Back-of-the-envelop calculations can be a springboard for interesting questions about a topic. It can be used to dissect government announcements or the opinions of experts. A calculation on one of the critical elements of life - food - unearthed a lack of government action.

As the name suggest a back-of-the-envelop calculation is just that: a calculation done on a piece of paper the size of an envelop. Taking some key numbers for a topic, a quick calculation can be done to to assess whether what is being claimed makes sense. If it doesn’t then more details can be sought or the assumptions made to do the calculation can be checked. Back-of-the-envelope calculations are used regularly by engineers and scientists to quickly check whether their ideas are doable. But they can be seen being used on TV. One prominent example where the use of the back-of-the-envelop calculations is Sir John Harvey-Jones in his series The TroubleShooter, where he visited businesses that were in financial trouble. As he went around the company talking to various people he would jot down numbers in a small book then using the resulting calculations he would give advice on the best way forward. Another example is on The Dragons Den where the dragons are seen scribbling down numbers during a pitch for investment then based on their calculations may offer a deal for a stake in the business.

Recently I was reading Yanis Varoufakis’ interesting book Talking to My Daughter About the Economy when I came across the term “surplus” in connection with agriculture. The book went onto describe it it as “… simply meant any produce of the land that was left over after we had fed ourselves and replaced the seeds used to grow it in the first place.” and goes on “ … the production of agricultural surplus gave birth to the following marvels that changed humanity for ever: writing, debt, money, states, bureaucracy, armies, clergy, technology and even the first form of biochemical war.” Quite a claim.

The idea of a surplus supporting life raised questions about how many people in agriculture support the rest of the country. Searching for a few numbers on the web I found that there are approximately 466,000 people working in the agriculture industry. The population in the UK is about 67.5 mn. The back-of-the-envelope calculation shows that it take one person to feed approximately 140. Is that ratio good or bad? Checking other countries such as Germany where the ratio is approximately the same as the UK. In Spain it is approximately 1 person feeding 58. The difference between Spain and the UK is probably down to levels of mechanisation. The thought that struck me while doing this calculation is that we depend on very few people to produce our food. Compared to other industries such as Management Consultancy where there are roughly the same amount of people as in agriculture yet given the UKs lack of productivity questions have to be asked about its effectiveness.

The next question that comes to mind was about the level of agricultural productivity. The UK is about 60% self sufficient in the growing of its own food. Whereas Germany food self-sufficiency is 80%. The only European country to be self-sufficient is France. Given that the global supply chains are being disrupted by climate change and geopolitics it would be prudent for the UK to increase its self sufficiency in food to say 80% ( we would still need to import food that we can’t grow such as tea and coffee etc. ).

Therefore, this increase in self sufficiency would require a 33% increase in either mechanisation or automation or employing about 100,000 more people in agriculture. The UK Goverment’s Food Strategy recognises that there needs to be an increase in food self-sufficiency but there are no clear plans to achieve that aim. For example there is lots of discussion about the increased use of robotics but looking at the current developments from companies such the Small Robot Company’s, where they are developing the exciting concept of per plant farming, it is tens of years away from main stream agriculture. There is very little discussion about how more people could be attracted into agriculture. Food production is a critical activity in our lives and the UK government must be more proactive in securing its future rather than leaving it to market forces which is undermining its sustainability.

Back-of-the-envelope calculation bypass a lot of complexity but it is a quick way to start a series of questions that digs down into the difference between what is being claimed and what is being done. Anybody who can do simple arithmetic can carry them out and in the case of government policy back-of-the-envelop calculations can be used to ask questions that can hold them to account.

In a search to find something to watch on the TV we stumbled across an old programme about cooking. It was Floyd In France, where Keith Floyd cooked his way around various regions of France. Although first broadcast over 30 years ago there is one theme running through it that is very relevant today.

Keith Floyd was a restaurateur and television personality who hosted televison cooking shows and wrote many books that combined cooking and travel. His flambouyant presentation style opened up cooking to many millions. Aided by a glass of wine and catch phrases such as “camera on the food Clive not me!” he is still remembered by many people to this day. His breakthrough series was Floyd on France which brought him into mainstream televison. In the series he cooked regional dishes in family kitchens, restaurants and on boats! He made cooking fun. A major theme that came through the programme, and all of the others that the he presented over a 25 year period, was producing delicious meals using local produce bought at local markets and produced by local farmers. Spin the clock forward to today where the world is in the grip of a Climate Crisis then the word ‘local’ means very low carbon miles.

