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        A  Plane Economy of Space Surfaces From  the Mathematics of Einstein and Euclid

 

        Marvin E. Kirsh1

        kirsh2152000@yahoo.com

       

            1 The California State University Los Angeles

                Department of Anthropology   

 

A reinterpretation of biological process, evolution and genetics, the physical world that integrates a re-interpretation  of Einsteins relativity that involves a visit to Euclids’ parallel postulate, and the mathematics and geometry of the mobius strip. An entity, the 'concept' , mass-less, unwitnessible  with both energy and location is proposed  to exist within a scheme,, extending beyond the plane of writing  paper, of energetic mobius parallels   that are accommodated to both relativity and Newtons laws of motion to account for open volumes of energy metabolizing space, the self (and external) as conceptually a mobius  with respect to both physiological and psychical functioning. A contrast is drawn between actual (in the frame of nature and apparent (in the frame of witness) emergence, the logical verses the illogical, respectively,  in light of a redefined notion of proximity to the senses, determined by behavioral habits of man as a hunter gatherer verses actual that assume definition based on the physical/temporal path of emergence..Rather than an account of evolution as an ascent of order, complexity, and diversity from the assembly of living materials from the inert, it is described as descent from higher total order and complexity that in addition to accounting  for  structural complexity, order and energy, assumes the actual physical and temporal  routes of emergence, a whole descriptive path of change, as a major factor  DNA, RNA, nucleic acids as examples of physical memory, embodied to all routes as the parameter of path  are discussed as the consequence of energy matter conversion, i.e. physical pieces of path.  A natural and non-arbitratable ethic is proposed to exist as a consequence of this model.  

 

Abstract

    This  manuscript is intended  to illustrate the existence of a natural ethic as a universal and special case in which the notion  of proximity differs from the reflexively perceived physical notion that is both commonly and scientifically employed.  In this case actual proximity in nature is proposed to diverge from the physical lines construed to connect points to be a function of  relations of the lines of perception as the components of a  universal volume that is energetic and active, yielding a conceptual active "line of sight" to a single unique surface composed  of all lines of sight, in contrast to a common notion of seeing based on connected points.  Notions in this conceptualization are  emerged as a function of past, transparent to witness, processes, in synergy with the more apparent, temporally and physically  proximal , and possess a logic that is based upon the same mathematical means of operations  that are commonly known reflexively.  This scheme, the nature of the natural ethic postulated precludes genetic manipulation as unethical in that it violates naturally inherent inherited  proximities, synergies of past and present  as, in name, nature itself as genetic and emerging.


 

 

   

 

Discussion

    I wish to comment on notions of man and nature as they relate to ethical controversy over  genetic manipulation experiments.  It would seem that the only existing plausible surface, the current substrate of discussion for this controversy would be at the juncture of common experience as it relates to the common  good and the self and those areas of science understanding that are accessible by the same reasoning to the common person.  This reasoning involves common perception of the world as space/volume and movement-i.e. distances and motion or energy-the familiar and proximal with which experience of the world is organized.  The common man in argument with the scientist is required to consider two cases, his own and those of the scientist, in the language of science that are inaccessible to him..  There are ultimately, from this perspective, two cases, the ordinary of the common person and the special case of the scientist.  In the following presentation I wish to demonstrate that in reality only one case exists  and that science theory and practice surround a  special self defined and self subscribing case that is not only accessible only from the perspective of science study but entails a contradiction such that  either the world as a singly namable whole unique entity either possess a similar divide or is itself a special case.

