In Extended Exploration Techniques for Exploration Geologists © 2012, I relied on material I generated with the writing of two other papers; Riemannian Geology © 2010, and my earlier paper; Creative Exploration Geology © 2008.
With Riemannian Geology, I did not feel as though I did a very good job of explaining some of the reasoning behind this newly defined science. It was difficult to write because I had to take what I intuitively knew to be the case on the subject and put it into words, and yet, I felt that I could have done a better job. Therefore, I set out to improve upon my efforts.
This new work is titled, Manifold Geology. With this new effort I try to use a more descriptive language and a more in-depth discussion of the subject matter so as to more fully engage my reader. I employ much of the text of my previous Extended Exploration Techniques (2012) paper and all of the text from my Riemannian Geology (2010) paper as that text is central to the discussion. I tried to improve on that language as well with some editing.
I started this newer version by editing my Extended (2012) paper, and that editing process has progressed since, up to and including this 2020 version. Along the way, I have learned that my insights may have relevance and application under what those who study Riemann refer to as; "embedded manifolds". The "multiple connected manifolds" that I have identified in geology are in fact embedded manifolds in very much the same sense as those "embedded manifolds" referenced by many of the mathematicians who have studied Riemann. This is very encouraging to me as a conceptual geologist as it provides supporting evidence that I am on the right track.
As I write and re-write this paper, I learn more about how to accomplish my objective of better communication. I hope this work helps in that process.
The realization that embedded manifolds do indeed occur in geology led to the title; Manifold Geology.
In order to get a handle on the creative processes of nature which are 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.
The use of the practice of forming multiple working hypotheses in geology allows geologists to discover and reflect upon the actual creative processes of nature that were responsible for forming the geology of a mineral deposit.
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. 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.
Our development of a competent and comprehensive understanding of the geology of a mineral deposit comes about via this use of the practice of forming multiple working hypotheses. As exploration work progresses, 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 of the exploration site is understood.
When we generate hypotheses and test them, we are doing so to see if we can discover what ordering of the creative processes of nature were responsible for producing a particular geological setting and/or the minerals contained within that setting. Additionally, by this manner of exploration practice we can actually be led to the making of a discovery.
With a "mastered working hypothesis" in hand, we are in a command position to fully understand 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 can actually create our discovery as we search for it. It becomes for us, a "process of discovery". If we try to by-pass this creative process, it's a fair bet that we may end up with little or nothing. So it becomes important to ask; just what is this "process of discovery" and how does it work?
In the course of my experience as a coal 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 new found capability.
The text of that paper follows here as I once again set out to explain the science behind this fortuitous insight. 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 methodology behind the science of 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 may describe 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 being 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 subsequently, continuous progress within it, either forward or backward.(3)
Georg Cantor's 1871-1883 development of his own concept of transfinite orderings reflects upon a similar approach.(4) 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.(5)
An individual geological formation for example, can be thought of as a discrete manifold marked off in time. When formations are connected to one another they establish a continuous manifold. 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 column or backward in the geological column, or think of it this way; 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.
Superimposed upon this is the 'deformation geometry' established by the deformation of those geological formations. The form of this deformation geometry is reflective of the forces applied to bring about that 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 the shape of the deformation geometry. In short, a suggestion of the solution is contained within the deformation geometry of the problem. Our geologist must remain receptive to the influence of this 'suggestive' mechanism.
For example, geological formations that are deformed by geological forces into some sort of geometric form, such as an anticline, are by virtue of their geometry, reflective and/or suggestive of the forces applied to bring about their deformation. This 'suggestion of a solution' contained within the geometry of every structural characteristic involved, is linked up with force and form, throughout geological time. It is this, "suggestion of the force responsible" that is transmitted to the mind (perception) of the geologist by the geometric form of that deformation geometry. By this means, our geologist becomes informed to know something of what is going on.
Devising 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. This understanding will also connect up with several other fields of study in the geological sciences as those fields of study relate to the exploration work being performed.
For example, Physical Geology can be seen as the study of physical (stressing physics) forces translated into form. We do this when we look at Glacial Geology or Geomorphology or Structural Geology and we study the various landforms, faults and folds, and the various forces that create them. With Historical Geology we connect geometric form to geometric form through geological time. Stratigraphy itself 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 manifold geometries in the geological sciences is Historical Geology. With Historical Geology we seek to develop a sound, comprehensive, geo-chronological order or sequence of events so we can begin 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 impact of such forces upon 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 and alluded to in the work of Georg Cantor.
