Probabilities crop up in the news, documentaries and blogs everyday. They cover a wide range of activities: will it rain today?, what are chances of becoming ill ?, or to place a bet or not? They seem to cover most aspects of life. But what is a probability?

When we flip a coin into the air to decided whether to stay in and watch TV or go out for a meal, then as it twists and turns there is no way to predict which way it will land. The decision has been left to a random outcome. It could land heads, or it could land tails. There is no way to predict. To quantify the uncertainty we calculate a probability. To do this we need to know the number of possible outcomes, in the case of a coin it is 2 - landing heads or landing tails. Therefore the probability of landing heads is 1 of 2 possible events which gives “1 in 2 chance of heads” or a probability of 1/2 or 0.5 ( in percentages “50% chance of landing heads” or in gambling terminology “evens” ). All probabilities follow the same principles but the calculations can be different.

In the case of predicting the weather it can’t be flipped up in the air like a coin ! Instead, the UK Meteorological Office uses mathematical models. The models describe the relationship between a very large number of variables for example temperature, pressure, wind speed and direction at points across the country. Combining the models with measurements from weather stations they use lightening fast computers to calculate the probability of rain in a region. Chances of rain are watched eagerly by farmers about to harvest their crops, events organisers wondering how many umbrellas to order, and supermarkets making sure they have enough ice cream to sell.

To plan the amount of resources required for patients, health organisations use medical records to calculate probabilities of developing a disease. In the case of cancer, medical records show how many people have developed one of the many different forms during a lifetime. All this information is gathered together and probabilities are calculated. For example in the UK population there is a 1 in 3 chance of developing cancer at some point in a lifetime.

Gambling is big business, in the UK it is approximately £14bn per year, and covers many activities from sport to whether it will snow on Christmas Day. Take football, at the beginning of the football season all teams have an equal chance of coming top of the league table by the end of the season. However, some teams have a stronger squad of players, or new managers bring different ideas about improving the performance of the team, and so on. Bookmakers take all of the factors and assess the chances of a particular team winning the league and offer odds, say 6-1 ( “6 to 1” ). In other words, the bookmaker thinks there is 6 times more chance of the team not winning the league compared to it winning ( equivalent probability is “1 chance in 7” or 14% chance of winning ). A gambler ( or punter ) places an amount of money with the bookmaker hoping that they are wrong and they win lots of money !

Probabilities quantify the level of uncertainty that a particular event will occur - they are a guide and not a prediction. They can be used to plan for rainy days, help the health system to prepare for future illnesses, and avoid losing money !

Dear Nobel Prize Committee Members,

For many years I have read the lectures given by the Nobel Prize winners. They give a great insight into the personalities of the winners and their struggles to break new ground in their subjects. The Nobel Prize highlights some of the greatest breakthroughs in our understanding of the world that we live in, and although I don’t claim to understand every aspect of the lectures, I find them inspiring. However, it is a curious fact that there is no Nobel Prize for mathematics.

I understand that when Alfred Nobel left most of his fortune for a series of prizes which he stated were for those who have shown the “greatest benefit on mankind.” However he limited the subjects to physics, chemistry, physiology or medicine, literature and peace. Although I can appreciate that there are many reasons for limiting the number of prizes, missing out mathematics is a serious lack of recognition of its impact on the “benefits of mankind.”

I would like to you to consider a Nobel Prize for Mathematics. Mathematics forces a clear understanding of concepts and assumptions involved in a problem. It provides a logical framework for exploring and understand the world - where would we be without numbers, geometry and algebra ? Mathematicians use their skill, determination and imagination to extend the boundaries of our knowledge and develop methodologies and techniques that when applied improve the way that we live. It is interesting to note that outside of the awards for literature and peace there is invariably some form of mathematics supporting the subject that has been awarded a prize.

Since the first Nobel Prize awarded in 1901 mathematicians have made significant breakthroughs in our understanding of the world, for example: Alan Turing ( widely considered to be the father of theoretical computer science and artificial intelligence ), Emmy Noether ( landmark contributions to abstract algebra and theoretical physics, in particular explaining the link between symmetry and conservation laws in physics), John von Neumann ( a pioneer in too many fields to list but include physics and computing, in particular the underlying computing structure used by every computer today ), Rudolf E. Kálmán ( breakthrough in filtering theory which was first used in Apollo navigation systems and today is guiding commercial aircraft and analysing the weather ), Beniot B. Mandlebrot ( developing insights into rough or chaotic physical phenomena seen in shore lines to societies ) are just a few who could have been considered for a Nobel Prize in mathematics. Imagine how many more breakthroughs in mathematics there would have been with the support of £600,000 prize money !