    Consider the writing of Albert Einstein  in The Theory of Relativity (Einstein,1). The Theory of Relativity is divided into two cases, The Special Theory of Relativity and The General Theory of Relativity. The General Theory of Relativity is entailed from the case in which  energy is postulated to exist  in spaces absent of mass or gravity, its’ notions  are mathematically extrapolated to include notions of closed space in explanation and  is held applicable  to  all cases of open or closed spaces (2).  The Special Theory of Relativity  deals with the case of open spaces as those able to support the life processes -i.e. is  capable to define the life processes.  It is these two cases of special and general that I wish to discuss, not only in analogy to the above described cases of the common description verses scientific description but as exactly exemplary of unresolved and civilization life long issues regarding the physical interpretation of nature and its’ relation to life and mankind. A new case for nature will be described as a single special case. Inherent to the necessity of the evolution  of divisions of specific cases in the theory of relativity for explanation, the creation of a divide in nature, is the implication of a great influence of historical behaviors and events on scientific elucidations. The products of science  not only shape our thoughts, but if one assumes a broad perspective and a unity to nature,  render the accomplishments of science, in content,  as an exclusive affect of history as a path of behaviors and actions  related to human conflict with nature  in which language born of perception, shaped by history,  and not mathematics, mathematical or physical constants  are  the only existing influence on interpretation. Modernly, the juncture of man and nature, is only barely highlighted ethically with reference  to human rights and environmental damage from technology- i.e., what constitutes an individual in the case of embryonic experimentation and the green house effect of global warming.  Put to test in ethical discussions are all the conceivable actions of man as a potential set with wish to judge and create ethics.   The potential existence of a special case, a universal ethic (3) that is beyond arbitration bears no witness in discussions that are immersed within conceptualizations that place nature subservient, servant to man.   

    Science in the construction of its cases has come to focus narrowly, in tunnel view to define from within the narrow view of ‘the witnessable as an accounting for the whole  by instantiation, to characterize that which can only be partially tested  but is shrouded in a paradox of duality of cases as it takes no caution with experimental constructions that do not exceed its established logic for processes .  Accounting figures, yet  always show deficits  that lead  us searching, for example, for dark matter, new forces,  particles and entanglements to accommodate theory in which obvious paradox endures continually. Theoretical constructions of nature,  dependant on the path and processes of history serve as a general case in which the  more nebulously understood components are nourished within the darker areas of understanding,  perpetually, from the more experimentally affirmed products..  Within the range of ordinary experience, nature, taken as an assertion towards the open, emergence, is given interpretation  as an entity that does not necessarily fall into an accord with the best construed directions for and needs for human survival.  Unfilled spaces, one is hardly able to describe, much less fill with theory are inflated to life  by  diffusion of established ideas from within the narrow tunnels that comprise our test and model building areas. The general case is held and perennially maintained.  From this unavoidable, (unavoidable. if one contemplates  need to impose change) and commonly oriented conception of nature science naturally, without alternative,  finds fit to act accordingly in a manor parallel to the construed, commonly held notions of emergence that are born from ordinary witness of nature itself,  yet appears to have no awareness of its own potential quality as incomplete, unwhole, emerging itself in a manner in which the facets of the process of its’ own emergence are excluded from conceptualizations of emergence in nature.   Facts of both men and animals using tools to move natural objects to build shelters in order to survive, employing  living entities as sources of food, engaging in wars involving imposed death in order to guard  borders and  dwelling areas make the prospective application of force to nature seem more natural.  

    It is at the juncture of man and nature verses the authority of science as an ally of government that the subtle differences in interpretation of nature as either one or two cases is very obscured, relegated authority leaning towards the scientist and avoiding concepts and issues that are ubiquitously laden in shadow, with an assumption, hope, that knowledge will come to be more compete as the consequence  of their endeavors.  Footing is always on the shaky precipice of the unknown.

   Nature as a Special Case

    At the root of misconceptions is the absence of an conceptual test of the  notion of proximity,  as either a general case involving physical distance, temporal distance or as a special case in which a logic of experience extended to be a universal logic involves both the temporal and physical in a synergism to yield an unsuspected unity that is  entailed by and  entails all the elements, both natural and man made divisions of the universe  into a genetically structured emergence, a single surface as a special case to describe all. For example  the locks and keys of genetics, gene sequence and action, the three  dimensional objects of the world composed of both energy and matter are presented as the consequence of  an inherited proximity as a synergism of those aspects of the world  available to witness and those that emerged from past processes;  a synergism that is conceptually singular, a universal ingredient for all to account for the world as a special case. In this discussion focused on proximity and the investment of science facilities for the manipulation of nature,  non-proximity, though conceivable and the added ingredient to perceptual accounts postulated to birth the commonly construed general case is made not to exist. 

