Extended Exploration Techniques for Exploration Geologists
and the Science behind Riemannian Geology.

By

George Stuart Green, B.A. Geol.

© 2012 George S.Green

ISBN: 978-0-9919761-3-3 (html)

 

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PREFACE

In Extended Exploration Techniques for Exploration Geologists, I rely on the material I generated with the writing of two other papers; Riemannian Geology and; Creative Exploration Geology. Creative Exploration Geology was written as a hint to what came forth with the writing of Riemannian Geology.

With Riemannian Geology I did not however, feel as though I did a very good job of explaining some of the reasoning behind this newly defined science. It was difficult enough to write, as I had to take what I knew to be the case on this matter and put it into words, and yet I felt that I could do a better job.

This new work is titled; Extended Exploration Techniques for Exploration Geologists and the Science behind Riemannian Geology and with it I try to use a more descriptive language. It employs much of the text of my two previous papers; especially and perhaps all of the text of my Riemannian Geology paper as that is central to this discussion. There has been some minor editing of each of these papers.

I would, if I could, regale you with the tales and exploits of an exploration geologist but that would be more like literature and I am not that good of a writer.

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Creative Insight

In order to get a handle on the creative processes of nature which were responsible for forming a particular mineral deposit, we (geologists) must use a method of exploration practice that will enable our own creative consciousness to come into alignment (in terms of understanding) with the natural creative processes of nature. Contained within this manner of exploration practice is a 'process of discovery' which if properly understood and applied, can be used to successively generate successive mineral discoveries.

Mineral deposits just do not happen instantaneously. They grow. Minerals and mineral deposits grow. And as they grow, certain processes (which must be discovered) govern and direct their growth and emplacement.

The use of the practice of forming multiple working hypotheses in exploration geology, allows geologists to discover and reflect upon the actual, creative processes of nature that were responsible for forming the geology of any particular mineral deposit. As our understanding of these processes grows, we eventually find ourselves being led towards the making of additional discoveries concerning these processes and the minerals and deposits they produce.

As exploration work progresses therefore, a body of knowledge and insight is developed, sufficient enough to allow us to be able to predict results in advance of testing. At this point it can be said, that we have achieved a 'mastered working hypothesis'. This is an operational working hypothesis that enables a geologist to confirm how well the geology is understood by being able to predict results in advance of further testing.

When we generate hypotheses and test them, we are doing so to see if we can discover what ordering of creative processes of nature were responsible for producing a particular geological setting and the minerals deposited within that geological setting. By this manner of exploration practice, (the formation and testing of hypotheses) we can actually be led to the making of an additional discovery.

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With a "mastered working hypothesis" in hand, we are in a command position to understand fully a particular geological setting and to know where a particular mineral is and why it is where it is. By knowing this, we are now in a position to predict the likely location of another mineral deposit. In a manner of speaking, by this process, we can actually create our next discovery as we search for it. What then is this "process of discovery" and how does it work?

If we try to by-pass this creative effort, we may end up with little or nothing or nothing more than what was originally discovered or originally indicated. So what is it about this manner of exploration practice that makes it work?

In the course of my experience as an exploration geologist, I began to realize that it was possible to generate successive mineral discoveries from a properly orientated and properly directed exploration program. My first paper on this subject was titled; Riemannian Geology and it came about as I set out to define the science behind this capability.

The text of that (2010) paper follows here, as I once again set out to explain the science behind this capability. In this particular work, and with aid of text taken from my other paper; Creative Exploration Geology, I am going to elaborate upon these observations and try to help my reader better grasp the methods of the science behind Riemannian Geology.

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Riemannian Geology

In 1854 Bernhard Riemann put forward his insight into the process of discovery that he used as a mathematician to conduct research investigations into the subject of geometry. That paper was titled; On the Hypotheses Which Lie at the Foundations of Geometry (1). Apart from questioning the hypotheses upon which Euclidian Geometry is based and offering an alternative, Riemann indicates that mathematical processes that describe an evolving geometric process are similar to the observational processes used by the mathematician to examine that geometric process.

In his own way, Riemann managed to give mathematical (and indeed geometrical) expression to the evolution of higher levels of perception. So, just as an evolving geometric process describes a lower order geometry going over into higher order geometry, conceptual perception can be added to conceptual perception to generate an even higher order conceptual perception. This is possible so long as one's object of study be regarded as being variable, and re-evaluated as a subsumed feature of each new higher order conceptual perception (2).

In the geological sciences this principle is known as, the Law of Multiple Working Hypotheses. The practice of forming multiple working hypotheses is an approach to problem solving, wherein the suggestion of a solution contained within new evidence, is weighed in view of the evidence gathered to date, while the hypothesis overall, remains open to productive alteration. It is not a process of logical deduction or a deductive method. Perhaps best described as ‘productive reasoning’ it is a process for generating a correct conceptual perception of reality; in this case, a geological reality.

Riemann viewed not only geometry but the mental processes involved in objectively studying geometry, as a construct of multiple connected manifolds (interconnected geometries). He deals with geometry, the geometry of a concept, a concept whose modes of determination form a continuous manifold-geometry, that continuous manifold-geometry, and continuous progress within it, either forward or backward (3).

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Georg Cantor’s 1871-1883 development of his own concept of transfinite orderings reflects upon a similar approach. All of these elements are involved in what constitutes geological reality. They are also present in the conceptual processes defining and underlying exploration practice in exploration geology (4).

An individual geological formation can be thought of as being a, discrete manifold geometry, marked off in time. When formations are connected to one another they establish a continuous manifold geometry. In terms of geological history they begin to establish a time continuum. A time continuum, as a concept whose various modes of determination (it being made up of geological formations) form a continuous manifold. Continuous progress is possible in two directions, forward in the geological time continuum or backward in the geological time continuum. This is Bernhard Riemann's concept of a geometry of multiple connected manifolds functioning in the geological sciences. Cantor’s concept of the transfinite is also being reflected in this approach (5).

