|I made this collage when thinking about All Lines Converge - the title for an exhibition
at the Govett Brewster Gallery.|
That thinking led to .....
The Mythic Line
Once upon a … do you remember? … we really believed in lines.
We would scratch along a ruler to indicate the infinite number of points to satisfy an equation. Uncountably infinite
points but we were confident of our line. Gradient, intercepts, all accounted for. With little arrows at the ends to
show that the line was greater than the graph, went beyond the desk, bigger than the whole school, forever.
As though the whole universe was laid out in Cartesian coordinates.
So many smug facts: a line is shortest distance between two points; parallels never meet (the older kids might add
‘except at infinity’ and we’d imagine a vanishing point of perspective, further away even than Auckland).
Knowledge chips away at belief. A line is one-dimensional, has zero width. So our graphs were gross and ragged
approximations. Perhaps the closest we can get to a line is an edge. The edge between two colours in a Mondrian
painting, neither one colour nor the other but between. So much like our idea of ‘now’. Between the long past and
the long future there is our now, occupying no time at all as future becomes past.
We live on a more-or-less spherical planet. So the shortest distance between two points is part of a great circle … those
sweeping curves we see in the in-flight magazines. The latitude parallels go around the world and join up, making
smaller circles towards the poles. Whereas the great circles showing longitude all converge and cross at the poles.
And yet the latitude parallels cross the longitudes at right angles, everywhere. By a school theorem, longitudes are
all parallel. But meeting at the poles.
So, to save our concept, we step away from our planet. Surely our x and y axes and our brave little graphs have meaning
out in space? And our beliefs have truth? Einstein’s theory of relativity gained its first supporting proof when
the path of light was observed to bend in the gravitational field as it skimmed past our Sun.
Space-time is curved. The line is dead.