[Paleopsych] BBS: Boden, Margaret A. (1994). Precis of The creative mind
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BBS: Boden, Margaret A. (1994). Precis of The creative mind
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Boden, Margaret A. (1994). Precis of The creative mind: Myths and
mechanisms. Behavioral and Brain Sciences 17 (3): 519-570.
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Precis of "THE CREATIVE MIND: MYTHS AND MECHANISMS" London: Weidenfeld &
Nicolson 1990 (Expanded edn., London: Abacus, 1991.)
Margaret A. Boden
School of Cognitive and Computing Sciences
University of Sussex
England FAX: 0273-671320
maggieb at syma.susx.ac.uk
creativity, intuition, discovery, association, induction,
representation, unpredictability, artificial intelligence, computer
music, story-writing, computer art, Turing test
What is creativity? One new idea may be creative, while another is
merely new: what's the difference? And how is creativity possible? --
These questions about human creativity can be answered, at least in
outline, using computational concepts.
There are two broad types of creativity, improbabilist and
impossibilist. Improbabilist creativity involves (positively valued)
novel combinations of familiar ideas. A deeper type involves METCS:
the mapping, exploration, and transformation of conceptual spaces. It
is impossibilist, in that ideas may be generated which -- with respect
to the particular conceptual space concerned -- could not have been
generated before. (They are made possible by some transformation of
the space.) The more clearly conceptual spaces can be defined, the
better we can identify creative ideas. Defining conceptual spaces is
done by musicologists, literary critics, and historians of art and
science. Humanist studies, rich in intuitive subtleties, can be
complemented by the comparative rigour of a computational approach.
Computational modelling can help to define a space, and to show how it
may be mapped, explored, and transformed. Impossibilist creativity can
be thought of in "classical" AI-terms, whereas connectionism
illuminates improbabilist creativity. Most AI-models of creativity can
only explore spaces, not transform them, because they have no
self-reflexive maps enabling them to change their own rules. A few,
however, can do so.
A scientific understanding of creativity does not destroy our wonder
at it, nor make creative ideas predictable. Demystification does not
Chapter 1: The Mystery of Creativity
Creativity surrounds us on all sides: from composers to chemists,
cartoonists to choreographers. But creativity is a puzzle, a paradox,
some say a mystery. Inventors, scientists, and artists rarely know how
their original ideas arise. They mention intuition, but cannot say how
it works. Most psychologists cannot tell us much about it, either.
What's more, many people assume that there will never be a scientific
theory of creativity -- for how could science possibly explain
fundamental novelties? As if all this were not daunting enough, the
apparent unpredictability of creativity seems (to many people) to
outlaw any systematic explanation, whether scientific or historical.
Why does creativity seem so mysterious? Artists and scientists
typically have their creative ideas unexpectedly, with little if any
conscious awareness of how they arose. But the same applies to much of
our vision, language, and common-sense reasoning. Psychology includes
many theories about unconscious processes. Creativity is mysterious
for another reason: the very concept is seemingly paradoxical.
If we take seriously the dictionary-definition of creation, "to bring
into being or form out of nothing", creativity seems to be not only
beyond any scientific understanding, but even impossible. It is hardly
surprising, then, that some people have "explained" it in terms of
divine inspiration, and many others in terms of some romantic
intuition, or insight. From the psychologist's point of view, however,
"intuition" is the name not of an answer, but of a question. How does
In this book, I argue that these matters can be better understood, and
some of these questions answered, with the help of computational
This claim in itself may strike some readers as absurd, since
computers are usually assumed to have nothing to do with creativity.
Ada Lovelace is often quoted in this regard: "The Analytical Engine
has no pretensions whatever to originate anything. It can do [only]
whatever we know how to order it to perform." If this is taken to mean
that a computer can do only what its program enables it to do, it is
of course correct. But it does not follow that there can be no
interesting relations between creativity and computers.
We must distinguish four different questions, which are often confused
with each other. I call them Lovelace questions, and state them as
(1) Can computational concepts help us to understand human creativity?
(2) Could a computer, now or in the future, appear to be creative?
(3) Could a computer, now or in the future, appear to recognize
(4) Could a computer, however impressive its performance, really be
The first three of these are empirical, scientific, questions. In
Chapters 3-10, I argue that the answer to each of them is "Yes". (The
first Lovelace question is discussed in each of those chapters; in
chapters 7-8, the second and third are considered also.)
The fourth Lovelace question is not a scientific enquiry, but a
philosophical one. (More accurately, it is a mix of three complex, and
highly controversial, philosophical problems.) I discuss it in Chapter
11. However, one may answer "Yes" to the first three Lovelace
questions without necessarily doing so for the fourth. Consequently,
the fourth Lovelace question is ignored in the main body of the book,
which is concerned rather with the first three Lovelace questions.
Chapter 2: The Story so Far
This chapter draws on some of the previous literature on creativity.
But it is not a survey. Its aim is to introduce the main psychological
questions, and some of the historical examples, addressed in detail
later in the book. The main writers mentioned are Poincare (1982),
Hadamard (1954) Koestler (1975), and Perkins (1981).
Among the points of interest in Poincare's work are his views on
associative memory. He described our ideas as "something like the
hooked atoms of Epicurus," flashing in every direction like "a swarm
of gnats, or the molecules of gas in the kinematic theory of gases".
He was well aware that how the relevant ideas are aroused, and how
they are joined together, are questions which he could not answer in
detail. Another interesting aspect of Poincare's approach is his
distinction between four "phases" of creativity, some conscious some
These four phases were later named (by Hadamard) as preparation,
incubation, inspiration and verification (evaluation). Hadamard,
besides taking up Poincare's fourfold distinction, spoke of finding
problem-solutions "quite different" from any he had previously tried.
If (as Poincare had claimed) the gnat-like ideas were only "those from
which we might reasonably expect the desired solution", then how could
such a thing happen?
Perkins has studied the four phases, and criticizes some of the
assumptions made by Poincare and Hadamard. In addition, he criticizes
the romantic notion that creativity is due to some special gift.
Instead, he argues that "insight" involves everyday psychological
capacities, such as noticing and remembering. (The "everyday" nature
of creativity is discussed in Chapter 10.)
Koestler's view that creativity involves "the bisociation of matrices"
comes closest to my own approach. However, his notion is very vague.
The body of my book is devoted to giving a more precise account of the
structure of "matrices" (of various kinds), and of just how they can
be "bisociated" so as to result in a novel idea -- sometimes (as in
Hadamard's experience) one quite different from previous ideas.
(Matrices appear in my terminology as conceptual spaces, and different
forms of bisociation as association, analogy, exploration, or
Among the examples introduced here are Kekule's discovery of the
cyclical structure of the benzene molecule, Kepler's (and Copernicus')
thoughts on elliptical orbits, and Coleridge's poetic imagery in Kubla
Khan. Others mentioned in passing include Coleridge's announced
intention to write a poem about an ancient mariner, Bach's
harmonically systematic set of preludes and fugues, the
jazz-musician's skill in improvising a melody to fit a chord sequence,
and our everyday ability to recognize that two different apples fall
into the same class. All these examples, and many others, are
mentioned in later chapters.
Chapter 3: Thinking the Impossible
Given the seeming paradoxicality of the concept of creativity (noted
in Chapter 1), we need to define it carefully before going further.
This is not straightforward (over 60 definitions appear in the
psychological literature (Taylor, 1988)). Part of the reason for this
is that creativity is not a natural kind, such that a single
scientific theory could explain every case. We need to distinguish
"improbabilist" and "impossibilist" creativity, and also
"psychological" and "historical" creativity.
People of a scientific cast of mind, anxious to avoid romanticism and
obscurantism, generally define creativity in terms of novel
combinations of familiar ideas. Accordingly, the surprise caused by a
creative idea is said to be due to the improbability of the
combination. Many psychometric tests designed to measure creativity
work on this principle.
The novel combinations must be valuable in some way, because to call
an idea creative is to say that it is not only new, but interesting.
However, combination-theorists often omit value from their definition
of creativity (although psychometricians may make implicit
value-judgements when scoring the novel combinations produced by their
experimental subjects). A psychological explanation of creativity
focusses primarily on how creative ideas are generated, and only
secondarily on how they are recognized as being valuable. As for what
counts as valuable, and why, these are not purely psychological
questions. They also involve history, sociology, and philosophy,
because value-judgments are largely culture-relative (Brannigan, 1981;
Schaffer, in press.) Even so, positive evaluation should be explicitly
mentioned in definitions of creativity.