Superimposed upon this, is the ‘deformation geometry’ established by the deformation of those geological formations. The form of this geometry is reflective of the forces applied to bring about such deformation. Underlying and connecting structural form to the forces responsible for producing said form, is the suggestion of the force or forces responsible, conveyed to the mind of the geologist by this deformation geometry. In short, the suggestion of a solution is contained within the deformation geometry of the problem. The geologist must remain receptive to the influence of this ‘suggestive’ mechanism.

Geological formations, deformed by geological forces into some sort of geometric form, like an anticline, are, by virtue of their geometry, reflective and/or suggestive of the forces applied to bring about that deformation. This 'suggestion of a solution' contained within the geometry of every structural characteristic, is linked with force and form throughout geological time. It is by this means that our geologist becomes informed to know something about the forces and forms of expression of those forces as they affect and shape the geology of the area under study.

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Divining a comprehensive understanding of the geology of a mineral deposit involves a developed understanding of the forces responsible for producing those geological phenomena. This understanding should be consistent throughout geological time. It should correlate concisely in the local and regional geological settings and it should connect up with several other fields of study in the geological sciences as they relate to the exploration work being carried out.

For example, Physical Geology (as a discipline of study) can be seen as the study of physical (stressing physics) forces translated into form. Historical Geology, connects form to form throughout geological time. Stratigraphy represents in form, a reflection of the energy throughput of the forces responsible for producing that stratigraphic expression. (In terms of conceptual perception this later observation is akin to Georg Cantor’s "concept of the transfinite").

Principles incorporated in Cantor’s work on transfinite orderings have a correlative in geology with the concept of the ‘facies change’. Facies changes signal a kind of relativistic transformation in form through time. The coming into existence of a new manifold or perhaps at least, a transformation of form within a manifold (6).

The conceptual medium connecting the many manifold geometries in the geological sciences is Historical Geology. Developing a sound, comprehensive geo-chronological order or sequence of events is necessary in order to understand the interplay of the forces and the forms of expression of those forces through time. This becomes especially important when it is realized that the interplay of such forces and geological formations often combine to produce environments of deposition wherein mineral deposits may grow.

Physical Geology, where physical forces are translated into geometric form; Historical Geology, which connects form to form through geological time; and Stratigraphy, which represents a reflection of the energy throughput of the forces responsible for forming those stratigraphic expressions, are all examples of geometries of a multiple connected kind as hypothesized by Bernhard Riemann. They are also examples of the kind of transfinite geometries alluded to by the works of Georg Cantor. This is what we are looking at.

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While the progress of an exploration program proceeds via the application of the principle of forming multiple working hypotheses to generate successive (higher order) conceptual perceptions of geological reality, those higher order advances are themselves mediated by an underlying geometry. That geometry too is, in essence, Riemannian.

Thus, the conceptual processes employed by an exploration geologist to understand geological reality, as well as that geological reality itself, are defined or mediated by an underlying, Riemannian defined geometry.

This perception thus occurs, through a geometry of multiple connected manifolds of conceptual geological understanding of the forces and forms of expression of those forces, through time. Understanding forces through time and connecting those forces through form, helps create a sequence of events that can be projected either forward or backward through geological time.

Progress, as defined as the qualitative growth in understanding comes about via the employment of the practice of forming multiple working hypotheses. This is a practice which is necessary when dealing with matters that establish ‘relativistic relationships’ with one another. It is yet another example of a multiply connected kind of 'transfinite geometry'.

If the underlying geometry of geological reality is Riemannian in nature; and the processes driving the manifestation of that geological reality are Riemannian as well; and if our geologist's exploration practice mirrors that fact; our geologist's perception of things geological, should come into alignment with the fundamental ordering of the affairs of things geological. If this happens, our geologist should be in a position to know where the minerals are, and why they are where they are; and to be able do it well in advance of any subsequent exploration work.

After seeing this, I had to find a way to explain it to other people. When I set out to describe just what it was that I was sensing regarding this new found capability; I began to describe the exploration process from the standpoint of the activity of an exploration geologist. I began that effort with an attempt to draw or map out my movements, and with aid of this map reflect upon the activities and the thought processes involved.

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This mapping process began with a principle area of interest. It was a place where a particular coal discovery had been made. I understood it to be a local area of interest where the details of the local geology of this particular discovery were under study. This ‘local geological setting’ was itself surrounded by a ‘regional geological setting’ the geology of which had had a major impact upon the shaping of the local geological setting.

At the same time that the geological features of these local and regional geological settings were being examined, it occurred to me that there was a corresponding intellectual process that had to be accounted for. As each area was studied and new insights were generated, any working hypothesis will begin to expand. The process behind the generation of this higher order level of perception had to be patterned into the mapping process. The mental activity involved and the results obtained had to be understood and presented. The following section discusses this mapping program and the thought processes involved.

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The Exploration Process

As I set out to explain just what it was that I was sensing regarding my newfound capability to generate successive mineral discoveries, I found myself trying to describe the exploration process from the standpoint of the activity of the exploration geologist. It was the process by which this capability came to mind that I was out to articulate and I began that discussion with an attempt to draw a map of my movements and to describe the actions and the thought processes involved with the aid of this map.

This mapping process began, as I have stated, with a principle area of interest. In this case the site of a particular coal discovery. To me, it was a "local area of interest" where the details of the local geology of the discovery were under study. This 'local geological setting' was itself surrounded by a 'regional geological setting'; the geology of which had had a major impact upon the shaping of the local geological setting. That regional setting was also being studied.

At the same time that these geological settings, and the forces responsible for shaping them were being identified and examined, it occurred to me that there was a corresponding intellectual process that had to be taken into account.

As each area is studied and new insights and information are generated, a working hypothesis will begin to take shape. This working hypothesis will expand as more and more of the geological events involved are uncovered and explained by the exploration process. The process of generating this higher order level of understanding had to be patterned into my mapping program. It had to take into account the mental activity involved and the results obtained, as well as the effect that those results had on the advancement of the working hypothesis and the exploration program in general.

