RIEMANNIAN GEOLOGY

 

An application of Bernhard Riemann's concept of a geometry of multiple connected manifolds; to geology, geological exploration and fusion energy physics.

 

By

George Stuart Green, B.A. Geol.

© 2010 George S. Green

ISBN: 978-0-9919761-4-0 (html)

 

Preface

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. Riemannian Geology came about as I set out to define the science behind this capability.

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An Overview

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 expression to the evolution of higher levels of perception. Just as an evolving geometric process describes a lower order geometry going over into a 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) 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)

 

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An individual geological formation 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 time continuum or backward in the geological time continuum. Forward in the geological column or backward in the geological column.

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. The movements so generated, establish relativistic relationships as far as the various structural characteristics are concerned.

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, 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 so traversed, is linked with force and form throughout geological time.

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, as well, be consistent throughout geological time. It should correlate concisely in the local and regional geological settings.

 

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Physical geology represents physical (stressing physics) forces translated into form. Historical geology connects form to form through geological time. This is also akin to Riemann's concept of a geometry of multiple connected manifolds. 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 is akin to 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 manifolds 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 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.

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, that reality itself is composed of an interplay of force and form.

Advances in successive orders of conceptual geological understanding are indicative of Riemann's concept of a geometry of multiple connected manifolds. Geological reality itself, in the final analysis is composed of two elements, force and form, both of which are at root, geometrically defined.

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

 

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With a geological column and the use of historical geology as a necessary form of proof, it can be seen that a functioning relationship exists between force and form throughout geological time.

This perception 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, and is 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 a geologist's exploration practice mirrors that fact, that geologist's perception of things geological should come into alignment with the fundamental ordering of the affairs of things geological. If this happens, that exploration geologist should be in a position to know where the minerals are, and why they are where they are.

 

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The Exploration Process

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 that property.

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 is 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.

With respect to the geological exploration of a potential mining property, the most immediate work 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. Combining this with an air photo study, this data is then plotted on to a base map. It is, as this data is collected and this work preformed, that 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 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 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) successive mineral discoveries.

 

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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.

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 an 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. 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.

 

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Under such a conceptual perception of exploration processes, such work can be extended from the local geological setting, into the 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.

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 production might occur.

The important thing to do, is to establish a comprehensive (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 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 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 and to add to the information base used to generate successive, 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. 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 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 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 comprehensive understanding, it is possible to predict results in advance of drilling. As this occurs, it indicates that things are rightly understood.

The path of the evolution of this comprehensive or mastered understanding proceeds from the local geological setting into the regional and back again. Eventually this effort opens up an ability to leave that local geological setting with things well understood, enter the regional geological settingwith 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.

 

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Regional geological forces acting to affect a local geology do so by deforming geological formations. That deformation 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 through a regional geological understanding into a new local geological setting. Because that deformation process is understood, 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 at which mineral development might occur.

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 the exploration geologist.

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

 

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Extended Exploration Geometry

This 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 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 mastered understanding (3) begins to evolve that encompasses that local geological setting sufficient enough to allow for the prediction of results in advance of drilling at the site of those local geological 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 (a mastered working hypothesis) becomes confirmed. Confidence increases to the point of being able to predict results in advance of drilling.

With this mastered working hypothesis in hand, it 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 in other local geological settings.

In conceptual terms, a kind of geological time travel becomes possible; 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 a command ability to predict or perceive 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.

 

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1. Local geology (principle area of study and exploration).

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

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

 

That comprehensive understanding (4) is carried forward.

 

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

 

 

It is next focused or narrowed down into a new local geological setting (6) with the command ability to predict results in advance.

 

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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 any local geological exploration activities, a working hypothesis expands in accordance with the acquisition of this information.

On returning to the 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 in the 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, 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 to predict results in advance at the site of any local geological exploration activities with this mastered understanding in hand, 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 the regional geological forces and how they will act to affect a new, local geological setting makes it possible to predict in advance, the impact of those forces upon that new, local geological setting.

This capability portends a qualitative leap in exploration geology. It means a new, higher order level of practice for exploration geologists. A higher standard of excellence of practice. It is now possible, to actually generate mineral discoveries from 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 proceeds 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.

Mental processes and/or action 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. Therefore, its necessary geometric form must as well reflect to contain contra-entropic processes.

 

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When the efforts of an exploration geologist, directing the exploration process, carrying out an exploration program are combined to picture this action and those thought processes into an appropriately descriptive geometry, that picture becomes reflective or characteristic of the necessary geometric field-form wherein may reside a fusion energy plasma.

The process; 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; that process is akin to the transformation process going on between evolving, related physical geometries as described by Bernhard Riemann in his 1854 paper. The process of forming multiple working hypotheses is the same as for forming or generating higher order geometries out of lower order geometries.

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 the 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 extended exploration programs 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 action 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.

 

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This 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 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 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 (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 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; encompassing the regional geological setting, with a mastered working hypothesis in hand (4) 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 exist.

 

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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. 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.

 

Local geology (1) Regional geology (2)

 

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The movement from (1) to (2) begins with conical spiral action.

 

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.

 

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

 

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.

 

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

 

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 geometry.

 

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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.

 

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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 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 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.

 

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Author's note

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, my contra-entropic sense of things, and 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.

 

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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 that subsequently generated 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 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.

 

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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 also 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 (2) to (3). Clearly this would not do.

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.

 

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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.

.....End.....

 

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Endnotes

(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 147;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 31)

(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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