On First Reading Wittgenstein

Over the years, a handful of books have pointed my curiosity in new directions. But there is one book that is still opening up new areas to explore.

In the late 70’s, after completing my first degree in Agricultural Engineering, there was a sudden drop in the job market as many manufacturers left the UK. I have always, and still do, enjoy mathematics and decided that I had better job prospects building up my mathematical skills. Cranfield University provided a course that took engineers, programmers, and scientists and developed their mathematical skills to Masters level in Applied Mathematics.

The course was full of mathematical terminology that was strange to me and I struggled. Luckily a normal day was structured with lectures in the morning and then we were free in the afternoon to catch up with the work. Most of my fellow students went back to their rooms in the hall of residence but I stayed in the students room at the end of the maths block along with one other, Mike. Mike was much older than me and after a BSc in mathematics had been writing software for the Civil Service. The course was a way to get a better job to support his increasing family. I was sure that I irritated him with my many questions about mathematical problems but with great patience he always had an answer.

During summer, the maths building would get very warm and to cool down I would go to the library situated in the middle of the campus. It had high ceilings and big windows and was well stocked with mathematics books that I could search through to help with the course work. One day I found a copy of Bertrand Russell and Alfred North Whithead’s three large volumes of the Principia Mathematica which was their attempt to establish the foundations of mathematics. It was notorious in world of mathematics for taking over four hundred pages to prove that 1 + 1 = 2. I could read the first few pages but my eyes glazed over when logical symbols filled the pages. On returning to the maths department I asked Mike if he knew of anybody who had ever read the three volumes. He replied that there was at least four people: the authors, Kurt Gödel and Ludwig Wittgenstein. I had heard of Gödel because I attended a seminar held in the department, which was way beyond my comprehension. But not Wittgenstein. Mike went on and described how he came from a very rich family in Vienna, started as an engineer and became interested in mathematics and its foundations. After studying with Russell he produced not one but two great works in philosophy the Tractatus Logico-philosophicus and the Philosophical Investigations. The thought of an engineer turning out to be a great philosopher gave me a some hope with my mathematical struggles.

A few days later I was walking past the campus book shop and I dropped in my my regular visit. It contained text books that covered the wide variety of course that the Institute offered. However, I was surprised to come across a copy of the Tractatus. I read a few pages and, although I didn’t understand, it caught my attention with its short sentences that had the appearance of logical statement yet have a poetic feel to them:

1 The world is everything that is the case.

1.1 The world is the totality of facts, not of things.

1.11 The world is determined by the facts, and by these being all the facts.

I bought the book.

Over the months of reading the Tractatus it emerged that it was not a text book about philosophy but a solution to all philosophical problems. Wittgenstein’s approach was to recognise that when we misuse language then words can lose their meaning and when meaningless words are used they lead to problems in philosophy. The Tractatus was an attempt to show when words lose their meaning and when this happens in the case of philosophy the problems disappear.

I successfully graduated in Applied Mathematics, and over the years gathered many books and papers, about Wittgenstein and his work, including his second philosophical work the Philosophical Investigations. The Philosophical Investigations criticised large sections of the Tractatus and developed a new approach to identify when words lose their meaning.

Wittgenstein’s work is full of sharp observations about the use of language in a wide range of subjects ranging from mathematics and logic to music, religion and culture. I continue to enjoy exploring these subjects which I probably wouldn’t have explored if it hadn’t been for a chance conversation that lit my curiosity.

Three Improvements for Online Learning

Online learning is increasing the access to education and training. However the quality of the courses is very mixed. I have gathered some of the problems that I have experienced and suggested some solutions.

Over the years I have used online learning to increase my knowledge about a wide range of subjects and develop new skills. The online courses that I have taken include: creative writing, journalism and film making courses through the Open University and FutureLearn, developing business skills using digital technology with Digital Business Academy, learning about the underlying algorithms of Artificial Intiligence by entering into Kaggle competitions, and the impact functional programming on bioinformatics by solving problems on the Rosalind website. I have enjoyed these courses and learned a lot but there are some key changes that could be implemented to improve the quality of future online course:

1. Course Description

Often the course description is aimed more at marketing the course rather than specifying what the student will achieve. Although this approach can attract student numbers it can fail to meet a students expectations by either being too easy or too difficult.

Another aspect is pitching the entry competence at too low a level for the course to attract numbers of students. For example “ … it involves no computer programming, although you need some experience with using computers for everyday tasks. High-school maths is more than enough”. But once the course has started the competence levels required suddenly shoot and up moves into highly advanced topics that would be considered difficult at first year university!

