Crystallography with its rigid rules of form and symmetry provides a way to consider undiscovered facts and properties of complex problems.
Crystallography is a course that is dreaded by Geology students worldwide because it requires the mastery of solid geometry and considerations of three-dimensional forms that have planes and axes of symmetry which meet at varying angles and may also be inclined. It is comforting to know at the outset that there are only 32 crystal classes what may be expressed in a wide variety of regular and distorted forms. All crystalline matter including diamonds, salt and metals can be classified into one of these forms.
This is hardly new science. The basic concept that any given mineral had a distinctive crystalline form was recognized in the Greek and Roman classical period. Galena, the common ore of lead, fascinated people because when it was broken it was reduced to smaller and ever smaller crystals which kept their distinctive cubic shape. The same was found to be true of salt, calcite, fluorite and other minerals that were commonly encountered when mining metallic and non-metallic ores. By the 1700s, minerals were being named and described and the science of crystallography emerged, with a lot of pioneering work done in German Universities. In 1898 Edward S. Dana of Yale published the first edition of Dana’s Textbook of Mineralogy. Because it was in English and used frequent references to old mining districts in the U.S., the early editions are particularly important. My personal favorite is the Fourth Edition published in 1932 which includes information obtained from the X-ray studies of minerals which for the first time definitively illustrated why crystal forms existed as they were seen. Current editions of Dana’s textbook are still in print and are recommended to anyone interested in crystallography or gems and minerals.
Crystallographic Shapes as Applied to Complex Problems.
When faced with any possible action it is possible to believe that there may be an infinite number of possible impacts and effects. Because of the huge number of possibilities it is easy to ignore even some of the more obvious in the drive to push forward to get the product released or the concept put into action. Using crystallographic forms enables a person to regularly consider a large number of possibilities that can also allow space for the later inclusion of things that are not presently known. These forms are gateways to multi-dimensional thinking that can regularly incorporate considerations of space, time and environmental impact and may be expanded, in the manner of fractals, to cover any number of present and future possibilities while building on the same structure.
Nature is always a good teacher, if we humans take the time to investigate its properties and what billions of years of trial and error have produced. In fact, the R&D work has already been done, it is up to man to recognize it, adapt it and use it to its best advantage.
The Crystal Classes
- Isometric (Cubic ex. Salt) This system has two axes of equal length that meet at right angles.
- Tetragonal (ex. Rutile)Two equal horizontal axes and one that is non-equal.
- Hexagonal (ex. Quartz) One center axis (usually the longest) and three horizontal axes of equal length.
- Orthorhombic (ex. Chrysolite) Three axes at right angles to each other all of different lengths.
- Monoclinic ( ex. Feldspar ) Three axes of unequal length with two intersecting at 90 degrees and the third being inclined.
- Triclinic (ex. Axinite ) Three axes of different length with all inclined to each other.
In picking a crystal model to best reflect the question being considered the most significant impact of whatever is being considered can be considered the long axis of the crystal, which the lesser influencing factors can be considered the shorter axes. Inclined axes provide a way to illustrate that one property of the subject influences one of the other properties more than another.
Just to discuss the potential utility of the Isometric and Hexagonal Classes. The cube has six sides. Using what I will call the Hovey Investigation Cube, these sides are used to respectively examine the following:
- What would be the results if the system, plan or invention was not adopted?
- What are the consequences over time?
- What are the environmental consequences?
- What are the volumetric consequences?
- What are the financial considerations?
- What are the results if the plan was adopted?
With a cube each of these considerations is given equal weight. If two or more questions are only partly answered and more work is needed another and they somehow react, say environment and time, another cube is constructed that joins those two planes on their intersecting edge. If three questions interact then another cube is done that joins on a corner. In the unusual event that only one factor remains to be investigated a cube would be joined on a face of the cube.
If the questions were much more specifically stated then another form in the cubic crystallographic system could be selected, say an 8, 12, 24 or 48 sided form could be chosen and the different areas allowed to the crystal faces signifying the degree of that components’ impact on the final result. An outcome with a large impact would have a larger face on the crystal-form appearance of the concept immediately indicating its supposed significance. Perhaps there were at the time only 14 known consequences which would have to fit, under this system, on a 24-sided solid form. This allows for those unused crystal faces to be utilized for the “unknown unknowns” and emphasize that there were a large number of unknown possible consequences. This is in sharp contrast to linear thinking which goes event-result-consequence.
In the Hexagonal crystal class a fully formed quartz crystal has a long central axis, the C axis, and three intersecting A axes yielding a six-sided crystal with a hexagonal pyramid at the top and bottom. This would be useful in visualizing a concept where the central idea, say river flooding could be divided into six components which in turn had two individual impacts. This would allow 18 different aspects of river flooding to be illustrated in one figure. Again, any blank faces could be left to illustrate the impact of potential unknown consequences. If more results were to be considered the number of faces on the crystal could be doubled which would also double the number of faces on the terminal pyramids.
To an investigator any blank faces on his crystal model would be considered bothersome which will encourage independent thought on other perhaps previously not considered factors to complete his crystal model. Using such a model also forces the investigator to decide in this presentation which factors have higher values than others. While Nature loves symmetry, real world actions are often not symmetrical with some events related to the same cause outweighing others, and are shown as such by the relative sizes of the crystal model’s faces.
Once the models have been put into the system and possible consequences identified, Machine Learning and model computing will allow the construction of such models which, in the manner of fractals, can be extended to encompass any size system. To my present knowledge no one has taken this significant step. The preparation and presentation of such systems aided by Machine Learning is an untapped source of potential Theses and Dissertations.
This system of modeling complex systems using crystallography can assist in making the best choices when making decisions where there are complex interactions. Problems that might be investigated using this method include:
- Political policy decisions
- Sea level rise
- Water allocation
- Social questions
- New product development
- Scientific discoveries
- Artistic expression
- Macro and micro finance
- Air quality
- Global warming
- Earthquake risks
- Weapons development
- Resource extraction
These are some applications that come immediately to mind, but doubtless there are many more. Inquiries like this are but one potential example of the results that might be obtained from completing the career or job selecting exercise discussed in my book, “Create Your Own Job Security: Plan to Start Your Own Business at Midlife.” Many when they think of businesses they consider only a store selling something. While this is business, it is far from being the only type of business that a person who is gifted in another direction might take on and do well at.
New knowledge and new approaches have more value than comes from personal satisfaction, provided that they can be publicized and acted on. Knowledge without action will have little or no consequences. The world will not beat a path to the door of the inventor of a better intellectual mousetrap, regardless of what the popular saying says.
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