In the western world supermarkets have developed convenience to a fine art. Food from all corners of the country, and the world, are brought to local shelves. But behind this convenience is many hundreds if not thousands of carbon miles. Take a staple of most diets in the UK, the potato. The British Potato Council estimates that the UK imports about 350,000 tonnes of potatoes a year. These are mostly the “baby” or “salad” potatoes varieties and are imported from the Middle East. Potatoes from Israel will have travelled over 2000 miles before they land in a supermarket warehouse where they could stay for over six months with a corresponding loss of nutrients. Trying to buy local potatoes fresh from the field is nearly impossible. I’m sure that Keith Floyd would be turning in his grave when he saw where we are getting our food from.

The current crop of celebrity chiefs owe a large debt to Keith Floyd for putting cooking firmly on TV which has opened up their careers. However, when they appear on the screen waving around locally grown produce it is usually heading towards an expensive restaurant and not to our tables. When they demonstrate a recipe they throw in some ingredients that can only be bought from an expensive supermarket, usually only in London, where they have some sort of connection ( watch the ‘sponsored by’ at the beginning of most programmes ). The situation is not much better in the hot bed of revolution the ‘socials’. The top Tik-Tokers such as newt, cookingwithshereen or eitan are more about the process of following the recipe and furthering their careers rather than singing the praises of locally produced food.

Ah! I hear you saying that locally produced food is too expensive. It is expensive relative to the food bought at a supermarket but their prices don’t take into account the impact it has on the environment due to its carbon miles. If there was a tax on carbon miles that would be used so that it would pay for say larger reserervoirs to irrigate crops through dry periods or improve medical support for those at risk during a heat wave, then the prices would start to look equivelant.

There is a glimmer of hope on the horizon with initiatives such as Growing Communities inititaive which bring together farmers and growers to supply food to their community. Their group is based on Key Principles that include: trading for social purpose, not to maximise profit, promote ways of eating and cooking that are good for people and planet. They distribute food in a low-impact and low-carbon way. This is something I feel Keith Floyd would have been proud to support.

Supermarkets will always be with us. However, just like Oil and Gas companies, they are part of the solution. Although some have a few token shelves of local produce it needs to be part of their main offering. As for celebrity chefs whether on TV or socials, how about re-invoking the pioneering spirit of Keith Floyd and work with local producers to make nutritious food that we can all afford?

Maths is the last thing you would expect to find in the middle of a popular TV programme. But during an episode of a BBC show there it was hiding behind the jokes.

Would I lie To You is a comedy panel show that was first broadcast in 2007. It consists of two teams of three people that are captained by well known comedians. A team gains a point for correctly guessing whether a statement from the opposing team is true or not, but if they guess incorrectly the opposing team gets the point. In one particular episode Lee Mack, one of the captains, read out a statement about an object that he owned, his lucky dice: ”This is my lucky dice. I can always roll a six with it in three goes.” During the next five minutes he joked his way through three attempts to roll a 6. Behind the humour there was some maths at work which show some misconceptions about chance and how probability could answer a deeper question.

There are lots of events in life that can’t be predicted with total certainty. We often use a range of words such as certain, likely, evens and impossible, to describe the likelihood of an event happening. However, maths, in particular Probability, can be used to calculate the chance of an event happening but care must be take in interpreting its results.

Dice are used in many games, including gambling, as a way to generate a random number. It is a square object with numbers 1 to 6 on each of its six sides. After it has been rolled then the number shown on the top is taken as the number that is used to proceed to the next step in the game. Probability assumes a perfect world and in the case of a dice then there are only six possibilities. To calculate the probability of a particular number being shown there is one chance in six, in other words the dice will show one of its six sides. For example the probability that a number 6 is shown is 1 / 6 or 17% percent. But what does that mean? If we had asked Lee to roll the dice 10,000 times and then count the number of times that 6 came up the answer that he get would be approximately 1600 times or 17%. The more times he rolled the dice then the closer he would get to 17%. Probability can be used to calculate the opposite question which is: “what is the probability that a 6 is not rolled?” We know that there are five other sides that don’t show a 6 therefore the answer is 5 / 6 or 83%. Notice that both cases - rolling a 6 ( 17% ) and not rolling a 6 ( 83% ) - add up to 100%. When Lee rolled the dice for the first time there was a greater chance that it would not be a 6. He got a 5.

On the next roll the dice showed a 3. As Lee took the third and final roll of the dice it was apparent that the studio was getting tense - would it actually be a 6? After all we already had two numbers that were not 6 therefore the next roll must have a greater chance of producing a 6. But each new roll of the dice is independent of the previous one. A dice does not have a memory of the previous results and therefore is not affected by its history. The chances of getting a 6 on the third and final roll of the dice is still 1 / 6 or 17%. The expectation that ones luck is going to change because of previous results is called The Gambler’s Fallacy and has been, and remains, the ruin of many people. On the final roll the number 2 came up.

