Articles

Maths in a minute: Local connectivityHow crinkly is crinkly?

Slow down, Universe!The Universe's expansion may not be accelerating as fast as we thought.

The future of proofWill computers ever replace human mathematicians?

Why we want proofWhat are mathematical proofs, why do we need them and what can they say about sheep?

Sexual statisticsDavid Spiegelhalter's new book Sex by numbers takes a statistical peek into the nation's bedrooms. In this interview he tells us some of his favourite stories from the book. Read the article or watch the video!

Information: Baby stepsIf I tell you that it's Monday today, then you know it's not any of the other six days of the week. Perhaps the information content of my statement should be measured in terms of the number of all the other possibilities it excludes? Back in the 1920s this consideration led to a very simple formula to measure information.

Information is sophisticationKolmogorov 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.

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?

Information is complexityThere 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.

Information is noisyWhen 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.

Information is bitsComputers 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.

Quantifying OccamAn 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.