The Creativity Code. Marcus du Sautoy

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      The trouble with modern Go is that conventions had built up about ways to play that had ensured players hit peak A. But by breaking those conventions AlphaGo had cleared the fog and revealed an even higher peak B. It’s even possible to measure the difference. In Go, a player using the conventions of peak A will in general lose by two stones to the player using the new strategies discovered by AlphaGo.

      This rewriting of the conventions of how to play Go has happened at a number of previous points in history. The most recent was the innovative game play introduced by the legendary Go Seigen in the 1930s. His experimentation with ways of playing the opening moves revolutionised the way the game is played. But Go players now recognise that AlphaGo might well have launched an even greater revolution.

      The Chinese Go champion Ke Jie recognises that we are in a new era: ‘Humanity has played Go for thousands of years, and yet, as AI has shown us, we have not yet even scratched the surface. The union of human and computer players will usher in a new era.’

      Ke Jie’s compatriot Gu Li, winner of the most Go world titles, added: ‘Together, humans and AI will soon uncover the deeper mysteries of Go.’ Hassabis compares the algorithm to the Hubble telescope. This illustrates the way many view this new AI. It is a tool for exploring deeper, further, wider than ever before. It is not meant to replace human creativity but to augment it.

      And yet there is something that I find quite depressing about this moment. It feels almost pointless to want to aspire to be the world champion at Go when you know there is a machine that you will never be able to beat. Professional Go players have tried to put a brave face on it, talking about the extra creativity that it has unleashed in their own play, but there is something quite soul-destroying about knowing that we are now second best to the machine. Sure, the machine was programmed by humans, but that doesn’t really seem to make it feel better.

      AlphaGo has since retired from competitive play. The Go team at DeepMind has been disbanded. Hassabis proved his Cambridge lecturer wrong. DeepMind has now set its sights on other goals: health care, climate change, energy efficiency, speech recognition and generation, computer vision. It’s all getting very serious.

      Given that Go was always my shield against computers doing mathematics, was my own subject next in DeepMind’s cross hairs? To truly judge the potential of this new AI we are going to need to look more closely at how it works and dig around inside. The crazy thing is that the tools DeepMind is using to create the programs that might put me out of a job are precisely the ones that mathematicians have created over the centuries. Is this mathematical Frankenstein’s monster about to turn on its creator?

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       ALGORITHMS, THE SECRET TO MODERN LIFE

       The Analytical Engine weaves algebraic patterns, just as the Jacquard loom weaves flowers and leaves.

      Ada Lovelace

      Our lives are completely run by algorithms. Every time we search for something on the internet, plan a journey with our GPS, choose a movie recommended by Netflix or pick a date online, we are being guided by an algorithm. Algorithms are steering us through the digital age, yet few people realise that they predate the computer by thousands of years and go to the heart of what mathematics is all about.

      The birth of mathematics in Ancient Greece coincides with the development of one of the very first algorithms. In Euclid’s Elements, alongside the proof that there are infinitely many prime numbers, we find a recipe that, if followed step by step, solves the following problem: given two numbers, find the largest number that divides them both.

      It may help to put the problem in more visual terms. Imagine that the floor of your kitchen is 36 feet long by 15 feet wide. You want to know the largest square tile that will enable you to cover the entire floor without cutting any tiles. So what should you do? Here is the 2000-year-old algorithm that solves the problem:

      Suppose you have two numbers, M and N (and suppose N is smaller than M). Start by dividing M by N and call the remainder N₁. If N₁ is zero, then N is the largest number that divides them both. If N₁ is not zero, then divide N by N₁ and call the remainder N₂. If N₂ is zero, then N₁ is the largest number that divides M and N. If N₂ is not zero, then do the same thing again. Divide N₁ by N₂ and call the remainder N₃. These remainders are getting smaller and smaller and are whole numbers, so at some point one must hit zero. When it does, the algorithm guarantees that the previous remainder is the largest number that divides both M and N. This number is known as the highest common factor or greatest common divisor.

      Now let’s return to our challenge of tiling the kitchen floor. First we find the largest square tile that will fit inside the original shape. Then we look for the largest square tile that will fit inside the remaining part – and so on, until you hit a square tile that finally covers the remaining space evenly. This is the largest square tile that will enable you to cover the entire floor without cutting any tiles.

      If M = 36 and N = 15, then dividing N into M gives you a remainder of N₁ = 6. Dividing N₁ into N we get a remainder of N₂ = 3. But now dividing N₁ by N₂ we get no remainder at all, so we know that 3 is the largest number that can divide both 36 and 15.

      You see that there are lots of ‘if …, then …’ clauses in this process. That is typical of an algorithm and is what makes algorithms so perfect for coding and computers. Euclid’s ancient recipe gets to the heart of four key characteristics any algorithm should ideally possess:

       1. It should consist of a precisely stated and unambiguous set of instructions.

       2. The procedure should always finish, regardless of the numbers you insert. (It should not enter an infinite loop!)

       3. It should give the answer for any values input into the algorithm.

       4. Ideally it should be fast.

      In the case of Euclid’s algorithm, there is no ambiguity at any stage. Because the remainder grows smaller at every step, after a finite number of steps it must hit zero, at which point the algorithm stops and spits out the answer. The bigger the numbers, the longer the algorithm will take, but it’s still proportionally fast. (The number of steps is five times the number of digits in the smaller of the two numbers, for those who are curious.)

      If СКАЧАТЬ