CYRIL STANLEY SMITH
31 MADISON STREET
CAMBRIDGE, MASS. 02138
April 1, 1981
Mr. Kenneth Snelson
140 Sullivan Street
New York, New York 10012
Dear Mr. Snelson:
Thanks for sending me your exhibition catalogue.
I can understand why most respectable scientists don't like your model of the atom - it is too definite and static - but I feel strongly that some kind of "portrait" rather similar to the ones that you build is necessary and proper for lay understanding, if not for detailed calculation. Like you, I think the indeterminacy principle has been misinterpreted and used to give a kind of fuzziness in regions where it is unnecessary to do so. Though it may be uncertain whether some electron/photon interaction will happen in a given time, there is no uncertainty in the kinds of interaction that do occur. The nodes of probability waves are perfectly definite when seen on the next scale of either time or space, and the interaction between the nodes and spins is quite as definite as in your models. At least I think so, though none of my theoretical-physicist friends are willing to see it this way. Neither do they like to think of an electron as localized, though it is (more or less) when the extended but decreasing strain field associated with it is cut off by a closed set of interactions with others surrounding it.
I'm increasingly coming to feel that interactions within atoms and between them depend on, or at least can be represented as, the same hierarchy of interaction between strain and structure that gives the mechanical interlock of the macro world of our sensual experience. There is a balance between reversible elastic strain within closed units and irreversible plastic strain involving the breaking of connections and their transfer between neighbours to give a new topology of larger closure. The soap froth is a superb model of all this.
Have you read Ernst Gombrich's new book, the Sense of Order? He makes much of the same elements in decorative art that I had been using in connection with super-atomic aggregations of structure. He talks of three elements in pattern - framing, filling and linking. These define selection of a boundary limiting the scale and region of interest pro tem; the particular pattern of interaction within the set limits of forces or of perception, or of thought; and the connections between this microscosm and the outer world.
In simple terms of connection closure and continuity. between vertices and polygons in a net this reduces to the following equation
where Pn and Vr , respectively, are
the numbers of polygons with n sides and of vertices of valence r, (r=l) and Eo
and Eb are the number of edges
on the outer boundary and those extending outside, respectively. You can see
this beautifully in Islamic mosaic patterns but any relationship that is
extended has at some scale a self-dual quality. Individuality is an internal
and local departure from a quadrilateral net of quadrilateral vertices. The
solid-state physicist's lattice dislocation is the basic key to hierarchy. It
gives grain boundaries in crystal aggregates but it also gives electrons in
atom orbits. Space is a lattice of unit cells of oscillation. between electric
and magnetic interactions of polar and equatorial expansion in adjacent
Planckian cells in a BCC lattice. This allows time and change of neighbours, or
constancy depending on thing-and-neighbour interaction. A spiral dislocation in
this lattice has all the properties of the photon; and two spiral dislocations
of opposite hand intersect to give an electron. And energy and curvature of the
whole results from the omission of entire unit cells. The inert gas atoms are
simple polyhedra with junctions between 2, 8, 18 or 32 quadrivalent vertices
formed by crossed closed dislocation
loops. Your rings cross 
perhaps.
Note that, since quadrivalent vertices and 4-sided polygons cancel in continuity, projections in two dimensions, despite their overlap and false vertices, conform to the above equation and reveal dislocations and anomalies in structures of any higher dimensionality. Your Chinese ball is like my atom, except that the net is entirely and the holes, representing the electrons, are dislocation junctions.
IÕll have a draft of a paper in a few weeks, but I don't expect it to be accepted by physicists any more than your nice models. Keep up the good work.
Very truly yours,
(signed) Cyril Stanley Smith
CSS/lc