insight from a rubik's cube

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16 August 2014 | NewScientist | 25 For more opinion articles, visit newscientist.com/opinion well what is happening but “enter into unwritten agreements about what can be publicly remembered and acknowledged”. Our response to climate change is uncannily similar to an even more universal disavowal: unwillingness to face our own mortality, says neuroscientist Janis Dickinson of Cornell University in New York. She argues that overt images of death and decay along with the deeper implications of societal decline and collapse are powerful triggers for denial of mortality. There is a great deal of research showing that people respond to reminders of death with aggressive assertion of their own group identity. Dickinson argues that political polarisation and angry denial found around climate change is consistent with this “terror management theory”. Again, there is a complex relationship between our psychology and the narratives that we construct to make sense of climate change. For all of these reasons, it is a mistake to assume that the scientific evidence of climate change will flow directly into action – or, conversely, that climate denial can be dismissed as mere misinformation. The systems that govern our attitudes are just as complex as those that govern energy and carbon, and just as subject to feedbacks that exaggerate small differences between people. The problem itself is far from perfect and the situation is not hopeless, but dealing with it will require a more sophisticated analysis of human cognition and the role of socially shared values in building conviction. n George Marshall is the author of Don’t Even Think About It: Why our brains are wired to ignore climate change, which is published in August in the US, September in Australia and October in the UK (Bloomsbury). He is the founder of the Climate Outreach and Information Network in Oxford, UK Insight from a Rubik’s cube ONE MINUTE INTERVIEW COURTESY OF MANJUL BHARGAVA Manjul Bhargava explains how a moment of visual inspiration led to him winning mathematics’ most prestigious prize Does the Fields medal mean more to you than any other award you have won? Any award is a milestone, which encourages one to go further. I don’t know that I think of any award as meaning more to me personally than any other. The mathematics that led to the medal was far more exciting to me than the medal itself. The award citation says that you were inspired to extend Gauss’s law of composition in an unusual way. Can you explain what that is, and what you did? Gauss’s law says that you can compose two quadratic forms, which you can think of as a square of numbers, to get a third square. I was in California in the summer of 1998, and I had a 2 x 2 x 2 mini Rubik’s cube in my dorm room. I was just visualising putting numbers on each of the corners, and I saw these binary quadratic forms coming out, three of them. I just sat down and wrote out the relations between them. It was a great day! Have any of your other discoveries had unusual origins? I do tend to think about things very visually, and the Rubik’s cube is a concrete example of that visual approach. But that one is probably the most unusual and unexpected origin of all. You have proved several theorems. Do you have a favourite? Mathematicians often say that choosing a favourite theorem is like choosing one’s favourite child. Although I don’t yet have any children, I understand the sentiment. I enjoyed working on all the theorems I have proved. Are there any mathematicians, living or dead, that you have particularly looked up to? My mother [Mira Bhargava, a mathematician at Hofstra University in Hempstead, New York] has been a source of inspiration to me from the very beginning. She was always there to answer my questions, to encourage and support me, and she taught me how much the human mind is capable of. This year a woman, Maryam Mirzakhani at Stanford University, has finally won one of the Fields medals, after 52 consecutive male winners. How do you view this achievement? This is long overdue! Hopefully in a few years we will not even need to discuss this, as more and more females receive the award. I am honoured to be a recipient in the same year as Maryam. It has been a pleasure to know her – we overlapped for a year early in our careers at Harvard, and later at Princeton. Her work is absolutely fantastic. I hope the media will not speak of her only as a top-rate female mathematician, but also as a top-rate mathematician who is doing truly groundbreaking work. Interview by Dana Mackenzie PrOfiLe Manjul Bhargava has just won a Fields medal for his work on number theory. Now 40, he was one of the youngest people to be made a full professor at Princeton University, aged 28. He has extended the work of classical mathematician Carl Friedrich Gauss

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Page 1: Insight from a Rubik's cube

16 August 2014 | NewScientist | 25

For more opinion articles, visit newscientist.com/opinion

well what is happening but “enter into unwritten agreements about what can be publicly remembered and acknowledged”.

Our response to climate change is uncannily similar to an even more universal disavowal: unwillingness to face our own mortality, says neuroscientist Janis Dickinson of Cornell University in New York. She argues that overt images of death and decay along with the deeper implications of societal decline and collapse are powerful triggers for denial of mortality.

There is a great deal of research showing that people respond to reminders of death with aggressive assertion of their own group identity. Dickinson argues that political polarisation and angry denial found around climate change is consistent with this “terror management theory”. Again, there is a complex relationship between our psychology and the narratives that we construct to make sense of climate change.

For all of these reasons, it is a mistake to assume that the scientific evidence of climate change will flow directly into action – or, conversely, that climate denial can be dismissed as mere misinformation. The systems that govern our attitudes are just as complex as those that govern energy and carbon, and just as subject to feedbacks that exaggerate small differences between people. The problem itself is far from perfect and the situation is not hopeless, but dealing with it will require a more sophisticated analysis of human cognition and the role of socially shared values in building conviction. n

George Marshall is the author of Don’t Even Think About It: Why our brains are wired to ignore climate change, which is published in August in the US, September in Australia and October in the UK (Bloomsbury). He is the founder of the Climate Outreach and Information Network in Oxford, UK

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Manjul Bhargava explains how a moment of visual inspiration led to him winning mathematics’ most prestigious prize

Does the Fields medal mean more to you than any other award you have won?Any award is a milestone, which encourages one to go further. I don’t know that I think of any award as meaning more to me personally than any other. the mathematics that led to the medal was far more exciting to me than the medal itself.

The award citation says that you were inspired to extend Gauss’s law of composition in an unusual way. Can you explain what that is, and what you did?gauss’s law says that you can compose two quadratic forms, which you can think of as a square of numbers, to get a third square. I was in California in the summer of 1998, and I had a 2 x 2 x 2 mini Rubik’s cube in my dorm room. I was just visualising putting numbers on each of the corners, and I saw these binary quadratic forms

coming out, three of them. I just sat down and wrote out the relations between them. It was a great day!

Have any of your other discoveries had unusual origins?I do tend to think about things very visually, and the Rubik’s cube is a concrete example of that visual approach. But that one is probably the most unusual and unexpected origin of all.

You have proved several theorems. Do you have a favourite?mathematicians often say that choosing a favourite theorem is like choosing one’s favourite child. Although I don’t yet have any children, I understand the sentiment. I enjoyed working on all the theorems I have proved.

Are there any mathematicians, living or dead, that you have particularly looked up to?my mother [mira Bhargava, a mathematician at Hofstra University in Hempstead, New york] has been a source of inspiration to me from the very beginning. She was always there to answer my questions, to encourage and support me, and she taught me how much the human mind is capable of.

This year a woman, Maryam Mirzakhani at Stanford University, has finally won one of the Fields medals, after 52 consecutive male winners. How do you view this achievement?this is long overdue! Hopefully in a few years we will not even need to discuss this, as more and more females receive the award. I am honoured to be a recipient in the same year as maryam. It has been a pleasure to know her – we overlapped for a year early in our careers at Harvard, and later at Princeton. Her work is absolutely fantastic. I hope the media will not speak of her only as a top-rate female mathematician, but also as a top-rate mathematician who is doing truly groundbreaking work.Interview by Dana Mackenzie

ProfileManjul Bhargava has just won a fields medal for his work on number theory. Now 40, he was one of the youngest people to be made a full professor at Princeton University, aged 28. He has extended the work of classical mathematician Carl friedrich gauss

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