Archive for the ‘Mathematics’ Category

Ireland and the Race to Mars

First broadcast on Today with Sean O’Rourke (23-11-2016)

mars

The Martian landscape as depicted in The Martian, a film by 20th Century Fox (Credit: 20th Century Fox)

Both NASA and China have announced plans to land rovers on Mars in 2020, while a number of ambitious non governmental organisations also joining the dash to the Red Planet. It is anticipated that a manned mission from Earth to Mars and back will take five years, and Irish researchers and companies are part of global efforts to make sure that a manned Mars mission is a success.

The ‘Race to Mars’ has well and truly started, and, it’s about time some might argue, as it is now 47 years since Neil Armstrong walked on the Moon, and those of us around back then might have expected to see more progress by now.

Unlike the 1960s, when the technology was really being stretched to the limit to get to the Moon, there are far less technical obstacles in the way of us reaching Mars, and the reason we haven’t done so is due to US politics and money.

That said the scientific challenges of getting humans to Mars, establishing a permanent presence there, and returning them safely to Earth are enormous. In October, President Obama set a goal of sending humans to Mars by the 2030s, and commented that he expects to be still around to see it happen.

But, what drove NASA on in the 1960s, of course, was fear of the Soviet Union and the militarisation of space. There is no Soviet Union threatening US existence anymore, but China is showing signs of emerging as viable new rival. The emergence of China as a space rival can only help efforts to get to Mars.

Challenges

Mars is 34 million miles away, and that is more than 140 times further than the Moon. The entire duration of the mission to the Moon in 1969 was just over 8 days, but getting to Mars safely, spending time there and returning safely to Earth will take in the region of 5 years.

On the journey to Mars, the craft must be designed so that it protects the astronauts from cosmic radiation, while providing them with healthy food to eat, and a means to exercise and stay physically and mentally healthy, and prevent the muscle and bone tissue wastage that will impact astronauts living in microgravity.

NASA are planning to have a habitat module where astronauts will eat a healthy diet from crops grown on ‘green walls’ inside the craft. The air and water will be constantly recycled, and the people chosen will be individuals with a high level of psychological resilience who can endure boredom and are not prone to conflict.

The NASA timeline is that Mars astronauts will spend one year preparing for the launch, one year travelling to Mars, 18 months orbiting and then landing on Mars, and 18 further months on the surface of Mars. They will come home when the Earth and Mars are again favourably aligned to make the return trip home.

This will be a space mission like none in human history requiring a lot of material, some experimental, some to sustain life, some of which would be sent ahead of the crew, such a descent vehicle which would await the astronauts while in Mars orbit, and a shelter on the surface of Mars, assembled by robots.

Cost

There are some who doubt that NASA will be able to get humans to Mars by the 2030s, or even 2040s because of some financial realities. It is estimated that the Apollo moon landings cost $140 billion in today’s dollars, while the realistic price tag to get humans on Mars is somewhere around $450 billion.

NASA’s annual budget for human spaceflight is currently around $9 billion, which is a long, long way short. There needs to be another JFK figure to set out the vision, and secure the budget, but the US has little competition, and there is no ‘clear and present danger’ such as the old Soviet Union to give it a push. That said, ‘Red’ China is creeping up again as a threat to the US psyche.

Will it happen? It is probably unlikely that the US taxpayer will be prepared to pay the entire $450 billion bill to do something for the vague good of mankind.

Commercial 

The answer might come from NASA taking on Mars as a kind of joint venture with commercial companies such as Elon Musk’s SpaceX. This can help secure private investment and access to potential useful new technologies. For example,

SpaceX are working on cheaper rockets, costing about $1 million to launch.

Some other companies involved are Inspiration Mars, which is a non profit company founded by Dennis Tito the first space tourist. He is planning a trip for a select crew of Americans, who will travel to Mars, orbit, but not land. The plan here is to leave Earth in 2018, or failing that to try again in 2021. The estimated cost of this flyby mission is between $1 and $2 billion.

Then there is the Mars One mission, the one way trip, proposed by Dutch entrepreneur Bas Lansdorp. This is regarded by some as a ‘suicide mission’ as once people are there, there is no way home. Despite that, there were 2,782 applications to be astronauts on the trip, some of which came from Ireland, including Trinity College astrophysicist, Dr Joseph Roche. The plan is that these applicants will be whittled down six groups of four astronauts, and the first crew of four will leave Earth in 2024. Mars One plan to document the trip on a reality TV show, which they hope will provide much of the finance for the trip.

