Two clay pieces.

A tagua nut carved in 1986,
that often hangs on my neck.

My small bronze copy of a favela goddess,  near a ruled Boy surface

seen whole here.

A different take on the ruled Boy,
in red-blue stereo.


I started to sculpt as a graduate student, to improve my mathematics:
specifically, my sense of three-dimensional space, and up.
That sense of shape is still nothing like my brother's,
but it has recovered somewhat from my education.

Kindergarten was very 3D and tactile, but from about age 7 my teachers had systematically flattened my imagination.  All subjects had more and more intricate diagrams in the plane, more and more complex reasoning in the plane, but near nothing in three dimensions.  At university it was worse.  'Calculus in n variables' is really diffential geometry and topology, but I got Jacobian matrices and formulæ.  Graduate exposure to
Klaus Jänich and Max Newman, true geometers, showed me how much I had lost.  I began to cut wood and shape wire, to rescue my mind. (After an interruption to be student union president, elected on the Academic Thug ticket, I moved to Warwick to study under Chris Zeeman: later I had shape poured into my mind by Bernard Morin, who sees more with his fingers than most people do with their eyes.)  My brother patiently corrected my worst errors with matter.

I have moulded and carved a little figurative work (see left), but more of what some call 'abstract'.  I can half-agree, but when they call it 'non-representational' I beg to differ.  The brass piece above is a representation of a very real object in my world (a Möbius band with a hole around it).

Mathematical objects push back, as firmly as a wall: we cannot just decide that a circle is to be exactly three times as long around as it is wide, or that 93 is to be a prime number, the way we decide the boundaries of a nation or a time zone.  If Mount Everest is a real object, what is its lowest point?  Mathematical structures are a lot less arbitrary than that &mdash so much less arbitrary that Model Theory can actually prove there is a residuum of arbitrariness, so my mental version of 'the' Real Line can never be guaranteed identical to yours. They are thus a lot more real than the tragic empires built while we dream, but not quite as real as Plato would have liked.

I like to feel mathematics push back: in the mind, on paper, in the behaviour of computer code, and in the ways that physical stuff behaves.  One way to do this is called engineering and invention, and I have a few patents and papers about that.  Another is to explore mathematical form for its own sake in graphics and solid stuff (or liquid stuff: I would love to design fountains), and that is called sculpture.  I don't try to keep these apart: I started thinking about tensegrities when I had an idea for a new shape that could be beautiful.  Moving from graphics to materials I found how hard tensegrities can be to build, and set out to see why, mathematically.  Now I do see why, and also see how they can be easier to build, more robust, and tougher than people have been designing them.  This is sculpture leading to engineering.

Some of my early visual work appeared in 1977 in the gallery; shapes for communication of mathematical ideas, shapes for the pleasure in the shape, drawn or carved, mixed as they should be.  I shudder at most uses of the word 'mere', and 'mere decoration' and 'mere diagram' are among the worst.  The brain as a 'mere machine' is perhaps the silliest, showing determined ignorance of the subtle power of organised matter, but the most irritating is to value fine Art for its pure fineness, and to condescendingly admit mediaeval icons or Samurai knuckle-dusters that 'rise above' what the makers merely thought they were doing.  To excuse a maker's concern with Enlightenment or Cosmography or water supply, because it somehow achieved an artefact worthy of the Art Historian, is a deeper insult than honest narrow-minded disdain.

The Impressionists and Cubists didn't merely break rules: they built, gloriously.  Art fashions since have celebrated the rule-breaking for itself, not the creation of powerful disciplines that the old rules obstructed.  I like most typographers more than most painters.  Making your own rules is a deeper thing than sneezing on the rules of others.

I enjoy 'Pure Mathematics' though (contrary to my undergraduate expectations) much of my life has been in joyfully applying it.  G H Hardy boasted that "I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world," and would have been sad at his work's importance in the cryptography of web banking, but I delight in watching and feeling mathematics enacted by stuff: in the mind, on paper, in the behaviour of computer code, and in the ways that bronze and markets and clay and digital images behave.

Sculpture pages

Sculpture home
Ti.Zero Exhibition in Torino
Möbius band rearranging the hole
Klein bottle symmetrical views
Boy surface ruled and unruly

            Seven views of one hanging form.

Pages here and there

Where I've been
Anarkik3D (external)
Nordic River (external)
Therataxis (external)
Xelular sets (1st look)
Tensegrities (1st look)
Freedom by degrees
Ultrasound hotspots
Walk to NIAS
Joy of Ignorance

Carved wax for casting: surface spanning Borromean rings.

A virtual horned sphere volume rendered in 1999, that shows how the strange points can line up as a standard Cantor set.  Back before I had seen a computer, I hand-drew
two horned spheres for Manifold in 1971.  It pops up still on the Web.

The linked-ring pattern of the site background. Remove rings of one colour ⇒ the other two fall apart.

          foot of the page
          mostly plasticine