The Grail Code 

Archive for January, 2008

Holy Grail handed over

Wednesday, January 30th, 2008

The Anglican Archbishop of York has handed over the Holy Grail to Pope Benedict. And if you were wondering what it looks like, here’s a picture:

Yes, it’s a beer and a movie tie-in. And it has “a distinctive taste with plenty of fruity hops,” which is about how I’d describe the movie it commemorates.

Chalices everywhere!

Monday, January 28th, 2008

I’ve had a couple of comments on this story that may be borderline spam, but since they have to do with chalices they’re certainly right up our alley.

They point to this site, which is peddling a theory that Leonardo da Vinci’s paintings are full of hidden images.

Briefly, the argument is this: that when you flip one of Leonardo’s paintings, and place the reversed image next to the original, you see shapes. Especially you see chalices, or closely related forms of stemware.

“We asked a probability expert [to] form a proper hypothesis and to do a calculation relative to the probability of the discoveries being random or coincidental based on these facts.” Not surprisingly, the probability expert decided that there was no possibility that the discoveries were random.

I think the probability expert is all wrong.

First of all, let me say that I know very little about statistics. Let me also say that, for the purposes of this argument, I don’t have to know a whole lot about statistics. No complicated mathematics will be involved. A bit of multiplication, but we have calculators for that.

So, first, what’s the probability of finding a random image (not stated beforehand) in a rich and complex painting flipped and set beside the original? About 1 in 1, I’d say. You will find something if you keep looking. You will also find an image in the wood grain on your desk if you keep staring at it, or in a marble floor.

Now, on to the probability of finding a particular image at random. Here is where it gets a little more complicated, because there’s an enormous difference between declaring what the image will be before you find it and declaring what it was after you’ve found it.

Suppose I have a room ten feet long by ten feet wide, and suppose I have the floor marked in one-inch squares. That makes 14,400 squares, which we’ll number according to their positions along the length and width of the room. For example, one corner will be square L=1, W=1; the square next to it will be L=2, W=1; and so on.

Now, if I close my eyes, spin around three times, and throw a penny into the air, the odds of its landing on any particular square are 1 in 14,400—a pretty high number. So if I tell you that the penny is going to land on square L=83, W=29, and then it does land on that square, you’ll be suitably amazed. I must be psychic, you’ll say. If I can do it again and again, I’ll be rushing to apply for the Amazing Randi’s million-dollar prize before it’s too late.

But suppose I don’t tell you before I throw the penny. Instead, I wait till it lands and then announce that it fell on square L=14, W=111. Amazing! The odds of its hitting that one particular square were 1 in 14,400! That can’t possibly be chance! Well, now you think I’m not really the brightest bulb on the Christmas tree. You patiently explain to me that the penny had to land somewhere, and although it’s true that there was a 1 in 14,400 chance of its landing on any particular square, it’s only amazing if I called L=14, W=111 before I tossed it.

You’re perfectly right, of course. Yet this basic error in statistics underlies more than half the conspiracy theories and supposed amazing discoveries you read about on the wonderfully weird web. It underlies the statistical argument against evolution.

The question gets more complicated when you start to have sequences of events—more complicated in the sense that the numbers get bigger. That’s really all.

Here’s an example: five random lines of text. I generated them at, so they should be random enough for our purposes.






Now, the odds of finding any one letter in any particular position are 1 in 26, since there are 26 letters in the alphabet. So, right off the bat, there’s only a 1 in 26 chance that the first line would begin with i, which it does.

The odds of finding any particular two-letter sequence in a particular position are 1 in (26 x 26), or 1 in 676, so it’s beginning to look extremely unlikely that the first two letters would be ic, and yet there they are.

Looking at the third line, I can see that the word “bunk” is spelled out at the end. What are the odds of that? The odds of finding any four letter sequence in any particular spot are 1 in (26 x 26 x 26 x 26), or 1 in 456,976. It simply can’t be random chance. Some invisible hand must have written that word as some sort of message to me.

Once again, if you thought I was serious, you’d be either amused or dismayed, depending on how well you liked me. Yet this is the sort of argument we’re facing in this comment.

