2016 - unlucky for some?

There is a well established link between superstition and numbers. In the West we have such trepidation around the number 13 that certain buildings lack a thirteenth floor, airplanes lack a thirteenth row and streets miss out a building number 13. In other cultures different numbers evoke fear - in Japan the number 9 is avoided (perhaps because in Japanese the word nine sounds like suffering) and in China the number 4 is considered unlucky because it sounds similar to the word for death


After this year I am left wondering what level of fear the number 2016 will inspire in future generations. 


Many have commented on the vast numbers of talented and famous people who have died this year: David Bowie, Prince, Muhammed Ali and Leonard Cohen to name only a few. The state of British politics has become virtually indistinguishable from an awful cross between “In the Thick of It” and “House of Cards” and even Stephen Hawking considers the current political landscape beyond his understanding. The British MP Jo Cox was murdered. Most recently (and possibly most worryingly) one of the most right-wing demagogues in recent years - a man who believes climate change is a conspiracy, who seemed remarkably unfazed by his endorsement by the Ku Klux Klan and (at the time of writing) is seriously considering creating a register for Muslim Americans - is now the US president-elect and is set to be Commander in Chief of the most powerful military in the world. Far-right groups are gaining strength and popularity across Europe and Marie Le Pen is openly talking about creating a “New World Order


I remember learning the Ancient Greeks believed the world was built around numbers and when they discovered irrational numbers this shattered their beliefs. Such numbers, including pi and the square root of 5, are impossible to express exactly as a fraction and when expressed as decimals are unending and without discernible pattern. I confess I’m starting to empathise with the Greek philosophers: only a couple of years ago I would have been certain that the progress towards a kinder and more equal society (exemplified by the USA electing its first black president in 2008) would be so secure that someone like Trump could never win an election and now I know I was wrong (and that there are even people who consider Trump not extreme enough!).


In my tutoring work I have been lucky enough to know so many wonderful students and families. One of the the things I still love about my job is the number of other languages, customs, cultures and nationalities I have had the chance to learn about. And now I read reports of spikes in the number of hate crimes and find I have a little bit of fear for so many of my current and former students. 



One of possible measures anyone may be able to take to try and ensure 2017 does not continue this regressive trend into nationalism and xenophobia is to support charities that will uphold civil liberties and mitigate the environmental damage caused by Trump et al. Nearer to home, we cannot forget that an ever growing number of families are relying on food banks and the number of people let down by the current benefits system runs into the thousands. This version of an Advent calendar (putting one item for a food bank in a box each day in December and then donating the box to the nearest local charity on Christmas Eve) may be of some help, and a petition to suspend the fit-for-work assessments may be found here. Others have suggested donating to reputable news organisations as they need more support than ever if they criticise or challenge regressive practices. 



Despite the depressing tone of this post I would like to leave you with some hope for 2017. The first comes from the life long work of Abdul Sattar Edhi, founder of the Edhi foundation that provides an incredible range of vital services in Pakistan, including ambulances, hospitals and orphanages, Sadly, Edhi is one of the many luminaries who passed away this year but I think his example of how much good a single person can do is needed now more than ever. The second is this illustration of the votes cast in the American election by those aged 18 - 34 who, more than any other age group, voted against Trump and the myopic racism he espouses. 





Lets make 2017 a better year!


Have yourself a geeky little Christmas!

I often use typical attitudes towards Christmas as a way of explaining why I enjoy my tutoring work so much. Many people find that when they are children they love Christmas and find it a magical and exciting holiday. As they grow older this excitement fades to ambivalence and ennui, until perhaps they have children of their own(or nephews/nieces, much younger siblings etc.) Then the disillusioned adults are able to reconnect with the the joy they once had at Christmas because they get to experience it again with someone who still counts down to December 25th and still stays up late on Christmas eve to listen for sleigh bells.



