Plus Blog

December 4, 2012

Maths is now an integral part in the study of evolution, describing how mutation and natural selection affect a reproducing population. And now maths has shown that it if you want to get ahead in the evolutionary race, it really does pay to be nice. We were lucky enough to visit the other Cambridge earlier this year to interview Professor Martin Nowak about the mathematics of altruism.

Does it pay to be nice? – the maths of altruism part i — Does it pay to be nice? Yes, it does. And we're not just talking about that warm fuzzy feeling inside, it pays in evolutionary terms of genetic success too. We talk to Martin Nowak about how the mathematics of evolution prove that being nice is unavoidable.


Does it pay to be nice? – the maths of altruism part ii — It does pay to be nice if you repeatedly deal with the same person. Martin Nowak explains why cooperation also wins in matters of reputation, neighbourliness and family. But can evolutionary game theory save the world?


Does it pay to be clever? — Why are we so clever? In evolutionary terms this isn't obvious: evolution tends to favour cheap solutions and the human brain is expensive. It consumes about 20% of our body's energy budget yet it only makes up 2% of our body mass. So why did it make evolutionary sense for us humans to develop powerful brains? Game theory provides a possible answer.



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December 3, 2012

As we are having a little cake of our own today, we thought we'd look back on another great birthday celebration... Stephen Hawking turned 70 in January 2012 and to celebrate, the University of Cambridge put on a scientific conference as well as a public symposium. Plus went along, of course, and here are the articles and podcasts we have produced from the conferences. Happy reading and listening!

A brief history of mine — This is an excerpt from Stephen Hawking's address to his 70th birthday symposium which took place on 8th January 2011 in Cambridge.


From planets to universes — This is an article version of the lecture given by Astronomer Royal Martin Rees at Stephen Hawking's birthday symposium. It comes in two parts, the first is here and the second here.


Happy birthday Stephen Hawking! — This is our brief report from Stephen Hawking's birthday symposium, which comes with a podcast featuring Martin Rees, some of Hawking's ex-students and his graduate assistant.


Supergravity to the rescue? — In the corner of the garden between the Centre of Mathematical Sciences and the Isaac Newton Institute in Cambridge, sits a reminder of our ongoing quest to understand gravity: an apple tree that was taken as a cutting from the tree at Newton's birthplace, the tree that is said to have inspired his theory of gravity. Newton's theory was extended to the cosmological scales by Einstein's theory of general relativity – but can supergravity explain how gravity works in the quantum world? Find out in this interview with Renata Kallosh, which you can also hear as a podcast.


Bang, crunch, freeze and the multiverse — Some of the things we overheard at Stephen Hawking's 70th birthday conference did make us wonder whether I hadn't got the wrong building and stumbled in on a sci-fi convention. "The state of the multiverse". "The Universe is simple but strange". "The future for intelligent life is potentially infinite". And — excuse me — "the Big Bang was just the decay of our parent vacuum"?! You can also listen to the accompanying podcast.


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December 2, 2012

Here at Plus we love everything Vi Hart produces. But her recent series on hexaflexagons (suggested by our good friend Sharon) is superb! In addition to the history of these mathemagical objects and how to make them (part 1 and part 2) there's a hilarious Hexaflexagon Safety Guide and our favourite, Tex Mex Hexaflexagons! Enjoy!


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December 1, 2012

Are you reading this page because you decided to or because you were destined to from the start of time? Plus shares Mick's sentiment that we are free to do what we want, any old time. But what does physics and mathematics have to say about free will? In one of our most mind-bending yet enjoyable investigations (published in January this year), we spoke to philosopher of physics Jeremy Butterfield, quantum physicist Anton Zeilinger, cosmologist and mathematician George Ellis and mathematician John Conway to find out more.


Freedom and physics — Most of us think that we have the capacity to act freely. Our sense of morality, our legal system, our whole culture is based on the idea that there is such a thing as free will. It's embarrassing then that classical physics seems to tell a different story. And what does quantum theory have to say about free will?


Free, from top to bottom? — A traditional view of science holds that every system — including ourselves — is no more than the sum of its parts. To understand it, all you have to do is take it apart and see what's happening to the smallest constituents. But the mathematician and cosmologist George Ellis disagrees. He believes that complexity can arise from simple components and physical effects can have non-physical causes, opening a door for our free will to make a difference in a physical world.


John Conway: discovering free will (part I) — On August 19, 2004, John Conway was standing with his friend Simon Kochen at the blackboard in Kochen’s office in Princeton. They had been trying to understand a thought experiment involving quantum physics and relativity. What they discovered, and how they described it, created one of the most controversial theorems of their careers: The Free Will Theorem.


John Conway: discovering free will (part II) — In this, the second part of our interview, John Conway explains how the Kochen-Specker Theorem from 1965 not only seemed to explain the EPR Paradox, it also provided the first hint of Conway and Kochen's Free Will Theorem.


John Conway: discovering free will (part III) — In the third part of our interview John Conway continues to explain the Free Will Theorem and how it has changed his perception of the Universe.


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November 15, 2012

Make your childhood dreams come true and join the Paris Fire Brigade as part of the 2012-13 Mathematical Competitive Game. This year's game is brought to you by the French Federation of Mathematical Games, Société de Calcul Mathématique SA as well as The Paris Firemen Brigade and is open to anyone to enter either individually or in groups.

Siberia

The previous games have also all been based on real life problems – designing a bus or electricity network or searching for the best car itinerary in partnership with transport or electricity companies – and solving them usually takes several months of work.

This year's game is to decide how best to use your limited resources of firefighters and equipment to fight fires and minimise their damage across the whole of Siberia. This huge region is broken up into cells defined by latitude and longitude, so these vary in size as well as the their level of population and landscape. There are mathematical descriptions of the ways the fires start, spread and the damage they cause as well as for modelling your firefighting capacities and the way they can combat the fires. Your job is to decide how to distribute your firefighters and specially equipped planes and then estimate the cost from damage from the fires in one summer, the cost of your firefighting strategy and the probability that your strategy to keep costs to this level will work.

And there's not only mathematical glory and the gratitude of Siberia on offer, there's also up to 500 Euros in prizes for the winners. You can find the details of this year's competition here and download the data. Good luck!

To get you thinking about how you can mathematically model fires, read our article Matrix: Simulating the world Part II about simulating the spread of forest fires using cellular automata.. The example below has either bare earth (grey squares) or trees (green squares), with squares turning green as new trees grow. Tree's catch fire (and their squares turn orange) as a result of lightning strike and the fire spreads to all adjoining squares with trees.

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October 31, 2012
The Lie group E8

This is a visual representation of the Lie group E8, which encodes the symmetries of a 57-dimensional geometrical object. Find out more here. Image: Claudio Rocchini.

Tomorrow, 1st November 2012 at 4pm GMT, Plus will be part of a MOOC (massive open online course)! For an hour we will be talking about the beautiful subject of symmetry in a way that is accessible to everyone and there will be questions and answers too. This online talk is open to everyone and it's free. To join, register here.

We will explore a range of symmetry topics, from the beautiful patterns in the Alhambra to mathematical group theory and symmetry breaking in physics.

This talk is part of a whole series called VizMath which explores the many images of maths, from crocheted hyperbolic curves to the mathematics of origami. VizMath was created by Betty Hurley-Dasgupta and Carol Yeager and it's published by SUNY/Empire State College, USA.

Come and join us!

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