But, Space X is a serious, space exploration company founded by Elon Musk, a billionaire, playboy who has also made a success out of Tesla electric cars. He is working on developing a fleet of reusable rockets, launch vehicles and space capsules to transport humans to Mars and back again. He wants to build a self sustaining Martian city of 80,000 people, which could be a bolt hole for humanity in the event of some natural or manmade catastrophe here. The plan is to have a human step on Mars by 2026 (10 years!) and for it to be a round trip.

Musk may charge people as little as $0.5 million for a round trip to Mars.

Ireland 

There are a surprising number of researchers and companies based in Ireland doing work that can help make the mission to Mars a success.

For example, the work of Brian Caulfield, Professor of Physiotherapy at UCD, has led to the design and development of a device that can enable astronauts exercise properly so that their physical and mental health can be maintained on the long voyage to Mars. The work has been funded by the European Space Agency (ESA).

The device stimulates the large muscles of the legs to produce aerobic exercise training and muscle strengthening effects in space. This ‘Neuromuscular Electrical Muscle Stimulation Technology’ has been successfully tested by the ESA and was developed as a collaboration between UCD and researchers at the Galway based Biomedical Research Limited.

Research by Trinity College’s Mary Bourke, and Ulster University’s Derek Jackson has investigated Martian wind patterns and how they shape the giant sand dunes that can be seen on the surface of Mars – like a red Saudi Arabia.

Scientists know that Martian weather can be volatile and potentially very dangerous for a Martian landing as well as for human colonists, with huge sandstorms from time to time, for example.

The research is of potential value to NASA and others planning to go to Mars as it shows how the enormous sand dunes on mars influence the local wind speeds on the planet, and how these wind speeds, then in turn shape the sand dunes.

It is like developing a Martian wind and weather forecasting ability on Earth.

In Athlone Institute of Technology Dr Diana Cooper is working on the effects of microgravity on human physiology. The insights gained from this work could be crucial to developing methods to ensure that humans can survive long periods in space, travelling between Earth and Mars, without their bone tissue being reabsorbed back into the blood, or losing significant muscle mass.

Mathematics 

Something less obvious and immediate, but of enormous importance to the success of any space mission to Mars concerns something invented by an Irish mathematical genius in 1843. These are quaternions, which are mathematical equations, which are used to represent the relative movement of 3D objects in space, and the man that invented then was called William Rowan Hamilton.

A few years back, after the NASA curiosity rover landed on Mars, I spoke to one of the mission controllers, a man called Miguel San Martin. He told me that the incredibly precise landing of the car sized curiosity, near an area which NASA believed may show former evidence for life on Mars, was only possible because the precise navigation of curiosity was underpinned by quaternions.

So, incredibly, something invented by a Dubliner, while walking along the banks of the Royal Canal in 1843 with his wife, will be vital to ensure that any future Mars mission lands close to a pre-planned safe, and viable landing site.

Industry

There are a number of companies in Ireland who are doing work which feeds to the development of the technology required to get to Mars.

For example, A specific type of engine, called a Mars Apogee Engine is under development at Moog, Dublin, in work supported by Enterprise Ireland.

This engine is a liquid propellant engine capable of providing more thrust, with less fuel, than is possible with existing propulsion systems. The idea is that these new engines will be efficient enough to save 150kg of propellant on a Mars mission, which will make space available for other things, such as scientific instruments, which will give any Mars mission more ‘bang for its buck’.

The Curtiss-Wright Aviation and Electronic company, which has its origins all the way back to the Wright brothers, has a branch in Dublin. The people here are working on launch vehicles that can take payloads into orbit and build the Martian ‘in orbit’ infrastructure that will be required to supply and sustain human missions to Mars. This will build a supply chain if you like.

Curtiss-Wright are also developing technologies to enable the safe re-entry of spacecraft through planetary atmospheres including Mars, as well as technology that will be central to sustaining life & generating fuel for human explorers on the surface of Mars

Danny Gleeson, Chairman of the Irish Space Industry Group, said that development of human missions to Mars will take decades and that it was unlikely that the human mission  to Mars will be a single shot but rather a choreographed series of missions that build the necessary infrastructure in Earth orbit and Mars orbit & surface to sustain human missions.

