A Mappa Mundi for the new millennium

 

At the end of the Middle Ages, Europe's thousand year sleep - or perhaps thousand year germination - between antiquity and the Renaissance, wondrous things were happening. High culture, long dormant, began to stir again. The spirit of adventure grew once more in the human breast. Great cathedrals rose, the spirit captured in stone, embodiments of the human quest for understanding. But there were other cathedrals, cathedrals of the mind, that also embodied that quest for the unknown. They were maps, like the fantastic, and often fanciful, Mappa Mundi - the map of everything, of the known world, whose edges both beckoned us towards the unknown, and cautioned us with their marginalia - 'Here be dragons'.

I want to sketch a little more completely the links between these different sorts of cathedrals and will do so through a story I first heard from my friend and former boss, Neil Williams, the Executive Director of the Australian Geological Survey Organisation.

The king, it seems, was visiting the construction site of the great cathedral and was speaking to the workers, amid all the medieval chaos. He asked them what they did. They each replied: 'I am a mason, your highness, I shape the great stone blocks for the nave' or 'I am a carpenter, your highness, I am fitting the doors to the vestry' and so on. At last he came to a young boy sweeping up amongst the rubble, and, when asked what he did, he replied with shining eyes 'I am helping to build a cathedral!'

That's what I want to do today: to build a cathedral, to look at the big picture. I want to explore what a modern Mappa Mundi, a map of everything, might be like. We need to do this for the next millennium because 'everything' is exactly what the environment is, and 'everything' is what we need to know if we want to continue to survive. We need to know what it is that we know, and we need to know what it is that we don't know - we need to know where the dragons are.

In exploring this idea, I will need to say something quite serious about maps and what they are, and about the profound responsibilities mapmakers have in capturing, preserving and disseminating knowledge. I will also need to say something about the modern function of maps and about the technology that underlies them, about maps as the intermediary between man and data. And I want to say a little about the data that will be required to create this Mappa Mundi.

But first I want to ask, Why? Why do we need a map of everything? To this audience, the answer is obvious, but it needs to be stated for the record firmly and clearly. As with the medieval maps, it is much more than a romantic quest for knowledge for its own sake. It is a precondition for our future success. Our ancestors were driven by the twin mercantile needs of trade and flag in a world with edges, we are driven by the needs of survival in a world without edges, a recursive world of feedbacks and interactions.

This learned society put the case succinctly to the new Prime Minister in a letter arguing the need for a national spatial data infrastructure. It pointed out that the issue is important because we need access to spatial information if we are to manage our nation and its resources efficiently and in an ecologically sustainable manner. But it went further and argued that we need, as a nation, the ability to answer 'What if' questions that go to the heart of informed progress.

Mapmakers and the grand debate

Earlier this year, I had the honour of giving the opening address to the annual conference of your kindred organisation, the Institution of Surveyors, Australia. At that meeting, I argued that there is a grand debate occurring in society at the present time, and that mapmakers have a pivotal role in it. I want to recap that argument briefly, because understanding the special role of maps and their makers in these times illuminates our mutual concern with why we need a new Mappa Mundi.

I argued that this debate is about how we should understand difficult things. We have not joined this debate with society for more than 300 years - since the renaissance, when Galileo confronted the church, and argued for a new physics - argued that the physical world could be understood through a rational and material process which came to be called the scientific method. This, in the end, transformed society and swept away the Middle Ages.

We now face a debate of similar proportions and consequence.

I want to enter the problem through another, the problem of sustainable development, by arguing that sustainable development is really just a stalking horse for our problem, much as the contentious motion of the planets was Galileo's stalking horse for the then-emerging science of dynamics, which led on to the breathtaking, all-encompassing sweep of Newton's physics.

Sustainable development is a subversive issue

Now sustainable development is an issue which has exercised the public mind for some years, even if few have a clear understanding about it. At one level, it is one of those fuzzy ideas that everyone is in favour of, because it means all things to all people. At another, it has a concise description: it is about taking better care of the environment while ensuring economic growth. It is where ecology meets economics. But at its deepest level, sustainable development is not a motherhood issue at all, it is a subversive issue.

It is subversive in exactly the same way that Galileo's dynamics was subversive - it intends to replace one way of thinking with another. It uses exactly the same strategy that Galileo used 300 years ago. First, a nod of deference to the establishment to get standing, to get the necessary permission to air the argument. This is then followed by the unfolding of the argument, from its unexceptional premises to its ultimately destructive conclusion. Destructive, that is, of the status quo, of the established way of thinking.

