Car parking game strategy

See the original puzzle

The Car Parking Game isn't really a "puzzle" in the usual sense.  It's a game.  But it's one of those games which is simple enough that it is feasible to analyze who is winning at any given time.  Given any game-state, either the current player can force a win, or the other player can force a win.  I will denote these game-states as W and L respectively.

W and L states have a particular structure:

1. If the current player cannot make a move, then it is a W state, since the rules say that the current player wins.
2. If the game is in a W state, and the current player can make a move, then it is possible for the current player to make a move leading to an L state.
3. If the game is in an L state, then the current player can only make moves which lead to W states.

If you know which game-states are W and which are L, then the strategy is simple: always make moves leading to L states.  The implied puzzle is: which game-states are W, and which are L?

There are several ways to figure it out.  One is to do it by hand.  Or you can do it with a computer.  I did it both ways.  But I'm not going to show you that.

I also solved the problem using the third method: research!

The most difficult part of researching this kind of problem is finding the right keyword.  The keyword is "Kayles".  Kayles is a game involving a row of bowling pins.  Each player can either knock down a single bowling pin, or knock down two adjacent bowling pins (if there is no gap between them).  Kayles is equivalent to the Car Parking Game, because you can either park your car efficiently, taking up one spot, or inefficiently, parking across two spots.

There are two versions of Kayles.  There is "normal play", where if the current player has no possible move, then the current player loses.  And then there is "misère play", where if the current player has no possible moves, then the current player wins.  In Normal Kayles, you can use a simple strategy, similar to that of the Coins on a Table Game.  From a mathematical standpoint, normal play is also easier to completely analyze than misère play, because we can apply the Sprague-Grundy theorem.

The Car Parking Game is equivalent to Misère Kayles.  I was pleased to find that Misère Kayles has been completely solved!  Unfortunately, the solution is very complicated, and will not fit in the margins of this blog.  If you are able to decrypt the paper, that's quite an accomplishment, and I welcome you to use it to beat me at the Car Parking Game.

Some statistics on sex

Yesterday, I talked about the question "How sexual are people?"  People seem to have overarching views on this question, despite the fact that it is so poorly defined and we have no solid knowledge about it.

Okay, but we do have some knowledge after all.  We have statistics.

When I first saw statistics on sexual behavior, I thought, "That's higher than I thought, all across the board!"  And then I sort of forgot, until I saw the statistics again.  Then I thought, "I remember it being higher than I thought, but it's still higher than I remember!"  So I know for a fact that my views and impressions were/are inaccurate.  People think that as an asexual, I must think everyone else is just crazy about sex.  But as it works out, I tend to persistently think everyone is like me.

I want to show you some statistics of some North American university students, mostly age 18-19.  My questions: Do you find them surprising?  In what direction?

"Mean Age" refers to the average age of people's first experience among those who had the experience.  "Mean Liking" refers to how students felt after their first experience.  The shading of the boxes has no meaning.

These statistics come from a free preview of Sex and Youth, chapter 2.  There are 252 women, and 191 men, and I believe people with same-sex experiences were excluded from the sample.  I did not "cherry pick" these statistics to support my conclusions, I picked them because I find Bob Altemeyer's writing entertaining, and he explains his methodology well.  One of these days I should buy the book and read the whole thing.

Note that the statistics neither support nor deny the thesis, "Humans are very sexual", because they do not solve the problem of defining "very sexual."

How sexual are people?

The Asexual Catch-22

Being involved in asexual visibility efforts has made me aware of a particular aspect in people's worldview.  That is, how sexual is society?  How sexual are people?

There are some people who think that sex is just the greatest thing, and everyone wants to have sex (especially the guys).  According to this worldview, all teenagers are super horny, all Republicans are repressed, and the internet is for porn.

Other people think the media just exaggerates the amount of sex in society, and there are plenty of married couples who just stop having sex.  According to this worldview, people are not actually having as much sex as it would seem, or if they are, it's because society tells them they want it.

That's just my caricature of the positions.  I'm sure people actually have more complex and developed views than that.  But you wouldn't know it based on their response to asexuality.

Asexuals are caught in a catch-22.  If an asexual is too sexless in comparison to someone's worldview, then that person thinks there is something wrong with them.  If an asexual is not sexless enough in comparison to someone's worldview, then that person thinks, "What's the point of the label?  They must buy into society's exaggeration of sex!"

