Frontiers are peripheral, they challenge external space – Frontiers are borderline extensions in space and time, they imply a hitherto movement, displacement or journey. Frontiers are considered good, fashionable, a necessary and desirable evolution of human cultural development.

Human civilisation has extended the boundaries of human experience of the known world, in diverse ways:

Freud probed the frontiers of the mind, plumbing the unconscious and discovering Id and other mental inhabitants. Neil Armstrong became the first man on the moon. The frontiers of the earth were flat and circular, but are now spherical and 3-d. (in the evolution of art, representation moved also from the flat drawing and painting, through to photography, stereoscopy and holography).

In ancient Greece, Ptolemy conceived the earth as surrounded by concentric spheres upon which the planets and fixed stars were attached. Aristotle and Ptolemy believed that the earth was the centre of the universe, but Coepernicus believed that the sun was the centre – the heliocentric theory. Galileo also championed the idea. Newton extended the frontiers of knowledge in many ways, most importantly, the universal law of gravitation; the laws of motion; the mathematical invention of calculus - extending the knowable from discrete fixed points to the infinite continuum of flux. Einstein went further than Newton both with regard to local and general universal events. The conception of mass, energy, light and gravity were transformed.

Even our own senses have been extended:

In the 17th century, Leeuwenhoek pushed the frontiers of the observable, opening up a whole new world waiting to be discovered, with his invention of the compound microscope. At once, the morphology of nature at the microscopic level, became known in all its forms of physical, fauna and flora and inorganic. Similarly, Galileo could see the moons of Jupiter through his invention of the telescope.

The great explorers of the world extended the knowledge of the world, charting and navigating new territories – many played a role in this. Telescopes revealed the forms of the moon and planets. Man landed on the moon, sent probes into space and even landed a robot on mars. The Hubble Space Telescope now penetrates deep intergalactic space. In the words of Star Trek, Space is the final frontier. But not for long…..

The frontiers of knowledge are continually being extended. Frontiers are a dynamic process, a provisional state, only to be later overtaken by another state. The avant guard in art is a phenomenon in which the frontier is its lifeblood. To be modern, is to be of the moment with an eye to the future, pushing the barriers of convention and breaking the rules and creating the new. Eventually these new ideas become customary and a tradition is formed. If we think of great classical art, they were all modern in their day – a limited number that have been successively selected over history, due to their capability of transcending history. Precisely what the source of this capability is, is unknown. We do seem to regard these as important signposts that mark the various frontiers of history.

These frontiersmen, have deepened the space of what we regard as art, and we see it evolving, changing and expanding into new territories. Taking a Darwinian view, art adapts to the circumstances of its history.

The limits of the physical world has been challenged and expanded through the curiosity of man, his creativity and intelligence, and the evolution of science. The parameters of primitive man’s existence were severely limited by today’s standard – the transformation is mind boggling. There is an argument that the boundaries are being merely displaced and the primitive may be more aware of the natural environment.

The geographical boundaries of our existence as widened considerably, due to the invention of transportation. Thus we have progressed from foot to horse, train to car, plane and rocket. Many years ago, people seldom moved much further than their own village or town. The invention and development of railways and roads, allowed people to commute between cities, and boats, ships and planes have extended our worlds to other continents across to other nations. The world has shrunk.

Where is the limit of the person? Two clones are not the same; they are two separate points of reference. They both exist at distinctly different locations in space and time. Is the limit of the person their skin? Or is it their sphere of influence? Is it in the probabilistic subatomic clouds? A statistic, an object’s extent defined by 2 standard deviations each side of the mean of a normal distribution.

In philosophy, Aristotle bequeathed to us the law of the excluded middle, which states that ‘...every statement is either true or false: there is nothing in between’. This proposition seems to tally with our common sense intuitions about our experience of the world. Although the law is one applying to language, the principle seems instantiated in our consciousness of the world; it forms an important analogy of our experience. This principle has formed the basis of logic for centuries, and has been subject to various criticisms by the proponents of modal and fuzzy logic. And it is this ambiguity about the status of such a law that seems to highlight the ambivalence of our understanding of the world in terms of the finite and infinite nature of things, and their boundaries.

If we consider objects extended in space and time, the edge of an object exists at a point contiguous to the limit of another adjacent object (taking space itself as constituting another object). These limits do not overlay each other; they exist adjacent or contiguous to each other. But on the other hand, these limits may intermingle; if the edge of an object is fuzzy and made of discrete quanta with space in-between; then it is possible for a limit of another object to extend into that object. The limit of fuzzy objects is the outermost point – these must be defined to exist at points a distance from an object’s centre of centre of gravity. It must be noted that this is a static conception of matter. Reality is on the move; the conception of extended objects in space and time is a dynamical process. But notwithstanding this, it ought to be possible to specify the location of a boundary relative to a minimum of 2 contiguous distinct objects.

