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Anyone who subscribes via my PayPal button
will see that I uploaded a banner image onto the payments
page. Unfortunately, PayPal seems to have
trouble preserving resolution. It asked me to upload
an image that was 1200×800, but then scaled it to
616×200 in a particularly horrible way.
This is my original:
And this is the image as PayPal prefers to display it. Its fuzziness is
but there is one good thing. It gives me an
excuse to introduce the topics I'll probably write
most of my articles about: art, meaning, maths, and
cartoons. I'll start with
the need for more "intelligence" in
image processing, and then explain how this relates to the objects
depicted in the image.
The Power of Line
Artists often talk about "the power of line". For example,
here is the
for a recent
of essays, The Power of Line: Linea III:
There are no lines in nature — they are always the creation of
manifestations of human action, perception, and design. Lines can divide
or connect, may be static or full of movement, and represent and create
forms in space and time. And in many cultures, lines take center stage in
science, art, writing, drawing, and construction. Employing a vast array
of academic perspectives, this fascinating collection delves into the
phenomenon of the line, as well as the power it holds for us.
From the history of art and science to philosophy, the essays in
of Line elucidate the semantic and conceptual depth of the line in
European, Asian, and Islamic cultures. As they trace the continuity and
transformation of the line over the course of centuries, the authors not
only reveal it to be a constitutive element in architecture, art, and
writing, but also uncover its importance as a medium of expression in both
choreography and the scientific and technological fields. With copious
full-color images, The Power of Line is a captivating exploration
line as an essential artistic and cultural means of expression.
But what do artists mean by this? I know few
who have described their own reactions to line,
and many non-artists who look puzzled when I
this essay, I set out my own experiences.
Some of these may arise from quirks and
cross-connections of brain wiring that
we might not expect to find if our brains
had had a rational designer.
We can easily show that drawings are
about more than just the objects they depict.
Here are recent or current logos of
Labour, the Liberal Democrats, and the Conservatives,
England's three main political parties:
The Uses of Line
This month, I'll turn from connotation
to denotation, looking at
the surprisingly varied ways in which the lines
are used to convey geometry, surface
quality, and tone. I'll show that
the lines in drawing are an invention. They
give the artist a chance to collaborate with the
original scene in new and surprising ways, inventing
or adapting a graphic language into which to translate them.
I'll look at a few
examples of such languages. I'll also argue that
it is not wrong to omit or exaggerate information;
in fact, the constraints of the language
mean doing so is essential.
Line drawings can be very simple:
Artistic Style, Mirror-Earth, and the Twelve O'Clock Rule
In my introduction, I said that category theory
has been used in some impressive
mathematical approaches to semiotics.
Taking the view that the relations
between mathematical objects are more important
than the objects themselves,
this branch of mathematics provides
conceptual tools for working with networks
of objects linked by relations, and
for relating these to other networks.
I'm going to explain how I applied this to
a mathematical description of
what artistic style is.
Let's start by imagining a car driver
who can magically jump to a mirror-image
Earth where everything is reflected, including roads.
In mirror-England, people drive on the right
and overtake on the left, while roundabouts go