Welcome

I use two-dimensional, three-dimensional knots and even four dimensional knotted spheres, as my inspiration. Mathematical knots have no loose ends and are, to me, always sinuous and beautiful. The mind-boggling aspects of knot theory hold tantalising mystery.

I would like to think that through my work, people can get a tiny peek into the extraordinary and strange branch of mathematics.

I have to admit that I do not do the mathematics! For the last 8 years I’ve had the patient, often humorous, explanations of the complex subject from professor Scott Carter, professor emeritus University South Alabama.

Knot theory has many important, real world applications. I urge you to google it.

If you are interested in buying one of my pieces, please contact me at

hocking.reid@gmail.com

KNOTS

The knot wall at the Crypt Gallery exhibition

Oct-Nov 2024

Big knot, 11_34, the Conway knot as a ribbon.

Black and white Pastel

Smooth Slice, a counter offering.

The black swirls and curves are taken from the solution to the long standing problem in knot theory. Lisa Piccirillo, an american mathematician solved the problem, finding that knot 11_34, the Conway knot, was not smooth slice. (Don’t ask!!) I emailed her and asked if we might meet on zoom sometime to talk about her work. I did not hear back from her. So I decided to have a bit of fun. I inserted a smooth slice into her solution. My slice is in no way mathematical, it is purely humorous.

Pastel, pencil and siberian charcoal

Two studies for Smooth Slice Pencil and pastel

Blue Knot 10-15 Giclee print

Three Knots

7_6, 8_6 and 9_4

Pencil

8-6 Emerging

This is a plaque 30cm by 20cm by 8cm. It is a 3D version of the center knot in the Three Knots drawing above. It is cast in plaster. It can be cast in almost any material

Zero, Three, Four.

Pencil

Five, Six, Seven

Pencil

Copper Knots

3,4,5,6,7,8

These knots are made from 3mm copper bar and are mounted on a lovely piece of cherry wood which was an extension leaf from my mother-in-law’s dining table.

White 5-2 knot

Giclee print

Knot 5_2 Suspended on an Idea.

Pencil

Mystery Knot

Giclee print

BRAIDS

Braids are basically knots that are flattened into 2D diagrams that show how the knot strand crosses over and under itself,  as in the adjacent image.

On Point The dancing braid of knot 10_55

Pencil

Copper Braid of the Conway Knot 11_n 34

3 mm copper bar mounted on wenge wood

Unfurling

A braid opening and unfurling, returning to its knot form.

Pencil

Kind of Like a Quantum Computer

I drew this before I learned that quantum computers employ braiding

to perform computations.

Pastel and coloured pencil

CONTINUOUS DEFORMATION

Curtain

An imagined diaphanous changing surface of a two-twist spun trefoil knot diagram.

Coloured pencil and pastel

Reidemeister Moves

These are the three moves which allow for the continuous deformations that are at the center of knot theory and its mathematical cousin, topology

Pencil

Reidemeister Flowers

This is a decorative play on the Two Twist Spun Trefoil knot stacked diagram as a vase and the Reidemeister moves stretched and extended as colourful flowers.

Coloured pencil and pastel

Spun Trefoil Knot

The spinning trefoil knot sweeps out a surface which passes through and around itself.

Giclee Print

Spun 5_2 Knot

Giclee Print

Spun Mobius Ban

Almost a Klein bottle

Giclee print

This wall was a mix of work based on fantasy and studies of the Hopf Link.

Fantasy

Hopf links drift through screens towards a mysteriou light.

Pencil and Siberian charcoal

Seeking

A fantasy of Mobius band seeking the 4th dimension to unite with their other selves to become Klein bottles.

Pencil

Chopped

Here I am playing with Mobius bands encountering the triangulation of the Klein bottle and being chopped into pieces. This uses mathematical idioms but is utterly unmathemathematical

Pencil

Study for Chopped

Charcoal

Naughty Knots

four pairs of knots adapted from the online catalog of mathematical knots; KnotInfo.

Pencil and coloured pencil

the following four images are Conversations in a Foreign language

Scott’s Secret

Three Solid Arguments

15 Statements, some a bit Fanciful

and

Twisting the Narrative

This series takes the Hopf link through several iterations. All the individual images represent the same two linked circles.

Pencil and coloured pencil