=Paper=
{{Paper
|id=Vol-1616/invited1
|storemode=property
|title=The Shape of Creativity
|pdfUrl=https://ceur-ws.org/Vol-1616/invited1.pdf
|volume=Vol-1616
|authors=John A. Bateman
|dblpUrl=https://dblp.org/rec/conf/shapes/Bateman15
}}
==The Shape of Creativity==
https://ceur-ws.org/Vol-1616/invited1.pdf
The shape of creativity
A discussion paper
John A. BATEMAN
Bremen University, Bremen, Germany
Abstract. In this discussion paper, several proposals are made for potential inter-
connections between notions of ‘shape’, ‘ontology’, ‘design’ and ‘creativity’. The
purpose of the paper is to summarise the points made in the Shapes 3.0 presentation
and to promote further discussion and consideration of some of the connections
drawn. Shape is proposed as an essential embodied construct deeply anchored into
our way of dealing with the world and capable of deployment for a broad range of
comprehension and production processes, including creative design.
Keywords. shape, ontology, creativity, perception, embodiment, design
1. Introduction
In this discussion paper, the course of the argument will start from the notion of ‘shape’
and ontology, run through some of the current discussions of ‘creativity’ – particuarly
approaches to computational creativity (cf. Colton & Wiggins 2012) – and then return
to ‘shape’ at the conclusion. To begin, however, we can ask the question as to why the
title of the paper so blatantly commits a category mistake: how can ‘creativity’ have a
‘shape’?
Here we need to observe a continuum of more or less extended usages of the term
‘shape’. These begin with presumably unproblematic cases where material objects are
talked of having shape, but quickly move on to discussions where shape takes on a more
metaphorical flavour. Certainly aggregates of material objects can have some shape, even
though the aggregates themselves are no longer entirely physical: ontologically more
complex notions need here already to play a role (cf. Galton 2013). Detailed discus-
sions already exist for such notions as ‘holes’ (Casati & Varzi 1994) and even the shape
of ‘empty space’ (Bhatt & Schultz 2013). It is also equally common to talk of certain
quite immaterial ‘objects’ as having shape however: for example, shapes of arguments or
shapes of mathematical figures (e.g., the abstract notion of a triangle) appear just as well
suited to descriptions in terms of shapes as their more material relatives. There is also
the common practice of referring to temporal phenomena in terms of shapes: in partic-
ular, musical phrases or pieces may well have shapes in some sense (Wattenberg 2002).
So there does not appear to be a clear ‘cut off’ that provides a boundary between what
might have a shape and what might not – evidently some rather more abstract notion of
what is occurring when we talk of, or use, notions of shape other than that inherent in
material objects is going to be necessary. This leads to our particular focus for current Figure 1.: Watternberg’s
song shapes
purposes: just what is it about shape that lends itself to drawing connections of these
kinds so freely?
7
2. Where might ‘shape’ belong ontologically?
Here we take up previous discussions, such as that of Galton (2013) in a previous Shapes
meeting, to ask where in a formal foundational ontology might we best locate the notion
of ‘shape’. If we take the DOLCE ontology (Masolo et al. 2003, Borgo & Masolo 2010)
as representative of an appropriately well articulated and ontology of this kind, then
we would probably be led to suggest a placement of ‘shape’ alongside other physical
qualities, such as spatial location. Physical qualities are necessarily linked with physical
objects and take a value drawn from within corresponding physical regions.
Figure 2. Quality and quality spaces (taken from Masolo et al., 2003)
The usual diagrammatic representation of these interrelationships is as shown in Fig-
ure 2, drawn from Masolo et al. (2003). Here we see that some physical endurant, such
as a rose, necessarily has a physical quality of ‘colour’: this is time independent and un-
changing. The particular colour of that object then has a value drawn from a correspond-
ing region, in this case the colour region shown on the righthand side of the figure. This
region may have several qualitatively distinguished and named subregions, such as ‘red’.
