Models

  1. The Scientific Model
  2. Modelling Languages
  3. Written language
  4. Icon models
  5. Topological models
  6. Arithmetic models
  7. Analogous models
  8. Artistic Modelling Languages

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The Scientific Model

Empiria and model The object of empirical study exists in the tangible world, or in empiria, as researchers call it. One of the first goals of most research projects is to create a theoretical picture of the empirical object of study into the conceptual world of thinking and theory. Scientists often use the name of model of this picture of the object of study, as can be seen in the diagram on the right. In the initial phases of a research project the model often exists only as an idea in the researcher's mind, but quite soon he will want to put it on paper or computer, too.

In a research project, two types of theoretical models are used: those that depict one empirical object (or other case of study), and those models that describe a population of more or less similar cases.

The first alternative, a case study focuses on only one object or occurrence, and the model is made to depict this object or phenomenon. As a contrast, in all other types of study there are quite a number of study objects that are more or less similar, and in this case the model should describe what is common to all (or at least to most) of the cases or objects in the population. The model is in this case said to be general.

The last mentioned goal of empirical study - constructing a single generalizable model on the basis of a number of empirical observations - can be difficult or impossible to attain completely. Today most scientists agree that it is not only practically but also logically impossible to write an absolutely reliable model on the basis of a class of empirical observations. It would almost never be possible to know all relevant cases that should be measured, or approach them; sometimes the number of cases would be so great that you can afford to study only a sample of them, and this sample can be biased; and finally all empirical observations can contain errors. In a word, it would never be possible to exclude totally the possibility that at least one case remains unnoticed that invalidates the general model and prevents calling it categorically "true".

While scientists thus today accept the fact that general models never can be absolutely reliable, these models are all the time being constructed and used in nearly all research projects. The reason is that even as imperfect they belong to the most indispensable tools of research. Besides, they are invaluable for transmitting the results of research to practical applications.

In a research project, a general model helps analyzing data obtained from the object and finding the answer to the researcher's problem. A scientific model need not enumerate all the properties of every object that is being studied. On the contrary, you will normally want to take into account only the "interesting" properties, i.e. those that are related to the purpose of your study. Restricting your view to just the essential measurements, attributes and properties of the object will help you to manage a large material and unearth the answers to your questions.

Model in forecasting Those patterns or characteristics which are common to several or all cases in the material of study - in other words, which are invariable from case to case - are often called invariances. As was already said above, there is no certainty that these patterns are true in other cases than those that have been studied. Nevertheless such a generalization has to be done always when somebody wants to apply the findings of research into practice, for example for predicting the future development of the studied phenomenon (figure on the left), or for the development of new products (below, on the right). This is why almost all researchers are all the time boldly generalizing their empirical findings into general models.

Model and its useThe method of audacious generalizing works often quite well in practice, because as long as the present high activity of research persists, invalid generalizations will always be discovered and rectified sooner or later. Findings of descriptive (or "disinterested") research are today quite effectively tested, first in the internal peer critique in a field of research, and a second time when other researchers are using them as a basis of their own work. For the results and proposals of normative (or "applied") research, the final test arrives at once when somebody tries to apply them into practice. Results of this current practice of scientific self-correction have been commented by Popper (1959, p. 111) as follows:

"Science does not rest upon rock-bottom. The bold structure of its theories rises, as it were, above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or 'given' base; and when we cease our attempts to drive our piles into a deeper layer, it is not because we have reached firm ground. We simply stop when we are satisfied that they are firm enough to carry the structure, at least for the time being".

Because a model is made to be an image of the object of study, its indispensable material will be observations and measurements from the object of study. Sometimes - but not very often - no other material is available to help you in constructing a model because very little or nothing is known about the object in advance. In such a situation of exploratory research you have to collect all the substance for the model by meticulously examining the objects. Often it will be laborious, because much material will have to be collected and in the beginning you do not quite well know which data are important and which are not.

Layers of theoryFortunately, today the normal situation at the outset of a novel research project is that you already know quite a lot about your object, and in the best case there are already published research reports where you can find models that have been used successfully by earlier researchers in the field. At least you will find vocabulary and instruments - such as concepts, definitions, and methods of measurement - for building a new variant of model that serves your purposes. This quite usual approach of study is discussed elsewhere under the title Research on the Basis of Earlier Theory.

