Sandwich proofs and odd orders

Revisiting an old piece of work I reflect on the processes that led to it: intuition and formalism, incubation and insight, publish or perish, and a malaise at the heart of current computer science.

A couple of weeks ago I received an email requesting an old technical report, “Finding fixed points in non-trivial domains: proofs of pending analysis and related algorithms” [Dx88].  This report was from nearly 30 years ago, when I was at York and before the time when everything was digital and online. This was one of my all time favourite pieces of work, and one of the few times I’ve done ‘real maths’ in computer science.

As well as tackling a real problem, it required new theoretical concepts and methods of proof that were generally applicable. In addition it arose through an interesting story that exposes many of the changes in academia.

[Aside, for those of more formal bent.] This involved proving the correctness of an algorithm ‘Pending Analysis’ for efficiently finding fixed points over finite lattices, which had been developed for use when optimising functional programs. Doing this led me to perform proofs where some of the intermediate functions were not monotonic, and to develop forms of partial order that enabled reasoning over these. Of particular importance was the concept of a pseudo-monotonic functional, one that preserved an ordering between functions even if one of them is not itself monotonic. This then led to the ability to perform sandwich proofs, where a potentially non-monotonic function of interest is bracketed between two monotonic functions, which eventually converge to the same function sandwiching the function of interest between them as they go.

Oddly while it was one my favourite pieces of work, it was at the periphery of my main areas of work, so had never been published apart from as a York technical report. Also, this was in the days before research assessment, before publish-or-perish fever had ravaged academia, and when many of the most important pieces of work were ‘only’ in technical report series. Indeed, our Department library had complete sets of many of the major technical report series such as Xerox Parc, Bell Labs, and Digital Equipment Corporation Labs where so much work in programming languages was happening at the time.

My main area was, as it is now, human–computer interaction, and at the time principally the formal modelling of interaction. This was the topic of my PhD Thesis and of my first book “Formal Methods for Interactive Systems” [Dx91] (an edited version of the thesis).   Although I do less of this more formal work now-a-days, I’ve just been editing a book with Benjamin Weyers, Judy Bowen and Philippe Pallanque, “The Handbook of Formal Methods in Human-Computer Interaction” [WB17], which captures the current state of the art in the topic.

Moving from mathematics into computer science, the majority of formal work was far more broad, but far less deep than I had been used to. The main issues were definitional: finding ways to describe complex phenomena that both gave insight and enabled a level of formal tractability. This is not to say that there were no deep results: I recall the excitement of reading Sannella’s PhD Thesis [Sa82] on the application of category theory to formal specifications, or Luca Cardelli‘s work on complex type systems needed for more generic coding and understanding object oriented programing.

The reason for the difference in the kinds of mathematics was that computational formalism was addressing real problems, not simply puzzles interesting for themselves. Often these real world issues do not admit the kinds of neat solution that arise when you choose your own problem — the formal equivalent of Rittel’s wicked problems!

Crucially, where there were deep results and complex proofs these were also typically addressed at real issues. By this I do not mean the immediate industry needs of the day (although much of the most important theoretical work was at industrial labs); indeed functional programming, which has now found critical applications in big-data cloud computation and even JavaScript web programming, was at the time a fairly obscure field. However, there was a sense in which these things connected to a wider sphere of understanding in computing and that they could eventually have some connection to real coding and computer systems.

This was one of the things that I often found depressing during the REF2014 reading exercise in 2013. Over a thousand papers covering vast swathes of UK computer science, and so much that seemed to be in tiny sub-niches of sub-niches, obscure variants of inconsequential algebras, or reworking and tweaking of algorithms that appeared to be of no interest to anyone outside two or three other people in the field (I checked who was citing every output I read).

(Note the lists of outputs are all in the public domain, and links to where to find them can be found at my own REF micro-site.)

If this had been pure mathematics papers it is what I would have expected; after all mathematics is not funded in the way computer science is, so I would not expect to see the same kinds of connection to real world issues. Also I would have been disappointed if I had not seen some obscure work of this kind; you sometimes need to chase down rabbit holes to find Aladdin’s cave. It was the shear volume of this kind of work that shocked me.

Maybe in those early days, I self-selected work that was both practically and theoretically interesting, so I have a golden view of the past; maybe it was simply easier to do both before the low-hanging fruit had been gathered; or maybe just there has been a change in the social nature of the discipline. After all, most early mathematicians happily mixed pure and applied mathematics, with the areas only diverging seriously in the 20th century. However, as noted, mathematics is not funded so heavily as computer science, so it does seem to suggest a malaise, or at least loss of direction for computing as a discipline.

Anyway, roll back to the mid 1980s. A colleague of mine, David Wakeling, had been on a visit to a workshop in the States and heard there about Pending Analysis and Young and Hudak’s proof of its correctness . He wanted to use the algorithm in his own work, but there was something about the proof that he was unhappy about. It was not that he had spotted a flaw (indeed there was one, but obscure), but just that the presentation of it had left him uneasy. David was a practical computer scientist, not a mathematician, working on compilation and optimisation of lazy functional programming languages. However, he had some sixth sense that told him something was wrong.