Galileo was faced with all the power of the church, and he deferred to it. His works all carry the church's imprimatur. He argued from the world of experience, using his clever invention, the Galilean dialogue: a dialogue between the simple man who but seeks to be put on the right path, and the learned man who stands for the status quo. Galileo's simple man, Simplicio, does not set out to destroy the established view, only to understand it by asking naive, but dangerous questions based on his own experience with the material world. Through this powerful tool, Galileo was able to engage the establishment in an argument that led inexorably to its overthrow.

In the same way, sustainable development engages the establishment in a debate which is seemingly on the establishment's terms. It uses a clever invention: the need to bring environmental and economic concerns together - an admirable goal, especially when also couched in terms of bringing the environment into the mainstream of political debate. Sustainable development is as much about deferring to the establishment in order to get standing as Galileo's trick of couching his argument as a dialogue was in getting his imprimaturs from his establishment, the church. Sustainable development is really about finding a palatable way to get a hearing for some very subversive ideas.

It is the Galilean dialogue of our times.

But what then is 'today's Galilean idea' and who is 'the establishment' - what is this new physics and who is the church?

Complexity - today's Galilean idea

Let me deal first with 'today's Galilean idea' by considering Newton's physics a little more closely.

The key to Newton's success lay in the simplicity of the systems, or better, the simplicity of the relationships he studied. The relationship between gravity and mass is simple and strong, so strong that it dominates the observable dynamics of celestial bodies. It is characterised by an inverse law. For all practical purposes, we need only consider the largest and nearest bodies when calculating the forces holding, say, the Earth in its orbit. Even though every other body in the universe affects the motion of the Earth, we can safely ignore nearly all of them except the Sun and perhaps a few of the planets. As a first approximation, Newton's laws explain the motions of stars, planets and apples with great economy and elegance.

As for gravitation, so also for radiation. Much of physics is governed by inverse laws. In a sense, the triumph of physics as an explanatory system is the triumph of explaining relatively simple systems to a first approximation. There are, of course, complex physical systems, but Newton's physics does not have much that is practical to say about them. Weather is an example. We can say that the weather is governed by relatively simple and well known physical laws, but the number of variables is so great that analytical solutions evade us. We cannot arrive at a useful first approximation to the weather in the same way we can describe and understand the motions of the planets.

If Newton's equations were simple and elegant, it was because the systems he studied were themselves simple and elegant. His genius was in seeing the underlying simplicity and similarity in the motions of planets and apples. But he left science with a terrible legacy because he was, in a sense, too successful. Newton's success encouraged the belief over the next couple of hundred years that the trick to science lay in finding clever ways to see through the apparent complexity of the natural world to its underlying simplicity - in reducing the complexity to its more fundamental simplicity.

One by one the simple systems have fallen to this approach: for example, in physics, the theory of electromagnetism; in chemistry, the theory of valency; and in biology, the theory of cells.

But this success left a knot of hard problems intractable to this reductionist approach. These were most obvious in biology: ecosystems, for example, must be more complex by several orders of magnitude than the weather.

These problems were most obvious in biology because, in contrast to the sway of inverse laws in physics, biology is conspicuously affected by exponential relationships. The ecologist who first enunciated 'The Tragedy of the Commons', Garrett Hardin (1969), made the point eloquently in an essay nearly 30 years ago on ecology as a subversive science:

There could hardly be a more trifling physical event than dropping a single bacterium onto a human pharynx - the mass of one body is 18 orders of magnitude greater than that of the other. But if the bacterium is a living pathogen, and the pharyngeal membrane is susceptible to the disease, the consequence may literally be of world-shaking importance. A man may sicken and die, starting an epidemic that weakens an empire and changes the course of history. All this is possible. It is also possible that nothing of historical importance happens. The difference between the two extremes is connected with nothing a physicist would notice. The initial bacterium weighs only about 7 x 10^-14 grams in either case; the significant differences are infinitely subtle.

While a physicist asks 'How big is it?' or 'How far away?', a biologist asks 'Does it increase exponentially?' or 'Is positive or negative feedback involved?'. To the biologist, nothing is, a priori, insignificant. There can be no Newtonian first approximation. The whole system must be considered.

It is not surprising that disciplines like ecology were the first to feel dissatisfied with the promise of simplicity implicit in the Newtonian tradition. Their complexity is irreducible in the sense that their systems are so closely intertwined, so closely interacting, that they cannot be studied sensibly through their simpler components. Unlike Newtonian systems, where first approximations can safely ignore small effects to create satisfactorily simple linear solutions, complex systems like ecosystems do not respond to first approximations.

To put it bluntly, linear dynamics apply best to the behaviour of simple systems composed of few entities, while more complex systems exhibit non-linear dynamics. The trouble is most of the observed universe, from galaxies to societies to viruses, is more like the latter, more complex than simple.

