Spatial Connections

An Informal Introduction to Qualitative Space &its Interdisciplinary Connections

John Stell

School of Computing, University of Leeds

November 2015

In a nutshell:

I Some approaches to spatial thinking are not well-knownoutside artificial intelligence

I The approaches are qualitative in that they don’t usenumerical co-oordinates, but they can still be processed in thecomputer – using logic rather than arithmetic

I Some of these appear to have connections with Art, Design,Cultural Studies, Ethnography, . . .

I Exploring these connections might lead to discussions andeventually to research collaborations, bids for funding, writingand other outputs

What I’d like to do:

I Say something about myself and my background

I Introduce the spatial ideas

I Suggest some possible connections

I Hear your ideas about other connections and possible ways ofexploring these further

I’m a Senior Lecturer in the School of Computing at the Universityof Leeds

My academic work includes research in mathematical aspects ofknowledge representation (as part of artificial intelligence) . . .

. . . but I also have a background which is much moreinterdisciplinary than such papers might suggest

I was fortunate to be able to study part time for a degree in FineArt at Leeds College of Art (2004–2010)

I was especially interested making work about processes oftransmission and representation.The following, which can be read as a map, is from the 2010degree show . . .

as long ago as 2005 I had funding from AHRC and EPSRC for‘Spatiality in Design’ which included collaboration on 3D drawingwith the artist Claude Heath

we built a system where artists could easily create 3D drawingswithout having to learn how to use a complicated piece of software.

this system no longer exists, but it would be very interesting to seehow a system with more recent technology might be built

Claude (well known for blindfold drawings in the 1990s) often usedthe system without looking at the drawing developing on thescreen.

In the next two slides he transcribes the whole universe . . .

my own more recent involvement with drawing projects appears inthe recently published Drawing Paper 8. (I have several copies togive away – please ask)

This came out of a small part of a much larger project led bySheffield University and funded by AHRC under the ConnectedCommunities programme

Maybe we could could use drawing as a way of exploring spatialconnections and opportunities for collaboration?

To understand some of the spatial ideas I’d like to introduce, letsstart with mapping.

Conventional maps look like the next slide whether on paper or thescreen

this is a classic example of space as a rigid framework in which weplot an imagined external world by conventional notations. Spatialthinking in modern geographic information systems is essentiallythe same as in the map from a 100 years ago on the previous slide

but artists, psychogeographers, and many others, don’t use thiskind of rigid objective space in mapping activities. The next slidesshow a couple of examples . . .

Sohei Nishinosoheinishino.com/en/works/dioramamap/london/

Simonetta Morowww.cartagram.com/3343/painting-personal-cartography/

the following could be seen as a collision between a kind ofpsychogeography and conventional mapping . . .

biomapping.net

. . . the Greenwich Emotion Map places a creative vision of socialspace into a computer based mapping paradigm which may notaccommodate it.

One of my main points in this talk is to say that there are muchmore flexible ways of thinking about space that you can also docomputation with but which psychogeographers, artists, etc seemto be unaware of.

What would happen if we could explore these less known spatialideas? This is somewhat speculative but is exactly the kind of riskyand novel activity that the Research Councils say they want tofund.

but it’s emphatically not just mapping. The ways of thinkingabout space I’m referring to appear to have connections muchmore widely

let’s start to see what these ways are . . .

the following is part of a mapping project of my own

Here notations are created by a process of walking through anenvironment. The places and events co-create the mapping withthe walker.

One topic to explore would be the way this generates acorrespondence between the space of the environment and thespace of the image and to ask how this relates to conventionalmapping

Euclidean Container (Conventional Cartesian space)

(2, 3)

(6, 1)

in this view everything is built out of points

even two-dimensional regions are just (infinite) collections ofindividual points which can in principle be separated easily fromsuch collections

Regions not points

Is it helpful to think of space as built out of points?

Can we experience points?

What about regions as the primary components of space?

Connection (A. N. Whitehead 1920s)

Connection

think of regions being connected when they overlap or just touch

Dis-Connection (an alternative approach)

Leonard and Goodman, Calculus of Individuals

“discreteness” (separation or apartness)

x eb y

part defined in terms of separation:

x is a part of y if everything that is separate from y is alsoseparate from x

using connection other spatial relationships can be defined usinglogic (which means we can use computers to carry out or supportreasoning and argumentaion about these concepts)

Next we see eight ways that two regions can be related

The slide shows how the Yellow region relates to the Blue region. . .

