Some months ago I wrote a short piece touching on innumeracy and promised to return to the theme later. By one of those strange, but probably predictable, coincidences, I was thinking about this again and low and behold there was an article in the Independent about a Government commissioned report into the state of mathematics in the UK. Again, quite predictably, the article began, "Next month a Government-commissioned inquiry into the state of mathematics in Britain will report that radical measures are needed to save the subject from slipping into terminal decline in schools and universities." And, as you might expect, Professor Adrian Smith, the author of the report, said, "We need to make the material much more inspirational so that people want to study maths for longer than they do now."
I would agree that we need to make the material more inspirational, but fear that, in practice, this would mean using more practical examples like changing money into foreign currencies. What might actually be inspirational would be to communicate the fact that mathematics gives us a different way of understanding the world. And, perhaps, as a kicker, that it can offer a means of uncovering some of the dirty little secrets that others use numbers to conceal from us.
I had begun thinking about the question of innumeracy again after coming across the work of Steven Levitt. He has just won The Clark medal - for the most important economist aged under 40. "Levitt won the medal for his genius in crunching data afresh to answer real-world questions. For instance, if drug dealers are so rich, why do so many of them live with their mothers? (Answer: most drug dealers are poor.)". He has also looked at things as diverse as the relationship between legalised abortion and crime and the most effective tactics for scoring penalties in soccer.
As you will probably have gathered, my interest in Levitt is because he is someone who is using maths to understand the world. My concern is that I, like most people, have to take his work on trust. We can apply some tests as to the plausibility of his conclusions, but those tests are all non-mathematical. The reality is that most of us are in varying degrees mathematically illiterate, including many who use maths in their work. What tends to be missing is an understanding of what we are doing. The process is largely taught as a series of mechanical operations, even at graduate and postgraduate level in subjects like, science, the social science and medicine.
Speaking as someone who is at the higher end of the innumeracy scale, I feel a sense of deprivation that I still have struggle with numbers and that there so many areas where it is hard for me to make informed judgements, because I can't test the calculations myself.
Up until about the age of eleven or twelve I appear to be quite good at maths - despite some problems with the rote learning of times-tables. But I say appear because all I had learned were some tricks that I was able to carry out mechanically, but with no understanding. After twelve my interest in maths went into freefall as the sense of tedium of carrying out mechanical operations grew and I failed my "O" level - the exam we take at sixteen - several times. Since I could do the simple stuff, like checking my change, this didn't seem to be too much of a handicap.
Then in my late teens, in my first job, maths came back into my life. I was working in a film lab that specialised in 16mm films, mostly industrial, a bit of TV work, some medical and a few art films. We had got into a real mess with delivery times, which up until then had been given with a few simple rules of thumb. The mess had occurred because we'd got one new printing machine, which when it worked was very fast, but was also very unreliable, breaking down often. So we had a vast backlog of work and a lot of angry customers.
The MD of the company asked me to set up and run a system to control and monitor the flow of work through the company, which I did. It was a very primitive but effective system based on a form for each order that travelled through the plant with the job and was returned to me at the completion of each stage, a white board where I tracked the progress of each job and a very simple adding machine which enabled me to calculate how many orders we could put through the printing machines each day.
What I didn't realise at the time was that I was constructing a model of the plant based on numbers - the numbers in this case being chunks of time - and that even a very crude numerical model could be more effective and reveal things that rule of thumb models couldn't. What I did realise using my primitive adding machine, and that came as a staggering insight, was that multiplication was the same thing as adding a number together several times. Now to many of you this may seem blindingly obvious, but it had never occurred to me in all the years I was being formally taught arithmetic.
My next insight came many years later. At that time I was working in a college that was so old fashioned in its governance that perhaps it should have been preserved as a historical monument. The only person who knew what was going on in terms of finances and resources was the Vice-Principal and he and the Principal handed out resources and budgets to departments rather like Royalty rewarding their Barons.
I had come from a College where I had sat on a finance and resources committee and, as a student knew more about the College's finances than the Heads of Department in the College where I was now working. My Head of Department believed that we were being starved of resources that rightly should be ours, but had no way to prove it and asked me to look into it.
By one of those odd conjunctions, that seem to occur so frequently, my mother had a lover who was a management consultant and was helping her sort out the finances of a shop she ran. He used a technique of indexing to get a clearer picture of what going on and I clicked that I could use this same technique at my College.
So I gathered together figures that were scattered over a variety of reports and documents and indexed them. Very soon a picture began to emerge of two successful departments, ours and another, that were effectively subsidising others. With a bit more digging around it began to look as if what was happening was that one department, in particular, was being artificially boosted so that its Head of Department who due to retire soon would get a bigger pension.
