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Which chart should you use?

February 22nd, 2011


I just stumbled upon this graphic for choosing which chart you should use to represent different data. It seems well done and is definitely worth a look. Click the image for a closer look on Flickr:

How to Choose Chart Types

Elections, Journalistic Rhetoric, Electoral Reform

May 8th, 2010


On May 6th the British People voted for a hung parliament.

There is a tradition in journalism to seek to reduce complex issues down to the simple; to form a narrative which describes in terms that a casual reader/viewer/listener can consume with the minimum of effort. So far as the reduction accurately describes the situation they attempt to convey, the journalist succeeds.

Facts are simple, but their analysis is complex. Let’s start with some facts: excluding the one constituency that has not yet returned at the time of writing, 29,653,638 people voted in 649 constituencies for dozens of parliamentary candidates, the majority of whom were representatives of political parties. Within each constituency, candidates who received the most votes won their seat and became an MP. 306 of those were Conservative, 258 were Labour, 57 were Liberal Democrat. Other parties got 28 seats between them.

The first-past-the-post system means that the votes for a losing party in a constituency count for nothing. If we disregard these votes, then actually 13,863,530 people voted for their MP, which is 47% of the overall turnout. 7,279,220 voted for a Conservative MP which is 25% of all the people who voted. The turnout was around 65%, so as a percentage of people who could have voted, the people actually responsible for returning the 306 Conservative MPs constitutes 16.25% of the electorate.
(Data Source The Guardian DataBlog).

As I have suggested, analysis of these results is complex, so I will attempt to be minimalistic in my interpretation. What is clear, I think is that the signal that is produced by this (perhaps any?) election is chaotic, and complex. However the analysis that the the British People ‘spoke with one voice’ is absurd. Patently they spoke with many, many voices. How then can the journalistic trick of reducing the signal of the election down to the pithy simplification that “the British people voted for a hung parliament”? It confuses intention with consequence in the most pathetic manner. To restate it correctly, the British people voted, the result of which is a hung parliament.

So What?

The electoral system manipulates the votes of the electorate to produce a result. If you infer from the consequences of the vote to what the voters intended then you are bound to ascribe to the voters their support for the electoral system. That is to say, because the result was a hung parliament, voters voted for a hung parliament. Or, going further: Voters got exactly what they wanted. Concluding by going further still on this grotesque line of reasoning, therefore Voters rejected electoral reform; they got what they voted for.

Wait, what? If you remove the result from that, doesn’t that come down to arguing that because voters voted under a particular electoral system, they voted for that electoral system? That line of reasoning is preposterous. Surely no serious journalist would use such a slight-of-logic?

Kay Burley, Sky News

This interview exchange between Kay Burley of Sky News and David Babbs of 38 Degrees may sound familiar…

  • Burley The public have voted for a hung parliament, we got exactly what we voted for
  • Babbs What the people voted for [we believe] is they voted with hope for something better…
  • Burley 65% of the public who were eligible to vote, voted for a hung parliament
  • Babbs Yes, and people who… [gets cut off, the first of many]

Kay Burley’s analysis of the election is exactly the sort of lazy analysis I suggested above. She does herself no favours by the interview disintegrating into a series of ugly attacks on Babbs that is frankly painful to watch, but the crux of the interview is that she has swallowed the ‘voted for a hung parliament’ narrative lock-stock and barrel, and refuses to discuss electoral reform outside that narrative.


The real argument about electoral reform is about enfranchisement. This goes back to my earlier numbers; it could be argued that if the Conservative party were to govern as a minority, then only 16.25% of people in the country are responsible for that government, or 23.5% if you include the people who voted for Conservatives who weren’t elected, or 36.1% if you further disregard the people who did not vote. Whichever percentage you choose, they achieved 47.1% of the seats at the election. There is the source of the inequality that Babbs is arguing against.

The discussion about electoral reform should be: can people live with an electoral system that has that statistical reality? The only relevance that the current election should have in this discussion is that the result brings about the sorts of power brokerage necessary for a discussion on electoral reform to happen at high levels, because the Liberal Democrats could act as king-makers.

This is not particularly relevant to this blog, but I have no other forum on which to express these views. Ordinarily I try not to get involved in such discussions. However, there is much to discuss here from a philosophical and political perspective (as well as a statistical one). If the general election is not being discussed in classrooms, then it should be. I can’t believe that it is not.

If you are interested in doing your own statistical analysis of the election (or previous elections), then the Guardian offers data for you to do so:

Finland’s Education System

April 10th, 2010


An interesting report on Finland’s education system was on the BBC News website today:

Report on Finland’s Education System

I think there are a few things that they miss out from the report, like a very homogenous population, a smaller wealth gap between rich and poor, and a very low density of population. Still, it does paint the picture of an idyllic scenario of an educational system free from interference from politics. I wish a party in the UK would put that in their manifesto!

Mandelbrot Set

February 12th, 2010


An incredible rendering of the MandelBrot Set, which drives home the notion of infinite complexity!

As the comments underneath the video allude to, there is some utility here to attempt to consider the size of magnification that occurs during a portion of the video, and how to express magnifications of such a magnitude.

