (Selfish) Solution.

The most obvious solution to the indulgence-offering problem is to apply all indulgences for the remission of one's own temporal punishment, according to CCC 1471. However, while applying indulgences to oneself removes one's own current sentence in purgatory, it does nothing to remit the temporal punishment incurred by future sins. Obviously, this is a short term solution, where there is no long-term benefit to the indulgence. This strategy is only recommended if death is feared to be imminent.

We will assume that helping another soul attain heaven produces some long-term benefit. That is, the soul, now in the presence of God, will have an ongoing and lasting influence in our life. Essentially, we are assuming that B is not temporary. As such, offering indulgences for the Church Suffering will have a better long-term ROI, whereas applying them to ourselves is the best solution until we commit our next sin.

Let us further examine the long-term case.

B is Constant.

In this trivial case, the gratitude showed by a soul we have helped does not differ based on the length of the soul's temporal punishment. This may be the case if a soul does not know the period of its time in purgatory. For the trivial case, it is best to maximize the number of souls we have helped from purgatory, since the benefit we receive is the same for each one.

B Increases Logarithmically.

In the case that the spiritual benefit offered by the soul whose temporal punishment we have helped to absolve increases at a logarithmic rate with respect to the length of said punishment, it is clear that applying the indulgence to a soul with a longer sentence suffers from diminishing returns. That is, the benefit received from the soul does not increase at a comparable rate with the time. This is because,

x(c ln T) > c ln (xT), for x, c positive.

In other words, if I receive x partial indulgences, where each one will remit t amount of temporal punishment, I have the option of getting x souls with sentences of length t out of purgatory, or I can get one soul with sentence xt out of purgatory. Since the latter case suffers from diminishing returns, the first case provides the most benefit to me.

In general, B = ^x/_p c ln (^p/_x t),

where x is the number of indulgences obtained, p is the number of indulgences applied to each given soul, and t is the total amount of temporal punishment remitted by all received indulgences. A simple calculation will show that this is maximized at p = 1.

B Increases Linearly.

In the case that B increases in a linear relation to the amount of time, T, remitted by our indulgences, there is no difference between which souls we apply our indulgences to. This is because,

x (cT) = c (xT)

In other words, the benefit to us is the same, regardless to whether we help one soul, with temporal punishment xT or x souls, with temporal punishment T.

B Increases Geometrically or Exponentially.

In these last two cases, it is more beneficial to apply an indulgence to a soul with a long temporal punishment, as the spiritual benefit we receive will increase at a rate exceeding the temporal punishment we help to remit. This is because,

x (kT^c) < k(xT)^c

and,

x (c^kT) < c^kxT

For this strategy, it is best to offer partial indulgences for the soul with the longest time in purgatory, that we can remit during our lives.

Why's that?

It is important to note that even in the last case, it is not most beneficial to offer our indulgences for the soul with the longest temporal punishment. One must consider the possibility that the sum total of all partial indulgences we earn will not equal the sentence length of the soul we offer them for. In this case, as of the time of our death, we will not have elevated the soul to the status of Church Triumphant, and will not have begun to receive our spiritual benefit, B. This is why it is important to make sure we at least get one soul out of purgatory with our indulgences.

A Soul's Access to the Church's Treasury.

Another variable to take into account is the holiness of the souls we are helping. It is conceivable that a holier soul would have greater access to the spiritual goods of the Church's Treasury, and thus elevating a holier soul could have a greater benefit, even with less gratefulness on the part of the soul. In this case, even though soul A, whose temporal punishment, and therefore gratitude, is much greater than that of soul B, soul B may have much greater access to spiritual goods. 

In other words, we wish to maximize,

B' = B · H_s,

where B' is our adjusted spiritual benefit, B is the unadjusted benefit, derived from the gratefulness calculations above, and H_s is the holiness of the soul whose punishment we have remitted. In this case, reasonable assumptions must be made about the likely holiness of the souls.

