Cambridge University Engineering Dept.,*
Trumpington St., Cambridge CB2 1PZ, UK
[*when the majority of this was written: 1992-5. Now at Laser-Scan Ltd., Cambridge CB4 4FY.]
Many types of creativity appear to involve negotiation, exploration and discovery within the wider context of a design problem [Smith, 1992], leading to a redefinition of the design task with revised aims. This type of creativity which involves an open-ended exploration of unbounded human context is not the subject of this paper. This paper concentrates on manipulations of a bounded set of existing knowledge.
Individual 'creative actions' appear to be separately amenable, in principle, to automation (this assertion is expanded later in the paper) and there is good evidence that this is so [Boden, 1992; Navinchandra, 1992]. This raises the possibility that creativity is an emergent property. If so then it will naturally arise when all its component parts are simulated. There are only two alternative possibilities: that the 'component parts' are innumerable or that there is some 'vital essence' in creativity which is not emergent. The former, from what we know about creative designing by people, seems unlikely and the latter is not rationally believable (see Appendix).
If creative design is not to be achieved artificially then the most likely cause will be that some component action, though well-defined, is resistant to effective implementation in software, i.e. although algorithms are feasible in principle, devising them requires talent and hard work. This is therefore likely to be a temporary limitation since the history of computer science has shown that well-defined actions are either eventually implemented successfully or discovered to be not well defined after all.
The bulk of this paper takes the 'traditional' AI approach of explicit symbol representation and manipulation and uses it to define 'design spaces' that describe artefact structure and behaviour. The paper is reductionist in that a small number of 'creative actions' are being looked for, and the simplest structures that can provide those actions are described. Representation of design process concepts such as 'required function', version control or alternative generation are not attempted here.
The 'design theory' behind this paper is the multiple-viewpoint hypothesis which proposes that creativity is essential to all design because all design involves the reconciliation of incommensurate viewpoints. Each design viewpoint is formalized as a 'design space' which can be thought of as a self-contained module of 'knowledge'. These can be manipulated much like the 'problem spaces' of SOAR [Laird, et al., 1987] and provide a framework for the search for analogies. Creativity is analysed as the generation and evaluation of new design spaces.
Towards the end of the paper is a comparison with some other computational creativity approaches, implementation concerns, and a discussion on the relevance and utility of neural networks as an influence on explicit symbol structures.
It is not enough that some new properties or representations emerge from computation [Gero, 1992a; Stiny, 1991] they must be recognized as evoking some new, useful meaning and thus suggesting something to try next. One of AM's heuristics (see below) was to recognize that emergent properties were interesting, but it had only rudimentary methods for comparing the emergent property with others and could not recognize how to use it [Lenat, 1982]. Emergence introduces ambiguity and history-dependence from successive transformations by creating new shapes (or old shapes in unexpected places) which are then available to be selected for further transformation. However the definition of what constitutes a 'shape' is predefined, perhaps implicitly by a grammar [Carlson, et al., 1990; Rinderle, 1991; Stiny, 1991], but still predefined. A new shape or concept is evoked if it is not predefined within the space [Woodbury, et al., 1989] that the transformations occur. A new concept is evoked if some emergent property within one space suggests some new valuable concept in another space, either by analogy or because the spaces share a common goal or structure. Emergence thus occurs within a design space, 'evocation' occurs across design spaces.
Thus the process of finding or recognizing useful analogies also appears to be intimately involved with computational creativity. In addition, some design theory indicates that generating combined new representations for aspects of previously distinct bodies of engineering knowledge is a useful approach for studying fundamentals of the design process [Konda, et al., 1992].
Figure 1 shows an accommodation which has matured into a design sub-discipline of its own. Viewpoints selected from a materials worldview and a hydrodynamics worldview are combined into a new worldview, a new practical science: bearing design [Ashby, 1980].
The rationalization of the view points is local; it takes place only with respect to the specific artefact being designed. The shared memory of these rationalizations among the design team is a 'theory of the artefact' [Subrahmanian, 1992] (see Figure 2) and is a vital background to developing creative new variant designs in a short time [Clark and Fujimoto, 1991; Pugh, 1990]. It is not so much a knowledge of a particular artefact as a knowledge of the space of possible artefacts (similar to Dasgupta's 'Theory of Plausible Designs' [Dasgupta, 1989] or MacLean's Design Space Analysis [MacLean, 1992]) coupled with design rationale for all the options in that space.
Design prototypes, conceptual schemas for organising design knowledge, populate a space at a high level of abstraction in theories of artefacts [Gero, 1990]. Prototypes instantiated with context knowledge form part of the detailed space but there is much artefact theory which does not derive from prototypes because the phenomena are inherently one-way functions in the direction from detail to general and not vice-versa.
