## Some Basic Concepts:

i. What is Computational (Conceptual) Space:
It is the intention of this project to explore and define the concept of "Computational Space" so the concept cannot be defined at the start of the project.

However, presumably, we are concerned with the intersection of two other concepts: Computation and Space. Although these two may initially appear unrelated, in fact they may prove to be intimately connected, because closer inspection may show that both are, in fact, concerned with "finding" something.

In general, we are used to the principle of locating objects in physical space. We store various objects in a variety of containers which in turn are subsequently stored in various locations (perhaps inside other containers) in physical space. The storage system then becomes the "address system" which helps us to retrieve a chosen object from its storage space (i.e. "It's on the top shelf" or "In the bottom drawer of the small cabinet next to the window". Larger objects, such as houses, schools, shops and offices are also located in physical spaces -known as towns or cities -and can be located with the help of "maps" if we do not know the area well.

However, although such maps (of a city, a country -or whatever) should be closely related to that which they describe -they are clearly not the same: Distances will be scaled to fit the map, supposedly unimportant details will be omitted and some relationships may be changed completely if they make the map easier to read. In other words, the "map" although it nominally represents something in physical space -is in many ways an independent mental construction (or conceptual space) that can assist us in our search -if we understand how to interpret the map.

Although most people now associate computers and computing with machines -originally "computers" were people (mostly women) who made the repetitive calculations (computations) required for the mathematical tables used in navigation and astronomy. Indeed, the original conceptual model of a modern day computer was based on an imitation of human computation. However, thanks to modern developments in "computing" the concept now covers more than simple mathematical calculation.

Returning to the concept of a map -perhaps it is not unreasonable to claim that the interpretation of the map (i.e . locating a feature in physical space by relating the underlying conceptual space graphically presented in the map to the actual physical space that the map represents)  is actually a computational process. If we can accept this -then the the relationship between physical actions in physical space and conceptual actions in conceptual space may become clear. A Solution to a problem involves constructing a conceptual space that will enable us to change the system which is creating a problem for us. Apparently, we need to change this system from the undesirable state we are in (the problem) into a desrirable state (the solution). Computation then involves the calculation of what needs to be selected and what needs rejecting or ignoring in order to move to a satisfactory position under various circumstances.

In order to solve problems effectively and accurately, presumably, we must correctly understand the problem space, the nature of our conceptual map of that space -and our own aims and intentions.

How can we find something if we do not know what we are looking for?

ii. Space and Time
The concept of space leads naturally into time: Not only in terms of movement and change within the confines of the relevant space, but also with reference to the possibility of (evolutionary) changes in the nature of the space itself.

If, for the moment, we imagine physical space in terms of a city -then it is clear that as buildings and facilities are added so the nature of the city itself begins to change. Sometimes these changes can be gradual. However, sometimes infrastructural changes may involve a radical restructuring -which requires demolition and rebuilding of the existing space in a new form. This mutation of space over a period of time may be termed "timespace".

iii. Subjective Computing and Slow Computing
In a fast moving, politicised and highly commercialised world "computing" is generally seen as a purely pragmatic part of the process of making money -which is often socially promoted as being the sole aim of humanity. In this vision, "time is money" and so everything must happen as quickly as possible -with no time for any reflection that might undermine the principle aim of monitory profit.

Unfortunately, this widely accepted perspective is not very pragmatic. Successful problem solving often involves a change in viewpoint -and, throughout history, many useful discoveries have been made which were not recognised as being useful until some time after their actual discovery. Sometimes, what looks like a promising idea may fail in practice, while a modified version of a rejected concept may suddenly prove extremely useful. Evaluating the emotional and practical effects of change always takes time.

Slow Computing refers to computational processes that are not designed to compute quick and definitive answers to specific questions -but refers to processes which are infinite and perhaps have no meaning other than to reveal their own nature through the behaviour of the system over long periods of time. Weather (and climate) systems, geological and biological evolution -and even human history -can be seen in terms of "Slow Computing" processes.

The concept of Subjective Computing opposes the belief that computing is an objective process -with only one set of values and assumptions that are universally valid at all times.
Subjective Computing permits the inclusion of personal emotional and aesthetic values within the computatioan process. It allows the programmer to develop and explore their own personal vision of how the world might function.

iv. Bootstrapping
Bootstrapping is a fundamental technique used in the construction of complex computational systems. Instead of specifying the entire structure before it is implemented, one develops a simple basic structure and then uses this as a foundation which can then be used as a tool for constructing the next (more complex) level. On a technical level, the principle may sound quite difficult, but on a human level bootstrapping is a basic principle of good pedagogical practice: Once a student has learned to read, they can gain even more knowlege by reading books on any subject they choose.

Trevor Batten
Baclayon January 2011
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