Sunday, 26 December 2010

Two little things

As you probably know an ancient Middle East people, the Sumerians famously built huge temple platforms called ziggurats—towers with stairs at the sides and a shrine on top. For example this is a reconstruction image of the Ziggurat of Ur (modern-day Iraq):

The Ziggurat of Ur

Concerning ziggurats I found a fascinating little idea recently. It was stated by the late Dr. David Neiman, rabbi, archeologist and scholar, although I think it did not originate with him.

By the way: If you can spare the time, watch some of his lectures at Youtube. Despite the fact that I feel that his love of antiquity made him cast an unrealistically positive light on several things (slavery in antiquity, to name one), so this has to be taken with a grain of salt, there is a host of interesting material there.

The theory he put forward was this: He claimed that the ancestors of the Sumerians had migrated to Sumer from a mountainous region. This could be inferred from the fact that the early cuneiform symbol for “land” showed a picture of three mountains. It seems these people were used to worship their gods on mountain tops, and built their shrines and temples there.

When they later came to Sumer, which is a very flat country, it felt wrong to them to build temples on the ground. So they simply created artificial mountains and placed the temples on top of them—ziggurats.

The other one concerns the number 0. It is well known that the ancient European peoples generally had no sign for 0 in their number systems. The Greeks and Romans basically had nothing like it—they did not think it was a number at all, so why find a symbol for it? The Babylonians used a positional system to write numbers (as we do), so they had to have some kind of zero to discern, for example, 12, 120 and 102. They did so, but it was not allowed to stand alone, as pure 0. Neither did the Egyptians have it.

The first people to really understand the concept of zero, to write it and use it in calculations were Indians, and so it got into our number system, which is Indian in origin. This is all common knowledge.

Once I read in a book on the history of mathematics that the Indians were the only ones (or the first ones, anyway) to come up with a theory of zero for a special reason: The concept of nothingness (śūnyatā in Sanskrit) has been a very important idea in Indian philosophy since the earliest times. On the other hand Greek philosophers like Parmenides argued that “nothing” could not exist. They could not get their mind around the idea. The Indians did not have this trouble. They were used to 0.

I find these ideas very neat. In fact I have the strange feeling they fit together somehow. Let me try to clarify my point …

These things do not make you want to wear a tin foil helmet. They do not make you hate your neighbor. They do not make you feel you have been lied to your whole life.

Still, they are interesting. They are a little bit outside the canon of common knowledge. Outside the mainstream. You won’t find this information on Wikipedia. It’s one of the things they did not tell us. They are a little bit dubious. They might be true or they might not be, but is nice to belive they are. They do not rock your world like a flying saucer on the White House lawn but they might make you smile (or me at least). They might make you feel, in a tiny way, that the earth is a fascinating place if you lift the curtain. I will always have a place in my heart for things like these.

[I have started to make things like these into a series of articles. Here is the second one. Or just click the search key “little things”!]

Saturday, 18 December 2010

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.
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


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.)

Wednesday, 8 December 2010

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!)

Monday, 6 December 2010


Recently for the first time I watched Mel Brook’s movie Robin Hood: Men in Tights in English and was surprised it is actually a decent movie. I only knew the German version before, which is, like many German versions of foreign language comedies, abominable. Not only are they not able to translate gags correctly (which is pardonable, it can be really hard), they are trying to put gags where the original never intended them. Bad gags. For example: Monty Python’s Quest for the Holy Grail was a wonderful movie until the translators came along. First they changed the title to Ritter der Kokosnuss, which is, retranslated, “Knights of the Coconut”. But then things started getting really bad.

There is a scene at the beginning of the movie, where the valiant king shouts “It is I, Arthur, son of Uther Pendragon, from the castle of Camelot, king of the Britons, defeater of the Saxons, sovereign of all England.” In the German version he says, instead “I taught the Saxons angling, since then they have been called Anglo-Saxons. I’m the king of all anglers. I’m Arthur, inventor of the eucalyptus candy on a stick.”

Really! I’m not kidding you.

I am sure this is enough to convince you of the quality of German comedy translation. Still I want to mention another weird custom in that area:

If movies are made by well-known comedians, like Jerry Lewis, Louis de Funes or Woody Allen, they very often change the title as to include the first name of that actor. Yes, of the actor, not the character. For example, Woody Allen’s movie Take the Money and Run, was renamed Woody, der Unglücksrabe, which is “Woody, the Jinx”, although his character is still (as in the original) named Virgil Starkwell.

