What the Da Vinci Code and the Bible have in common

After holding out for a long time, I finally went out and read The Da Vinci Code. I'm generally too busy doing other stuff to read a lot of books, but I guess I was specifically holding out on this because I figured that with so much hype around it, it couldn't be any good. (Call me a snob if you will, but this philosophy has worked well in the past - for example just look at Britney Spears or Independence Day). But when they started promoting the movie it all became pretty unavoidable, and I figured I should read the book first. So I did - and I actually found it to be very good - certainly not the best book ever written, but highly enjoyable and very addictive.

Of course most of the hype and controversy around the book has involved comparisons between the "facts" it presents, with those in that other notable work of fiction. I'm neither informed enough nor interested enough to partake in that debate (and there appear to be more than enough people involved already). But as I was reading The Da Vinci Code I did notice one obvious inaccuracy - no it wasn't about art or architecture or religion, but mathematics - specifically the value of the Golden Ratio (aka φ or phi). Dan Brown states quite unambiguously that φ is equal to 1.618 - not approximately equal to, but exactly. 1.618 isn't a bad approximation, but the true value is actually (1 + √5)/2, which is irrational and hence can't accurately be represented as a decimal number using a finite number of digits. (It's actually very simple to prove the value of φ - a rectangle whose sides match the Golden Ratio has the property where if you were to mark off a square the size of the rectangle's shorter side, the remaining space also has sides that match the Golden Ratio. A simple application of the quadratic equation will give you the true value of φ).

But really, who cares? Probably not many people - but the irrationality of φ is actually one of its more interesting properties. In Charles Seife's enjoyable book Zero - The Biography of a Dangerous Idea he describes how the ancient Greeks were convinced the world was governed by ratios - and that every conceivable number was rational. They were also very big on the Golden Ratio, due to its many intriguing properties and its relevance to art, architecture and nature, as well as in mathematics. So the eventual discovery that φ was indeed irrational came as more than just a shock - in fact according to Zero the man who revealed this fact to the world was murdered by Pythagoras's cronies for forever ruining the beautiful, rational world.

But what's all this got to do with the Bible? As far as I'm aware there is no mention of the Golden Ratio (although I'll admit that I've read very little of it). However the Bible does indirectly refer to an even more famous irrational number, π, in 1 Kings 7:23:

And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about.

We all know that the circumference is equal to π multiplied by the diameter. So if the circumference is 30, and the diameter is 10, that means that π must be exactly 3. This is even less accurate than Dan Brown's value for φ - but both works commit the same crime of falsely representing irrational numbers as rational ones.

So what's the moral of my story? It's a good thing to read, to enjoy, and sometimes, to believe. But question everything, because truth is generally a matter of perspective and can rarely be proven (unless of course you constrain the universe to one governed by unambiguous axioms, as is the case in mathematics!). And for those of you about to post comments that point out flaws in my reasoning or facts, that just reinforces my point 🙂

Comments (6)
  1. Protagonist says:

    There is no reason to conclude that the writers were guilty of serious error. Jeremiah, who wrote First Kings, and Ezra, who penned Second Chronicles, were reliable men who wrote these accounts under divine inspiration.

    Persons who insist on scrupulous accuracy and consider the Bible to be in error in giving the measurements of the molten sea would do well to realize that, to be more accurate themselves, it would be appropriate to carry pi to at least eight decimal places, which would be 3.14159265, though even a figure in excess of 3.1415926535 could be used.

    Bible commentator Christopher Wordsworth quotes a certain Rennie, who made this interesting observation regarding the measurements of the molten sea: “Up to the time of Archimedes [third century B.C.E.], the circumference of a circle was always measured in straight lines by the radius; and Hiram would naturally describe the sea as thirty cubits round, measuring it, as was then invariably the practice, by its radius, or semidiameter, of five cubits, which being applied six times round the perimeter, or ‘brim,’ would give the thirty cubits stated. There was evidently no intention in the passage but to give the dimensions of the Sea, in the usual language that every one would understand, measuring the circumference in the way in which all skilled workers, like Hiram, did measure circles at that time. He, of course, must however have known perfectly well, that as the polygonal hexagon thus inscribed by the radius was thirty cubits, the actual curved circumference would be somewhat more.”

    According to 1 Kings 7:23 and 2 Chronicles 4:2, the molten sea was ten cubits, or fifteen feet, in diameter and it took a line of thirty cubits, or forty-five feet, to encompass it. That is a ratio of one to three, which, for practical purposes, was quite adequate for the sake of a record. Jeremiah and Ezra, therefore, gave approximate figures, which, of course, satisfy thoughtful Bible students.

  2. Olaf Conijn says:

    @Tom: amen!

  3. Erik says:

    This is why I am a programmer.  Because I think like this.  The excerpt below is taken from a programmer’s blog.  I have found that in general the very good programmers I’ve met tend to have this same curiosity and skepticism of the mystical.  The computer is not a mystery.  It operates the way it does for historical reasons.  Same with life if you look closely.

    I don’t know the significance of the Golden Ratio in Dan Brown’s book as I haven’t read it.  But, having read Richard Feynman’s essays on our Unscientific Time, I can imagine the wild explanations and conspiracies these mystical writers can extract from numbers due to their ignorance of mathematics and physics.  (Or due to their audience’s ignorance plus their greed and lack of scruples.)  The occultist abhors math and physics.

    I find the geometric explanation of the Golden Ratio fascinating.  It explains how the human desire for symmetry (rooted in all likelihood to our love of the symmetrical human body) compelled man to construct shapes who’s symmetry extended infinitely.  Divide the shape and find more occurrences of the symmetry ad inifinitum.

    It’s fascinating, it makes sense, and it requires no greater explanation.  And yet millions if not billions of our brethren go through life spooked by divine interpretations of this and other natural phenomena.  Fear of the mysterious ways of computers or the motions of the planets comes from this same lack of intellectual curiosity and a willingness, or preference, to be governed by those who give the most fearful explanations.

  4. Travis says:

    I read the post title in my feed reader and expected something much more controversial than this! Nicely played 🙂

  5. Mike Liddell says:

    I first read it when it was little known and I was blown away…until I did some research and found out most of the ‘facts’ were fabrications .  I have rarely felt so cheated.  The real story around the priory of scion is fascinating in its own right (ie total fabrication), and could have been the basis of an interesting story.  Opus Dei, however, does appear to have some mystery surrounding it – although a religion/society that targets the rich and powerful is nothing new.  

    I recently re-read the book, also inspired by the hype around the movie to see what I thought the second time around:

    My biggest complaints are:

    1. the controversial descriptions of art works are tenuous at best, and in general totally misleading.  I had a large book of da vinci art to hand this time and could not agree on any of Dan Browns interpretations.  I thought it was very cheap to use these conspiricies as major plot elements without reproducing the images for readers to view.  

    2. the writing is apalling.  sure, the story captivates like a paper version of _24_, but the literature content is zero.

    3. the narrative is a suprisingly thin veil for ‘let me tell you some cool conspiricy theories’.  

    re phi – Of course it should be explained better, but the maths is aimed at a low grade school audience.  I expect most lay people to think phi=1.6 and pi=3.14, and it doesn’t cause anyone difficulty.

  6. va says:

    They both are red

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