With this in mind, circles were used to define the principle areas of study. Additional circles were employed to reference an increase in the level of understanding being generated by these activities. The following section discusses this mapping program and the results it generated. Keep in mind that this is a multi faceted perception of the exploration process.

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Let's take a look at the exploration process and see how each of these elements comes into play with each of the other.

The geological exploration of a potential mining property involves several elements that work together to produce a satisfactory and beneficial understanding of the forces responsible for producing the geology of a property and we begin with the practice of forming multiple working hypotheses. The practice of forming multiple working hypotheses operates to build a foundation of understanding that eventually leads to the development of a mastered understanding of the overall geological nature of a property.

For a geologist, geological reality is viewed not so much as a construct of fixed geological features that can be examined, but rather as an unfolding, self-expanding, geometrically structured, on going process that can only be apprehended by adopting, in a like manner, a process for viewing that ‘fluid’ reality that offers a geologist the capability to keep up with that unfolding, geometrically defined process.

At the outset of exploration activities, the forces responsible for the present disposition of a property are not known or understood. Therefore an ‘hypothesis’ proceeding to and/or out of a series of hypotheses, based upon available data, is made. As new data is generated, as exploration work proceeds, any current hypotheses under consideration are reviewed in light of any new findings. This process continues until a comprehensive, verifiable understanding has been reached. This end result will have the unique characteristic that, with this particular hypothesis in hand, it will be possible to predict results in advance of further testing.

The most immediate work in this regard, has to do with the local geology of a deposit. At this point in the exploration process, various field observations are made to assemble local geological data. This data is then combined with an air photo study and plotted onto a base map. As this data is collected and this work preformed, hypotheses respecting the forces responsible for producing the present geological disposition of a property are generated.

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As well as the local geology, the regional geology must be examined to make sure that the local is consistent with the regional. This kind of cross-examination will provide useful insight to the task at hand, as local geological phenomena are often the lesser expression of a regional geological trend. An examination of the regional geology will provide clues as to the forces responsible for producing a local expression of those forces.

The next step involves drilling programs. Drilling programs provide the most direct means of obtaining subsurface geological information. By this method, new data is provided at the same time that outstanding hypotheses are tested. As drilling data is assembled, local and regional geological data is examined and discussed in reference to any new findings. This process involves the development of an historical understanding respecting the sequence of events that have acted regionally, as well as locally, to produce the present nature of the geology of the property under study. This historical understanding is vital for finally evolving the kind of comprehensive understanding that is being sought after in any exploration effort

As a form of proof, the historical geology pertaining to the deposition, lithofication, deformation (uplift and erosion) of a coal property (for example) must correlate concisely with observable data. The best test of this understanding comes when drilling results can be predicted in advance of drilling any particular hole at the site of any local exploration activities. This is a real confidence booster respecting any developed, comprehensive understanding of the geology of a property.

There is an added benifit to evolving such a sound, comprehensive understanding, and it is; that with such an understanding in hand, it is next possible, to extend any local exploration activities from a local geological setting into the surrounding regional geological setting and by this means evolve (or make) (additional) mineral discoveries elsewhere.

It is possible, in a manner of speaking, to extend such an understanding through time. To travel back and forth through geological time to discover points of departure, that might lead to the discovery of other mineral deposits or informational type discoveries that will operate to help extend this potential for making additional mineral discoveries.

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Up to now generally, exploration personnel have concerned themselves with individual mineral discoveries. Their efforts have been directed to discerning the extent and quality of these individual discoveries; and even though exploration activities, do as of necessity, extend to a degree into regional geology, such efforts have been conducted for the purpose of clarifying the geological nature of the local geology of an individual mineral discovery or deposit.

Few if any of these researchers have bothered or been financed to the point of being able to extend their geological explorations past a competent evaluation and understanding of the local geology of any individual discovery. At least not to the extent that such exploration processes can be extended.

With a conceptual orientation, perhaps best described under the title of Riemannian Geology it is possible to extend such exploration activities from the local geological setting into and through the regional geological setting, with an intention to discover, new sites of mineral deposition.

If extended exploration efforts, being carried out under the aforementioned conceptual mode of perception of geological processes are charted, something like the following is seen to happen.

On examination, such extended exploration activities are seen as the study of local geological activities, leading into a necessary examination of regional geological influences and processes. As exploration advances to confirm local and regional perceptions, an historical understanding begins to develop. This in turn, acts to catalyze views and data, into a mastered understanding such that results can be predicted in advance of drilling. At this point it seems reasonable to propose, that additional mineral discoveries elsewhere can be generated with as much confidence, as being able to predict results in advance.

Under such a conceptual perception of exploration processes, such work can be extended from a local geological setting, into a regional geological setting and then extended through geological time to a point of re-entry into a new, local geological setting. Moreover, re-entry should be achievable with such certainty as to be able to predict results in advance.

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The medium through which this understanding travels is geometry. The mechanism along which this understanding travels is the form/force relationship that exists between rock units throughout geological time.

For example, the Laramide Orogeny (force) produced physiographic expressions (form), the erosion (force) of which produced Paleocene strata (form). Thus, force produced form, which was made subject to forces that produced new form. This relationship exists throughout geological time such that it is possible to travel back and forth through geological time to discover points of departure where sites suitable for mineral formation might likely occur.

The important thing to do is to establish a comprehensive or mastered understanding of a key event in geological time. Like, for example, the deposition of coal in the early Tertiary Period.

The study of Tertiary (Eocene) coal field formation, distribution, lithofication, deformation (uplift and erosion) provides a means of generating significant information about the forces acting to affect that coal throughout the Tertiary Period. Relevant information as regards the paleogeography prior to and during its deposition, as well as its deformation offers an insight into those forces acting over an extended period of time. Finally, coal deposits are more extensively evaluated per square mile than are most other mineral deposits. The database is already extensive.

Once such a study is done, and the data plotted in accordance with the conceptual modes so discussed, then known mineral discoveries can be situated into the program to check the accuracy of the work. This then can be added to the information base used to (successively) generate new mineral discoveries.