Modelling Languages

Theory
consists
of...
...models
which
consist
of...
...concepts and...
...relations
between
concepts,
and there must also be
a few empirical definitions.
The principal building stones used when constructing scientific models are theoretical concepts. Concepts also serve as links between the model and empiria, by connecting to their empirical counterparts through the empirical definitions that the researcher has to provide for at least some of the concepts.

The relationships between the concepts, in other words the structure of the model, can be used to express invariances in the objects of study. This will be the most interesting part of the model, if an earlier unknown invariance has been found in the project.

In the beginning of the project the conceptual structure of the model often exists only as a vague idea in the researcher's mind, but during the project the researcher must give it a definite shape. Powerful tools for this are nominal definitions which specify a concept with the help of other concepts.

Nominal definitions are excellent and exact instruments to be used by the researcher when constructing a model, but because they can handle only one concept at a time they are not very communicative in presenting the general form of the model to outsiders. However, exactly this must be done in the research report, because the report is normally the only channel available for distributing the research findings to their eventual users. For this task the researcher normally selects a modelling language which can present the complete structure of the model at the same time on paper, a computer screen, or in other visible form that can be understood by the readers of the report.

The researcher has complete freedom in selecting the modelling language in such a way that it clearly conveys the essential features of the model, its concepts and relations. In sciences, several types of model languages are used. A researcher familiar with fine arts may notice that more than one of these scientific presentation languages have some resemblance with some genres of artistic presentation. This is not astonishing, as one cardinal goal of art is "to disclose what is invisible", in other words, to express an invariance behind conventional, visible things.

When selecting the most suitable modelling language, the researcher should remember that models are needed in several different phases of the project. When gathering empirical data by observation and measurement the model must be able to handle individual cases, but in the analysis phase a conceptual model which is also generalizable can be more effective. Finally, presenting the findings of analysis so that they can be applied to practice may require a straightforward presentation that can be understood by the layman users. It can be difficult to find a single language of presentation which would meet all these requirements. Sometimes it is possible to use different styles of presentation in the successive phases of a research project.

Usual scientific model languages include:

Lately a few researchers have also experimented with a few artistic modelling languages, i.e. these researchers have adopted from established fields of art methods of describing objects and phenomena. Besides, as research takes as its objects new phenomena, researchers often find it necessary to invent new modes of description for these. This is quite permissible if the researcher's aim is to give the reader a clear picture of the object of the study. The researcher must, however, make sure that his audience has a chance to understand the language of the model. When necessary, the researcher may explain the unusual symbols.

In the following the above mentioned types of models are discussed, including some remarks on the presentation of four sometimes problematic dimensions of models: time, variation between cases, the degree of uncertainty, and the normative aspect, if there is one.

There is no fundamental difference between descriptive and normative models. Many descriptive models can be made normative simply by adding an evaluative dimension, such as 'capacity', 'durability' or 'price'. When this is not feasible, you might consider making two or more models, one of which represents the preferable alternative.

A problem with scientific models is often the abundance of detail, which makes the model too large and difficult to grasp. One remedy to this problem is hypermedia presentation. The basic model then includes only the cardinal general structures and a number of links which point to less important details which are placed in separate files.

Written Language Models

Some sociological models of human activities and their contexts
Script: the subconscious model according to which a person tries to act.
Social episode, a typical situation recurring in people's behaviour.
Behavioural setting is a place (for example: a classroom, a church, a bank counter) where people act in conventional ways.
Institution: a permanent organization of society which includes people, procedures and location.
Describing the object with words of a natural language often go by the name of "qualitative" research, due to the frequent use of adjectives in written or verbal description. In daily life language is used for discussing occurrences and equipment in human life, and it can thus easily present research results about these topics. Besides, because language is familiar to all people and versatile, it is often used in the final study report when the original model is sophisticated and needs to be explained for people.

One more reason for switching to written description from another type of model is that it can be easier to present general invariances with words that with pictures, for example. Thus Päikki Priha used words when describing pictorial motives in Finnish liturgical textiles in the beginning of 20 century:

... "The cross, the lamb carrying a pennant of victory, the pelican feeding her offspring, the dove of the Holy Spirit, a dove carrying an olive twig, an eye, three intertwined circles, various monograms of Christ, plants such as rose, lily, thornbush, palm-tree and the ear of a cereal."