This approach would seem to favor souls with shorter temporal punishments, as these souls are likely to be holier than those with longer temporal punishments.

NB: I could find no indication in the Catechism that a soul's access to spiritual treasures depends on that soul's holiness during his life. If this is the case, one can safely discount holiness as a factor in application of indulgences.

Spiritual Interest Rates.

One more thing which we ought to consider is the moral decay, or lack of spiritual advancement in our lives brought about by delayed spiritual benefits. Simply put, having more members of the Church Triumphant, even those with a small benefit, praying for us now may, in the long run, provide us with greater benefit than having one soul praying for us in fifty years. This can be thought of as "spiritual interest", and can be likened to banking interest rates. For instance, is it wiser to invest $2000 now, or $5,000 in ten years?

To take this into account, one can simply apply the compound interest formula to the spiritual benefit we've calculated previously. In other words, we want to maximize the total lifetime benefit, B_L, where,

B_L = H(1 + B/n)^nt,

where H is our initial holiness, B is the spiritual benefit that we expect to receive from our strategy, as calculated above, n is the number of souls we expect to elevate to Church Triumphant per year with our current strategy, and t is our lifetime.

Plenary vs. Partial, Part Deux.

One more thought on plenary vs. partial indulgences: in order to maximize spiritual benefit during your life, you should never offer a plenary indulgance for a soul for whom you have already offered a partial indulgence. In such a case, the partial indulgences you've already spent on the soul will in essence be wasted, since they did not serve to remit the soul's punishment any faster. Instead, you might offer a plenary indulgence for the soul for whom your worst enemy has spent the most partial indulgences on, to minimize the spiritual benefit gained by him.

Note that while I could not find any evidence in the Catechism to indicate so, common sense might indicate that such a strategy would cancel out any earned indulgences, as part of the requirement for earning a plenary indulgence is to be "free from any attachment to sin," and such spiteful application of an indulgence would indicate the opposite.

God Knows What's Best.

With all these variables, and special cases, and unknowns, it seems that it is very difficult to find the optimum indulgence-application strategy. However, God always knows what is best for us. It is for this reason that I recommend we fall back on God. When you offer an indulgence, you can simply make a prayer as such, "Father in Heaven; I offer up the graces I receive today to that poor soul in purgatory whose gratefulness will maximize the equation:

B_L = H(1 + B'/n)^nt,

where B_L is the total spiritual benefit achieved in my lifetime, H is my current holiness, n is the number of souls I will help out of purgatory in my lifetime, t is my lifetime, B' = B(T) · H_s is the adjusted holiness of the soul (where applicable), and B(T) is the gratefulness function for a soul, based on the time of his temporal punishment. Amen."

God will know what you mean.

Fine then. 6 things that make me happy.

1) To supply and give aid and comfort to Joe's enemies.

2) Being done with a workout. I don't get any satisfaction from working out. I just like it when I can go back to being lazy for the rest of the day.

3) Harassing Hannah and teaching her things that are humorously untrue.

4) Making the Kessel Run in less than eleven parsecs. Beat that!

5) Drinkin' rum, shootin' stuff and rockin' out to Hair Metal with my groupie-for-life (that's all "one thing" the way I do it!)

6) Not tagging people or forwarding things on, but rather letting messages die in the abyss of digital-nothingness.

Ok, ok, ok. Six things that make me happy.

Since Mrs. Pickles demanded it.

(ZOMG! Stolen bandwidth!)

1) To crush my enemies, see them driven before me, and to hear the lamentation of their vomen.

2) Curling up on the couch with the Murloc, a bag of popcorn, and some hot apple cider, to watch a good movie.

3) Having Isis curled up in my lap, or next to me in bed, purring softly to herself.

4) Hearing people's thoughts on Space Pirates, writing a key scene or conversation I've had in my mind for years, and imagining the story with all its twists and turns as it unfolds to the end.