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 perceptions themselves are mediated by an underlying geometry. That is to say, 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 geometry. That geometry is in essence, Riemannian in nature.
This 'Riemannian' perception occurs through a geometry of multiple connected manifolds of conceptual geological understanding of the forces and forms of expression of those forces operating through geological time. Understanding those 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, well in advance of any subsequent exploration work. From this stand point, it should be possible to generate successive mineral discoveries; one right after the other.
When I set out to describe 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 the exploration geologist. I began that effort with an attempt to draw or map out my movements; and with aid of this map, look back upon my exploration activities and the thought processes involved in carrying out those activities and thereby generate a descriptive language and a means of communication.
This mapping process began with a principle area of interest. It was a place where a particular coal discovery had been made. This was understood to be "a local area of interest" where the details of the local geology of this 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 that 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 and the process behind the development of this higher order level of understanding had to be patterned into the mapping process. The mental activity involved and the results obtained had to be understood. The following section discusses this mapping program.
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 by drawing a map of my movements. I wanted to describe the actions and the thought processes involved in those movements with the with the aid of this map.
The mapping process began with a 'principle area of interest'. In this case, it was where a particular coal discovery had been made. I understood this to be a "local area of interest" where the details of the local geology of this discovery were under study. This became for me, a "local geological setting" that was itself surrounded by a "regional geological setting". The geology of the "regional geological setting" had had a major impact upon the shaping of this "local geological setting" and this fact, and the effect it had, had also to be mapped into consideration.
At the same time that these local and regional 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 well.
For example, as each area is studied and new insights and information are generated, a working hypothesis will begin to take shape. This working hypothesis will go on to expand as more and more geological data is uncovered. It's this process, of generating this higher order level of understanding that had to be patterned into my mapping process. I had to take into account the mental activity involved and the results obtained, as well as the effect that those results would have on the advancement of the program and the working hypothesis itself. With this in mind, circles were used to define the principle areas of study. Additional circles were employed to reference an increase in my level of understanding.
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.
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 coal property (for example) or any other mineral property up for exploration.
The practice of forming multiple working hypotheses is a practice which operates to build a foundation of understanding that eventually leads to the development of a mastered understanding of the overall geological nature of the property undergoing exploration.
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 geological forces that are responsible for the present disposition of a property are not known or understood. In consideration of this, we begin with the formation of, an ‘hypothesis’ that endeavors to explain the relationship of these forces and the geological settings they produce. Based upon this and any available data we are able to gather, we proceed on to generate a series of hypotheses.
As new data is generated, and as exploration work proceeds, any current hypotheses under consideration are reviewed in light of any new findings. This process of 'hypothesis formation and testing' will continue until a comprehensive, verifiable understanding is reached. This end result will have the unique characteristic that indicates that, with this particular, most recent hypothesis in hand, it will be possible to predict results in advance of any further testing. This then becomes, for the exploration team, a "mastered working hypothesis" thru the aid of which, exploration results can be predicted beforehand. We will look more closely at this process in the next few paragraphs.
With respect to the geological exploration of a potential mining property, the most immediate work has to do with the local geology of the mineral discovery. At this point in the exploration process, various field observations are made to assemble local geological data. Combining this with an air photo study, this data is then plotted onto a base map. It is as this data is collected and this work is preformed, that hypotheses respecting the forces responsible for producing the present geological disposition of the property are generated.
As well as the local geology, the regional geology surrounding our property must be examined to make sure that our local geological understanding is consistent with our regional geological interpretation. 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. Therefore an examination of our regional geology will provide clues as to the forces responsible for producing a local geological 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 sequence of deposition, lithofication, deformation (uplift and erosion) of a coal property (for example) must correlate concisely with observable data. And 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 well developed, comprehensive understanding of the geology of a property. We are now in a position to predict results in advance of further exploration.
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 understanding from a local geological setting into the surrounding regional geological setting and by this means evolve or make additional mineral discoveries.
It is possible, in a manner of speaking to extend such an "understanding" through time. That is to say, to travel 'conceptually' back and forth through geological time to discover points of departure that might lead to the discovery of other mineral deposits; or other informational type discoveries, that will operate to help extend this potential for making additional mineral discoveries.
Up to now, generally speaking, exploration personnel have concerned themselves with individual mineral discoveries. Their efforts have been directed at discerning the extent and quality of these individual discoveries; and even though these kinds of 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 exploration activities past a competent evaluation and understanding of the local geology of an individual discovery. At least not to the extent that such exploration processes and programs can be extended.