What is needed is a clear description of what the learner will achieve by the end of the course. One approach would be to have a simple quiz to help the student decide whether they had the correct competence level for the course. Another is a system that could be developed which would monitor the progress of the student and if they were struggling then other online course or additional material could be recommended e.g. top up via Khan Academy.

2. Rate of Learning

My experience has been that the rate at which new concepts are introduced and reinforced can vary: one minute the ideas are straight forward and clearly described with supporting examples but suddenly jump to new concepts which are difficult to understand. All this can make the rate at which I learn very difficult as I find myself going back to the beginning of the course to find the content that I misunderstood, or search the web for a better explanation.

Another barrier to the speed of learning is the presentation of the material. Unfortunately some of the material looks like cut-and-paste from a lecture notes, or worse, sections are written by different authors and are not consistent in the use of terminology. Sometimes videos are involved, but they can be difficult to link to the course content because they usually cover areas outside of the course.

Usually the student can monitor their own progress through the course by answering questions at the end of each section but the questions rarely test a deep understanding of the material. Also, the answer can be of the yes/no type but if the learning requires the application of a concept then the workings are not checked only the final answer. A lot can be learned from applying a concept and therefore it would be helpful to analyse and point out where the application was going wrong.

The courses produced by the Open University remain the benchmark for online learning and the book Teaching Through Self-Instruction: How to Develop Open Learning Materials gives an excellent description of the process of developing a course. Their approach could be adopted for future online courses. Another aspect is improving the style of writing and lessons could be taken from Look and Learn which was a British weekly educational magazine for children. Its aim was to inspire the imagination of its readers with sharply written articles and with a mix of photographs and diagrams gave it an overall feeling of adventure.

Finally, progress of the student could be be monitored using an approache similar to Knewton with its technology that adapts to students’ proficiency levels with each interaction. Students don’t have to complete a formal assessment or diagnostic to get the instruction and practice they need — it’s provided just-in-time as students work to complete assignments. For problems where the application of a concept is important then there is an opportunity to develop AI based technology using similar approaches to Q-Learning.

3. Student Support

An important aspect of online learning is the level of support provided to the student, which in most cases is via forums where questions are asked and fellow students help to answer them. The answers are usually voted on and the best one has the most votes. The forums that I have experienced have moderators but unfortunately their involvement has been minimal and therefore opportunities to help with learning have been missed. For example when a question is asked sometimes the people answering may answer a different question. If the moderator had intervened to tease out the underlying problem that is troubling the student then a better answer would be found. All forum moderators should be trained to get the most out of forum activity. Or technology could be developed to analyse the question and relate it to the course content in a way that provides guidance to an answer.

Another aspect is helping students who are struggling to keep up with the course due to motivation, or othe emotional issues. A lot of research has been done in this area for example the work carried by Ormond Simpson contains lots of practical advice.

Online learning has increased the access to education around the world which has had an impact on many peoples lives. However, the next challenge for online learning is to improve the quality of the course content so that the participants will approach the same levels as universities and therefore have a credible level of knowledge. This will require more investment in developing the courses as well as identifying new opportunities for ground breaking technology.

The Shipping Forecast

The Shipping Forecast with its steady and clear voice takes our imagination out to a ship that is clinging onto a cold grey sea.

"Forecast issued by the Met Office on behalf of the Maritime and Coast Guard Agency at 5:05 on the 6th September. The general synopsis at midnight Low 50 miles west of Bailey 979 expected Norwegian Sea 991 by midnight tonight. New low expected 125 miles west of Fitzroy 999 by same time. High Biscay 1025 dissipating The area forecasts for the next twenty four hours. Viking Southerly, veering southwesterly, 5 to 7 occasionally gale 8 at first. Moderate or rough, occasionally very rough for a time in north. Rain at first.Moderate or poor, becoming good. North Utsire, Southerly gale force 8 expected soon, Southerly, veering southwesterly, 5 to 7 occasionally gale 8 at first, Moderate or rough, occasionally very rough for a time in north, Rain at first. Moderate or poor, becoming good..."

The Air Ministry started broadcasting its weather shipping programme in 1924, using 13 maritime zones, twice daily on the Home Service. It was suspended during the Second World War, but was relaunched in 1949. Today the Shipping Forecast is produced by The Meterological Office and it’s broadcast four times throughout the day: 5:20 am, 12.01 pm, 5.45 pm and 00.48 am. Sailing By is a short piece of light music composed by Ronald Binge is used before the late forecast to give the helmsman time to tune in. When the late forecast is finished the National Anthem is played.