In the space of mechanical linkage designs, the inherent and fundamental difficulty of parametizing very non-linear, non-differentiable curves means that there is no useful qualitative abstraction of the space [Shrobe, 1992]. Prototype-based design techniques (irrespective of implementation technique) are therefore inappropriate; or at least, the abstraction gap between behaviours representable in sensible prototypes and the behaviours displayed by fully instantiated designs is very large indeed. Another such area with predictability problems is that of multi-mechanism materials properties [Sargent, 1991]. Thus while prototypes are clearly used in design by designers, there are definitely types of design in which they are not used at all.
Since the interactions between separately derived worldviews are in principle unpredictable, past design cases representing design idioms are thus shown to be irreplaceably valuable in the generation of new designs from a fundamental philosophical standpoint. Indexing a theory of an artefact, including all the design idioms and past cases, is a serious problem but is well addressed by noticing that designers remember idioms by functional intention as well as by actual artefact structure [Chakrabati, 1993]. This is where design prototype data and analogical reasoning using deep causal knowledge is particularly valuable [Gero, 1990; Qian and Gero, 1992].
Learning can be viewed as a general 'ability enhancer' for computational systems, and is clearly indispensable for intelligent behaviour in the real world [Reich, et al., 1993]. However it is instructive to consider non-learning systems to see whether some core of a key capability (such as a specific type of creative action) can be isolated and emulated, and then later 'amplified' by adding a learning capability. If learning is removed from consideration, then the distinction between search and exploration appears to lie in whether single or multiple search spaces are used and whether new search spaces are generated as part of the process [Steier, 1992a].
Although some still feel that creativity is possible within a single space [Faltings, 1992], many feel that an essential aspect of creative design is the management of multiple representations [Chakrabati, 1992]. Innovation, the 'merely novel' has also been defined an unfamiliar result obtained by operating existing generative rules which must operate in an existing design space [Boden, 1992; MacMahon, 1994]. A simplified scale of design types might be:
| routine design | new values for existing variables |
| innovative design | new variables in existing design space |
| creative design | new design spaces |
There is a common viewpoint that represents design as inhabiting a single space within which 'branches', distinguished by different constraints, are investigated and compared. Strictly speaking, this is a valid, alternative view. However it is a profoundly less useful view either for understanding design creativity or for producing algorithms which aid design by going beyond traditional optimization methods.
Inductive learning isusually thought of as only being capable of setting values for existing variables, in the same way that linear regression does when it 'explains' a body of data by deriving from it a least-squares fitted relationship. However, a combination of a clustering algorithm, which produces a finite set of classes from some training set, together with a classifier, which assigns new objects to those defined classes, is effectively building an explicit and entirely new symbol space [Reich, et al., 1993]. Such a symbol space has the precise property required of spaces used creatively in the generation of analogies [Boden, 1992]: the addition of a single new class (which may result from a single newly learned training example) can completely but subtly change the relationships between all the objects represented in the space.
This rationalization knowledge is most useful if it is explicit rather than just remaining in the minds of members of the design organization; so it is more valuable if it is represented in as formal a reasoning system as possible [Lee, 1991; Ruecker and Seering, 1991; Ruecker and Seering, 1992; Webster, 1988]. Research in explicitly mapping this kind of artefact space at a high level of abstraction for specific designs is rare, but is being explored at Cambridge as symbolic configuration optimization in the space of Rolls Royce aeroengines [Murdoch and Wallace, 1992].
A design space is being used here as a general term encompassing classic AI search spaces, a problem-space of a Soar system [Laird, Newell and Rosenbloom, 1987; Steier, 1992a], or the object world of a frame-based 'expert' system. A design space is an ontologically consistent representation of factual and procedural design knowledge onto which goals and functional requirements can be applied and from which artefact structures, behaviours, performances and ideas for potential revised goals can be retrieved. This broad definition is given because the principles developed below for the generation and evaluation of such spaces can be applied broadly, though if a design space were a simple search space then simpler versions of those principles would apply.
This paper takes the 'traditional' AI approach of explicit symbol representation and manipulation, as contrasted with neural-net approaches, but this distinction is revisited at the end of the paper.
This paper is concerned with design spaces that describe artefact structure and behaviour. Representation of design process concepts such as 'required function', version control or alternative generation are not attempted here.
A simpler example of a denser design space, and one that is totally automated, would be the use of AutoCAD's Advanced Modeling Extension (AME) to run interference checks overnight on all component designs done during the working day. This is possible when all engineering drawings for a new design are done using the same CAD system (AutoDesk's AutoCAD, and many other CAD systems have the same capability). Implicit interference between components is made explicit for designers to fix the next day.
Thus the generation and recognition of useful new design spaces need not involve entirely disjoint areas of engineering; instead, a new space (for example the space of worm-gear devices) could be explicitly and completely representable in some 'lower' space of mechanisms or 3D shapes. Thus while worm-gears and cable-stayed bridges might both be representable as mechanical structures, they are in no sense the same or even slightly related as design spaces. Nevertheless, computational systems which can generate new higher-level spaces ñ which may be disjoint, even though they are based on the same lower level representation ñ would appear to be both deserving of the title 'creative' and relatively easy to implement. The remainder of this paper, however, considers both disjoint and layered design spaces more generally.