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Third Order Perceptions

If the earth’s geology is looked upon as a series of multiple connected manifolds (or multiple connected geometries) that establish a continuum, linked together in a series of form/force relationships, from the least complex to those of a greater complexity, then in a mental manner of speaking, it is possible to travel back and forth through that geological time continuum. Think of it as a kind of geological time travel.

These ‘extended exploration techniques’ involve finding the manifest form and force responsible in the regional geological setting, that produced the local geological expression of those forces. Once those forces and their regional expression are identified, a sequence of events can be exposed as being involved. Once this is clarified, it becomes possible to project an overall expression of those forces in areas that are, as yet, un-drilled. In this way structural data that drilling results would produce can be predicted in advance of drilling. This helps establish confidence in the overall understanding of the nature of the local geology of an area with respect as well to the regional geology surrounding that area.

By crossing form/force relationships, the suggestion of a solution contained within the deformation geometry permeating those relationships is encountered. Accounting for the historical geology in terms of a sequence of events causes this information to be assembled into something that makes sense completely. By evolving such a sound, comprehensive understanding, it becomes possible to predict results in advance of drilling. As this occurs it indicates that things are rightly understood.

As the evolution of this comprehensive understanding oscillates between the local geological setting and the regional geological setting, it eventually opens up an ability to leave that local geological setting, with things well understood, enter the regional geological setting with that understanding in tact, develop it still further, and eventually re-enter into another local geological setting; and do it with such certainty as to be able to predict results in advance. Thus establishing a kind of geological time travel that can be used as a form of extended exploration process. Regional geological forces acting to affect a local geology do so by deforming the geological formations found at that local geological setting.

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That deformation process establishes a time line that is consistently the same in other local geological settings located some distance from our original work. This then establishes a time line that connects us with other sites. It is this time line that makes it possible to travel from a particular local geological setting, through a regional geological setting and on into a new local geological setting. Because that deformation process is understood at one local geological setting, it becomes possible to predict its effect upon strata at a new, local geological setting. It also becomes possible to identify at that new setting specific sites wherein mineral development might occur.

Please consider that mineral deposits just do not happen in an instantenous fashion. They grow. They grow because an appropriate environment has been provided for the deposition of the mineral or minerals held in solution. Looking for the environment of deposition instead of the mineral itself, is another way to go about conducting a minerals exploration program. The development of a unified understanding of the overall geology of an entire Period of geological history, makes it possible to identify numerous or successive sites of depositional potential. Such a process, when set out as a clearly understood method for carrying out these kinds of extended exploration programs, becomes a superior manner of practice for an exploration geologist.

Extended exploration geology, indeed Riemannian Geology, as a conceptual perception of extended exploration processes, becomes an outline of the process of discovery itself. This is what makes it possible to successively generate successive mineral discoveries.

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Extended Exploration Geometry

The following series of diagrams cross correlates the physical actions taken, with the mental effort involved, to arrive at the point of being able to generate successive mineral discoveries.

On proceeding from a, (1) local geological setting into a, (2) regional geological setting to gain insight into the regional forces responsible for forming a local expression of those forces, the acquisition of this information causes a working hypothesis to expand. Upon returning to the local geological setting a, (3) mastered understanding begins to evolve that encompasses that local geological setting sufficient enough to allow for the prediction of results in advance of drilling in the area of that local geological setting.

At this point in the exploration effort, things become self-organizing and self-sustaining, such that the more drilling that is done, the more an outstanding hypothesis (a mastered working hypothesis) becomes confirmed. Confidence increases to the point of being able to predict results in advance of drilling in the area of that local geological setting.

In addition to this, with this “mastered working hypothesis” in hand, it becomes possible to take it through geological time, so as events relative to a specific Period of geological history are confirmed, that rightly understood conceptual perception, has applied relevance in other local geological settings.

In conceptual terms, a kind of geological time travel becomes possible; encompassing the regional geological setting (with that mastered working hypothesis in hand) it becomes possible, to carry that, (4) mastered understanding through geological time, to a point where it can, by reflection upon those, (5) regional geological influences be narrowed down into a, (6) new local geological setting with a command ability to predict or perceive in advance, sites wherein a potential for mineral development might occur.

By knowing how those regional geological forces might act to affect a new local geological setting, it becomes possible to foresee or predict results in advance.

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1. Local geological setting and principle area for exploration study.

2. Regional geology (lies outside yet encompasses area of study).

3. Comprehensive understanding (able to predict results in advance).

 

That (4) comprehensive understanding, is carried forward. It overlaps our regional geological understanding.

 

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That comprehensive understanding (4) is narrowed down through or by reflection upon our understanding of our regional geology (5).

 

 

Our perception of regional geological events is next focused down or narrowed down into a, (6) new local geological setting, with the command ability to predict results in advance. We have traveled from one local geological setting through geological time, to the site of a new local geological setting some distance from our original work and we have arrived with an ability to perceive in advance, sites wherein a potential for mineral development might occur.

 

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Beginning with local geology, a working hypothesis is formed out of the information gained at that local setting. Proceeding into the regional geological setting to gather information as to the regional forces responsible for producing the structural disposition of the strata encountered at the site of our local exploration activities, our working hypothesis expands in accordance with the acquisition of this information.

On returning to our local geological setting with this expanded working hypothesis in hand, it becomes possible to predict results in advance of drilling. As this is proven to be the case, a mastered working hypothesis becomes confirmed. This mastered working hypothesis functions to generate a mastered understanding of the geological forces and forms of expression of those forces operating over an extended period of time.

This approach makes it possible to confirm a geo-chronological order or sequence of events relative to the deposition, lithofication, deformation (uplift and erosion) of the deposit under study. This sequence of events, conceptualized in terms of form/force relationships, makes it possible to expand this mastered understanding, which has applied relevance for a particular geological setting, into a comprehensive understanding which has extended application over an entire Period of geological history. In the case of the coal property cited, major events throughout the Tertiary Period and all of the Pliestocene were identified and understood.