Of course there are already awards for mathematicians, for example The Abel Prize which is considered the ‘maths Nobel’ and through the media raises the profile of mathematics. However, the Nobel brand would raise the profile of mathematics to a higher level and a wider audience.

Although the list of Nobel prizes has stuck to the original list of prizes, adding another subject has been done. The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, donated by Sweden’s central bank to celebrate its tercentenary in 1968 has remained on the list. I can appreciate that money will be required to support the on going prize for mathematics. However, if you signalled that you were open to the idea of adding mathematics to the list of prizes, then maybe some of the major companies who rely on mathematicians such as Amazon, Google, Apple, and Microsoft, might be willing to set up an endowment to provide the on-going financial award - what do you think ?

I can appreciate that you are busy assessing future recipients for the Nobel Prizes, but please can you find time to consider adding mathematics to the list. Its inclusion to the list of Nobel Prizes will finally recognise its impact on the “greatest benefits of mankind”.

Best regards,

A Mathematician

Sustainability seems to be everywhere: from fish to farming and everything in between. But what does it mean to be a 'sustainable' business ?

A few years ago I watched an interview with the famous golfer Greg Norman, whose nickname is The Great White Shark, where he discussed his career on the golf course. Towards the end of the interview the discussion moved onto his success as a businessman, his estimated net worth of $300 Million. He started talking about a 12 and even a 200-year horizon for his business, or approximately 10 generations. Greg put forward the case that it was about creating a solid business that would support customers, employees and suppliers which would outlive his and their children’s children: a form of sustainability. So what makes a business sustainable and last for more than 200 years ?

Looking about for things that have been around for over 200 years there are many examples outside of business: stately homes, castles and estates. Then there are the ancient trees that have weathered many storms for hundreds of years but are facing their greatest storm from pollution and global warming! However in the world of business there are a few companies that are still going after 200 years of economic turbulence, wars, and major social change. Some produce my favourite products: Shepard Neames, brewer since 1698, with their wonderful beer: Spitfire and Bishops Finger, and Mornflakes, oats and cereals since 1675, that get me started every morning. Are there any common threads from these examples?

A clue to sustainability started to take shape in my mind during a discussion with a teacher about initiative overload. In particular how many government sponsored initiatives lack any sustainability, and when the money dried up they faded out. During our discussion he said that to be sustainable it needs to affect the core activities which in eduction is reading, writing and arithmetic - or the ‘3Rs’. If it didn’t then it quickly disappeared and the next initiative rolled in.

Drawing a few threads together from business and eduction some rough conclusions can be drawn. First, businesses longevity depends on a core product e.g. food and drink - something that everybody needs regularly and is an integral part of life. Packaging may change, marketing channels redirected but the core product will have been the basically the same for hundreds of years. Secondly, businesses that are still going after 200 years appear to be run by families, which suggests that the core values of the business, and the deep understanding of customers, markets and competition, are more easily passed onto subsequent generations. Finally, every business uses some form of technology and as far as I can establish a sustainable business understands the importance of using just enough to improve its performance. Just a few conclusions but I am sure that many more can be drawn from analysing 200+ year old businesses.

I hope that Greg Norman’s business is still around in 200 years so that my great-great-great-great-great-great-grandchildren can play golf !

PRESS RELEASE - 7 October 1702

The Royal Swedish Academy of Sciences has decided to award the Noble Prize in Physics for 1702 to

Isaac Newton
Cambridge University, Cambridge,
United Kingdom

“for the invention of a mathematical foundation in natural philosophy which led to the discovery of a universal force, gravity, which applies to all objects in all parts of the universe.”

This year’s Noble Laureate is rewarded for answering the question: how does a force make a body move ? This fundamental question covers every object in the Universe from cups on a table to the planets in the Heavens. Newton’s breakthrough was to develop a new mathematical approach: the calculus, that he successfully used to reason about the forces on a body and its resulting motion.

In his work Newton developed three laws of motion. The first states that a body will stay at rest, or remain in uniform motion in a straight line, unless a force acts upon it: a cannonball resting on the ground will remain stationary, however as it flies through the air both the forces of air resistance and gravity will bring it back to the earth. Newton also reasoned that the force applied to the object is equal to its mass times its acceleration, which is his second law of motion. For example, the force from the exploding gunpowder in a cannon accelerates the cannonball through the air. The greater the explosion the faster the cannon ball flies towards its target. Finally, when a cannon is fired, the cannon will be pushed backwards a yard or two. This action and reaction is described by Newton’s third law, which states that every action has an equal, and opposite reaction.