I get more of the latter response because I am gray-A.  But I have indeed gotten both responses.  I sorely wish people with the former response and people with the latter response would talk to each other, and not put me in the middle!

I don't know and you don't either

The most common response from asexuals is to argue: You have an incorrect view of how sexual people are (and I have the correct view).  Of course, this can't really be true.  Asexuals can't all have the correct view; they don't even have the same views as each other.

It's not that we're all equally wrong.  There is, after all, some underlying objective truth to the matter.  There is a certain percentage of people who have a certain kind of sex at a certain kind of frequency, and there are certain set of chemicals going through their brain under those circumstances.  Some people have more accurate views of this than others.  And some people believe definitively wrong things, such as the "men think about sex every seven seconds" myth.

But there are two problems: The definition of "sexual" is unclear, and our knowledge of the facts is unclear.

I think it's comparable to the question, "Is human nature essentially good?"  What does it mean for human nature to be good?  Does it mean humans, untouched, would perform more good actions than bad ones?  Which actions are good, and how much weight should different actions receive?  What does "untouched" mean?  And even if the question were more clearly defined, how would we know the answer?  "Good nature" presumably involves thousands of factors, each of which would require dozens of experiments to really pin down, many of which would require some mad (unethical) social science.  Without experiments, we must resort to media depictions and personal experiences, which are both afflicted with all sorts of biases.  For example, we hang out with people who are like us, thus creating the illusion that most people are like us.

Likewise, what does it mean for people to be more or less sexual, and how would we know the facts of the situation?

I know when uncertainty has me beat.  I know when it's time to admit, I do not know just how sexual people are.

Now, if only I could convince other people to admit the same.  Non-asexuals should admit it when responding to asexuals.  The existence of asexuals who label themselves as such is an empirical fact that should inform one's worldview, not something that should be denied because of a prior worldview.  Asexuals too, should be aware of their own uncertainty (and they frequently are).  One's own experience is known directly, but the "typical" experience is only inferred from clues.  I feel it is safe to conclude that most people experience sexual attraction (and that's enough for most asexuals), but some of the finer details are fuzzy.

Tomorrow, I will continue this thread by posting some statistics on sexual behavior.  See next post.

Christian apologies

One of the trends among more liberal Christians is to apologize behalf of other Christians.  A recent example is a guest post on Blag Hag.  But I've bookmarked a few older examples.  I also vaguely recall one or two Christian groups at UCLA offering apologies on the main public walkway.

I have a slightly negative reaction to these apologies.  I've criticized religion, but to be honest I don't really expect religious people to apologize in response.  Somehow it just seems like the wrong reaction, a sort of faux pas.   As is frequently the case with these things, it's an emotional reaction, and I need to do some forensics to figure out why I feel that way.

One common objection raised is that people aren't really apologizing for their own actions, they're apologizing on behalf of other people.  One of my examples is about Christians apologizing for pastor Terry Jones, who is famous for burning a copy of the Quran.  It's a well-intentioned sentiment, but it doesn't do what apologies are supposed to do, which is promise improvement.  Most Christians have no power to change Terry Jones' behavior.  The person who should be apologizing is Terry Jones himself.

On the other hand, I feel like there are times when apologizing on behalf of others is appropriate.  If you're at a party, and a friend you brought is misbehaving, you would apologize on their behalf.  There are also public examples of this kind of apology, such as the British PM apologizing for the prosecution of mathematician Alan Turing for homosexuality in 1952.  In this case, the apology is mostly about repudiating the principles that led to Turing's prosecution.  Apologies are a rather complicated social practice, so perhaps the promise of improvement isn't the only legitimate purpose of an apology.

Another common objection raised is that Christians are not really following up on their apologies.  Even when it comes to their own actions, they're failing to really improve things.  One of my examples was about people putting up these signs at a pride parade.

If you look at the people behind these particular signs, you'll see that they explicitly don't take a stance on the question, "Is homosexuality a sin?"  I believe they're trying to be a "bridge" between people who would answer that question in different ways.  Perhaps that is a useful role to play, but it makes me feel that the apologies are dishonest.  They may be sorry, but they're not really trying to be unequivocal LGBT supporters.  It's like they're there just to score points without really deserving those points.

On the other hand, I'm sure plenty of Christians who make apologies really are part of LGBT- and female-friendly churches.