With a conceptual orientation, perhaps best described under the title of Riemannian Geology, I propose to indicate to you, that it is possible to extend such exploration activities from the local geological setting, into and through the regional geological setting, with an intention to go after and discover new sites of mineral deposition. The intention being to make additional subsequent, and successive discoveries. And to be able to do it with a much higher degree of accuracy than has here-to-fore been the case.
If such 'extended exploration efforts' as are carried out under the afore-mentioned conceptual mode of perception of geological and exploration 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. That is to say; as exploration advances to confirm local and regional perceptions, an historical (sequence of events) 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 testing; and at this point, it seems reasonable to propose that mineral discoveries can be generated with as much confidence as being able to predict results in advance of any further exploration activities.
Under such a conceptual perception of exploration processes, such work can be extended from a local geological setting on into the surrounding regional geological setting, and with the aid of an expanding, mastered working hypothesis, down through geological time, to a point of re-entry into a new local geological setting. Moreover, re-entry into that new local geological setting should be achievable with such certainty as to be able to predict results in advance of any exploration at that particular site.
The medium through which this "understanding" travels is geometry. And 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 occur. Think of it as a kind of, conceptually vectored, geological time travel.
The important thing to do is to establish a comprehensive (mastered) understanding of a key event in geological time. For example, the deposition of coal in the early Tertiary Period.
The study of Tertiary (Eocene) coal field formation, distribution, lithofication and deformation 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 (uplift and erosion) 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 for this is already extensive.
Once this kind of a study is done and the data is organized in accordance with the conceptual orientation previously discussed for this kind of work; then known mineral discoveries can be situated into this program to check the accuracy of the work, and to add to the information base that will be used to successively generate new mineral discoveries.
We are dealing here with a new, higher order conceptual perception of the exploration process itself; and we will be taking a closer look at that process in the next section.
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. A kind of geological time travel, so to speak.
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 local forces and their local and regional forms of 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 into 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 predictability helps establish confidence in the overall understanding of the nature of the local geology of the area under study, as well as the regional geology surrounding that local site.
By crossing the many form/force relationships involved in this process, the suggestion of a solution contained within the deformation geometry permeating those relationships is encountered. Moving along to account 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 further exploration drilling. As this predictability sharpens, it indicates that things are rightly understood.
The path of the evolution of this comprehensive or 'mastered' understanding proceeds from our local geological setting into our regional geological setting and back again. Eventually, this effort 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 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.
Think of it this way; regional geological forces acting to affect a local geology do so by deforming geological formations. That deformation process establishes a time-line that is consistently the same in other, local geological settings. It is this time-line that makes it possible to travel with a regional geological understanding, through a regional geological setting, and on into, a new local geological setting. Because that deformation process is understood in one local geological setting, it becomes possible to use it 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 additional mineral development might occur.
Now 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 (Riemannian Geology), as a conceptual perception of extended exploration processes, is also an outline of the process of discovery itself. This is what makes it possible to generate successive mineral discoveries. One right after another.
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 local geological setting [1], and going over into a regional geological setting [2] 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 our local geological setting with this higher order or "mastered working hypothesis" in hand [3]; we are now in a position to expand upon that understanding to the point where it begins to encompasses our local geological setting sufficient enough to allow for the prediction of results in advance of any further drilling at this site.
At this point in the exploration effort things begin to become self-organizing and self-sustaining, such that the more drilling that is done, the more an outstanding hypothesis becomes confirmed as a mastered working hypothesis. Now our confidence increases to the point of being able to predict results in advance of drilling.
With this "mastered working hypothesis" in hand, it (next) 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; even some distance from our original work. In conceptual terms, a kind of geological time travel becomes possible.
Upon encompassing the regional geological setting (with a mastered working hypothesis in hand) it next becomes possible to carry that understanding [4], through geological time to a point where it can, by reflection upon those regional geological influences [5], be narrowed down into a new local geological setting [6], with the command ability to perceive or predict in advance, sites wherein a potential for mineral development can be seen to exist. 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 of further testing.
Beginning with local geology, a working hypothesis is formed out of the information gained at that local geological setting. As we proceed from our local geological setting on into the regional geological setting, we 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. As we acquire more and more information our working hypothesis begins to expand.