Looking back, this intuition about formalism fascinates me. Again there may be self-selection going on, if David had had worries and they were unfounded, I would not be writing this. However, I think that there was something more than this. Hardy and Wright, the bible of number theory , listed a number of open problems in number theory (many now solved), but crucially for many gave an estimate on how likely it was that they were true or might eventually have a counter example. By definition, these were non-trivial hypotheses, and either true or not true, but Hardy and Wright felt able to offer an opinion.

For David I think it was more about the human interaction, the way the presenters did not convey confidence.  Maybe this was because they were aware there was a gap in the proof, but thought it did not matter, a minor irrelevant detail, or maybe the same slight lack of precision that let the flaw through was also evident in their demeanour.

In principle academia, certainly in mathematics and science, is about the work itself, but we can rarely check each statement, argument or line of proof so often it is the nature of the people that gives us confidence.

Quite quickly I found two flaws.

One was internal to the mathematics (math alert!) essentially forgetting that a ‘monotonic’ higher order function is usually only monotonic when the functions it is applied to are monotonic.

The other was external — the formulation of the theorem to be proved did not actually match the real-world computational problem. This is an issue that I used to refer to as the formality gap. Once you are in formal world of mathematics you can analyse, prove, and even automatically check some things. However, there is first something more complex needed to adequately and faithfully reflect the real world phenomenon you are trying to model.

I’m doing a statistics course at the CHI conference in May, and one of the reasons statistics is hard is that it also needs one foot on the world of maths, but one foot on the solid ground of the real world.

Finding the problem was relatively easy … solving it altogether harder! There followed a period when it was my pet side project: reams of paper with scribbles, thinking I’d solved it then finding more problems, proving special cases, or variants of the algorithm, generalising beyond the simple binary domains of the original algorithm. In the end I put it all into a technical report, but never had the full proof of the most general case.

Then, literally a week after the report was published, I had a notion, and found an elegant and reasonably short proof of the most general case, and in so doing also created a new technique, the sandwich proof.

Reflecting back, was this merely one of those things, or a form of incubation? I used to work with psychologists Tom Ormerod and Linden Ball at Lancaster including as part of the Desire EU network on creativity. One of the topics they studied was incubation, which is one of the four standard ‘stages’ in the theory of creativity. Some put this down to sub-conscious psychological processes, but it may be as much to do with getting out of patterns of thought and hence seeing a problem in a new light.

In this case, was it the fact that the problem had been ‘put to bed’, enabled fresh insight?

Anyway, now, 30 years on, I’ve made the report available electronically … after reanimating Troff on my Mac … but that is another story.


[Dx91] A. J. Dix (1991). Formal Methods for Interactive Systems. Academic Press.ISBN 0-12-218315-0

[Dx88] A. J. Dix (1988). Finding fixed points in non-trivial domains: proofs of pending analysis and related algorithms. YCS 107, Dept. of Computer Science, University of York.

[HW59] G.H. Hardy, E.M. Wright (1959). An Introduction to the Theory of Numbers – 4th Ed. Oxford University Press.

[Sa82] Don Sannella (1982). Semantics, Imlementation and Pragmatics of Clear, a Program Specification Language. PhD, University of Edinburgh.

[WB17] Weyers, B., Bowen, J., Dix, A., Palanque, P. (Eds.) (2017) The Handbook of Formal Methods in Human-Computer Interaction. Springer. ISBN 978-3-319-51838-1

[YH96] J. Young and P. Hudak (1986). Finding fixpoints on function spaces. YALEU/DCS/RR-505, Yale University, Department of Computer Science

Who not to feel sorry for facing an uncertain Brexit

map of areas with high indices of multiple deprivation in CornwallReading Julia Rampen’s “11 things I feel more sorry about than Cornwall losing money after Brexit” in the New Statesman, I agree with all the groups she cites who are going to suffer the effects of Brexit, but did not vote for it.

However, it is clear that, when considering Cornwall, which voted 56.5% to leave, where affluent second home owners and retirees are cheek-by-jowl with post-industrial poverty and decay, and which is now worried about the loss of regional funding; Rampen’s sympathy is, to say the least, muted.

This made me ponder other groups for whom I have little sympathy as we face the uncertainty, and quite likely utter disaster, of Brexit.

  • those, like myself, academics, professionals, who have reaped the benefits of open markets and labour, but ignored the plight of those who have suffered because of it
  • those who have accepted the narrative that those who suffered most were in some way to blame
  • the newspapers that lampooned and vilified Gordon Brown for his overheard private comment about a “bigoted woman“, but now happy to label leave voters who hold similar views as racist.
  • those that passively accepted the implicit racism of the leadership debates in the 2010 general election without comment
  • those who have accepted EU rules as an excuse for government inaction … such as happened with Port Talbot steel just before the referendum election
  • the governments and administrations of multiple hues over many years, who have applied EU regulations in ways that no other country would regard as reasonable

Some of these ‘unwilling vicitims’ will suffer from Brexit despite voting to remain. However, many of those who will suffer worst will have voted to leave, but only because remaining in offered them no hope either.

After a generation of closing our hearts to those suffering on our doorstep, we now demonise them yet again.



slaughter of the innocents – human shields or collateral damage?