When I was young I found learning about science fascinating - I was spellbound when I started learning about astronomy and discovered how tiny the Earth is compared to the Sun and that the Sun is only one of billions of stars in our galaxy. Similarly, a holiday to Lyme Regis to look for fossils was a thrill, one of my favourite days of the year would be a trip to either the Natural History of Science Museum in London and I still had considerable hope that sometime in the twenty first century everyday life would resemble something from Star Trek, complete with teleportation devices.


But as I continued studying science through A levels and then pursued physics for a degree and then a PhD the wonder of it all faded. Maybe it was because I came to associate the subject with exams and deadlines and worries about coursework grades and test results? Maybe it was because as you learn more about a subject you inevitably become more aware of its limitations and of just how limited your own expertise is compared to the entirety of your chosen field? Whatever the cause, by my late twenties I was very uncertain I would continue to work in an STEM career. 


While I was trying to figure out what I wanted to do I began tutoring as a way of making ends meet. I never anticipated how much I would love teaching and that I would tutor as a full time job. When I tried to explain to people why I loved my work I kept describing how wonderful it was to spend time with people who are still amazing by things that I had previously taken for granted - that pi is a number that continues on forever with no discernible pattern, the field lines around a magnet displayed using iron filings or just the simple joy of someone understanding long multiplication/electromagnetic induction/integration by parts for the very first time. I found working with people who still had enthusiasm and excitement around science and maths helped me reconnect with my own love of these subjects.


So, in case anyone else is in need of some geeky festive cheer, or a way of making science and maths relevant to the holiday season, here are a few ideas for STEM related Christmas activities…



Star Wars snowflakes - these beautiful templates feature several of the best known characters from the Star Wars universe. Designer Anthony Herrera has been producing these patterns for several years and a new set has been published for The Force Awakens (for all those who are counting down to Dec 18th as well as Dec 25th). I have found snowflakes like these to be a wonderful way of explaining reflective and rotational symmetry in maths.



Christmas cards made using conductive paint. Bare conductive released this innovative electrically conductive paint a few years ago. The paint can be used to draw circuits on cards and other pieces of artwork to allow the inclusion of LEDs and other electronic components. The company also have several templates for Christmas cards on their website, so if anyone wants to give Rudolf a really bright (flashing) red nose this year, this is the place to go. 




Fractal snowflakes using the Scratch programming language.  Scratch was developed by MIT as a way of introducing children to programming and coding. The intuitive way students can click together blocks of codes makes the language incredibly easy to learn and allows for endless projects that teachers and students can customise and refine. One favourite topic of mine is to use the program to draw a Koch snowflake - a fractal design in which simple triangles are repeated at smaller and smaller intervals. 



Merry Christmas!



p.s. I know that for some people the festive season can be much bleaker than a loss of enthusiasm in their subject and I didn’t want to forget those who might be alone and at risk over the holidays, so this year I will also be including Crisis at Christmas and Age UK on my Christmas list.

Junior Doctors' Contract

There are few things I value more than education: health is one of them. I also think it is the moral obligation of any wealthy, industrialised country to provide its citizens with healthcare that is free at the point of service rather than leaving people to the mercy of private companies where the major motive is profit and I am completely certain that without the NHS neither I nor most of my loved ones would be healthy or even alive today.


I am therefore horrified by the proposed changes to the contracts for junior doctors on the NHS


Since news of the new contracts became public many current doctors and medical students have voiced their opposition - including wondering how they would be unable to cope with pay cuts between 25% and 40% and concerns about the effects long hours would have on their concentration and patient safety. People have detailed the significant costs to practicing medicine - the 6 year degree that at present will see students graduate with £54,000 in debt for tuition alone, the compulsory registration for the GMC and other professional bodies and the the hefty indemnity insurance. Not to mention the resistance to the reclassification of normal working hours to include Monday to Saturday 7am to 10pm.