“The good news is that there is a plan to get to Mars and back again and the technologies required are almost all available now,” said Danny.

Can the next JFK please step up.

Was Sir Tim Hunt treated fairly? Are humans ‘walking dead’? Should we fear facial recognition technology? Why men are better at maths

Tim Hunt

Sir Tim Hunt was forced to resign from several prestigious positions following allegedly ‘sexist’ remarks (Credit: nobelprize.org)

The allegedly ‘sexist’ remarks made by Sr Tim Hunt, Nobel Prize winner, led to his resignation from several posts within days and his career is in shreds.

But were the remarks genuinely sexist? Was he treated fairly by the press?

Species of plants and animals are disappearing faster than any time since the dinosaurs. Legendary scientist and advocate Paul Ehrlich believes we have three generations left to do something about it, or we’ll end up like other ‘walking dead’, doomed species.

Facial recognition software is improving all the time, and governments and private companies are very interested in the data it provides. What’s now possible and how worried should be?

In education there is a well-known theory called the self-fulfilling prophecy. This is where a student meets the expectations of teachers and parents.

Does this explain the apparently strange reality where men are better at maths than women, while girls do better than boys in maths in primary school?

Click below to hear a discussion of these topics on The Morning Show with Declan Meehan

This was first broadcast on 25th June 2015 on East Coast FM

Science & the ‘benevolent sexist’; how a chameleon changes; why maths is not natural; near total eclipse

Dooropening

Are men that open doors for women displaying sexism? One scientific study indicates yes [Picture: http://www.gentlemensavenue.com%5D

It’s something that many men do without thinking; open a door for a women. It’s just common politeness, or is it?

A study by scientists at Northeastern University in Boston, led by Professor Judith Hall, indicates that men who open doors for women may be secret sexists, of a more damaging kind for women’s equality than the more obviously misogynistic male.

A male chameleon is usually green, and well camouflaged, but it can change colour in minutes in response to another male, or a receptive female. It does this, scientists believe, by altering the spaces between crystals in its skin cells, which produces different wavelengths of light.

A almost total solar eclipse will occur on the 20th March in Ireland at 9:35 am. For a few minutes, the Moon will almost completely block out the Sun from viewers here.

Our brains are not set up for mathematics. A lot of people would agree, but it is a surprise to hear a leading French mathematician, Cedric Villani, winner of the prestigious Fields Medal, which is akin to the Nobel Prize for mathematicians, also agree. We consider why.

Listen below for discussion on The Morning Show with Declan Meehan on East Coast FM

 

First broadcast on East Coast FM on 12th March, 2015.

What’s It All About? on RTE Radio 1, Maths on Mars (Episode 4)

Pure Maths Formula

Without maths men would not have walked on the Moon, and we wouldn’t appreciate Mozart or Beethoven’s great harmonic symphonies [Credit: Wikipedia]

LISTEN HERE

When many of us think of maths, we might instinctively suppress a yawn as we recall boring theorems, dull algebra and uninspiring teachers.

Yet without question, maths is exciting, challenging and responsible for some of humanity’s greatest achievements.

The landing of two men on the Moon in 1969 would not have been possible without maths, nor would we be able to appreciate the great harmonic symphonies of Mozart or Beethoven.

Without maths, in fact, there would be a lot less beauty in the world, and in this episode we explore the majesty, beauty and even poetry of maths.

The seven minutes of Martian terror

In August 2012 the most complicated robotic landing of a craft in the history of space exploration took place on the surface of Mars.

It was an amazing feat of engineering. The Mars Science Laboratory (MSL), weighing about two tonnes, landed safely with all its high-tech equipment.

The spacecraft decelerated in the Martian atmosphere from 13,000 miles per hour to zero miles per hour on the surface, using all manner of engineering tricks.

Throughout the complex landing and navigation sequence a type of mathematical equation, devised in 1843 by an Irishman in Dublin, proved crucial to its success.

That man was William Rowan Hamilton, a brilliant mathematician from Trinity College Dublin, and the equations in question are called quaternions.

We talk to the chief NASA engineer responsible for landing the MSL on Mars about the importance of quaternions to the success of the mission.

Miguel San Martin describes the terror he felt when his team had to wait seven minutes for a signal from Mars to confirm the craft was safe or destroyed.

It was a moment of high tension involving eight years of preparation and an investment of $2.5 billion – and quaternions were at the heart of the drama.