    In the  proposed special case the planets and the subminiature are held together  in the same category, the planets and the immense cosmos with the miniature components of organisms, the cells and chromosomes in order to demonstrate a meaning for proximity- because the interiors of cells  are  within reach it is thought  to change the agendas of cellular components  and, in essence, to bridge a divide that is contended to be related conceptually more to the mysterious contents of the folds of history, of meaning in language communications and history that are  by necessity not apparently organizible,  more transparent than apparent, as its’ origins  are not available to witness. To establish a more certain perspective of the analytical lines and angles of the scientific assessment of nature  it is proposed that a universal logic exists as a special case that is immediate and ever present, in which the lengths/and distances that delineate form might be derived and defined from the transmission of energy that can exist as states of matter or energy. Perceptual accounts of nature, of the external, though basically made from constructs of lengths are in actuality more movie like than picture like, bring upon the individual perceiver a frame of the world as a, more contiguous  than stationery assembly of temporarily associated still images and sensations.  However the actual machismo  of moving images  integrated into as  a state of memory/experience cannot  be easily,  but invalidly   related  to the constructions of moving pictures seen in a theater or on television,  though resembling, in defining facets and concepts of  the proposed universal logic.  Mechanically made videos are conceived, or viewed  in retrospect with respect to their invention,  as  ideas of physical and temporal proximity, i.e.  a plane ,i.e.  a simple movie frame,  is given a temporal component along a line  represented by the length the movie strip, or track upon which it is recorded and brought to life with the addition of energy –i.e. a motor or computer processor that can arrange the frames into a temporal order. Ancient Greek  geometry might had accounted  easily for this invention, less for the means of providing and converting energy to drive its’ process.  Without putting to test Euclids’ Parallel Postulate (Heath, 2) the notion  of a picture on a grid made of intersecting lines that define composing points requires little stretching of concepts.  However with respect to the nature of the world, the parallel postulate, its’ failure to accommodate non intersecting lines, parallel lines defined as those that form a 90 degree  angle each on the same side of an intersecting line cannot be shown to fail to insect as they do not intersect in the line of the paper, the parallel postulate in its’ referral off of the plane of the paper to spaces beyond  it, space, if it were a unity as the Ancient Greeks  suspected  still remains a perplexity, an, almost unaware perplexity of all of the curiosities  and endeavors of modern society.  Euclid might  had, in retrospect,  been able to account for a photograph, the assembly of photographs temporality to make a video but not the lack of mechanical connections involved in the energy metabolism  to make the photograph move-i.e. the movement of electrons in a conductor  to cause the turning of a motor, a light to light; within todays’ vast progresses of science in the assembly of theory and the manipulation of nature there is little reflection on the parallel postulate as a statement about concepts of proximity, the infinite and eternal, as they fit with the intuitive  sense of the world as a holism, an undivided, , indivisible unity. 