Now we never explicitly used what I had found, but even a few hints that we knew what was going on meant that we did get an increase in resources even though it was not as much as we were entitled to get.
So the insight I gained from that experience was that maths could be a very useful tool for uncovering dirty little secrets, even when the numbers had been presented in a way that was intended to mystify. However, to do this I needed two bits of technology. First, the idea of indexing itself and second an electronic calculator that helped me do the necessary calculations.
The next insight came a long time after. A friend of mine, a journalist, Paul Lashmar, wanted to construct a league table of local government performance, based on Audit Commission performance indicators. He knew I could use spreadsheets so asked me to help him. We constructed a fairly simple method for doing this, which while crude looked reasonably plausible. We checked it with someone who had worked with the Audit Commission in this area, who agreed that providing we put in appropriate caveats the method could provide some useful information.
We ran the League Tables for three years, first in the Observer and for two years in the Independent. Frankly, it was a nightmare of a job, because it generated a huge amount of controversy and I had deal with mass of queries and complaints from local councils who thought they were too low in the table. And, with each complaint there was always the fear that I had made a mistake, which fortunately I hadn't. Also there was the inherent problem with league tables that they amplify very small differences so that a council that was say twenty places lower than another might actually be pretty much the same. So when the Audit Commission, who had previously said that national league tables were too difficult to do, started to do it themselves I breathed a sigh of relief and was pleased I wouldn't have to do it again.
What I found most interesting from the exercise was an unexpected insight, which we mentioned, but nobody picked up. This was that the quality of management could make a difference. When we began I thought we would see a clear relationship between social deprivation and performance i.e. that the councils with the most prosperous populations would be at the top and those with the least would be at the bottom. In fact at one point we were seriously thinking of trying to factor in an index of social deprivation, but gave up because I couldn't see how to do it.
Now as a rule of thumb it was roughly true. But there was a big but. One of the best performing councils South Tyneside, in terms of almost any measure of social deprivation you could think of, was the same as one of the worst performing Kingston-upon-Hull. The only explanation we could come up with was that South Tyneside was better managed than Kingston-upon-Hull. I found this a very encouraging and hopeful lesson, but unfortunately the larger more important picture got lost in squabbling about relatively unimportant details of relative positions in the league tables.
Now what is it I am trying to say here? Making sense of and with numbers is a powerful way of understanding what is going on the world and seems to be one of those things you need to learn young. If you don't, you remain one way or another handicapped. Technology can help with the mechanics, but doesn't help with finding the right technique for helping to explore a question or to help with understanding the significance of a mathematical enquiry. In an interview I quoted in an earlier post, "Smart Heuristics", Gerd Gigerenzer suggested an approach that might help professionals and by inference could be useful in more general education.
But, I fear, the problem lies much deeper than just mathematical education. The central problem would seem to lie in an approach to education which is essentially about presenting a picture of the world as it is and rewarding the learners who can regurgitate this vision. Since this "world as it is" is a fiction or is intrinsically uninteresting its not surprising that so many young people get turned off.
Human beings are curious and creative creatures, who invented machines, but are not machines. Why then do I wonder, do we treat them as if they are? Just imagine what it would be like if we created forms of education that took account of our nature. What would happen if our education was seen as being about how to explore, interrogate and create our worlds? Who knows we might even find that innumeracy became a thing of the past.
A post on Karen Mahony's blog alerted me to an important article by Richard Florida, "Creative Class War" - there?s also a slightly different version, with a diagram, on one of his sites CreativeClass.org. It gives you a whole different take on what is stake in the current US elections and has lessons for the rest of us where ever we are. Essentially the argument is that creative people are the key to economic prosperity and that the places and countries who can attract the mobile creatives are those that will do well. But as Karen points out the argument for individual creatives maybe different from that of cities and countries. As she points out, "If we really are moving more towards a "do it yourself" kind of cultural collage, then things are going to come out of the places that support small, free and inexpensive. Like Berlin. Like Prague. Like Yalta even?"
John Kay begins a long article in the FT Magazine by saying:
"If you want to go in one direction, the best route may involve going in the other. Paradoxical as it sounds, goals are more likely to be achieved when pursued indirectly. So the most profitable companies are not the most profit-oriented, and the happiest people are not those who make happiness their main aim. The name of this idea? Obliquity."