Not being a physician myself, I may not be able to speak from personal experience of practising medicine. However I have taught many students who were hoping to go to medical school and so can speak to the level of dedication and diligence these people had. I was lucky enough to work with students who, even in Year 10, were doing extra work to ensure they achieved an A* in all their subjects and then saw their workload increase massively as they began on their A level courses. They spent hours volunteering in local hospitals, on extra circular activities, went through additional tests (BMAT, UKCAT, GMSAT), gruelling interviews and all in addition to getting spectacular grades.


And that was just to get into medical school, never mind successfully completing the course or embarking on any of the post graduate training required.


The amount of dedication and academic ability these students showed left me in no doubt that they could excel in numerous other careers if they ever decided to leave medicine. It also made me certain that their motivation was not simply a well paid job as there would be many other professions where they could command much higher salaries for the same amount of work (or even less).


I also do not envy anyone who is embarking on such a long university degree in the era of £9,000 per year tuition fees. True, these fees are paid by all students and not just prospective doctors but a medical degree is twice as long as many full time bachelor degrees and, given the massive workload, leaves students less able to take on part time and holiday work to support themselves. Not to mention the substantial costs of living in many parts of the UK. I have lived in London for over ten years and am still staggered by the cost of rental accommodation so can never quite forget the financial burden anyone who studies in London is taking on.


The question over what constitutes normal working hours is also rather familiar to me. Although my schedule is nothing compared to those typical for medical professionals I do know something of how working into the evening and at weekends disrupts time with family and friends and can leave a person isolated because they end up out-of-synch with almost everyone else. Jeremy Hunt insists that when changing the allowance for anti-social hours the basic pay for junior doctors will be adjusted to compensate so that no one loses pay — although I am mystified as to the calculation behind this and, even if it were true, worry that it would cause doctors to chose specialties with less night and weekend work (e.g. dermatology) over those that are 24/7 out of necessity (like A and E).


I notice that the integrity and selflessness of so many in the medical profession has continued even in their protests against the new contracts. How easy it would be for the doctors to simply walk away, let the NHS collapse and then find new jobs in private healthcare (which would be experiencing an unprecedented increase in demand) where they would have both better working hours and higher salaries. But so many doctors continue to fight, even when the general public will suffer far more than they will as a consequence of doctors becoming dangerously overworked and leaving the NHS. How sad it is that this fight was ever theirs in the first place.


The story of Ahmed Mohamed, a 14-year-old aspiring engineer from Texas who was arrested when he bought a digital clock to school, serves as a horrible reminder of how fearful and suspicious people can be of intelligence and technological curiosity. Ahmed, who brought the clock to school to show his teacher, was arrested when staff at his school were convinced it was actually a bomb. Police later informed reporters that they did not believe a student would build a clock merely for curiosity (!) Sadly, this story may also be indicative of the enduring prejudice surround people of the Muslim faith and culture. It also seems particularly baffling that a device that looks like a clock is perceived as threat in a Texas school when increasing numbers of teachers and lecturers in US schools and universities are being armed, which has already caused a least one fire arm related accident.


Sadly, history is full of scientists, engineers and inventors who have been berated and even arrested for their work –  Galileo Galilei, Charles Darwin and Alfred Kinsey to name just a few. While it is horrifying that anyone in the 21st century exhibits such regressive attitudes, the numerous means of mass communication in the modern world do offer students like Ahmed Mohamed a certain amount of protection from their antagonists and also a way to connect with people who support scientific and technical investigation. As the story of Ahmed’s arrest spread, numerous high profile public figures  (including Mark Zuckerberg) took to social media to offer their support. However, support was not limited to those in STEM related careers: the actor and activist George Takei sent an immensely empathic message that drew on his experiences as a Japanese American who was sent to an internment camp because his heritage was perceived as threatening. Artists and musicians (including Pharrell Williams, Janelle Monáe) have also rallied behind the #IStandwithAhmed hashtag – a fitting acknowledgement of the way penalising curiosity, imagination and investigation will damage all areas of society, not just science and technology.


