Articles

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    Information is sophistication

    Kolmogorov complexity gives a high value to strings of symbols that are essentially random. But isn't randomness essentially meaningless? Should a measure of information assign a low value to it? The concept of sophistication addresses this question.
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    Information is surprise

    If I tell you something you already know, then that's not very informative. So perhaps information should be measured in terms of unexpectedness, or surprise?

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    Information is complexity

    There are many ways of saying the same thing — you can use many words, or few. Perhaps information should be measured in terms of the shortest way of expressing it? In the 1960s this idea led to a measure of information called Kolmogorov complexity.
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    Information is noisy

    When you transmit information long-distance there is always a chance that some of it gets mangled and arrives at the other end corrupted. Luckily, there are clever ways of encoding information which ensure a tiny error rate, even when your communication channel is prone to errors.
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    Information is bits

    Computers represent information using bits — that's 0s and 1s. It turns out that Claude Shannon's entropy, a measure of information invented long before computers became mainstream, measures the minimal number of bits you need to encode a piece of information.
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    Quantifying Occam

    An idea called Occam's razor states that the simplest answer is always the best. But is this really true? Computer scientist Noson Yanofsky is trying to find out, applying Kolmogorov complexity to a branch of mathematics known as category theory.
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    Monsters, moonshine and shadows

    Rachel Thomas

    Monsters, moonshine and shadows sound like the ingredients for an excellent fairy tale. They are also part of a fascinating mathematical story that brings together some of our favourite things – number theory, group theory, string theory and even quantum gravity – as well as some of our favourite mathematicians.

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    Not just the ingredients for a fairy tale...

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    Folding fractions

    Folding a piece of paper in half might be easy, but what about into thirds, fifths, or thirteenths? Here is a simple and exact way for fold any fraction, all thanks to the maths of triangles.