Coats, Shopping and Algorithms: Mathematics in the Everyday World Kieran Kejiou

We do so love American things, here in good old Blighty. Doritos, Clifford the Big Red Dog, poptarts, trick or treating…Black Friday, however, was accepted more slowly by the tea-drinking populace of this tiny island nation. Perhaps it’s the ominous-sounding name – ‘Black’ often precedes bad things, making them sound a tad frightening and a potential threat to our stiff upper lip.

The Fine Art of Queuing

Nevertheless, I have to admit that I am greatly looking forward to the retail discounts coming on 23rd November. True, the sea of people crashing into John Lewis will be brutal, but it provides a wonderful opportunity to practice the fine art queuing. Yes, the stress of this entire affair will be intense, yet this only means I can turn to my dependence on tea to calm me down in the aftermath.

The last time Black Friday fell on the 23rd was in 2007 – I was quite a young child then. Around this time, my school was inexplicably visited by a fellow who had claimed to have played a “rigour deer” on TV. I began watching this mysterious ‘Doctor Who’ in April, failing to identify any deer (rigorous or otherwise), but realising that I rather liked this programme. In fact, I liked it so much that I vowed to get myself a great, long coat – like that worn by Captain Jack or like the Doctor’s. I wanted to emulate both. At the same time. Despite their being completely different coats…

Eleven years on – with the word ‘brigadier’ firmly included in my vocabulary – I’m still searching for my long coat. There have been a couple of contenders, but none that quite billowed out behind me with the aplomb of the ‘hero coats’ that John Barrowman had described all those years ago. But this Black Friday falls on the 55th Anniversary of Doctor Who’s first episode. The universe is calling. This is my time.

It will also be time to don my lesser coats as armour, to charge out into the winter maw of Cambridge’s high street. How will I ensure, after such an ordeal, that this coat is the true heir to my childhood dream, and not another pretender?

With mathematics, of course!

Doctor Who has helpfully provided me with several coats for reference – there have been 847 episodes of the show, and counting. To narrow the field, I have arbitrarily limited the pool to coats featured in the show that I, as an individual, would actually want to wear. Sadly, this meant ruling out the Thirteenth Doctor’s coat due to the cut of the garment being designed for a female figure – hardly flattering for my centrally rotund physique!

Thus, the included coats were: the two worn by the Eighth Doctor; the Fourth Doctor’s brown and grey coats; Twelve’s two sartorial affairs; Ten’s overrated, yet iconic overcoat; Jack Harkness’ military masterpiece; the two full-length coats worn by Matt Smith’s Doctor; and the coats of the Fifth, Sixth and War Doctors.

To begin, I applied the Shuttle Sort algorithm to the list of coats – comparing each coat to every other coat in turn to produce a ranked list of coats in order of coolness. Naturally, this required extensive research to view these garments in action.

(Editor’s Note: the author failed to submit this article by the initial deadline because he spent two weeks watching Doctor Who.)

Ahem. With a final ranking obtained, I then went through the coats and identified factors that led me to place each coat in their final position. These were, in order of importance:

  • Length
  • Lapel shape
  • Colour
  • Double-breasted vs single
  • Material
  • Lapel contrast
  • Button contrast

 

For each factor, I devised a scoring system and combined all the variables into the following equation:

However, that equation did not adequately explain why I enjoyed Tom Baker’s long, brown coat more than Capaldi’s gorgeous velvet piece. Nor did it account for the shape of the lapels – which was a deciding factor in ranking Eight’s Time War coat above Matt Smith’s superiorly coloured burgundy one.

So, I fiddled with the equation so that the influence of the variables made more sense, given my decisions in the ranking. I measured ‘influence’ by calculating the minimum possible Heroicness score, then dialling up a certain variable, like colour, to its maximum value while keeping everything else at their minimum and noting that Heroicness score down. The difference between those Heroicness scores was a crude measure of the ‘influence’ of that variable – I repeated for the other variables to compare and check that my fiddling was actually changing the influence!

The new equation, after about 6 alterations was:

An H-Score of 0.98 corresponds to Jack Harkness’ coat. Which is a very, very cool coat.

Using this equation, I calculated a Heroicness score, or H-score, for each coat. Remarkably, the scores corresponded rather well to my initial rankings. The coats whose rankings the equation failed to predict were some interesting outliers. For example, it’s difficult to quantify just how garish the colour scheme is on the Sixth Doctor’s coat! And I still have no idea why I hate Eleven’s green coat so much…

The Perfect Doctor Who Coat

Anyway, the model works well enough for my purposes so I’ll just run with it for now. An H-Score of 0.98 corresponds to Jack Harkness’ coat. Which is a very, very cool coat. Therefore, I shall use that as my cut-off point when I assess potential purchases.

Isn’t maths useful? I can now ask a shop assistant for a coat with an H-score of above 0.98! Of course, I will have to get this nonsense published in some reputable academic journal and then the news before that request will ever make any sense to that poor member of staff…

Even the most inane and ridiculous things can be clarified with maths, from the heroicness of coats to the dreams of a goldfish. Sadly, after that Doctor Who marathon and the needlessly complex equation, I forgot to account for the state of my bank account. Pity. The next time Black Friday falls on the 23rd, I’ll be ready!

ENROL NOW