To show my support for Ahmed, here are a few of my resources linked to clocks and measuring time:


1)   A ferrofluid clock. Ferrofluids are a suspension of magnetic materials that create beautiful and complex patterns when exposed to a magnetic field.


2)   A clock based on the Fibonacci sequence

3)   A neat explanation of modular arithmetic (also known as clock arithmetic), which is widely used in computer science and cryptography.


4)   Some work based on convert between fractions of hours and minutes e.g. how 0.5 of an hour is 30 minutes not 50 minutes. I find this is a common sticking point for students doing calculations on speed, distance and time


5)   Clocks based on square roots, the Periodic Table and general maths geekery.

Volunteering with TutorFair

Throughout my first TutorFair volunteering event a single word kept coming to my mind – pluripotent. This term, which describes the capacity of stem cells to become almost any cells of almost any tissue or organ in the body, is the only word I could find to encapsulate the shear amount of potential present in a room filled with SEO scholars who are trying to decide which route to take for the next stage of their studies and how prepare themselves for a university education which could equip them for so many possible careers.


Around 100 students (who will be going into Year 12 in September) attended the event during the summer holidays which was designed to help students prepare for University admissions by providing information about university league tables and UCAS points, together with advising on personal statements and discussing the transferable skills someone can gain from studying at the university level. We also talked about the numerous different routes a person could take to end up in a specific career (e.g. some of the different subjects studied by people who are currently members of parliament) and how common it is for someone to switch careers several times over their working life. One exercise that I found particularly interesting was trying to imagine what jobs children currently in primary school might be doing when they become adults – might some of these jobs be in fields that we have barely discovered yet? And what skills and subjects will become vital in the future? Might computer programming be an essential skill as technology becomes a bigger part of everyday life or will artistic and creative subjects become more valuable as automation becomes able to take over from humans in roles where logic and calculation are required?


The event did make me more aware of the increased obstacles current school students face, including the increased tuition fees and ever more competitive job market that awaits them after graduation. It also made me remember how difficult it can be to accurately predict exactly which subjects will be most useful to a specific degree course and a given career – I studied physics at university but I found the topics covered in further pure maths an absolutely invaluable addition to physics and now will be teaching a course to help students with these topics so they can excel on a physical science or engineering degree. However, it did also leave me incredibly heartened to spend time with people who are only beginning an immensely rewarding and enjoyable phase of their lives and who really do have the potential to achieve and become so much.


Anyone interested in volunteering with TutorFair can get more information here https://www.tutorfair.com/user/register/volunteer


A copy of this post also appeared on the TutorFair website

What's in a name?

Some people might be wondering how I have the nerve to use the name Polymath Tutor when the term polymath is typically reserved for luminaries such as Leonardo Da Vinci and Bertrand Russell. I want to make it clear that the name is not intended as a boast about my own abilities but rather as a reflection of the multidisciplinary approach I try to take with my teaching and how I hope learning about maths and science can help many areas of someone’s life


I chose the name because


  •   I think encouraging a love of learning is as important as giving guidance about a particular subject.


  • Every student has a unique memorising and understanding information and will find different aspects of a subject engaging. Numerous different models of learning styles have been proposed, although the idea of specific learning styles is not universally accepted. However, for individual tuition to be fully effective, it is often necessary to use many different methods of presenting a topic and making it relevant to someone’s own interests and abilities. I have taught many students about the periodic table but my lessons often contain songs and artwork in addition to material about sub-atomic particles and reactivity trends.


  •   It is often inaccurate to think of the subjects I teach as completely separate entities. So much of physics relies on maths that they overlap on many topics and there are countless crossover areas between biology, chemistry and physics.


  • Most scientific research requires a huge amount of collaboration between scientists and engineers from different specialities.