Combination-theorists may think they are not only defining creativity,
but explaining it, too. However, they typically fail to explain how it
was possible for the novel combination to come about. They take it for
granted, for instance, that we can associate similar ideas and
recognize more distant analogies, without asking just how such feats
are possible. A psychological theory of creativity needs to explain
how associative and analogical thinking works (matters discussed in
Chapters 6 and 7, respectively).
These two cavils aside, what is wrong with the combination-theory?
Many ideas which we regard as creative are indeed based on unusual
combinations. For instance, the appeal of Heath-Robinson machines lies
in the unexpected uses of everyday objects; and poets often delight us
by juxtaposing seemingly unrelated concepts. For creative ideas such
as these, a combination-theory, supplemented by psychological
explanations of association and analogy, might suffice.
Many creative ideas, however, are surprising in a deeper way. They
concern novel ideas that not only did not happen before, but which --
we intuitively feel -- could not have happened before.
Before considering just what this "could not" means, we must
distinguish two further senses of creativity. One is psychological, or
personal: I call it P-creativity. The other is historical:
H-creativity. The distinction between P-creativity and H-creativity is
independent of the improbabilist/impossibilist distinction made above:
all four combinations occur. However, I use the P/H distinction
primarily to compare cases of impossibilist creativity.
Applied to impossibilist examples, a valuable idea is P-creative if
the person in whose mind it arises could not (in the relevant sense of
"could not") have had it before. It does not matter how many times
other people have already had the same idea. By contrast, a valuable
idea is H-creative if it is P-creative and no-one else, in all human
history, has ever had it before.
H-creativity is something about which we are often mistaken.
Historians of science and art are constantly discovering cases where
other people have had an idea popularly attributed to some national or
international hero. Even assuming that the idea was valued at the time
by the individual concerned, and by some relevant social group, our
knowledge of it is largely accidental. Whether an idea survives, and
whether historians at a given point in time happen to have evidence of
it, depend on a wide variety of unrelated factors. These include
flood, fashion, rivalries, illness, trade-patterns, and wars.
It follows that there can be no systematic explanation of
H-creativity, no theory that explains all and only H-creative ideas.
For sure, there can be no psychological explanation of this historical
category. But all H-creative ideas, by definition, are P-creative too.
So a psychological explanation of P-creativity would include
H-creative ideas as well.
What does it mean to say that an idea "could not" have arisen before?
Unless we know that, we cannot make sense of P-creativity (or
H-creativity either), for we cannot distinguish radical novelties from
mere "first-time" newness.
An example of a novelty that clearly could have happened before is a
newly-generated sentence, such as "The deckchairs are on the top of
the mountain, three miles from the artificial flowers". I have never
thought of that sentence before, and probably no-one else has, either.
Chomsky remarked on this capacity of language-speakers to generate
first-time novelties endlessly, and called language "creative"
accordingly. But the word "creative" was ill-chosen. Novel though the
sentence about deckchairs is, there is a clear sense in which it could
have occurred before. For it can be generated by any competent speaker
of English, following the same rules that can generate other English
sentences. To come up with a new sentence, in general, is not to do
The "coulds" in the previous paragraph are computational "coulds". In
other words, they concern the set of structures (in this case, English
sentences) described and/or produced by one and the same set of
generative rules (in this case, English grammar). There are many sorts
of generative system: English grammar is like a mathematical equation,
a rhyming-schema for sonnets, the rules of chess or tonal harmony, or
a computer program. Each of these can (timelessly) describe a certain
set of possible structures. And each might be used, at one time or
another, in actually producing those structures.
Sometimes, we want to know whether a particular structure could, in
principle, be described by a specific schema, or set of abstract
rules. -- Is "49" a square number? Is 3,591,471 a prime? Is this a
sonnet, and is that a sonata? Is that painting in the Impressionist
style? Could that geometrical theorem be proved by Euclid's methods?
Is that word-string a sentence? Is a benzene-ring a molecular
structure describable by early nineteenth-century chemistry (before
Kekule had his famous vision in 1865)? -- To ask whether an idea is
creative or not (as opposed to how it came about) is to ask this sort
But whenever a structure is produced in practice, we can also ask what
generative processes actually went on in its production. -- Did a
particular geometer prove a particular theorem in this way, or in
that? Was the sonata composed by following a textbook on sonata-form?
Did Kekule rely on the then-familiar principles of chemistry to
generate his seminal idea of the benzene-ring, and if not how did he
come up with it? -- To ask how an idea (creative or otherwise)
actually arose, is to ask this type of question.
We can now distinguish first-time novelty from impossibilist
originality. A merely novel idea is one which can be described and/or
produced by the same set of generative rules as are other, familiar,
ideas. A genuinely original, or radically creative, idea is one which
cannot. It follows that the ascription of (impossibilist) creativity
always involves tacit or explicit reference to some specific
It follows, too, that constraints -- far from being opposed to
creativity -- make creativity possible. To throw away all constraints
would be to destroy the capacity for creative thinking. Random
processes alone, if they happen to produce anything interesting at
all, can result only in first-time curiosities, not radical surprises.
(As explained in Chapter 9, randomness can sometimes contribute to
creativity -- but only in the context of background constraints.)
Chapter 4: Maps of the Mind
The definition of (impossibilist) creativity given in Chapter 3
implies that, with respect to the usual mental processing in the
relevant domain (chemistry, poetry, music ...), a creative idea may be
not just improbable, but impossible. How could it arise, then, if not
by magic? And how can one impossible idea be more surprising, more
creative, than another? If an act of creation is not mere combination,
what is it? How can such creativity possibly happen?
To understand this, we need to think of creativity in terms of the
mapping, exploration, and transformation of conceptual spaces. (The
notion of a conceptual space is used informally in this chapter;
later, we see how conceptual spaces can be described more rigorously.)
A conceptual space is a style of thinking. Its dimensions are the
organizing principles which unify, and give structure to, the relevant
domain. In other words, it is the generative system which underlies
that domain and which defines a certain range of possibilities:
chess-moves, or molecular structures, or jazz-melodies.
The limits, contours, pathways, and structure of a conceptual space
can be mapped by mental representations of it. Such mental maps can be
used (not necessarily consciously) to explore -- and to change -- the
Evidence from developmental psychology supports this view. Children's
skills are at first utterly inflexible. Later, imaginative flexibility
results from "representational redescriptions" (RRs) of (fluent)
lower-level skills (Clark & Karmiloff-Smith, in press;
Karmiloff-Smith, 1993). These RRs provide many-levelled maps of the
mind, which are used by the subject to do things he or she could not
For example, children need RRs of their lower-level drawing-skills in
order to draw non-existent, or "funny", objects: a one-armed man, or
seven-legged dog. Lacking such cognitive resources, a 4-year-old
simply cannot spontaneously draw a one-armed man, and finds it very
difficult even to copy a drawing of a two-headed man. But 10-year-olds
can explore their own man-drawing skill, by using strategies such as
distorting, repeating, omitting, or mixing parts. These imaginative
strategies develop in a fixed order: children can change the size or
shape of an arm before they can insert an extra one, and long before
they can give the drawn man wings in place of arms.
The development of RRs is a mapping-exercise, whereby people develop
explicit mental representations of knowledge already possessed
Few AI-models of creativity contain reflexive descriptions of their
own procedures, and/or ways of varying them. Accordingly, most
AI-models are limited to exploring their conceptual spaces, rather
than transforming them (see Chapters 7 & 8).
Conceptual spaces can be explored in various ways. Some exploration
merely shows us something about the nature of the relevant conceptual
space which we had not explicitly noticed before. When Dickens
described Scrooge as "a squeezing, wrenching, grasping, scraping,
clutching, covetous old sinner", he was exploring the space of English
grammar. He was reminding the reader (and himself) that the rules of
grammar allow us to use seven adjectives before a noun. That
possibility already existed, although its existence may not have been
realized by the reader.
Some exploration, by contrast, shows us the limits of the space, and
identifies specific points at which changes could be made in one
dimension or another. To overcome a limitation in a conceptual space,
one must change it in some way. One may also change it, of course,
without yet having come up against its limits. A small change (a
"tweak") in a relatively superficial dimension of a conceptual space
is like opening a door to an unvisited room in an existing house. A
large change (a "transformation"), especially in a relatively
fundamental dimension, is more like the instantaneous construction of
a new house, of a kind fundamentally different from (albeit related
to) the first.