Complex systems are messy. The equations describing them are generally not solvable, they generally do not move gracefully to equilibria, their behaviours are generally not predictable. And yet they are what the real world is made of. We need to understand them.

Thus the subversive idea, the Galilean idea that we need to take up to the establishment is not the idea of sustainable development, it is the idea of complex systems. It is the idea that there exist many important systems for which simple, linear approaches - Newtonian approaches, if you like - do not work, and for which we must develop a new science.

Economics and the establishment

Now let us consider our establishment, our body politic. It is fair to say that it is suffused by economics. We may even say that economists take the place of priests in our secular society. Galileo would have had no difficulty recognising them as such, in the ways in which they infiltrate all the seats of power as leaders or advisers, in the ways in which they prophesy and prognosticate, but most of all in the ways in which they explain their unfulfilled prophesies after the event. Not for them what Galileo called his "wise, ingenuous and modest sentence, 'I know it not' " (Dampier 1961, p 133).

And what sort of economics do they preach? Here is the rub: the economists jumped too soon. At the end of the 19th century, economics adopted the sort of Newtonian mechanics that I have just argued cannot be useful in explaining complex systems. In a bid to become more 'scientific', they proposed that economies be thought of as if they were the simplest physical systems with a single point of stability, and governed by a strictly linear dynamics: the simplest kind of Newtonian dynamics.

The economists have even invented an 'invisible hand' to replace Newton's God to rule serenely over these mechanics, and have then packaged it all up into a central dogma called the 'general equilibrium theory'.

As this simplistic synthesis was occurring in economics, in the natural sciences, the opposite was happening. In the early years of the 20th century, the Newtonian certainty began to unravel. The Darwinian revolution had begun to bite, and the dominant roles of chance and history in the affairs of living things were becoming apparent. At the same time, Heisenberg's quantum mechanics showed that there were limits not only to Newtonian physics, but also to what could be known.

As a result, the awkward bits of science, the complex refractory bits of geology, chemistry, biology and so on that had been confined to taxonomy - science's attic - began to assert themselves, and new disciplines, such as ecology, emerged.

But this self-evident complexity has not been sufficient to turn the broad church of economics from its defining idea. Economics parodies Newtonian physics to create a linear equilibrial theory which ignores reality. This would not be a problem if economists were just 'academic scribblers' as Keynes called them (Toohey 1994), but economists have achieved what scientists have not: they are the gatekeepers of the establishment, and they can be expected to hold fast to their Newtonian universe even as science discards it.

The grand debate then is about replacing linear thinking with non-linear thinking in the body politic. It is about replacing simple, outdated nostrums with more realistic approaches to the complexity of the real world. It is about the subversive idea that we can do better by acknowledging that we know less.

Mapmakers visualise complexity

I said before that mapmakers have a special responsibility in this debate - a responsibility that comes with the territory because, through their maps, they try and visualise the complexity of the world.

Consider maps for a moment. They are intensely non-linear ways of capturing information. If you doubt this, imagine trying to describe a map in words - in its uttermost detail. As anyone here who remembers 'metes and bounds' descriptions can tell you, it is well nigh impossible, and any attempt to do so is much 'bigger' than the map itself. And what are words, but a linear way of capturing information?

In fact, human beings have invented two parallel and independent ways of capturing and transmitting information: words and maps. Maps form an authentic, independent non-linear tradition running in parallel to the development of the linear tradition of language and the written word.

And mapmakers, since at least the Middle Ages, and probably since the time of the pharaohs, have been the key custodians of one of those traditions, the mapping tradition.

This gives you a special place in the grand debate. You are the mappers, the visualisers of complex systems. You have been doing this for generations, making complex systems understandable, and the rest of science, and indeed society, has much to learn from you.

Let us think about maps and words a little more deeply. What can we say of the ascendency of words at the present time, indeed for such a long time that we instinctively equate literacy with education? The dominance of literacy is nothing more than the dominance of linear thinking, mankind's first response to understanding the world, mankind's first approximation of the real world.

Now linear thinking and its attendant literacy are perfectly adequate for understanding much of the world. Indeed they have stood us in good stead for a long time. The first tens of thousands of years of human civilisation have been able to muddle along quite adequately using a linear approach to the world. But as we have uncovered the complexity of the world, we have begun to exhaust the possibilities of the linear approach. We have begun to run out of useful first approximations.

We are now encountering the dragons at the edges of the known for which linear first approximations are neither useful nor productive - of which sustainable development is only the most plangent.