By Huynh Cong Ut (also known as Nick Ut), image from Wikipedia

From the ‘Napalm Girl‘ in Vietnam, to Alan Kurdi’s body on a Turkish beach in 2015 and endless images of White Hat’s pulling children from the rubble in Aleppo, it is easy to become inured to the death of innocent children around the world.

In the church calendar, December 28th1 is the Feast of the Innocents or Childermas, a day to remember the children killed by King Herod as he sought the baby Jesus.

In Matthew’s Gospel we read:

 When Herod realized that he had been outwitted by the Magi, he was furious, and he gave orders to kill all the boys in Bethlehem and its vicinity who were two years old and under (Matt. 2:16, NIV).

However, for many it is the words in the Christmas carol, “Unto us a boy is born“, which is most familiar:

All the little boys he killed at Bethlehem in his fury.

Mary and Joseph had already fled, refugees to Egypt, so the babies were not simply slaughtered, but slaughtered in vain, an action missing its true target, like the bombs that killed Gaddaffi’s children and grandchildren in 1986 and 2011.

I’ve been reading Simon Garfield’s “Timekeepers‘ (a Christmas gift).  Garfield describes a meeting with Nick Ut, the photographer of ‘Napalm Girl’2.  The common story is that the US attack on the village from which Phan Thi Kim Phuc was running was a mistake, but Ut describes how in the village there were many dead Viet Cong, so that the mistake was more likely inadequate intelligence that the villagers had fled (Timekeepers, p.168).

A few weeks ago a BBC reporter in Yemen was visiting a school, which Saudi air strikes had repeatedly hit.  This was one example of many such incidents targeting schools during this conflict3. The reporter talked of how the school kept on working and pupils kept attending, despite the damage and the danger.  However, the report also showed the Houthi rebel arms dump next to the school.  “Can’t you move the school away from this?”, asked the reporter. “They would simply move the dump to follow us”, replied the headmaster.

Again this is a story we have heard so many times before: missiles fired from hospital grounds in Gaza, Ukraine keeping its air corridors open whilst in the midst of its air campaign against separatists4, ISIS preventing civilian evacuation from Mosul, or the South Korean artillery firing into disputed areas from a populated island.

In some cases civilians are deliberately put in the way of danger (as with ISIS); in others fighting in built up areas makes civilian presence inevitable (Aleppo, Gaza).  In some cases terror is the main aim of an attack or the civilians are seen as legitimate targets (as with ISIS attacks in Europe); in others terror is a deliberate secondary war aim (as with Dresden or Nagasaki). In some cases attackers seem to show flagrant disregard for civilian life (as in Gaza), and in others all care is take, but (often substantial) civilian deaths are accepted as collateral damage (probably the case with US drone extrajudicial killings).

Whether you blame those on the ground for using human shields or those attacking for disregarding human like, often depends on which side you are on5.

In most conflicts the truth is complex, especially where there are mismatches of firepower: Hamas in Gaza, anti-Assad rebel groups in Syria, or ISIS in Iraq would all have been slaughtered if they fought in the open.  And for the attacking side, where does the responsibility lie between callous disregard for human life and justifiable retaliation?  How do we place the death of children by bombs against those of starvation and illness caused by displaced populations, siege or international sanctions?

If the events in Bethlehem were to happen today, how would we view Herod?

Was he despotic dictator killing his own people?

Was the baby Jesus a ‘clear and present danger’, to the stability the state and thus the children of Bethlehem merely collateral damage?

Or were Mary, Joseph and God to blame for using human shields, placing this infant of mass disruption in the midst of a small town?

It is worryingly easy to justify the slaughter of a child.

Some organisations that are making a difference:

  1. The date varies in different churches, it is 28th December in most Western churches, but 27th, 29th Dec, or 10th January elsewhere[back]
  2. The ‘Napalm Girl’ recent obtained fresh notoriety when Facebook temporarily censored it because it showed nudity.[back]
  3. Another BBC report,amongst many, “Yemen crisis: Saudi-led coalition ‘targeting’ schools” documents this.[back]
  4. Before MH17 was shot down a Ukrainian military transport and other military planes had been shot down, and the first messages following the destruction of MH17 suggest the rebels thought they had downed another military aircraft.  Instead of re-routing flights the flying ceiling was raised, but still within distance of ground-to-air missiles, and carriers made their own choices as to whether to overfly.  Some newspapers suggest that the motives were mainly financial both for Malaysian Airways, and for the Ukrainian government decisions, rather than Ukraine using civilian flights as a deliberate human shield.[back]
  5. Patrick Cockburn’s comparison of Aleppo and Mosul in The Independent argues this is the case for the current conflicts in Syrian and Iraq.[back]

the rise of the new liberal facism

Across Europe the ultra-right wing raise again the ugly head of racism in scenes shockingly reminiscent of the late-1930s; while in America white supremacists throw stiff-armed salutes and shout “Heil Trump!”  It has become so common that reporters no longer even remark on the swastikas daubed as part of neo-Nazi graffiti.