View video depiction of seven minutes of terror below:

Moon landings: The Dublin link

Regan Hutchins describes the often troubled life and work of one of Ireland’s greatest mathematicians, William Rowan Hamilton.

WR Hamilton, a Dubliner born on Dominick Street, lived in the 19th century, but his mathematics continues to have enormous impact on the world today.

For example, his work is considered crucial to the navigation and landing of spacecraft, and is also used to design the latest high-tech video games.

His most important piece of work stemmed from an insight he had while walking along the banks of the Royal Canal one bright morning in 1843.

Regan Hutchins visited the spot at Broom Bridge in Cabra with Dr. Fiacre O’Cairbre, senior lecturer in maths at NUI Maynooth, where Hamilton had a flash of inspiration about quaternions.

Regan also paid a visit to Hamilton’s home in Dunsink Observatory with Professor Iggy McGovern from Trinity College Dublin, to find out more about Hamilton’s life.

Pythagoras and musical harmony

The reason we hear music as “nice” or “not nice” depends on mathematical ratios, Dr. Bob Lawlor, NUI Maynooth, told our reporter Lorcan Clancy.

Pythagoras, the famous mathematician of the ancient world, invented the theorem we learned in school, but he also developed the original musical scale.

It is thought Pythagoras gained insight into how mathematical ratios explain pitch and harmony by listening to blacksmiths striking anvils.

He built a monochord – an early single-stringed instrument – and found that pitch was inversely proportional to the length of the monochord string.

This work by Pythagoras explains why we can recognise a discordant sound in the midst of a beautiful, harmonic piece of music.

We humans, it seems, prefer symmetry, even when it comes to music.

Maths can forecast volcanic eruptions

You might be surprised to learn that scientists are still unable to predict the precise time, date and location of a volcanic eruption.

However, scientists like Professor Chris Bean (University College Dublin), a mathematician by training, are getting far better at forecasting the chances of an eruption.

We visited the UCD campus to talk to Chris about maths and its importance in his volcano work.

Maths is used to forecast the weather. It’s not possible to predict that it will rain on Grafton Street at 2pm tomorrow, but we can say there is a “strong chance of showers”. The same applies to how scientists predict volcanic eruptions.

Chris Bean was inspired to apply his mathematical skills to the study of volcanoes after watching the Mount Saint Helens eruption in 1980 on TV.

Sensors are placed on the volcano to measure things like how the ground is shaking, the nature of gas leakages, and the surrounding water chemistry.

Mathematics are used to analyse the resulting data, which then allows scientists to make reliable forecasts.

Each volcano is different, but the scientific strategy is the same: monitor the patterns leading up to a known eruption to try and predict the next one.

Why do we use certain numbers?

Fiacre O’Cairbre tells Lorcan Clancy why certain numbers like 12 are important to us.

The use of 12 as a so-called base number – a basic multiplication unit underpinning a system of numbers – has its origins in the ancient world.

The fact that there are seven days in a week can be traced back to the Babylonians who believed there were seven planets, including the Sun. The Babylonians dedicated one day each to a planet, which is how we came to have seven days in a week.

Meanwhile, the reason that 60 is important, says Fiacre O’Cairbre, is because it is the smallest number divisible by 1, 2, 3, 4, 5 and 6.

The Babylonians saw that 60 was a good base number for doing divisional calculations in real world, such as dividing up inheritances or bags of grain.

Today, base 10 is the key to the metric system. However, number systems go in and out of fashion and today’s system could change again in the future.

The majesty of maths in ancient Ireland

There is plenty of evidence that the people of the ancient world, the builders and architects at least, had a very good knowledge of mathematics.

The builders of Stonehenge, for example, clearly had an understanding of squares and circles, but in Ireland we something just as fascinating.

The Céide Fields near Belderrig, north Mayo, were discovered by Patrick Caulfield in 1934 when he found stone walls buried beneath the bog.

Researchers, including Patrick’s son Seamus Caulfield, have since unearthed a huge, buried landscape 5,500 years old.

Our reporter Lorcan Clancy visited the Céide Fields Visitor Centre and spoke to site manager Greta Byrne about why the site is so special.

Lorcan also spoke to Seamus Caulfield, who began work on the Céide Fields in 1970, and who gave up his job as a teacher to become an archaeologist.