I think my main problem with the apologies is that they're making it about themselves.  They're saying, "Look at me, I'm not like those people. I'm trying to be better!"  They're expecting a reward for being decent human beings.  Sometimes the way it plays out, the next step is to complain that we're not being very appreciative of their hard efforts.  And the next step is to say that it would really help our cause if we weren't so mean to would-be allies.

Oh, and another problem (last one, I promise).  The guest post at Blag Hag said that the church's wrongdoings were contrary to Jesus' teachings.

Those of you who consider yourself atheists are, in my experience, pretty familiar with the things Jesus said, and are even more familiar with the way followers of Jesus, at best disregard and at worst, contradict and insult those teachings. And it probably makes you angry.

This is slightly ignorant, because the mainstream atheism I'm familiar with would not necessarily concede that Jesus was all nicey nicey.  More generally, I don't appreciate the argument that if people practiced Christianity "correctly", then they'd behave a lot better.  That's just an attempt to score points for Christianity, despite the actions of Christians.  I'm not impressed.

Balances and bottles

I served as a juror last week.  It was a civil case, as opposed to a criminal case.  Civil cases and criminal cases have different burdens of proof (in the US system).  In a criminal case, the defendant must be proven guilty beyond a reasonable doubt.  In a civil case, the claims against the defendant must be shown to be more likely true than not true.

In the closing statements, each attorney used a different metaphor for the burden of proof.

The plaintiff's attorney said it was like a balance.  Each side places evidence on the balance, and they are weighed against each other.  If the balance tips just a little way towards the plaintiff, then it meets the burden of proof.

The defendant's attorney said it was like a water bottle that you fill up with evidence.  It starts out empty, and the plaintiff has to fill it up half-way.  Even if the defendant makes no effort to empty that bottle, the plaintiff may still fail to fill it up half-way.

I felt this was an interesting demonstration of how you can totally BS with metaphors.  Which metaphor do you think is more accurate?

Forming infinity, one by one

This post is a continuation of "A few things wrong about the cosmological argument," a series which criticizes trivial details in the cosmological argument while going on frequent tangents.

For the sake of completeness, I must mention that William Lane Craig has a second way to argue that the universe must have a beginning.  It goes as follows.

2.21 A collection formed by successive addition cannot be actually infinite.
2.22 The temporal series of past events is a collection formed by successive addition.
2.23 Therefore, the temporal series of past events cannot be actually infinite.

I am not afraid to concede a few points to William Lane Craig, and that is what I am going to do here.

The first premise (2.21) is correct, though perhaps imprecisely phrased.  By successive addition, I believe WLC means adding a finite sequence of finite numbers together.  So if you add 1 minute and 1 minute and 1 minute together, you will only get a finite interval of time.  You can add finite intervals, one by one, all you want, and you will never get an infinite interval of time.

As for the second premise (2.22), that could be correct too.  If you believe that time works such that any moment must be "formed" by successive addition from some sort of beginning moment, then you would accept WLC's argument.  It sounds like a reasonable enough philosophy of time to me.

The problem is that if I had some evidence suggesting that the universe did not have a beginning, then I would simply have to find a different philosophy of time.  As a scientist, I just can't let little philosophical hangups get in the way of determining what's really true, am I right?  I gotta be practical about it, that's my attitude.

As it is, I think physics already uses a different philosophy of time.  Not because it is the metaphysically correct philosophy of time, but because it's a convenient model.  Time... is just a variable.  A coordinate.  The state of any physical system is a function of time.  The entire function of time can be determined from the state at any particular time, just as a unique solution to a differential equation is specified by a single point.  Physics doesn't say anything about the future being "formed" from the past.  It doesn't say anything about adding finite sequences of finite intervals together.

But I'm not saying WLC is wrong.  For all I know, all moments really are formed from the past by successive addition.  We may never know, since there aren't any obvious ways to put the claim to the test.

WLC does not address other ways of viewing time, but instead refers to G. J. Whitrow's The Natural Philosophy of Time, 2nd ed.  Supposedly, Whitrow defends a form of WLC's argument without presupposing WLC's view of time.

Funny story, I could only find the 1st edition, which appears to contain no such defense.  Instead, I found Whitrow discussing one of Kant's antinomies.  Kant argues that the universe must have begun for the same reason WLC suggests.  He also argues that the universe couldn't have begun, because the idea of beginning makes no sense without time being there in the first place.  From these contradicting arguments, Kant concludes that time is not applicable to the world, but rather a way for us to visualize the world.  Immanuel Kant, ladies and gentlemen.