Here is a general rule of statistical interpretation: whenever someone tells you that something can’t be random chance because the odds against it are astronomical, suspect a misunderstanding of statistics. The higher the stated odds, the more you should suspect a misunderstanding. Pretty much every event is extraordinarily unlikely if you use the ex-post-facto method of applying statistics, but that’s what we expect in a rich and varied universe.

All right, now for some fun. Part of our correspondent’s argument from probability hinges on this statement: “We searched a minimum of over 5000 paintings of the period and were unable to locate any use of the Perpendicular Mirror Process outside Leonardo da Vinci’s works.” In other words, 5000 paintings and no mirror chalices.

So I went to the wonderful Web Gallery of Art and looked at paintings of the Renaissance period. I picked the paintings as randomly as I could, which is to say I just started at the beginning of the As. Then I took a few paintings and subjected them to the Perpendicular Mirror Process. I didn’t look at 5000 paintings. More like a few dozen.

Here are some images I came up with. Note the prominent chalice shape in the center of each picture.

Andrea del Sarto: Portrait of His Wife

Andrea Del Sarto: St. John the Baptist

Bergognone, St. Agnes

(in this one, note also what appears to be the ghostly outline of a smiling mask!)

So I had no trouble finding chalice shapes. They’re all over the place.

After a while, I began to wonder just how easy it is to find chalices this way in pictures where human bodies are concerned. So I tried the same technique on a photograph of me, because I’m the only one I know who doesn’t object to being manipulated this way.

Christopher Bailey: Self-Portrait

Wow! Spooky, huh? This is starting to freak me out.

An atheist fantasy? Hard to tell

Sunday, January 27th, 2008

I’ve just seen The Golden Compass, the movie version of Philip Pullman’s book of the same name. (For American readers, at least; in England it was The Northern Lights. American publishers always change the names of British books, I assume on the grounds that it makes the marketers look like they’re working for a living.) Now, I haven’t read the book, and I haven’t even followed the controversy except in its broad outlines.

Briefly, it is said that Philip Pullman is an atheist who deliberately wrote a fantasy designed to poison the minds of young people against Christianity and lead them toward atheist humanism, whatever that is. Pullman himself makes no secret of being anti-religious and anti-supernatural.

But as I say, I haven’t read the book. Certainly there are obvious anti-Christian elements in the movie. The organization at the heart of all the villainy is called the Magisterium—a word that, as far as I know, occurs in exactly two contexts: as a name for the teaching authority of the Catholic Church and as the name of the sinister all-controlling power in Philip Pullman’s novels. In the movie’s world, if you run foul of the Magisterium, it prosecutes you for heresy—another loaded word. The officials of the Magisterium get their fashion sense from Catholic bishops and cardinals. The usual sources on line say that the anti-Christian message of the book has been toned down a good bit for the movie, but it’s hard to miss anyway.

So if you think anti-Christian movies shouldn’t be made, you won’t like this one. If you like to judge movies by their own merits, however—well, you still might not like this one. It just feels shallow. The most interesting conceit in the fantasy world is the idea that people’s souls live outside them in the form of animal-shaped daemons (pronounced “demons”), but the movie seems to miss all the best opportunities for spinning metaphors and allegories out of that conceit. As for the rest, it’s difficult to decide what the moral is supposed to be. Freedom = Good, Dogma = Bad: I got that much. To judge by the actions of the admirable characters in the story, we are also to understand that war is good for its own sake, and revenge is an important humanistic value. I’m pretty sure I don’t like those ideas.

One more complaint: the narrative is full of cliches cribbed from every action and fantasy movie. At the climax, for example, our heroine destroys the evil soul-splitting doomsday machine in the villains’ secret hideout, and—just as in every parody of every James Bond movie—the destruction of that one machine somehow sets off a chain reaction that blows the whole complex to smithereens, taking just long enough for all the major characters to run around in a panic for a while before escaping just as the flames engulf the building. As my wife pointed out, the story has to have some reason why the villains can’t just fix the evil doomsday machine and go on with their villainy right away. What would you have come up with? she asked. I frankly admitted that I didn’t know; but if I were writing the script, I would have spent half an hour thinking about it, and at the end I would have come up with something.