Yet against this we are beginning to see a counter movement, spoken in the soft language of liberalism, often well  intentioned, but creating its own brand of facism.  The extremes of the right become the means to label whole classes of people as ‘deplorable’, too ignorant, stupid or evil to be taken seriously, in just the same way as the Paris terrorist attacks or Cologne sexual assaults were used by the ultra-right to label all Muslims and migrants.

Hilary Clinton quickly recanted her “basket of depolarables”.  However, it is shocking that this was said at all, especially by a politician who made a point of preparedness, in contrast to Trump’s off-the-cuff remarks.  In a speech, which will have been past Democrat PR experts as well as Clinton herself, to label half of Trump supporters, at that stage possibly 20% of the US electorate, as ‘deplorable’ says something about the common assumptions that are taken for granted, and worrying because of that.

My concern has been growing for a long time, but I’m prompted to write now having read  ‘s “Welcome to the age of anger” in the Guardian.  Mishra’s article builds on previous work including Steven Levitt’s Freakonomics and the growing discourse on post-truth politics.  He gives us a long and scholarly view from the Enlightenment, utopian visions of the 19th century, and models of economic self interest through to the fall of the Berlin Wall, the rise of Islamic extremism and ultimately Brexit and Trump.

The toxicity of debate in both the British EU Referendum and US Presidential Election is beyond doubt.  In both debates both sides frequently showed a disregard for truth and taste, but there is little equivalence between the tenor of the Trump and Clinton campaign, and, in the UK, the Leave campaign’s flagrant disregard for fact made even Remain’s claims of imminent third world war seem tame.

Indeed, to call either debate a ‘debate’ is perhaps misleading as rancour, distrust and vitriol dominated both, so much so that Jo Cox viscous murder, even though the work of a single new-Nazi individual, was almost unsurprising in the growing paranoia.

Mishra tries to interpret the frightening tide of anger sweeping the world, which seems to stand in such sharp contrast to rational enlightened self-interest and the inevitable rise of western democracy, which was the dominant narrative of the second half of the 20th century.  It is well argued, well sourced, the epitome of the very rationalism that it sees fading in the world.

It is not the argument itself that worries me, which is both illuminating and informing, but the tacit assumptions that lie behind it: the “age of anger” in the title itself and the belief throughout that those who disagree must be driven by crude emotions: angry, subject to malign ‘ressentiment‘, irrational … or to quote Lord Kerr (who to be fair was referring to ‘native Britains’ in general) just too “bloody stupid“.

Even the carefully chosen images portray the Leave campaigner and Trump supporter as almost bestial, rather than, say, the images of exultant joy at the announcement of the first Leave success in Sunderland, or even in the article’s own Trump campaign image, if you look from the central emotion filled face to those around.

guardian-leaver  telegraph-sunderland-win
guardian-trump-1  guardian-trump-2

The article does not condemn those that follow the “venomous campaign for Brexit” or the “rancorous Twitter troll”, instead they are treated, if not compassionately, impassionately: studied as you would a colony of ants or herd of wildebeest.

If those we disagree with are lesser beings, we can ignore them, not address their real concerns.

We would not treat them with the accidental cruelty that Dickens describes in pre-revolutionary Paris, but rather the paternalistic regard for the lower orders of pre-War Britain, or even the kindness of the more benign slave owner; folk not fully human, but worthy of care as you would a favourite dog.

Once we see our enemy as animal, or the populous as cattle, then, however well intentioned, there are few limits.

The 1930s should have taught us that.


the internet laws of the jungle

firefox-copyright-1Where are the boundaries between freedom, license and exploitation, between fair use and theft?

I found myself getting increasingly angry today as Mozilla Foundation stepped firmly beyond those limits, and moreover with Trump-esque rhetoric attempts to dupe others into following them.

It all started with a small text add below the Firefox default screen search box:


Partly because of my ignorance of web-speak ‘TFW‘ (I know showing my age!), I clicked through to a petition page on Mozilla Foundation (PDF archive copy here).

It starts off fine, with stories of some of the silliness of current copyright law across Europe (can’t share photos of the Eiffel tower at night) and problems for use in education (which does in fact have quite a lot of copyright exemptions in many countries).  It offers a petition to sign.

This sounds all good, partly due to rapid change, partly due to knee jerk reactions, internet law does seem to be a bit of a mess.

If you blink you might miss one or two odd parts:

“This means that if you live in or visit a country like Italy or France, you’re not permitted to take pictures of certain buildings, cityscapes, graffiti, and art, and share them online through Instagram, Twitter, or Facebook.”

Read this carefully, a tourist forbidden from photographing cityscapes – silly!  But a few words on “… and art” …  So if I visit an exhibition of an artist or maybe even photographer, and share a high definition (Nokia Lumia 1020 has 40 Mega pixel camera) is that OK? Perhaps a thumbnail in the background of a selfie, but does Mozilla object to any rules to prevent copying of artworks?


However, it is at the end, in a section labelled “don’t break the internet”, the cyber fundamentalism really starts.

“A key part of what makes the internet awesome is the principle of innovation without permission — that anyone, anywhere, can create and reach an audience without anyone standing in the way.”

Again at first this sounds like a cry for self expression, except if you happen to be an artist or writer and would like to make a living from that self-expression?