He goes on to show how a narrowly goal orientated approach in areas as diverse as business, town planning and forest management is often less succesful than a broader, value based approach. He explains:
"Obliquity is relevant whenever complex systems evolve in an uncertain environment, and whenever the effect of our actions depends on the ways in which others respond to them. There is a role for carrots and sticks, but to rely on carrots and sticks alone is effective only when we employ donkeys and when goals are simple. Directness is appropriate. When the environment is stable, objectives are one dimensional and transparent, and it is possible to determine when and whether goals have been achieved. Obliquity is inevitable when the environment is complex and changing, purposes are multiple and conflicting, and when we cannot tell, even with hindsight, whether they have been fulfilled."
It reminds me of one the original inspirations for Purposive Drift:
"The Japanese anthropologist, Tado Umesao, observes that historically the Japanese have always done better when they drifted in an empirical, practical fashion (' Even during the Meiji revolution, there were no clear goals; no one knew what was going to happen next') than when they attempted to operate by 'resolute purpose' and 'determined will'. This is true of other peoples, too, although Umesao believes what he calls 'an esthetics of drift' is distinctively Japanese and one of the major differences between Japanese and Western cultures. Had he been looking at Europe and America in the past rather than the present, he would have seen, I think, that 'an esthetics of drift' was distinctively Western too, and worked better for western cultures than 'resolute purpose' and 'determined will'.
And a more recent node of support:
This is one of the most counterintuitive ideas. We are traditionally taught to be really focused, to be really driven, to try really hard at tasks. But in the real world, you've got opportunities all around you. And if you're driven in one direction, you're not going to spot the others. It's about getting people to have various game plans running in their heads. Unlucky people, if they go to a party wanting to meet the love of their life, end up not meeting people who might become close friends or people who might help them in their careers. Being relaxed and open allows lucky people to see what's around them and to maximize what's around them."
For years I have been telling students and any one else who would listen that they should explore the potential for the use of sound in interaction design or as I preferred to call it hypermedia. So I was pleased to see that at IVREA, this was becoming a focus of concern. As Molly Wright Steenson reported in a post on 9 December last year:
"I was talking to a group of second-year students here today about their thesis projects and realized that sound is becoming a major focus for interaction designers. Currently, several thesis projects are focusing on it and three from last year explored it to varying degrees: Dianna Miller?s Wrapt, Ryan Genz?s Embedded Theater and Line Ulrika Christiansen?s Re-Lounge."
"Every media element within hypermedia presents intriguing possibilities for development. But the issue of how we use sound maybe one of the most important factors in making hypermedia a truly distinctive medium, with unique characteristics and qualities. From Vannevar Bush onwards, one of hypermedia primary metaphors up until now has been print. As we learn to use sound more intelligently and more effectively this metaphor may breakdown. Already many of the other metaphors we use to describe the experience of using hypermedia are spatial. The increasing use of sound to create a sense of inclusive space, where we are within the experience rather than simply observing, may be a crucial element in establishing the new, more fruitful spatial metaphors that the medium demands."
Maybe at last we are beginning to get there.
"I've always said that all successful systems were small systems initially. Great, world-changing things - Java, for instance - always start small. The ideal project is one where people don't have meetings, they have lunch. The size of the team should be the size of the lunch table."
I also liked some of the things he had to say about the possibilities for innovation, which relate to some of the things I discussed in "It's hard to predict"
All in all, an interview worth reading and a man to keep an eye on.
Sometimes I think I'm really slow on the uptake. Despite a number of signals I should have noted, I didn't take much notice of Howard Dean's run to be the Democrats' Presidential Candidate. Maybe it was because I was looking for a winner and he looked like just another political maverick. Whatever the reason, the Dean campaign looks significant, even if he doesn't get much further. What is significant about the campaign is that it looks as if it represents a shift away from the idea of politics as a subset of marketing to the idea of politics as if people matter. My sense is that this is a phenomenon that won?t go away. My evidence is in the links below:
On the other hand maybe Michael Wolff is right and the very success of the campaign so far carries the seeds of its own destruction.
Whatever the outcome, this one is worth watching.
I think I may have found a new role for myself as an "On-Line Vicarious Expediter and Responder", an OLIVER - though I'm not sure I want to be a bit of software. The concept of the "Oliver" was developed by J.C.R.Licklider, who as well as being one of the early instigators of the internet, also "..foresaw knowbots and intelligent agents as he describe each network user having what he called an "Oliver." The Oliver would be a set of programs that learns about its user, finds information on the networks for the user, and does various on-line chores."
I came across this idea by accident in a vanity search - who would have thought there are so many Richard Olivers in the world - in a piece that had nothing to do with me or any other Richard Oliver. What made me read it was because I have long been interested Licklider, who is one of those people who have had an immense influence on our world, but is little known outside a small circle of people who are interested in such things.
