Trapped in a Drive Thru

The concert was great.

In case you're in need of an Al fix, here's the video of Trapped in a Drive Thru which is, of course, the parody of R. Kelly's Trapped in a Closet.

Kung-Fooie

A Shaolin temple, in China, is demanding an apology from an internet user who claimed that they were all once beaten by a ninja.

Correct me if I'm wrong, but isn't this the sort of thing that's usually settled with by an elaborately choreographed martial arts showdown?

Son of Al

I'm going to see "Weird" Al Yankovich tonight at the Coor's Amphitheater. In honor of the occasion, here's an animated interview that he did for Doogtoons where he explains how popular it was to be a Spelling Bee Winning / Accordion-playing prodigy.

Geek Pride

If you are a male geek, you probably know how disheartening it is to see that a lot of women prefer guys who are a bit more "conventionally cool". If so, here's an essay by a happy woman who urges her sisters to take a second look at us.

Among other things, she notes that we don't tend to hang out in bars, we're very good at remembering important dates and, lest we seem less than perfectly exciting, we're also very good at sex.

Of course, this does leave the question of how to spread the word. Somehow, I don't think that the internet is going to be the best way to get the word out.

Unstructured Snark

Sometimes the best reply to ugliness is mockery.

Recently Tucker Carlson stated that he and a friend beat up a gay may who was "bothering him" in a bathroom stall -- a admission that was, astonishingly, met with laughter by his television colleagues. One can imagine the sort of outrage that would have been generated if he had said that he had beaten up a black guy or a Jew that had been "bothering" him.

Be that as it may, for all the justifiably angry responses that this has generated, my favorite is a witheringly snarky comment from a Fark forum:

"I can just picture him now, delivering an adorable flurry of overhand punches with his thumbs inside his fists."

---

Update: Carlson has offered a clarification of the incident. He now states that it was an attempted sexual assault and that he and his friend did not attack the man in question but merely held him down until police arrived.

Frankly, the change of story seems a bit odd to me. Why would you initially describe a sexual assault as being "bothered"? This is especially puzzling given that the context of the original anecdote was with respect to Senator Larry Craig's alleged bathroom exploits. It's particularly odd the the story was originally told in a way to evoke laughter. If I had suffered an attempted sexual assault when I was younger, I don't think I'd be playing it up for laughs on national television.

It may be that Carlson did, in fact, misspeak (and, in all fairness, he does seem support such things as gay marriage) but I can't help but to feel like his clarification has the whiff of revisionism.

Lost Cities

The Greeks were astute when they made Cronus, who is Time, a devourer of his own children. Time is, indeed, the Great Devourer and though we may stand in the moment and look upon our monuments thinking that these are proof against the corrosive winds of change, in the fullness of time they, too, shall erode and fade away.

Troy, Abu Simbel, Machu Picchu, Mycenae... all of these places were once great cities. All that remains of them now are ruins and remnants to remind us that there was once a people there who were prosperous and who, like us, could not imagine a time that would not contain them.

Gaze upon this collection of dead cities and ponder that there shall be a time when London, New York, Bejing, and San Francisco shall, too, be nothing more than a faded memory.

Unstructured Ettiquette

Once upon a time, when I was working at mail order company, my brain stumbled between the phrases "Hello, may I help you" and "Hello, may I put you on hold". What actually came out of my mouth was, "Hello, may I hold you?"

Oh, we all know how to say please and thank you and we may even know which side of the plate the knife and the fork go on, but does anyone ever offer any practical ettiquette advice for dealing with the truly awkward situations that life often finds us in? Well, fear not, The Awkwardness Survival Guide is on the case!

The guide offers advice ranging from the embarrassment of using an inappropriate term of endearment with your mother to how to handle your bewilderment when confronted with an ethnic handshake.

Take heart, fellow traveler; help is but a mouse-click away.

Superthunderstingcar Go!

If you ever watched the weird puppet series "Thunderbirds" as a kid, you'll totally appreciate this Peter Cook send up of them.

Unfortunate Proximity

Location, location, location!

On Archetypes

I hope that you have been enjoying my series of articles exploring various archetypes. I think that, for the time being at least, I’m going to take a break from the topic (although I would still welcome reader submissions), but I did want to take a moment to talk a bit about the overall topic.

The first thing that I should point out is that I’ve been telling you a lie. By expressing archetypes as a series of factual statements I have implied that a given archetype is something definite and definitive. Worse, I’ve suggested that some characters fit neatly into given archetypes (“He is Jimmy Olsen. He is Bonzo. He is Captain Crunch.”) I have compounded my sin by implying that characters can be an exact representation of an archetype.

In my defense, I have done this precisely because, too often, archetypes are described in such fuzzy terms that I think that they start to lose all meaning. Consider Carol Pearson’s set of twelve heroic archetypes (which includes Innocent, Orphan, Warrior, Destroyer, etc). Her descriptions of these archetypes are, in my opinion, perilously vague. What does it really say about the Orphan to say that his quest is “To regain safety”? I would guess that King Arthur would be an Orphan, but I can’t think of anything about his story that would suggest regaining safety. If it were just Arthur I wouldn’t complain but the same holds true of most orphaned heroes. To be sure, you can force a given hero into the mold (“By fighting crime, Batman's trying to regain the safety of his childhood…”), but such efforts smack of narrative contortionism.

My goal in expressing these archetypes in definitive terms has been to indicate that there is a there over there; that archetypes have a reality and that a given archetype means something, even if the precise meaning is open to interpretation and disputation.

The way that I think of archetypes is to imagine a map of characters. The archetypes would be represented as hills on the topology of the map. Depending on the popularity of the archetype, some hills with be taller – mountains in the terrain – and some of those mountains will have hills of their own or will themselves be part of a range of hills and mountains (the Hero would be such a range). Finding the precise summit of a given hill is difficult, however, because the terrain is complex, with many rills and rifts on every surface.

Because of this, no particular hero is going to be at the summit of his local archetype. Indeed, many heroes will find themselves in the valleys between peaks. Roland the Gunslinger is capable of facing any circumstance and is the master of himself and his surroundings, therefore he’s a Competent Man, but he’s also on a lifelong quest to find the Dark Tower and he’s the social equivalent of a knight in the terms of his own society so he’s also a Paladin. I believe that Roland’s camp is on the side of the valley facing the peak of the Competent Man but others might well disagree.

Characters also evolve. King Arthur starts his life as a Special Boy, but the boy who pulls the Sword from the Stone is not the same person as the man whose body is borne away to Avalon. The trajectory of a character through the archetypal map is every bit as significant as their location on that map at any given point in time. Guinevere’s life progresses from maiden to first love, to wife, to damsel in distress, to adulteress, to penitent. To fit her into a single slot would be to fail to appreciate the tragedy of her story. And even this isn’t a sufficient view. Does knowing that Luke Skywalker takes a hero's journey from orphan to knight tell you everything you know about his character? Of course not. A successful character is more than a few pounds of putty thrown over the scaffolding of his archetype.

I do not, however, want to suggest that archetypes are unimportant. They are a kind of narrative shortcut. When we see a James Bond movie, we can support Bond because we know that he’s the hero. The reason that we can believe that he’s the hero is because we subconsciously recognize that he has characteristics that we associate with the heroic archetype. Imagine what it would be like if every time you read a story you had to puzzle out the nature of every character from scratch. To be sure, a little narrative ambiguity (is this person really a hero?) can be a good thing, but even narrative ambiguity partakes of the short-hand of archetypes by presenting us with conflicting cues. This is also true of stories that subvert the archetype. Such stories rely on our recognition of archetypes to surprise us (“Oh my, it looks like the Sidekick is actually the Hero!”).

Without archetypes, narrative becomes impenetrable, as amply demonstrated by postmodern fiction that seems designed as nothing more than a sadistic effort to frustrate and piss off the reader. Never the less, reliance of archetypes can distort our perception of reality. Historical narratives are particularly vulnerable to false archetypal associations.