Pie Chart Flags

November 4th, 2009


Another interesting website, this one visualises flags as pie-charts that reflect the proportions of the colours in their flags:

Flags By Colours

It would be a fun and worthwhile activity to use this site to exercise KS3 students’ abilities to mentally construct and destruct pie charts in a game of ‘guess the flag’

Visualising Tiny Things

November 4th, 2009


I stumbled across this lovely page from the University of Utah today, which is extremely simple, but nevertheless well done:

Cell Size And Scale

From a scientific perspective it is interesting to reflect upon the relative sizes of elements, from a Coffee Bean to a Carbon Atom (through various things such as a human Ovum, Sperm, various viruses, compounds and so on).

From a mathematical perspective it is also interesting for the way in which the relative scales are measured in the top-left. Exploring the different notations for small sizes would be a useful exercise in place-value for all levels of Key Stage 3 and 4.

Proportions v Magnitudes

October 25th, 2009


In the BBC Website Magazine today is an article about proportions and magnitudes. It made me reflect that we often spend time teaching students how to express numbers in different forms, but rarely attempt to give students an understanding of how the numerical forms differ, and what they represent.

This article is a little heavy on the politics for an average maths classroom, but is perhaps useful for A-level students, and is definitely useful for any teachers teaching the IB, as it has excellent cross-over with theory of knowledge. Worth a look

Another Report about Education

October 16th, 2009


The Cambridge Primary Review today published their recommendations for how the primary curriculum and classroom environment should be arranged. The briefing is an interesting read, the headlines of which can be found on the BBC News website.

As I read the part on SATs I reflected on the way in which the relationship between politics and education continues to work to this day. The review argues that SATs narrow the curriculum focus and put pressure on children unnecessarily. It argues that the concept of standards that underlies the system of SATs is “restricted, restrictive and misleading”. It further argues that assessment of childrens’ learning should be detached from assessment of schools’ accountability.

It is perhaps inevitable that this is how education and politics interact: governments change the way education works with an agenda justified by their electoral mandate, but often with no educational justification to back it up. It can then take a decade or more for evidence to be gathered, arguments to be made and reports to be compiled before the deficiencies of the system can be established to the satisfaction of politicians, and the scheme can be scrapped. Then, another government can come in with their agenda and try again.

I knew that SATs restricted curriculum, failed to assess students reasonably and were a monumental waste of time and money, years ago. I’ve blogged about it before, years ago. Most of the bright, intrested teachers that I’ve met have known similarly. But education is one of the few things that governments with mandates can interfere with almost at will, and the obvious truths for teachers on the ground are difficult to express to people living in the ivory towers of Westminster. It’s about to happen again. I believe that the best we can hope is that they (whoever they are) make a slightly less-bad set of decisions in this next round of reforms.

Mary Midgley

September 23rd, 2009


Mary Midgley was born on September 13, 1919 and was the Senior Lecturer in Philosophy at Newcastle University. Despite publishing her first book at the age of 59, she has a fearsome reputation in the Philosophical community. Her work has largely focussed on science; attacking the pretensions of ‘scientism‘, and arguing in favour of scientific pluralism; that we must recognise “that there are many independent forms and sources of knowledge” (Myths We Live By, pp 26-7).

Famously, she and Richard Dawkins have had a thirty-year disagreement. Midgley argues that Dawkins goes beyond the scientific to sell “the worship of competition”; that he projects Thatcherite free-market economic beliefs into his theoris of evolutionary biology; a charge which Dawkins disputes!

In May 2009, my dad Alan McEachran, who has taught Philosophy and Sociology all of his professional life, gave a talk about the work of Mary Midgley to the Erasmus Darwin Society in Lichfield, Staffordshire. The prepared text for this talk follows:

Mary Midgley, by Alan McEachran

This is the second talk that he has given to the Erasmus Darwin Society. His discussion of John Gray is also available from this website.

Book Review: Plato’s Shadow

September 18th, 2009


Neel Burton, Plato’s Shadow – A Primer On Plato

Academic texts try to appeal to specific readerships. Though Plato’s Shadow has merit, this reviewer is left wondering who it was written for. It works best as a reference book of sorts, since it contains easily-read summaries, each of between two and twenty pages, of all Plato’s dialogues. Each précis is faithful to the original text and provides the reader who is unfamiliar with any dialogue a clear account of what is to be found there. The author also devotes the first forty pages to a useful account of the historical context of Athens and its relations with other city-states, and to a discussion of Pre-Socratic Greek thought and the place of Socrates in the dialogues which follow. A final introductory chapter also looks at scholarly views of when Plato’s works were written, in what sequence, and with what connection to each other.

A student encountering Plato on a Philosophy or a Classics course would undoubtedly benefit from having this book to reach for as a preliminary step before reading one of the dialogues for the first time. A general reader would also find this a useful reference book because of the way it treats each dialogue separately – something you don’t usually find in such a short and accessible paperback.

However, to call this “A Primer On Plato”, as the author does, is misleading. Anyone trying to understand Plato’s thought won’t find much help here. Nothing is done to point the reader to where Plato is specifically exploring metaphysical, ethical, epistemological, political, etc. themes. This book cries out for an index; both the student and the general reader are likely to want help in finding where Plato talks about The Sun Metaphor, or Forms, or Diotima. The occasional attempt is made to enhance understanding by the use of an illustration; this makes most sense in the Meno and Republic dialogues, though in the latter it is The Cave which is illustrated rather than The Divided Line, which almost every other book about Plato rightly and helpfully presents as a diagram.

This text is a welcome addition to a shelf of reference books, but it shouldn’t be seen as a general introduction to Plato’s thought.