(On-line sources say that Tom Stoppard wrote the first screenplay for the movie, but the producers rejected it and had someone else rewrite it from scratch. I really, really want to get my hands on that Tom Stoppard script.)

So is there nothing to recommend the movie? I certainly wouldn’t say that. The story may be trite sometimes, and the moral may be muddied, but the pictures are beautiful. The landscape is dotted with gorgeous cities filled with a kind of Renaissance Deco architecture; I kept thinking that, if this Magisterium can provide a living environment like that, you might want to think twice about poking it in the eye. I also fell in love with Mrs. Coulter’s airship, which is positively the most beautiful dirigible ever seen on film. I want one for myself.

No less an authority than the Right Revd. Rowan Williams has suggested that The Golden Compass be taught and discussed in religion classes. He sees it as a plea against dogmatism rather than against religion, and I agree that dogmatism is bad (as opposed to dogma, which can be very good if it’s the right dogma). And I think that his approach is the best one. The movie isn’t suitable for very young children. But if your older children want to watch it, let them, and watch it with them. Then talk about it. You could start with something like “So, what did you think of Mrs. Coulter’s airship?”

And now an aside: Why would an anti-Christian fantasy retreat to more primitive forms of religion and superstition? The whole plot revolves around the separation of the soul from the body; the Magisterium’s evil plot is to get rid of the soul altogether, which is a very odd idea for someone to come up with if he doesn’t believe there’s such a thing as a soul. This, I think, is what has me more mixed up than anything else. To counter Christianity with magic and animism is all very well, if you want to lead the kiddies toward magic and animism. It seems like an odd strategy if you want to lead them toward scientism. But then, as I mentioned before, I haven’t read the book.

Relativism, right and wrong

Friday, January 4th, 2008

This fascinating essay by an archaeologist named Timothy Taylor started me thinking about how I understand history, which is always fun to think about. He wrote it in response to this question:


Science is based on evidence. What happens when the data change? How have scientific findings or arguments changed your mind?

Mr. Taylor has changed his mind about relativism: he used to be for it, and now he’s against it. “Where once I would have striven to see Incan child sacrifice ‘in their terms’, I am increasingly committed to seeing it in ours.”

He explains how useful what he calls relativism can be in understanding history and archaeological findings, but he finds now that there are limits. “But what happens when relativism says that our concepts of right and wrong, good and evil, kindness and cruelty, are inherently inapplicable?”

Recently, Mr. Taylor and a colleague have been applying some serious science to the remains of sacrificed Peruvian children of the Inca era.

Contrary to historic chronicles that claim that being ritually killed to join the mountain gods was an honour that the Incan rulers accorded only to their own privileged offspring, diachronic isotopic analyses along the scalp hairs of victims indicate that it was peasant children, who, twelve months before death, were given the outward trappings of high status and a much improved diet to make them acceptable offerings. Thus we see past the self-serving accounts of those of the indigenous elite who survived on into Spanish rule. We now understand that the central command in Cuzco engineered the high-visibility sacrifice of children drawn from newly subject populations. And we can guess that this was a means to social control during the massive, ’shock & awe’ style imperial expansion southwards into what became Argentina.

The “relativists,” however, have attacked these conclusions (not the science, of course: it’s much easier to skip that and just attack the conclusions). The archaeologists, these “relativists” say, have revealed only “the inner fantasy life of, mostly, Euro-American archaeologists, who can’t possibly access the inner cognitive/cultural life of those Others.” He finds special significance in that capital O: the Other is always virtuous, and always irreconcilably Other. “Here we have what the journalist Julie Burchill mordantly unpacked as ‘the ever-estimable Other’ — the albatross that post-Enlightenment and, more importantly, post-colonial scholarship must wear round its neck as a sign of penance.”

Relativism, Mr. Taylor concludes, has its use in understanding the past, but it goes too far. “By denying the basis for a consistent underlying algebra of positive and negative, yet consistently claiming the necessary rightness of the internal cultural conduct of ‘the Other’, relativism steps away from logic into incoherence.”