Other research revealed that Whitrow wrote an article called "On the Impossibility of an Infinite Past" for The British Journal for the Philosophy of Science.  Whitrow uses the Tristram Shandy paradox, which involves a person who writes a complete autobiography, but who takes a whole year to commit the events of one day to paper.  There was also a reply, which I judge to be a devastating critique.  I feel like my work's already been done.

Does anyone want me to summarize the two papers on the Tristram Shandy paradox, and add it as an appendix?  Otherwise, I will skip it.

"A few things wrong about the cosmological argument"
1. Actual and potential infinities
2. Actual infinities in physics
3. What is real?
4. The "absurdity" of Hilbert's Hotel
5. Interlude: God is infinite
6. Forming Infinity, one by one
7. Uncertain beginnings
8. Entropy: The unsolved problem  
9. Kalam as an inductive argument
10. Getting from First Cause to God  

Free will, definitions, and dogma

I have been thinking about free will.  I'm a compatibilist.  That means I believe free will is compatible with determinism.

For a person who has never heard of compatibilism, it may seem weird.  How can free will exist if our choices are determined before we were even around to choose them?  One possible response to this is that compatibilists are using a different definition of free will.  I do not claim to have thought this out fully, but my own conception of free will is as follows:

An act of free will is that which is proximately caused by human volition.

Take the metaphor of the chain of causation.  Each link in the chain causes the next.  If one link in the chain is human volition, then the next few links are acts of free will.  If the world is deterministic, then the chain never splits off into multiple possible branches.  But this clearly has no bearing on free will as I have conceived it.

Free will is on my mind because of Sam Harris' new book, Free Will (via Friendly Atheist).  Sam Harris argues that there is no free will.  I have not read the book, so I will try to avoid speculating on his arguments.  A commenter (Garren) on Friendly Atheist offered the following argument against compatibilism:

I see the situation as analogous to answering "Is the moon made of cheese?" with a 'yes' — not because the moon is made of cheese in the original sense, but because our society is so insistent that the moon IS made of cheese that _whatever_ it's made of, we rename that substance 'cheese.' And then philosophers can avoid the pitchforks from a public who is fooled by the use of language.

Funny thing about having a large blog archive... I have made the same argument myself!  I will not quote myself, because I was a terrible writer back then.  But my basic point was that religion has all these dogmas like "God is good", "The soul exists", and "The Bible is the Word of God."  And even as religious beliefs transform, people continue to believe these statements are basically true.  The result is a shift in the meanings of "good", "soul", "Word of God", often moving towards metaphorical interpretations.

However, I noted that this does not imply that the metaphorical interpretations themselves are wrong.  I invite the reader to name the relevant fallacy.

Now I am trying to imagine times where it is completely appropriate to change a definition.  For example, we might ignorantly define a particular person as particular set of cells.  But then when we learn that these cells get replaced with new ones periodically, we'd still want to preserve the basic truth that I am the same person as that guy from 10 years ago.  So we would need a new definition of a person.  Is that wrong?

There is also the question of whether I have in fact shifted my conception of free will.  My current conception of free will seems natural, and not like a shift just for the sake of preserving the basic truth of the statement, "Free will exists."  Of course my feelings could be wrong on this matter.  To be honest, I don't recall how I conceived of free will when I was younger.

QM broke logic!

Stand to Reason is some sort of Christian apologetics organization that I don't know much about.  They have this program for high school students where they come up to UC Berkeley and meet godless university students, presumably to "inoculate" them.  They did it last year, and it was all quite civil.  I didn't blog about it probably because nothing piqued my interest.  They're doing it again tonight, but I probably won't blog about it.  In fact I might not go at all, because I'm feeling a little sick.

But I was amused to have a glimpse of their YouTube channel.  For fun...



The main problem with this video is... who the hell claims that quantum mechanics casts doubt on the laws of logic?  I'm not sure if he actually met an atheist who said that, or if he misunderstood something an atheist said, or if it's made up from whole cloth.  The rest of the argument is well-reasoned enough, but he kind of missed the crucial step of citing his opponent.

Also, while it is true that we shouldn't be dazzled by complicated jargon, this is only heuristic reasoning.  Clearly there exist valid arguments which are difficult to understand and involve lots of jargon!  One possible resolution is to ask an expert.  As a physicist, I can tell you that quantum mechanics does not cast doubt on logic, and does nothing of the sort.