On returning to our local geological setting, with this expanded working hypothesis in hand, it becomes possible to predict results in advance of drilling at the site of our local exploration activities. 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 involving the entire area under study.
This approach makes it possible to confirm a geo-chronological order or sequence of events relative to the deposition, lithofication, deformation and distribution of the deposit under study. This sequence of events, when conceptualized in terms of form/force relationships, makes it possible to expand this mastered understanding which has applied relevance for a particular deposit, 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 to predict results in advance at the site of any local geological 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 possible to predict the impact of those forces upon any 'new' local, geological setting; even some distance from our original work. This capability portends a qualitative leap in exploration geology. It establishes a new, higher order level of practice for an exploration geologist. It may now be possible to force-draft, generate mineral discoveries from properly ordered and properly directed geological exploration.
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 and every 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 also, the multiple connectedness of the forces responsible for the deformation of those geological 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. This may as well, serve as an example of there being embedded manifolds contained within all aspects of the various fields of study making up the geological sciences.
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. It represents a new, higher order level of understanding in the geological sciences, as well as in exploration practice.
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, stable, fusion energy plasma. Why this is so, is as follows:
Mental processes and/or action that operate to generate a contra-entropic 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, so as to contain, contra-entropic processes. So, if you want to produce a stable fusion energy plasma, you must cause it to manifest within this kind of an appropriate, geometrically defined containment 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 a local geological setting [1], into a regional geological setting [2] to gain an insight into the regional geological forces that were responsible for forming a local expression of those forces; the acquisition of this information will then cause a working hypothesis to expand. Upon returning to the local geological setting, a mastered working hypothesis [3] 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.
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 (or 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 also becomes possible to take it through geological time. As events relative to a specific period of geological history are confirmed, that rightly understood conceptual perception has applied relevance to other local geological settings. In conceptual terms, a kind of geological time travel becomes possible.
Upon encompassing the regional geological setting with a mastered working hypothesis [4] in hand, it next becomes possible to carry that understanding through geological time to a point where it can, by reflection upon those regional geological influences [5] be narrowed down into a new local geological setting [6]; with the command ability to predict or perceive in advance, sites wherein a potential for mineral development can be seen to 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 the diagrams and studied so that an appropriate technology can be constructed to be able to 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. Why? If the movement of a fusion energy plasma, through the diagram, were linear, as from area [1] to area [2]; (as might be inferred from the charting of our geologist’s activities), the plasma could not reflect off of area [2] and carry on to area [3] without passing through itself. This would cause an interference problem. Conical spiral action, resolves this dilemma.
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 here; 'an ordering principle':
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.
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 Bernhard Riemann and introduced to Georg Cantor's concept of the transfinite. I was also 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 in my exploration work 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, together with my geological education (including structural geology) were all connected up with the subject of geometry.
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 stable fusion energy plasma's 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 these characteristics.
It was the act of 'mapping' out my activities and describing those activities through aid of the geometry generated, that subsequently generated for me a descriptive terminology. Geometry was the medium, through the aid of which, I became able to communicate. Indeed, one of the things that 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.
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; that being the regional geology surrounding the exploration site.
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. So, a larger, third “circle [3]” was drawn to include that regional geology and the larger, higher order level of understanding that came with it. It was drawn larger than the two previous circles because it represented this 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 (see page 19). The next question became; what would this movement look like if it were viewed in terms of fusion energy, 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 [2] to [3]. Clearly this would not do. A review of the mechanics of actually drawing these diagrams seemed in order.
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 tiny 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 after all, the medium through which I was initially being informed.
My work defines how and why it is possible to generate successive mineral discoveries from a properly orientated, and a properly directed, geological exploration program. 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 and do the math involved.
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 often mistakenly referred to as "exploration" by the Canadian mining and exploration industry. It usually involves four or five 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 merely 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 this 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".
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 been considered yet as 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 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 thereafter 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 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 real 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.
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 (geologists) 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 practice. 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. This approach to "creative exploration geology" involves and incorporates within it, a 'process of discovery'. The property evaluation method is something static; a simple probing; a 'seeing if this works' type of an 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 (formula orientated) property evaluation approach, is a lot of drilling and testing being 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; indeed, Riemannian or Manifold 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.
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. It is this, that is important.
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.
Now consider this: 97% of all "exploration" programs fail to generate a significant discovery. 2% find something, and only 1% ever make a discovery that results in a mine.
These figures were presented (as I recall) at a combined B.C. Ministry of Mines - Yukon Chamber of Mines conference in Vancouver, B.C. in the late 70's. The intent of the author was to show "how difficult it is to find a mine".
