Chapter 1 – Models (2nd Ed.)

(This Chapter comes from the 2003 2nd Edition of the book and has been updated in the 2015 3rd edition)

A message to mapmakers: highways are not painted red, rivers don’t have county lines running down the middle, and you don’t see contour lines on a mountain. 

W. Kent, Data and Reality, (1978).

 Man tries to make for himself in the way that suits him best a simplified and intelligible picture of the world and thus to overcome the world of experience, for which he tries to some extent to substitute this cosmos of his. This is what the painter, the poet, the speculative philosopher and the natural scientist do, each in his own fashion… one might suppose that there were any number of possible systems … all with an equal amount to be said for them; and this opinion is no doubt correct, theoretically. But evolution has shown that at any given moment out of all conceivable constructions one has always proved itself absolutely superior to all the rest.

A. Einstein, The World as I See It, (1935).

The study of healthcare is founded upon a few basic ideas like the cell or the concept of disease. Informatics is similarly built upon the concepts of data, models, systems and information. Unlike health, where the core ideas are usually grounded in observations of the physical world, these informatics concepts are abstract ideas. As a consequence, they can be difficult to grasp, and for those used to the study of healthcare, often seem detached from the physical realities of the clinical workplace.

This is further complicated because we use the same words that describe these informatics concepts in everyday language. It is common to ask for more information about a patient, to question what data support a particular conclusion, or to read a textbook that describes a physiological model. In informatics these intuitive ideas need to be much more precisely defined. Having mastered them however, it is then relatively easy to move on to the key informatics issues facing healthcare.

In this first chapter, we begin the study of informatics by exploring the pivotal concept of a model. Whether diagnosing a patient’s condition, writing a patient record, designing an information system or trying to deliver an efficient health service to the public, we use models to direct our actions. A deep understanding of what it means to create or apply a model underpins the way we interact with the world and how likely we are to be successful in achieving our goals. Models define the way we learn about the world, interpret what we see, and apply our knowledge to effect change, whether that is through our own actions, or through the use of technology like a computer.

Humans are naturally adept at developing mental models of the world, and manage to use them robustly, despite the inherent weaknesses of the models themselves. When these flexible mental models are transferred into a fixed technological system like a computer, the effects of modelling error can be amplified significantly, with sometimes disastrous consequences (Box 1.1). This is often because much of the knowledge used in creating the model has not been transferred along with it, and as a consequence, the technological system is unable to define the limits of its knowledge. One of the major ideas to be explored in this chapter is that the implicit and explicit assumptions we make at the time a model is created ultimately define the limits of a model’s usefulness. The motto for this Chapter is “A map is not the territory”.

A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness. . . . If we reflect upon our languages, we find that at best they must be considered only as maps. A word is not the object it represents . . . the disregard of these complexities is tragically disastrous in daily life and science.”

Alfred Korzybski, Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics, (1948)

1.1    Models are abstractions of the real world

What is a model and what does it do? Models are commonplace in our everyday lives. People are familiar with the idea of building model aeroplanes, or looking at a small-scale model of a building to imagine what it will look like when built. In health, models underlie all our clinical activities. For example, whenever we interact with patients, we use internalised models of disease to guide the process of diagnosis and treatment.

Models actually serve two quite distinct purposes, and both of these are of interest. The first use of a model is as some kind of copy of the world. The modelling process takes some aspect of the world, and creates a description of it. A simple example will make this clearer. Imagine a camera taking a photograph. The image that is captured upon the camera’s film is a model of the world:

Image1

 We can generalise from the way a camera lens and film record a physical object to describe the way that all models are created. The process of creating a model of the real world is one of abstraction:

Image2

Abstraction is the process of identifying a few elements of a physical object and then using these to create a model of the object. The model is then used as a proxy representation of the physical object.

The effects of the abstraction process are directly analogous to the effects of using a camera. In particular, the image captured upon film has four important features that are characteristic of all models.