Since it is possible with this mastered understanding in hand to predict results in advance at the site of our local exploration activities, it also becomes possible to do it at any other site, provided the effort stays within time continuum of the geology involved. This kind of an insight into regional geological forces and how they will act to affect a new, local geological setting makes it also possible to predict the impact of those forces upon that 'new' local, geological setting.

This capability portends a qualitative leap in exploration geology. It establishes a new, higher order level of practice for exploration geologists. A higher standard of excellence of practice. It may now be possible; to force draft generate mineral discoveries from properly ordered and properly directed geological exploration.

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Multiple Connected Geometries.

Everywhere in this view of geology, exploration and exploration practice there are numerous, underlying and interconnected geometries.

There is the exploration geologist with the geometry of multiple working hypotheses. There is the geometrically defined movement of the geologist through space gathering information to feed into those hypotheses, and there are the geometrically defined structural geologies of the local and regional geological settings associated with these exploration activities.

There is, within every formation, a geometrically defined reflection of the energy throughput of the forces responsible for forming each geological formation; and there is the geometry set up by the multiple connectedness of those geological formations through geological time reflected in the geological column.

There is the multiple connectedness of the forces responsible for the deformation of those formations reflected in successive deformation geometries. And there are the drills, spiraling down into the earth, transiting these various geometries and brining up evidence of their relationships to one another.

All of these geometries are examples of multiple connected manifolds of a kind hypothesized by Bernhard Riemann; and they are also examples of a transfinite kind of geometry as reflected in the work of Georg Cantor.

Riemannian Geology represents a new way to view geology, geological processes and exploration practice. It ushers in a new branch of study in the geological sciences. It goes beyond the current Euclidian approach to geometric analysis in structural geology. And it elevates exploration practice from mere property evaluation into a capability to (successively) generate mineral discoveries from properly orientated and properly directed exploration practice.

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The Fusion Solution

When a body performs an action within a field or space, that action distorts that field or space. That distorted field has therefore an appropriate field geometry which if properly interpreted describes the body and/or action that distorted it.

The field geometry established by such mental and/or physical action as occurs when a geologist employs the processes previously described to carry out an 'extended exploration program' is equivalent in geometric form to that of the field geometry set up by a self-sustaining, self-organizing fusion energy plasma. Why this is so, is as follows:

Mental processes and/or actions that operate to generate a contra-entropic reality or action in the universe (like being able to generate successive mineral discoveries) manifest an appropriate geometry. That geometry is therefore reflective of a contra-entropic action or process. Fusion energy processes are by definition contra-entropic processes; their necessary geometric form must as well reflect to contain, contra-entropic processes

So, if you want to establish a stable fusion energy plasma, you must cause it to manifest within this kind of an appropriate field geometry.

This next series of diagrams cross correlates the physical actions taken, with the mental effort involved, to eventually arrive at the point of being able to generate successive mineral discoveries.

On proceeding from, (1) a local geological setting into, (2) a regional geological setting (to gain an insight into the regional forces responsible for forming a local expression of those forces) the acquisition of this information will cause a working hypothesis to expand. Upon returning to the local geological setting, a (3) mastered working hypothesis begins to evolve that surrounds that local geological setting sufficient enough to allow for the prediction of results in advance of drilling at the site of those local exploration activities.

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At this point in the exploration effort, things become self-organizing and self-sustaining, such that the more drilling that is done, the more an outstanding hypothesis (a mastered working hypothesis) becomes confirmed. Confidence increases to the point of being able to predict results in advance of drilling. Confidence and stability are synonymous terms here.

With this “mastered working hypothesis” (this mastered understanding) in hand, it next becomes possible to take it through geological time; and as events relative to a specific period of time in geological history are confirmed, that rightly understood conceptual perception now has applied relevance to other local geological settings.

In conceptual terms, a kind of geological time travel becomes possible. On viewing the regional geological setting with a mastered working hypothesis in hand, it next becomes possible to carry that, (4) understanding through geological time, to a point where it can, by reflection upon those, (5) regional geological influences, be narrowed down into, (6) a new local geological setting; with the command ability to predict or perceive in advance, sites wherein a potential for mineral development might occur.

When seen in total these diagrams are representative of the necessary field- form wherein may reside a self-sustaining, self-organizing, stable fusion energy plasma. Perhaps the mathematics describing such a field can be determined from the philosophical intent of these diagrams and studied so that an appropriate technology can be constructed, which will reproduce this necessary field geometry to act as a home for a fusion energy plasma.

Movement through the full diagram is to be seen in terms of conical spiral action. If the movement of a fusion energy plasma through the diagram were linear from (1) to (2) as might be inferred from the charting of a geologists activities, it could not reflect off of (2) on its way to (3) without passing through itself. This would cause an interference problem. Conical spiral action resolves this dilemma.

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Local geology (1)

Regional geology (2)

The movement from (1) to (2) begins with conical spiral action. Imagine a fusion plasma bursting forth from area (1) on its way to area (2). It spirals its way from (1) to (2).

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This conical spiral action continues as the required comprehensive understanding necessary to predict results in advance of drilling at the site of exploration activities in area (1) is developed. The plasma vortex becomes circular at this point.

This rotation action continues as that comprehensive understanding is taken forward from (3) to (4). The apparent cylinder denoting some measure of stability.

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Because that comprehensive understanding(4) encompasses regional geology (5), it employs or reflects upon that knowledge as it proceeds to be narrowed down into a new local geological setting.

Because regional geological forces are understood, it becomes possible to for see their influence and impact at the site of any, (6) new local geological setting. Results at (6) are predictable beforehand.

(top page 27)

Since the understanding of regional geology is the same, diagram numbers, (2) and (5) can be merged. Yet for purposes of understanding fusion plasma flow, perhaps their merging point should be viewed as a point of reflection or rebound. As if the plasma were rebounding upon itself. There are two of these points; (2) and (5); and (3) and (4). Think of the diagram as if it were in the shape of a doughnut, then (3) would abut (4).