A computational model of this type of creativity in design is therefore best phrased in terms of multiple view points, each embodied as a set of design spaces, and the generation of new design spaces which will form the repository of the design rationale and the theory of plausible artefacts. When constructing software systems to support creative design, the types of manipulation of representations that will be required will eventually require the use of languages specifically designed for this type of task, e.g. prototype-based rather than class-based inheritance systems [Zucker and Demaid, 1992].
A design space could correspond to a single problem space or to an entire self-consistent Soar system comprising many problem spaces, but it is more productive to consider the simpler, single problem space case. Thus a design space would comprise a set of place-holders for designed features or objects (perhaps enumerable or perhaps constructable by a grammar), a goal state, several start states and a set of operators (see Figure 4). This is a slight variation of a Soar problem space since the underlying objects assume an important role whereas Soar spaces treat the reachable states as paramount.
A set of these simple design spaces can then represent some procedural facet of knowledge about an artefact; several start states are generally available since usually one piece of knowledge can be used in a number of different ways. For example, the strength of a carbon-fibre laminate can be calculated from its laminae sequence or the appropriate sequence can be determined for a specified strength. These are not merely inversions of a simple formula, the knowledge is procedural and common to both problems but the path taken through the design spaces is very different [Ige, 1990; Sargent, 1990; Tsai, 1988]. (Boden [Boden, 1992] goes so far as to suggest that the phenomenon of true understanding is rooted in multiple conceptual spaces arranged so that they can be flexibly and fruitfully arranged and transformed. This paper is consistent with that view.)
Current Soar systems contain problem spaces entirely programmed by hand in advance of execution, though there are some attempts to consider dynamic construction of new spaces by re-using and combining parts of hand-programmed spaces [Steier, 1992a; Steier, 1992b]. The focus on creativity here is on the generation of appropriate new design spaces and their incorporation into existing systems to solve impasses.
A new space which is analogous to a space already known to be subject to useful transformations (e.g. data-flow to entity-relationship, as mentioned earlier) is particularly interesting as there may be a further analogous transformation.
Recognition can be guided by a knowledge of the mechanism or heuristic used to create the new space, thus mechanism X may be known to be useful because it can generate new spaces with property Y, therefore it is easy to see that the first thing to check is whether the new space does indeed have property Y in any useful degree.
If a new space is generated to contain a subset of old objects with a new taxonomy (grammar) then the operators between pairs of objects can be compared one by one between the two spaces. If they correspond then it is a useful space; but what do we mean by 'correspond' ? We need a higher level view with some metrics and tests. One such metric is 'reachability'; if each object in a space is reached by applying an operator on another object (i.e. the space is a calculus and the objects are states) then an isomorphism of reachability of states can be use to compare the similarity of the operators in the two spaces.
An exact match between spaces is not needed and is indeed not particularly useful, the most interesting spaces are those where there is definite correspondence but much new behaviour. This is related to the matter of generality; in the long term it is useful to have design spaces which can be used for a variety of related problems. Exact matches of a design space to a particular problem are not usually useful except for that specific problem.
A useful new space is one with 'structural neatness', where it takes many of the members of a cluster of objects in an old space and represents them as a set of new objects with cleaner relationships (a smaller number of operators relating them, or a smaller number of operator applications). Also interesting is where a new space shows that a few objects in the cluster are now unusual whereas previously they would have been typical cluster members (another heuristic similar to one of AM's). This can occur when a new taxonomy is imposed on existing objects and indeed it is observed in design teams that agreeing the naming and partitioning of artefact components is constructive and creative [Bucciarelli, 1988]. Another particularly useful feature for a new space is if the new object representation captures constraints directly rather than leaving them to be handled by algorithms enforced on the operators [Johnson-Laird, 1989; Van Baalen, 1989].
Apart from structural neatness, a good new design space should make explicit useful goals (or subgoals) which perhaps only appear scattered among a number of other earlier spaces. This is the area of explicit reasoning about transforming required function into available behaviour via artefact structure [Chakrabati, 1993], which is a larger problem than the one considered in this paper.
The idea of 'counter-intuitive benefit' referred to earlier is an example of a characteristic which is desirable in a new design space: it is both surprising (interesting) and useful. Any design space which has this characteristic is a useful design idiom which should be retained even if, on evaluation, it is inappropriate for the current problem. It would still be useful raw material for new design spaces in other design problems.
This problem, and any others also based on knights moving on 3x3 boards, is rendered trivial once it is realized that the central square (e) is irrelevant and can be omitted and that the others topologically form a simple circle in terms of knights moves (Figure 7). So that if a vacancy is at i, it is simply shuffled to d, c, h and then a (or alternatively: b, g, f, a).