Thus, when the colour of the object changes, a different subregion within the associated
colour region is pointed to; in all cases the colour of the rose remains its own unique
quality, however.
Now, this sounds promising for shape also. Each physical object definitely has its
own unique shape that is its and no other’s. It may then be the case that one way of locat-
ing shape ontologically is within a corresponding physical region capturing the nature of
shape. Then, quite analogously to colour, if the shape of some object changes, then its
particular shape simply takes on a new value (or set of values over time). Let us pursue
this further.
3. Quality spaces and perception
For a ‘cognitively’-motivated construction such as the foundational ontology DOLCE,
one might expect that its quality spaces have something to do with perception. That
is, it is not just ‘colour’ in the abstract that is characterised within the corresponding
physical region but colour as it plays a particular role in our, i.e., human’s, dealings
8
with colour. This is necessary because it is well known that the relationship between
physically measurable properties of lightwaves, such as frequency and intensity, and
phenomenologically experienced ‘colours’ is quite complex.
Figure 3. Colour systems discussed by Gärdenfors (2000) and others
There are, moreover, various models of ‘colour’ as perceived, which can all be as-
sessed empirically according to how well and in what respects they ‘match’ our expe-
riences of colour. Two examples of such schemes discussed by Gärdenfors (2000) are
shown in Figure 3; there are several more. Each such scheme might serve as a way of
organising the internal details of a physical colour region: particular colours might then
be distinguished by articulating subregions within the spaces so modelled.
Regardless of which scheme one takes, however, the complexity of the relationship
between these qualitative representations and the physical properties of the generally
assumed carrier of colour, light, becomes particularly clear when the behaviour of the
human eye is considered. Although there is general awareness of the fact that the eye
contains components – the so-called ‘cones’ – that are sensitive to red, green and blue
frequencies, it is less generally realised that expressing the properties involved in this
way already serves to confuse somewhat the distinct levels of description involved. The
actual sensitivity of the three relevant components of the human eye according to light
frequency is shown in Figure I4.
Figure 4. Colour sensitivity of cones in the human eye
(URL: http://light-measurement.com/perception-of-color/ )
Here we can see that there are no ‘pure’ receptors and that there is considerable
overlap in sensitivities. Cones with a peak receptivity to ‘red’ are also very active when
receiving ‘green’; cones with a peak receptivity to ‘blue’ also overlap with both ‘green’
and ‘red’ (cf. also: Gärdenfors 2000, 13). It then might be asked just how clear colour
perceptions occur at all. The answer is that the actual colours perceived depend on further
9
levels of neural calculation. The overall brightness, or luminescence, is calculated from
the sum of the inputs of each of the cones; then one factor is derived from excitation from
the ‘red’ and the ’blue’ and inhibition from the ‘green’, while a further factor is derived
from excitation from the ‘red’ and the ’green’ and inhibition from the ‘blue’.
This differential procedure serves well to distinguish certain states of affairs rather
than simply to respond to frequencies. Taken together this then begins to approximate
our commonsense colour experience. There are many perceptual experiments that can
be performed that produce highly non-intuitive results that rely on these differential pro-
cesses of excitation and inhibition, demonstrating both their validity and their relevance
for colour perception. This means that colours offer an elegant example of where the
‘physical universe’ and our perception of it lie a long way apart.
Figure 5. Colour sensitivity of cones in various species, adapted from Osorio & Vorobyev (2005)
This point is emphasised further when we examine the visual make-up of several
other species. There is, in fact, a broad variety in ranges both of sensitivities and of how
those sensitivities are combined during ‘colour processing’. Figure 5 shows sensitivity
graphs for honeybees, pigeons and house flies similar to that shown above for humans.
One consequence of this is that although the overall ontological organisation proposed
by DOLCE may remain, the individual internal construction of quality spaces for colour
may well need to be quite different for differing species – indeed, it may well need
to be different even among humans, should we wish to characterise more adequately
differences in colour perception, such as colour blindness of various types. Returning to
the main line of argumentation for the current paper, however, we need to address just
why such differences occur and what they tell us about the role of the perceptual system.