5) Staying late at my parents' house talking about theology, politics, literature, and other intellectual topics.

6) Lying in bed with the Murloc, with my hand on her tummy, imagining our baby growing within.

Whale Biologist of Family Adams Magazine, I tag you!

Update on the Little One.

From BabyCenter.com, re-printed here in its unedited, politically-incorrect, inflammatory, and scientifically accurate form.

Though he's barely the size of a kumquat — a little over an inch or so long, crown to bottom — and weighs less than a quarter of an ounce, your baby has now completed the most critical portion of his development. This is the beginning of the so-called fetal period, a time when the tissues and organs in his body rapidly grow and mature.

He's swallowing fluid and kicking up a storm. Vital organs — including his kidneys, intestines, brain, and liver (now making red blood cells in place of the disappearing yolk sac) — are in place and starting to function, though they'll continue to develop throughout your pregnancy.

If you could take a peek inside your womb, you'd spot minute details, like tiny nails forming on fingers and toes (no more webbing) and peach-fuzz hair beginning to grow on tender skin.

In other developments: Your baby's limbs can bend now. His hands are flexed at the wrist and meet over his heart, and his feet may be long enough to meet in front of his body. The outline of his spine is clearly visible through translucent skin, and spinal nerves are beginning to stretch out from his spinal cord. Your baby's forehead temporarily bulges with his developing brain and sits very high on his head, which measures half the length of his body. From crown to rump, he's about 1 1/4 inches long. In the coming weeks, your baby will again double in size — to nearly 3 inches.

Coventry Carol

Holy Innocents, pray for us!

The Holly and the Ivy

Alma Redemptoris Mater.

Loving Mother of our Savior, hear thou thy people's cry

Star of the deep and Portal of the sky!

Mother of Him who thee from nothing made.

Sinking we strive and call to thee for aid:

Oh, by what joy which Gabriel brought to thee,

Thou Virgin first and last, let us thy mercy see.

O Emmanuel.

O Emmanuel, king and lawgiver,

desire of the nations, Savior of all people:

Come and set us free, Lord our God.

O Rex Gentium.

O King of all the nations, the only joy of every human heart;

O Keystone of the mighty arch of man:

Come and save the creature you fashioned from the dust.

O Oriens.

O Radiant Dawn, splendor of eternal light, sun of justice:

Come, shine on those who dwell in darkness

and the shadow of death.

O Clavis David.

O Key of David, O royal Power of Israel,

controlling at your will the gate of heaven:

Come, break down the prison walls of death

for those who dwell in darkness and the shadow of death;

and lead your captive people into freedom.

The Good Ship Redemptrix.

Long may she fly.

(Next in my series of "Space Pirate" posts. Let me know when you get tired of these.)

At some point while reading through SPE1, you may have wondered "what does Captain Jack Flint's BAE CT-1300 model corvette look like?"

Well, thanks to the miracle of modern technology, I can deliver images through the intertubes directly to your Technicolor Rasterizificationer.

But before I do that (that is, give you what you want), allow me to go through the evolution of the ship (that is, bore you with details you don't want).

My starting point for designing the ship was a C-130. I figured this basically described everything your average Joe space pirate could need. A large fuselage, capable of carrying lots of loot; the ability to load it with guns, for massive broadsides; and small enough (in spaceship terms), to be agile.

However,  I wanted to make some changes to this design. Firstly, I always liked how the nose cone on a C-5 could open to allow the loading of cargo in through the front or back. This seemed like a handy thing for a space pirate to be able to do. But I thought it should be able to do that in flight, so the idea of the entire nose opening, and blocking the view from the cockpit, was impractical. Instead, I opted for a cockpit that was above a loading ramp.

The first drawings were based on this idea. You can see how I worked through different hull shapes, trying to hone in on one I liked. Other changes I made involved wing shape and placement, turret placement, engine configuration (I always knew it would have four; again patterened off the C-130), and addition of tails. The drawing closest to the middle of that page (the side-view; second side-view down on the right) was the first one I really liked, so I drew a perspective of it, to get an idea of what it looked like from other angles. It was getting close, but it still lacked something. 