A complex example of structural exploration and change can be found in
the development of post-Renaissance Western music, based on the
generative system known as tonal harmony. From its origins to the end
of the nineteenth century, the harmonic dimensions of this space were
continually tweaked to open up the possibilities (the rooms) implicit
in it from the start. Finally, a major transformation generated the
deeply unfamiliar (yet closely related) space of atonality.
Each piece of tonal music has a "home-key", from which it starts, from
which (at first) it did not stray, and in which it must finish.
Reminders of the home-key were constantly provided, as fragments of
scales, chords. or arpeggios. As time passed, the range of possible
home-keys became increasingly well-defined (Bach's "Forty-Eight" was
designed to explore, and clarify, the tonal range of the well-tempered
Soon, travelling along the path of the home-key alone became
insufficiently challenging. Modulations between keys were then
allowed, within the body of the composition. At first, only a small
number of modulations (perhaps only one, followed by its
"cancellation") were tolerated, between strictly limited pairs of
harmonically-related keys. Over the years, the modulations became more
daring, and more frequent -- until in the late nineteenth century
there might be many modulations within a single bar, not one of which
would have appeared in early tonal music. The range of harmonic
relations implicit in the system of tonality gradually became
apparent. Harmonies that would have been unacceptable to the early
musicians, who focussed on the most central or obvious dimensions of
the conceptual space, became commonplace.
Moreover, the notion of the home-key was undermined. With so many, and
so daring, modulations within the piece, a "home-key" could be
identified not from the body of the piece, but only from its beginning
and end. Inevitably, someone (it happened to be Schoenberg) eventually
suggested that the convention of the home-key be dropped altogether,
since it no longer constrained the composition as a whole.
(Significantly, Schoenberg suggested new musical constraints: using
every note in the chromatic scale, for instance.)
However, exploring a conceptual space is one thing: transforming it is
another. What is it to transform such a space?
One example has just been mentioned: Schoenberg's dropping the
home-key constraint to create the space of atonal music. Dropping a
constraint is a general heuristic, or method, for transforming
conceptual spaces. The deeper the generative role of the constraint in
the system concerned, the greater the transformation of the space.
Non-Euclidean geometry, for instance, resulted from dropping Euclid's
Another very general way of transforming conceptual spaces is to
"consider the negative": that is, to negate a constraint. One
well-known instance concerns Kekule's discovery of the benzene-ring.
He described it like this:
"I turned my chair to the fire and dozed. Again the atoms were
gambolling before my eyes.... [My mental eye] could distinguish larger
structures, of manifold conformation; long rows, sometimes more
closely fitted together; all twining and twisting in snakelike motion.
But look! What was that? One of the snakes had seized hold of its own
tail, and the form whirled mockingly before my eyes. As if by a flash
of lightning I awoke."
This vision was the origin of his hunch that the benzene-molecule
might be a ring, a hunch that turned out to be correct. Prior to this
experience, Kekule had assumed that all organic molecules are based on
strings of carbon atoms. But for benzene, the valencies of the
constituent atoms did not fit.
We can understand how it was possible for him to pass from strings to
rings, as plausible chemical structures, if we assume three things
(for each of which there is independent psychological evidence).
First, that snakes and molecules were already associated in his
thinking. Second, that the topological distinction between open and
closed curves was present in his mind. And third, that the "consider
the negative" heuristic was present also. Taken together, these three
factors could transform "string" into "ring".
A string-molecule is an open curve: one having at least one end-point
(with a neighbour on only one side). If one considers the negative of
an open curve, one gets a closed curve. Moreover, a snake biting its
tail is a closed curve which one had expected to be an open one. For
that reason, it is surprising, even arresting ("But look! What was
that?"). Kekule might have had a similar reaction if he had been out
on a country walk and happened to see a snake with its tail in its
mouth. But there is no reason to think that he would have been stopped
in his tracks by seeing a Victorian child's hoop. A hoop is a hoop, is
a hoop: no topological surprises there. (No topological surprises in a
snaky sine-wave, either: so two intertwined snakes would not have
interested Kekule, though they might have stopped Francis Crick dead
in his tracks, a century later.)
Finally, the change from open curves to closed ones is a topological
change, which by definition will alter neighbour-relations. And Kekule
was an expert chemist, who knew very well that the behaviour of a
molecule depends partly on how the constituent atoms are juxtaposed. A
change in atomic neighbour-relations is very likely to have some
chemical significance. So it is understandable that he had a hunch
that this tail-biting snake-molecule might contain the answer to his
Plausible though this talk of conceptual spaces may be, it is -- thus
far -- largely metaphorical. I have claimed that in calling an idea
creative one should specify the particular set of generative
principles with respect to which it is impossible. But I have not said
how the (largely tacit) knowledge of literary critics, musicologists,
and historians of art and science might be explicitly expressed within
a psychological theory of creativity. Nor have I said how we can be
sure that the mental processes specified by the psychologist really
are powerful enough to generate such-and-such ideas from such-and-such
This is where computational psychology can help us. I noted above, for
example, that representational redescription develops explicit mental
representations of knowledge already possessed implicitly. In
computational terms, one could -- and Karmiloff-Smith does -- put this
by saying that knowledge embedded in procedures becomes available,
after redescription, as part of the system's data-structures. Terms
like procedures and data-structures are well understood, and help us
to think clearly about the mapping and negotiation of conceptual
spaces. In general, whatever computational psychology enables us to
say, it enables us to say relatively clearly.
Moreover, computational questions can be supplemented by computational
models. A functioning computer program, in effect, enables the system
to use its maps not just to contemplate the relevant conceptual
territory, but to explore it actively. So as well as saying what a
conceptual space is like (by mapping it), we can get some clear ideas
about how it is possible to move around within it. In addition, those
(currently, few) AI-models of creativity which contain reflexive
descriptions of their own procedures, and ways of varying them, can
transform their own conceptual spaces, as well as exploring them.
The following chapters, therefore, employ a computational approach in
discussing the account of creativity introduced in Chapters 1-4.
Chapter 5: Concepts of Computation
Computational concepts drawn from "classical" (as well as
connectionist) AI can help us to think about the nature, form, and
negotiation of conceptual spaces. Examples of such concepts, most of
which were inspired by pre-existing psychological notions in the first
place, include the following: generative system, heuristic (both
introduced in previous chapters), effective procedure, search-space,
search-tree, knowledge representation, semantic net, scripts, frames,
what-ifs, and analogical representation.
Each of these concepts is briefly explained in Chapter 5, for people
who (unlike BBS-readers) may know nothing about AI or computational
psychology. And they are related to a wide range of everyday and
historical examples -- some of which will be mentioned again in later
My main aim, here, is to encourage the reader to use these concepts in
considering specific cases of human thought. A secondary aim is to
blur the received distinction between "the two cultures". The
differences between creativity in art and science lie less in how new
ideas are generated than in how they are evaluated, once they have
arisen. The uses of computational concepts in this chapter are
informal, even largely metaphorical. But in bringing a computational
vocabulary to bear on a variety of examples, the scene is set for more
detailed consideration (in Chapters 6-8) of some computer models of
In Chapter 5, I refer very briefly to a few AI-programs (such as
chess-machines and Schankian question-answering programs). Only two
are discussed at any length: Longuet-Higgins' (1987) work on the
perception of tonal harmony, and Gelernter's (1963) geometry
Longuet-Higgins' work is not intended as a model of musical
creativity. Rather, it provides (in my terminology) a map of a certain
sort of musical space: the system of tonal harmony introduced in
Chapter 4. In addition, it suggests some ways of negotiating that
space, for it identifies musical heuristics that enable the listener
to appreciate the structure of the composition. Just as speech
perception is not the same as speech production, so appreciating music
is different from composing it. Nevertheless, some of the musical
constraints that face composers working in this particular genre have
been identified in this work.
I also mention Longuet-Higgins' recent work on musical expressiveness,
but do not describe it here. In (Boden, in press), I say a little more
about it. Without expression, music sounds "dead", even absurd. In
playing the notes in a piano-score, for instance, pianists add such
features as legato, staccato, piano, forte, sforzando, crescendo,
diminuendo, rallentando, accelerando, ritenuto, and rubato. But how?
Can we express this musical sensibility precisely? That is, can we
specify the relevant conceptual space?
Longuet-Higgins (in preparation), using a computational method, has
tried to specify the musical skills involved in playing expressively.
Working with two of Chopin's piano-compositions, he has discovered
some counterintuitive facts. For example, a crescendo is not uniform,
but exponential (a uniform crescendo does not sound like a crescendo
at all, but like someone turning-up the volume-knob on a wireless);
similarly, a rallentando must be exponentially graded (in relation to
the number of bars in the relevant section) if it is to sound "right".