For years we thought of Christopher Columbus as the Great Explorer. Later, after the political climate changed, he was recast into the role of the Oppressor. The real person, however, is neither. He was a complex human being who was, by turns, heroic, mercenary, visionary, short sighted, oppressive, brave, and many other things besides, nor is it possible to understand Columbus without understand his world and culture. As it has been said, we are complex and contradictory creatures. When we tell ourselves our history, we should be aware that we want to simplify it; we want the narrative to conform to archetypal stereotypes and our desire for such a narrative will cause us to warp the narrative into a story.

Jung was convinced that archetypes were fundamental clues to the mystery of what is Man. While I have deep reservations about Jung’s psychological theories, to say nothing of his archetypal schema, I suspect that he was not that far off the mark with his intuition: archetypes do say something about us. I think that they may well be mile markers on the road to understanding our human nature.

We are man. We are woman. We are Humanity.

Unstructured Archetype: The Great Old One

He is Cthulhu. He is Vulthoom. He is Q'yth-az. He is Hastur, He Who
Must Not Be Named.....

Oh no!

AAAAAAAAAAAAARGHHHHHHH!!!

---

This post was contributed by Arturo Magidin who is enjoying a very restful stay at Arkham asylum.

Unstructured Lunar Eclipse

If you're willing to stay up late, and you're at a good longitude, you can see a lunar eclipse tonight. Details here.

Still no word on the next time there's going to be a total eclipse of the heart.

Unstructured Archetypes: The Thug

He is the bankrobber. He is the minion. He is the kidnapper. He is the extortionist

The Thug is a man.

Although the Thug shares much of the demeanor of the Brute, he is fundamentally human.

The Thug has a soul, albeit a small one. This means that the Thug can be redeemed, but it is unlikely.

The Thug is not a threat to the Hero. Quite the contrary.

His purpose is demonstrate the prowess of the Hero. He is a paper tiger and a punching bag.

He is nameless. He may be called Bruno, or Boris, or what have you, but these are only labels. In truth, he is a slate.

He is stupid, but he is aware of his stupidity.

He admires the intelligence of the Boss. He despises the intelligence of everyone else.

The Thug wants sex but cannot easily find it. Woman are repelled by him. His only option is force or prostitution. He is a lousy lover.

His moral universe is divided between the weak and the strong. He bullies the weak and cowers before the strong.

He has no history. He was not born, nor does he have a family. When he is killed, he will be unmourned.

He is vicious but not Evil. He lacks the intelligence to be Evil. He is, however, drawn to Evil as a moth to a flame.

He is a willing thrall. A slave. He freely subordinates his will to that of the Boss.

He has a dim but determined sense of loyalty. It is a loyalty predicated on fear and worship.

The Thug has no taste. He wears cheap suits, he smokes cheap cigars and he drinks cheap beer. To the extent that he has any relationship with women, they too are cheap.

If he wasn’t a bully, he would be pitied. On a deep level, he knows this. That is why he bullies.

The Thug has no God except for the Boss. The Boss is a wrathful God.

Ahhh-Ahhhh-Ahhhhh-Aaaaaah!

There is one and only one way to improve on The Most Kick Ass Song, Ever, and that is to have it sung by Viking kittens.

(Click here for a higher quality version)

Camelot Meets Star Trek

"It's a silly place."

Unstructured Archetypes: The Brute

He is the Cyclops. He is the Cave Troll. He is the Ogre.

He is male. He is, in fact, an exaggeration of masculinity.

The Brute is stupid. He is also evil. He is evil because he is stupid.

He embodies the Id. He destroys everything that he touches and revels in the destruction.

He is and agent of entropy.

There are only three things that he enjoys: eating, fucking and killing. If these can be combined, all the better.

He likes to fuck. He never asks permission to fuck. He does not perceive that this is rape, however, because there is no psychology to the act. He simply assumes that all women (and men) scream when they are being fucked.

The Brute is soulless. He did not sell his soul; he never had one to start.

He does not understand empathy or love. He doesn’t understand anything at all, really, except the aforementioned eating, fucking and killing.

Children are to be seen as appetizers.

The Brute is a monster but not a villain. He does not desire power or wealth. He is what he is.

The Brute may be employed by a villain. If this is so, the Brute neither understands nor cares to understand their relation. He will obey the villain only because the villain can hurt him.

The Brute can only be killed by a Hero or a heroic Sidekick. Anyone else who opposes the Brute will be killed, eaten and, perhaps, fucked.

He is too stupid to know that he is stupid. The Hero will usually exploit this.

The Brute is godless. The idea of God is beyond him.

Unstructured Red Riding Hood

A friend of mine and his wife are leaving for Japan for two weeks so, in his honor, I present to you this rather odd Japanese commercial featuring a singing Red Riding Hood and her animal friends (including one rather special fellow).

As near as I can tell, it's a commercial for an architectural firm. Go figure.

Unstructured Archetypes: The Warlock/The Witch

He is Sauron. She is the Baba Yaga. He is Voldemort. She is the Wicked Witch of the West.

He is a man. She is a woman. Neither is truly human.

They have vast power but their power is illegitimate and unholy. It was bought at the price of their soul.

They know things that Man Was not Meant to Know. This knowledge has corroded any remnants that have remained of their souls.

He is not to be confused with The Wizard who is a Mentor who knows magic.

If she is a woman, she is either a hag or inhumanely beautiful. If she is beautiful, she is only beautiful by virtue of her magic. She is, in truth, a hag.

He is old. If he appears to be young it is because he has used magic to preserve himself. Once the spell is broken he will be proven to be old and withered.

They are asexual. The only sexual acts that they will ever engage in will be as part of a dark rite. Any such acts will be perverse, shocking and blasphemous.

They have sold their souls to dark forces. They are damned and beyond any hope of redemption.

Although they have vast power, they will always crave more power, especially over others. This is the instrument of their downfall.

They believe in Good but they hate it. They hate it will a personal passion. Their choice to be Evil is deliberate and fulfilling.

They are sadistic. It is not sufficient to kill one’s enemies; they must be made to suffer.

They are Satanists. Even if they don’t worship Satan, himself, they worship Evil, which is the same thing.

The Down

They took me down
To the Down

Where the river runs slow
and sour

Where reptile things,
Cold, slow and hidden,
Lurk in the thick of the mud

Where lost things go
To never be found

And they gave me an understanding

They could sink me down,
And whoever would miss me?

So I said what I said
To get out and away from there
And you know what I told them

I'm sorry, so sorry
That it had to be done

Now they're here for you
To take you to the Down
And it won't matter what I say
But I'll ask you anyway

When you're there
With all the lost and rotting things,

Would you say hello to my soul?

---

Photo courtesy of James Good

Hello Kitty, Hello Shame

Thai police departments have been having a problem with officers violating minor rules such as littering and parking in prohibited areas. The departments have been reluctant to fire the officers but efforts to discipline them have proven ineffective.

In the face of this, they've decided to attack the machismo of the officers by forcing them to wear Hello Kitty armbands as a mark of disciplinary shame. I have no idea if this will work about one only needs to ask dread Cthulhu about the power of the kitty.

Unstructured Awwwwww!

Warning: cute bomb!

Unstructured Archetypes: The Companions

They are the Argonauts. They are the Merry Men. They are the 300. They are Odysseus’ Men.

They are men. Manly men! Women can not be Companions. Don’t be silly.

They may be Heroes in their own right but the Hero will be first among equals. This is his story, after all.

They are there to help the Hero on his Journey which may or may not be a Quest.

They are manly but not gay. There is no hanky panky in the camp.

They are dedicated and loyal. They will see the Hero through to the end and follow him into the Gates of Hell if necessary.

They aren’t wimps. Grrr!

They are vulnerable. They can be killed. However, unless they are killed by a betrayal, they will not be avenged. They will, however, be mourned.

They may have Sidekicks. Their sidekicks will almost certainly die before the Journey is over.

They know how to party but they also know when to Get Down to Business.

They aren’t always the brightest bulbs in the bunch. Lucky the Hero is around.

Sometimes they will have a False Companion in their midst who will betray them. The False Companion will die as a direct consequence of his Betrayal.

They probably believe in God but who cares? There’s manly stuff to be done!

Unstructured Oscillations

If you've ever played with an oscilloscope (and who hasn't!?), you'll love this marvelous applet that lets you simulate standing waves. The applet is part of the larger set of math and physics applets at Falstad.com.

