the imaginary one with no edges that we referred to – is not translationally invariant because when one moves two squares to the right, one is not in a position identical to the starting point. One is two squares closer to the edge, closer to the defect.

Surfaces are only one example of crystalline defects. Another type of defect is called a vacancy and results from removing an atom from its proper place in the crystal and leaving nothing in that place. Vacancies can be responsible for the color in some precious stones as, for example, in a diamond where large numbers of vacancies produce a yellow color. If one takes cheap, less than perfect, diamonds and subjects them to high energy radiation, some carbon atoms are knocked out of position, leaving vacancies, and creating a ‘yellow diamond,’ which is considered attractive and can be sold as jewelry.

Still another kind of defect is the substitutional, in which a normal atom in the array is replaced by something foreign to the array. In the checkerboard, we could, for example, paint one white square red. The red is a substitutional. The color and value of emeralds and rubies result from substitutionals: emeralds result from substitution of chromium for aluminum in a silicate of aluminum and beryllium; rubies result from a substitution of chromium for aluminum in sapphire. Sapphire is simply aluminum oxide (e.g., corroded Coke cans) as are oriental amethyst and topaz with different substitutionals giving them different colors.

The chemists on Jubal who investigated the Presences would have found that they did not look at all like the silicon crystals used in computers, which have the fewest possible defects, but that they had very many vacancies and substitutionals – and dislocations.

This defect, dislocation, is the one that makes it possible for metals – and all metals are crystalline as they occur naturally – to be bent and deformed. Since dislocation is the only defect that ‘moves,’ it is an important one to consider in analyzing the Presences.

Figures 1 and 2 (see page 384) show the two types of dislocations that occur to some degree in all crystals. The first of these is called an edge dislocation (Fig. 1). It can be visualized as resulting when one makes a ‘half cut’ through a crystal and displaces the upper face perpendicular to the lower face, usually by one atomic distance. The second type of dislocation is called a screw dislocation (Fig. 2) and results from displacing the upper face perpendicular to the direction of the cut. Real dislocations are not as idealized as ‘edge’ or ‘screw’ represent them. Sometimes they form dislocation loops that wrap back on themselves, and at each point along the loop they will have varying proportions of edge and screw character. The region inside the dislocation loop is said to be ‘slipped.’ When deformed, the size of the slipped region changes. Sometimes it increases, sometimes it decreases. The amount of slipped region is proportional to the amount of energy stored in the crystal.

Dislocations represent small regions of deformation and they move in response to mechanical loading so that the deformation can migrate or extend from one region of the crystal to another. Dislocations exert forces on one another, sometimes forming stable arrays that are bound together and sometimes exerting repulsive forces that drive the dislocations apart. Energy is stored in dislocation arrays and can be released suddenly, manifested as fracture.

All of the requirements for ‘life’ can be supplied by dislocations. The storage and utilization of energy, which in biological life is accomplished through chemical means, can be provided by the interaction of dislocations, which would act as the molecules of a crystalline life form. Does this mean it could think? Is there some mechanism through which information could be stored and recalled?

Let us imagine a dislocation moving through a crystal in response to some deformation. Let us suppose that while this dislocation is moving on a straight front, it encounters two or more substitutionals. It has been observed that the substitutionals ‘pin’ the dislocation and do not allow it to move further. Between the substitutionals, however, the dislocation begins to ‘bulge,’ much as a sail bulges when pushed by the wind and pinned by the mast. When the deformation energy reaches some critical value, the dislocation can bulge no further and pinches off, wrapping back on itself and forming a dislocation loop. This loop is then free of its pins and moves forward, leaving behind a dislocation segment still pinned, which becomes the source of the next dislocation as the loading continues. This source of dislocations is called a Frank-Reed source.

From examination of the distance between dislocations generated by a Frank-Reed source, one could, in principle, reconstruct the deformation history of a crystal. Thus dislocation arrays contain information and could make up the most important component of a ‘mind’, that is the ability to store and recall information. A very elaborate and complicated array of Frank-Reed sources could operate as an anabolic path for the storage of information – not visual information, which is what we are accustomed to, but mechanical information, the entire deformation history of the crystal. The arrays would record heating and cooling, shifts in the earth, changes in the crystal’s own weight, and, very important on Jubal, sounds. Sunlight would be received only as heat and be perceived in the infrared. People and animals and climatic manifestations would be perceived by the sounds they make. Wind would be perceived as push, lightning perceived as heat and shock. The crystal would be, in fact, one enormous tactile being that could feel a wagon moving on its surface or feel a Tripsinger’s music.

How about growth? Crystal growth is also frequently dependent on dislocations. When a seed crystal is in contact with a solution or bath of the constituent atoms that make up a crystal, and when the conditions are right, a crystal will grow. Anyone with house plants has observed crystals growing on the soil surface or edges of

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