  • Firstly, the image is simpler than the real thing. There are always more features in the real world than can be captured on film. One could, for example, always use a more powerful lens to capture ever finer detail. Equally, models are always less detailed than the real world from which they are drawn. A map for example, will not contain every feature of the city streets it records. Since models are always less detailed than the thing they describe, data are lost in the abstraction process.        
  • Secondly, the image is a caricature or distortion of the real world. The three physical dimensions occupied by the photographed object are transformed into two upon the film. Through the use of different filters, lenses or films, very different images of the observed world are obtained. None of them is the ‘true’ image of the object. Indeed there is no such thing. The camera just records a particular point of view. Similarly, abstraction  imposes a point of view upon the real world, and inevitably the resulting model is distorted in some way. Thus a map looks very little like the terrain it models. Some land features are emphasised, and others de-emphasised or ignored. In physiology, one view of the heart models it as a mechanical pump. This model emphasises one particular aspect of the organ system, but it is clearly much more than this. It also has a complex set of functions to do with the regulation of blood pressure, blood volume, and organ perfusion.
  • Thirdly, as a consequence of distortion and data loss, there are many possible images that can be created of the same object. Different images emphasise different aspects of the object or show different levels of detail. Similarly, since there are a variety of aspects that could be modelled of any physical object, and a variation in the level of detail captured, many models can be created. Indeed, the number of possible models is infinite. Since we all carry different “lenses” when we see the world, it is no surprise that different individuals see the world so differently. Psychiatrists for example, might consider the brain from a Freudian or Jungian perspective. Neurologists may model it as a collection of neurones each with different functions. Physiologists may model the function of a brain on that of a computer. When a clinician meets a patient, do they see a person, an interruption, a client, a task, a disease, a problem, a friend, or a billing opportunity?
  • Finally, the camera records a particular moment in time. Thus as the model remains static and the physical object it represents changes with time, the similarity between the model and the physical object it represents degrades over time. The difference between you and a photograph taken of you increases as you get older. A map of a city becomes increasingly inaccurate as time passes because of changes to the city’s roads and buildings.

Karl Popper would ask his students to “observe and describe”. They would be puzzled, and eventually ask “observe what?” That was his point. We always have to observe something in order to describe something. The notion of pure observation, independent of direction, is a myth.  Skolimowski, (1977)

As a consequence of these four characteristics of abstracted models, a final one now becomes evident. All models are built for a reason. When we create a model, we actively choose amongst the many possible models that could be created, to build one that suits our particular purposes. For example, the point of view captured in a map is determined by the way the map will be used. A driver’s map emphasises streets and highways. A hiker’s map emphasises terrain and altitude. Thus, one actively excludes or distorts aspects of the world to satisfy a particular purpose. There is no such thing as a truly “general purpose” model.

This last point is crucial to much of what will follow in later chapters. It leads on to a related idea, which has already been touched upon. Just as a camera cannot capture a ‘true’ image of an object, one cannot ever build a ‘true’ model of an object.

In philosophy, the argument against things ever being inherently correct or true is equivalent to arguing against the Platonic ideal. This is the idea that pure forms of physical objects exist outside the realms of the physical world. Thus, while a physical sphere may always have an imperfection, Plato believed there existed an ‘ideal’ mathematical spherical form. The arguments against Plato’s ideas say that there is no such ideal or objective truth in the world. There can only be our subjective and local point of view or need, and based upon the input of our senses.

Even in ‘pure’ geometry, there is no ideal sphere, just an infinite family of possible shapes that vary depending on the rules of the geometric system you choose. We cannot say that only one of these geometries is correct. Rather, they are different explanations of space, based upon different assumptions. We use the one that gives the most satisfactory explanation of the phenomenon we are interested in. For example, Reimann geometry works best for Einstein’s relativity theory, rather than classic Euclidean geometry, since it handles the notion of curved space. (Fig 1.1)

CR01F01

Figure 1.1: There is no’correct’ geometric shape, just an infinite number of possible geometries. The angles in classic Euclidian triangles always add up to 180°, but in Riemann geometry they always add to greater then 180°, and with Lobachewsky-Bolyai always less than 180°.

And though the truth will not be discovered by such means – never can that stage be reached – yet they throw light on some of the profounder ramifications of falsehood.

Franz Kafka, Investigations of a Dog

This philosophical argument continues into the present century, as the process of scientific enquiry has been debated, and the nature of experimental evidence defined. This is because a scientific hypothesis is nothing more than a model of some aspect of the world, which is to be tested by an experiment. However, if a model can never be correct and thus objective truth never be known, then our experiments can never actually prove anything to be true. We are never sure that we are right. The best that experiments can do is show us when our models of the world are wrong (Popper, 1976). What remain are theories that are in some way more or less useful than others in managing the world.