Behind the ‘lucky dice’ part of the show there is a much more interesting question and that is: “how many times do I need to roll the dice so that, on average, it would be a 6?”. The phrase ‘on average’ is an important part of the question. We come across averages in our daily life, for example the average spend of a cyclist at a tea shop is around £8 per visit. Some cyclists spend less maybe just buying a tea and cake, some spend more say tea, cake, bacon filled roll and maybe another piece of cake! However, if you take the total spend of all of the cyclists in say a day and divide by the number of cyclists it would give the average spend per cyclist. Averages are calculated for a wide range of subjects ranging from family diet to the spend on weekly shopping and is mainly used to look for trends. Therefore to calculate the average - yes you guessed it - we would ask Lee to roll the dice and keep count but this time count how many rolls it took to get a 6. He may roll a 6 on the first roll, he may roll a 6 after the tenth roll, and so on. Once he had carried it out for 10,000 attempts to get a 6 he would add up the total number of rolls to get a 6 and divide it by 10,000 to calculate the average. The answer is that it take six rolls, on average, to get a 6 ( see the video which describes three different ways to calculate the average number of rolls to get a 6 including the one discussed above ).

Lee’s lucky dice shows how maths can be used to clarify ideas such as chance as well as ask some interesting questions. Picking up ideas from popular TV programmes, and social media, is a good way to introduce maths concepts to a wider audience. Maybe the mathematics community could adopt this approach?

   

Recently I was asked to add my name to a campaign about reducing sewage pouring into our rivers during a storm. Rather than taking my usual approach of clicking a few buttons and sending a prepared email to my MP, I decided to read all of the material that I had been sent. What I unearthed was the complexity of the underlying problems and therefore the likelihood of the campaign’s success.

There is nothing better than walking along a river, whatever size, trying to spot the movement of a fish and once sighted, watching it feed. It can absorb many enjoyable hours. But it is becoming harder to see any fish movement because of the poor state of the rivers. After heavy rain I have seen sewage flowing through my favourite brooks and I hate to think of the pollution that can’t be seen from small particles of rubber being washed from the roads.

When I was contacted by The Angling Trust asking for my support with their campaign; I signed up. Their main concern was that the government’s proposals will take too long to clean the water in our rivers. The targets aim to reduce spills at “high priority sites” – by which they mean Sites of Special Scientific Interest, Special Areas of Conservation, eutrophic sensitive areas i.e. found to contain excessive levels of nutrient waste, chalk streams and waters currently failing our ecological standards due to storm overflows – and bathing water sites. Only after that will water companies be required to tackle the remaining storm overflows. But the target dates they have set are 2035 to achieve 75%+ of the high priority sites and achieve the targets for all remaining storm overflow sites by 2050. Therefore, it is going to take nearly 28 years before all of the rivers are free of the damage caused by storm overflows.

There were a range of issues that The Angling Trust wanted addressing: a broader scope of the plan that addresses the root causes of the problem, targets for government action with more detail on how different government departments will implement the plan in an integrated way and much greater ambition and urgency in the targets set for water companies, and a higher and more immediate action to reduce harm by 2030. In summary The Angling Trust’s view, and mine, was that the government’s plans were too little and too late!

The information that I had been sent was from The Angling Trusts’s perspective and is one that I agree with. However, I felt that it was important to get the government’s view. Digging further into the various links that I had been sent I came across the Consultation on the Government’s Storm Overflows Discharge Reduction Plan which describes a number of issues including the age of the sewage system and how it operates during a heavy storm. For example, during a heavy storm the excess water is combined with the sewage system to manage the overload. With the increase in storms due to the Climate Crisis then the problem is going to get worse. In amongst the documentation were various estimates to completely separate the sewage from storm overflows which would cost between £350 billion to £600 billion and would cause significant disruption. Most of the combined system runs under our towns and cities and would have to be dug up. Reducing discharges to zero in an average year at all inland waters using other options, such as building storage tanks to capture excess water during heavy rainfall, would cost between £160bn and £240bn. Reading between the lines the government is trying to find a balance between reducing, and eventually stopping, storm overflows and the price that we as consumers pay for water and sewage.

However, there were a number of elements missing in the documents. First, it wasn’t clear how the storm overflow reduction would be integrated into an overall pollution programme such as the reduction of pollution from other sources such as agriculture and industry. Secondly, there were no initiatives being sponsored to look at innovative solutions to the problem. For example, developing ideas such as Connected Stormwater Management with Smart Water Butts which uses water butts installed at customer’s houses. They are monitored and controlled to manage the flow of storm water. Finally, there were no initiatives to promote local communities to both monitor and manage their own parts of the rivers such as at Chalgrove Brook in Oxfordshire which brings together local conservation groups, schools, landowners and artists to recover the ecology of their local brook.