Slaying the dragons

I hope I have established that sustainable development, as a complex system, is a problem worthy of your attention. Now I want to consider what demands that will place on you as mapmakers, as visualisers of complexity.

Let us dispatch these dragons in order, from easy to hard, that is from conceptually easy to hard.

The first of these is data - observations about the world. If we want to really understand sustainable development we will need swags of data, all spatially organised. We will need data about both the biophysical and socioeconomic aspects of the world. It will need to be up to date, or better, a time series, and at appropriate spatial and temporal scales. Inevitably, that means the never ending chase of finer and finer resolutions for larger and larger chunks of the world. For Australia and for many ecological processes, this will mean resolutions of metres and days, with continental coverage. This sounds daunting, but we are almost there for many datasets, thanks to the dedicated work of our national mapping and surveying organisations, such as AUSLIG and AGSO. Our data goals are achievable by the millennium.

The second is databases - such datasets as I have described may exhaust our current database paradigm, swamp our data storage systems, and prove impossible to search effectively, so large are they. But there are software and hardware solutions available now, or in technology's seemingly inexhaustible pipeline, that will make the storage and retrieval, the sharing and exchange of these datasets possible. New database structures, such as distributed databases and object oriented databases, will probably underpin our Mappa Mundi. New hierarchical data management systems are now becoming more common. They seamlessly combine amazing robotic tape storage systems (capable of holding data by the terabyte (10¹² bytes) or indeed petabyte (10¹⁵ bytes)) with conventional disc arrays to produce, for the user, the effect of one enormous disc. And the second generation of metadata systems, such as the ImageNet system being tested by the National Resource Information Centre and ACRES, will allow users to find data visually over the World Wide Web - a far cry from NRIC's pioneering metadata efforts with FINDAR.

And the last is visualisation of these data - the maps themselves. Mapmakers are now comfortable with GIS. Indeed GIS is the hybrid response of the competing demands of environmental scientists to visually analyse their spatially based data and the mapmakers demand to create maps using modern information technology. But I get a strong feeling that GIS has had its day, that it has peaked. Now, there can be no doubt that it is a mature technology. A quick look at any of the GIS systems reveals a plethora of gadgets and widgets, tools and functions. But that is not the same as saying that it is a permanent feature of our intellectual landscape. The more important thing is not the present functionality of GIS, but whether its underlying conceptual base has the room for growth into the next millennium - not whether it can become more complex, but whether it can embrace the idea of complex systems. When I look at today's GISs, I am reminded of the gas guzzlers of the 1960s, with their huge tailfins and abundance of chrome, but underneath they still had 1940s leaf-spring suspensions and drum brakes. And yet their makers were surprised when Mazda and Honda wiped the floor with them! GIS may be the first dinosaur technology of spatial analysis.

Bewilderingly complex in its interface, GIS is awfully simple underneath. And so has difficulties in capturing some of the contingent complexity of the real world. It doesn't really like any world which is not 2-dimensional. It reluctantly handles the third spatial dimension as a sort of Clayton's dimension - the dimension you have when you really don't want a dimension. And as for time, the fourth dimension of any Cartesian representation of the world, well, don't ask. What it does with those 2-something dimensions is also pretty simple - it basically allows the set of Boolean logical operations, themselves a primitive arithmetic. Now this is all pretty linear and simplistic. It sure ain't nonlinear or complex.

Unfortunately you don't have to go very far into the real world, and particularly the world of sustainable development, to come across problems which stymie GIS. The problems of sustainable development are all to do with dynamics, with the contingent past and the possible future, with interactions. They are to do with those difficult 'What if' questions that, as your society rightly pointed out to the Prime Minister, go to the heart of sustainable development.

So I don't think our Mappa Mundi will be a GIS. Like Gaul, it will be divided into three parts. One part will be a complex data system, capturing the real complexity of the environment. A second part will be a powerful modelling system which dynamically models the constraints and possibilities of the ecologically sustainable development of that environment. The last part will be the interface, through which it is interrogated and its results are made known. This last part will be utterly visual, it will be the modern incarnation of the Mappa Mundi. And it should be, will be, multidimensional - three proper spatial dimensions and the dimension of time represented as an animation, with other higher dimensions capturing complex phenomena, using all the tricks of colour and transparency that computer graphics allows.

And, finally, like Gaul, it will be a whole: Gallia est omnis divisa in partes tres. It will work as an integrated system, through the cooperative efforts of many disciplines formed together into what Larry Smarr of the US National Centre for Supercomputing Applications calls 'renaissance teams' - a lovely allusion to the multi-talented renaissance men who strove to build cathedrals of the mind.

There is certainly much for mapmakers to do, even if all the dragons have been slain.

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