Maps as theories, Theories as maps – John Ziman

An intellectual and entrepreneurial passion of ours is the acceleration of scientific discovery through the capture of scientific knowledge in a structured form that allows the use of reasoning tools. Our goal is to bridge the gap between the literature of medical sciences and the formal languages of machine learning by providing straightforward tools that can be used by normal medical scientists and provide valuable research insights. We don’t believe that ‘robot scientists’ are the answer, but we also believe that scientific discovery can be accelerated through the encoding of knowledge by humans and the use of tools that allow for the combination of computational analysis and human intuition.

With those goals in mind, we have been avidly reading philosophy of science and knowledge (Popper, Quine, Ayer, etc), and the history and anthropology of real scientific discovery (Kuhn, Ziman, etc). We have been influenced by the intuition pump put forward by Quine of our beliefs forming a web, with our most firmly entrenched beliefs at the center and those at the outer being open to revision based on experience. But here we wanted to highlight the work of John Ziman, who through several books provides a detailed and highly readable view into how Real Science works. He has been a great inspiration to us by exposing the strengths and weakness of the scientific process and helping us to identify where knowledge and discovery tools could most effectively be applied.

We highly recommend that you read Real science: What it is and what it means. John Ziman. Cambridge University Press, 2002. We feel that it should be required reading for all scientists. A favourite section of ours from the book is section 6.5 Maps as theories. We have provide the text of the section below (without references) and hope that it inspires you to read the whole book.

Maps as theories

“A map is not just a picture. In everyday language, a picture is a representation of some segment of the world, as seen from a particular viewpoint. For scientific purposes, the ideal form of a picture is a photograph, pinning down a specific configuration of events and differentiating it from others. By contrast, the essence of a map is that it does not have a particular perspective. In principle, every location is equally unprivileged as a possible viewpoint. In other words, as we have already remarked, a scientific theory, like a scientific ‘fact’, must be sufficiently free of subjective elements to be equally acceptable to all members of a scientific community.

But the notion of a ‘view from nowhere’ is not meaningful. A map has to represent a particular territory, and cannot be interpreted or used without some idea of its relative viewpoint. The standard cartographic convention is that a map should be read as if it were a picture taken through a telescope, looking straight down from a great height — e.g., like a photograph from a space satellite. This convention is so familiar that it is often forgotten. Nevertheless, it reminds us that a scientific theory is not a pure abstraction like a mathematical theorem. It is only meaningful as a representation of a particular aspect of reality as it might appear in principle to some human intelligence.

In practice, most maps are not derived from single space photographs. Even apparently lifelike satellite images are often mosaics of pictures and survey data taken from a number of points, reconciled and harmonized one big picture. As cartographers know, the unity of this picture is an illusion. The curve of the earth is artificially flattened and the play of light, shade and colour varies unnaturally over the whole scene. In other words, scientists have to do a good deal of work on the empirical ‘facts’ to fit them together into coherent theories — and these are usually more contrived and less consistent than we are often led to believe.

This choice of a common viewpoint is particularly difficult in the human sciences where people have their own individual ‘pictures’ of the social world and of themselves in it. These overlap and can often be fitted together, through empathy, into a generally agreed ‘map’. But as every novelist knows, it is not easy to establish a common standpoint outside any particular human mind from which to look at this map as a whole. Thus, the social scientist often has to choose between adopting the stance of an all-knowing anthropoid god, or theorizing about the social world in non-human terms, as if it were a biological organism or a machine.

Maps are drawn to different scales. A world atlas fills a page with Europe, another page with England, and another page with London. To plan a car journey from Oxford to Edinburgh, I use a motorway map of 1 centimetre to 50 kilometres. To plan a cross-country ramble to the next village, I use a map of 5 centimetres to 1 kilometre. Each map turns out to be reliable for the use I make of it. Each map is entirely truthful on its own scale. Yet even where they include the same geographical feature, they present it differently. On the motorway map, the villages are not shown and Oxford is a mere dot: on the rambler’s map, Oxford is an irregular patch, as large as my hand, crowded with lines, coloured symbols and names.