Did you ever think you’d hear me make a defense of relativism? Well, here we go. The problem with Mr. Taylor’s admirably clear analysis, I think, is that he’s confusing two layers of understanding: the intellectual and the moral. I’ll explain what I mean in a moment. I think Mr. Taylor is actually much more of a relativist than he knows, and far more of one than the people he calls “relativists.”

Oddly enough, I see Mr. Taylor’s late epiphany, not as a rejection of relativism, but as a triumph of right relativism over wrong relativism. Wrong relativism is the kind displayed by the people he calls “relativists”: it assumes that all other cultures are basically good and only ours is corrupt and evil. Thus the human sacrifices of the Inca can only have come from the purest religious motives, whereas the Conquistadors alone were greedy, self-serving tyrants.

Now, you won’t find me arguing that the Conquistadors weren’t greedy, self-serving tyrants. Some apologists for colonialism would tell you that they weren’t as bad as they were painted; I think they were, every bit. But the notion that the Conquistadors alone were bad men is not real relativism at all: it is bigoted and uncompromisingly dogmatic absolutism, though a topsy-turvy sort that attributes virtue to anyone but ourselves.

Real relativism attempts to understand a foreign time or culture on its own terms, and allows the possibility that the Other may be as complex as we are, with as much vice admixed with virtue—in short, fully human. This is the relativism Mr. Taylor and his colleagues are exercising when they suggest that the Inca human sacrifices may have been part of a totalitarian empire’s oppression of the masses. They are attempting to understand the culture from inside, to see it not as a monolith but as a complex society made up of groups and individuals with conflicting motivations. This is the real route to understanding history: not to see the objects of your study as uniformly admirable, but to see them as human.

What the so-called relativists are doing, on the other hand, is something like trying to understand American society by listening only to what the White House press secretary says. Presidents and their spokespeople will tell only those parts of the story that suit them. In the not-too-distant past, presidential administrations have even lied to the American public, although we can of course be certain that such a thing is no longer happening and will never happen again in the future. Would we have a true history of the early 1970s if we went only by the announcements that came from Richard Nixon’s staff—at least the ones he hadn’t fired?

So I say that real relativism is essential to understanding history. That may be called the intellectual layer of our understanding. We have to come to that kind of understanding before we can move up to the next layer, which is the moral layer of understanding. Here we stop studying and start judging. This is where we can say that, whatever the culture, it is repugnant to natural law—or, if you prefer David Hume’s term, the “moral sense”—when a government arbitrarily kills to terrorize a conquered population. That, of course, is what was so horrible about the Conquistadors; but if it is horrible in Pizarro, then it must be horrible in Huayna Capac as well. Oddly enough, the peoples Huayna Capac conquered would almost certainly agree with me. In a peculiar way, even my moral absolutism is relativistic, because natural law is universal. People feel injustice as keenly whether they are twenty-first-century Americans or fifteenth-century Peruvians.

So I say this to Mr. Taylor: Don’t abandon relativism so quickly. You still do need to understand a culture in its own terms, and you’re already doing a better job of it than the so-called relativists are doing. But do make the distinction between intellectual understanding and moral judgment. Both are necessary, but they are separate operations, and one precedes the other.

Intellectual property gone mad

Tuesday, January 1st, 2008

I usually stay out of politics on line, because I think it distracts from the messages I consider more important. You don’t have to know whether I’m a Republican or a Democrat—or Labour or Tory or Lib Dem, or Progressive Conservative or Regressive Liberal, or whatever the parties are in your part of the world. You can just assume that I agree with everything you believe, and you don’t have to know that I always vote straight Bull Moose. (Anyway, that’s a lie. I don’t have many opportunities to vote Bull Moose, and when I have them I don’t take them. It is literally true that a candidate for city council in my rather colorful district ran on the Bull Moose ticket a few years ago, but I didn’t vote for him. That’s as much of my voting record as I care to divulge right now.)

But once in a while I do take a stand on issues I consider both important and relevant. For example, I came out against throwing bloggers in jail, on the important and relevant grounds that I am a blogger and don’t want to go to jail. There, in a nutshell, are my criteria for importance and relevance: namely, blatant self-interest.