Around this time, I decided that many of my ideas were too close to Star Trek, and I wanted to move the feel of the story back about four centuries, closer to Master and Commander. This led to many other changes in the story (which I may talk about later), and I strived for less futurism and more anachronism.

The way this manifested in Redemptrix was that I decided it should be more like a sailing ship and less like an airplane. The obvious way to change this was to move the bridge to the stern of the ship, and you can see this in the drawings towards the bottom of the page. The only other things I played with from there were changes to the slope of the hull.

This is the drawing I made about the time I started writing the book, and was the first "final" drawing. As I wrote, I realized I needed to make a few minor changes. The engines, which were supposed to be atop the wings, on the downward slope of the hull, were moved. (I realized that if you are accelerating a ship at 9.8 m/s², you would want your thrust to be downward, and not aftward, so you could walk on the floor, not the wall.) Also, all the weaponry was moved forward to be in the nose cone, and the number of cannons was reduced from eight to six. (Moving the cannons into the nose cone meant that, due to the slant, all six guns could point forwards, which meant you could bring more firepower to bear on a single target.) But this drawing is still pretty close (although the final design is proportionally longer).

From that drawing I was able to build a very simple 3D model in Anim8or.

This model is completely untextured, and no details, such as the rail gun turret, cannon portals, or throats, are shown. 

Since no one has yet opted the rights to make Space Pirates into a multi-million dollar blockbuster and it remains only a book, you will have to use the old-fashioned technique of using your imagination to visualize the details. To help you along, I have provided this quote from near the beginning of chapter two of the work-in-progress Space Pirates Episode II.

"The hull was colored a dark bluish-gray, except for the vertical stabilizers at the ends of the wings, which were painted gold, and the word "REDEMPTRIX", painted across the stern of the ship in large, serifed, gold, electro-opaque paint. This special type of paint only turned opaque when an electric current was supplied, meaning that if the crew didn't want to broadcast who exactly it was that was stealing from you, they could simply turn off the incriminating name."

Even though it is very simple, it really did help me visualize what the ship looked like, and from there I was able to work out the details of the interior.

In those schematics, the dashed lines represent the ceilings of the respective decks, since the sloping of the hull makes most of the decks wider at the floor.

"The entire ship was sixty meters, stem to stern, fifteen meters, keel to dorsal, and thirty meters, wingtip to wingtip, which put it squarely in the standard classifications as a corvette: slightly larger than a sloop or sloop-of-war, and smaller than a frigate."

(In Episode I, Jack says that Redemptrix is 100 meters. That was before I worked out the exact size, and it will be corrected when I go back and edit it.)

As for the name, there was no real evolution. When trying to come up with a name for Jack's ship, I sort of knew the direction I wanted to go. Redemptrix occurred to me, I liked it, and, more importantly, choosing the name helped shape the plot; obviously I had to figure out why Jack chose that name (his reasons will be revealed at a later date).

O Radix Jesse.

O Flower of Jesse’s stem,

you have been raised up as a sign for all peoples;

kings stand silent in your presence;

the nations bow down in worship before you.

Come, let nothing keep you from coming to our aid.

One of the things I love about our faith is how rational it is; that is, how much it just makes sense. It is very rare that, so long as I am looking at the world from a Christian perspective, that it confuses me or doesn't make sense, particularly where human behavior is concerned. With the concepts of Original Sin, or man's fallen nature, or our innate desire for God, or the natural law, or guilt, or conscience, Holy Mother Church has very well instructed those who, like me, are not wise enough to figure out why people act as they do.