Point (6) is a point of fusion, so points (1) and (6) do not rebound; point (6) is fused or pushed through into a new, higher order (1); a new, higher order manifold. A new, ‘higher order’ fusion plasma geometry.

(top page 28)

In this diagram, points (2) and (5) have been merged together to form a common plane. The conical spiral action established by cone (1) to (2) is in mutual rebound with that of cone (4) to (5). If this diagram were evolved via computer assisted 3-D graphics into the shape of a doughnut, it might indicate the appropriate field-form wherein may reside a self-sustaining, self-organizing, stable fusion energy plasma. The mathematical dynamics of such a field could be worked out from such a diagram.

The first half of this diagram (1) to (4) goes from fusion ignition to stable plasma. The second half, (4) to (6) goes from stable plasma back into a more concentrated form of energy; power for work at fusion ignition temperatures; or re-ignition and hence the generation of a self-sustaining plasma.

This could also be viewed as a seven step process. Area (3) is an area as well as a conceptual understanding. That understanding is carried forward as number (4) which then becomes area (4) the higher order understanding of our regional geology which surrounds a new local geological setting.

The numbering system might also have gone, 1, 2, 3, 4, 5, 6, 7.

I’ll consider it for a future paper.

(top page 29)

Nevertheless, fusion energy processes are by definition, contra-entropic processes. The necessary 'field-form' wherein may reside a contra-entropic fusion energy plasma must 'contain to reflect' contra-entropic processes.

If current difficulties with the 'magnetic confinement' of fusion energy plasmas revolve around some tendency of the plasma to twist or spiral, then the resolution to this problem may be to accommodate this tendency rather than to oppose it.

Spiraling acts to organize a fusion plasma.
Conical spiral action acts to establish direction.
Cylindrical spiral action acts to stabilize a fusion energy plasma.

There is what appears to be 'an ordering principle' here:

1. First order, spiraling for organization.
2. Second order, conical spiral action for direction.
3. Third order, cylindrical spiral action for stabilization.

Rather than trying to take the twist out of a fusion energy plasma it may be more appropriate, to accommodate it. Give it a 'home' to reside in. These diagrams offer a conceptual aid as to understanding how this may be accomplished.

A fusion energy plasma is, upon ignition, raw unorganized energy. It must be brought into an appropriate geometric form of expression denoting stability. Or it must be caused to manifest into an appropriate geometric form of expression that will facilitate its organization, direction and stabilization.

(top page 30)

Why Fusion Energy Processes?

What is he talking about? What does this have to do with generating successive mineral discoveries?

When I looked at my efforts as an exploration geologist, directing the exploration process, carrying out an exploration program, I began to picture my combined action and thought processes into an appropriately descriptive geometry. I realized that my capability to generate successive mineral discoveries was indicative of a contra-entropic process. That is, a process that runs opposite to entropy (pro-generation as opposed to de-generation).

In the fifth grade, I was educated in the conceptual orientation to geometry of Riemann and introduced to Cantor's concept of the transfinite. I was given a solid grounding in physical geometry. In the ninth grade I was given an understanding of the processes involved in fusion energy physics. I understood fusion energy processes as being contra-entropic in nature and I carried that contra-entropic sense of things forward with me since that time.

By 1980-81, I began to see exploration geology functioning as a contra-entropic process. I had a sense of things that indicated to me that there was a way to generate successive mineral discoveries from my particular approach to directing an exploration program. However, while I could see it or sense it, I could not yet explain it. I could even do it. However, I could not put it into words. I was not yet aware of a common denominator around which I could generate an explanation. Geometry turned out to be that common denominator.

It was the deformation geometry of the geological formations involved that was casually informing my mind as to the forces responsible for deforming those geological formations. My earlier educational training in geometry and the perspectives of Riemann and Cantor, along with my contra-entropic sense of things, and my geological education (including structural geology) were all connected up with the subject of geometry.

(top page 31)

As I began to diagram (map out) my actions and thought processes, I began to generate what amounted too, an 'appropriately descriptive geometry'. As I continued to review and describe my actions and thought processes with aid of this geometry, I began to find the words I required in order to be able to communicate to others, just what it was, that I was sensing.

As I considered my movement from the local geological setting into the regional geological setting and back again, and the attendant results, I began to 'map' my movement. As I recognized this movement to be indicative of a contra-entropic activity, I began to account for it as well in terms of fusion energy plasma flow. This meant that the geometry being generated had to be reflective of the flow pattern geometry of a fusion energy plasma. The geometry of this plasma flow eventually became expressed in terms of what turned out to be 'conical spiral action'.

Assuming that some of the philosophical characteristics of fusion energy plasmas might be that they are self-sustaining, self-organizing and stable, in consideration of this, I began to see that the geometric field-form that I had become aware of began to fulfill some, if not all of those characteristics.

It was the act of 'mapping' out my activities and describing those activities through aid of the geometry generated, which subsequently generated for me a descriptive terminology. Geometry was the medium through aid of which, I became able to communicate. Indeed, one of the things I learned from this exercise was that all communication proceeds via the medium of an appropriately descriptive (or reflective) geometry.

The deformation geometry encountered through study of a property's structural geology for example, has the effect of informing a geologist as to the force or forces responsible for that deformation. This ‘informing’ process goes on via the subtle agency of suggestion (like sign language). Thus my principle; “geometry suggests force responsible”.

The application of the Law of Multiple Working Hypotheses helps keep the mind of the geologist open to the suggestion of a solution contained within new evidence, while an 'hypothesis overall' remains open to productive alteration.

(top page 32)

Since my ability to generate successive mineral discoveries was recognized as being a contra-entropic activity, and since the diagrams being generated were indicative of the flow of the activity of these contra-entropic processes, it seemed reasonable to conclude that this pattern of flow was indicative of the pattern of flow of a ‘contra-entropic’ fusion energy plasma. The geometry of the one was reflective of the geometry of the other.