RCC8 (Region-Connection Calculus)

Topology not Geometry

The systems of Qualitative Spatial Representation I’m talkingabout are not the same as conventional Topology (which in oneapproach reagards everything as built from points)

but they would (at the RCC8 level of description) regard therelationship of the red region to green region to be the same in thetwo cases on previous slide.

but don’t assume that regions have to be one piece or to lack holes– they can be far more complex. The following slide shows a singlered and a single green region that are disjoint from each other . . .

Topology not Geometry

Aestheticodes (Collaboration with Nottingham)

This is two current EPSRC funded projects, led by Nottingham, inwhich I am bringing Qualitative Spatial Representation into theirwork on aestheticodes

These are codes like QR codes but work by the topologicalstructure of a design or image like these . . .

Aestheticodes (Collaboration with Nottingham)

Egg Yolks (Vague Regions)

Much more can be said about different kinds of regions

They need not have definite boundaries.

In the next slide the Egg can be interpreted as a region withuncertain boundary (it lies somewhere in the white, between theyolk and the outside

Egg Yolks (Vague Regions)

Relations between paths, tracks, etc

Qualitative space doesn’t only consider regions of two or threedimensional space.

Relations between two tracks could be that they never meet, thatthey touch briefly, that they converge and become one, that theycross just once, . . .

Spatial relations can be also considered between a trajectory and atwo-dimensional region. For example one trajectory crosses adomain, another enters it and never emerges, a third follows theboundary but never encounters the interior, . . .

We can think of paths in continuous space or as routes in anetwork (often called a graph by mathematicians). For example asequence of stops on the London Underground or in Tokyo . . .

Discrete Space

“To understand what we mean when we say that space isdiscrete, we must put our minds completely into therelational way of thinking, and really try to see the worldaround us as nothing but a network of evolvingrelationships. These relationships are not among thingssituated in space – they are among the events that makeup the history of the world. The relationships define thespace, not the other way round.”

(Smolin 2000)

Discrete Space

Discrete Space (Different kinds of outside)

Boundary

NegationRegion

Supplement

Boundary as site of contradiction

Mel Bochner

What is the relationship of Mathematics to Conceptual Art?

Many diagrams in work on qualitative space resemble MelBochner’s spatial-linguistic pieces.

This is more than a superficial analogy and suggests anotherdirection for investigation

There is a formal logic associated with networks where the usualcontradiction in and not in is no longer a contradiction but reallydoes describe the boundary of a part of a network

Logic not Arithmetic

The role of computation is to support reasoning about spatialsituations, not to calulate exactly where things are.

The kinds of logic this needs may not be classical Boolean logicwhere everything is either true or false and nothing is both.

The concept of a boundary naturally suggests a logic admittingcontradictions – what kinds of logic do other spatial situations leadto?

Qualitative descriptions of space are not a fixed set of things thatmight be “applied” to problems elsewhere – we can think aboutinvestigating new sets of qualitative relationships ininterdisciplinary situations in a process of co-production.

Discrete Granularity (Level of Detail)

what happens to spatial relationships as you zoom in or out?

what does it really mean for two representations to represent ‘thesame thing’ but at ‘different levels of detail’?

These questions are not easy for conventional geometry and spatialthinking; in qualitative space or outside classical logic they areeven less straightforward

Some of my current research is about using a lens to view networksat different levels of detail.

Mathematically the ‘lens’ is a relation on the network and this isapplied to mathematical morphology on graphs and to generalizingrough set theory to rough graph theory.

More . . .

Much more could be said

What about spatial regions that change over time?

What about combining change in level of detail with change overtime?

What about qualitative descriptions of regions containing things,for example crowds of people or migration?

What about the interaction of space and sound?

What about knots? Can Qualitative spatial reasoning talk aboutknots as physical objects and knottedness as opposed tomathematically ideal knots?

To move on:

I Some approaches to spatial thinking are not well-knownoutside artificial intelligence

I It’s about commonsense space.

I Some of these approaches appear to have connections withArt, Design, Cultural Studies, Ethnography, . . .

I The approaches are qualitative in that they don’t usenumerical co-oordinates, but they can still be processed in thecomputer – using logic rather than arithmetic

I Exploring these connections might lead to discussions andeventually to research collaborations, bids for funding, writingand other outputs