Now it’s time to talk about another area that engages my blatant self-interest: intellectual property. In this area I admit that my views are on the wacky radical side. I believe that the purpose of copyright and patent law is not to build up dynasties of intellectual-property billionaires, but to promote the progress of science and useful arts, by securing for limited times to authors and inventors the exclusive right to their respective writings and discoveries. Since I’m an unreliable radical, however, let’s see what powers the founders of the United States of America gave Congress in this area. Let’s see—here it is: “To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.” Well, what do you know.

Remember those words as I tell you that the government of Egypt is moving to “copyright” Egypt’s ancient monuments.

Egypt’s MPs [the BBC tells us] are expected to pass a law requiring royalties be paid whenever copies are made of museum pieces or ancient monuments such as the pyramids.

Zahi Hawass, who chairs Egypt’s Supreme Council of Antiquities, told the BBC the law would apply in all countries.

The money was needed to maintain thousands of pharaonic sites, he said.

Correspondents say the law will deal a blow to themed resorts across the world where large-scale copies of Egyptian artefacts are a crowd-puller.

Now, I’ve never met Dr. Zahi Hawass, but he’s one of my heroes. He combines scientific rigor and vast learning with a theatrical flair that succeeds in conveying the excitement of history and archaeology. He has his own fan club. How many archaeologists can say that? It’s true that he’s made a lot of enemies, but that seems to be mostly because he doesn’t have much patience for people whose standards don’t meet his own. The people who think Martians built the pyramids positively hate Dr. Hawass, and I’m sure that’s fine by him.

I’ve given Dr. Hawass such a big buildup because I’m disagreeing with him here, and I want to make it clear that I don’t ordinarily take it upon myself to disagree with someone who’s both an august authority and an international media phenomenon. One or the other, but usually not both.

But the precedent for copyright laws, and intellectual property in general, is very bad if people take this Egyptian initiative seriously. Works of art, literature, and architecture should belong exclusively to their creators for limited times, because artists, writers, and architects have to make a living somehow. From society’s or government’s point of view, the purpose of such exclusive copyrights is to encourage the growth of art and literature.

But that exclusivity can’t and doesn’t need to be indefinite. After a certain time, the original creator is dead, and the exclusive copyright can’t possibly encourage him to create anything more. Works of lasting value become part of our heritage. All art progresses by learning from the works that have come before. Every great artist, at least until the past few generations, learned to paint by copying the works of old masters. The plots of Shakespeare’s plays are taken almost entirely from older sources, to be transformed by his genius into things far greater than the originals.

There are no monuments more ancient than the monuments of Egypt. If those are to be “copyrighted,” then there is no time limit at all on copyright. If people who did not build the Pyramids can, thousands of years after they were built, begin to demand a fee for representations of them, then there is no more culture. Anyone with enough power and chutzpah can take any human accomplishment out of the domain of shared human heritage and demand royalties for it. Artists can no longer paint views of ancient ruins; calligraphers can no longer copy the inscription on Trajan’s column; architects can no longer use elements of ancient monuments in new and unusual ways; poets and novelists can no longer re-imagine Homer; hacks like me can no longer bring the literary wealth of the Middle Ages to a new audience. My wife wouldn’t even have the rights to her high-school graduation photos, since she went to high school in Cairo and graduated in front of the Pyramids. Culture, in short, grinds to a halt, because culture grows by building on the great accomplishments of our ancestors.

Fortunately, as justifiably high as Dr. Hawass’ opinion of himself is, he can’t really make a law that “applies in all countries.” There are reciprocal treaties that govern intellectual property, to be sure, but the United States, for one, cannot make a treaty that abrogates its own constitution. I am not a constitutional scholar, but the words “for limited times” must have some meaning, and if the Pyramids can be under copyright in the United States then there is no limit. I don’t think our Supreme Court would allow any copyright claims to be enforced in such obvious violation of the letter of the Constitution. But then I’ve disagreed with the Supreme Court’s interpretation of the Constitution before, and where has it got me? I’m keeping an eye on this issue.

(C) 2006 Mike Aquilina and Christopher Bailey