1.2    Models can be used as templates

So far, models have been described as copies or images of the world. There is a second way in which we use models that is equally commonplace. Some models, rather than being copies of real things, are used as templates from which a new thing will be created. An architect, for example, creates a set of drawings that will be translated into a building. Economists build mathematical models of a country’s economy, and then use these models to predict the effects of changes in monetary policy. An emergency procedure is written down, and will come into effect if a hospital team is called to a major civil disaster.

Again, a simple example will make this second use of models clearer. If we take an image captured on a photographic slide or strip of movie film, a lamp can be used to project a copy of the image onto a screen:

Image3

The image stored on the film is a model of the real world. The projection process uses this model to create a second, slightly altered, image. We can generalise from this to understand how models can act as templates. The process begins with the creation of a model. This might be a design, perhaps recorded as a set of blueprints or specifications. This is followed by a process of construction or model instantiation. In mathematics and logic, we instantiate the variables in an equation with data values. The equation is a template and it interacts with the supplied data values to arrive at the result.  Instantiation uses the model as a template to build an artefact or process that is an instance of the model in the physical world.

Instantiation is the process of building an example or instance of a model, using the model as a template to guide the process

Image4

Thus, the process of creating an instance has a variable outcome, and the impact of the instance of a model in the real world also varies. Two very different examples will help reinforce these ideas. Despite having identical DNA, two individual biological organisms are never truly identical. If DNA is a model (see Box 2.1) then the process of DNA transcription results in the ‘manufacture’ of an instance of an individual organism. Even if we take identical DNA as the starting point, local variations in the process of protein manufacture will introduce minor changes that at some level distinguish the clones.

Similarly, while two patients may be treated according to the same guideline, which is a template for treatment, no two actual episodes of treatment are ever exactly the same. The features of the specific situation in which a treatment is given results in variations in the way the treatment proceeds and in its final effects upon a patient. Variations in the timing of treatments, availability of resources, and the occurrence of other events all can conspire to change the way a treatment is given. Equally, the physical and genetic variations introduced by the patient will result in variations of the effects of a treatment.

Fig2Ch1

Figure 1.2: Models of the world are used as a basis for creating template models which define how artefacts like devices or processes will be constructed.

One can consider the effects of this instantiation process as directly analogous to the effects of projecting a movie image. In particular, the image that is projected is an instance of the image model contained on the film. Many of the effects of the instantiation process are similar to the abstraction process.

  • While abstraction loses data to create a model, the process of instantiation adds data to create an instance. The image you see from a projector varies depending upon whether it is projected on a white screen, a wall or the side of a building. The physical surface adds in its own features to shape the final result. The image is the result of the interaction of the projected image and the physical surface it strikes. Thus an artefact is more complex than the model that it came from, because it is situated in the physical world.
  • The constructed artefact is thus a distortion of the original template, since we can transform it in many different ways. The projected image can be shaped by the use of filters and lenses to produce a variety of different images.
  • No two projected images are ever exactly the same, because of variations introduced by the physical process of construction. No two physical artefacts are similar even if they are instances of the same template. Even mass-produced objects like light-bulbs, syringes or clay pots have minor imperfections introduced during manufacture that distinguish one instance of an object form another. In contrast, in digital or ‘virtual’ worlds, where we can guarantee that the exact conditions for creating instances are identical, we can say that no two images need be the same.
  • The effect of the captured image changes with the passage of time as the physical world changes. A movie has a greater impact on release than many years afterwards as audiences change. A treatment guideline becomes increasingly inappropriate as time passes and new knowledge indicates that newer methods are better treatment options. Similarly, the effect of an artefact may change while the original template stays the same.

A more general principle follows from these four characteristics of templates. Since the process of creating an instance from a template has a variable result, and the process of doing things in the real world is uncertain because we can never know all the variations that are ‘added in’ as we follow a template, then there is no such thing as a general purpose template. All we can have are templates or designs that are better or worse suited to our particular circumstances, and are better or worse at meeting the needs of the task at hand.

As we will see in later chapters, this means that there can be no ‘correct’ way to treat an illness, no ‘right’ way to describe a diagnosis, nor a ‘right’ way to build an information or communication system. There can thus never be an absolutely ‘correct’ design for a treatment protocol or information system, nor a ‘pure’ set of terms to describe activities in healthcare. This principle explains why clinical protocols will always have varying effectiveness based upon local conditions, and why medical languages can never be truly general purpose. What we do have are treatments, protocols, languages, information and communication systems that are better or worse suited to our specific purpose than others.

