The shape of two-dimensional space

Genomics, so fashionable today, is only half of the secret of life. The other half of the secret is shape, form, morphogenesis and metamorphosis. The gene may prescribe what is synthesised, but the proteins appear and operate in a pre-existing environment which they then change. The first step towards life is the appearance of a micelle, a spherical membrane, a surface which separates the world into inside and outside. We are here concerned with surfaces, with a particular subset of two-dimensional manifolds embedded in three-dimensional Euclidean space, namely the non-self-intersecting, periodic minimal surfaces of cubic symmetry, which separate the world into two regions as an infinite plane would do, but with much more complex topologies. Like the Platonic solids , these cubic surfaces are geometrical absolutes and have distinctive topologies but entail no arbitrary parameters . The objective is to enumerate at least some of these surfaces, for probably an infinite number answer to this description, to draw attention to their geometry and to point to some of their applications and occurrences on various scales between mega-engineering and nano-technology. These objects are solutions looking for problems

Generalized crystallography

X-ray crystal structure analysis can now be seen as a special kind of microscopy which is being extended to the recognition and examination of many kinds of ordered structure more general than crystals and which leads to their synthesis or construction by various methods. Electron microscopy and many other techniques now combine to give a coherent science of structure at the scale range of Ångstroms to microns, atoms to assemblies visible to the eye, which should continue to be called crystallography although it overlaps with nanotechnology, molecular biology, and solid state physics. Most generally, a crystal is a structure the description of which is much smaller than the structure itself and this view leads to the consideration of structures as carriers of information and on to wider concerns with growth, form, morphogenesis, and life itself

Lucretius or the philosophy of chemistry

A world view deriving from the objective knowledge acquired by the physical sciences is contrasted with the fashionable subjective philosophical view that all systems of thought are equally valid ways of structuring the universe. As Lucretius guessed, atoms are real and are not simply arbitrary constructs to explain the observations. Mathematics and computing have an important role in permitting long and sophisticated arguments to be carried through

From “the dialectics of nature” to the inorganic gene

The concept of projection from one space to another, with a consequent loss of information, can be seen in the relationships of gene to protein and language description to real situation. Such a transformation can only be reversed if extra external information is re-supplied. The genetic algorithm embodying this idea is now used in applied mathematics for exploring a configuration space. Such a dialectic – transformation back and forth between two kinds of description – extends the traditional Hegelian concept used by Engels and others of change as resulting from a resolution of the conflict of two opposing tendencies and provides for evolution of the joint system

Quick disconnect latch and handle combination Patent

Quick disconnect latch and handle combination for mounting articles on walls or supporting bases in spacecraft under zero gravity condition

Periodic minimal surfaces of cubic symmetry

A survey of cubic minimal surfaces is presented, based on the concept of fundamental surface patches and their relation to the asymmetric units of the space groups. The software Surface Evolver has been used to test for stability and to produce graphic displays. Particular emphasis is given to those surfaces that can be generated by a finite piece bounded by straight lines. Some new varieties have been found and a systematic nomenclature is introduced, which provides a symbol (a ‘gene’) for each triply-periodic minimal surface that specifies the surface unambiguously