Dan Brown part 2: φ

Just as I recently announced I have written an article about one of the many things Dan Brown could and should have gotten right in his books but did not. Those things are legion; and people more patient than me have already had their shot at it. For example there is a really excellent (and really long) article in Danny’s (don’t know his surname, I’m afraid) blog No Loss for Words titled Dan Brown is a fraud: A list of errors in Angels and Demons, which deals with this one book alone, and to which I, some years ago, had the honor of contributing a little thing as well.

Despite this abundance of material I have decided to confine myself to a single passage in the book The Da Vinci Code, which deals with a mathematical fact, which naturally interests me.

For your enjoyment here is the passage in its whole atrocious glory:

He felt himself suddenly reeling back to Harvard, standing in front of his “Symbolism in Art” class, writing his favorite number on the chalkboard. 1.618 Langdon turned to face his sea of eager students. “Who can tell me what this number is?”

A long-legged math major in back raised his hand. “That’s the number PHI.” He pronounced it fee.

“Nice job, Stettner,” Langdon said. “Everyone, meet PHI.”

“Not to be confused with PI,” Stettner added, grinning. “As we mathematicians like to say: PHI is one H of a lot cooler than PI!”

Langdon laughed, but nobody else seemed to get the joke.

Stettner slumped.

“This number PHI,” Langdon continued, “one-point-six-one-eight, is a very important number in art. Who can tell me why?”

Stettner tried to redeem himself. “Because it’s so pretty?”

Everyone laughed.

And I laughed too, a kind of sad, hollow laugh. Who would have thought it possible to get so much wrong in so little a piece of text? We are indeed witnessing a master at work. (Please excuse my bitterness, this thing happens to touch the field of my profession—who wouldn’t be touchy there?)

Most of which can be said (complained) about the matter has been said by the world’s most intelligent human being, the uncomparable Cecil Adams, but I’d like to add a few points of my own.

First of all, we are talking about a Greek letter here, φ. Am I too demanding in assuming that it should be possible, in the 21st century, to print some Greek letters in a book instead of writing it as “phi”? I mean, obviously this blog can do it, why not Doubleday Group publishers? Alright, minor point. By the way, if anything it should be “phi”, not “PHI”. “PHI” is obviously uppercase, which in Greek is Φ. The Golden Section (which is the thing meant here), however, is always a lowercase φ.

Secondly, the main point of Cecil Adams, φ is not 1.618. Just like 1/3 is not 0.333. φ is an irrational number, which have a unending, nonrepeating sequence of decimals after the comma. You just cannot write them that way. How to do it, then? Well, simply write

φ

=

which is the definition of φ. If you like to have the decimal expansion, please at least write it with dots: φ=1.618… But this thing that Brown (or Langdon, depending on how you look at it) wrote down, simply is not φ.

But this has been said before. Now I come to that which has not.

It is this: There are much too few letter in the alphabet for mathematics. There are 26, each lowercase and uppercase. Letters from other latin script variants are not used (e.g. ä, ç, ñ). And then there are the greek letters, where those that look like latin letters are excluded (an uppercase α, for example, looks just like an A). There are even a couple of hebrew letters that are used. Still it is too little. Therefore all letters are reused all the time and each one is used to name at least half a dozen things from various areas of mathematics. φ too. The most important are as angle parameters in functions, and the Euler φ function.

The point I’m trying to make here is that the Golden Section is not an important mathematical concept, and even less a frequently encountered one. I must have written several thousand φs since I began studying mathematics, and at most 20 of them denoted the Golden Section. If you ask a mathematician what φ is, in 99 of 100 cases (or more) the answer will not be Brown’s. The concept of Brown is called the Golden Section or Golden Ratio. If we name it with a letter, it is traditionally φ, but most of the time φ denotes something else.

And finally:

“Not to be confused with PI,” Stettner added, grinning. “As we mathematicians like to say: PHI is one H of a lot cooler than PI!”

If that guy is a mathematician he must be very drunk. Or on drugs. Or both. Because what he say is utter, utter bosh.

How can anyone confuse φ with PI (π)? Once a tutor told us not to confuse “angles” with “angels”, but that was a joke. A singularly lame one, but still. Anyway, “As we mathematicians like to say: PHI is one H of a lot cooler than PI!”. No, we mathematicians don’t say things like that.

Dan Brown, as he has showed on other occasions, has a rather weird conception of the sense of humor of scientists. There are indeed mathematicians’ jokes and physicists’ jokes, which other people don’t find funny at all (neither do mathematicians, to be honest). Its an interesting phenomenon and I may write a short piece about it some time. [Here it is.] Anyway, these jokes are in no way like these things Brown puts into our mouths. Not a bit. It’s a completely different style.

And finally, no mathematician would say that φ is cooler than π because it isn’t. It simply isn’t. φ does have a couple of beautiful properties, mathematically, but they are rather trivial. There is nothing a high school student could not understand. For example, that there is a relationship between φ and the Fibonacci numbers is completely correct, but it is no difficult or deep thing. I have written a PDF document that shows how it is done and you will probably not need more than 10 minutes to read and understand all of it (it’s also in Wikipedia).