I do believe that I have attained Nerdvana.

Fight, fight!

It would seem that little stick dudes fighting is now, officially, a genre.

Unstructured Archetypes: The Bad Mother

She is Cinderella's Step-Mother. She is the Wicked Queen.

She is a woman, but she has no womanly virtues.

She is evil. Worse, she is wicked.

She is a usurper. She steps into the place of the Good Mother, after the Good Mother dies, but she can not replace her.

She rarely has a name, only a title.

She is hateful.

She is jealous of the Good Mother’s child.

She is a witch and a bitch.

It is to be assumed that she is a slut and a whore, although we never catch her in the act.

She is a deceiver.

She wants to deprive the True Children of the Good Mother of their rightful place in the world. She wants to see them humiliated and killed.

She must be killed but only after she is humiliated.

She is dangerous and powerful.

She is an atheist and probably a Satanist.

Unstructured Meeeeeow

For you viewing pleasure, here are some hot, fantasy babes.

Unstructured Archetypes: The Lolcat

It is a hungry gray cat. It is a white owl. It is a voyeuristic tabby. It is a bereaved walrus.

The Lolcat is usually a cat, but not always. It may also be a dog, a furry rodent, or an aquatic mammal. Any cute mammal may be a Lolcat.

Owls may also be Lolcats. They were grandfathered in because an owl
was instrumental in starting the Lolcat craze.

The Lolcat is social. It always greets you with a friendly "Oh hai!"

The Lolcat is polite. It always says "Plz", "KThx", and "Scuze Meh".

The Lolcat likes to help you. It may clean your dishes, fix your pillow, buff your floors, even repair your computer. You may decide that its help is more trouble than it's worth.

The Lolcat has a Flavor. The Lolcat also knows that you has a Flavor, and seeks to taste it.

The Lolcat has no respect for personal boundaries. It will often get In Ur Property. Then it will start Doin Thingz to it.

The Lolcat may has a Title which relates to its appearance, disposition, or occupation.

The Lolcat can see Invisible objects and will often make use of them.

If a Lolcat is a cat, it has a Quest to find Cheezburgers. If a Lolcat is an aquatic mammal of any kind, it has a Quest to recover its Stolen Bucket. No other type of Lolcat has a Quest.

The Lolcat has Idiosyncratic Conjugation.

The Lolcat's favorite day is Caturday.

Beware a staring Lolcat. Its stare is a warning that It Is Not Amused. If you anger a Lolcat, you will soon need medical "Halp".

---

This article was contributed by Rob Berry. Rob is a programmer who lives in Hilliard, Ohio with his wife and three sons. He epitomizes the archetype of The Geek.

Stardust

I may give a more detailed review later on but, in the meanwhile, I want to encourage everyone to consider seeing the movie Stardust.

The trailers and commercials for the movie are, frankly, horrible. It doesn't seem like the people who are marketing it quite know how to handle what they have and the result is that they give the impression of something that's cheap and cheesy.

The actual movie isn't perfect (it takes about half an hour to really find its pace) but it is, in my opinion, a very enjoyable and often humorous fairytale (suitable for adults and children) with the sort of stylistic flourishes that one expects from Neil Gaiman.

Unstructured Aurora Borealis

This gorgeous photograph of the aurora borealis was taken from low Earth orbit. Click on the picture for a much larger version.

Unstructured Archetypes: The Good Mother

She is Gertrude. She is Mary. He is Geppetto.

She is usually a woman but can occasionally be a man if he embraces feminine virtues.

She is the true mother. The Bad Mother may have usurped her, but she can not replace her.

She is nurturing and loving. She is not remote. This is her virtue but it is also her weakness.

She is to be protected by the Good Son.

She is to be despised and hated by the Bad Son.

She is the One True Love of The Father. It is never the Other One True Love of his.

She has no Legacy or Treasure to bequeath. She can only offer comfort and love. She may, however, pass only a bequeathment from The Father if he is absent.

When she is killed she is to be mourned and then avenged.

It is to be understood that she does not have sex with The Father. She is fundamentally chaste. This is a paradox and, yet, never the less true.

She is often a widow. If she is, she will remain faithful to The Father unless she is Seduced and Deceived.

If she is Seduced and Deceived, she will die, but not before she repents of her seduction and is forgiven because she is, of course, weak.

She is kind and charitable. This is part of her virtue but, again, also part of her weakness.

She wants to protect her children even though the Good Son needs to Go Out Into the World.

The Good Son has her love but can earn more by making her proud of him.

She is ageless but not old.

She is beautiful.

She believes in God. Her god is The Father.

Unstructured Levitation

In spite of the fact that the narrator sounds like he's been hitting the valium, this is an extremely cool demonstration of superconductive levitation.

Of Batarangs and Bottles

Many people consider it a social faux pas to bore your friends with stories about your dreams. I'm not sure I quite agree with that but I do agree that dreams have a way of seeming a lot more cool to the person who dreamed them than to the audience to whom they are being conveyed.

With that said, a segment of a dream I had last night just seems so darned cool that I feel compelled to share it, so brace yourself.

The background isn't really important. Basically, some unnamed female superheroine with a gun shtick has approached Batman for help. For reasons that weren't entirely clear to me, she needed to infiltrate a circus and she needed Batman's help with an act (which, apparently, they could do in costume... don't ask me why; this isn't the cool part).

So they come up with a kind of trapeze act where they're swinging around while trying to break bottles set up on a platform. First she shoots a few while tumbling through mid-air and then he breaks a few with his batarang until finally there's just a few bottles left.

Finally, he releases her into the air, throws his batarang, which hits and breaks two out of three of the bottles before curving back towards Batman. While the batarang and our heroine are both in flight she throws her gun into the air, the batarang connects with the gun, pulls the trigger and shoots the final bottle, all to immense applause.

Now tell me that wouldn't make an awesome comic-book movie moment!

Unstructured Archetypes: The Scientist

He is Victor Frankenstein. He is Henry Jekyll. He is Edward Mobius.

The Scientist is usually male, though the Scientist can be female.

In the Scientist's own eyes, his work is always for the Greater Good. He believes himself selfless. He is arrogant, though he clothes himself in modesty.

He secretly relishes the fame his success will bring him. He honestly believes he is in fact The Hero. Yet he loudly proclaims his own humbleness.

The Scientist is not crazy or power hungry. His Quest is not for domination. His Quest is not for power or riches. He is not a Mad Scientist, nor is he an Evil Genius.

The Scientist is not good; the scientist is not evil. The Scientist is focused on achieving his goal and success and nothing else.

Obstacles to his goal will be swept aside by his brilliance. Side-effects are unlikely or impossible.

The Scientist never achieves his goal. The Scientist always succumbs to his Great Mistake.

In the instant of his Great Mistake, the Scientist realizes nobody should pry so deeply into the Great Mysteries.

Though the Scientist is not evil, his Great Mistake creates Evil.

The Scientist is all the reasons we should remain ignorant for Our Own Good.

The Scientist is always ultimately destroyed by his Great Mistake.

He finds atonement only through self-sacrifice, helping The Hero stop the Mistake.

The Scientist is functionally celibate; he is not a family man, even when he has a family.

The Scientist is often the father of the Hero's One True Love.

The Scientist does not worship God. God is either superstition, or the Ultimate Mystery; in neither case does God deserve the Scientist's worship.

At the instant of his Great Mistake, the Scientist realizes God has always been there and that the Great Mistake is attempting to usurp God.

---

This post has been contributed by Arturo Magidin. Arturo is a mathematician living in Louisiana. If there were such an archetype, he would be The Reader.

Unstructured Archetypes: The Father

He is Oberon of Amber. He is Abraham. He is Odin.

The Father is always a man. This may seem obvious, but it is not.

The Father is distant. The Father loves his children, but he is not close to them.

The Father children can be Heroes or Villains. When they are Villains they betray him and may murder him. When they are Heroes, they serve him and avenge him if he dies.

The Father is wise, powerful and frightening.

If the Father dies, he lives on in memory.

The Father does not intervene in the affairs of his children other than to express pride or disappointment.

The Father may bequeath a Treasure to a deserving son. That treasure may take the form of a Legacy.