Skeptically queer

An essay I've already written

I'm excited about what has happened in the skeptical blogosphere.  There was the appearance of Queereka, and then Sincerely, Natalie Reed.  These are skeptical and queer blogs, and I'm watching them combine these two topics in fantastic ways.  Since I am also blogging about skepticism and queerness, I want to be more like them!

For example, there was a post on Queereka about cognitive biases that keep us closeted.  And Natalie Reed had a coming out story in which skepticism plays an important role.  I felt inspired... I should retell my coming out story, and how skepticism played into the process.

But then I reread the coming out series I wrote as I was coming out, and it appears there is no need for retelling.  My writing was positively dripping with skepticism.  I talked about how scared I was of asexuality, and how I recognized this as a source of bias.  I talked referred to scientific studies, and to the experiences of other asexuals.  I discussed contrary evidence, and why I dismissed it.  I talked about tentative identification, and descriptive label use.  I changed my mind several times, because that's what you should do in light of new evidence.

I've been operating on the concept that queerness and skepticism are only really related in that they are both topics that I blog about.  And so it came as a shock to me to read my old writing.  I sort of have this vague idea that everything I wrote more than two years is terrible and embarrassing.  But I've been giving past!me too little credit.  And it turns out that I've been blogging about queerness skeptically all along.

I'm not sure why I thought otherwise.  As has been said countless times before, skepticism is not any particular conclusion, it is a method of thought.  Queerness is something that is important for me to think about, so I make a special effort to think about it critically.

Non-canonical skepticism

"Skepticism is not any particular conclusion, it is a method of thought."  Let's examine that statement, skeptically.  The fact of the matter is that there is a loosely defined skeptical community.  If someone identifies as a skeptic, I don't know that this is particularly good evidence to suggest that they are "better" at critical thinking, though it usually suggests they have some connection to the community.  And this community, while not uniform, shares quite a number of conclusions on a number of canonical topics.  Creationism, alternative medicine, conspiracy theories, urban legends, paranormalism, and so forth.

Superficially, it seems like there isn't much commonality between these topics.  Some people think there isn't really much in common, that these are the topics because that's what we've talked about before.  Some people, like Daniel Loxton, say that there is a logic to it.  They're the topics where skeptics, as lay-people, can legitimately claim some expertise.  This is all very controversial, and no one agrees on the proper scope of skepticism.

My boyfriend noted the other day that my blog doesn't really cover canonical skeptical topics most of the time.  Which is correct.  That's because I've realized that lots of other writers do it better than I can.  I only have expertise on a few topics like math and physics.

And I now have "expertise" in being queer.  I don't know if I believe queerness is properly within the scope of skepticism.  But I don't care.  I'm blogging about being queer, and I can't help but do it skeptically.  I don't know if other people can see it, but it's there, in the way I approach ideas and claims, and in my language

And yeah, every skeptic should know at least a little about queer people, just as every skeptic should know a little about Creationism and alternative medicine.  If for no other reason, skeptics need to know about various gender and sexual minorities so they have quick counterexamples to any generalizations about human nature.  Sensitivity to minorities within the skeptical community would be nice too.

Are skeptics better equipped to come out?

In Natalie Reed's coming out post, she speculated that if she had taken skepticism more to heart, her coming out would have been easier:

Maybe then I would have taken my skepticism seriously enough to have been able to spot the cognitive distortions, lies, excuses, rationalizations, selection biases and logical fallacies when I saw them in myself. Maybe I could have spared myself those additional years of self-inflicted torture.

I was into skepticism for years and years before I came out.  Instead of skepticism, I could have been into a whole lot of other things.  I could have been into heavy metal, or Doctor Who fandom.  And my coming out experience would be interpreted in light of the attitudes common to those communities.  But I was into skepticism and interpreted my experience in a skeptical light. Did that ultimately help me?

I'd like to say that it did, but skepticism compels me to say that there is no real evidence for this.  I have no idea how it would have played out otherwise.  And if I compare my own experience with that of other people's, I find that many other people dealt with it better than I did.  I hear stories where people were ecstatic or relieved about finding asexuality.  I, on the other hand, was depressed for months.