We appear to be finite beings, we are limited in extension in space and time, our bodies having limited mass, and a finite mind that experiences sensations and perceptions. And we find ourselves confronting infinity, even if infinity only really exists for us as an idea, a conception in our heads. Our historical experiences have implicated to us, ourselves as finite beings, existing in an infinite universe.

Our senses furnish us with discrete phenomenon, cups, tables, chairs, colours, heat, weight, mass and pain – all these are as real to us as our noses. Our bodies we perceive as our own, a discrete entity of a definite and unique character. Our bodies, senses and our brains all are such that they limit our world. But we must not forget that they also create our world, or make experience of it possible. In this process, our world is limited, constrained by sensory limitations, a priori knowledge, ignorance, and by the nature of the world we are experiencing.

Limits are characteristics or features of our normal everyday consciousness. Limits may sometimes be illusory or misleading, or they may serve us well – if I’m drinking a cup of tea, it seems improbable or foolish to say that neither the cup nor the tea, nor my mouth, throat and stomach, have definite boundaries or only probable boundaries – this is counter-intuitive. And there is no doubt that the tea I drank tasted good, satisfied my thirst and stimulated me!

There are hard and soft boundaries. Boundaries can be physically hard and impenetrable like granite or the earth’s crust, or they can be soft, flaccid or ductile like a fried egg, jelly or the mobile metamorphosing cell-membrane of an amoeba. In the human body, foreign bodies such as bacteria can become bounded by white blood corpuscles. Our bodies and minds limit the world to make it an object of experience. Without limits there could be no experience.

The definition of the object has proved elusive. There are logical/sensory constructions that we apply to experience but they do not always fit, and increasingly the evolution of logic has been necessary to accommodate the complexity of the world, the more we discover. Our capacity to experience the limits that demarcate and form the objects of the world, is evolving and expanding according to our cumulative experience and knowledge over history. We are the boundaries and boundary-makers!

The last frontiers are said to be: Space/time – unified theory of nature, a theory of everything; the discovery of life outside earth; mind/body problem and theory of consciousness; nature of morality. These subjects have taxed mankind for centuries but still remain insoluble mysteries. This leaves us with the ineffable philosophical problem of how we define an object. As soon as we do, our definitions become challenged over time, and the definition changes – and our formal definitions become obsolete. Is this true of all things? That depends on how we look at it .We must not confuse the ideas of knowledge, facts and their referents. Knowledge is not just language, but perceptual. Facts too, can be perceptual.

Wittgenstein regarded language as forming the limit of the world. I think this is an extreme view and erroneous. How things appear, their components, how they are arranged, and dynamical interactions, all display an order; this natural order of things we can call the logic of appearances. It is from the world of appearances, that language and logic are derived – not speech or writing!

Whitehead willingly admitted that language was not up to the job of describing and articulating metaphysical ideas or knowledge, In fact, it would be true to say that language is incapable of communicating conscious experience – only conscious experience can do that. However, language does function by inference and logic – which does connect experience with ourselves - that is, it conveys part of the structure of experience – the logic of appearances, through perceptions appropriated as concepts logically arranged in our minds.

How does this come about? There are those who say that these structure or forms in which we perceive the world are innate (a priori). There are others who regard environmental conditions or learning by inductive processes, e.g. trial and error and the accumulation of correlations established through repeated experience (a posteriori). These are psychological questions and even psycho-neurological questions. The whole debate it seems, is not profitably going to be answered by armchair theorizing – some field work must be done and real observations made. But we do seem to be on the horns of true philosophical dilemma – what the nature of the real world is, and our place in it. Locke enunciated it well, it is a form of the mind/body problem; the notion of primary and secondary qualities – the world must exist independently of its being sensed by an individual. This proposition is based on mutual inference, a combination of inductive and rational processes. Hume saw the dilemma here, enunciating his induction thesis of ‘no necessary connection’ where he could see no basis for our inference of cause and effect - this leaves us in a puddle that exists somewhere, and at some indefinite moment, but only probably so! In the form of the law of the excluded middle: either the world exists in Newtonian mold, as discrete fixed objects in absolute space and time; or the world is to be considered as Whiteheadean Process: a seamless continuum of indefinite moments, constantly metamorphosing in relative time and space. The truth probably lies in what is excluded………., and this we might call the Law of the Excluded Muddle!

Roy Amiss, 2001