For instance, a man commits an evil. "Why did he do it?" people ask. "Because of his fallen nature, he inordinately desires created things, or things of this world, and is inclined to love himself over others," I know. Or, a group of people who commit evil may seek to legitimize it, or gain public acceptance for their evil acts. I understand this to be an act designed to assuage a guilty conscience. Or if a person acts with heroic selflessness, risking his life to save a child from a burning building, I can understand this as the person acting on his innate desire to do what is good, and he knows what is good through the natural law. It may be that all three of these happen within the same context; for instance a association aimed at the repeal of anti-arson laws sets fire to a building, causing a passerby to rush in to save the occupants. In fact, historically, these have all happened in the same context: Hitler was an evil man who sought to massacre the undesirables because he was fallen and prone to sin; the Germans who worked to accomplish his ends made excuses for why it was right, because they needed to appease their consciences and bury their guilt; and even in the midst of great evil, some rose above it all to show incredible love and compassion, because of a heroic desire for God and what is good.

(NB: the question of how people come to act as they do is, as are all questions of how, a matter of the sciences, particularly psychology and sociology, and are worth studying. For instance, what biological and environmental influences cause one man to commit evil and another to do good.)

It is because of this instruction that I am sometimes briefly astonished that, to this day, some people defend the sexual revolution as a good thing, until I remember that not everyone has the benefit of being brought up with such wisdom. To someone like me, who has a bit of intelligence but not a shred of wisdom, the revolution may look like a good thing. I mean, what could be wrong with throwing away outdated and pointless sexual mores? But when you look at the issue with the understanding provided by the Church, the problems become immediately obvious.

Chastity is part of the natural moral law, which is inscribed into our hearts and discernible through right reason. It governs our actions and helps us to act lovingly towards and promote the dignity of others and ourselves. By following the natural moral law, we can work to bring happiness. To act contrary to the natural law brings unhappiness and sorrow.

"The natural law, present in the heart of each man and established by reason, is universal in its precepts and its authority extends to all men. It expresses the dignity of the person and determines the basis for his fundamental rights and duties:

"For there is a true law: right reason. It is in conformity with nature, is diffused among all men, and is immutable and eternal; its orders summon to duty; its prohibitions turn away from offense . . . . To replace it with a contrary law is a sacrilege; failure to apply even one of its provisions is forbidden; no one can abrogate it entirely." (CCC 1956)

From this perspective it is easy to see what will happen when you casually toss aside these morals, "when you empty the relationship between the sexes of all moral significance and destroy the customs and institutions that govern it": women become a commodity, children become a possession, family becomes unnecessary, and murder becomes justifiable.

All the previous is just a very long-winded and roundabout way of introducing this article, which highlights one particular negative outcome of the sexual revolution: an increase in violence towards and abuse of women. 

And it makes sense.

O Adonai.

O Sacred Lord of ancient Israel,

who showed yourself to Moses in the burning bush,

who gave him the holy law on Sinai mountain:

Come, stretch out your mighty hand to set us free.

O Sapienta.

O Wisdom, O holy Word of God,

you govern all creation with your strong yet tender care:

Come and show your people the way to salvation.

28 / 1 = 28

28 / 2 = 14

28 / 4 = 7

28 / 7 = 4

28 / 14 = 2

1 + 2 + 4 + 7 + 14 = 28

I'm perfect!

(Thanks Mom!)

"So for the Blizzard Christmas party," the Resident Murloc says to me a couple days ago, "I'm going to get my hair done like Elsa's."

There is a short pause.

"Schneider?" I reply.

"Yeah."

I pause again, briefly, while images like the one below, and thoughts of the Austrian Goodbye dance through my head.

"We may have to go home early."

"Very early."

A Moral Quandry.

Perhaps I've been reading John C. Wright's blog too much (why aren't you?), but a question of morality popped into my head yesterday and has been bugging me since. It concerns science fiction/fantasy.

If voluptuous space alien babes were to land on the planet Earth tomorrow, could I (assuming I'm single), morally wed one? The answer I devised for this question was based on the intercompatibility of the species. Since marriage is an institution designed to promote the family, and since we know through faith and reason that the sex act must be ordered towards procreation, I think the morality of that marriage would depend on if the voluptuous space alien babes (VSAB from here on in) are biologically similar enough to humans to be able to procreate.