  •   A certain level of literacy and numeracy is required to function in the adult world. Think how vulnerable someone who has problems reading becomes when they have to decide whether or not to sign a legal contract such as the tenancy agreement on a flat, or write a covering letter when applying for a job. It may be that a certain level of scientific knowledge is also becoming vital as technology becomes a bigger and bigger part of everyday life and complex and controversial scientific topics enter public and political debate. The recent controversies over vaccination and the outbreaks of contagious diseases such as measles are a stark example of the risks of limited scientific literacy.


  •   Perhaps it is more constructive and more accurate to think of subjects adding to each other rather than detracting from each other. The great Richard Feynman explained this better than I ever could and a beautiful illustration of his argument can be found here.


  •  Speaking of Feynman, how many of the truly great scientists were able to achieve so much because they retained the creativity and imagination needed to link together previously disparate topics in their own fields and to form novel views on existing research? One of my favourite examples of this would be Albert Einstein’s theory of general relativity in which gravity is considered as a curvature in spacetime as opposed to simply a force of attraction between objects with mass. While there were many people who had studied the mathematics Einstein used to make his breakthrough he was the only person with the ingenuity to understand what the results of their calculations meant. 



  • The indirect benefit that a subject can give a student should never be ignored. I know that my physics and maths benefitted greatly from the logical and structured way I was taught Latin and I am sure a big part of the reason I am able to stand in front of a class is because of the confidence I gained from performances for music and drama.


  •  Many people find themselves hindered in their professional life because their areas of expertise are so narrow. There are numerous examples of scientists who are brilliant when carrying out their own research but lack the communication skills to make others interested in their projects and thus struggle to get funding for their work or attract students to their research groups.  Conversely, many people in creative careers struggle to do their accounts and keep track of their finances because they find maths problematic.


  •  As it becomes increasingly rare to stay in the same career for one’s entire working life it may become increasingly valuable to study a wide range of subjects and skills.

R.I.P. Terry Pratchett

Like so many around the world I was greatly saddened by the death of Sir Terry Pratchett earlier this year. Pratchett’s books, especially the discworld series, have been favourites of mine for many years: I would eagerly await the publication of a new title and also find myself returning to old favourites again and again. Many people watch The Sound of Music or It’s a Wonderful Life each Christmas but I would reread Hogfather each year.


Pratchett was not only an immensely prolific author, writing more than 70 novels over the course of a four-decade career, but an incredibly skilled one. He achieved the almost impossible feat of dealing with complex and controversial topics in a way that was accessible, thought provoking and incredibly funny. He was also unfailing moral without being self-righteous, intelligent without being pretentious and astute without being cold[1]. The worlds created in his imagination were wonderful mirrors of our own where I (and so many others) happily got lost countless times. Pratchett’s down-to earth and irreverent sense of humour continued into his later life, when he referred to his Alzheimer’s as “the embuggerance.” I cannot imagine how distressing a neurological condition must have been more someone who relied on their imagination for their living and could create a world behind their eyes that was as rich, varied and bizarre as anything reality could offer.


The topics covered in Pratchett’s work were greatly varied and include religion, gender equality, the movie industry, fairy tales and several Shakespearean works. A fair number of scientific and tech related topics are also referenced; among them cryptography, chaos theory and the many-worlds theory of quantum mechanics. One of my favourites of his treatments of the scientific world is the idea of a new colour (octarine, the colour associated with magic that can only be seen by wizards).  The idea of different colours corresponding to different wavelengths is a fairly common topic on most KS3/GCSE physics courses but the way in which our eyes register different colours is slightly more complex, involving specialised cells our eyes which are sensitive to different wavelengths. However, while humans have three types of these cells (that are sensitive to red, blue and green light) some creatures have many more, enabling them to see colours we have no name for and no way of describing or visualising. An excellent summary of this idea may be found here.


Perhaps the most fitting tribute to Pratchett has been the news that his name will be incorporated into unseen scripts used by the software and hardware that make up the internet. The idea that his name will be ever present in the everyday life of so many people seems a richly deserved honour for such a prolific and much loved author. GNU Terry Pratchett!


[1] Not to mention incredibly fond of footnotes.