Using a circle to (map) define the local area of study seemed a reasonable first step. This first circle defined the site of any local exploration activities. This site was circled and identified as “circle (1)” and defined an area where these local geological/exploration activities were taking place. A second 'circle (2)' was used to define an area of interest which lay outside this local area of interest, yet pertained to the regional geology surrounding that local area of interest. This circle was larger because it involved a larger area of study.

As exploration proceeds, a geologist will go from the local geological setting into the regional geological setting to gather information as to the forces responsible for shaping the nature of that local geological setting. Upon returning to the local area of interest, the information gained will have caused a working hypothesis to expand. Therefore a larger, third circle (3) was drawn to be able to include regional geology and to overlap or encircle the local area of interest. It was larger than the two previous circles because it also represented an expanded level of understanding.

Although, connecting these circles with straight lines established truncated cones, the principle intent for doing so was to signify the direction in which these processes were moving. With this in mind, arrows were added along the sides of these cones to provide for this sense of direction. The next question became; how would it look if this movement were viewed in terms of fusion plasma flow?

If this plasma flow were linear, as the straight lines might suggest, the plasma would have to pass through itself on its way from circle (2) to the area of circle (3). By just looking at the geometry involved, it becomes evident that this would not work because an interference problem would develop. The plasma would have to pass through itself on its way from (1) to (2) to (3). Clearly this would not do. A review of the mechanics of actually drawing these diagrams was in order.

(top page 33)

As I looked backward through the process of generating this description, I was impelled to look very closely and very slowly at the process of drawing the first circle.

In my minds eye (this actually happened while I was (almost) asleep and thinking over this problem) I began to picture my pen going around and around, tracing out the outline of the first circle. Slowly, almost at a microscopic level, I watched the point of the pen go around and around this first circle. Around and around it went. Then again, very slowly, almost to a stop and then, all of a sudden, all on its own, I watched the line being drawn by the pen, arc up and outwards, and over along the side of the cone!

From circle number (1) to circle number (2) I watched the point of my pen arch up, outward and over, along the side of the cone! ‘Spiraling’ its way on towards circle number (2). Eureka! When this flow pattern was reviewed in terms of plasma flow the ‘interference’ problem was resolved.

It was 2:30 AM. I leapt out of bed and rushed off to get paper and pen. Over and over again, I went though the process of generating successive mineral discoveries, drawing my diagrams and looking at the geometry being generated in terms of fusion plasma flow.

It was the process of drawing these diagrams, reviewing my actions and the thought processes involved, cross-correlated to the results obtained, that caused me to generate a descriptive geometry. Along with this descriptive geometry came a descriptive terminology through aid of which, I became able to communicate. Geometry, as it turns out, is the medium through which all communication occurs. It was the medium through which I was initially being informed.

My work defines how and why it is possible to generate successive mineral discoveries from properly orientated and properly directed geological exploration. It also presents diagrams and a conceptual orientation that might be useful in bringing about the advent of fusion energy as an energy source. Perhaps those closer to the fusion energy question will find this to be of some interest.

(top page 34)

A Higher Order Conceptual Perception of the Exploration Process.

With a "mastered working hypothesis" in hand, we are in a command position to understand fully a particular geological setting and to know where a particular mineral is and why it is where it is. In a manner of speaking, we actually create our discovery as we search for it. If we try to by-pass this creative effort, we may end up with little or nothing.

Many companies with good intentions quite often fail when this approach to exploration is neglected or superceded in some way. For example, under current exploration practice a 'formula orientated' approach often substitutes for true exploration. Such "exploration" efforts are usually based upon a step-by-step procedural approach, aimed at 'evaluating' a property. Drilling and testing are done in the 'hope' of making a discovery. In this case, 'property evaluation' substitutes for true exploration.

This 'step by step' formula orientated approach is quite often, mistakenly referred to as "exploration" by the Canadian exploration and mining industry. It usually involves four basic steps; prospecting to find a trace or indication of a mineral or mineral deposit; followed by a geochemical survey to define a target area; followed by a geophysical survey to define a target; and finally, drilling to hit the target, in the hope, of making a discovery.

What most mining and exploration companies and consulting geological companies are engaged in, is property evaluation. It is not geological exploration as properly defined or conceptually designed. It is simple property evaluation; and in part, this situation seems to have developed because of the history and the structural nature of the mining business in Canada.

In the 1800’s it was the prospector who came into the wilderness ahead of the mining companies. There were few if any “exploration” companies at that time, only prospectors and their backers and later on, some mining companies with their head offices “back east”. It was these prospectors who would search the land and make “discoveries”.

(top page 35)

These prospectors would stake their claim; sometimes work their claim and at other times, sell or option their claim to a mining company. The mining company in turn, would send its engineer out to evaluate its newly acquired property. They would send an engineer because, being a mining company, their main interest was in placing property into production. This objective was an engineer’s responsibility and mining companies had many more engineers on staff than geologists, so the engineer got the call.

Besides that, in the 1800’s geology as a science was still quite young and for the most part had not yet been considered to be a valid exploration tool. Geologists were thought of as those fellows who worked for the government and ran around identifying, naming and mapping everything geological. They were not necessarily in the business of finding mineral deposits, let alone evaluating them and placing them into production.

Over time, this “property evaluation” effort, undertaken by company engineers, began to be referred to as “exploration”. Companies would ‘option’ property and initiate ‘exploration’ programs. However, it was not proper geological exploration that they were engaged in. It was really only property evaluation, and the situation remains much the same today.

Even the geology that is being done within this property evaluation mandate is ‘after the fact’ geology. In this regard, a property’s geology is evaluated as a project advances and an understanding is worked out as a form of referenced based explanation of the results. Sometimes this shows up as a comparison discussion, wherein similar property elsewhere is used as reference property, around which a ‘characterization’ of a current property’s geology can be generated.

At other times, this property evaluation effort produces a geological study that adequately maps out a property’s geology but fails to explain how or why anything is as it is. Usually concerns over the quantity, quality and disposition of an ore body take precedence over any in depth pursuit of the more seemingly academic aspects of the data. How a property came to be as it is or why it happened are not of any great concern. Leave it for the government geologist to play with. The main objective is to prove up the economic potential of the company’s property, secure its option and place the property into production.