Indeed, the form of a map depends greatly on its intended use. I regularly use maps of London in four different forms, each for a different purpose. For getting around by car, I have a Highway Map, showing the network of main routes — including one-way streets. To find my way to a specific address, I then turn to a Street Directory, which helpfully indicates house numbers. Often, however, I travel by bus, and need to consult Bus Route Map — typically quite complex, in spite of showing only the roads where buses run. Finally, there is the Underground Map, whose schema of tube lines, stations and interchanges is etched on my memory from frequent use. These four maps all cover the same region on much the same scale, and in spite of various simplifications are all essentially ‘truthful’. Yet they emphasize such different characteristics that they are not equivalent in use or meaning. Indeed, as we all learn from the experience of exploring a foreign city, it takes quite an effort to identify their common features — the relation of bus stops to underground stations, and so on.

In other words, scientific theories have to be understood as purposeful generalization. Indeed, one of the achievements of the social sciences is to provide people with unsuspected ‘meanings’ for many cultural features of their lives. The entities that figure in a scientific theory are selected and simplified to suit its scope and function. Theories of different degrees of generality or with different purposes include or emphasize quite different features. Factual distinctions that are of significance in one theory are glossed over or lumped together in another. Relationships that are merely incidental for one theory are explanatory concepts for another. Even many-sided entities that we quite properly believe to be unitary are not always shown as such. For example, the entity labelled ‘DNA’ is presented differently and plays a different theoretical role in organic chemistry, biochemistry, physiology, genetics and ecology.

The fact that maps are human artefacts does not, of course, imply that they are untrue to nature. Indeed, the whole purpose of making a map is to convey reliable information about the domain it claims to represent. But cartography is never a purely mechanical process. The need for a map emerges out of a sea of other needs and interests. A publicly available map is a social institution. It is designed to serve a specific social function, such as running a railway or avoiding traffic jams.

In practice, the skilful cartographer has considerable freedom in selecting and symbolizing the geographical entities and relationships that best serve the functions of their products. This freedom is very obvious in the marketplace. For example, try to buy The Motorway Map. What you will be offered will not be a unique document: it will be one or more out of a whole family of variants, all perfectly genuine as maps but differing in format, scale, date of revision, details of junctions and service areas, etc.

The same goes for scientific theories. It cannot be denied that they are ‘constructed’ to satisfy human purposes. This does not automatically imply that the knowledge they claim is untrustworthy. It only means that in evaluating a theory we have to take into account the needs and interests of its makers. Indeed, the whole argument of this book is that theories constructed by academic scientific communities should be evaluated in the first instance on this basis — i.e., as primarily serving the needs and interests encapsulated in the academic ethos.

Scientific theories, like maps, are under-determined. They are products of their time and place. They emerge out of the exercise of originality and scepticism in a disputatious community. Of course there are moments when a novel scientific theory seems precisely right. But its form and substance are neither pre-ordained nor permanent. Even the most compelling theory is usually shaped by unconscious aesthetic and utilitarian criteria. Theoretical entities such as ‘DNA’ have to be redefined to meet the demands of new fields or other disciplines. As aspiring textbook authors soon discover, scientific theories, like maps, are not uniquely specified. They come in families, where sometimes the differences are of form rather than substance, but sometimes the supposed relationships and resemblances are more notional than real.

Let me emphasize, moreover, that we are not talking here about obvious inconsistencies calling for resolution by further research. Even good scientific theories, like good maps, can present the same ‘domain’ in a great variety of very different forms. But this theoretical pluralism is very disconcerting for the Legend of a unique scientific world picture. To avoid further embarrassment, the Legend insists that such apparent pluralism is not genuine: it is just a consequence of our present ignorance. The diverse theories of today are merely provisional: in due course, so it is argued, they will be seen as different approximations to the ‘theory of everything’ that will eventually be completed.

But any such ‘theory of everything’ — including, of course, all the contingent features of the world as well as their fundamental equations of motion — is not merely hypothetical: it is not a meaningful concept. Here again, the cartographic example is instructive. A ‘map of everything’ would have to be drawn on an enormous scale so as to make visible every microscopic detail. As Lewis Carroll pointed out over a century ago, the concept of a total 1 inch to 1 inch map is not only impractical — the farmers would object to all their land being covered by it — but also absurd in principle. As formal mathematical theory has now shown, any domain as complex as the real world cannot be fully ‘mapped’ by anything less extensive than itself.

A naive cartographical realist might insist that we should indeed consider the world as its own perfect map. But the whole concept of a map implies that it can be detached from the actual domain of which it is an icon, and used for other purposes. That is to say, a map is not the same as geography it represents. Nor is it an approximate version of a perfect abstract replica — a hypothetical, super-duper, Ordnance Survey map — of that geography. Like any other scientific theory, it is simply an image built upon factual data obtained by direct exploration of the domain it represents.”