Your first thought might be that when studying pictorial motives these should be presented as pictures, and indeed Priha's study contains many illustrations. However, when looking at them you will quickly note that many pictorial motives, such as a cross, appear in the study material in various quite different shapes. Their general invariance can be better expressed in words.

The dimension of time, which appears in dynamic invariances, can easily be presented with words like "grow up", "evolve", "the trend is that..." etc.

Variation can be presented in words: "Objects were generally like this, but some were..." - "As a contrast, a small minority think that"... etc. Also for uncertainty or probable error there are words: "approximately", "usually" etc. If such phrases seem too vague it is always possible to insert more exact complementary models like percentages or tables.

Normative written language presentation is usual in the early phases of designing a new product. It takes shape as a written list of requirements, examples of which can be found in the chapters on Design Driver and on Product Concept.

From antiquity until our day the layout of written research reports has not developed much, which means leaving unused the rich possibilities of expression that printing technology can offer, not to speak of the technology of computers and multimedia. Such variations of text as italics, bold, text size, font, text color and background color are available in every printer, and they need not be used as decoration only - they could as well convey important dimensions of the conceptual model, once the researcher defines them as such.

Icon Models

An icon model gives a pictorial representation of the object. The object is usually presented as a two dimensional projection; the scale and the colours are often changed, the less interesting details are omitted, and the presentation concentrates on those details or attributes of the object that are interesting -- these are often such static invariances that are common to all or most of the objects which were studied.

Today we have excellent instruments, like cameras and video recorders, to facilitate the task of making pictures. However, photographs and recordings made with these machines often include a great amount of detail, thus hiding the theoretically more interesting features of the objects. Therefore, in research projects, the method of drawing is often preferred. On the left is depicted a coffee pot and some static invariances (circles etc.) that seem to govern its shape (Gunzenhäuser p. 203).

Cars When selecting the method of presentation, one possibility is to adopt the drawing methods of designers. This includes views and sections from one or more directions drawn to a scale. However, such methods are designed for the manufacture of objects. For the purposes of research it can be more rewarding to develop a method of depicting which emphasizes exactly those features of the objects which are interesting. This can be accomplished, for example, by an ink drawing in perspective where the not essential details are simply omitted.

In some fields of study, there are standard methods of depiction. Below on the left, there is an example of a usual archaeological method of presenting pottery in such a way that one picture portrays both outward and inward decoration and also the cross section.

The dimension of time, for example the historical evolution of a type of product, is not quite easy to be presented on two-dimensional medias like paper, because two dimensions of the image are already reserved for presenting the physical shape. A usual solution is to make a series of pictures like the succession of car models in Raymond Loewy's book Industrial Design, above. (See the complete series.)
Another solution, made possible by modern medias of information, is the animated picture of TV or computer.

Drawing of a potUncertainty. An advantage of the method of drawing by hand is that if something is not known exactly you can draw it in thin, dotted or blurred lines, without giving the wrong idea of precision. An example is the picture (on the left) of an ancient pot: the shape of the missing handle is not known and in the picture it is presented in dotted lines.

Old buildingsVariation between objects can sometimes be presented by superimposing several images. In the diagram on the right, Sture Balgård shows several cross-sections of old buildings in Härnösand. He has also added into the same model an invariance which he has found existing in the objects: they follow uniform proportions of width and height (the red line) with just a few exceptions.

Plan of kitchenNormative icon models that are used in the development of new products take the shape of drawings and three-dimensional mock-ups. In the beginning these are often blurred sketches, from which the initial ambiguity gets gradually expelled during the design process. On the right here, we have an example of a sketch in which the exact form of the design is not clear yet. (From Keiski, 1996, p.136; the project produced eventually a new type of kitchen.) Later on the product development project proceeds to prototypes and their evaluation. These operations make use of more and more realistic illustrations, mock-ups, virtual prototypes and interactive models described in Presenting the Draft and Prototype.

Topological Models

UsabilityThe placing of the elements in a topological model reflects the structure of the object. This model can be used for conceptual structures as well as for presenting holistic classifications of objects.