Where sforzandi are concerned, the mind is highly sensitive: as little
as a centisecond makes a difference between acceptable and clumsy
This work is not a study of creativity. It does not model the
exploration of a conceptual space, never mind its transformation. But
it is relevant because creativity can be ascribed to an idea
(including a musical performance) only by reference to a particular
conceptual space. The more clearly we can map this space, the more
confidently we can identify and ask questions about the creativity
involved in negotiating it. A pianist whose playing-style sounds
"original", or even "idiosyncratic", is exploring and transforming the
space of expressive skills which Longuet-Higgins has studied.
Gelernter's program, likewise, was not focussed on creativity as such.
(It was not even intended as a model of human psychology.) Rather, it
was an early exercise in automatic problem-solving, in the domain of
Euclidean geometry. However, it is well known that the program was
capable of generating a highly elegant proof (that the base-angles of
an isosceles triangle are equal), whose H-creator was the
fourth-century mathematician Pappus.
Or rather, it is widely believed that Gelernter's program could do
this. The ambiguity, not to say the mistake, arises because the
program's proof is indeed the same as Pappus' proof, when both are
written down on paper in the style of a geometry text-book. But the
(creative) mental processes by which Pappus did this, and by which the
modern geometer is able to appreciate the proof, were very different
from those in Gelernter's program -- which were not creative at all.
Consider (or draw) an isosceles triangle ABC, with A at the apex. You
are required to prove that the base-angles are equal. The usual method
of proving this, which the program was expected to employ, is to
construct a line bisecting angle BAC, running from A to D (a point on
the baseline, BC). Then, the proof goes as follows:
Consider triangles ABD and ACD.
AB = AC (given)
AD = DA (common)
Angle BAD = angle DAC (by construction)
Therefore the two triangles are congruent (two sides and included
Therefore angle ABD = angle ACD.
By contrast, the Gelernter proof involved no construction, and went as
Consider triangles ABC and ACB.
Angle BAC = angle CAB (common)
AB = AC (given)
AC = AB (given)
Therefore the two triangles are congruent (two sides and included
Therefore angle ABC = angle ACB.
And, written down on paper, this is the outward form of Pappus' proof,
The point, here, is that Pappus' own notes (as well as the reader's
geometrical intuitions) show that in order to produce or understand
this proof, a human being considers one and the same triangle rotated
(as Pappus put it, lifted up and replaced in the trace left behind by
itself). There were thus two creative aspects of this proof. First,
when "congruence" is in question, the geometer normally thinks of two
entirely separate triangles (or, sometimes, two distinct triangles
having one side in common). Second, Euclidean geometry deals only with
points, lines, and planes -- so one would expect any proof to be
restricted to two spatial dimensions. But Pappus (and you, when you
thought about this proof) imagined lifting and rotating the triangle
in the third dimension. He was, if you like, cheating. However, to
transform a rule (an aspect of some conceptual space) is to change it:
in effect, to cheat. In that sense, transformational creativity always
Gelernter's geometry-program did not cheat -- not merely because it
was too rigid to cheat in any way, but also because it could not have
cheated in this way. It knew nothing of the third dimension. Indeed,
it had no visual, analogical, representation of triangles at all. It
represented a triangle not as a two-dimensional spatial form, but as a
list of three letters (e.g. ABC) naming points in an abstract
coordinate space. Similarly, it represented an angle as a list of
three letters naming the vertex and one of the points on each of the
two rays. Being unable to inspect triangles visually, it even had to
prove that every different letter-name for what we can see to be the
same angle was equivalent. So it had to prove (for instance) that
angle XYZ is the same as angle ZYX, and angle BAC the same as angle
CAB. Consequently, this program was incapable not only of coming up
with Pappus' proof in the way he did, but even of representing such a
proof -- or of appreciating its elegance and originality. Its mental
maps simply did not allow for the lifting and replacement of triangles
in space (and it had no heuristics enabling it to transform those
How did it come up with its pseudo-Pappus proof, then? Treating the
"ABC's" as (spatially uninterpreted) abstract vectors, it did a
massive brute-search to find the proof. Since this brute search
succeeded, it did not bother to construct any extra lines.
This example shows how careful one must be in ascribing creativity to
a person, and in answering the second Lovelace question about a
program. We have to consider not only the resulting idea, but also the
mental processes which gave rise to it. Brute force search is even
less creative than associative (improbabilist) thinking, and
problem-dimensions which can be mapped by some systems may not be
representable by others. (Analogously, a three-year old not showing
flexible imagination in drawing a funny man: rather, she is showing
incompetence in drawing an ordinary man.)
It should not be assumed from the example of Pappus (or Kekule) that
visual imagery is always useful in mapping and transforming one's
ideas. An example is given of a problem for which a visual
representation is almost always constructed, but which hinders
solution. Where mental maps are concerned, visual maps are not always
Chapter 6: Creative Connections
This chapter deals with associative creativity: the spontaneous
generation of new ideas, and/or novel combinations of familiar ideas,
by means of unconscious processes of association. Examples include not
only "mere associations" but also analogies, which may then be
consciously developed for purposes of rhetorical exposition or
problem-solving. In Chapter 6, I discuss the initial association of
ideas. (The evaluation and use of analogy are addressed in Chapter 7.)
One of the richest veins of associative creativity is poetic imagery.
I consider some specific examples taken from Coleridge's poem The
Ancient Mariner. For this poem (and also for his Kubla Khan), we have
unusually detailed information about the literary sources of the
imagery concerned. The literary scholar John Livingston Lowes (1951)
studied Coleridge's Notebooks written while preparing for and writing
the poem, and followed up every source mentioned there -- and every
footnote given in each source. Despite the enormous quantity and range
of Coleridge's reading, Lowes makes a subtle, and intuitively
compelling, case in identifying specific sources for the many images
in the poem.
However, an intuitively compelling case is one thing, and an explicit
justification or detailed explanation is another. Lowes took for
granted that association can happen (he used Coleridge's term: the
hooks and eyes of memory), without being able to say just how these
hooks and eyes can come together. I argue that connectionism, and
specifically PDP (parallel distributed processing), can help us to
understand how such unexpected associations are possible.
Among the relevant questions to which PDP-models offer preliminary
answers are the following: How can ideas from very different sources
(such as Captain Cook's diaries and Priestley's writings on optics) be
spontaneously thought of together? How can two ideas be merged to
produce a new structure, which shows the influence of both
ancestor-ideas without being a mere "cut-and-paste" combination? How
can the mind be "primed" (for instance, by the decision to write a
poem about a seaman), so that one will more easily notice
serendipitous ideas? Why may someone notice -- and remember --
something fairly uninteresting (such as a word in a literary text), if
it occurs in an interesting context? How can a brief phrase conjure up
from memory an entire line or stanza, from this or some other poem?
And how can we accept two ideas as similar (the words "love" and
"prove" as rhyming, for instance) in respect of a feature not
identical in both?
The features of connectionist models which suggest answers to these
questions are their powers of pattern-completion, graceful
degradation, sensitization, multiple constraint-satisfaction, and
"best-fit" equilibration. The computational processes underlying these
features are described informally in Chapter 6 (I assume that it is
not necessary to do so for BBS-readers).
The message of this chapter is that the unconscious, "insightful",
associative aspects of creativity can be explained -- in outline, at
least -- in computational terms. Connectionism offers some specific
suggestions about what sorts of processes may underlie the hooks and
eyes of memory.
This is not to say, however, that all aspects of poetry -- or even all
poetic imagery -- can be explained in this way. Quite apart from the
hierarchical structure of natural language itself, some features of a
poem may require thinking of a type more suited (at present) to
symbolic models. For example, Coleridge's use of "The Sun came up upon
the left" and "The Sun now rose upon the right" as the opening-lines
of two closely-situated stanzas enabled him to indicate to the reader
that the ship was circumnavigating the globe, without having to detail
all the uneventful miles of the voyage. (Compare Kubrick's use of the
spinning thigh-bone turning into a space-ship, as a highly compressed
history of technology, in his film 2001, A Space Odyssey.) But these
expressions, too, were drawn from his reading -- in this case, of the
diaries of the very early mariners, who recorded their amazement at
first experiencing the sunrise in the "wrong" part of the sky.
Associative memory was thus involved in this poetic conceit, but it is
not the entire explanation.