It seems as if this absurd practice at least has stopped in the last decades, but when it was around, it even sometimes happened to movies that weren’t even comedies, like the original Ocean’s 11, which became “Frankie and his cronies” (where they at least changed Danny Ocean’s first name to Frankie to match Sinatra’s).

But I digress. As much fun as rants like that are, my topic was something different. As I mentioned, I watched Men in Tights and there I noticed a curious thing. There is that scene where Robin Hood is to be hanged and the hangman is making silly comments. This hangman had sewn on his frock a golden shield with a halberd shape in it. It does not make too much sense, but then I remembered where I had seen this exact thing before. It was in that legendary, infamous anti-masterpiece by Ed Wood, Plan 9 from Outer Space.

Men in Tights   Plan 9 from Outer Space

Note that the person waring this is “the Ruler”, who is the, well, ruler of a band of extraterrestrials who arrive on earth in a flying saucer (played by John “Bunny” Breckinridge, who in real life seems to have been a drag queen). This person wearing a knight’s shield with a halberd on his breast is saying a lot about Ed Wood and why this movie has the kind of reputation it does have. By the way, if you ever have the chance of watching it, do so by all means! It is easily on par with the best of Mystery Science Theater 3000, even without Tom Servo and all.

So anyway, the executioner has that halberd and the Ruler has it. And it seems to me it is the same. Not similar; identical to the last slight bend in the back. See for yourself! Plan 9 being black and white, we don’t know the color of the shield, but I strongly suspect it was golden too. But, in the name of all that is good, why?

Basically, there are two explanations. One is, that Ed Wood and Mel Brooks happened to buy at the same costume shop (although Wood, considering the kind of budget he had, more probably scrounged the stuff costume shops threw away). With 34 years between the two movies, it does not seem too probable to me. But then again, you never now …

The other possibility is that Mel Brooks knew Plan 9 (this I think, at least, is certain) and intentionally choose to hide this reference in his own movie. What makes this weird is that there just is no reason at all to hide this reference in this place. It is completely non sequitur.

In short, I can’t believe it is a coincidence, but beyond that I don’t have a clue. If you know more, please let me know! (I might try to write to Mel Brooks about it, but then again it is not all that important.) What’s your take?

What it is all about …

So now I’ve started a blog of my own. Although the world clearly has not been waiting to receive my two cents about anything, here it is anyway.
Originally I planned to publish all I wanted to publish on a website of my own — but I found that that was, for several reasons, not the best idea. So here is my blog, with the sad restrictions it imposes on individuality. I will try to make the best of it.

What can you expect to find here?

Firstly, I hope, something at all, that is, I hope I will find the time to post new articles once in a while.
Secondly, all kinds of stuff. I will try to only write stuff, which I can reasonably expect to be of interest to someone — I’ve spent too much time on Youtube, for example, watching stuff that was — let’s call it … strange and I really do not wish to become the reason for anyone’s “facepalm” gestures. Also there’s way too much gibberish out there.
I expect my topics to include science (especially mathematics), literature, music, history, alternate history (a branch of literature, really), archeology, some of my own curious ideas and projects, various odds and ends and whatnot.

Another topic I will sometimes take up is the various kinds of weird theories that float around in the western world: Crop circles, UFOs, all the historic weirdness (Atlantis, pyramids, etc.), and so on.
With these I might just as well tell you what not to expect from me:
If you look for a “believer”, that is someone who basically says “It must be true, so let’s find out how it is”, look somewhere else.
If you look for a “debunker”, that is someone who basically says “It can’t be true, so let’s find out how it isn’t”, look somewhere else too.
I consider myself a scientist, and, having taken courses in the theory of science as well, I have specific views of what that means. Believe it or not, it means having an open mind and going where the evidence leads.
But, as the saying goes, not so open that the brain falls out. This is very important! By the way, this is what being a skeptic really is about. So I’m a skeptic.
Then again, I write about these thing for enjoyment. I may play around with a point and then drop it without a conclusion. Expect a certain amount of tongue-in-cheek. No aggressive sarcasm, though (I hope). I will ask inconvenient questions. I will ask both sides. I may carry things to the extremes and beyond (that’s what mathematics is all about). If I can’t prove a thing, I will say so. Feel free to stay unconvinced. In short, I won’t bother too much.

Now that was a long paragraph concerning a single topic for my blog. Don’t think it will dominate all the other topics. Well, see for yourself!

Have fun!