Again, it is clear that current laws have not kept up with change and in areas are unreasonably restrictive.  We need to be ale to distinguish between a fair reference to something and seriously infringing its IP.  Likewise, we could distinguish the aspects of social media that are more like looking at holiday snaps over a coffee, compared to pirate copies for commercial profit.

However, in so many areas it is the other way round, our laws are struggling to restrict the excesses of the internet.

Just a few weeks ago a 14 year old girl was given permission to sue Facebook.  Multiple times over a 2 year period nude pictures of her were posted and reposted.  Facebook hides behind the argument that it is user content, it takes down the images when they are pointed out, and yet a massive technology company, which is able to recognise faces is not able to identify the same photo being repeatedly posted. Back to Mozilla: “anyone, anywhere, can create and reach an audience without anyone standing in the way” – really?

Of course this vision of the internet without boundaries is not just about self expression, but freedom of speech:

“We need to defend the principle of innovation without permission in copyright law. Abandoning it by holding platforms liable for everything that happens online would have an immense chilling effect on speech, and would take away one of the best parts of the internet — the ability to innovate and breathe new meaning into old content.”

Of course, the petition is signalling out EU law, which inconveniently includes various provisions to protect the privacy and rights of individuals, not dictatorships or centrally controlled countries.

So, who benefits from such an open and unlicensed world?  Clearly not the small artist or the victim of cyber-bullying.

Laissez-faire has always been an aim for big business, but without constraint it is the law of the jungle and always ends up benefiting the powerful.

In the 19th century it was child labour in the mills only curtailed after long battles.

In the age of the internet, it is the vast US social media giants who hold sway, and of course the search engines, who just happen to account for $300 million of revenue for Mozilla Foundation annually, 90% of its income.


lies, damned lies and obesity

2016-07-15 11.02.43 - inews-obesityFacts are facts, but the facts you choose to tell change the story, and, in the case of perceptions of the ‘ideal body’, can fuel physical and mental health problems, with consequent costs to society and damage to individual lives.

Today’s i newspaper includes an article entitled “Overweight and obese men ‘have higher risk of premature death’“.  An online version of the same article “Obese men three times more likely to die early” appeared online yesterday on the iNews website.  A similar article “Obesity is three times as deadly for men than women” reporting the same Lancet article appeared in yesterday’s Telegraph.

The text describes how moderately obese men die up to three years earlier than those of ‘normal’ weight1; clearly a serious issue in the UK given growing levels of child obesity and the fact that the UK has the highest levels of obesity in Europe.  The i quotes professors from Oxford and the British Heart Foundation, and the Telegraph report says that the Lancet article’s authors suggest their results refute other recent research which found that being slightly heavier than ‘normal’ could be protective and extend lifespan.

The things in the reports are all true. However, to quote the Witness Oath of British courts, it is not sufficient to tell “the truth”, but also “the whole truth”.

The Telegraph article also helpfully includes a summary of the actual data in which the reports are based.


As the articles say, this does indeed show substantial risk for both men and women who are mildly obese (BMI>30) and extreme risk for those more severely obese (BMI>35). However, look to the left of the table and the column for those underweight (BMI<18.5).  The risks of being underweight exceed those of being mildly overweight, by a small amount for men and a substantial amount for women.

While obesity is major issue, so is the obsession with dieting and the ‘ideal figure’, often driven by dangerously skinny fashion models.  The resulting problems of unrealistic and unhealthy body image, especially for the young, have knock-on impacts on self-confidence and mental health. This may then lead to weight problems, paradoxically including obesity.

The original Lancet academic article is low key and balanced, but, if reported accurately, the comments of at least one of the (large number of) article co-authors less so.  However, the eventual news reports, from ‘serious’ papers at both ends of the political spectrum, while making good headlines, are not just misleading but potentially damaging to people’s lives.


  1. I’ve put ‘normal’ in scare quotes, as this is the term used in many medical charts and language, but means something closer to ‘medically recommended’, and is far from ‘normal’ on society today.[back]

Alan’s Guide to Winter Foot Care

My feet are quite wide and so I prefer to wear sandals.  I wore sandals for over 700 miles of my round Wales walk back in 2013, and wear them throughout the winter.

When the temperature drops below zero, or snow gathers on the ground, I am often asked, “don’t your feet get cold?“.

Having been asked so many times, I have decided to put down in writing my observations about healthy winter feet in the hope it will help others.

Basically, the thing to remember is that it is all about colours, and follows a roughly linear series of stages.  However, do note I am a sallow-skinned Caucasian, so all reference to skin colour should be read in that context.

Look at your toes.

What colour are they?

Stage1.  White

Press the side of your toe with your finger.  Does it change colour?

1.1   Yes, it goes a bit pink and then fades rapidly back to white.

That is normal and healthy, you clearly aren’t taking this whole extreme winter walking thing seriously.

1.2  Yes, it goes deep red and only very slowly back to white.

You have an infection, maybe due to stage 2.2a on a previous walk.  Visit the doctor to avoid stage 3.

1.3 No, it stays white.

Bad news, you are a zombie.

Stage 2. Red

Are your toes painful?

2.1 Yes.

Well at least they are still alive.

2.2. No.

Well at least they don’t hurt.  However numbness means does cause certain dangers.