An example is on the right, where Shackel has analyzed the concept of usability of products. The model he has used is a logical tree.

Logical tree Holistic models consist of physical events or specimens, like people or products. This presentation is particularly suitable for taxonomies, i.e. classifications. On the right is an example of a taxonomy of home furniture. Logical tree is perfect to its presentation, if each individual and every class belongs to no more than one superior class.

However, if a case, an individual or a class belongs to more than one class, a Venn diagram (on the left) might be a better presentation. Here, you can read from the model that you can place the dining table either to the living room or kitchen. (John Venn, 1834-1923, an English logician.)

Venn diagramThe researcher should consider if the sizes of the symbols describing the elements should carry any meaning: for instance, does a big box in a picture denote that the class is numerous? Moreover, the shapes of symbols which in a typical Venn diagram mean nothing: should they?
It is up to the researcher to provide the reader with instructions as to how to read the diagram, i.e. with an explanation of the symbolism in the presentation.

Plan of dwellingHow should you place the elements of a topological model?

Traffic diagram A meaning can be assigned not only to the relative placing of the elements but also to the lines or arrows connecting the elements: their width, colour etc. Such options allow you to show simultaneously several different types of relations between the elements of the model. For example the above chart of a person's movements in a house can be amplified by adding the direction of the motion (see figure on the left).
Moreover, influences and causal relationships are often presented with arrows in a topological model. Examples.

UML diagramUnified Modeling Language (UML) is a much used topological modeling language for presenting and planning the relationships between elements that belong to a system. It is often used to describe and plan classifications of objects, uses of objects, sequences, activities, states of activities, and collaboration, especially in business and industrial software research and planning. The standards, which are freely available in the internet, give numerous examples of different diagrams, specify exactly how they are to be drawn and what each component in the diagram means.

For example, in the diagram on the right (from Allen Holub), describing the activity of buying coffee, the upper diamonds with outgoing arrows specify OR operations (branches), with the necessary conditions for each alternative defined in brackets. The lower diamond with incoming arrows (a merge) simply provides an end to the OR operation.

A common problem with scientific models is that abundance of detail makes the model too large and difficult to grasp. One remedy to this problem is hypermedia presentation, for which topological models are well suited. The basic model includes then only the most important general structures and a number of links to the detailed texts or other material which are placed in separate files.

ProductionThe dimension of time, which appears in dynamic invariances, can easily be presented by letting the horizontal axis of the model indicate time. In this way you can present quite complex chains of events, for example the progress of work or circulation of information. On the right is a model of production process; elsewhere is shown a model of a research project.

Variation, subjective or objective, is not quite easy to show in a topological model. You might, for example, try varying the style or colour of the elements.
Uncertainty is also difficult because topological models usually give an undue impression of exactness. You could perhaps express uncertain relations with thin or dotted lines, for example.

Arithmetic Models

Arithmetic models require that your data are measured with an arithmetic scale. There is a vast selection of mathematical models. You will often have great freedom when choosing the type of model; your data usually allows several alternatives and you should try to select the most illustrative one. For example, the traffic flow of the apartment shown above could be presented as an arithmetic table:

The subject moved from - the kitchen - the living room - the bathroom - the lobby
to the kitchen: . 8 times 9 times 6 times
to the living room: 7 times . 5 times 5 times
to the bathroom: 10 times 5 times . 2 times
to the lobby: 7 times 4 times 2 times .

Other common mathematical presentations include equations and diagrams.

If a model is constructed with a computerized programming language, nothing prevents it from being extremely complicated if necessary for simulating a complicated object of research. A single model may thus combine arithmetic and Boolean calculations, time bound events and conditional branches of processes; even random variation. In addition to making such a large model for the computer, you often want to present a simpler and more illustrative one, for example a topological one.
Sometimes you could consider dividing the original, clumsy model in pieces. Example.

The dimension of time which appears in dynamic invariances, presents no problem in mathematical models because these are invariably capable of including several independent dimensions.
The same goes for subjective variation.