Chapter 7: Unromantic Artists
This chapter and the next describe and criticize some existing
computer models of creativity. The separation into "artists" (Chapter
7) and "scientists" (Chapter 8) is to some extent an arbitrary
rhetorical device. For example, analogy (discussed in Chapter 7) and
induction and genetic algorithms (both outlined in Chapter 8) are all
relevant to creativity in arts and sciences alike. In these two
chapters, the second and third Lovelace-questions -- about apparent
computer-creativity -- are addressed at length. However, the first
Lovelace question, relating to human creativity, is still the
The computer models of creativity discussed in Chapter 7 include: a
series of programs which produce line-drawings (McCorduck, 1991); a
jazz-improviser (Johnson-Laird, 1991); a haiku-writer (Masterman &
McKinnon Wood, 1968); two programs for writing stories (Klein et al.,
1973; Meehan, 1981); and two analogy-programs (Chalmers, French, &
Hofstadter, 1991; Holyoak & Thagard, 1989a, 1989b; Mitchell, 1993). In
each case, the programmer has to try to define the dimensions of the
relevant conceptual space, and to specify ways of exploring the space,
so as to generate novel structures within it. Some evaluation, too,
must be allowed for. In the systems described in this chapter, the
evaluation is built into the generative procedures, rather than being
done post hoc. (This is not entirely unrealistic: although humans can
evaluate -- and modify -- their own ideas once they have produced
them, they can also develop domain-expertise such that most of their
ideas are acceptable without modification.)
Sometimes, the results are comparable with non-trivial human
achievements. Thus some of the computer's line-drawings are
spontaneously admired, by people who are amazed when told their
provenance. The haiku-program can produce acceptable poems, sometimes
indistinguishable from human-generated examples (however, this is due
to the fact that the minimalist haiku-style demands considerable
projective interpretation by the reader). And the jazz-program can
play -- composing its own chord-sequences, as well as improvising on
them -- at about the level of a moderately competent human beginner.
(Another jazz-improviser, not mentioned in the book, plays at the
level of a mediocre professional musician; unlike the former example,
it starts out with significant musical structure provided to it "for
free" by the human user (Hodgson, 1990).)
At other times, the results are clumsy and unconvincing, involving
infelicities and absurdities of various kinds. This often happens when
stories are computer-generated. Here, many rich conceptual spaces have
to be negotiated simultaneously. Quite apart from the challenge of
natural language generation, the model must produce sensible plots,
taking account both of the motivation and action of the characters and
of their common-sense knowledge. Where very simple plot-spaces, and
very limited world-knowledge, are concerned, a program may be able
(sometimes) to generate plausible stories.
One, for example, produces Aesop-like tales, including a version of
"The Fox and the Crow" (Meehan, 1981). A recent modification of this
program (Turner, 1992), not covered in the book, is more subtle. It
uses case-based reasoning and case-transforming heuristics to generate
novel stories based on familiar ones; and because it distinguishes the
author's goals from those of the characters, it can solve
meta-problems about the story as well as problems posed within it. But
even this model's story-telling powers are strictly limited, compared
Models dealing with the interpretation of stories, and of concepts
(such as betrayal) used in stories, are also relevant here.
Computational definitions of interpersonal themes and scripts
(Abelson, 1973), programs that can answer questions about (simple)
stories and models which can -- up to a point -- interpret
motivational and emotional structures within a story (Dyer, 1983) are
So, too, is a program that generates English text describing games of
noughts-and-crosses (Davey, 1978). The complex syntax of the sentences
is nicely appropriate to the structure of the particular game being
described. Human writers, too, often use subtleties of syntax to
convey certain aspects of their story-lines.
The analogy programs described in Chapter 7 are ACME and ARCS (Holyoak
& Thagard, 1989a, 1989b), and in the Preface to the paperback edition
I add a discussion of Copycat (Chalmers et al., 1991; Mitchell, 1993),
which I had originally intended to highlight in the main text.
ACME and ARCS are an analogy-interpreter and an analogy-finder,
respectively. Calling on a semantic net of over 30,000 items, to which
items can be added by the user, these programs use structural,
semantic, and pragmatic criteria to evaluate analogies between
concepts (whose structure is pre-given by the programmers). Other
analogy programs (e.g. Falkenhainer, Forbus, & Gentner, 1989) use
structural and semantic similarity as criteria. But ARCS/ACME takes
account also of the pragmatic context, the purpose for which the
analogy is being sought. So a conceptual feature may be highlighted in
one context, and downplayed in another. The context may be one of
rhetoric or poetic imagery, or one of scientific problem-solving
(ARCS/ACME forms part of an inductive program that compares the
"explanatory coherence" of rival scientific theories (Thagard, 1992)).
Examples of both types are discussed.
The point of interest about Copycat is that it is a model of analogy
in which the structure of the analogues is neither pre-assigned nor
inflexible. The description of something can change as the system
searches for an analogy to it, and its "perception" of an analogue may
be permanently influenced by having seen it in a particular analogical
relation to something else. Many analogies in the arts and sciences
can be cited, to show that the same is true of the human mind.
Among the points of general interest raised in this chapter is the
inability of these programs (Copycat excepted) to reflect on what they
have done, or to change their way of doing it.
For instance, the line-drawing program that draws human acrobats in
broadly realistic poses is unable to draw one-armed acrobats. It can
generate acrobats with only one arm visible, if one arm is occluded by
another acrobat in front. But that there might be a one-armed (or a
six-armed) acrobat is strictly inconceivable. The reason is that the
program's knowledge of human anatomy does not represent the fact that
humans have two arms in a form which is separable from its
drawing-procedures or modifiable by "imaginative" heuristics. It does
not, for instance, contain anything of the form "Number of arms: 2",
which might then be transformed by a "vary the variable" heuristic
into "Number of arms: 1". Much as the four-year-old child cannot draw
a "funny" one-armed man because she has not yet developed the
necessary RR of her own man-drawing skill, so this program cannot vary
what it does because -- in a clear sense -- it does not know what it
is that it is doing.
This failing is not shared by all current programs: some featured in
the next chapter can evaluate their own ideas, and transform their own
procedures, to some extent. Moreover, this failure is "bad news" only
to those seeking a positive answer to the second and third Lovelace
questions. It is useful to anyone asking the first Lovelace question,
for it underlines the importance of the factors introduced in Chapter
4: reflexive mapping of thought, evaluation of ideas, and
transformation of conceptual spaces.
Chapter 8: Computer-Scientists
Like analogy, inductive thinking occurs across both arts and science.
Chapter 8 begins with a discussion of the ID3 algorithm. This is used
in many learning programs, including a world-beater -- better than the
human expert who "taught" it -- at diagnosing soybean diseases
(Michalski & Chilausky, 1980).
ID3 learns from examples. It looks for the logical regularities which
underlie the classification of the input examples, and uses them to
classify new, unexamined, examples. Sometimes, it finds regularities
of which the human experts were unaware, such as unknown strategies
for chess endgames (Michie & Johnston, 1984). In short, ID3 can not
only define familiar concepts in H-creative ways, but can also define
However, all the domain-properties it considers have to be
specifically mentioned in the input. (It does not have to be told just
which input properties are relevant: in the chess end-game example,
the chess-masters "instructing" the program did not know this.) That
is, ID3-programs can restructure their conceptual space in P-creative
-- and even H-creative -- ways. But they cannot change the dimensions
of the space, so as to alter its fundamental nature.
Another program capable of H-discovery is meta-DENDRAL, an early
expert system devoted to the spectroscopic analysis of a certain group
of organic molecules. The original program, DENDRAL, uses exhaustive
search to describe all possible molecules made up of a given set of
atoms, and heuristics to suggest which of these might be chemically
interesting. DENDRAL uses only the chemical rules supplied to it, but
meta-DENDRAL can find new rules about how these compounds decompose.
It does this by identifying unfamiliar patterns in the spectrographs
of familiar compounds, and suggesting plausible explanations for them.
For instance, if it discovers a smaller structure located near the
point at which a molecule breaks, it may suggest that other molecules
containing that sub-structure may break at these points too.
This program is H-creative, up to a point. It not only explores its
conceptual space (using evaluative heuristics and exhaustive search)
but enlarges it too, by adding new rules. It generates hunches, which
have led to the synthesis of novel, chemically interesting, compounds.
And it has discovered some previously unsuspected rules for analysing
several families of organic molecules. However it relies on
sophisticated theories built into it by expert chemists (which is why
its novel hypotheses, though sometimes false, are always plausible).