First and foremost, such biological results provide strong evidence that percep-
tion is functional in the sense of being rather precisely targeted at the capabilities
that species require to survive. As Matthen (2005) sets out in considerable detail,
the relative sensitivities of the cones in the human eye result in a system that is
excellent for discriminating red and green and it is then no accident that red-green
Figure 6.: Chillis separation is an ideal capability for recognising, for example, berries against back-
against a green back- ground vegetation. A perceptual system that evolves to make red stand out against
ground green is then well suited for finding food of this particular kind; Figure 6 (when
viewed in colour!) suggests this more visually.1 This relation between behaviour and
the perceptual systems that have evolved to support that behaviour can be found
across species. Figure 7, for example, shows a simulation of a bee’s visual percep-
1 Image of cheiro roxa bush taken from URL: http://thehotpepper.com/topic/27468-pjs-2012-glog-with-a-
kaleidoscope-of-colored-peppers/page-8.
10
tion produced by Nicolas Chalwatzis of some flowers at different stages of devel-
opment (cf. URL: http://www.ultravioletphotography.com/content/index.php/topic/648-
simulation-of-bee-colours-ii). Whereas under daylight these flowers would appear the
same colour for a human observer, the differential organisation of the colour receptors
for bees show them (again only when the figure is viewed in colour) quite differently,
Figure 7.: Simulated bee
thus allowing finer discrimination very much along the same lines as that just illustrated vision (Chalwatzis, 2013)
for humans with berries.
Now, it has been suggested above and by Galton (2013) that shape may be simi-
lar ontologically to colour, appearing as a kind of physical quality. This then requires a
corresponding kind of physical quality region. Given that, as we have now argued, the
organisation of such a physical quality region for colour needs to pay appropriate atten-
tion to how the perceptual system has evolved to support particular kinds of behaviours,
we should in all likelihood expect a similar kind of structuring to take place for ‘shape’.
What might that look like?
4. Shape as a functional perceptive category
We have asked questions of colour concerning the behaviours that experienced colour
differentiation affords for its perceivers. So, crucially, if shape is going to be seen as
a quality region, there is very little reason to consider our perception and use of shape
differently to the situation for colour. This means we will need to capture just what it is
that shape does for us in various contexts of physical interaction with the environment.
One source of relevant behaviour here is going to be found in very early interaction as
we develop the skills necessary to support more complex abilities – that is, in interaction
of the kind suggested in Figure 8.2
Figure 8.: Acquiring the
The quality region for shape may thus be similar to that suggested above for the perception of shape?
physical region for colour, but we still have very little idea of just what dimensions of
variation are going to be necessary for its classification. Indeed, it may turn out to be
a quality space far more like a pigeon’s or housefly’s complex versions of colours than
like simpler 3D Euclidean space or colour wheels. Considering perception as situated
embodied action, as Matthen (2005) and many others now propose, would mean that
we also need to consider the distinct kinds of physical interactions that some notion of
‘shape perception’ would afford. A starting point for such a construction is sketched in
Figure 9, organised around bundles of ‘behaviours’.
Here we see a range of dimensions of interaction with physical objects, each of
which gives potentially useful information concerning the object in the world being en-
countered. It is likely that there are considerably more such dimensions, all encoding
various parameters that might be found beneficial for low-level body motion and ma-
nipulation. Relevant bodies of research for taking such a consideration further would,
therefore, include neuroimaging and related techniques exploring just how the brain is
making sense of the world it interacts with physically and directly on a close personal
scale.
Such categorisations may also play a role for grounding aspects of linguistic be-
haviour and descriptions of shapes. This is suggested in Figure 10, which overlays sev-
2 Image taken from URL: http://www.parentsareimportant.com/2010/05/benefits-of-blocks.html.
11
Figure 9. Suggestive dimensions for organising ‘space’ as an embodied, functional perceptive category
eral regions and corresponding labels over the dimensions suggested in the first figure.