All legitimacy flows from the Father.

The Father must not be questioned. To question the Father is to betray him.

The Father is not weak. If a father is weak, he is merely a parent.

It is possible for a Father to be fallible, but it is improper for a Son to point out his Father’s failings.

The Father is old. He is as old as time.

A Good Son will love his Father. Only Good Sons can become Heroes. Bad Sons who do not love their Father are doomed to become Villains.

A Father only has one Good Son. He may have any number of Bad Sons.

He may have daughters, but they are largely irrelevant except as items that his Good Son must protect.

The Fathers only overt expression of love is in the form of pride for his sons, which is reserved for those times when they have performed heroically and virtuously.

The Father does not believe in God. The Father is God.

Unstructured Mural

What you see here is a small segment of a much larger digital mural entitled Universe. It is well worth your while to see the entire picture.

Comment Verification

Well, it took a long time to happen but it seems that I'm finally starting to get hit with comment spam, so I've decided to turn on word verification for comments. You've probably already seen this "feature" on other blogs and forums; basically you need to prove that you are a live human being by copying a set of distorted letters whenever you post a comment.

For the record, I was hoping to avoid this. This blog is small enough that I didn't expect that I would be much of a target for spamming and I also consider word verification to be a bloody nuisance.

Please accept my apologies for the inconvenience. I do like the comments I get and I hope that this won't turn you off from making them.

Sparta!

I know that 300 jokes are starting to go a bit stale but I thought that this one was rather clever.

Why Are the Weasleys Poor?

Now that I've finished the Harry Potter series (and liked it very much, thank you), I've been stumbling around looking for reviews and commentary. I think the most thought provoking was a rather snippy piece written by Megan McArdle, an economist who complains that the economy of the wizardly world just doesn't make any sense. For instance she asks

Why are the Weasleys poor? Why would any wizard be? Anything they need, except scarce magical objects, can be obtained by ordering a house elf to do it, or casting a spell, or, in a pinch, making objects like dinner, or a house, assemble themselves. Yet the Weasleys are poor not just by wizard standards, but by ours: they lack things like new clothes and textbooks that should be easily obtainable with a few magic words. Why?

While I have no doubt that a sufficiently motivated Potter fan could come up with a plausible theory of wizardly economics, I'm sure that the real answer is that Rowlings never really put much thought into it.¹ Indeed, I think that many high fantasy works are going to suffer the sin of having unrealistic economies. Be that as it may, I thought it might be fun to briefly consider the economies of few fantasy worlds to see if we can answer of the question of the Weasleys poverty in their contexts and to address the question of how we can have a system of economics in a fantasy setting that allows for the existence of a family such as the Weasleys.

Middle Earth
J.R.R. Tolkien's high fantasy opus, set in the world of Middle Earth, has a very simple interaction between magic and the economy of his world: there really isn't any. Magic is utterly scare. There are only a handful of beings (none of them truly human) who can work magic and what magical artifacts exist, such as Sting and The One Ring, are quite utterly and literally priceless. As such, the basic feudal economy of his world isn't particularly impacted by the existence of magic since the majority of people will never encounter it.²

In Middle-Earth the Weasleys are probably poor for the simple fact that they are peasants. They don't have any magical ability and neither do they have any access to magical artifacts. If one of them stumbles across an artifact, it's unlikely that he'd be able to sell it for a fair price (assuming he'd want to part with it in the first place) since only a king could afford it -- and a king might well simply take it.

Ethshar
Lawrence Watt-Evan's Ethshar novels are set in a high-magic world which takes its inspiration from fantasy roleplaying. In the Ethshar universe there are a multitude of distinct magic styles ranging from Wizardry as the most powerful sort all the way down to such minor crafts as rhythmic dancing and Science (yes, Science).

Each type of magic has advantages and limitations. By way of example Wizardry is extraordinarily powerful and can do nearly anything that can be done with the other forms of magic, but it is also dangerous, complex, and often expensive. Warlockry, to offer a counterexample, is simple and powerful, albeit limited to telekinetic effects, but it has the drawback that warlocks are eventually compelled to fly off to a mysterious location in the north where they are never heard from again thus making warlocks reluctant to overuse their power.

Depending on the type of magician, magic can be used to provide both goods and services. Because of the inherent risks and limitations, however, magical items and services tend to come with a premium costs which allows for competition by tradesmen and craftsman who can provide lower quality goods and services at a far more reasonable price.

Magic is strictly segregated into guilds. Practicing magic outside of a guild is a capital offense (to say nothing of being nearly impossible to manage without the necessary training or induction) which prevents magicians from proliferating to the point where anyone can practice it (which would undercut the demand for magical goods and services). More over, the quality of training one receives is directly correlated to the quality of the master that one apprentices under. An apprentice wizard will only have access to his master's list of spells, for example. If his master only has a dozen spells, the demand for the apprentice's services will be limited once he becomes a master in his own right (although he can attempt to swap spells with other wizards in an effort to expand his catalog). His repertoire will also be limited by his innate talent -- it doesn't do you much good to know a high level spell if you can't safely cast it.

Finally, the Wizard guild deliberately limits the influence of magic in the world. Mages are, for instance, prohibited from holding political office. Any magician, or group of magicians, who attempts to usurp too much power or authority is destroyed. The gods of the world also set certain basic limits on how much influence magic users can have over the world and its economies.

In Ethshar, the Weasleys may be poor because they don't practice magic. It is also possible that they are poor because the style of magic that they practice isn't in high demand. Finally it is possible that they are magicians but that they simply aren't very talented at what they do and, thus, can't command a lucrative price for their goods or their services.

Dragaera
Steven Brust's Dragaera cycle is set in a world with two major sentient races: Dragaerans and Easterners (both of whom consider themselves "human", although the Easterners are much closer to our world's description of humanity). There are also two major styles of magic which are largely divided along species lines.

Easterners (and a handful of Dragaerans) practice something called "witchcraft". Witchcraft utilizes the psychic energy of the practitioner and requires complex rituals. Because it utilizes the energy of the practitioner, spells tend to be fairly subtle in effect. Becoming a witch takes long years of apprenticeship and requires the acquisition of a familiar (with whom the witch has a psychic link). As a consequence of this, demand for witchcraft is limited to specialized requests.

Dragaerans (and a handful of Easterners) practice something called "sorcery". Sorcery takes the form of magical power collected in an artifact called the Imperial Orb. A practitioner will basically grab a portion of the communal energy and shape it. The shaping of the energy can take numerous forms such as teleportation, healing (even to the point of reviving the dead), and various physical manipulations.

All Dragaeran citizens have a link to the orb that allows them to do this but the ability to shape the energy is based on skill. Some "spells" are so basic as to be effectively ubiquitous (such as teleportation) while others require decades or even centuries of study (Dragaerans have very long lifespans).³ Those who dedicate themselves to spellcraft can earn the distinction of being considered to be Wizards.

Sorcery is not typically used to produce artifacts (although there are a few exceptions). Consequently, the main impact that sorcery has in the world is in the form of services rather than goods. In those cases where a spell is common, such as teleportation or telepathy, the effect is to displace the mundane competition: there are no taxis in Dragaera. In the cases where a spell requires specialized training, there may be competition depending on the relative costs.⁴

In addition to the two major types of magic there is a type of magic that utilizes the direct manipulation of chaos. This form of magic is extremely powerful but also dangerous and, thus, forbidden. Because of the degree of training required to master it and because of its illegality and rarity, it doesn't have any apparent impact on the Dragaeran economy (although one can theorized that there might be sufficient demand to allow for the creation of a small black market).

Finally, a species known as the Serioli are known to produce a sort of magical weapon called a Morganti blade. Morganti blades are semi-sentient weapons that have the capacity to destroy souls. Given that reincarnation is known to be real beyond a shadow of a doubt, the possession and use of Morganti weaponry is forbidden on pain of death. There is, however, a definite black market for the weapons albeit not one that directly competes with the legitimate weapon's market.

In Draegara the Weasley's may be poor because they are Easterners and don't have access to sorcery putting them at a competitive disadvantage with Dragaerans. They may not even be witches but, if they are, the demand for their talents is probably not enough to offset their expenses.