Another, non-visual, example is any instance of Post's correspondence problem, known as 'the word problem' [Harel, 1987]. In this puzzle a set of transformation rules is given between letter sequences and the problem is to determine whether a given word can be transformed into another by successive substitutions, i.e. the rule 'EAT'='AT' means that any appearance of the string 'AT' within a word can be replaced by 'EAT' and vice-versa. Thus if we have the rules 'EAT=AT', 'ATE=A', 'LATER=LOW', 'CARP'='ME' and 'PAN=PILLOW', then it is true that 'LAP' can go to 'LEAP', and 'MAN' to 'CATERPILLAR'; but can 'CARPET' go to 'MEAT' ?
Rather than exploring the matter within the design space defined by the rules, it is better to look for a new space. In this case there is a one-dimensional space based on the numbers of letters in words and on invariants: the total number of 'A', 'M' and 'W' letters in any word is unchanged by the given rules, so 'CARPET' (invariant value = 1) cannot be transformed into 'MEAT' (invariant value = 2) [Penrose, 1989]. This type of word problem is particularly significant since it has no general algorithmic solution; new problems require arbitrarily many new insights expressed as new design spaces, it is 'partially decidable' [Harel, 1987].
These two examples are problem-solving rather than design problems, but the intention of the earlier description of world-view accomodation was to illustrate that creative design requires the solution of just this type of problem as part (perhaps a small part) of the creative process.
Systematic methods for accessing appropriate analogues of useful design spaces are, however, well known in the teaching profession and are well documented for mathematical problem solving [Pólya, 1957]. In design research this corresponds to design by case-based reasoning and using goals, structures or behavior to index a design case-base (e.g. [Bardasz and Zeid, 1992]).
If we have software systems with relatively few design spaces to begin from (the usual case) then correspondingly greater leaps of analogy are required for both new spaces and for translating concepts, and thus more work is required in testing and assessing potential new spaces.
People do not have any assured systematic ways of constructing new design spaces because a profound new space is always incommensurable in some sense; it enables entirely new concepts to be represented which can only be understood by exploring the behaviour of the new space. These new concepts might be 'alluded to' in earlier spaces, people have intuitive feelings that a set of ideas have some relationship, then a new way of looking at the problem (a new space) yields an 'Aha!' where the previously vague feeling becomes explicit either as a new object (as in the small square in the right hand space in Figure 5) or as a new operator which embodies this concept.
Johnson-Laird argues that the only reasonable class of algorithms for creating analogies are those where some constraints are built in to the generation process and some more constraints are used as a filter on the results [Johnson-Laird, 1989]. However he views this pyschological theory of 'profound analogy' generation as computationally intractable because the number of possible types of links the between the generated space and previous experience increases exponentially with the number of links in the chain. Penrose has recently reviewed inspirational insight and also identified a largely unconscious 'putting-up' (generation) process and a largely conscious 'shooting-down' process: he then further proposed that the unconscious process must have 'a powerfully impressive selection process' probably based on aesthetic criteria which in turn had been decided upon consciously [Penrose, 1989].
For a computational model we can approximate Penrose's unconscious aesthetic selection criteria with a small number of scalar parameters which are different approximate metrics of 'appropriateness'. It is important that only a small number of such parameters exist in order that the necessary vagueness and generality is captured. This also rescues the intractability of Johnson-Laird's argument which rests on the principle that no aggregate metrics are used. Clearly if one can aggregate 'faster' than the space expands in size then computational tractability is regained at the expense of accuracy.
The idea that scalar aggregate metrics play a part in general cognition, and particularly in behaviour generation and real-time problem solving, has been strongly proposed by Albus based on experience with complex computer-integrated manufacture systems [Albus, 1991]. These metrics can be termed 'emotions' and identified with comfort, frustration, confidence, happiness etc. where some are properties of the design space under test and some (frustration for example) are properties of the history of the search for these spaces and are used to prune an unproductive avenue. It has been strongly proposed that emotions such as anxiety and confidence will be found in any intelligent creature with different and potentially conflicting goals because they play an essential role in integrating diverse structures [Boden, 1992].
One characteristic that distinguishes a design engineer from a technician is the appreciation of the useful tension between what is known generally (vaguely) about the problem domain and what is available as precisely understood tools which can be used directly to achieve something useful. The designer uses the vague (intuitive) knowledge to identify areas where new designs or precise tools should be developed. There will always be such a gap for non-algorithmic problems such as design.
A more immediate design space generation occurs on a shorter time scale when sketching. The shapes on the page are interpreted simultaneously in a number of different plausible ways by the human visual recognition system. Thus by using part of the mind (including the retina) which, for its own reasons, needs to produce new representations rapidly and repeatedly, we can force the generation of new design spaces at a high rate [Schön and Wiggins, 1992; Simon, 1992]. Visual recognition is strongly conditioned by expectation, but the good designer or artist is able to suppress expectation in favour of looking for emergent shapes which evoke useful designs.