Note that the subregions as well as the naming here is purely suggestive of how such
a procedure might unfold; the particular labels and regions identified are not intended
as hypotheses in their own right. The analogy being drawn here is that with the use of
colours in the original figure concerning DOLCE above (Figure 2), i.e., particular sub-
regions of the space are picked out by a culture for specific labelling. It is to be as-
sumed, here following Gärdenfors (2000), that such labels pick out connected subregions
in some sense – this may then well serve as an additional source of information for the
organisation of the space as a whole or in part. Interesting here is how languages typi-
cally have a very limited range of potential shape ‘names’ and that very often labels are
drawn from the objects that possess particular shapes. This is occasionally described as a
metaphorical usage, although the connection drawn appears rather more straightforward
within an architecture of the kind being sketched here.
Figure 10. Shape subregions used for grounding shape terms
We also need to remark, if only in passing, that there are other kinds of shape-related
interactions that will be relevant. For example, drawing further on Bhatt & Schultz’s
(2013) discussion of the nature of ‘empty space’ mentioned above, we can see that
‘shape’ is equally relevant for the spaces we inhabit or move within: i.e., shape is not
only an external perceptive feature of objects but also of our environment. We return to
this briefly below as well.
12
5. Shapes and image schemas and blending
If ‘shape’ ties into rich collections of affordances of these kinds, all physically embodied,
then we can see some of the reasons why the notion of shape’ is so productive. Assigning
some entity a shape is a powerful way of characterising what can be done with that
object in terms of manipulations of various kinds. Similarly, assigning some shape to
our environment tells us much of our potential for action in that environment. There is
potentially much to draw on from the nature of such perceptual spaces themselves. The
idea that such spaces are anchored not only in perception but in embodied perception then
opens a further significant line of contact with the growing body of research concerning
image schemas as one foundation for explaining not only flexible action and interaction
with the world but also our construction of complex conceptual understandings of that
world (Fauconnier & Turner 2003, Turner 2014).
Accounts of image schemas providing links grounding conceptual organisation in
embodied experience of the physical world are growing in popularity and power. An in-
troduction and suggestive formalisation in terms of families of theories is discussed by
Hedblom et al. (2015). This has been used to lead directly towards accounts of com-
putational creativity. For our current purposes, we can consider any dimensions of de-
scription of the space of shape as being necessarily linked into image schema-like and,
consequently, to ‘bodily-formatted’ representations (cf. Gallese & Sinigaglia 2011); the
contribution of brain studies as pursued by Gallese and colleagues to the perception of
shape is for example explicitly considered by Uithol et al. (2015) among others.
Assuming such a level of deep representation that may participate in image schemas
and combinations of image schemas, as characterised in terms of blending (cf. Kutz et al.
2015), opens up the door to offering explanations of a variety of further phenomena.
For example, it becomes more straightforward to imagine the motivation for pre-
viously challenging effects such as shape’s evident cross-modality as discussed, for ex-
ample, by Deroy & Auvray (2013), also in a previous Shapes meeting. Certain appar-
ently arbitrary associations with shape across different sensory modalities have long been
known. Classic studies asking experimental participants to associate nonsense words and
abstract shapes, such as those reported in Köhler (1947) or Ramachandran & Hubbard
(2001), have shown that connections are systematic and reliable. A rounded shape, for
example, would be correlated reliably with the nonsense word ‘maluma’, while a pointed
or jagged shape would be correlated reliably with the nonsense word ‘takete’; Deroy
& Auvray (2013) offer further references to work of this kind discussing aspects of the
general phenomenon of cross-modal association. Such connections show that a simple
consideration of space only in terms of geometry is not yet sufficient. What is more likely
is that there is a fairly deep connection being drawn in the brain across quite diverse do-
mains and employing rather abstract features. Blending at level of affordances and image
schemas may offer a useful way of characterising such connections.
