Traditionally, the recipe for jugged hare begins with the instruction; ‘First catch your

hare’. There is a lot to be said for a recipe like this. Not the least of which is that it

doesn’t miss the obvious. With this example in mind perhaps the ﬁrst instruction for

Intense Seeing has to be, deﬁne your space of exploration. In order to make this instruction

widely useful we should not be limited to thinking about the three-dimensional,

Euclidean, space we are used to navigating around in everday life. In fact it is useful

to learn a few visualisation and conceptual tricks from physicists, who are very used

to manipulating spaces that are different from 3D space. In particular the concept of

a phase space repays consideration, this is an idea that was originally developed by

the brilliant American theoretical physicist Josiah Willard Gibbs (1839-1903), but it’s

general approach is very widely used.

In maths and physics a phase space is the space of all possible states of a physical

system, with each possible state of the system corresponding to one unique point in

the phase space. This mapping of what a physical system is to a single point in a

high-dimensional space is a ﬂexible and powerful concept and by using the word ‘state’

physicists do not simply mean the spatial positions of all of the objects in the system

of interest, these would occupy a physical space or conﬁguration space, but also their

velocities or momenta. These two sets of quantities allow a physicist to understand not

only the initial state of the system but also allow them to follow the evolution of the

system over time. In phase space a changing set of positions and momenta track out a

path over time, to produce a distinctive ’phase portrait’ of the dynamics of the system.

In any scientiﬁc or artistic exploration then it pays to have, or develop, a sense of

the shape and scale of the phase space of interest. In order to keep the following free of

mathematics, I will not explain phase space in the strict manner that physicists use the

expression, butt rather try and widen the concept to signify a high-dimensional space

that encompasses the entire range of exploration, taking into account ‘dimensions’ that

are not spatial; cultural, temporal, intellectual.

This is best illustrated with an example inspired by the lifelong work of Ed Ricketts

in the tide-pools of the Paciﬁc coast.

The figure (a) shows a simpliﬁed map of the coastline of the Monterey peninsula

on the Paciﬁc coast in California. Using this map we can deﬁne any point along

the coastline between Monterey (M) and Carmel-by-the-Sea (C) by giving the linear

distance along the coast line in kilometres. For example, take the point p which is 3.4

kilometres from Monterey. Zooming into this point we show a 200 metre stretch of the

shoreline facing Spanish Bay. The hatched regions shows the extent of the inter-tidal,

or littoral, region of this stretch of beach, which has an area of about ?? m2. Zooming

in again to the line a − b and looking at this line as a cross-section through the beach we see in (c) the topography of the shoreline and the mean sea level. During the

normal ebb and ﬂow of the tides the sea level rises and falls around this mean level

and maps out on the shore an intertidal area that reﬂects both the range of high and

low tides and the local topography of the shoreline. Now in (d) we show a phase space

representation of the rise and fall of the sea level at the point p. The position of the

point is a one-dimensional distance and this is the x co-ordinate measured in kilometres

and the sea level height is the h co-ordinate measured in metres. This is a new way of

looking at the state of the sea level on the Monterey coast. Each and every point in this

new two-dimensional phase space represents one particular ’state’ of the interaction

between sea level and the coastline of the Monterey peninsula. We can also deﬁne

volume of interst within this space – for example, the grey bar shown is the volume of

the phase space represented by the beach at Spanish Bay, over the course of the full

cycle of the tides.

Using this phase space representation we can conceptually interogate the Monterey

peninsula coastline in a number of different ways by describing different ’volumes of

exploration’ within the phase space (they are strictly areas but we soon extend to 3

dimensions and higher in which volume is a better term to use).