The view taken here is that new design space generation for enlarging the theory of the artefact is led by the need to find a new space for analogues of existing objects. (There are other ways of generating new spaces, such as to find spaces of the same objects where analogous operations, or extended or restricted sets of operations, exist.) This means that the path of new space generation is contingent on the set of objects at the focus of attention, a different set of objects will lead to different spaces as will different previous experiences of the designer (or designing software). The sequence of the design exploration (the generation of new spaces) is thus determined both by the precise characteristics of the design problem as it unfolds and the library of previous spaces available. Thus when computationally-based creative designing systems become available, each individual will quickly become different in capability and point of view even if they were programmed identically. Therefore a design studio would profitably 'employ' not just one computational designer, but several hundred because of the value of their different points of view and insights. Even though initial design systems will be narrow minded and extremely rudimentary in capability, the prospect of increasing the total number of designers available to industry by two or three orders of magnitude is intriguing.
This type of approach to the automation of numerical experiments has demonstrated that visual recognition algorithms are almost irreplaceably useful in inducing qualitative insights [Abelson, et al., 1989], even when the 'diagram' is only envisioned internally by software. This supports the importance of sketching for creative design as described earlier and demonstrates that 'envisioning' the solution to a design problem may be quite general to all types of intelligence.
In the linkage case it is possible to define interesting features of the artefact to be looked for at the outset (many are common to most linkages) but in general any kind of pattern identification system could be pressed into service to find useful features in a mass of numerical and symbolic information. Natural language analysis as used in bibliographic searching or full-text databases is also appropriate for identifying 'important' terms in design documents (not known in advance [Reich, et al., 1993]), which would then be candidates for inclusion in new design spaces [Monarch and Nirenburg, 1987; Subrahmanian, 1992].
Zhao approaches the creativity problem by defining a global data model of 5 categories and 11 link-types in which all artefact and design process knowledge is represented [Zhao and Maher, 1992]. Schemas representing new artefacts are generated by combining parts of existing artefacts and assessed by reasoning over their behaviours and comparing with required functions. Graph matching and slot-value matching are used to compare schemas. However, what is proposed here as being necessary for world-view accommodation is generation of design spaces from entirely different data models. (Of course, at some very abstract level there must be some data model in common otherwise it will not work.) This will be much harder because much of the effectiveness of Zhao's system comes from the correct assignment of categories which facilitates the reasoning and enables purely syntactic operations to perform useful functions.
Van Baalen's work shows two things: that constructing design spaces ab initio automatically is entirely feasible for some tasks, and also that using a representation specifically for a particular problem class is far more efficient (6 times in his case) than using general purpose algorithms on highly generalized design spaces [Van Baalen, 1989].
Combining the insights from Zhao and Van Baalen we can see that a complex global data model is not the way to proceed. Instead one should explore the automatic generation of data models in which appropriate design spaces can be constructed. These spaces should embody constraints directly in their structural representations so that purely syntactic operations are fast and have useful meaning.
It must be borne in mind that any explicit symbols and design spaces in human minds (or probably in any evolved individuals' minds) are themselves the result of more fundamental processes: they are emergent characteristics of underlying neural networks making up the brain hardware. (Note that this is emergent behaviour at a level below that referred to earlier: then, emergence of new relationships in an observer's mind was used as a diagnostic symptom to indicate that a creative act by another person had been observed.) Here we are saying that all the 'hard' symbols and design space structures which are the subject of this paper are in reality only stable eddies of behaviour in turbulent neural networks [Lewin, 1993]. This has some implications for the design space model of creativity proposed here in that some concepts may apparently spontaneously change their characteristics or even disappear (extinctions of even very long-lived patterns as a result of normal network fluctuations are well known to occur in all networks exhibiting 'class 4', i.e. 'interesting', behaviour in the regime between periodic order and random noise [Lewin, 1993]). We do not know whether this potential instability of concepts and spaces (because they are really emergent aspects of networks) is an essential or merely an occasionally useful aspect of design creativity. This paper suggests that this aspect is not essential and that some type of creative behaviour can be achieved by explicit symbol manipulation in multiple design spaces.
It seems to be clear that software will eventually appear which will be capable of some activities which we now think of as creative. If so, we must consider the possibility that such design expertise will be available on relatively cheap hardware: what then are the implications of increasing the number of effective (if uninspired) designers within an organization by a factor of a hundred, or a thousand ?
One common misunderstanding is that Turing machines work within a fixed, finite symbol system. This is not true: an elementary Turing machine operates in a finite set of states, but it has access to an infinite memory. Thus by 'writing notes to itself' it can store and manipulate an infinite number of symbol systems each containing an infinite number of symbols. This is powerful indeed, even a non-deterministic Turing machine cannot solve harder problems. To consider the elementary Turing machine directly is in any case somewhat misleading since all different types of machine or mathematics which can solve 'algorithmic' problems are equivalent (in polynomial time) in the tasks they can perform (the Church/Turing thesis).