I'm inclined to say that if there's any interest that could have better equipped me for coming out, it would be LGBT allyship.  (I don't mean just being fine with gay guys and supporting gay marriage like I was, I mean actually making an effort to educate yourself about the many varieties of queer experiences.)  General critical thinking skills cannot compete with specific knowledge about a topic!

But even if I cannot say that skepticism improved my experience, I'm still convinced critical thinking is the right way to think about it.  What is it we know, and how do we know it?  Our largest body of evidence is the variety of anecdotes and experiences of queers.  Anecdotes are excellent to prove existence and non-universality, but are not so good at proving overarching theories about attraction or gender.  Knowing this gives me confidence to assert my own experience.  It doesn't matter if I defy categories, or if my experience is different from others.  I never had much evidence to suppose that these categories and experiences were universal in the first place.

The evil of theodicy

Earlier a commenter told me I should stop bashing religion. This left me wondering, where did they see me bashing religion?  I feel like I've mostly said neutral things about it lately.  I should do more religion bashing!

The problem of evil asks: How can there be a all-powerful and all-good god if there is evil in the world?  Obviously this only applies to religions with an all-powerful and all-good god, and I might as well say that I'm thinking of Christianity in particular.

I'm not sure I've ever talked about the problem of evil before.  I don't really like it, because there's no math involved.  And the argument is too sprawling, with a multitude of rebuttals.  In fact, we even have the word "theodicy", which means a defense against the problem of evil.

Most theodicies are not very compelling, but that's not what I want to talk about.  I want to talk about how theodicies, above and beyond being bad arguments, are also evil arguments.  That is, many theodicies involve defending evil, or denying the existence of certain kinds of evils.

The free will defense

The free will defense says that evil exists in the world because of human free will.  The obvious problem with the free will defense is that it ignores natural evils, like hurricanes and disease.  But let me tell you about some of the other kinds of evils it ignores.

There is the kind of evil which is caused by ignorance of the consequences of a free action.  To use a silly example, someone could open a door, not knowing someone was there to be smacked in the face.  Or, someone could buy a diamond, not knowing that the money is used to fund a terrible war.  Or if someone votes for X political party, not knowing that God truly endorses the opposing party (har har).  This is evil not caused by free will, but by ignorance, which is arguably a hindrance to true freedom.

There are various kinds of responses to the problem of natural evil.  One of them is that natural evil was released into the world by Adam and Eve's original sin.  Or, if you're Pat Robertson, natural evil was released into the world by modern actions such as homosexuality.  Or if you're Alvin Plantinga, natural evil was caused by the free will of nonhuman beings, like angels or spirits.  Presumably, the means of causation are magical (divine), but it's kind of funny that earthquakes and hurricanes mostly occur where you would expect them if they were caused by chaotic physical processes.

Now here's another problem being ignored: the sheer injustice and cruelty of this situation.  We deserve to be punished for the sin of a couple ancestors?  Or for the sins of other people within our society?  Or for the sins of some otherworldly beings we don't even know about?  The causal chain leading from sin to natural evil isn't very clear, but it's hard to imagine that God really doesn't have any control over it.  Is it interfering with the free will of gay people to change ocean temperatures and prevent a hurricane?  As far as I'm concerned, this theodicy only succeeds by conceding that God is not actually all-good.

The greater good

There are a variety of other theodicies which claim that natural evils are necessarily to achieve the greater good.  Suffering builds character!  (Except when it kills you, then it builds character among your relatives.)

For some reason, theodicy makes me think of classic Calvin and Hobbes

Or, if it's not character building, perhaps the lesser evil prevents some other greater evil.  Like the story about the guy who breaks his leg, and thus avoids a car accident.  God couldn't think of another way, that's not in his omnibenevolent nature.

I see this explanation as rather awful, and not just in the lacking-evidence sense.  It's also awful because now we're all supposed to see the silver lining in our suffering.  Our suffering is for a greater good!  Screw that.  It seems to me that evil comes about by completely natural means, irrespective of what ultimate good will come it.  People with terminal illnesses aren't all dying for the greater good, and it's awful to suggest that they are, or that this is how it should be.

Other theodicies off the top of my head include: "Good cannot exist without evil, just as black and white cannot exist without each other," and, "All wrongs are righted in the afterlife."  I've decided to cut this post short, so I leave it to the reader to decide if there is anything evil about these theodicies.  Are they denying some particular kind of evil?  Are they being callous to people in suffering?  Or perhaps they are not evil arguments at all, just uncompelling?