It casts no light on how those theories might have arisen in the first
Some computational models of induction were developed with an eye to
the history of science (and to psychology), rather than for practical
scientific puzzle-solving. Their aim was not to come up with
H-creative ideas, but to P-create in the same way as human H-creators.
Examples include BACON, GLAUBER, STAHL, and DALTON (Langley, Simon,
Bradshaw, & Zytkow, 1987), whose P-creative activities are modelled on
H-creative episodes recorded in the notebooks of human scientists.
BACON induces quantitative laws from empirical data. Its data are
measurements of various properties at different times. It looks for
simple mathematical functions defining invariant relations between
numerical data-sets. For instance, it seeks direct or inverse
proportionalities between measurements, or between their products or
ratios. It can define higher-level theoretical terms, construct new
units of measurement, and use mathematical symmetry to help find
invariant patterns in the data. It can cope with noisy data, finding a
best-fit function (within predefined limits). BACON has P-created many
physical laws, including Archimedes' principle, Kepler's third law,
Boyle's law, Ohm's law, and Black's law.
GLAUBER discovers qualitative laws, summarizing the data by
classifying things according to (non-measurable) observable
properties. Thus it discovers relations between acids, alkalis, and
bases (all identified in qualitative terms). STAHL analyses chemical
compounds into their elements. Relying on the data-categories
presented to it, it has modelled aspects of the historical progression
from phlogiston-theory to oxygen-theory. DALTON reasons about atoms
and molecular structure. Using early atomic theory, it generates
plausible molecular structures for a given set of components (it could
be extended to cover other componential theories, such as particle
physics or Mendelian genetics).
These four programs have rediscovered many scientific laws. However,
their P-creativity is shallow. They are highly data-driven, their
discoveries lying close to the evidence. They cannot identify
relevance for themselves, but are "primed" with appropriate
expectations. (BACON expects to find linear relationships, and
rediscovered Archimedes' principle only after being told that things
can be immersed in known volumes of liquid and the resulting volume
measured.) They cannot model spontaneous associations or analogies,
only deliberate reasoning. Some can suggest experiments, to test
hypotheses they have P-created, but they have no sense of the
practices involved. They can learn, constructing P-novel concepts used
to make further P-discoveries. But their discoveries are exploratory
rather than transformational: they cannot fundamentally alter their
own conceptual spaces.
Some AI-models of creativity can do this, to some extent. For
instance, the Automatic Mathematician (AM) explores and transforms
mathematical ideas (Lenat, 1983). It does not prove theorems, or do
sums, but generates "interesting" mathematical ideas (including
expressions that might be provable theorems). It starts with 100
primitive concepts of set-theory (such as set, list, equality, and
ordered pair), and 300 heuristics that can examine, combine,
transform, and evaluate its concepts. One generates the inverse of a
function (compare "consider the negative"). Others can compare,
generalize, specialize, or find examples of concepts.
Newly-constructed concepts are fed back into the pool.
In effect, AM has hunches: its evaluation heuristics suggest which new
structures it should concentrate on. For example, AM finds it
interesting whenever the union of two sets has a simply expressible
property which is not possessed by either of them (a set-theoretic
version of the notion that emergent properties are interesting). Its
value-judgments are often wrong. Nevertheless, it has constructed some
powerful mathematical notions, including prime numbers, Goldbach's
conjecture, and an H-novel theorem concerning maximally-divisible
numbers (which the programmer had never heard of). In short, AM
appears to be significantly P-creative, and slightly H-creative too.
However, AM has been criticised (Haase, 1986; Lenat & Seely-Brown,
1984; Ritchie & Hanna, 1984; Rowe & Partridge, 1993). Critics have
argued that some heuristics were included to make certain discoveries,
such as prime numbers, possible; that the use of LISP provided AM with
mathematical relevance "for free", since any syntactic change in a
LISP expression is likely to result in a mathematically-meaningful
string; that the program's exploration was too often guided by the
human user; and that AM had fixed criteria of interest, being unable
to adapt its values. The precise extent of AM's creativity, then, is
Because EURISKO has heuristics for changing heuristics, it can
transform not only its stock of concepts but also its own
processing-style. For example, one heuristic asks whether a rule has
ever led to any interesting result. If it has not (but has been used
several times), it will be less often used in future. If it has
occasionally been helpful, though usually worthless, it may be
specialized in one of several different ways. (Because it is sometimes
useful and sometimes not, the specializing-heuristic can be applied to
itself.) Other heuristics generalize rules, or create new rules by
analogy with old ones. Using domain-specific heuristics to complement
these general ones, EURISKO has generated H-novel ideas in genetic
engineering and VLSI-design (one has been patented, so was not
"obvious to a person skilled in the art").
Other self-transforming systems described in this chapter are
problem-solving programs based on genetic algorithms (GAs). GA-systems
have two main features. They all use rule-changing algorithms
(mutation and crossover) modelled on biological genetics. Mutation
makes a random change in a single rule. Crossover mixes two rules, so
that (for instance) the lefthand portion of one is combined with the
righthand portion of the other; the break-points may be chosen
randomly, or may reflect the system's sense of which rule-parts are
the most useful. Most GA-systems also include algorithms for
identifying the relatively successful rules, and rule-parts, and for
increasing the probability that they will be selected for "breeding"
future generations. Together, these algorithms generate a new system,
better adapted to the task.
An example cited in the book is an early GA-program which developed a
set of rules to regulate the transmission of gas through a pipeline
(Holland, Holyoak, Nesbitt, & Thagard, 1986). Its data were hourly
measurements of inflow, outflow, inlet-pressure, outlet-pressure, rate
of pressure-change, season, time, date, and temperature. It altered
the inlet-pressure to allow for variations in demand, and inferred the
existence of accidental leaks in the pipeline (adjusting the inflow
Although the pipeline-program discovered the rules for itself, the
potentially relevant data-types were given in its original list of
concepts. How far that compromises its creativity is a matter of
judgment. No system can work from a tabula rasa. Likewise, the
selectional criteria were defined by the programmer, and do not alter.
Humans may be taught evaluative criteria, too. But they can sometimes
learn -- and adapt -- them for themselves.
GAs, or randomizing thinking, are potentially relevant to art as well
as to science -- especially if the evaluation is done interactively,
not automatically. That is, at each generation the selection of items
from which to breed for the next generation is done by a human being.
This methodology is well-suited to art, where the evaluative criteria
are not only controversial but also imprecise -- or even unknown. Two
recent examples (not mentioned in the book, but described in: Boden,
in press) concern graphics (Sims, 1991; Todd & Latham, 1993). Sims'
aim is to provide an interactive environment for graphic artists,
enabling them to generate otherwise unimaginable images. Latham's is
to produce his own art-works, but he too uses the computer to generate
images he could not have developed unaided.
In a run of Sims' GA-system, the first image is generated at random.
Then the program makes various independent random mutations in the
image-generating rule, and displays the resulting images. The human
now chooses one image to be mutated, or two to be "mated", and the
process is repeated. The program can transform its image-generating
code (simple LISP-functions) in many ways. It can alter parameters in
pre-existing functions, combine or separate functions, or nest one
function inside another (so many-levelled hierarchies can arise).
Many of Sims' computer-generated images are highly attractive, even
beautiful. Moreover, they often cause a deep surprise. The change(s)
between parent and offspring are sometimes amazing. The one appears to
be a radical transformation of the other -- or even something entirely
different. In short, we seem to have an example of impossibilist
Latham's interactive GA-program is much more predictable. Its mutation
operators can change only the parameters within the image-generating
code, not the body of the function. Consequently, it never comes up
with radical novelties. All the offspring in a given generation are
obviously siblings, and obviously related to their parents. So the
results of Latham's system are less exciting than Sims'. But it is
arguably even more relevant to artistic creativity.
The interesting comparison is not between the aesthetic appeal of a
typical Latham-image and Sims-image, but between the discipline -- or
lack of it -- which guides the exploration and transformation of the
relevant visual space. Sims is not aiming for particular types of
result, so his images can be fundamentally transformed in random ways
at every generation. But Latham (a professional artist) has a sense of
what forms he hopes to achieve, and specific aesthetic criteria for
evaluating intermediate steps. Random changes at the margins are
exploratory, and may provide some useful ideas. But fundamental
transformations -- especially, random ones -- would be
counterproductive. (If they were allowed, Latham would want to pick
one and then explore its possibilities in a disciplined way.)