Another common misunderstanding is the definition of what constitutes an 'algorithmic' task: it is any task which is not 'undecidable' or 'non-computable', i.e. any problem which can be stated in an algorithmic manner for which an algorithm (which will supply the answer) can eventually be determined in principle [Harel, 1987]. Both the statement and the algorithm can be expressed in any formal language at all. Fitzhorn [1994] has recently shown that, even for the case where initial specifications are not fixed, design as an activity is indeed computable in this technical sense. (He has also shown that several properties of the design process are undecidable.)
A much more important distinction, for the purposes of producing software which might exhibit creative activity, is the distinction between tractable and intractable tasks [Harel, 1987] (both of which are in the computable/decidable class). Clearly our minds are limited in the amount of information they can store and the length of time a thought can take to conclude, so inevitably there will always be many problems which a Turing machine can solve in principle which we, in practice, cannot. Thus this whole discussion of Turing machines and creativity may be entirely beside the point.
Finally, Penrose [1989] proposes that human minds are necessarily and essentially not Turing machines. His argument is that because we can understand Gödel's theorem, this necessarily proves that we are not Turing machines (which cannot prove such undecidable questions). The proof rests on an assumption that we can 'see' the truth of some types of statement without being able to derive them within a symbol system (the 'reflection principle') and depends on a fine distinction in the definition of 'truth' for statements of high complexity [Rucker, 1987; Traub, 1990]. It appears possible (to me) that this direct appreciation of truth may just be a familiarity with the way the world works, brought about by a lifetime's training of the neural nets in our heads (cf Boden's description of 'understanding' referred to earlier [1992]). If so, the Penrose's argument fails.
If Penrose's argument succeeds, then the implications are startling: to support his thesis Penrose has to propose an entire new body of physics (gravitational effects on the collapse of wave-functions and a resolution of special relativity with the non-locality of quantum mechanics) to explain how mammalian brains (ours) might be able to perform non-Turing computations. He may well be right about the physics from other evidence, but if it has anything to do with brain function then consciousness may have an essential role in physics, and as a very minor side effect, algorithms may never be able to be quite as good as some people are at creative design.
Adelson, Beth. Cognitive research: uncovering how designers design; cognitive modelling: explaining and predicting how designers design. Res. Eng. Design 1 (1) (1989) 35-42.
Aelion, Vital, Jon Cagan, and Gary J. Powers. Input variable expansion: a formal innovative design generation technique. Res. Eng. Design 4 (1992) 101-113.
Albus, James S. Outline for a theory of intelligence. IEEE Trans. Systems, Man and Cybernetics 21 (3) (1991) 473-509.
Ashby, M.F. Engineering Materials I: An introduction to their properties and applications, Pergamon Press, Oxford, UK, 1980. ISBN 0-08-026138-8, 278 pages.
Bardasz, T., and I. Zeid. 'DEJAVU: a case-based reasoning designer's assistant shell', AI in Design'92, Ed. J.S. Gero. Carnegie Mellon University, Pittsburgh, PA: Kluwer Academic Publishers, (1992) 477-496.
Boden, Margaret. The creative mind: myths and mechanisms, Abacus, London, UK, 1992. ISBN 0-349-10469-7, 303 pages.
Bucciarelli, Louis. Reflections on Engineering Design practice. Design Studies 5 (5) (1984) 185-190.
Bucciarelli, Louis. An Ethnographic Perspective on Engineering Design. Design Studies 9 (3) (1988) 159-168.
Cagan, Jon, and Alice M. Agogino. Innovative design of mechanical structures from first principles. Artificial Intelligence in Engineering, Design, Analysis and Manufacturing 1 (3) (1987) 169-189.
Carlson, Chris N. , R. McKelvey, and Robert F. Woodbury. An introduction to structure and structure grammars, Technical Report, EDRC 48-20-90 , Engineering Design Research Center, Carnegie Mellon University, 1990.
Chakrabati, Amaresh. Creativity in design, Draft Report, (November), Engineering Design Centre, University of Cambridge, 1992.
Chakrabati, Amaresh. 'Towards a theory for functional reasoning in design', International Conference on Engineering Design (ICED), Aug.17-19, The Hague, Netherlands: (1993)
Clark, K., and T. Fujimoto. Product Development Performance, Harvard Business Press, Cambridge, Mass., 1991.
Dasgupta, S. The structure of design processes. Advances in Computers 28 (1989) 1-28.
deMillo, R. A., R. J. Lipton, and A. J. Perlis. Social Processes and Proofs of Theorems and Programs. Comm. ACM 22 (5) (1979) 271-280.
Dixon, John R. On a Research Methodology Towards a Scientific Theory of Design. AI-EDAM 1 (3) (1989) .
Faltings, Boi. 'Supporting creativity in symbolic computation', 2nd. Intl. Round-table Conference on Computational Models of Creative Design, Ed. John S. Gero and Fay Sudweeks. Heron Island, Queensland, Australia: Dept. Architectural and Design Science, University of Sydney, (1992) 191-205.