(Note that the chances of some random ET landing on Earth and being able to produce offspring with humans are probably something in the order of one in the XKCD number, where the XKCD number is the Ackermann function, with Graham's number as both arguments. This is one problem with Star Trek, where people are always mating with other aliens. There is no way Spock, being half-human, half-vulcan, is even remotely biologically likely.)

So with the easy question out of the way, we come to the hard one. What if you don't know if you're biologically capable of producing offspring with VSABs?

Of course, with modern technology, we could probably answer this question just by examining the genetics of the two species. But suppose that technology is not available.

Perhaps I should go back to what inspired the question in the first place.

In World of Warcraft (those of you who didn't see that coming obviously don't know me very well), one of my main characters is a Draenei, while The Resident Murloc's is a Night Elf. We typically play these two characters together, and I began to wonder whether they could marry. (Note that I am presupposing, even though Christianity doesn't exist in the Warcraft universe, that sex is intended for procreation and any use if it that contradicts that purpose is illicit and contrary to the natural law, which is independent of religion.)

Within the lore, I don't know if it has been established if Night Elves and Draenei are biologically compatible enough to produce offspring with one another. (I know other races are compatible; Garona is a half-human, half-orc.) So, the question poses serious ramifications for Golyath, being an upstanding and noble Shaman who wishes to do what is right by Nevlonniel. How can he, morally, determine if he is biologically compatible with a night elf, and until that is known, how does that affect his prospects for marriage to this lovely night-elf?

(For all zero of you who are interested, I used to play another Night Elf, Legolamb, along with Nevlonniel. I imagine that Outland changed Lego, and he became cold and distant from his former love, until he finally left her (his change is manifested in his new haircut). In reality, I got tired of playing the most useless class in the game, and wanted to actually feel like I was contributing something in a raid.)

This question has plenty of other contexts aside from WoW, too. For instance, what if some humans were taken by Ra through the Stargate, where they lived separated from their Earth-living relatives for tens of thousands of years, before being reunited, only to discover that they have evolved along different paths and are not biologically compatible with each other? In this case, they might even still be considered the same species.

It does have interesting ramifications, too. We know that homosexuality is disordered because it involves the desire to use the sexual facilities in an unnatural way, that is, in a manner that is contrary to the nature of the sexual act (that nature being the unity of the spouses and procreation). But what about my heterosexual desire for the non-biologically-compatible VSABs? Even though that union is innately contradictory to the nature of sex, is my desire for the well-endowded female aliens also perverse? Suppose we take it one step further and say that they look like Earth-women, only hotter, how is my... how am I supposed to know the difference?

It would also make for an interesting science fiction story. Space Babe lands on earth. Earth man falls in love with, and weds, Space Babe. 193 pages of hot alien-tentacled love later, they determine their species are biologically incompatible. Action sequences ensue, perhaps involving Space Pirates. And of course the Space Babe is also a Space Princess, so it can be considered part of the New Space Princess movement of speculative fiction.

Someone call Mr. Wright. I would write it myself, but with 4 and 2/3 books left to go in my own series, it will be a while before I can get to it.

Why yes, it has been slow at work recently.

A mathemetician, an engineer, and a liberal arts major....

This article is an interesting read for two reasons: firstly, and most obviously, is the discussion of the problem in question. Secondly, is because the user comments highlight the basic difference between mathemeticians, engineers, and liberal arts majors.

The mathemeticians take the problem at face value, and solve it as an interesting puzzle that is to be reasoned through. The engineers all say the problem is stupid because it makes no sense and ignores all sorts of real world considerations, like micro-fractures in the surface of the bowling ball. Then they try and come up with all sorts of other ways to solve the problem, such as vise grips, terminal velocity calculations, etc.