1.3    The way we model the world influences the way we affect the world

In the previous sections we saw how models acted either as copies of things in the world, or as templates upon which new things are created. These two aspects of modelling are deeply interrelated. In the photography example, decisions at the moment an image is created influence the way it can ultimately be used.

Fig3Ch1

Figure 1.3: An artificial heart is based upon two kinds of model. Firstly, the cardiovascular system has to be modelled, and secondly, a mechanical blueprint is used to model the way the heart will be constructed.

Assumptions about the purpose of an image will determine how useful it will be when the time comes to use it, since our belief about expected purpose shapes the form and the content of the image. Slides are created with the assumption that they are to be used in a particular type of projector. The value of the projected image in meeting a particular need depends in part on what was originally photographed. An X-ray may be of less value than a CT scan of a skull when managing a head injury.

When artefacts are created, it is assumed that they too will be used for a particular purpose. If the purpose changes, then a design becomes less effective. Thus, the physical design of the waiting room and treatment areas for a general practice clinic will assume a certain number of patients need to be seen during a day, and that certain kinds of therapy will be given. If the clinic was bought by radiologists, they would have to remodel the clinic’s design to incorporate imaging equipment, and to reflect a different throughput of patients.

Before the work of the famous physician Galen, it was assumed that the arteries contained air. This was because arteries were observed to be empty after death (Schafer and Thane, 1891). The physicians making these observations had thought they had created a model of arterial function in living humans, but all they had created was a model valid in cadavers. So, the context in which a model is created affects its validity for any other context within which it might be used.

Equally, we can consider a particular treatment of a disease written in a textbook to be a template for what should be done to any given patient. If that treatment was based upon assumptions about the incidence of diseases in a given population, then it may not work well if attempted in a different one. Treating infant diarrhoea in a developed nation is not the same task in underdeveloped nations where poorer resources, malnutrition, and different infecting organisms change the context of treatment. Before a model is used, one therefore has to be clear about what has actually been modelled. This is because, when models are created, the circumstances at the time have a strong influence on the final value of the model.

Similarly, a set of rules and procedures might be developed in one hospital, and be spectacularly successful at improving the way it handles its cases. One would have to be very cautious, given that these procedures implicitly model many aspects of that particular institution, before one imposed those procedures on other hospitals. Very small differences, for example in the level of resources, type of patients seen, or experience of the staff, may make what was successful in one context, unhelpful in another.

More generally, any designed artefact, whether it is a car, a drug or a computer system, has to be designed with the world within which it will operate  in mind. In other words, it has to contain in its design a model of the environment within which it will be used. These specifications constitute its design assumptions. Thus there is a connection between the process of model creation, the construction of artefacts based upon such models, and their eventual effectiveness in satisfying some purpose (Figure 1.2).

A few examples should make the cycle of model abstraction and instantiation clearer. Firstly, consider an artefact like a car. The design blueprints of the car reflect both the purpose of the car, as well as the environment within which it will operate. The car’s engine is built based upon the not unreasonable assumption that it will operate in an atmosphere with oxygen. The wheels and suspension are designed with the assumption that they will operate on a highway or local street. The car thus carries within its construction a kind of implicit model of the world within which it is designed to work. If the car was put into another physical environment like a desert or the lunar surface, it probably would not work very well. Sometimes such design assumptions are left implicit, and only become obvious when a device is used in a way in which it was not intended, sometimes with catastrophic results (Box 1.1).

The human body also makes assumptions about its environment. The haemopoietic system adjusts the number of red blood cells needed for normal function based upon the available oxygen in the atmosphere. As a consequence, individuals living at sea level have calibrated their oxygen carrying system differently to those living in high altitudes. An athlete training at sea level will not perform well if moved quickly to a high altitude because these ‘working assumptions’ are no longer met.

Finally, consider an artificial heart (Figure 1.3). Such a device must model the heart in some way, since it will replace it within the cardiovascular system. The artificial heart thus is based upon a model of the heart as a mechanical pump, and is designed with the assumption that supporting the pump mechanisms will be beneficial. It is also designed on the assumption that it will need to be implanted, and as a consequence is crafted to survive the corrosive nature of that environment, and to minimise any immune reaction that could be mounted against it.

1.4    Conclusions

In this chapter, the basic concept of a model has been explored in some detail. Models underpin the way we understand the world we live in, and as a consequence guide the way we interact with the world. We should never forget that the map is not the territory and the blueprint is not the building.

