Classifications

In this section, we examine the basic types of perspective.

Introduction

Perspective is a complex topic with multiple classifications that can be identified, whereby many of the same categories appear to be wholly unrelated, one to another. Yet often, such differences are only apparent. With deeper analysis, we find that one type of perspective does have fundamental relations with one or more of the other types.

For example, the visual and graphical perspective types are fundamentally related to, determined, and explained by, aspects of mathematical perspective. We aim to bring a rigorous understanding to the central topic of perspective. Accordingly, we shall develop a new categorical theory of perspective that elucidates links between the different types of perspective, outlines the big picture, and encompasses all aspects of perspective in a single model. 

Before we get underway, it is helpful to explore how the topic of perspective has been categorised in past times.

Classification of Perspective

It is salient to consider what Professor Kim Veltman has to say on the topic of Perspective Classification.

From the outset, the classification of perspective posed problems. Etymologically it was linked with optics, which could not be classed simply. Historically it was linked with architecture, which equally eluded simple classification. By the nineteenth century the nature of the problem began to come into focus. Systems of classification had forged clear distinctions between (subjective) art and (objective) science, as well as between (theoretical) science and (practical) technology. Perspective had the embarrassing characteristic of belonging clearly to all of these. It belonged to art, because it created spatial effects in paintings and it was accordingly classed under drawing. At the same time its theoretical principles were so clearly connected with the mathematical projections underlying scientific demonstrations, that it came to be listed under descriptive geometry. Finally, it also involved instruments, such that it was also classed under technology. These three headings, plus the historical one connecting it with architecture, have been maintained in the Library of Congress classification to this day.

On the surface, this was merely a matter of semantics, a search for convenient cubbyholes in the case of a borderline subject. There were, however, dramatic consequences. It meant, for example, that numerous innovations pertaining to perspective accrued to the larger categories to the extent that, when the artistic aspects of perspective came under fire, it could reasonably appear to some that perspective had died although the number of treatises on perspective in these other fields continued to grow. The continued association with optics perpetuated a confusion between subjective optical questions of how an object is seen, and objective geometrical questions of an object’s projections. The connection with drawing meant that perspective became entangled in conflicting philosophies of artistic education and was affected by changing fashions therein.

Ironically, the connection with mathematics, which seemed the most obvious of all, proved to be the most perplexing. By the mid-sixteenth century mathematicians such as Commandino had established the mathematical foundations of perspective. These were further clarified by Guidobaldo del Monte and Stevin, and consolidated by Desargues. In the nineteenth century, with the development of descriptive geometry, it seemed obvious to class perspective as a branch thereof. In the twentieth century, with the development of algebraic geometry, this more general concept embraced both descriptive geometry and perspective. The problem was that algebraic geometry was non-visual, which posed a curious paradox: perspective, the chief means for visualizing space and objects, was classed as a subset of a non-visual method. Meanwhile, where perspective stands in relation to other branches of projection such as isometry, affinity and topology has become an open question. In order to gain further insight into these problems of classification it will be useful to consider each of them in turn.

Kim Veltman, Sources of Perspective (Chapter 4).

Kim draws attention to the paradoxes that accrue when we attempt to classify the patently fundamental yet multi-faceted topic of perspective. Once again, it is salient to consider what Kim has to say on these matters in conclusion to Chapter 4 of the Sources of Perspective.

Perspective is often described as something particularly linked with the Renaissance which continued until the nineteenth century and then died out. In the opening chapters we showed that this was not the case, that perspective has in fact continued unabated to the present. In this chapter we explored an underlying cause for its apparent demise. Perspective never became an independent concept and was therefore subject to the vagaries of classification of four branches of learning: optics, architecture, drawing and geometry. This had two important consequences. First, changes in classification, particularly in geometry, have shifted the definition of what actually constitutes perspective. In the nineteenth century, perspective included not only one-, two-, and three-point perspective but also various branches of parallel perspective. In the twentieth century, the scope of the term has frequently been restricted to one, two and three point perspective, whereas all parallel versions are classed as projections.  Indeed, some would see perspective merely as an example of dilatation, as one of a number of mathematical transformations with no special role in spatial organization. A second consequence has been no less dramatic. A good deal of literature pertaining to perspective has simply been classed as part of the larger fields. Hence, although work on perspective has continued, it has been classed as work in optics, architecture, drawing or geometry.

Our bibliography has ignored the artificial barriers imposed by these fields, collecting hitherto disparate materials relating to perspective. Part one has created a framework for a larger picture of the phenomenon of perspective (the Sources of Perspective). Part two will explore the consequences of this phenomenon (the Literature of Perspective).

Kim Veltman, Sources of Perspective (Chapter 4).

The upshot is that perspective is central to topics in art (drawing, painting, etc), optics, mathematics (geometry), and instrumentation. But stating such tells us little about the nature of perspective. But what is perspective? How does it arise (in each case), and what are its fundamental features?

Perspective is a foundational topic, having much in common with ‘analytical’ and ‘theoretical’ subjects like algebra, geometry, and number theory, but it also has close links to physical disciplines like art, representation, and scientific imaging/measuring instruments, etc. Perspective is a set of analytical and experimental methods that enable humans to better perceive, measure, model, and create views of reality according to our particular needs and desires.

Truly perspective enables the ‘conquest of the real’. Ergo, herein we shall assign perspective as a way to perceive, analyse, and dominate reality—in both theoretical and practical terms.

One way to explore these questions is to develop and test a new perspective theory. We can begin by considering perspective in terms of the analytical techniques it deals with (plus related action potentials or practical methods).