We can also see the role of this embodied anchoring of ‘shape’ in higher level con-
ceptual and linguistic behaviour. Consider, for example, a description offered of one of
his own works by Paul Klee, an artist who was particularly concerned with ‘cross-medial’
effects and who proposed ‘polyphonic painting’ as exhibiting many properties of music,
‘made spatial’. The work in question is shown in Figure 11; his description is as follows:
“A wide span from pole to pole lends space to breathe in and out deeply, which
can even turn into a wheezing struggle for air. A lesser span muffles the breath to
13
a sotto voce. Around about the grey area, it is only possible to whisper. Either you
raise yourself above this position to the violins or sink below it to the violoncellos.”
(quoted in Düchting 1997, 60)
Regardless of how we might judge this piece of text, and its performance of the genre of
‘aesthetic description’, one thing is clear: Klee is invoking an extremely high degree of
Figure 11.: Paul embodiment throughout. In his attempts to deal with his personal response to the various
Klee. Colour Table, shapes and their textures, he is thrown into a deeply embodied style of description.
1930, 83. Zentrum We can also draw attention to the potential role of this anchoring of shape in embod-
Paul Klee, Bern iment for even more abstract activities, such as mathematical reasoning. Morales & Sara-
cho (2013), again from a previous Shapes meeting, discuss the role of shape for problem-
solving in mathematics, arguing that much can be explained by appeal to rendering ab-
stract problems as shapes that can be manipulated. This they quite correctly relate to no-
tions of iconic representations as pursued in approaches to diagrammatic reasoning more
generally. As they write:
“Let us start by focusing on the idea of ‘shape’ in the sense of ‘iconic representation’.
Representations may be iconic, symbolic or indexical depending upon their role in
reasoning with signs in specific contexts of work. According to the traditional view
representations are iconic when they resemble the things they represent.” (Morales &
Saracho 2013, 118)
The notion of iconicity, and its contrast with ‘indexes’ and ‘symbols’ of course goes back
to the semiotics of Peirce, and it is then useful to pick this up again with more of the
Peircean background explicitly included.
The implications of Peirce’s categorisations are often still less than fully appreciated
and there is much to make use of. Particularly relevant here is the fact that Peirce’s
conception of ‘resemblance’, or likeness, that serves as the basis for iconic signs, is by
no means to be limited to purely visual resemblance. Examples given in the literature
readily focus on visual cases because these are far simpler to illustrate – but, in general,
iconicity can range across any senses and combination of senses. This applies equally
to the three subcases of iconic signs that Peirce distinguishes (cf., for an introduction:
Jappy 2013): hypoicons (i.e., icons at their simplest, relying only on physical qualities),
diagrams (where abstractions are drawn over the physical qualities so that only some
dimensions are considered relevant for the sign and others not), and metaphors (where
distinct domains are set into structural correspondence via ‘abstract’ resemblance). The
latter also overlaps interestingly with the notions of blending currently being developed.
Iconicity thus plays a central and foundational role for Peirce’s view of reasoning and
knowledge, precisely analogous to the role now being given to blending:
“The first things I found out were that all mathematical reasoning is diagrammatic
and that all necessary reasoning is mathematical reasoning, no matter how simple it
may be. . . . This was a discovery of no little importance, showing, as it does, that all
knowledge without exception comes from observation.” (Peirce 1976 [1902], 47–48)
If, then, we focus more on ‘resemblance of shape’, rather than resemblance of appear-
ance, as a basis for iconicity, and also combine this with the embodied perception view
of shape as a multidimensional structuring of affordances of particular kinds, then this
suggests even more strongly why shape is so foundational for many of our activities and
why it is so readily applied to such diverse cases, both physical and abstract.
14
6. Shapes and design and creativity
Finally, let us readdress some of the notions of creativity touched upon above and de-
sign – particularly the role of aesthetics in design. Everaert-Desmedt (2006) develops a
Peircean-inspired view of aesthetics and the creation of art works by recasting some of
Peirce’s accounts of logic and accounts of scientific creativity as artistic creativity. An
overview of her account is shown in the graphic reproduced in Figure 12.
