The Creativity Code. Marcus du Sautoy

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      Eventually he spotted the mathematical rule behind the escalating prices. Divide the profnath price by the bordeebook price from the day before and you always got 0.99830. Divide the bordeebook price by the profnath book on the same day and you always got 1.27059. Each seller had programmed their website to use an algorithm that was setting the prices for books they were selling. Each day the profnath algorithm would check the price of the book at bordeebook and would then multiply it by 0.99830. This algorithm made perfect sense because the seller was programming the site to slightly undercut the competition at bordeebook. It is the algorithm at bordeebook that is slightly more curious. It was programmed to detect any price change in its rival and to multiply this new price by a factor of 1.27059.

      The combined effect was that each day the price would be multiplied by 0.99830 × 1.27059, or 1.26843. This ensured that the price would grow exponentially. If profnath had set a sharper factor to undercut the price being offered by bordee-book, you would have seen the price collapse over time rather than escalate.

      The explanation for profnath’s algorithm seems clear, but why was bordeebook’s algorithm set to offer the book at a higher price? Surely no one would buy the more expensive book? Perhaps they were relying on their bigger reputation with a greater number of positive recommendations to drive traffic their way, especially if their price was only slightly higher, which at the start it would have been. As Eisen wrote in his blog, ‘this seems like a fairly risky thing to rely on. Meanwhile you’ve got a book sitting on the shelf collecting dust. Unless, of course, you don’t actually have the book …’

      Then the truth suddenly dawned on him. Of course. They didn’t actually have the book! The algorithm was programmed to see what books were out there and to offer the same book at a slight markup. If someone wanted the book from their reliable bordeebook’s website, then bordeebook would go and purchase it from the other bookseller and sell it on. But to cover costs this would necessitate a bit of a markup. The algorithm thus multiplied the price by a factor of 1.27059 to cover the purchase of the book, the shipping and a little extra profit.

      Using a few logarithms it’s possible to work out that the book most likely first went on sale forty-five days before 8 April at about $40. This shows the power of exponential growth. It only took a month and a half for the price to reach into the millions! The price peaked at $23,698,655.93 (plus $3.99 shipping) on 18 April, when finally a human at profnath intervened, realising that something strange was going on. The price then dropped to $106.23. Predictably bordeebook’s algorithm offered their book at $106.23 × 1.27059 = $134.97.

      The mispricing of The Making of a Fly did not have a devastating impact for anyone involved, but there are more serious cases of algorithms used to price stock options causing flash crashes on the markets. The unintended consequences of algorithms is one of the prime sources of the existential fears people have about advancing technology. What if a company builds an algorithm that is tasked with maximising the collection of carbon, but it suddenly realises the humans who work in the factory are carbon-based organisms, so it starts harvesting the humans in the factory for carbon production? Who would stop it?

      Algorithms are based on mathematics. At some level they are mathematics in action. But they don’t really creatively stretch the field. No one in the mathematical community feels particularly threatened by them. We don’t really believe that algorithms will turn on their creators and put us out of a job. For years I believed that these algorithms would do no more than speed up the mundane part of my work. They were just more sophisticated versions of Babbage’s calculating machine that could be told to do the algebraic or numerical manipulations which would take me tedious hours to write out by hand. I always felt in control. But that is all about to change.

      Up till a few years ago it was felt that humans understood what their algorithms were doing and how they were doing it. Like Lovelace, they believed you couldn’t really get more out than you put in. But then a new sort of algorithm began to emerge, an algorithm that could adapt and change as it interacted with its data. After a while its programmer may not understand quite why it is making the choices it is. These programs were starting to produce surprises, and for once you could get more out than you put in. They were beginning to be more creative. These were the algorithms DeepMind exploited in its crushing of humanity in the game of Go. They ushered in the new age of machine learning.