Conversely, if the Weasley's can use sorcery, their poverty may be accounted for by the fact that the only spells they know are so common as to be worthless meaning that they can afford neither luxury goods nor those services that are beyond their personal level of training. They probably have a higher standard of living than their Easterner neighbors but they aren't living high on the hog.

It is possible that the Weasleys could supplement their income if they could learn chaos magic or if they were willing to deal with black market Morganti weapons. The former would be dangerous, illegal and require specialized knowledge that would be difficult to acquire and the latter would be a high-risk/high-reward occupation that would require them to become part of the criminal underground.

The Land of Oz
The Land of Oz represents a high magic world. Magic creatures and artifacts are utterly common but magical power is tightly concentrated in the hands of a few individuals (e.g., the cardinal witches).

Although L. Frank Baum didn't elaborate on the economics of Oz (unless there were some oblique references to the Gold Standard), we can deduce that the ubiquity of magical goods would hamper competition from mundane goods, however, magical services would be neigh well impossible to obtain.

In this case, the Weasleys are poor because they aren't part of the select circle of magic practioners and are limited to making their living either trading in magical artifacts (which are so common as to have low value) or by providing non-magical services to their neighbors. If one of the Weasleys did, however, learn magic he would, in all probability, be able to live like a king.

Xanth
Finally we have Xanth. In the world of Xanth, magic is even more ubiquitous than in Oz and everyone, furthermore, is a magic users. However, every magic user is unique, usually limited to a single effect (which might be called a spell). Some people are gifted with very powerful magics, such as the ability to transform people into animals, while others are limited to minor effects such as being able to make a spot of color appear on a wall and some people have talents that are more approximately resemble curses.

Because every birth introduces new and potentially disruptive magics into the world, it would follow that the economy of Xanth would be subject to constant perturbation. We could, for instance, imagine someone being born with the ability to duplicate any item thus automatically devaluing any goods that he has access to, including whatever might be used as currency. In addition to the economic disruptions, the rise of new talents can be socially destabilizing. Xanth has a history of wars where powerful magicians have taken on (and occasionally overthrown) the established order.

In Xanth, the Weasleys may be poor because they have fairly worthless talents. They might also be poor because the local economy has collapsed due to the influence of a person with an economically disruptive talent. It may also be the case that the Weasleys are having the misfortune of living through a time of war and chaos.

Conclusion
If one postulates the existence of magic, one needs to be aware that such an existence would have an impact on the economy of the world it exists in. If magic is common, easy to master, and sufficiently powerful, we encounter the paradox of the Weasleys.

In order to avoid the paradox is seems that that there are a number of options:

• Magic is so rare that the average person has no access to it
• It is dangerous to use
• It is expensive to use
  
• There are practical limitations to its use
  
• There are legal or social restrictions on the use of magic
• There are limitations to its power
• It requires intensive skill and training to use

There is at least one other option of course and that is to play it straight. Posit a world where magic is ubiquitous, easy to use and powerful. A world where anyone can conjure up whatever they desired and where anyone could deploy vast amounts of power at will.

Such a world would not have Weasleys in it; however, it does not follow that everyone would be happy and prosperous, either. It is, in fact, difficult to imagine what a world would be like. I doubt that one would have anything analogous to our own social instutitions. I suspect that the world would, in fact, be a vast and dangerous anarchy. A Hobbsian nightmare magnified and made surreal.

I don't think that that story has been written but I think that I would love to read it.

---

¹ I have a similar complaint about the game of Quidditch. The fact that snagging the Golden Snitch is worth a whopping hundred points would seem to make the rest of the game an exercise in pointlessness in the vast majority of cases.

² There's a certain irony to the fact that Lord of the Rings was a major source of inspiration for Dungeons and Dragons given that the D&D world is so thoroughly saturated with magic that all but the very rarest of items sell for less than the equivalent price of a cheap gas grill (factoring in the massive devaluation of gold and other coins).

³ My favorite manifestation of the Orb's power is that it acts as a clock. Anyone with a link to the Orb can easily tell what time it is. I'm a bit disappointed that the Orb can not, however, be used for voicemail.

⁴ One might draw a parallel to IT professionals in our world. Anyone could, theoretically, program an application but relatively few people have the knowledge. This disparity of knowledge gives IT professionals the ability to market their talents, often for a very good price.

Unstructured Archetypes: The Lovers

They are Romeo and Juliet. They are Antony and Cleopatra. They are Jack and Rose.

They are of both genders, but never of the same gender.

They can be both Hero and Victim.

The Lover’s story is tragic and romantic.

The Lovers are defined by their Beloveds.

Every lover is a Beloved.

The Beloved is similar to but distinct from the One True Love of the Heroic cycle.

The Lovers are both driven by and at the mercy of Fate.

Their moral universe is divided between their Beloved and all that stands between them and their Beloved.

Their love is pure and virtuous. There is a sexual component to the love but only in as much as it is an expression of love. Be that as it may, the erotic aspect can be charged and may take many forms.

The lovers will often die before they can consummate their love for one another.

They are young, naïve and optimistic.

Their love always takes the form of love at first sight.

If there is a Villain, the Villain’s goal is to keep the Lovers separate and to destroy their love. If there is no Villain, Fate will play this role.

A lover will either die in the arms of his beloved or at her side.

In the cases where one lover survives, it shall be the woman.

The Lovers are more prone to think about Heaven than God.

Unstructured Dream

What you see here is a frame from a rather serene and meditative flash animation called Dream. Please enjoy.

The Eschatologist

This story is a "Best of the Blog" repeat.

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It's Monday. At precisely 7:16 in the morning, Eastern Daylight Time, the world ends. It does that a lot on Mondays.

It's a standard Christian apocalypse which means a long morning for me. It used to be that these things would just be a couple of days of plague, famine, et al, followed by a nice, neat Heavenly ascension and Judgment — hallelujah! Ever since the fundies polluted the zeitgeist, they've invariably included a tedious thousand-year reign of the Antichrist in which every last little tidbit of biblical hallucigenia gets played out in endless, banal variety.

If there's one thing I can't stand, it's a drawn out eschatology. That's why I love the techno-nerds. When they end the world it's usually something like some rogue grey goo that escapes from a secret lab — there's always a secret lab — that eats the world in three days, or some super-virus that makes everyone puke their innards up in a week, or an accidental black hole that devours the planet before lunch.

At 10:28 its zombies. Fucking horror freaks.

At 1:10, 1:31 and 1:56 we get Hindu, Islamic and, so help me, Mayan endings. This is why I drink.

I get a nice break before there's a nuclear holocaust at sundown. I haven't seen one of those since 1998. I actually like the nuke scenarios, at least when they don't have any damned mutant cannibal hoards. Nuclear wars are all pretty fireworks followed by a pleasant nuclear winter as mankind's dominion over the world comes to an end. They're also easy to clean up

Elder Gods at eight, war against the machines at nine, everything's a dream and the Dreamer is now waking up at ten and, finally, aliens destroy the planet at a quarter to midnight.

---

I was twelve years old when I got my gnosis. It was May of 1958. Most of the apocalypses back then were of the nuclear variety but this time it was giant bugs. Of course I didn't know anything about the ways that the world ends, back then. I was twelve and, as far as I was concerned, everything was ending for the first time ever.

The bugs in question were locusts. It was a standard horror movie. They came out of the Alamogordo but, in no time flat, they were everywhere.

I was a smart kid, a nearly perfect stereotype of a 50's science geek. I even, swear to The Great Unknown, had a junior chemistry set, a backyard telescope and, yes, a slide rule and a pocket protector. I knew that the bugs just didn't make any sense. Giant bugs violate the laws of physics and biology. They should have collapsed under their own weight, exoskeletons cracking from the strain. They shouldn't have been able to breath. The sure as hell shouldn't have been able to fly.

I remember being trapped in school, looking out at the street where the locust were ripping open cars and tearing apart pedestrians, and it just didn't make any sense, so I stopped believing in it. That's when things got weird.