World Theory

In 1967, Karl Popper developed his Three Worlds theory to analyse reality. 

World 1 is the realm of states and processes typically studied by the natural sciences (physics, chemistry, and biology). World 2 is the realm of mental states and processes. These are sensations and thoughts, and include both conscious and unconscious mental states and processes. World 3 is the realm of the ‘products of thought’ when considered as objects in their own right. In Popper’s terms, World 3 ‘objects’ encompass a very wide range of entities, from scientific theories to works of art, from laws to institutions.

Accordingly, we have three classes of perspective. Whereby, firstly we have Technical Perspective (visual aspects of the physical world), and secondly Mental Perspective (cognitive aspects of nature/culture), plus finally Knowledge Perspective (conceptual aspects surrounding works of art, science, and culture). 

We can summarise the basic classes of perspective as follows:

• Technical Perspective – Analysis of medium of physical space (things, states and processes in the physical universe). Deals with visual/spatial topics.
• Mental Perspective – Analysis of medium(s) of cognitive space(s) (mental things, states and processes). Deals with visual/spatial or logical/ontological or literal topics.
• Knowledge Perspective – Analysis of medium(s) of knowledge space(s) (things, states and processes in the human-built or human-prescribed world). Deals with visual/spatial or logical/ontological or literal topics.

The upshot of this approach is that we have three kinds of media or space/time regions of being: physical, cognitive, and knowledge, leading to three basic classes of perspective: Technical, Mental and Knowledge Perspectives. 

As stated, on this site we are concerned with Technical Perspective.

Technical Perspective

Technical Perspective refers to any systematic process that produces a detailed visual image, measurement, model or view, of a dimensional object or scene. Noteworthy is that said process(es) may be of natural or human origin.

According to our new theory of Technical Perspective, it has six sub-categories:

• Natural Perspective (natural and built worlds) – including Visual Perspective or direct looking at reality (view of a dimensional form / scene);
• Mathematical Perspective – modelling reality / shaping appearance(s);
• Graphical Perspective – copying reality / creating appearance(s);
• Instrument Perspective – looking at, capturing and measuring reality; and projecting appearance(s);
• Forced Perspective (aka ‘false’ or ‘trick’ perspective) – visual illusion by the construction of a false reality, or by the representation of a false reality (distorted/transposed scene geometry);
• Media Perspective – connecting/linking, ordering, constructing (mimesis), matching, mixing, exploring, and cross-matching: multiple perspective view(s).

To some extent, the different categories of Technical Perspective tend to overlap in terms of geometrical origins, and similarity of visual effects. Nevertheless, it is helpful to identify the sources of Technical Perspective by utilising categories.

Perspective, in general, works to enable viewing, prescribing, matching, modelling, exploring, representing, and making images, of the physical world. These are the methods of perspective, which are supported by each perspective category, to a greater or lesser degree.

With perspective, we can approach objects from different viewpoints and scales, leading to distinct functions that can be isolated, catalogued and explored. Hence perspective allows accurate systemised worlds to be developed on media, and in the human mind.

Goals, Methods and Domains Perspective

As stated, the different kinds of perspective do tend to overlap and interrelate. This means that one kind of perspective, for example, instrument perspective, can involve other kinds. Looking through a telescope, for example involves visual space (visual perspective), optical space (instrument perspective) and geometrical space (mathematical perspective) simultaneously. 

 Why then do we split up perspective into these different kinds? Could we not just develop a single all-encompassing theory to explain all types and classes of perspective? The answer is that it is helpful to split up perspective into different kinds to better understanding the sources of perspective effects, and so better understand visual processes of one kind or another.

Three goals of perspective can be identified. They are first viewing reality: observing spatial form; second, matching reality: surveying or modelling spatial form; and finally making representations of reality: copying / constructing images of spatial forms. These are the goals of perspective (in human terms), and it is clear that visual knowledge (or images) are fundamental to each type.

Note a careful distinction that we are making between a perspective image, defined as a fixed visual representation, copy or picture of any dimensional thing, and a perspective view. A perspective view refers to the act of looking directly at the thing itself, being a ‘live aspect’, real-time sight or vision of a dimensional thing or apparent dimensional thing. Said view is in the form of an optical vista seen directly by the eye, captured in real-time by a camera or perspective instrument, or projected onto a screen or computer display.

We can further analyse Technical Perspective in terms of the type of (primary) space involved:

• Visual Perspective = Visual Space (physiological and psychological optics)
• Instrument Perspective = Optical Space (physical/wave optics of light)
• Graphical perspective = Graphical Space (theory of representation)
• Mathematical Perspective = Geometric Space (theory of projection)

It is important to recognise that on many occasions, one kind of perspective will involve multiple types of space; for example when looking at painting of a mountain-scape scene, the viewer of the painting creates a Visual Space from a painting consisting of elements of Graphical and Mathematical Space(s) (for example).

Note that we have not defined the primary kinds of space involved in Forced and Media Perspectives, and this is due to the fact that both types of perspective do not have a preferable type of space within which they tend to operate; but rather multiple layered and juxtaposed spaces are commonly employed.

In Figure 1 below we see a concept digram for Technical Perspective.

In the sections below we

Visual Perspective

Blah

Mathematical Perspective

Blah

Graphical perspective

Blah

Instrument Perspective

Blah

Conclusion

Not looked at Forced or Media Perspective types.

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Dr Alan Radley FRSA | Scientific Director
e: alansradley@gmail.com

Perspective Research Centre
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