Newton’s work cumulated in an answer to the question of why objects fall to earth. Using the insights on the motion of bodies his answer identified a new force called gravity. He showed that gravity is an attractive force between bodies. The Earth, which is a very massive body, will exert a force on an apple, a relatively tiny body, as it hangs on a tree. The gravitational force is pulling the apple to the earth and the earth is being pulled towards apple ! Newton then reasoned that the same force is acting like a web on the planets, holding them in the Heavens, and stopping them from crashing into the Earth. He went on to develop a mathematical relationship for the gravitational force that involved the mass of the bodies and their distance apart from each other. Newton took this result and solved many outstanding problems, for example the deflection of the planet’s orbit around the sun by the pull of the its gravity, and the gravitational pull of the moon and sun to explain the ocean tides.

The Noble Committee agreed that the intellectual break through, and subsequent discoveries, made by Sir Issac Newton would benefit mankind for many years into the future.

Issac Newton, British citizen, Born 1642, England. Lucasian Professor of Mathematics at Cambridge University, United Kingdom. https://en.wikipedia.org/wiki/Isaac_Newton#Life

There is a danger when recommending books on a subject: too difficult and the reader will not get past the first few pages, too easy and they will start to get bored and wonder why they should bother. This fine line becomes precarious when recommending books about the philosopher Ludwig Wittgenstein.

Wittgenstein attracts a lot of attention: he gave away a fortune that he inherited from his millionaire father; was decorated for valour for his service on the Eastern front and against the British army during the First Wold War; was a hospital porter; a gardener’s assistant in a monastery; designed a house in the modernist style for his sister in Vienna and at one time thought about being a monk. Against the background of his life he is considered by many to have been one of the greatest philosophers of the 20th century ( Bertrand Russell being the other ). His life and work has generated over two thousand books, a large number of web sites, and what feels like a library full of academic papers. It is very easy to get lost in the growing material! However, the following books I have found helpful in developing my understanding of Wittgenstein’s work.

The first book that I would recommend is The Principles of Linguistic Philosophy by Frederich Waismann. The early chapters describe how philosophical problems arise and gives an overview of Wittgenstein’s solutions in non-technical language.

There are many general books on philosophy that have a section on Wittgenstein, but one of the most accessible is the chapter with John Searle in Bryan Magee’s The Great Philosophers ( pg 322 - 347 ) which gives a short and clear overview from the two major periods of his life: the Tractatus Logico-Philosophicus ( known as the Tractatus ) and the later work Philosophical Investigations. Another accessible book with a clearly written section about the Philosophical Investigations is by Stephen Law The Great Philosophers ( pg 156 - 161 ).

A short introduction to Wittgenstein’s life and work is Norman Malcolm’s Ludwig Wittgenstein A Memoir. Malcolm was one Wittgenstein’s students and he gives a fascinating insight into his character. A more extensive book about Wittgenstein is Ray Monk’s The Duty of Genius.

To get a flavour of Wittgenstein’s solutions to philosophical problems, A. C. Graylings’s book Wittgenstein A Very Short Introduction gives enough detail to start understanding Wittgenstein’s approach to philosophical problems.

There are many specialised introductions for the Tractatus and Philosophical Investigations but Ray Monk’s How To Read Wittgenstein, explains passages from his work in a way that is understandable. Another short introduction to Wittgenstein’s approach to solving philosophical problems is Wittgenstein by P. M. S. Hacker ( part of the The Great Philosophers series ) which contains a section on whether a machine, in particular computers, can think ( very topical for todays world with the heated debates about Artificial Intelligence ).

The book that I first read about Wittgenstein, following a recommendation by a philosopher specialising in his work, was Wittgenstein by Anthony Kenny, which I regularly refer to.

A good preparation for reading Wittgenstein’s work directly ( he only published the Tractatus in his own life time but there are several books of his notes ), is Wittgenstein’s Tractatus an Introduction by H. O Mounce. Another book that gives a good overall in prepartion for reading the Philosophical Investigations is Marie McGinn’s Wittgenstein and the Philosophical Investigations. Both books are not easy to read but with perseverance then his work should start to make sense.

Hopefully the above will help you navigate through the forest of material about Wittgenstein - Good Luck!