Objective variation and uncertainty. Mathematical models easily exaggerate the clarity and definition so that it by far exceeds the factual exactness of the empirical registration of facts. There are, however, arithmetical methods of expressing the precision, or the lack of it, in data. They include concepts like the error of measurement, moreover variation and significance of the measurements. There are also some graphical methods of presentation.

Optimizing insulation(Normative arithmetic models are often equations or graphs where one or more of the variables is evaluative, for example 'cost'. They often allow finding the optimum or the best one of alternatives. An example is the diagram on the right which helps finding an optimum for wall isolation. Their use is discussed on the page Theory of Design.

Analogous Models

Usually, the researcher assembles his model "on an empty table" using the elements offered by the modelling language he has chosen. But sometimes he may happen to find, in another environment, an invariant structure which logically resembles the object of study. The other, foreign structure or object can then perhaps be directly used as a model. Analogy refers thus to the procedure of transferring a model (i.e. copying and adjusting it) from a "system" to another. Analogy does not necessitate any specific language of modelling, on the contrary it allows importing models in any language of modelling.

Examples of analogous models used in research:

The method of analogy is easy to use, but it has serious drawbacks. It is difficult to present the uncertainty of the model or the variation between cases, and it stays unclear how generally valid the model is. Analogous presentation is, even at its best, relatively nebulous and is is often advisable, once you have found a suitable model, to define it anew with the help of concepts that relate to your object of study and not to the original setting of the model (by using empirical or nominal definitions).

Remember that the essence that you want to import into your project is only the invariance that the analogous model is expressing. Beside this invariance, the imported model usually contains much detail that relates to its original environment, which you have to clean out. You can then either replace the details with new ones describing your own object of study, or leave out the not interesting particulars definitely, thus enhancing the generality of your final model.

Artistic Modelling Languages

It is possible to seek and present knowledge not only with scientific methods, but also with some methods of arts. As a matter of fact, art and science have common roots in antiquity, when the Greek term 'tekhne' and Latin 'ars' covered several areas of culture which only later were differentiated into arts and sciences.

Even today art and science have much in common, starting from their principal goals. The target of scientific research is to uncover and publish knowledge, information about the object of study, which knowledge then other people perhaps can use for solving their problems. This target is in principle similar to an important goal in art.

Another similarity is that the knowledge which is gathered and presented can be either descriptive, "disinterested", i.e. accepting the state of things as it is) or normative (i.e. explaining how you can change things).

As well in sciences as in arts we seek primarily new knowledge that has not been published earlier. Moreover, we consider that the better the presented knowledge is generalizable, the more valuable it is, because more people can then use it.

Some time ago most scientists and artists believed that there are two types of knowledge, one of them suitable to be presented as art and the other in the language of science. In works of art it has always been usual to present tacit knowledge that the artist has grasped from the surrounding world through empathy, or which he has inherited from earlier generations of artists. As a contrast, operating with tacit knowledge has been condemned in science. According to the so called positivistic school of thought it is the researcher's duty to explicate everything into plain language and disregard those things that he cannot explicate. "Whereof one cannot speak, thereof one must be silent" (Wittgenstein, B).

Today most scientists think that the positivistic ideal is feasible in some fields of study, but in other fields it is permissible to relax the requirements on explicity and precision of data if the alternative is to have no data at all. The attitudes towards tacit knowledge are thus today no more in sharp contrast in arts respective sciences. Lately, the Finnish universities of art have begun to accept even doctoral theses which consist of a "scientific" part and a parallel work of art which elucidates, exemplifies or complements the scientific findings. In this way, those research findings that can be explicated are placed into the "scientific" part and the remaining tacit knowledge in the artistic part.

Beside the above listed habitual scientific modelling languages, notably written language, icon models, and analogies, there are there are a few artistic styles of presentation that could also be useful for scientific description, if the scientist is capable of using them. These artistic modes of presentation include:

1. Music has much been used for describing natural phenomena, such as the succession of summer and winter, of day and night, and the atmospheres of each of these: sunrise, sunset, moonlight, nocturnal peace. Moreover rain, storm, tempest, flow of a river, waves of the ocean. States of mind, such as serenity, enthusiasm, distress, love or anger.

Beside describing empirical phenomena, music could sometimes be used for expressing the conceptual relations that have been revealed in the analysis phase of a research project, especially the concepts of harmony or discrepancy, repetition, rhythm, growth and decay, similarity and contrast, order and disorder of a series of things, the state that something follows the general order or deviates from it.

