Such a problem, in standard form, presents an objective function Z=f(x), of n variables x, to be minimized and a system of linear equations and/or inequalities, on the same variables, which represent the constraints and which define an admissible area for the solution.

The architectural organism is modelled as an assembly of parallelepiped shaped space entities or units, provided with a certain number of "holes" that permit functional corresponding connection. The pursued intent being optimal assembly.

The model, in its mathematical form, fits a standard Non-Linear M.P. (N.L.P.) problem, since the objective function Z is non-linear and the constraints are represented by inequalities. In its graphic form it reproduces an image of all the space units constituting the organism; moreover it is able to represent these units, in their logical and physical individuality, and their mutual relationship, as well as the ones with the external environment.

From overall curriculum planning to specific exercises, language study provides a model for building a learner-centered education. Educating students about the learning process, such as the variety of metacognitive, cognitive and social/affective strategies can improve learning. At an introductory level, providing a conceptual framework and enhancing resource-finding, brainstorming and coping abilities can lead to threshold competence. Using kit-of-parts problems helps students to focus on technique and content in successive steps, with mimetic and generative work appealing to different learning styles.

Practicing learning strategies on realistic projects hones the ability to connect concepts to actual situations, drawing on resource-usage, task management, and problem management skills. Including collaborative aspects in these projects provides the motivation of a real audience and while linking academic study to practical concerns. Examples from architectural education illustrate how the approach can be implemented.

Within contemporary digital environments, there are increasing opportunities to explore and evaluate design proposals which integrate both architectural and landscape aspects. The production of integrated design solutions exploring buildings and their surrounding context is now possible through the design development of shared 3-D and 4-D virtual environments, in which buildings no longer float in space.

The scope of landscape design has expanded through the application of techniques such as GIS allowing interpretations that include social, economic and environmental dimensions. In architecture, for example, object-oriented CAD environments now make it feasible to integrate conventional modelling techniques with analytical evaluations such as energy calculations and lighting simulations. These were all ambitions of architects and landscape designers in the 70s when computer power restricted the successful implementation of these ideas. Instead, the commercial trend at that time moved towards isolated specialist design tools in particular areas. Prior to recent innovations in computing, the closely related disciplines of architecture and landscape have been separated through the unnecessary development, in our view, of their own symbolic representations, and the subsequent computer applications. This has led to an unnatural separation between what were once closely related disciplines.

Significant increases in the performance of computers are now making it possible to move on from symbolic representations towards more contextual and meaningful representations. For example, the application of realistic materials textures to CAD-generated building models can then be linked to energy calculations using the chosen materials. It is now possible for a tree to look like a tree, to have leaves and even to be botanicaly identifiable. The building and landscape can be rendered from a common database of digital samples taken from the real world. The complete model may be viewed in a more meaningful way either through stills or animation, or better still, through a total simulation of the lifecycle of the design proposal. The model may also be used to explore environmental/energy considerations and changes in the balance between the building and its context most immediately through the growth simulation of vegetation but also as part of a larger planning model.

The Internet has a key role to play in facilitating this emerging collaborative design process. Design professionals are now able via the net to work on a shared model and to explore and test designs through the development of VRML, JAVA, whiteboarding and video conferencing. The end product may potentially be something that can be more easily viewed by the client/user. The ideas presented in this paper form the basis for the development of a dual course in landscape and architecture. This will create new teaching opportunities for exploring the design of buildings and sites through the shared development of a common computer model.

Cyberspace is an electronic extension of this cognitive space. Designers of virtual environments already know the power these spaces have on the imagination. Computers are no longer just tools for projecting buildings. They change the very substance of design. Cyberspace is itself a subject for design. With computers architects can design space both for physical and non-physical media. A conscious integration of cognitive and physical space in architecture can affect construction and maintenance costs, and the impact on natural and urban environments.

This paper is about the convergence of physical and electronic space and its potential effects on architecture. The first part of the paper will define cognitive space and its relationship to cyberspace. The second part will relate cyberspace to the production of architecture. Finally, a recent project done at the University of Michigan Graduate School of Architecture will illustrate the integration of physical and cyberspaces.