(top page 36)

This “formula orientated” approach to conducting such property evaluation efforts, has to a large degree, been adopted as standard operating procedure by Canada’s exploration industry; much to the detriment of geologists and the work they should otherwise be capable of doing.

Through properly orientated geological research and exploration practice, we can actually create a discovery as we search for it. Through proper exploration practice, a track record of higher order discoveries precedes and directs subsequent decisions. As if, the projected direction of many little discoveries along the way equals a big discovery in the end.

This is not however, a mathematical matter. It is something contained within the ‘creative process’ incorporated within our scientific approach to exploration. When followed, it puts the geologist in a command position to ‘know’ where the minerals are, and ‘why’ they are where they are. To be in a position to go after them with a higher degree of certainty than simply that of ‘hope’ alone.

There is a big difference between true geological exploration and mere property evaluation. Creative exploration geology involves and incorporates within it, a ‘process of discovery’. Property evaluation is something static. A simple probing. A ‘seeing if’ approach. It does not necessarily lead you anywhere. You may occasionally make a discovery because of it but not as a result of it.

What seems to occur under this property evaluation (formula orientated) approach, is a lot of drilling and testing carried out in the hope of making a discovery. When this approach fails, it is said that; “they failed to make a discovery”. From the perspective of the creative exploration geologist, they did not fail to make a discovery, so much as they failed to create a discovery.

Creative Exploration Geology (Riemannian Geology) is yet, a higher order conceptual perception of the exploration process and goes well beyond anything currently being done. Riemannian Geology is a 'pro-generative' scientific practice, which makes it possible to (literally) generate mineral discoveries from properly applied geological research and properly applied exploration practice.

(top page 37)

The creative exploration geologist would want to know what forces were responsible for shaping the geology of the region, as well as what forces were responsible for shaping the local geology of the discovery itself.

It's this understanding of those forces and the forms of expression of those forces, operating over an entire region, throughout the geological history of that region, that need to be mastered and subsequently projected onto one's own property. This way the identified geology from your own property can be situated into that picture and by this means, you can come to know or understand where upon your own property the discovery bed or horizon might be located.

It's not the information itself or the way the information is put together. It's the process by which the information is gathered that creatively generates the prescient insight.

The process of discovery operating within the exploration process, coupled with the manner of practice of the exploration geologist, helps order the perceptive capabilities of the mind of the geologist, in such a way, that the direction of growth in his or her understanding is 'pro-generative' to the end intent of creating (actually generating) a discovery.

These methods of exploration practice go far beyond today's approach to exploration practice. Today, property evaluation substitutes for true scientifically based geological exploration. And the term 'scientific exploration' has been reduced to mean, primarily, technological methods of exploration practice; i.e. technological prospecting.

Riemannian Geology opens up a new branch of study for the geological sciences and in particular, a new, higher order conceptual perception of the exploration process itself.

(top page 38)

(1) Title as per World Book Encyclopedia © 2008, page 337. Bernhard Riemann's 1854 paper can be found on the Wikipedia web site. Locate "writings in English" or "external links" and look for "Bernhard Riemann's inaugural lecture". A translation into English by William Kingdon Clifford can be found there. Try also; http://www.emis.de/classics/Riemann/

(2) See Riemann's 1854 inaugural lecture paper, paragraph 6. (Reference as per endnote #1 above)

My own view is that in Riemann's day, a renaissance in science was under way due to the wide spread education in universities of the principles of the scientific method. Advances in chemistry and physics in particular were in the news, and Riemann would no doubt have been aware of these discoveries and the methods by which they were being made.

This may have influenced Riemann to set about to apply the scientific method of thought to his own studies in the field of geometry. Indeed the title of his famous 1854 paper would seem to indicate as much.

Riemann extracted a mathematical form of expression for the processes underlying the art of hypothesis formation and testing, and he defined it in terms of an evolving geometry. He took the scientific method and applied it to his own work in geometry. He gave expression to the process underlying the generation of his conceptual perceptions. As a result, he gave expression to the process of discovery underlying the act of discovery itself.

While other researchers were going about their business making discoveries in their own particular fields of study, Riemann gave us the answer as to how and why such discoveries were being made.

Here was a road map to the act and art behind scientific discovery. Here was a way to generate, successive scientific discoveries. When you apply this to geology and the processes underlying exploration practice, you end up understanding how and why it is possible to generate successive mineral discoveries.

 

(top page 39)

(3) See Riemann's 1854 inaugural lecture paper, paragraph 6. (Reference as per endnote #1 above)

(4) Georg Cantor (1845 - 1918) appears as well on the Wikipedia web site. His 'concept of the transfinite' or "theory of transfinite numbers" paralleled conceptually the work of Riemann. Cantor's work was not as welcomed by his contemporaries as was Riemann’s and Cantor spent a great deal of time defending his own work, most of which is accepted without reservation by today's mathematicians.

(5) In Riemannian Geology I make use, by way of reference to the conceptual orientation of Riemann and Cantor. I am not trying to equate my work or insights to their mathematical work. I am a conceptual geologist and Cantor’s concept of the transfinite and Riemann’s concept of a geometry of multiple connected manifolds, have applied relevance to me in geology and geological exploration practice.

(6) In this respect, I am referring to an instance where a sandstone formation, when traced laterally, transitions into a siltstone and perhaps further on into a mudstone or a shale formation. This "facies change" example represents a transformation of form within a defined, discrete, geological manifold. It is the geological equivalent of Georg Cantor's concept of the transfinite. The sandstone, siltstone, mudstone and the shale are the same age but not of the same composition.

In my conceptual representation of Cantor's concept of the transfinite, I am referring to the process of transiting the medium between the finite and the infinite. How do you otherwise get from the one to the other? And how do we otherwise define what that process entails except by way of its geometry and or its mathematics.

Hence the concept of a continuum and movement through that continuum, either forwards or backwards; up and down the geological column, through geological history or laterally through the process of a facies change.

The End

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