The bit about "Olivers" amused me for obvious reasons. What I found still more interesting was an idea earlier in the essay where the author, Dr. Kenneth L. Hacker describes how Licklider, "... provided an early sociocognitive view of human communication which describes how each communicator in social interaction has mental models of conversation topics. Licklider noted that communication works best when the models become more similar. More importantly, he articulated a definition of communication as "cooperative modeling," meaning that communication involves coordination and coactive building of a model that is shared and exists simultaneously with the individual communicators' mental models."
This reminded me of an entry I read in Douglas Rushkoff's blog some time ago. In an entry for October, 15 2003 he describes giving five talks in the UK about his Demos book, Open Source Democracy. What struck him was that, "instead of engaging in conversation, most of these folks played high school debate. This sort of banter looks fun when it's people playing "Parliament" on TV, but it's not so very productive."
This echoed my own feeling that the long tradition of debate, which is essentially adversarial, with winners and losers, is a very limited way of exploring new ideas and may even be a way of perpetuating out-of-date ones.
I guess the problem with debate is that as a form of "cooperative modelling" the room for change and learning is limited, by its adversarial nature. The idea is supposed to be that the best arguments win. But the for or against nature of debate limits room for exploration and the possibilities for reframing what is being discussed.
Hence Rushkoff's sense of frustration. As he said, "The majority of government ministers with whom I spoke seemed bent on finding ways to prevent themselves from considering new ideas - as if even wrapping their minds around a new concept for a even a moment would wreck the sanctity of their current established methodology." And that would seem to apply to his other audiences here too.
What I have found more encouraging is the way that the idea of conversation is taking hold. I wrote a bit about this in my entry "Purposive Drift" where I linked to an article by Steve Bowbrick where he talked about the way that many of the best blogs were conversational in tone. As he said, "Conversation is a softer, less hard-edged and "goal-oriented" form of interaction than most of the highly-functional encounters we have in daily life, especially at work, but it needn't be wishy-washy. Theodore Zeldin, who's written a book about conversation, says that conversation only works if you're ready to be changed in the process, if you're ready to ask and be asked hard questions."
Gordon Pask, the cybernetician, who developed a whole theory of learning based on the idea of conversation, ".. warned about confusing mere "communication" (exchanging messages containing what is already known) with "conversation" (a generative activity that gives identity to participants and leads to what is new)."
Personally I think that we have to accept that the vast bulk of conversation is probably phatic - speech used to share feelings or to establish a mood of sociability rather than to communicate information or ideas - but none-the-less valueable for that. For even phatic conversation creates the framework and possibility for more creative interactions.
Max Perutz, the Nobel Prize winner, also achieved a high reputation as a manager of scientists (his lab produced a number of Nobel Prize winners). In an essay on how to manage and plan a research lab he included the advice, "Discussion thrives at mealtime. We have a roof canteen where people congregate for lunch and for coffee and tea breaks, and argue as long as they like. "
Now I suspect that many, if not the majority of the conversations in his canteen were phatic, but a vitally important minority were the ones that provide the spark for the big breakthroughs.
Perutz later quotes another Nobel Prize winner Sir Nevill Mott writing about Niels Bohr, ?We were in and out of each others? rooms all day, and so was Bohr. Nobody dreamt of keeping an idea to himself; our joy in life was to tell it to other people to get it criticized and if possible accepted. Bohr himself, if he had a new idea, would ... tell it to the first person he could find... I learned [from Bohr] Bobri what physics was all about, that it was a social activity and that a teacher should be with his students.?
We are living in strange days where sometimes the old rules work and sometimes they don't. If there was ever a time when creative thinking was an imperative, that time is now. But to repeat what Rushkoff said, "The majority of government ministers with whom I spoke seemed bent on finding ways to prevent themselves from considering new ideas - as if even wrapping their minds around a new concept for a even a moment would wreck the sanctity of their current established methodology." And that reluctance to engage in conversation and to fall back on debate is all too common.
My friend, Alex McKie, wrote a paper for the Work Foundation, "Virtual value: Conversations, ideas and the creative economy". In it, among other things, she proposed two simple things. First, if an organisation feels the need to be more creative they need to define what it is they want people to create? Ideas? Profit? Value? Relationships? And, second that a quick and simple way of doing this is through encouraging "creative conversations."
As she goes on to say, What does 'creative conversation' mean? Simply that conversation is at the root of all ideas and creativity. This is where to start. Develop a culture and structure which supports people in listening and talking. See what happens when they felt able to create, express and share ideas. Give people time and space to talk with each other."
This was what Perutz and Bohr seemed capable of doing. If this can help produce Nobel Prize winners, perhaps we should think about where else it can be applied.