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# Review of The Code

In reviewing The Code I should note that this is a TV programme not aimed at me. Nonetheless as a mathematician I do like to see the portrayal of my subject in the number one mass medium. Actually, I’m unsure who the target audience is. At one point pi is introduced slowly over a number of minutes which would indicate that the producers thought that even the most basic ideas could not be assumed.

Leaving that minor criticism aside (after all it’s a problem with TV output rather than a specific fault of this programme), what was the programme like? What’s it about? Well, the intro said that it was about answering the question Why is the world the way it is? The precise definition of ‘The Code’ was a bit obscure but we all know they’re talking about maths.

The programme began with Marcus du Sautoy pacing around a cathedral at night with an echoing voiceover from a girl. We had fancy graphics, moody lighting, long shadows, strange camera angles and occasional uses of black and white. Hidden in the cathedral was a code, said du Sautoy, and then showed how mathematics showed up in its design. In particular the relation with harmonious combinations of notes. For example the altar divides the nave into a ratio of 8 to 5 which is a minor sixth in music.

This episode was about numbers, so primes, pi, i, acceleration due to gravity and a constant associated with a nautilus shell were explored. See the video below for a clip about this last constant.

To exemplify the appearance of pi the normal distribution was used. Unfortunately, the idea was to get the daily catch from a fisherman and weigh the fishes. From the mean and variance of this catch it is possible to estimate the largest fish the fisherman had caught in his 40 years of fishing the English channel. Marcus du Sautoy estimated 3 pounds as the largest. The fisherman said 3 to 3 and half pounds so the estimate was a bit out as it was at the lower end. Of course why anyone in the production team thought that a fisherman – known as a group for exaggerating – would give a realistic value for the largest fish is a mystery so Marcus’ calculation was probably right.

In addition to fishes and nautilus shells the programme featured cicadas, frequency analysis, psychological aspects of sounds, stone circles, air traffic control, some nice shots of the Alps and the night sky, and a trebuchet throwing a flaming ball. I liked that last bit, if only I could do it in my class, instead I have to make do with children’s toys.

Overall the programme is a slow and gentle walk through a part of mathematics. It ends with more moody night time shooting and spooky voiceovers. The central topic was numbers, which are not my thing – as a geometer I am interested in seeing next week’s programme on shapes.

Can you explain a detail of this programme, please? In the clip on the nautilus, Sautoy gives the ratio as 1.08, yet all the literature I’ve consulted seems to indicate that the nautilus, fern fronds, sunflowers, etc obey (fairly closely) the ‘golden ratio’ of 1.618, or phi. Why was he getting a different ratio?

Good point. When watching du Sautoy write down the figures I expected the golden ratio to appear but I could see as the list developed that the ratios were close to 1 to 1. Indeed as we saw the ratio was 1.08. He was measuring the “dimensions of the chambers” and what this means is not precise, probably deliberately so. I think that the point was that he was showing that there is hidden ratio. In order to get the golden ratio from a nautilus shell he would have had to

1. explain the golden ratio and

2. explain the method of taking the measurements.

Taking these in turn:

1. You saw how long it took to explain pi so phi would have taken even longer. There is a limit to what can go into a programme.

2. The object to measure to get the golden ratio is:

I got this from http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html#spiral.

Now if you measure something else, eg, the “dimensions of the chambers”, then it is unlikely that you will get the golden ratio but you should get

aconstant ratio.On the other hand it could be a myth that nautilus shells produce the golden ratio! I’ve never conducted the experiment or rigorously checked the theoretical working…

Also related to this program i was very interested in how the pi distribution bit worked and was hoping he would show the calculations involved, but alas this was missing. On searching online for a clue all i have found are some rather confusing graphs, could u please explain how that worked and how he calculated the biggest fish caught? thank you

I think what he did was work out the mean and standard deviation of the fisherman’s catch that day. These will approximate the mean and standard deviation of the true fish population. Let m be the mean and s be the standard deviation. Then it is likely that 95% of the fishes are less than m+2s in size. It is likely that 99.7% of them are less than m+3s. I guess Marcus calculated m+3s and that was the figure he used. See the Wikipedia page on the 68-95-99.7 rule .

The point is that if you know the mean and standard deviation of a population, then the biggest in the population will be around m+3s. Note that we as users of the theory don’t use the value of pi in this calculation. However, the people who created the theory for us needed pi when working out that 99.7% of the population are less than m+3s in size.

Does that explain the calculation?

Thank you Kevin. Please confirm if i’m understanding it right: Pi shows up in the normal distribution (outside the exponential) as a factor to make sure the area under the curve is 1. In this particular case MdS calculates the standard deviation and mean from the fish samples, as PI is not used at all to get to the mean + 3*stdev value (that would have 99.97% of the values covered).

Dear Dave,

Yes, that’s right. It is also explained at https://www.mathsisfun.com/data/standard-normal-distribution.html

Kevin

The fish example is WRONG! I am surprised that such a mistake ever made it on tv, especially with a statistician narrating.

A population of fish is NOT normally distributed!!! Within a single age class, it can be assumed that a normal distribution describes their lengths. However, fish populations (all wild populations) experience mortality, which means that there are many more small (young) fish than large (old) fish (data are heavily skewed right). The maximum size can be calculated using the Von Bertelanffy growth equation, which requires additional knowledge about growth rates. Average length can be calculated by estimating mortality, and weighting age classes proportional to abundance.

It is so long since this has been on TV I don’t really recall where the discussion fits in! However, I believe you are right. Another example is when discussing average height amongst people we need to talk about average _adult_ size (for male and female).

Kevin