This fits the account of (impossibilist) creativity given in Chapters
3 and 4. Creativity works within constraints, which define the
conceptual spaces with respect to which it is identified. Maps or RRs
(or LISP-functions) which describe the parameters and/or the major
dimensions of the space can be altered in specific ways, to generate
new, but related, spaces.
Random changes are sometimes helpful, but only if they are integrated
into the relevant style. Art, like science, involves discipline. Only
after a space has been fairly thoroughly explored will the artist want
to transform it in deeply surprising ways. A convincing
computer-artist would therefore need not only randomizing operators,
but also heuristics for constraining its transformations and
selections in an aesthetically acceptable fashion. In addition, it
would need to make its aesthetic selections (and perhaps guiding
recommendations) for itself. And, to be true to human creativity, the
evaluative rules should evolve also (Elton, 1993).
Chapter 9: Chance, Chaos, Randomness, Unpredictability
Unpredictability is often said to be the essence of creativity. And
creativity is, by definition, surprising. But unpredictability is not
enough. At the heart of creativity, as previous chapters have shown,
lie constraints: the very opposite of unpredictability. Constraints
and unpredictability, familiarity and surprise, are somehow combined
in original thinking.
In this chapter, I distinguish various senses of "chance", "chaos",
"randomness", and "unpredictability". I also argue that a scientific
explanation need not imply either determinism or predictability, and
that even deterministic systems may be unpredictable. Below, it will
suffice to mention a number of different ways in which
unpredictability can enter into creativity.
The first follows from the fact that creative constraints do not
determine everything about the newly-generated idea. A style of
thinking typically allows for many points at which two or more
alternatives are possible. Several notes may be both melodious and
harmonious; many words rhyme with moon; and perhaps there could be a
ring-molecule with three, or five, atoms in the ring? At these points,
some specific choice must be made. Likewise, many exploratory and
transformational heuristics may be potentially available at a certain
time, in dealing with a given conceptual space. But one or other must
be chosen. Even if several heuristics can be applied at once (like
parallel mutations in a GA-system), not all possibilities can be
simultaneously explored. The choice has to be made, somehow.
Occasionally, the choice is random, or as near to random as one can
get. So it may be made by throwing a dice (as in playing Mozart's
aleatory music); or by consulting a table of random numbers (as in the
jazz-program); or even, possibly, as a result of some sudden
quantum-jump inside the brain. There may even be psychological
processes akin to GA-mechanisms, producing novel ideas in human minds.
More often, the choice is fully determined, by something which bears
no systematic relation to the conceptual space concerned. (Some
examples are given below.) Relative to that style of thinking, the
choice is made randomly. Certainly, nothing within the style itself
could enable us to predict its occurrence.
In either case, the choice must somehow be skilfully integrated into
the relevant mental structure. Without such disciplined integration,
it cannot lead to a positively valued, interesting, idea. With the
help of this mental discipline, even flaws and accidents may be put to
creative use. For instance, a jazz-drummer suffering from Tourette's
syndrome is subject to sudden, uncontrollable, muscular tics, even
when he is drumming. As a result, his drumsticks sometimes make
unexpected sounds. But his musical skill is so great that he can work
these supererogatory sounds into his music as he goes along. At worst,
he "covers up" for them. At best, he makes them the seeds of unusual
improvisations which he could not otherwise have thought of.
One might even call the drummer's tics serendipitous. Serendipity is
the unexpected finding of something one was not specifically looking
for. But the "something" has to be something which was wanted, or at
least which can now be used. Fleming's discovery of the dirty
petri-dish, infected by Penicillium spores, excited him because he
already knew how useful a bactericidal agent would be. Proust's
madeleine did not answer any currently pressing question, but it
aroused a flood of memories which he was able to use as the trigger of
a life-long project. Events such as these could not have been
foreseen. Both trigger and triggering were unpredictable. Who was to
say that the dish would be left uncovered, and infected by that
particular organism? And who could say that Proust would eat a
madeleine on that occasion? Even if one could do this (perhaps the
laboratory was always untidy, and perhaps Proust was addicted to
madeleines), one could not predict the effect the trigger would have
on these individual minds.
This is so even if there are no absolutely random events going on in
our brains. Chaos theory has taught us that fully deterministic
systems can be, in practice, unpredictable. Our inescapable ignorance
of the initial conditions means that we cannot forecast the weather,
except in highly general (and short-term) ways. The inner dynamics of
the mind are more complex than those of the weather, and the initial
conditions -- each person's individual experiences, values, and
beliefs -- are even more varied. Small wonder, then, if we cannot
fully foresee the clouds of creativity in people's minds.
To some extent, however, we can. Different thinkers have differing
individual styles, which set a characteristic stamp on all their work
in a given domain. Thus Dr. Johnson complained, "Who but Donne would
have compared a good man to a telescope?". Authorial signatures are
largely due to the fact that people can employ habitual ways of making
"random" choices. There may be nothing to say, beforehand, how someone
will choose to play the relevant game. But after several years of
practice, their "random" choices may be as predictable as anything in
the basic genre concerned.
More mundane examples of creativity, which are P-creative but not
H-creative, can sometimes be predicted -- and even deliberately
brought about. Suppose your daughter is having difficulty mastering an
unfamiliar principle in her physics homework. You might fetch a gadget
that embodies the principle concerned, and leave it on the
kitchen-table, hoping that she will play around with it and realise
the connection for herself. Even if you have to drop a few hints, the
likelihood is that she will create the central idea. Again, Socratic
dialogue helps people to explore their conceptual spaces in (to them)
unexpected ways. But Socrates himself, like those taking his role
today, knew what P-creative ideas to expect from his pupils.
We cannot predict creative ideas in detail, and we never shall be able
to do so. Human experience is too richly idiosyncratic. But this does
not mean that creativity is fundamentally mysterious, or beyond
Chapter 10: Elite or Everyman?
Creativity is not a single capacity, and nor is it a special one. It
is an aspect of intelligence in general, which involves many different
capacities: noticing, remembering, seeing, speaking, classifying,
associating, comparing, evaluating, introspecting, and the like.
Chapter 10 offers evidence for this view, drawing on the work of
Perkins (1981) and also on computational work of various kinds.
For example, Kekule's description of "long rows, twining and twisting
in snakelike motion", where "one of the snakes had seized hold of its
own tail", assumes everyday powers of visual interpretation and
analogy. These capacities are normally taken for granted in
discussions of Kekule's H-creativity, but they require some
psychological explanation. Relevant computational work on low-level
vision suggests that Kekule's imagery was grounded in certain
specific, and universal, visual capacities -- including the ability to
identify lines and end-points. (His hunch, by contrast, required
special expertise. As remarked in Chapter 4, only a chemist could have
realized the potential significance of the change in
neighbour-relations caused by the coalescence of end-points, or the
"snake" which "seized hold of its tail".)
Similarly, Mozart's renowned musical memory, and his reported capacity
for hearing a whole symphony "all at once", can be related to
computational accounts of powers of memory and comprehension common to
us all. Certainly, his musical expertise was superior in many ways. He
had a better grasp of the conceptual spaces concerned, and a better
understanding -- better even than Salieri's -- of how to explore them
so as to locate their farthest nooks and crannies. (Unlike Haydn, for
example, he was not a composer who made adventurous transformations).
But much of Mozart's genius may have lain in the better use, and the
vastly more extended practice, of facilities we all share.
Much -- but perhaps not all. Possibly, there was something special
about Mozart's brain which predisposed him to musical genius (Gardner,
1983). However, we have little notion, at present, of what this could
be. It may have been some cerebral detail which had the emergent
effect of giving him greater musical powers. For example, the
jazz-improvisation program described in Chapter 7 employed only very
simple rules to improvise, because its short-term memory was
deliberately constrained to match the limited STM of people. Human
jazz-musicians cannot improvise hierarchically nested chord-sequences
"on the fly", but have to compose (or memorize) them beforetimes. A
change in the range of STM might enable someone to improvise and
appreciate musical structures of a complexity not otherwise
intelligible. But this musically significant change might be due to an
apparently "boring" feature of the brain.
Many other examples of creativity (drawn, for instance, from poetry,
painting, music, and choreography) are cited in this chapter. They all
rely on familiar capacities for their effect, and arguably for their
occurrence too. We appreciate them intuitively, and normally take
their accessibility -- and their origins -- for granted. But
psychological explanations in computational terms may be available, at
least in outline.
The role of motivation and emotion is briefly mentioned, but is not a
prime theme. This is not because motivation and emotion are in
principle outside the reach of a computational psychology. Some
attempts have been made to bring these matters within a computational
account of the mind (e.g. Boden, 1972; Sloman, 1987). But such
attempts provide outline sketches rather than functioning models.