You ever have a dream and you wake up just enough to know that it's not making sense but not enough to realize that you're actually dreaming? It was like that. Time suddenly got jumpy as my mind tried to force what was happening into some kind of semi-sensible template. The bugs flickered and were replaced by insectile robots. Then they flickered back. Everything jerked and then I realized that the bugs were really aliens. Hugh saucers floated in the afternoon sky. Then the disks crashed to the ground and the bugs went back to being bugs. The world lurched and, instead of bugs, they were Commie tanks cleverly disguised as bugs. Then they went back to being bugs again.

I don't know how long this went on. Time didn't make sense. All I knew is that there was no well in hell that overgrown locusts were destroying the world and that I was not going to let that be the case. Eventually a hand clasped my shoulder and some guy I didn't know said, "Kid, what the hell do you think you're doing?"

I turned around. He was a tall, muscular guy with a weirdly feminine look, especially around his eyes.

I remember stammering that none of this made any sense. He smiled and told me that I had to relax and let it play itself out. He told me that I couldn't force it. I had no idea what "it" was supposed to be. He touched my forehead and everything went hazy.

---

Tuesday is a trifecta of ecological, economic and epistemological collapses, which is not a bad day as these things go.

---

I woke up in my own bed. I got up and ran to the living room in a panic. I remember my mom being very cross with me. She told me to march back into my bedroom and put some clothes on because, "We're not animals!"

I knew better than to ask about rampaging radioactive monstrosities. Clearly it had, after all, been a dream even though it seemed far too vivid to be one. It was Saturday (so what the hell happened to Friday?) and I desperately needed to clear out my head, so I told my folks that I was going to the park.

When I got there, I found myself lost in thought. I think that I'd finally managed to convince myself that I'd imagined everything when, off in the distance, an air raid siren went off.

"Don't panic."

There he was, again: the same big frame, the same feminine eyes. I don't mind telling you that he really creeped me out.

"Who are you," I demanded. "What's going on?"

He said that, from the sounds of it, we were about to experience a nuclear war. I could feel my legs going rubbery. Giant bugs, no way, but a nuclear war was something that I could, in fact, believe in. I wondered how soon it would be before the soviet bombers dropped their awful cargo on us.

"My name is Elaios," he told me, "I'm the archon of the North American continent. You can call me El."

I had no idea what he was talking about. All I knew was that I was about to die. It must have shown on my face.

"Look, kid, this isn't any more — or less — real that what happened yesterday. The world's about to end, but that's nothing to worry about. It does it all the time."

---

Wednesday is sci-fi day: comets, gamma ray bursts, a planet busting anti-matter explosion (from a secret lab), and the Borg.

---

The world has been coming to an end since the beginning. I'm told that, in the first fractions of a femtosecond after its creation, the universe collapsed back on itself, or expanded out into a thin haze of nothingness, more times that can be counted. Even when the expansion was just right there were other things that went wrong. Sometimes there was too much gravity and everything collapsed into black holes. Other times the strong force was a bit too weak and we ended up with a universe that only had hydrogen. Lots of things could, and did, go wrong. Apparently it took a fair amount of tuning just to get something stable enough to allow for the existence of people.

Once we were on the scene, things really got out of hand.

---

The world doesn't end on Thursday. The world never ends on Thursday. Don't ask me why. I'm just glad that I get a regular day off.

---

An A-bomb went off less than half a block away. I was instantly flashed into atoms as was "call me El". It's a painless way to die, which is another reason why I like nuclear wars.

I suppose that I should have been more surprised to still have any sense of awareness, but I assumed that I was a ghost and that I'd be going up to Heaven soon. I was, however, surprised at how solid I felt and at how solid Elaios looked. He knelt down to my eye level and asked me, "Do you wonder why the world doesn't ever seem to completely fall apart?"

---

The highlight of Friday was a rampaging queer hoard running around buggering, burning and applying forced makeovers to unwilling straight guys. When you've seen as many rampaging hoards as I have you appreciate the fine details that illuminate the specific angsts that generate them.

---

Awareness changes reality. I suppose that there's some deep quantum explanation to account for this but it's been decades since I lost my simple faith in the explanatory power of science. All I know is that it's so.

The very first intelligence was the Demiurge. He's El's boss, which makes him my boss's boss. In the beginning, he touched the spark that ignited the universe and has been spending the rest of Time doing his best to make sure that that precious, divine flickering, which is our Cosmos, doesn't fade. Or so El says. Some folks who've heard about him think that he's a godly semi-abortion who created this universe to trap us in a world of lies and illusions. Whatever.

The important thing is that we're all bending reality to our expectations. If you want to put some kind of postmodernist or New Age spin on that, be my guest. What matters is that, most of the time, our competing desires to remake the universe into our own images cancels out. The Demiurge is the tie-breaker. It prefers a universe of orderly physical laws, which is what we mostly get. Frankly, that works for me, too.

The problem is that reality just isn't very stable. People are pessimistic. They look out at the universe and some deep part of them thinks that it's all just a little good to be true. That doubt translates into eschatology. Sometimes — often — the balance tips and the world goes spiraling down into one of a million different oblivions.

---

Saturday starts with run away global warming and ends with an endless ice age. The irony fails to amuse me.

---

"You ever hear the story of the virtuous men?"

I shook my head.

"It's a story that you find in a lot of mythologies. Supposedly there are a handful of virtuous men — sometimes seven, sometimes nine, or some other mystically significant number — whose virtue prevents the world from ending."

Off in the distance I could see blasted buildings. Every so often there'd be a flash on the horizon that I assumed was another bomb going off. I toyed with a chunk of fused glass that I had pulled from the ground.

"I suppose that you're going to tell me that you're one of those guys, right?"

He smiled. "No. I'm not particularly virtuous and the world keeps ending whether I like it or not. I'm just one of the guys who gets to put it back together after it falls apart."

---

It's Sunday. Aside from a lone AI gaining godlike intelligence and turning the whole solar system into computronium, it's been a quiet morning.

I'm having coffee with El. I've been the sub-archon in charge of the Eastern Seaboard for almost five decades now.

"What's the point, El?"

I'm tired. I'm tired of living through catastrophe after catastrophe. I'm tired of getting murdered. I'm tired of being blown to smithereens. I'm tired of being butchered, raped, dismembered and eaten. I'm tired of being sucked into black holes and tired of living through every inane nihilistic fantasy that the Collective Unconscious spews out.

I'm tired of fixing everyone else's mess.

He absently taps his mug with his spoon a few times. It's just one a dozen annoying habits that he has.

"What I can I tell you, kid? I've been doing this since King Tut was in diapers and I've thought about calling it quits thousands of times. I never do, though."

He shrugs. "I know it sounds corny, but I believe in the world. I believe in humanity."

I tell him that I can't do it anymore, that I just want to end it all, even if that means ending myself. I tell him that I've got a gun at home with a bullet in the chamber. I tell him that I just wanted to say goodbye and that he's going to need to find someone else to manage this little corner of our fragile world. I've got my own eschatology to take care of.

He tells me that I just need a vacation. He leans over and takes my gnosis. I had no idea that he could do that.

---

It's Monday, again. I've got the hangover from Hell. I clutch my head, trying not to puke. I can tell it's going to be one of those days.

At least it's not the end of the world.

Is Mathematics a Science?

Today's article is a "Best of the Blog" repeat.

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Is mathematics a science? Well, the answer depends on what one means by "mathematics", and what one means by "science". There are well known and respected philosophers of science that will tell you the answer is 'no', while others are just as emphatic that the answer is 'yes'.

So before we can provide an answer to the question, we must agree on what we are talking about.


WHAT IS SCIENCE?

This is in itself a rather tricky question. People bandy about the words "science" (with or without first or last names) and "scientific" quite easily, but most would be hard pressed to provide a coherent answer to the question of what qualifies something as science and what does not.

Since I am writing at the behest of Andrew, I asked him that question when he asked if I was interested in writing this essay. So I will quote his answer and use that as a general guide.

Science is a form of epistemology that, like any good epistemology, attempts to distinguish true statements from false statements thereby leading to an accumulation of knowledge. One of the primary things that distinguishes science from other epistemologies is that it is a) systematic and b) nondogmatic. A proper science must have a means of validating its claims as well as a means of identifying and rejecting false claims. This, too, ought to be systematic.

Let us agree to this definition, and also agree that here "true" and "false" refers to an objective agreement with the 'outside' world.