2.2a – You might prick your toe on a thorns, or rusty wire and not notice, leading to infection.

2.2b – You might step on broken glass and bleed to death.

2.2c – You might step in a fire and burn yourself.

Stage 3.  Yellow

Blood poisoning, you missed warning 2.2a

Stage 4.  Blue.

Your circulation has stopped entirely.  This will lead ultimately to limb death, but at least you won’t bleed to death (warning 2.2b).

Stage 5. Black.

Is that charcoal black?

5.1.  Yes

You forgot warning 2.2c didn’t you?

5.2  no, more dull grey/black.

Frostbite, get to the hospital quick and they may save some of your toes.

Stage 6. Green

Gangrene, no time for the hospital, find a saw or large breadknife.

Stage 7.  What toes?

You missed stages 5 and 6.

Download and print the Quick Reference Card so that you can conveniently check your foot health at any time.

Quick Reference Card

Last word … on a serious note

My feet are still (despite misuse!) healthy.  However, for many this is a serious issue, not least for those with diabetes.  When I was child my dad, who was diabetic, dropped a table on his foot and had to be constantly monitored to make sure it didn’t develop into gangrene.  Diabetes UK have their own foot care page, and a list of diabetes charities you can support.


Into the heart of darkness

Life is not all joy and fun, but often dark, depressing and painful.

Easter and Christmas are part of popular culture: Easter bunnies, Easter eggs, Christmas presents and Santa Claus. However, except for the odd Hot Cross Bun, Good Friday slips under the radar. The birth of a child and the glory of renewed life are images that are obvious causes for celebration, but a tale of abandonment followed by painful and bloody execution maybe has Gothic overtones, but is hardly party-worthy.

And yet, for those of different and no faith as well as for Christians, Good Friday touches issues of mythic as well as deeply personal significance.

Sometimes we simply need someone to share the darkness with us.

In days past the season of Lent with its fasting and sobriety helped build a sombre tension. Reading the Gospel accounts of Easter week is like one of those disaster films, where life appears to go on as normal, but with small and growing signs of the catastrophe to come. While we also know of the Easter story that follows, this does not shield us from the deep pit of despair that precedes it, “My God, My God, why have you forsaken me1.

I love Nina Bawden‘s books for children, and often in them are very real and flawed characters who, while young, can sometimes cause real pain and harm; they dig at one’s own buried memories and knowledge of our own flaws.

The Easter story is full of such characters, Peter falling asleep as Jesus prayed in Gethsemane, just at the point he was needed most as a friend; and later, after Jesus was arrested, in fear for his own life, denying that he ever knew Jesus. Each time I read it part of me wants to shout at him, warn him, encourage him, knowing that in his position I would do the same.

And Judas, the friend turned betrayer. Just like the actions of Lubitiz, who crashed the plane in the alps, many have speculated on the reasons in Judas’ heart: disillusionment that Jesus was not going to oust the Romans, greed for the bribe of silver, self-destruction, or maybe simply that bitter rancour in the presence of someone better than ourselves.

The 1960s protest song “There but for fortune” talks of the prisoner, the hobo, the drunk and the war-torn, but now I often think of the Auschwitz guard, the Rwandan militia, the ISIS terrorist — what are the life chances and life choices that brought me to where I am compared to those that took them?

Reading of Judas his betrayal, his remorse, throwing the tainted money back at the Priests’ feet, and taking his own life — there but for fortune.

And it is no accident that the blood money, the price of a life, the price of Jesus’ life, was used to buy a burial ground for strangers and foreigners2. The death of one who sought out the marginal, the poor, the disabled, and the ‘immoral’ buys a resting place for the same.

Jesus death on the cross is, of course, at the heart of Christian theology, Paul once wrote to early converts on Corinth, “I resolved to know nothing while I was with you except Jesus Christ and him crucified.”3. The main focus is often on sacrifice, both personal, “greater love has no man than he lay down his life for his friends4, and also theological, cosmic atonement for sins.

However, as well as this message that Jesus died for us, there is also a parallel message, that Jesus died with us, alongside us in the darkest hour. This is the end point of the Christmas story, one who was “like us in every respect5, entering the world, a tiny head crowned in the blood of childbirth, and leaving crowned by bloody thorns.

While the early Church was never at doubt as to the resurrection of Jesus, the completeness of this moment, Jesus dying, flanked by criminals and a weeping prostitute at his feet, is so intense that the earliest versions of Mark’s gospel rush through the Easter morning itself in a mere 8 verses, and end with the empty tomb, the astonished disciples and the words, “for they were afraid6.

The Apostles’ Creed repeated in various forms across all Western churches says Jesus “was crucified, died and was buried; he descended into hell“. Hell is not an easy concept for the modern mind, filled with images of half-comic horned demons. But despite its B-movie connotations, and irrespective of whether you read it literally, figuratively or mythically, Hades, Gehenna, the pit are powerful images.

Hell of 1st century Palestine is not just for the lifeless shades of Greek Hades, but more like Tartarus, the place of damnation, the abode of the sinner. Peter says that Jesus “preached to the dead7, and other authors simply that death could not ultimately hold him8, but all agree that for three days that was where Jesus was, not simply dying for and with us, but entering the very place of the Auschwitz guard, of Judas, of the ISIS killer, of our own deepest darkness, and sharing it.