Seamus describes how the buried Fields, which cover thousands of acres of north Co. Mayo, were systematically divided up thousands of years ago.

For more on the Céide Fields visit

http://www.museumsofmayo.com/ceide.htm

UCD team break cryptography world record

Online security may have to be reviewed after a UCD team broke the world record for solving a famously hard problem used for encryption. Credit [www.geekersmagazine.com]

Online security may have to be reviewed after a UCD team broke the world record for solving a famously hard problem used for encryption. Credit [www.geekersmagazine.com]

A team of mathematicians from University College Dublin (UCD) has set a world record by breaking the code used by the security industry to protect credit cards and bank account details online.

Using a supercomputer provided by the Irish Centre for High-End Computing (ICHEC), the research team from UCD’s Claude Shannon Institute solved a famously difficult conundrum known as the discrete log problem.

To perform secure transactions online, mathematicians create algorithms using numbers stretching to hundreds of digits. These numbers must be large enough to prevent decryption by criminals, but small enough not to slow down transactions, which should take place instantenously.

As part of the process, the Dublin-based research team, led by Professor Gary McGuire, broke the world record last week, previously held by mathematicians in France, by solving the discrete log problem using a 1,971 bit number. The largest number previously used to solve it was a 1,425 bit number.

McGuire, from the School of Mathematical Sciences in UCD, said secure online transactions were now reliant on the discrete log problem or its variations. Most use codes based on numbers larger than the highest number ever to be decrypted but not so large as to slow down transactions.

“Online banking, buying something on Amazon or your airline tickets – any secure website that you put your credit card in [is based on it],” he said. The problem is also used to secure e-voting machines around the world.

Michael Scott, chief cryptographer with CertiVox, an online security firm, said the achievement woudl force his industry to review security levels.

“All of our security depends on variations of the discrete logarithm problem, so if the problem isn’t as hard as we thought it was, then that could be a bit of a worry,” he said.

Scott said the UCD team’s success in cracking such a “tough nut” had been noted by those interested in cryptography. “Out in the cryptographic blogosphere people are talking about it – people are impressed,” he said.

The record for the biggest number used to solve the problem was set at 127 bits by Don Coppersmith from IBM in America in 1984. It has since been broken several times, with French researchers vying with each other and a Japanese team from Fujitsu, until the Irish triumph last week. The UCD team is making plans to break its own record.

McGuire decided to tackle the problem after reading about the Japanese world record last summer. He gathered a team of post-doctoral researchers, made up of Dr Robert Granger from England, Dr Jens Zumbragel from Germany and Dr Frank Gologlu from Turkey for the record attempt, and Science Foundation Ireland provided the funding. The team applied to ICHEC to use its supercomputer and created a mathematical formula to solve the problem.

Measured in bits – the most basic units of computer calculation – their record stands at 1,971 bits. In layman’s terms the number is 594 digits long.

McGuire said their formula meant they should be able to break their own record, given time. “We can push things on quite a bit,” he said.

“Over the next month we hope to go up to 4,000 bits. That would never have been imagined a year ago.”

World records

1984, Don Coppersmith (IBM), USA, 127 bits

1992, Daniel Gordon (Google), Kevin McCurley (Georgia IT), USA, 401 bits

1998, Damien Weber, Thomas Denny, (Universitat des Saarlandes) Germany, 512 bits

2001, Antoine Joux (Ecole Normale Supérieure), Reynald Lercier (Université de Rennes), France, 521 bits

2004 Emmanuel Thomé (Institute National de Recherche en Informatique et Automatique), France, 607 bits

2005, Antoine Joux, Reynald Lercier, France, 613 bits

2012, Fujitsu, Kyushu University, National Institue for Information and Communications Technology, Japan, 934 bits

2013, Antoine Joux, Frances, 1,425 bits

2013, Gary McGuire, Faruk Gologlu, Rogert Granger, Jens Zumbragel (UCD), Ireland, 1,971 bits

First published in The Sunday Times, Irish Edition, 3rd March 2013

Social ‘Net Searching, Ireland’s Animals & Prime Numbers

Science Spinning: ‘The Show with an Irish Spin on Science’, Presented and Produced by Seán Duke

Broadcast on Dublin City FM, 20/01/2011

Social ‘Net Searching, Ireland’s Animals, & Prime Numbers

To contact the show email: sciencespinning@dublincityfm.ie

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