Mathematics seems to have the deck stacked against her: the axioms are very close to dogma, and it seems not to care about truth or falseness, or even the outside world for that matter. There are proofs, but there seems to be no experimentation; mathematics does not follow the scientific method. Is that really the case?

SOME HISTORY

Most people are never exposed to modern research mathematics. They either know mathematics as a collection of recipes, algorithms, and rules (e.g. the formula for solving a quadratic equation, the rules of differentiation, how to multiply two numbers together, etc), or perhaps know the axiomatic model of Euclid (lemma, proof, theorem, proof, corollary, proof, all based on abstract notions and 'self-evident truths' known as axioms). Or both. The truth is that it is in reality neither, though at one time it (sort of) was close to those impressions.

Up until the 19th century, people who did "abstract mathematics" were called Geometers; they were usually either philosophers, amateurs, or physicist/mathematicians in their spare time. Major mathematical works dealt either with the sort of development similar to Euclid, or were collections of recipes and algorithms to solve problems (e.g., the works of Diophantus and Fibonacci). Almost everyone else who did mathematics was also doing physics. In fact, the most famous mathematical names up to the early 1800's were connected with physics in one way or another: Newton, the Bernoullis, Fourier, even Fermat; Gauss, the Prince of Mathematicians, officially held a post as Astronomer, and did much work in physics. That kind of mathematics was intermingled with physics.

About the only kind of mathematics that did not fit in either one of the above molds was number theory, which was, until Gauss's landmark Disquisitiones Arithmeticae, considered recreational mathematics, and in particular, not a subject of serious study but of play.

Then, during the 19th century, something happened. Mathematics began to develop as an independent field. In part, this had to do with a number of problems that had been accumulating: the foundational problems in calculus, the constructions of monsters that highlighted the problems with naive and intuitive notions being used in proofs, and the discovery of non-Euclidean geometry. Another part was the explosion of new ideas and methods: the beginnings of group theory, complex analysis, and algebra; in the final years of the century, the development of naive set theory (later replaced with an axiomatic variant) and the appearance of non-constructive existence proofs (most notably, Hilbert's finite basis proof). [Please follow this link for a discussion of some of the relevant issues of this proof]

During this crisis, a break developed between physics and mathematics. While most mathematicians still engaged in solving problems derived from physics, and most physicists still solved mathematical problems, the emphasis became different. Physicists were, by and large, not very concerned with the foundational problems, since calculus and its derivations obviously worked. The monsters, paradoxes, and antinomies might be interesting to philosophers, but they were not things that one was likely to encounter in "real" problems. On the other hand, Mathematicians were very concerned with the problems, and struggled to try to place their edifices on solid grounding.

Out of this crisis, there arose two main schools of mathematical thought. Both agreed that mathematics needed to be placed on a more solid foundational footing. On the one hand there were those, led by Kronecker, who believed in an emphasis on algorithms and recipes that followed from clearly defined concepts which were based on some empirical reality; "empirical" here must be taken loosely: Kronecker's famous dictum was "God gave us the integers; the rest is the work of Man", meaning that he considered the (potentially infinite) set of integers to be an 'empirical reality', for example. They were called 'constructivists' or 'intuitionists'. On the other hand there was the school led by David Hilbert, sometimes known as the 'formalists'. To the Hilbert school, the ultimate arbiter was self-consistency and interest. A mathematical theory should be based on clearly stated axioms and rules, but it makes no sense to ask whether the axioms are "true" or "false". The only questions that one must ask are: (i) Is it possible to use the axioms and rules to prove both a proposition and its negation?; and (ii) Is the resulting theory interesting? Upon an answer of "no" and "yes" (respectively), the theory would be deemed acceptable. (The reason for asking the first question is that, under the rules of classical logic, if it is possible to prove both a proposition and its negation, then it is possible to prove anything. Such a theory, needless to say, is both uninteresting and useless.)

However, the axioms need not have any relation to "reality". Here again we have a famous dictum, this time attributed to Hilbert: "It must always be possible to substitute 'table', chair' and 'beer mug' for 'point', line' and 'plane' in a system of geometrical axioms." That is, the actual meaning of the axioms is immaterial; their semantic content plays no role in mathematics.

In the end, it was the Hilbert school that triumphed among most mathematicians (with come caveats). As a result, most mathematicians will describe mathematics as following the classic Euclidean axiomatic model. Perhaps the quintessential example is found in the works of Bourbaki. It has also strongly influenced the way in which mathematics papers are written and advanced mathematics is presented. More on this below.

These days, mathematics tends to be divided into two: applied mathematics and pure mathematics. Applied mathematics are the parts of mathematics that deal with problems that arise out of empirical concerns: statistics, differential equations, and the like. Pure mathematics deal with problems that arise out of theoretical frameworks, often purely mathematical. The distinction, however, is in large part artificial. For example, at one time Number Theory was considered the most pure of pure mathematics, a branch of mathematics that had absolutely no possible practical application. In recent years, however, it has become the cornerstone of modern cryptography and developed a very robust applied side.


WHY THE HISTORY?

What is the point of all of the above? Well, the point is that the Hilbert School exercised a very strong influence in mathematics in the 20th century and through today. This influence in turn helped to produce and enshrine a particular style of writing when one deals with mathematical research. This is the dry definition-lemma-theorem-corollary style that many are aware of.

The "problem" with this style is that it obscures how mathematics is done. A professional mathematician engaging in research does not produce a definition, then write a theorem and its proof, perhaps separating some crucial step as a lemma. The way in which mathematics is reported in research articles and books is very different from the way in which mathematics is done. (I should point out that it is my impression that there has been a slow but steady shift towards a more engaging style in mathematics articles in the past two or three decades; a style that allows the reader a look at some of the process the writer went through to produce the proof; there have always been gifted mathematical writers who did this anyway, such as Gauss, Dedekind, or Paul Halmos, for example, but it seems to me to be becoming more widespread.)

The effect of this prevalent style is that everyone but the professional mathematical researcher tends to get a skewed and inaccurate view of how mathematical research is done. This in turn has led some philosophers to conclude that mathematics is not a science, because its methods are (apparently) so different from those of other empirical sciences. I will argue below that, once we go past the facade provided by the writing style and into the way mathematics is done, that this conclusion is in fact quite unwarranted.

Another effect is that the Hilbert School, from its beginnings and especially in the wake of the work of Goedel, Turing, Church, and others, abandoned the ideas of "true" and "false" in favor of the ideas of "provable", "disprovable", and "undecidable". Our working definition of science places a strong emphasis on truth, and so it would also seem to follow that, insofar as mathematics seems unconcerned with truth and falsity anyway, it could not be considered a science or a scientific pursuit.


BUT IS IT SCIENCE?

Gauss called mathematics "the Queen and Servant to Science". Pretty much everyone agrees at least to the "servant" clause: it is undeniable that mathematics plays a major support role in science. And no longer just in physics, or chemistry, but increasingly in other sciences as well. Statistics was the cornerstone of the change in medicine from art to science. And most social sciences seem to feel that the more math they can put in, the more robust and scientific they will be. It is the claim that mathematics is a science (let alone the "Queen of Science") that seems to lack support.

For starters, does mathematics even follow the scientific method? Observation, hypothesis, experimentation, testing, verification?

In what may come as a surprise to some, yes, it does. This is where the prevalent style does a disservice to an accurate perception of research mathematics. A mathematician engaging in research does not produce a statement for a theorem and proceed to prove it. She is usually feeling her way in the unknown as much as any scientist. She will consider some specific examples (observations), and try to see if they have a property or not. She will formulate some questions, both general and specific, and try to see how she can answer them for specific cases. She may then attempt a general statement (hypothesis), and proceed to attempt a proof (experimentation); sometimes, if that fails, she will attempt to construct a counterexample (falsification and testing). This process continues until the mathematician finally obtains an argument establishing her hypothesis, or she manages to disprove it (or, finding herself unable to do either, sets it aside and tries something else...)