The one of whom they said, “Here is a glutton and a drunkard, a friend of tax collectors and sinners9, the one who spent his life with outcasts and prostitutes, would he be anywhere else?


  1. Matthew 27:46[back]
  2. Matthew 27:3-8[back]
  3. 1 Corinthians 2:2[back]
  4. John 15:13[back]
  5. Hebrews 2:17[back]
  6. Mark 6:8[back]
  7. 1 Peter 4:6[back]
  8. Acts 2:24[back]
  9. Matthew 11:19[back]

It started with a run … from a conversation at Tiree Tech Wave to an award-winning project

Spring has definitely come to Tiree and in the sunshine I took my second run of the year. On Soroby beach I met someone else out running and we chatted as we ran. It reminded me of another run two years ago …

It was spring of 2013 and a busy Tiree Tech Wave with the launch of Frasan on the Saturday evening. A group had come from the Catalyst project in Lancaster, including Maria Ferrario and she had mentioned running when she arrived, so I said I’d do a run with her. Only later did I discover that her level of running was somewhat daunting, competing in marathons with times that made me wonder if I’d survive the outing.

Happily, Maria modified her pace to reflect my abilities, and we took a short run from the Rural Centre to Chocolates and Charms (good to have a destination), indirectly via Soroby Beach, where I ran today.

Running across the sand we talked about smart grids, and the need to synchronise energy use with renewable supply, and from the conversation the seeds of an idea grew.


I started my walk round Wales almost immediately after (with the small matter of my daughter’s wedding in between), but Maria went back to Lancaster and talked to Adrian Friday, who put together a project proposal (with the occasional, very slow email interchange when I could get Internet connections). Towards the end of the summer we heard we had been short-listed and I joined Adrian via Skype for an interview in July.

… and we were successful 🙂

The OnSupply project was born.

OnSupply was a sub-project of the Lancaster Catalyst project. The wider Catalyst project’s aims were to understand better the processes by which advanced technology could be used by communities. OnSupply was the main activity for nine-months of the last year of Catalyst.

OnSupply itself was focused on how people can better understand the availability of renewable energy. Our current model of energy production assumes electricity is always available ‘on demand’ and the power generation companies’ job is to provide it when wanted. However, renewable energy does not come when we want it, but when the wind blows, the tides run and the sun shines. That is in the future we need to shift to a model where energy is used when it is available, ‘on supply’ rather than ‘on demand’.

The Lancaster team, led by Adrian consisted of four full time researchers, Will, Steve, Peter, and of course, Maria, and the other project partners were Tiree Tech Wave, the Tiree Development Trust, Goldsmiths University, and Rory Gianni, an independent developer based in Scotland specialising in environmental issues.

The choice of Tiree was of course partly because of Tiree Tech Wave and my presence here, but also because of Tilly, the Tiree community wind turbine, and the slightly parlous state of the electricity cable between Tiree and the mainland. In many ways the island is just like being on the mainland, you flick the switch and electricity is there. While Tilly can provide nearly a megawatt at full capacity, this simply feeds into the grid, just like the wind farms you see over many hillsides.

However, there is also an extent to which we, as an island population, are more sensitised to issues of electricity and renewable energy.


First is the presence of Tilly, which can be seen from much of the island; while the power goes into the grid, when she turns this generates income, which funds various island projects and groups.

But, the same wind that drives Tilly (incidentally the most productive land-based turbine in the UK), shakes power lines, and at its wildest causes shorts and breakages. The fragile power reduces the lifetime of the sophisticated wireless routers, which provide broadband to half the island, and damages fridge compressors.

Furthermore, the aging sea-cable (now happily replaced) frequently broke so that island power was provided for months at a time from backup diesel generator. As well as filling the ferry with oil tankers, the generator cannot cope with the fluctuating power from Tilly, and so for months she is braked, meaning no electricity and so no money.

So, in some ways, a community perfect for investigating issues of awareness of energy production, sensitised enough that it will be easier to see impact, but similar enough to those on the mainland that lessons learnt can be transferred.

wirlygigThe project itself proceeded through a number of workshops and iterative stages, with prototypes designed to provoke discussions and engagement. My favourites were machines that delivered brightly coloured ping-pong balls as part of a game to explore energy uses, and wonderful self-assembly kits for the children, incorporating a wind and solar energy gauge.

The project culminated in a display at the Tiree Agricultural Show.

While OnSupply finished last summer, the reporting continues and a few weeks ago a paper about the project, to be presented at the CHI’2015 conference in South Korea in April, was given a best paper award at the CHI’2015 conference.

… and all this from a run on the beach.


lies, damned lies, and the BBC

I have become increasingly annoyed and distressed over the years at the way the media decides a narrative for various news stories and then selectively presents the facts to tell the story, ignoring or suppressing anything that suggests a more nuanced or less one-sided account.