I took the standard letter and modified it to add in my thoughts, which I have outlined above, and sent it to my MP. I am still waiting for a reply. I am not hopeful that the government’s targets will be met because of the approach that they are taking. If we are going to save our rivers from pollution and return them to a pre-industrial state then we need: local communities, water companies, landowners, local and national government, consumers, and environmentalists to work together within an ambitious framework.

With energy prices on a steep upward curve fracking for gas has re-entered the energy debate. Ineos, a global petrochemicals manufacturer, has written to the UK government arguing that it should be allowed to restart fracking. But how strong is their argument?

On 11th April 2022 a Director of Ineos was interviewed during the business section of Radio 4’s Today programme. He put forward a number of points for restarting fracking ( for a transcript of the interview click here ).

The strength of an argument depends on the validity of each point supporting it and whether it leads to a valid conclusion. Also, it would be unfair to take the interview literally because of the time constraints of a radio programme, in this case just under 4 minutes. Therefore I have expanded and corrected some of the points to clarify their meaning ).

Fracking in the UK started in the late 1970s and it was mainly offshore. Onshore exploration for shale gas started in 2008 and was pursued until 2011 when drilling in Lancashire, by Cuadrilla, was halted after fracking caused two earth tremors. In 2019 the UK Government stopped its support for fracking because it was found that it was not possible to accurately predict the probability or magnitude of earthquakes linked to fracking operations. Ineos have a wide range of licences to pursue oil and gas activities in the UK. In 2015 they were awarded three shale gas exploration licences covering an area in the east Midlands. A further 21 licences were granted in December 2015. Against a background of increasing gas prices, it was reported on the 5th April 2022 that Business Secretary Kwasi Kwarteng had ordered a scientific review of fracking to assess any changes to the science around fracking.

During the interview the following points were made for restarting fracking:

Point 1: The company has spent £250 mn on exploratory fracking for gas.

It is not clear why this point was being made. Was it because Ineos had invested a large amount of money in fracking and therefore they didn’t want to lose it, or was it that they could quickly restart gas exploration to support the science?

Point 2: There is massive value for the economy and for deprived areas from shale gas.

There are two parts to this point. First the reliance of gas on the UK economy is significant. About 85% of households are heated using gas and around 50% of electricty is generated by gas. The UK imports at least 60% of its gas and is projected to increase to 70% by 2030. Secondly, linking deprived areas to a potential increase in shale gas production is complex issue. The factors affecting deprivation are more than economic. For example they include other factors such as crime, education and the environment all of which fall under the control of local and national government.

Point 3: Ineos will guarantee 6% of the value of the gas, not the profit, to local communities.

It was not clear how the guaranteed amount was arrived at. Why not other financial mechanisms to support local communities?

Point 4: There is a huge amount of shale gas but there is a need to do the science to assess how much can be extracted safely.

There is an ongoing debate about the amount of shale gas in the UK and estimates vary. For example in the UK there are shale formations bearing oil in the south and gas in the north. The Bowland Shale in the north of England is thought to contain about 1,300 trillion cubic feet (Tcf) of gas. By comparison, the UK consumes about 3 Tcf per year. However, it is believed that only a small proportion of gas in the Bowland can be extracted – maybe only about 4%.

Point 5: Although gas is not an energy security issue it can have a high price because it has to be bought on the spot market.

With a high dependency on imported gas ( see Point 2 ) then the spot price is driven by global issues. However, the UK government has stated in its latest British Energy Security Strategy, published on 6th April 2022, “that it will accelerate the deployment of wind, new nuclear, solar and hydrogen, whilst supporting the production of domestic oil and gas in the nearer term – with the target of 95% of electricity by 2030 being low carbon.” If the target is met then the UK’s dependency on gas would be reduced within the next 8 years. Against this time scale, it would be a steep challenge to establish the safe extraction of shale gas and produce it at a level that would have any impact on the UK’s gas imports.

Point 6 The UK government takes half in tax when produced in the UK.

The tax on oil and gas is a complex subject and depends on a number of factors. When I asked the North Sea Transition Authority about the level of tax on gas production in the UK they replied that it would be 40% but depended on certain criteria.

The strength of the points put forward in the interview are mixed. Although they did cover the strategic issue of energy security they didn’t address the climate crisis or how fracking would fit in with the UK governments stated medium to long term aims of reducing the UKs reliance on hydrocarbons.

I’m sure that many other companies with interest in fracking will be putting forward similar arguments to the UK government - will they frack or not frack?