For particularly troublesome problems, working out specific examples is considered a worthwhile pursuit, akin to experimental confirmation of details of difficult theories. Checking all odd numbers up to a large bound to see if any of them are perfect may not be considered mathematical evidence that no perfect odd number exists, but it still helps. Proving that the ABC Conjecture implies certain results which are known to be true does not establish the conjectures, but it lends them some "street cred" (and makes people more interested in trying to establish them as true or false). And so on.

On the other hand, there are some notable differences with sciences like physics: while there is observation, there seems to be no observation of the "real world". And mathematicians always demand "proof", a far more stringent standard than is met by any other science! Take, for example, Newton's Law of Universal Gravitation. The claim that this law applies everywhere (the "universality" of it) would never satisfy a mathematician. The fact that it has never been contradicted is not enough for such a claim. Only proof, meeting mathematical standards, would be. Compare this, for example, with Fermat's Last Theorem: 350 years of being unable to find a counterexample or proof was not considered (mathematical) evidence of truth or falsity. It was merely annoying. Only when a proof was produced (and checked and verified) was this accepted. Or the Goldbach Conjecture, which has been verified to very large numbers; such verification, while indicative, is not enough. Likewise with the existence of an odd perfect number. (As an illuminating aside, a joke has a mathematician, a physicist, and an engineer traveling on a train through Scotland, when they see a black sheep in the distance. The engineer promptly asserts "In Scotland, sheeps are black." To which the physicist replies "No, in Scotland, some sheeps are black." The mathematician then gently corrects him: "In Scotland, there is at least one sheep which is black... on at least one side.")

So: how do we deal with the apparent lack of observation, and the demand for "proof"?

Taking the last point first, I would argue that the demand for mathematical proof does not seriously distinguish mathematics from other sciences. It is merely that the standards which a mathematical result must meet are more stringent than those of, say, physics. But other sciences also set up their own thresholds for acceptance: no more than a certain amount of error, statistical significance to a certain degree of confidence, sufficiently varied observations, predictions, etc. The standards of math are merely quantitatively different (in that they appear to be stronger and with higher thresholds), not qualitatively different.

On to the first point, then. Aren't axioms arbitrary statements? Aren't they dogmatically followed, never questioned or modified? Is there any concern for "truth" and "falsity"? For the outside world?

The idealized model of mathematics presented by the Hilbert School would argue that the answers are, respectively, "Yes, they are", "Yes, but they are arbitrary and we can change to some other system at will", "no", and "no". But like all idealized models, this is not an accurate presentation.

Axioms can be arbitrary statements, but they almost never are. There is usually some reason for presenting a particular set of axioms over some other. They represent not so much "arbitrary statements" as they represent the "ground rules" for a particular development, the minimum agreed-upon assertions from which we will proceed. Often, these are distillation of actual observations, or attempts at abstracting real world situations in a way that makes it amenable for mathematical treatment. The ideas of differential calculus (an eminently empirical development, made for the express purpose of providing the tools to study motion) have been distilled into a series of "axioms" for the real numbers from which we proceed, based on centuries of work and observation. They represent the compromise between avoiding the paradoxes, contradictions, and antinomies which faces mathematicians in the 18th and 19th century, and keeping the properties that allows calculus to be practical and useful.

The axioms of group theory were developed from the study of equations; they represented the minimum conditions on which the arguments would follow. And while one works with groups, these axioms are not changed. On the other hand, people are free to drop, discard, add, or remove axioms at will to produce other systems with which they can also work: this is the case of semigroups (obtained by removing one axiom), or ring theory (obtained by adding a number of axioms).

The axioms are, to some extent, "unquestioned", because from the mathematical side there really is little concern on whether they are "true" in an empirical sense. On the other hand, when a mathematical theory derives from a real world situation it is attempting to abstract and study, the axioms seldom go unquestioned or unmodified, as people attempt to make sure the abstract theory stays as close as possible to the situation it is attempting to model. There is continual feedback and fine tuning between the mathematical theory and the real world.

And while it is true that mathematics usually refrains from saying "true" and "false", and instead talks about "provable" and "disprovable", this does not mean there is no contact or application with the outside world. Mathematical theorems are never simple declarative statements; rather, they are always implications. All mathematical theorems are of the form "If (some conditions are met), then (this conclusion will follow)." Moreover, this will hold true whenver we interpret the theory in a specific model.

As Hilbert noted with his comment on geometry, an axiomatic system should not depend on any specific meaning given to the undefined terms or the axioms. What this means, however, is that any mathematically correct conclusions we draw from those axioms will be true in any interpretation. If we take a theorem of geometry, and interpret "point" to mean "table", "line" to mean "chair", and "plane" to mean "beer mug", then the theorem will provide us with a true statement about tables, chairs, and beer mugs (assuming that the Axioms, when thus interpreted, are also true). In this respect, there most certainly is a connection to the real world and an ability to test and check the validity of the interpretation. In addition, even though we recognize that the semantic meaning we might give to undefined terms like "points", "lines", and "planes" should play no role in a proof, nonetheless these semantic meanings are often used to inspire proofs and theorems. We will make a drawing of a circle and a line to help fix ideas or inspire a proof, even though "circle" and "line" are terms that should carry no semantic content in the proof itself.

The standards of proof that mathematics requires in fact ensure that the conclusion will be true whenever the premises (including the axioms) are also true; and that at least one premise will be false if the conclusion can be seen to be false. What the reliance on provability instead of truth gives us is flexibility and certainty. By relying on abstract rather than concrete considerations, we ensure (or at least, attempt to ensure) that our deductions will indeed follow for any particular interpretation.

Most mathematicians will usually have some specific interpretation in mind when doing mathematics. The danger is that we may use specific properties of that interpretation inadvertedly in a proof, and thereby obtain a result which will not be valid in other interpretations. This was the pitfall into which Euclid himself fell, for example. Proposition 1 of Book 1 relies on the obvious fact that two particular circle segments have a point in common. However, this "obvious" fact does not in fact follow from the axioms. It takes an enriched set of axioms before the theorems of Euclid become actual theorems that will be true whenver all the axioms (both classical and new) are true.

It is because this danger is present that mathematics has developed its standards of proof; just as other sciences have developed their own based on their own experiences. In this it is also that mathematics presents the characteristics of a science.


CONCLUSIONS

Is mathematics a science? I believe so. It follows the scientific method (though this fact is sadly obscured by the prevalent writing style). And while it seems (and sometimes claims) to live in its own little world, cast adrift from concerns about reality, the truth is that, even in its "purest" guise, it keeps an eye out to reality for both applications and inspirations. In its "applied" guise there can be no doubt that it sticks close to reality, and that its assumptions, problems, and conclusions are continually tested and refined against that backdrop. Nonetheless, it is also different from other sciences in that its standards are a bit higher and a bit more certain. But this part of its strength as a science, not a disqualifying property.

So, coming back to our working definition of science, does mathematics meet the requirements? It attempts to distinguish true statements from false statements. However, we must understand here that a "true statement" does not refer to a theorem or lemma in isolation, but rather to the implicit statement given by a theorem, that whenever all axioms and hypothesis are interpreted in such a way as to make them true, then the corresponding interpretation of the conclusion from the theorem will also be true. Likewise, "false statement" would mean that there is at least one interpretation of the axioms and hypothesis which makes them true, while at the same time making the conclusion false.

It is certainly true that mathematics accomplishes this in a systematic manner, through the use of proof. The proofs are open to scrutiny by any and all investigators, who are encouraged to "repeat the experiments", as it were, by going over the proofs line by line and agreeing to their validity (or requesting clarification, or even pointing out mistakes). It is not unheard of that results that had been considered correct are suddenly cast into doubt by a mathematician pointing out a flaw in the argument; sometimes this damns the entire original enterprise, sometimes it merely requires a "fix".

And mathematics has a very systematic way of validating its claims, again through the use of proofs; false claims may be identified by presenting counterexamples or pointing out gaps in proofs. This is done in a systematic and commonly accepted way.

It should then be clear that mathematics does meet the requirements; its particular interepretation of the scientific method, its particular thresholds, may be quantitatively different from other sciences, but they are qualitatively the same. It plays, moreover, a singular role among sciences, being an indispensable tool to so many other facets of science.

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This article was contributed by Arturo Magidin. Dr. Magidin is a professor of mathematics at the University of Louisiana.