Finger, Susan, and John R. Dixon. A Review of Research in Mechanical Engineering Design, Parts I and II. Res. Eng. Design 1 (1,2) (1989) .
Fitzhorn, Patrick A. Engineering design is a computable function. AI EDAM 8 (1) (1994) 35-44.
Gero, John S. Design Prototypes: a knowledge representation schema for design. AI Magazine 11 (4) (1990) 26-36.
Gero, John S. 'Creativity, emergence and evolution in design', 2nd. Intl. Round-table Conference on Computational Models of Creative Design, Ed. John S. Gero and Fay Sudweeks. Heron Island, Queensland, Australia: Dept. Architectural and Design Science, University of Sydney, (1992a) 1-27.
Gero, John S. 'Why search and exploration in design are different, but not that different, and how do you explore ?', Workshop on search-based and exploration-based models of the design process, associated with 'AI in Design'92', Ed. D. Corne. Carnegie Mellon University, Pittsburgh, PA: (1992b) 39.
Harel, David. Algorithmics: the spirit of computing, Addison-Wesley Publ.Co., Menlo Park, 1987, 425 pages.
Ige, David O. Optimizing Composite Laminate Stacking Sequence - A Knowledge-Based System's Approach, Technical Report, CUED/C-MATS/TR.184 , Dept. of Engineering, University of Cambridge, 1990.
Johnson-Laird, Philip N. 'Analogy and the exercise of creativity' Similarity and analogical reasoning. Ed. Stella Vosniadou and Andrew Ortony. Cambridge University Press, Cambridge, UK, 1989. ISBN 0-521-38935-6, 313-331.
Konda, Suresh, Ira Monarch, Philip M. Sargent, and Eswaran Subrahmanian. Shared Memory in Design: A Unifying Theme for Research and Practice. Res. in Eng. Design 4 (1) (1992) 23-42.
Laird, J.E., A. Newell, and P.S. Rosenbloom. Soar: an architecture for general intelligence. Artificial Intelligence 33 (1) (1987) 1-64.
Lee, Jintae. 'Extending the Potts and Bruns model for recording design rationale', 13th International Conference on Software Engineering, Austin, TX: IEEE, (1991) 114-125.
Lenat, D.B. 'AM: discovery in mathematics as heuristic search' Knowledge-based systems in artificial intelligence. Ed. R. Davis and D.B. Lenat. McGraw-Hill, Inc., New York, 1982. ISBN =0-07-015557-7, 3-228.
Lewin, Roger. Complexity: life on the edge of chaos, Orion Books Ltd., London, 1993. ISBN 1 85799 028 5, 208 pages.
MacLean, A. 'Innovative and routine design with Design Space Analysis', Workshop on search-based and exploration-based models of the design process, associated with 'AI in Design'92', Ed. D. Corne. Carnegie Mellon University, Pittsburgh, PA: (1992) 45-46.
MacMahon, Christopher A. Observations on modes of incremental change in design. J. Eng. Design 5 (3) (1994) 195-209.
Minsky, Marvin. The Society of Mind, Heinemann, London, 1987. ISBN 0-434-46758-8, 339 pages.
Monarch, Ira, and S. Nirenburg. 'The Role of Ontology in Concept Acquisition for Knowledge-Based Systems', First European Workshop on Knowledge Acquisition for Knowledge-Based Systems, University of Reading, Reading, UK: (1987)
Murdoch, Tim N.S., and Ken M. Wallace. An approach to configuration optimization. J. Engng. Design 3 (2) (1992) 99-116.
Navinchandra, D. Innovative design systems, where are we and where do we go from here ? Part 2: design by exploration. The Knowledge Engineering Review 7 (4) (1992) 345-362.
Newton, Sid. 'Categorizations in design', AI in Design'92, Ed. J. Gero. Carnegie Mellon University, Pittsburgh, PA: Kluwer Academic Publishers, (1992) 861-882.
Penrose, Roger. The emporer's new mind: concerning computers, minds and the laws of physics, Oxford University Press, Oxford, UK, 1989. ISBN 0-09-977170-5, 601 (p541-7) pages.
Pólya, George. How to solve it, 2nd Ed. Penguin Books, New York, 1957. ISBN0-14-012499-3, 253 pages.
Pugh, S. Total Design: Methods for Successful Product Design, Addison Wesley, 1990.
Qian, L., and J.S. Gero. 'A design support system using analogy', AI in Design'92, Ed. J.S. Gero. Carnegie Mellon University, Pittsburgh, PA: Kluwer Academic Publishers, (1992) 795-813.
Reich, Yoram, Suresh Konda, Sean Levy, Ira Monarch, and Eswaran Subrahmanian. New roles for machine learning in design. AI in Engineering 8 (1993) 165-181.
Rinderle, James R. Grammatical approaches to engineering design 2: melding configuration and parametric design using attribute grammars. Res. Eng. Design 2 (1991) 137-146.