There are now 31 zones, which are given out in strict order, beginning at Viking in the north-east bordering Norway, and proceeding in a clockwise direction round the British Isles. Only seven areas survive from the original list: Forties, Humber, Dogger, Thames, Wight, Shannon and Hebrides. The last change to the zones was in 2002 when Finisterre became FitzRoy, which is name of the pioneering meteorologist Admiral Robert FitzRoy and who was captain of HMS Beagle on which Charles Darwin sailed to South America.

The forecast is full of precise technical terms that have to be decoded. For example, the terms ‘veering’ and ‘backing’ refer to the change in wind direction. When a wind is veering it is changing in a clockwise direction, whereas backing is anti-clockwise direction. Also, ‘variable’ means winds of less than force 4 that are changing by 90 degrees and ‘cyclonic’ means there will be considerable change.

The rhythmic, measured pace with which the Shipping Forecast is recorded has ensured that it is a as a cultural icon in the UK. Many artists have used it in their work, and it was prominent in Danny Boyle’s London 2012 Opening Ceremony. But it is best captured by the pen of Seamus Heaney in The Shipping Forecast:

Dogger, Rockall, Malin, Irish Sea:
Green, swift upsurges, North Atlantic flux
Conjured by that strong gale-warning voice,
Collapse into a sibilant penumbra.
Midnight and closedown. Sirens of the tundra,
Of eel-road, seal-road, keel-road, whale-road, raise
Their wind-compounded keen behind the baize
And drive the trawlers to the lee of Wicklow.
L’Etoile, Le Guillemot, La Belle Hélène
Nursed their bright names this morning in the bay
That toiled like mortar. It was marvellous
And actual, I said out loud, ‘A haven,’
The word deepening, clearing, like the sky
Elsewhere on Minches, Cromarty, The Faroes.

The Art Of Listening

Could sound be a form of art ?

Art is open to our own interpretation and it is based on our knowledge and experiences, in particular memories. Good art should be challenging and question our perceptions of both ourselves and the world that we inhabit, and even change them. Experiencing sound can have the same impact as pictures hanging in a gallery and over the years I have gathered a number of sounds, including songs, that have opened my ears to wider appreciation of of a sonic landscape.

Chris Watson, one of the world’s leading recorders of wildlife and natural phenomena, remains a constant source for going beyond sound. In the following clip entitled Winter, he creates the sonic environment of the Holy Island as it might have been experienced by St. Cuthbert in 700 A.D.( It is best to listen to this and all of the rest of the selected tracks through headphones or loudly through speakers ). Towards the end of the piece you can hear the distant ring of a prayer bell which pulls you through the space filled with the sound of the wildlife, and the cold wind, towards Holy Island and its spiritual life.

Sometimes a recording of the natural world captures more than was expected. On May 19 1942, three years into World War Two, the BBC was planning to broadcast the song of nightingales. During the recording they captured the sound of bombers flying overhead on their way to raids in Mannheim.

The nightingales song, which is part of their mating strategy, and signals the continuation of life, is juxtaposed with the drone of the bombers as they pass over on their deadly mission symbolises questions of life and death.


Stockhausen is regarded one of the greatest composers of the 20th century, but listening to any of his work for the first time it can seem incomprehensible: full of electronic squeaks, chopped up voices fading in and out, and no sign of a a melody. But perseverance can bring great rewards!

In Stockhuasen’s Gesang der Jünglinge ( Song of the Youths ), which is taken from the apocryphal Bible text “Song of the Three Youths in the Fiery Furnace”, in which youths are tossed into a fire by King Nebuchadnezzar, but are rescued by an angel due to their faith-based song, he explores the optimism and energy of youth.

It is interesting to note that this is one of Paul McCartney’s favourite pieces which influenced his early career.

Stockhausen’s influence can still be heard today. In Oneohtrix Point Never’s Chrome Country, a track with a title that could point to a landscape lacquered in mirror we hear a mix of sounds bursting with childlike voices, drifting through rapid piano sounds and builds to an organ sound which is like the triumphant end of a High Mass.

