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 🙂