BBC-news-headline-13-Feb-2015-croppedSometimes I agree with the overall narrative, sometimes I don’t.  Either way the B-movie Western accounts, which cannot recognise that the baddies can sometimes do good and the goodies may not be pristine, both distort the public’s view of the world and perhaps more damagingly weaken the critical eye that is so essential for democracy.

For the newspapers, we know that they have an editorial stance and I expect a different view of David Cameron’s welfare policy in The Guardian compared with The Telegraph. Indeed, I often prefer to read a newspaper I disagree with as it is easier to see the distortions when they clash with one’s own preconceptions.  One of the joys of the British broadsheet press is that whatever the persuasion, the underlying facts are usually there, albeit deeply buried towards the end of a long article.

However, maybe unfairly, I have higher expectations of the BBC, which are sadly and persistently dashed.  Here it seems not so much explicit editorial policy (although one hears that they do get leant upon by government occasionally), more that they believe a simplistic narrative is more acceptable to the viewer … and maybe they just begin to believe there own stories.

A typical (in the sense of terrifyingly bad) example of this appeared this morning.

After the wonderful news of a peace agreement in Ukraine yesterday, this morning the report read:

Ukraine crisis: Shelling follows Minsk peace summit

The ceasefire is due to start on Sunday, so one can only hope this is a last violent outburst, although to what avail as the borders are already set by the Minsk agreement.

The first few lines of the article read as follows:

New shelling has been reported in the rebel-held east Ukrainian cities of Donetsk and Luhansk, a day after a peace deal was reached in Minsk.

There are no confirmed reports of casualties. Both cities are near the front line where the pro-Russian rebels face government forces.

The ceasefire agreed in the Belarusian capital is to begin in eastern Ukraine after midnight (22:00 GMT) on Saturday.

The EU has warned Russia of additional sanctions if the deal is not respected.

If you have kept abreast of the ongoing crisis in Ukraine and can remember your geography, then you will know that this means the Ukrainian Army was shelling rebel-held cities.  However, if you are less aware, this is not the immediate impression of the article.

First notice the passive wording of the title.  Imagine if this had been Syria, the headline would have surely been “Assad’s forces bombard Syrian cities” or “Syrian Army shell civilian areas“.  While the BBC may want to avoid flamboyant titles (although do not demure elsewhere) the article itself is no better.

The opening paragraphs mention ‘shelling’, ‘rebels’ and the EU warning Russians to clean up their act.  The emotional and rhetorical impact is that in some way Russians are to blame for the shelling of cities, and indeed when I read the words to Fiona this was precisely what she assumed.

That is, while the facts are there, they are presented in such a way that the casual reader takes away precisely the opposite of the truth.  In other words, the BBC reporting, whether intentionally or unintentionally, systematically misleads the public.

To be fair, in the earliest version of the article its later parts report first Ukrainian army deaths and then civilian casualties in rebel-held areas:

On Friday morning, a military spokesman in Kiev said eight members of Ukraine’s military had been killed in fighting against separatists in the past 24 hours.

The rebels said shelling killed three civilians in Luhansk, reported AFP news agency.

(Although the second sentence is removed from later versions of the article.)

BBC-news-early-13-Feb-2015-cropped BBC-news-later-13-Feb-2015-cropped
early and later version of same BBC story

The early versions of the article also included an image of a wall in Kiev commemorating Ukrainian army deaths, but not the graphic images of civilian casualties that would be used in other conflicts1. This was later changed to a refugee departing on a bus to Russia ((Later still the image of an armoured vehicle was also added.  I’d not realised before just how much these news stories are post-edited)), which better reflects the facet behind the article.

Of course, this is not a one-sided conflict, and later reports from the region during he day include rebel shelling of government held areas as well as government shelling.  Both sides need to be reported, but the reporting practice seems to be to deliberately obfuscate the far more prevalent Ukrainian army attacks on civilian areas.

If this were just a single news item, it could be just the way things turn out, and other news items might be biased in other directions, but the misreporting is systematic and long term.  Many of BBCs online news items include a short potted history of the conflict, which always says that the current conflict started with Russian annexing of Crimea, conveniently ignoring the violent overthrow of the elected government which led to this.  Similarly the BBC timeline for Ukraine starts in 1991 with the Ukrainian referendum to separate from the USSR, conveniently ignoring the similar overwhelming referendum in Crimea earlier in 1991 to separate from Ukraine2.

To be fair on the journalists on the ground, it is frequently clear that their own raw accounts have a different flavour to the commentary added when footage is edited back in London.

In some way Ukraine could be seen as a special case, the Russians are the bogey men of the today, just like Germany was 100 years ago and France was 100 years previously, it is hard for a journalist to say, “actually in this case they have a point“.

Yet, sadly, the above account could be repeated with different details, but the same underlying message in so many conflicts in frequent times.  Will the media, and the BBC, ever trust the public with the truth, or will ‘news’ always be a B movie?

  1. Maybe this is just deemed too horrifying; a recent Times report of Donetsk morgue includes graphic accounts of shrapnel torn babies, but does not include the Getty images of the morgue preferring an image of an unexploded rocket.[back]
  2. While ignoring the history of Crimea. which does seem germane to the current conflict, the BBC timeline is overall relatively fair; for example, making clear that Yanukovych’s election was “judged free and fair by observers“.[back]