Misconceptions About the Universe

The expanding universe is a complicated place. During inflation the universe expanded faster than light, but that's something that actually happens all the time, it's happening right now. This doesn't violate Einstein's theory of relativity since nothing is moving through space faster than light, it's just that space itself is expanding such that far away objects are receding rapidly from each other. Common sense would dictate that objects moving away from us faster than light should be invisible, but they aren't. This is because light can travel from regions of space which are superluminal relative to us into regions that are subluminal. So our observable universe is bigger than our Hubble sphere - it's limited by the particle horizon, the distance light could travel to us since the beginning of time as we know it.

2014 • Astronomy

Part 2

Mathematical formulas can be found in the arrangement of seeds on a sunflower, the structure of the spirals in the shells of certain marine animals, and the distribution of leaves around a plant stem. These formulas recur in nature from snowflakes to the stripes on a zebra.

Nature's Mathematics • 2017 • Math

To Infinity and Beyond

By our third year, most of us will have learned to count. Once we know how, it seems as if there would be nothing to stop us counting forever. But, while infinity might seem like an perfectly innocent idea, keep counting and you enter a paradoxical world where nothing is as it seems.

The Joy of Data

A witty and mind-expanding exploration of data, with mathematician Dr Hannah Fry. This high-tech romp reveals what data is and how it is captured, stored, shared and made sense of. Fry tells the story of the engineers of the data age, people most of us have never heard of despite the fact they brought about a technological and philosophical revolution. For Hannah, the joy of data is all about spotting patterns. Hannah sees data as the essential bridge between two universes - the tangible, messy world that we see and the clean, ordered world of maths, where everything can be captured beautifully with equations. The film reveals the connection between Scrabble scores and online movie streaming, explains why a herd of dairy cows are wearing pedometers, and uncovers the network map of Wikipedia. What's the mystery link between marmalade and One Direction? The film hails the contribution of Claude Shannon, the mathematician and electrical engineer who, in an attempt to solve the problem of noisy telephone lines, devised a way to digitise all information. Shannon singlehandedly launched the 'information age'. Meanwhile, Britain's National Physical Laboratory hosts a race between its young apprentices in order to demonstrate how and why data moves quickly around modern data networks. It's all thanks to the brilliant technique first invented there in the 1960s by Welshman Donald Davies - packet switching. But what of the future? Should we be worried by the pace of change and what our own data could be used for? Ultimately, Fry concludes, data has empowered all of us. We must have machines at our side if we're to find patterns in the modern-day data deluge. But, Fry believes, regardless of AI and machine learning, it will always take us to find the meaning in them.

2016 • Math

The last banana: A thought experiment in probability

Imagine a game of dice: if the biggest number rolled is one, two, three, or four, player 1 wins. If the biggest number rolled is five or six, player 2 wins. Who has the best probability of winning the game? Leonardo Barichello explains how probability holds the answer to this seemingly counterintuitive puzzle.

Tails You Win: The Science of Chance

Professor David Spiegelhalter tries to pin down what chance is and how it works in the real world. A blend of wit and wisdom, animation, graphics and gleeful nerdery is applied to the joys of chance and the mysteries of probability, the vital branch of mathematics that gives us a handle on what might happen in the future. How can you maximise your chances of living till you're 100? Why do many of us experience so many spooky coincidences? Should I take an umbrella? These are just some of the everyday questions the film tackles as it moves between Cambridge, Las Vegas, San Francisco and Reading. Spiegelhalter discovers One Million Random Digits, a book full of hidden patterns and shapes, introduces us to the unit called the micromort (a one-in-a-million chance of dying), and uses the latest infographics to demonstrate how life expectancy has increased in his lifetime and how it is affected by our lifestyle choices - drinking, obesity, smoking and exercise.

2012 • Math

What is Zeno's Dichotomy Paradox?

Can you ever travel from one place to another? Ancient Greek philosopher Zeno of Elea gave a convincing argument that all motion is impossible - but where's the flaw in his logic? Colm Kelleher illustrates how to resolve Zeno's Dichotomy Paradox.