There is however, another way to look at these figures:
97% of all exploration programs conducted along the lines of this formula orientated approach, fail. 2% find something. And only 1% ever make a significant discovery.
What is going on here is not geological exploration. It's technological prospecting and it fails 97% of the time!
Why raise all that money and pour it into a manner of exploration practice (property evaluation) that for all intents and purposes is a near virtual, if not a proven failure? Perhaps there is a better way.
Manifold Geology opens up a new branch of study for the geological sciences. It represents a new, higher order, conceptual perception of the exploration process. Also identified as Riemannian Geology, it represents a new way to view the geological sciences.
This concept of a "geology of multiple connected manifolds" i.e. Manifold Geology contains within it Bernhard Riemann's idea of "embedded manifolds". Much of what I have tried to present here involves numerous, interconnected layers of embedded manifolds within the geological sciences as well as within the exploration practice of the exploration geologist.
In respect to the prescient insight. It is a difficult thing to take the mechanism of the prescient insight and to first, recognize it and secondly to deconstruct the mechanism by which it functions so that we may be able to discuss it. This necessarily creates knowledge of it; which paradoxically, is 'after the fact' of it functioning as a prescient insight. So, paradoxically, 'knowledge of it' may not help you to enable it to happen. You more or less have to sense it and go on from there. With that said, how then do we de-construct the mechanism of the prescient insight?
A "prescient insight" comes about because of a silent informing process that gradually blossoms into consciousness as a useful perception as to how things might better function. It comes to mind without a descriptive language and occurs as a kind of "knowingness" in the mind of the witness.
Since all knowledge of the prescient insight is consequently after the fact of its functioning as a prescient insight, we might describe this kind of information as "the knowledge of knowing". All of this particular kind of 'knowledge' is after the fact of the knowingness that subsumes it. So, knowledge of it is not it; and knowledge of it can not necessarily be a means by which to cause it to happen.
A prescient insight functions as a silent informing process. It is a "sense of things" that develops by way of the subtle agency of suggestion. The medium through which this kind of suggestion based informing process operates is geometry. In exploration geology, my principle for this is stated thusly; "geometry suggests force responsible."
Most geologists come to projects to carry out what are (at best) described as 'property evaluation programs'. This type of work is often, mistakenly labeled an "exploration program" (as previously stated). Most such programs do not afford a geologist the opportunity to study and expand upon his or her work to a degree beyond a mere detailing of the geology affecting a particular property; and certainly not to the degree required of our Manifold Geologist. As a result, the freedom to pursue a prescient insight is sometimes muted by the simpler purpose behind this kind of exploration work; and so, true exploration practice becomes reduced to mere property evaluation.
To be able to successively generate mineral discoveries, you need to be a "Manifold" orientated exploration geologist, complete with the liberty to follow the suggestion of a solution that comes within any prescient insight.
You also need to adopt a 'contra-entropic' sense of direction and see your own geological work very much like Riemann and Cantor would have viewed their own work. You might also endeavor to supplement this with an understanding of fusion energy processes since they too, are contra-entropic in nature; and relevant to the orientation of the Riemannian or Manifold orientated exploration geologist.
When you do this, you will see that the mental and physical action taken in forming a series of multiple working hypotheses; which result in a mastered understanding of the local and regional geology of a property, are akin to the transformation processes going on between evolving, related, physical geometries; as described conceptually by Riemann in his 1854 paper, and as well, alluded to by Cantor with his own “Concept of the Transfinite”.
The process of forming multiple working hypotheses is the same as for forming or generating higher order geometries out of lower order geometries (as per Riemann and Cantor). This is the kind of an orientation to your geological work that you will need to replicate in order to successively generate, successive mineral discoveries.
As I set out to explain just what it was that I was sensing as regards to this newfound capability, I found myself trying to describe the exploration process from the standpoint of the activity of an exploration geologist. It was the process by which this capability came into being that I was out to articulate. As previously stated, I began this discussion with an attempt to draw a map of my movements and to describe, both my actions and the thought processes involved, in relation to the diagrams generated and the results obtained, as they occurred during an exploration program.
I began this mapping process by reflecting upon my experience of having worked on several coal exploration programs. All of them began with a principle area of interest. In all cases, this was an area where a particular coal discovery had been made. Each of these discovery sites was understood by me to be a "local area of interest" where the details of the local geology of the discovery were under study.