Rucker, Rudy. Mind Tools: The mathematics of information, Penguin Books, London, 1987. ISBN 0-14-014681-4, 328 pages.
Ruecker, Lucas, and Warren P. Seering. 'A dialectical reasoning system for design documentation', Conference on Design Theory and Methodology, ASME, (1991)
Ruecker, Lucas, and Warren P. Seering. 'User-oriented intelligent indexing and retrieval in a design documentaiton system', Engineering Database Symposium, San Francisco, CA: ASME, (1992)
Sargent, Philip M. Random Search, Simulated Annealing and Genetic Algorithms: A Survey for designing Laminate Layups, Technical Report, EDRC 24-41-90 , Engineering Design Research Centre, Carnegie Mellon University, 1990.
Sargent, Philip M. Materials Information for CAD/CAM, Butterworth-Heinemann, Oxford, UK, 1991. ISBN 0-7506-0277-5, 170 pages.
Sargent, Philip M. 'A computational view of creative steps', 2nd. Intl. Round-table Conference on Computational Models of Creative Design, Ed. John S. Gero and Fay Sudweeks. Heron Island, Queensland, Australia: Dept. Architectural and Design Science, University of Sydney, (1992a) 29-43.
Sargent, Philip M. 'A multiple world-view design hypothesis', Workshop 7 on search-based and exploration-based models of the design process, associated with 'AI in Design'92', Ed. D. Corne. Carnegie Mellon University, Pittsburgh, PA: (1992b) 47-48.
Schön, D.A., and G. Wiggins. Kinds of seeing and their functions in design. Design Studies 13 (2) (1992) 135-199.
Shrobe, H.E. 'Understanding linkages', National Conference on Artificial Intelligence, AAAI, (1992)
Simon, Herbert A. The Sciences of the Artificial, 2nd Ed. MIT Press, Cambridge, MA, 1981.
Simon, Herbert A. 'People and computers: their role in creative design', AI in Design'92, Ed. J. Gero. Carnegie Mellon University, Pittsburgh, PA: Kluwer Academic Publishers, (1992)
Smith, Ian. 'Functional contexts and creativity', 2nd. Intl. Round-table Conference on Computational Models of Creative Design, Ed. John S. Gero and Fay Sudweeks. Heron Island, Queensland, Australia: Dept. Architectural and Design Science, University of Sydney, (1992) 45-51.
Smithers, Tim. 'Design as exploration: puzzle-making and puzzle-solving', Workshop on search-based and exploration-based models of the design process, associated with 'AI in Design'92', Ed. D. Corne. Carnegie Mellon University, Pittsburgh, PA: (1992) 1-22.
Steier, David. 'Design as multiple problem space search', Workshop on search-based and exploration-based models of the design process, associated with 'AI in Design'92', Ed. D. Corne. Carnegie Mellon University, Pittsburgh, PA: (1992a) 28-29.
Steier, David. Dynamic construction of new problem spaces, Verbal statement during workshop at 'AI in Design'92', (21 June 1992), 1992b.
Stiny, George. The algebras of design. Res. in Eng. Design 2 (1991) 171-181.
Subrahmanian, Eswaran. The Theory of the Artefact, Personal communication, work in progress on the n-Dim project, (30 June 1992), 1992.
Traub, J.F. 'What is scientifically knowlable ?', Invited lecture, 25th Anniversary Symposium, Computer Science Dept., Carnegie Mellon University: Addison-Wesley, (1990)
Tsai, Stephen W. Composites Design, 4th. Ed. Think Composites, Dayton, Ohio, 1988. 0-9618090-2-7.
Van Baalen, J. Toward a theory of representation design. PhD thesis, Technical Report 1128. MIT, Artificial Intelligence Laboratory, 1989.
Vincenti, W. G. What Engineers Know and How they Know It, (1 vols.) Johns Hopkins University Press, Baltimore, 1990. ISBN 0-8018-3974-2.
Webster, D.E. Mapping the design representation terrain. IEEE Computer 21 (12) (1988) 8-23.
Woodbury, Robert F., Chris N. Carlson, and Jeff A. Heisserman. Geometric Design Spaces, Technical Report, EDRC 48-13-89 , Engineering Design Research Center, Carnegie Mellon University, 1989.
Young, R. Multi-disciplinary modelling of interface design issues, Seminar, (March 4), University of Cambridge Computer Laboratory, 1992.
Zhao, Fang, and Mary Lou Maher. 'Using network-based prototypes to support creative design by analogy and mutation', AI in Design'92, Ed. J.S. Gero. Carnegie Mellon University, Pittsburgh, PA: Kluwer Academic Publishers, (1992) 773-793.
Zucker, John, and Adrian Demaid. 'Modelling heterogeneous engineering knowledge as transactions between delegating objects', AI in Design'92, Ed. J.S. Gero. Carnegie Mellon University, Pittsburgh, PA: Kluwer Academic Publishers, (1992) 141-159.