Some would say this indicates that engineers are better at thinking "outside the box", and that mathemeticians are not as creative. I would argue that the converse is true, that instead this shows that engineers are incapable of thinking of anything but the box, i.e. the real world. Mathemeticians have no trouble dropping the pretext of reality and imagining something simply in the abstract for the sake of an interesting puzzle that demonstrates how well you can reason through a problem. Of course they know that there are better ways to test bowling ball resilience, and that there are inherent flaws in the test, but that's not the point of the problem. Engineers, on the other hand, can't get their heads around the idea of a problem that doesn't use the normal rule set they are accustomed to, and instead, try and change the problem to better fit into the box in which they are used to thinking.

In short, Kirk thought like an engineer. When presented with a problem that didn't allow him to work within his usual frame of reference, he changed the problem so he could.

And the liberal arts majors? I'm pretty sure this comment was left by one.

So do you think like a mathemetician, an engineer, or a liberal arts major.

My Wife's Curious Mind

We finally got around to watching Zulu, an excellent war movie I had been wanting to see ever since Dave recommended it. It arrived from Netflix not too long ago, but we hadn't had the time to watch it until tonight (good holiday movie!).

"On the January 22nd 1879 the British Army suffered one of its worst defeats when Zulu forces massacred 1,500 of its troops at Isandlhwana. A short time after the main battle a Zulu force numbering in excess of 4000 warriors advanced on a British hospital and supply dump guarded by 139 Welsh infantrymen. The film concentrates on this bloody 12 hour battle during which the British force, under their commander from the Royal Engineers who happened to be in the area building a bridge and happened to be senior to the infantry officer, won 11 Victoria Crosses." (plot summary by Dave Jenkins)

Ileana hadn't said anything during the entire movie. She appeared to be enjoying the movie much like she enjoys a good History channel documentary; silent and soaking it all in. Near the end of the movie, when the director pans across the line of Zulu warriors to add dramatic effect to the coming final battle, Ileana finally breaks her self-imposed vow of silence.




"Hey, a lefty!"

Those were the only words she uttered until the credits ran. I will continue to ponder the depths of her uncharted mind.

Take a look at this picture.

What do you think after seeing this picture?

a) That looks incredibly stupid.

b) That looks incredibly fun.

c) I'll bet alcohol was involved.

d) I'll bet testosterone was involved.

If you answered (a), you are a woman. If you answered (b), you are a single guy. If you answered (a) and (b), you are a married guy. If you answered (c), you are intelligent. If you answered (d), you are correct.

For the record, I was not actually in the buggy at the time this picture was taken, as I was holding the camera. My ride in the buggy came later, and involved a lot of this, but while going up and down a steep dune.

My Amazon.com wishlist has been updated.

Just an FYI.

Update on the Little One.

From BabyCenter.com

I took the liberty of changing the obviously pro-life-slanted language to a more neutral tone, in keeping with the diverse opinions of this site.

"How your baby's fetus is growing: This week's major developments: The nose, mouth, and ears that are currently only part of you and at some ambiguous point in the future will become a part of a separate entity that you'll spend so much time kissing in eight months are beginning to take shape. If you could see into your uterus, you'd find an oversize head and dark spots where your baby's parasitic growth's eyes and nostrils are starting to form. His Its emerging ears are marked by small depressions on the sides of the head, and his its arms and legs by protruding buds. His Your second heart is beating about 100 to 160 times a minute — almost twice as fast as yours main one — and a separate quantity of your blood is beginning to course through his body your new appendage. His Your new intestines are developing, and the bud of tissue that will give rise to his more of your lungs has appeared. His The growth's pituitary gland is forming, as are the rest of his your other brain, muscles, and bones. Right now, your baby lump of tissue, which can be removed with all the ethicical considerations of removing tonsils, is a quarter of an inch long, about the size of a lentil bean."

Anyone here play Dark Age of Camelot?

Because here's a free account if you want it.

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