Still less is it because motivation is irrelevant to creativity. But
the main topic of the book is how (not why) novel ideas arise in human
Chapter 11: Of Humans and Hoverflies
The final chapter focusses on two questions. One is the fourth
Lovelace question: could a computer really be creative? The other is
whether any scientific explanation of creativity, whether
computational or not, would be dehumanizing in the sense of destroying
our wonder at it -- and at the human mind in general.
With respect to the fourth Lovelace question, the answer "No" may be
defended in at least four different ways. I call these the brain-stuff
argument, the empty-program argument, the consciousness argument, and
the non-human argument. Each of these applies to intelligence (and
intentionality) in general, not just to creativity in particular.
The brain-stuff argument (Searle, 1980) claims that whereas
neuroprotein is a kind of stuff which can support intelligence, metal
and silicon are not. This empirical claim is conceivably correct, but
we have no specific reason to believe it. Moreover, the associated
claim -- that it is intuitively obvious that neuroprotein can support
intentionality and that metal and silicon cannot -- must be rejected.
Intuitively speaking, that neuroprotein supports intelligence is
utterly mysterious: how could that grey mushy stuff inside our skulls
have anything to do with intentionality? Insofar as we understand
this, we do so because of various functions that nervous tissue makes
possible (as the sodium pump enables action potentials, or "messages",
to pass along an axon). Any material substrate capable of supporting
all the relevant functions could act as the embodiment of mind.
Whether neurochemistry describes the only such substrate is an
empirical question, not to be settled by intuitions.
The empty-program argument is Searle's (1980) claim that a
computational psychology cannot explain understanding, because
programs are all syntax and no semantics: their symbols are utterly
meaningless to the computer itself. I reply that a computer program,
when running in a computer, has proto-semantic (causal) properties, in
virtue of which the computer does things -- some of which are among
the sorts of thing which enable understanding in humans and animals
(Boden, 1988, ch. 8; Sloman, 1986). (This is not to say that any
computer-artefact could possess understanding in the full sense, or
what I have termed "intrinsic interests", grounded in evolutionary
history (Boden, 1972).)
The consciousness argument is that no computer could be conscious, and
therefore -- since consciousness is needed for the evaluation phase,
and even for much of the preparation phase -- no computer can be
creative. I reply that it's not obvious that evaluation must be
carried out consciously. A creative computer might recognize
(evaluate) its creative ideas by using relevant reflexive criteria
without also having consciousness. Moreover, some aspects of
consciousness can be illuminated by a computational account, although
admittedly "qualia" present an unsolved problem. The question must
remain open -- not just because we do not know the answer, but because
we do not clearly understand how to ask the question.
According to the non-human argument, to regard computers as truly
intelligent is not a mere factual mistake, but a moral absurdity: only
members of the human, or animal, community should be granted moral and
epistemological consideration (of their interests and opinions). If we
ever agreed to remove all the scare-quotes around the psychological
words we use in describing computers, so inviting them to join our
human community, we would be committed to respecting their goals and
judgments. This would not be a purely factual matter, but one of moral
and political choice -- about which it is impossible to legislate now.
In short, each of the four negative replies to the last Lovelace
question is challengeable. But even someone who does accept a negative
answer here can consistently accept positive answers to the first
three Lovelace questions. The main argument of the book remains
The second theme of this final chapter is the question whether, where
creativity is in question, scientific explanation in general should be
spurned. Many people, from Blake to Roszak, have seen the natural
sciences as dehumanizing in various ways. Three are relevant here: the
ignoring of mentalistic concepts, the denial of cherished beliefs, and
the destructive demystification of some valued phenomena.
The natural sciences have had nothing to say about psychological
phenomena as such; and scientifically-minded psychologists have often
conceptualized them in reductionist (e.g. behaviourist, or
physiological) terms. To ignore something is not necessarily to deny
it. But, given the high status of the natural sciences, the fact that
they have not dealt with the mind has insidiously downplayed its
importance, if not its very existence.
This charge cannot be levelled at computational psychology, however.
Intentional concepts, such as representation, lie at the heart of it,
and of AI. Some philosophers claim that these sciences have no right
to use such terms. Even so, they cannot be accused of deliberately
ignoring intentional phenomena, or of rejecting intentionalist
The second charge of dehumanization concerns what science explicitly
denies. Some scientific theories have rejected comforting beliefs,
such as geocentrism, special creation, or rational self-control. But a
scientific psychology need not -- and a computational psychology does
not -- deny creativity, as astronomy denies geocentrism. On the
contrary, the preceding chapters have acknowledged creativity again
and again. Even to say that it rests on universal features of human
minds is not to deny that some ideas are surprising, and special,
requiring explanation of how they could possibly arise.
However, the humanist's worry concerns not only denial by rejection,
but also denial by explanation. The crux of the third type of
anti-scientific resistance is the feeling that scientific explanation
of any kind must drive out wonder: that to explain something is to
cease to marvel at it. Not only do we wonder at creativity, but
positive evaluation is essential to the concept. So it may seem that
to explain creativity is insidiously to downgrade it -- in effect, to
Certainly, many examples can be given where understanding drives out
wonder. For instance, we may marvel at the power of the hoverfly to
fly to its mate hovering nearby (so as to mate in mid-air). Many
people might be tempted to describe the hoverfly's activities in terms
of its goals and beliefs, and perhaps even its determination in going
straight to its mate without any coyness or prevarication. How
wonderful is the mind of the humble hoverfly!
In fact, the hoverfly's flight-path is determined by a simple and
inflexible rule, hardwired into its brain. This rule transforms a
specific visual signal into a specific muscular response. The fly's
initial change of direction depends on the particular approach-angle
subtended by the target-fly. The creature, in effect, always assumes
that the size and velocity of the seen target (which may or may not be
a fly) are those corresponding to hoverflies. When initiating a new
flight-path, the fly's angle of turn is selected on this rigid, and
fallible, basis. Moreover, the fly's path cannot be adjusted in
midflight, there being no way in which it can be influenced by
feedback from the movement of the target animal.
This evidence must dampen the enthusiasm of anyone who had marvelled
at the psychological subtlety of the hoverfly's behaviour. The
insect's intelligence has been demystified with a vengeance, and it no
longer seems worthy of much respect. One may see beauty in the
evolutionary principles that enabled this simple computational
mechanism to develop, or in the biochemistry that makes it function.
But the fly itself cannot properly be described in anthropomorphic
terms. Even if we wonder at evolution, and at insect-neurophysiology,
we can no longer wonder at the subtle mind of the hoverfly.
Many people fear that this disillusioned denial of intelligence in the
hoverfly is a foretaste of what science will say about our minds too.
A few "worrying" examples can indeed be given: for instance, think of
how perceived sexual attractiveness turns out to relate to pupil-size.
In general, however, this fear is mistaken. The mind of the hoverfly
is much less marvellous than we had imagined, so our previous respect
for the insect's intellectual prowess is shown up as mere ignorant
sentimentality. But computational explanations of thinking can
increase our respect for human minds, by showing them to be much more
complex and subtle than we had previously recognized.
Consider, for instance, the many different ways (some are sketched in
Chapters 4 and 5) in which Kekule could have seen snakes as suggesting
ring-molecules. Think of the rich analogy-mapping in Coleridge's mind,
which drew on naval memoirs, travellers' tales, and scientific reports
to generate the imagery of The Ancient Mariner (Chapter 6). Bear in
mind the mental complexities (outlined in Chapter 7) of generating an
elegant story-line, or improvising a jazz-melody. And remember the
many ways in which random events (the mutations described in Chapter
8, or the serendipities cited in Chapter 9) may be integrated into
pre-existing conceptual spaces with creative effect.
Writing about Coleridge's imagery, Livingston Lowes said: "I am not
forgetting beauty. It is because the worth of beauty is transcendent
that the subtle ways of the power that achieves it are transcendently
worth searching out." His words apply not only to literary studies of
creativity, but to scientific enquiry too. A scientific psychology,
whether computational or not, allows us plenty of room to wonder at
Mozart, or at our friends' jokes. Psychology leaves poetry in place.
Indeed, it adds a new dimension to our awe on encountering creative
ideas, for it helps us to see the richness, and yet the discipline, of
the underlying mental processes.
To understand, even to demystify, is not necessarily to denigrate. A
scientific explanation of creativity shows how extraordinary is the
ordinary person's mind. We are, after all, humans -- not hoverflies.
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