![]() ![]() For a lot of examples of spurious correlations see this website. For example they can lead to false accusations and even to false convictions. This phenomenon can actually be quite dangerous, when spurious correlations are found in data to prove a point. As an example look at this BBC News article reporting on a "warrior queen" having been observed in a cloud pattern. Sooner or later you will find a cloud, which fits some novel pattern. ![]() A good way to see this is to go outside on a nice sunny day and look at the clouds. Indeed given enough data it is possible to find patterns that agree with almost any hypothesis. Also remember that as the golden ratio is an irrational number (see below) you will never see it exactly in any measurement.Īll of this is an example of the way that the human brain finds spurious correlations. Similar spurious patterns are also observed in the solar system (which also has lots of different ratios that you can choose from). Indeed most numbers between 1 and 2 will have two parts of the body approximating them in ratio. If you look hard enough you will also find proportions in the human body close to 1.6, 5/3, 3/2, the square root of 2, 42/26, etc, etc. This is especially true if the things that you are measuring are not particularly well-defined (as in the picture on the left) and it is possible to vary the definition in such a way as to get the proportions that you want to find. If you consider enough of them then you are bound to get numbers close to the value of the golden ratio (around 1.618). The body has many possible ratios, lots of which lie somewhere between 1 and 2. However, none of this is true, not even remotely. You can superimpose all sorts of rectangles on a beautiful face and then claim that beauty derives from the proportions of the rectangle. You'd like to divide it in such a way that the ratio between the whole segment and the longer of the two pieces is the same as the ratio between the longer of the two pieces and the shorter one. Imagine you have a line segment which you would like to divide into two pieces. It was defined by the ancient Greek mathematician Euclid as follows. Let's start by quickly recalling what the golden ratio actually is. Yes, twice! So are any of these great claims made for the golden ratio true? What's the golden ratio again? Yet in my whole career of applying mathematics to the real world I have come across the golden ratio exactly twice. ![]() It has also been claimed that the golden ratio appears in the human body, for example as the ratio of the height of an adult to the height of their navel, or of the length of the forearm to that of the hand. For example it is claimed that both the Parthenon and the pyramids are in this proportion. It is claimed that much of art and architecture contains features in proportions given by the golden ratio. It has been described by many authors (including the writer of the da Vinci Code) as the basis of all of the beautiful patterns in nature and it is sometimes referred to as the divine proportion. It appears, for example, in the book/film The da Vinci Code and in many articles, books, and school projects, which aim to show how mathematics is important in the real world. Most of you will have heard about the number called the golden ratio. This article is based on a talk in an ongoing GreshamĬollege lecture series. ![]()
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