Of course the richness of the human voice to express something beyond music is beyond doubt. One of the best examples is Meredydd Evans, who was collector, editor, historian and performer of folk music of Wales written in the Welsh language. Although I am not a welsh speaker, in Robin Ddiog ( Lazy Robin ) in his voice we can ‘see’ the cheekiness a robin sitting inside a house and asking us to open the door slightly so that he can see the sea:

Sometimes a choir can catch a the strength of a community that goes beyond the everyday and in the Treorchy Welsh Male Voice Choir’s version of When I Survey The Wonderous Cross. I have never been down a mine but their deep, low voices seems to sweep up from its depths into the bright sunlight:

I find that the clips above, and many more that have not been included, go beyond their original purpose, whether it is the melody and harmony of a song or recording the detail of natural world, to catch something that is difficult to express - is that art ?

Counting on A&E

The closest I have got to experiencing the demands on Accident and Emergency (A&E) of a hospital is watching the TV series MASH, but recently I was right in the middle of it!

Waiting for attention I was interested in the way that the staff were managing the wide range of medical problems that were rolling through the door. There were: people holding limbs in great pain, a head covered in sticking plasters, two to three people bright red and coughing, a queue of wheel chairs with a legs in plaster, and somebody hobbling around in too much pain to sit down. In the background Ambulances were rushing in and trollies were rattling along corridors. All of this activity is, in a management sense, ‘unplanned’ e.g. people could arrive at A&E anytime of the day or night with a wide range of problems. I started to wonder how a typical A&E is organised and operates to manage the situation and to meet the 4 hour waiting target.

A few days later I was waiting in another queue this time in my local coffee shop. As I slowly moved along I did a quick sum1 to work out how long I would have to wait and came up with the following calculation:

(4 customers) x (1 min/customer) = 4 minutes.

If the queue had been longer then I would have waited longer. Or if there had been more staff serving then the quicker the service and the shorter the waiting time. To apply the same approach to A&E I took some statistics from the data published monthly on A&E performance where the average number of people attending A&E per hour is approximately 12 / hour ( on average there are 8,500 people attending A&E for each hospital in NHS England per month ). I also assumed that a typical A&E department can manage 10 cases per hour then the using the same approach as a the coffee shop I calculated:

(12 A&E attendees ) x ( 6 minutes per attendees ) = 72 minutes or approximately 1 hour

which was close to my experience in A&E. The calculation confirms what we would expect: if the A&E department’s capacity was increased by adding more doctors and nurses then the waiting time would reduce. Similarly if the number of people attending A&E was reduced then the waiting time reduces.

Of course the calculation is too simplistic to be applied to the complex operation of an A&E Department because it assumes average quantities. But trying to answer the question: Why can it not be applied ? - highlights some of the underlying factors that are adding to the complexity of its operation.

Starting with the average arrival rate of A&E attendees, A&E statistics show that there is a wide variability during a typical week. For example Monday is the busiest day at A&E with attendance 13% above the daily average and also 13% above the next - busiest day, Sunday. Also, in 2013/14, 24% of A&E attendances arrived by ambulance or helicopter who require immediate attention. All of this starts to show the variability in the arrival rate of people requiring medical attention.

Similarly the wide range of patient’s medical problems will affect an A&E department’s capacity to manage their diagnosis and subsequent treatment. For example if there was a major emergency situation, say a train crash or a flu epidemic, then the capacity of A&E would be overloaded. Another area is diagnosing the medical condition. For example 3% of patients attending A&E have severe life threatening conditions and must be seen immediately. Also, if about 40% of attendees are not seen within an an hour of arrival at A&E their condition could deteriorate to life threatening.

There are many more factors affecting the performance of A&E for example the well publicised bed blocking and transfer to social care which can increase the time seen by the doctors and nurses. Other factors are not so obvious for example the impact of weather - when average daily temperatures hit 20°C compared with 5°C, trips to A&E rise by nearly 20%. However, very cold weather does also cause longer waits.

Although the assumption of using average quantities to describe the operation of A&E is over simplistic, asking the question “why do the assumptions break down ?” can gives a better understanding of the underlying factors that contribute to its performance. Based on my experience, the way that the staff manage the range of the medical problems that come through the doors of A&E is much more impressive than the TV characters Hawkeye and Trapper John!

1. More formally the calculation is an example of Little's Law which states that the long-term average number of customers in a stable system L is equal to the long-term average effective arrival rate, λ, multiplied by the average time a customer spends in the system, W. For a different and more detailed discussion on the application of Little's Law to staffing levels in A&E see: Little’s Law: The Science Behind Proper Staffing