π, on the other hand, is a monster that has baffled mathematicians for millenia. It drove the ancient Greeks crazy. There’s still many unsolved question left that involve it. It pops up in unexpected places. It is the reason you cannot square the circle.

(Here is my first article about Dan Brown.)

That does it for Dan Brown

In a way I admire Dan Brown. His books are filled with errors and general foolishness and his writing style is rather cringeworthy; I think he is a very good specimen of a generation of authors who not learned their craft by reading other literature but by watching television. It shows in the structure of his books. They can be converted into movies very neatly. In fact, when reading Dan Brown I always had a very clear feeling where exactly the commercial breaks would fit in.

But it is effective! I am sure, his goal has never been to win the Nobel price for literature but to accomplish that which he has accomplished. Which nobody else in the world has pulled off quite like him. Millions of people have read and bought his stuff and quite a few think it is real. It was made into major movies before the ink was even dry. (Now that’s an exaggeration but you know what I mean.) It’s one hell of an accomplishment.

Speaking of errors in Dan Brown’s books: By this I don’t mean all that historic stuff about Jesus, Leonardo, the Illuminati, even the Opus Dei. I don’t mean having a counterfactual base to your plot. I don’t even mean lying and deceiving to make it more believable. This is just the way of fiction and it isn’t a bad thing. Do we think less of Indiana Jones because the Holy Grail isn’t actually hidden in Syria? Do we think less of Stargate because the Pharaos weren’t actually extraterrestrial parasitic worms?

No, what I mean is little things that should have been correct and aren’t. I will soon write a short article that gives an example of such a thing.

This being said, I have to contradict myself. I don’t mind taking liberties with history (in fact I love them) as long as they are not presented as fact! As long as it is a literary game and not meant to convince me that this is the way it really happened. But this is what Brown does in the Da Vinci Code. (In his other books he does not, and so I don’t have a thing against them). As long as I can ignore it, I can take it as fiction in the same way as Indiana Jones, or Stargate or whatever. But when I feel that he presents his story as fact, then I feel the urge to contradict and disprove. And I am clearly not alone in this. There are quite a few books and documentaries and filmed lectures by various scholars around that consider and disprove, in meticulous detail, every single point of Brown and of Leigh, Baigent and Lincoln, from whom he took his theory. On the other hand I’m yet to find a book that tries do disprove Jonathan Strange & Mr. Norrell or The Discovery of Slowness.

Although I really don’t intend to duplicate any of these efforts, I would like to add here a little piece of evidence I found myself, which, at least for me, would demolish one of Dan Brown major points very elegantly, even if there were no other ways to do it.

Some while ago I visited in the Alte Pinakothek art museum in Munich, Germany, where I came across a certain painting by the french artist Nicholas Poussin titled The Lamentation of Christ.

As you undoubtedly know, one of Browns major points is, that one person in Leonardo da Vinci’s masterpiece, The Last Supper, is not, as commonly believed, John the apostle, but rather Mary Magdalene. The debatable person is shown in the detail image in the left.

  

The right one is a detail from The Lamentation of Christ and the description on the plaque tells us the painting does indeed feature Mary Magdalene. They look similar, don’t they?

Incidentally, Poussin is deeply mixed up in the whole business. One painting of his, The Arcadian Shepherds is claimed by Baigent, Leigh and Lincoln to depict the real tomb of Jesus as well as containing hints in the form of an anagram of the latin phrase “et in arcadia ego” which appears in the painting. Clearly Poussin must have been in on the secret.

Now where is the catch? Simple. The catch is that the person shown in the detail of the Lamentation is not Mary Magdalene. How do we know? Because Mary Magdalene is there, right in the center of the painting. This is her:

Looks more female too, doesn’t she? The other person is—guess who?—John the apostle. This means, that an artist who would have known if it was not the apostle but Mary in Leonardo’s painting chose to paint the same person but this time it really is the apostle, because it can’t be Mary. This just doesn’t sound credible to me and so I conclude that it was John all along.

Of course I don’t expect to convince anyone with this find who does not want to be convinced and it isn’t proof in the way I understand the word (as a mathematician) either. In fact it is easy enough to concoct several theories which still allow John the apostle to be seen as Mary Magdalene in Leonardo’s painting. Let me see:

• Poussin had not even seen Leonardo’s work and all is a conincidence really.
• Poussin painted the apostle like Leonardo because he did not know it was Mary really, as Leonardo had not even told his friends in the Prieuré de Sion this particular secret.
• It is Mary in both paintings and the woman is some other woman, whose name we don’t know.
• Poussin knew Leonardo’s secret and feared people would find out, so he produced a painting to convince people it wasn’t Mary in the Last Supper and thus allay suspicion.

In some perverse way, I am amused by the last theory because it is perfect accord with conspirational thinking. In fact, if you prefer one of these to my own explanation, have fun! Just don’t quote me.

(Go here to see part 2!)