In the next chapter, a second basic concept of information will be introduced. These two ideas will then be brought together, as we begin to see that knowledge is a special kind of model, and is subject to the same principles and limitations that afflict all other models.

Box 1.1 – Therac-25

Between June 1985 and January 1987, Therac-25 linear accelerators operating in the USA and Canada delivered massive radiation overdoses to at least 6 patients, causing death or serious radiation injury. Patients received doses of up to 20,000 rads where a dose of 200 rads was a typical therapeutic dose, and a 500 rad whole-body dose will cause death in 50% of cases. These were arguably the worst radiation incidents associated with medical accelerators in the history of radiotherapy.

Medical linear accelerators operate by creating a high energy electron beam. The beam is focused onto a patient to destroy tumour tissue, and leaves healthy tissue outside the beam focus relatively unaffected. The high energy beam produced by these devices is focused through a tungsten shield. This ‘flattens’ the beam to therapeutic levels, and acts like a lens to focus the beam to a tissue depth appropriate for a given patient.

In the Therac-25 accidents, the tungsten shield was not in place when the radiation dose was delivered, resulting in patients receiving a full dose of the raw 25 MeV electron beam. There were a number of different causes of the various overdoses, but each essentially resulted from modelling errors in the system’s software and hardware (Leveson and Turner, 1993).

One critical error resulted from the reuse of some of the software from a previous machine, the Therac-20. This software worked acceptably in the 20, but when reused in the 25 permitted an overdose to be given. This was because while the 20 had a physical backup safety system, this had been removed in the design of the 25. The Therac-20 software was thus reused in the 25 on the assumption that the change in machines would not affect the way the software operated. So, software modelled to one machine’s environment, was used in a second context in which that model was not valid.

Another problem lay in the measurement system that reported the radiation dose given to patients. It was designed to work with doses in the therapeutic range, but when exposed to the full beam strength, became saturated and gave a low reading. As a result, several patients were overdosed repeatedly, because technicians believed the machine was delivering low doses. Thus, the measurement system was built upon an assumption that it would never have to detect high radiation levels.

All of these failures occurred because of the poor way models were used by the designers of the Therac-25. They did not understand that many of the assumptions that were left implicit in the specifications of the device would quickly become invalid in slightly changed circumstances, and would lead to catastrophic failure.


Discussion Points

  1. “The map is not the territory”. Why not?
  2. Observe and describe. Compare. Why?
  3. Biologists argue whether nature, expressed in an organisms DNA, or ‘nurture’, via the physical world, is most important in shaping an organism’s development. If ‘nature’ is the template, and ‘nurture’ creates instances of an organism, which is more important in shaping an organism, based upon the first principles of modelling?
  4. In what ways could the limitations of models result in errors in the diagnosis or treatment of patients? Use figure 1.2 as a template to guide your thinking, if it helps.

Chapter one summary

  1. Models are the basis of the way we learn about, and interact with, the physical world.
  2. Models can act either as copies of the world like maps, or as templates that serve as the blueprints for constructing physical objects, or processes.
  3. Models that copy the world are abstractions of the real world:
  • Models are always less detailed than the real world they are drawn from.
  • Models ignore aspects of the world that are not considered essential. Thus abstraction imposes a point of view upon the observed world
  • Many models can be created of any given physical object, depending upon the level of detail and point of view selected.
  • The similarity between models and the physical objects they represent degrades over time.
  • There is no such thing as a truly general-purpose model. There is no such thing as the most ‘correct’ model. Models are simply better or worse suited to accomplishing a particular task.

4. Models can be used as templates and be instantiated to create objects or processes that are used in the world.

  • Templates are less detailed than the artefacts that are created from them.
  • An artefact is a distortion of the original template.
  • No two physical artefacts are similar even if they are instances of the same template.
  • The effect of an artefact may change while the original template stays the same.
  • The process of creating an instance has a variable outcome, and the impact of the instance of an artefact in the real world also varies. As a consequence, there is no such thing as a general purpose template. All we can have are templates or designs that are better or worse suited to our particular circumstances and task.

5. The assumptions used in a model’s creation, whether implicit or explicit, define the limits of a model’s usefulness.

  • When models are created, they assume that they are to accomplish a particular purpose.
  • When models are created they assume a context of use. When objects or processes are built from a model, this context forms a set of design assumptions.

6. We should never forget that the map is not the territory and the blueprint is not the building.

© Enrico Coiera 1997-2014

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