Conceptually, this 'local geological setting' will itself be surrounded by a "regional geological setting" the geology of which will have been found to have had a major impact upon the shaping of the geology of that 'local' geological setting. At the same time that these geological settings and the forces responsible for shaping them are being identified and examined, it happens to be that there is a corresponding intellectual process that has to be taken into account. All of this had to be diagramed into a visual aid to assist with communication.
As each geological element in this exploration effort is being studied, and new insights and information are being generated, a working hypothesis will begin to take shape. This working hypothesis will begin to expand as more and more of the geological processes affecting a property are discovered. This process will necessarily generate higher-order levels of understanding, which then, can be patterned into the mapping of the conceptual process.
This descriptive (mapping) process had to take into account, the mental activity involved and the results obtained, as well as the effect that those results would have on the advancement of the program and its objectives. With this in mind, circles were used to define the principle areas of study and additional circles were employed to reference an increase in the level of understanding being generated by these activities. Layers upon layers of geological data and reasoning had to be mapped and explained. These "layers" were seen as examples of Riemann's concept of geometric manifolds. It was a unique conceptual consideration to link this up with Riemann and Cantor. Continued research along these lines would find support for such an insight.
Further research into the other kinds of discussions that mathematicians have been conducting into Riemannian ideas, has led to the discovery of the concept of "embedded manifolds". This conceptual orientation has relevance to my own concept of multiple connected manifolds in geology. It turns out, that much of what I have tried to present here involves numerous, interconnected layers of what might be described as "embedded manifolds" in geology! It is confirmation that I have been on the right track all along.
We can see that there are Riemannian defined manifolds embedded throughout the geological sciences. Such is the case with the study of Structural Geology, and the same is true within the study of Historical Geology. There are as well, the manifold and transfinite geometries associated with the study of facies changes in Sedimentary Geology.
All of this testifies to Riemann's concept of multiply connected manifolds in geometry having application to geology; and that these perspectives have application in other fields of study within the geological sciences. The conceptual point of view underlying all of this is put forth here, under the title; Manifold Geology. Otherwise, and originally defined as Riemannian Geology.
There may be more of the same to be found in other fields of study like Geophysics, Geochemistry, Mineralogy and Crystallography.
The field of Quantum Physics also comes to mind as well, as it relates to one's perception of things geological. Quantum consciousness if you will. A topic to be explored in another paper.
The end.
Coal Exploration Dynamics Geophysical Logging and Insitu-Analysis - Selective Mining Methods
© 2013 George S. Green
ISBN: 978-0-9919761-6-4
Coal Exploration Geology In-situ Analysis - Selective Mining Methods
© 2015 George S. Green
ISBN: 978-0-9919761-8-8
Riemannian Geology.
An application to geology, geological exploration and fusion energy physics of Bernhard Riemann's concept of a geometry of multiple connected manifolds.
© 2010 George S. Green.
ISBN: 978-0-9919761-5-7
Riemannian Geology.
© 2008 GeorgeS. Green. Unpublished form. All Rights Reserved
Extended Exploration Techniques for Exploration Geologists and the Science behind Riemannian Geology.
© 2012 George S. Green.
ISBN: 978-0-9919761-2-6
Coalbed Methane. The potential in British Columbia Tertiary coal deposits. Emphasis: New Deposits.
© 2010 George S. Green
Creative Exploration Geology. A look at the creative aspect of exploration practice.
© 2003 George S.Green. All Rights Reserved
Creative Exploration Geology. Part 2. Influences on exploration practice.
© 2007 George S. Green
All rights Reserved
Creative Exploration Geology, part 3, A flawed approach leads to problems.
© 2008 George S. Green. All rights Reserved
A Tectonic History of The Hat Creek Coal Deposit (2008).
© 2008 George S. Green. All Rights Reserved
ISBN 978-0-9919761-0-2
A Tectonic History of The Hat Creek Coal Deposit.
© 1992 George S. Green. All Rights Reserved
The Gold Coal Relationship. A look at the relationship between gold and coal.
© 1987 George S. Green. All Rights Reserved
The Gold Coal Relationship. A look at the relationship between gold and coal.
© 1986 George S. Green. All Rights Reserved
Thank you.
(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/
Return to previous location(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.
Return to previous location(3) See Riemann's 1854 inaugural lecture paper, paragraph 6. (Reference as per endnote #1 above)
Return to previous location(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.
Return to previous location(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.
Return to previous location(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.
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