2. Drama, dance and performance of action are effective for presenting actions of people and emotional relations between two or more people. Acceptance and disapproval can also here be exactly indicated when necessary, which means that these genres of art can be used for giving normative messages, i.e. showing that the present state of things can or should be changed.

3. Plastic visual art or sculpture is often used for describing situations in human life, and is also capable of expressing evaluations.

Typical of art is that the message is seldom given explicitly - it cannot be so given when the vocabulary of art does not include the necessary expressions. Normally a work of art can only give an inspiration to the public, who hopefully then creates the final message in their minds. The advantage is that a larger public can in this way find the work of art relevant to them, but the disadvantage is that many misinterpretations occur.

A usual method for clarifying or intensifying the message of art is to use several modes of presentation simultaneously. Combinations of music and play or dance are today established genres of professional art, but numerous other combinations are imaginable, not forgetting combinations with scientific model types, all of which are today easily feasible with the modern technology of multimedia.

The scope of validity. Artists as well as scientists usually want to reach a large public, and therefore they try to formulate their message (which can be descriptive or normative) so that it is valid and applicable in many different contexts, perhaps everywhere when possible. In order to improve universality and generalizability, both artists and scientists try to simplify their presentation and subdue its particularity and detail. Despite the common goal of science and art their modes of presenting the intelligence are different.

A work of art presents information as a model of a singular case, but the mode of presentation is chosen so that it will be easy for the public to apply the knowledge to new contexts, for example to situations in their personal lives. One usual technique for this is that the artist first "studies" the motif on a more general level and then, when returning to the naturalistic level avoids unnecessary details in the presentation or makes deliberately the work ambiguous. It remains the task of the public, first to interpret the work of art into a more general level and thereafter to apply the content to their personal use (see figure on the left). These techniques differ from those used in the sciences, but the purpose is the same: make the model generalizable.

Scientific researchers, too, sometimes make case studies or study a class of cases in order to find the typical case in the class. The findings of these studies are often generalizable to some extent, but a more usual method for presenting general knowledge is to make a conceptual model, see diagram on the right. A usual technique to attain a generalizable scientific model is to detect invariances in data by removing random variation, 'noise' and 'disturbances'.

The Simpson family In the same purpose an artist often prefers to depict what is typical, instead of what is particular. In order to clarify what is typical, the artist often exaggerates it, thus creating an caricature, often seen in comic strips such as Matt Groening's Simpson family, here on the left.

Showing only the invariance in the model, however, has the disadvantage that the receiver of the message, the public, cannot easily know how universal the message is intended to be - if the work of art seems to depict 'tempest', does it mean 'tempest in Italy', 'tempest of emotion' or 'the climate change will kill us'?

In sciences the delimitation of validity is easily done by demarcating the population which has been studied or which shall be the object of development. In arts such a demarcation is seldom used, though a common means of hinting to the expected scope of validity is to give a name to a work of art.

Many artists seem to think that their works have best chances to make an influence when their scope of validity has not been defined, thus leaving it to the public to decide whether they can apply the message to their lives, or not. This method is, of course, acceptable in free arts, but not in the illustrations that accompany scientific reports or development proposals because it leaves to the public no means to know or evaluate the truthfulness of description, or the possible scope of application. This however would be essential when somebody plans to apply research findings to practice.

Explanation of symbols. In scientific reports, the meanings of symbols and concepts have traditionally been explained in the list of used definitions. In arts, explanations are unusual, because many members of the public have their favorite artists, the earlier works of which they have already seen and they thus have learned to know what the artist usually means with his symbols. Besides, part of the aesthetic pleasure of the public comes from the very act of deciphering the hidden messages of the works.

The question remains whether those members of the public who fail to get the message of a work of art should be assisted with explanations? For such works of art that are intended to assist in communicating important results of research, for example proposals for new products, the answer must be affirmative. Explanations need not be so purely linguistic as scientific definitions are - proven methods in arts are, for example, simultaneous combinations of various media such as pictures, music and action.

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August 3, 2007.
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Original location: http://www2.uiah.fi/projects/metodi