Figure 12. Everaert-Desmedt’s (2006) characterisation of a Peircean-inflected view of artistic creation
It is useful and suggestive to run through Everaert-Desmedt’s (2006) steps in artistic
creation in slightly more detail and then to construe these simultaneously in relation to
design and to shape. First, then:
“At the outset, the artist is in an unsettled state, not due to a surprising fact, but to an
unsettling feeling. [He or she] is plunged into firstness, into a chaos of ‘qualities of
feelings’ (Peirce, 1931-1935, 1.43): a feeling arises that seems appropriate, but there
is no object to which it is appropriate.”
Subsequent to this, the process of semiosis steps in, as always for Peirce driven primarily
by abduction:
“The artist begins creating the work of art by using abduction. But while scientific
abduction consists in hypothesizing a solution to a conceptual problem, artistic ab-
duction or hypothesis consists in trying to express the problem, in letting qualities of
feelings arise, in trying to capture them, in ‘thinking’ them, and considering them as
appropriate.”
Here we can consider the particular spin and flavour given to this account when ‘thinking
them’ is seen in terms of embodied action and shape. The creation process then becomes
one of ‘thinking shape’.
This is a very different perspective to that pursued in the interest of scientific mod-
elling, or even of constructing ontologies. One common position adopted when consid-
ering ontology is that of Varzi, quoted below, where it is emphasised that one needs to
start from a deeper consideration and understanding of what is the case, rather than how
it may or may not be described in language:
15
“There is, in fact, no way of telling what sorts of things there are given the sorts of
things we say. But neither is there a complete gap between our words and the world
out there. It’s just that that bridge must be built from below, as it were: ontology
comes first, and depending on what we think there is, we must attach a meaning to
what we say. Going the other way around is wishful thinking.” (Varzi 2007, 35)
This is no doubt good advice for ontology construction, even though much more needs to
be said concerning the precise relations and, potentially, mutual dependencies between
language and ontology. When we are in the domain of design, however, where the aim is
not to find out what is in the world but to add to that world, then we can draw more pro-
ductively on the role of shape as guiding such processes. Perhaps then, to adapt Varzi’s
pronouncement:
This can involve creating ‘purposively shaped’ artefacts – not only for manipula-
tions in personal space but also to ‘inhabit’. The former naturally overlaps with the area
of product design, the latter closely with issues in architectural design. Particularly in
architectural design the role and effects of ‘shape’ have long been a central concern. In
Figure 13, we see a particularly finely articulated ‘shape’ of empty space. Again, much
of what makes this (and other cases) effective (or not) is the transferral of embodied ex-
perience across the diverse scales of experience. Further formalisations and experiments
Figure 13.: Interior
view: Church of the
in this direction are then clearly of considerable importance for gaining more theoretical
Gesù, Palermo, Sicily. and practical control of the notion of ‘shape’.
7. Conclusion
In this purely exploratory paper several lines of thought and literature have been brought
together in order to suggest that shape may need anchoring in a more encompassing view
of embodied perception and then, with the functionalities this affords, may go on to help
characterise a variety of processes of creative thought and design.
This anchoring of shape would naturally support the extremely broad application of
‘shape’ in a variety of discourses that is readily observed, providing more technical detail
to the commonsense notion that something ‘shapelike’ may be metaphorically extended
to apply in domains ranging from mathematics to music to argument and so on. The
nature of this metaphor can be connected directly both to Peirce’s particular view of
‘metaphor’ as a form of iconicity and its foundational role in reasoning and knowledge
on the one hand, and to currently developing notions and formalisations of blending and
its centrality for creative thinking on the other.
From the perspective sketched here, it does not become too far a stretch to consider
creative design as essentially a process of shaping, of forming shapes that have not been
16
formed before, for new purposes and in new domains – an interrelationship and process
summed up graphically as a final picture in Figure 14.
Figure 14. Design as shaping: the creative loop
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