    In order to extend the planar geometry of Euclid into a three dimensional space, I will employ the mobius strip (Figure 4).  A  mobius strip  has as a center to its surface, not a point, but a unique line drawn exactly midpoint of its width through its length.  It is made so that it has a twist in it as if an open belt closed with a half twist so that its’ inside surface is contiguous with its’ outside surface.    A cut made along the exact center of the mobius strip results in two linked loops, each loop the same length as the starting loop but possessing half the area.  As a beginning product the mobius strip has one continuous  surface, after its’ division the linked loops have a finite surface area that is the same for each loop, each loop half of a whole transit of its’ parent strip.  Intuitively as a candidate  substrate   and or catalyst, generator  of open nature it has gross qualities amenable to descriptions of nature as infinite and continuous, possessing  finite structures, composed of many kinds.  A video film strip  may be cut and sealed to resemble a mobius strip, create a functional movie, but, possessing necessary intersections and attachments  is still within the realm of Euclids’ renditions of plane geometry.   As a free floating figure, without the physical attachment of a movie projector the mobius strip is quite interesting and distinct from a plane untwisted movie strip that is joined to be round.  When cut to form loops the mobius, divided into two parts can still be viewed as a single structure.  The loops free floating but confined to one another, are necessarily parallel to one another, having originated from the same line.  Thus conceptually, it is a bridge from the geometry of figures drawn on planes, on paper, to open space. Progeny loops from a mobius strip, geometrically parallel to one another, are necessarily not parallel to one another in the ‘plane’  of perceived open space because of the mechanical hindrance imposed by the twist in the parent loop.   If one  can envision  many mobius strips held parallel in the plane of space, all loops produced from divisions are necessarily parallel in the original perspective  because all of the (parent) lines are parallel to one another.  Sets of parallel chained loops can be composed of parent strips of an infinite number of dimensions of length or width, each distinct from one another, confined into malleable pairs, together  can be envisioned sufficient to include all of the points in a volume of space, the center lines of parent structures, parallel to one another define  a contiguous surface  and all other lines are not only distinct from those and  not contained in that same flat or unflat surface , but all possible lines other than those from the center line, each given by a unique angle to the midline,  are able to form sets composed  in dimension of  the number of parallel parent strips. All points defined by sets, whether in looped chains or parents comprise a unique set in the second plane of real space but are confined in description to the Euclidean coordinates for parent structures   in the parent plane. In this presentation the set of mobius strips has two members, those that can exist in physical space and those that are abstracted to exceed physical constraints imposed by their surfaces to exist in space. There is a limit to the physical dimensions of model physical strips made of paper for instance; they must be sufficiently small in width so that they can be twisted and joined, intuitively a mathematical limit to width would appear to involve the construction of a whole transit as a limit circumference of circle of radius R such that R/2 specifies a maximum limit  to the width of strips so that mechanical interference does not occur; the circle occupies the greatest area for a given closed length, R is the maximum interval of separation for different faces of the strip.  Regardless of this complexity, a conceptual divide evolves in this example in which simple  mathematics elucidated for a geometry involving tangibly conceived and  non complex intersections finds, at the same time  both existence and a definable obstruction to the existence of actual physical  models-a  boundary exists between the set of, identical mathematically, abstracted and real possibilities.  Whether this boundary is consequential to the definition of real spaces and volumes  is not so certain or apparent, real designs  for space need to elucidate a unity/holism with a condition of uniqueness for  all coordinates.   The sets of lines for parallel sets of mobius strips, described with and without conditions limited to whole physical possibilities for models,  are obviously distinct and one must consider facts of potential redundancy in abstractions.  The criteria necessary to describe a special case verses the dualisms inherent to modern general cases might potentially translate to correspond at the surface of  this interface where attempts to elucidate a open universe repeatedly and perennially stumble at concepts of emergence with time,  necessarily find paradox with respect to the energy of assembly in the life sciences  and concepts of beginning and end in the physical sciences. 

    Intuitively, either the combined set of abstracted to exceed  the physical, or otherwise,  might be envisioned to accommodate all of the physical coordinates of space, volumes of any dimension and shape. The parent strip with a half twist composed of the center line and a plane that encompasses both inside and outside mathematically encompasses all of  the points of a plane, though not necessarily volume that is birthed from the twist; from the perspective of the coordinate system  of the parent uncut strip; many in parallel can be envisioned to fill completely volumes of space.  If one, however projects  to volumes of open spaces occupied physically and tangibly with non obstructed contiguous surfaces in three dimensions a separate (special) coordinate system emerges   The theoretical strip width limit of R/2 for circumference C of the center line not only precludes an infinite surface area to strips of finite size but specifies a physical maximum  of ¼ turn to the possible ½  turn of whole strips. and might be used to refer to empirically testable  physical parameters   Thus, the special set of  feasibly physically  existing parent strips/arranged in parallel  and the set of linked chains, by definition all geometrically parallel , generating  planes, in the coordinate system of the set of all  parent strips are but a subset of it.; the coordinate system  in open space is not only not equal to the coordinate system for the unconstrained  example which is able descriptively in sets of number that must be greater than one (because the twist displaces  lines made of its’ surface)  to fill space uniquely, but lesser and  yet must also fill completely the volumes of space. It seems plausible to bridge the difference physically and descriptively, accounting for energy to volume transformation  as an  embodiment  by the transformation of parent to progeny  loops from the  mirror symmetry in original structures that generate them, and  to assert to space  the property of ‘mirror’ that is embodied by the symmetry of parent strips in the center line such that all space is endowed with it.

    Many strips conceived to be parallel in the same frame as one views the coordinates of the parent strip, made to describe surfaces in that frame can  be rendered a twist with respect to one another such that the geometry of  the mobius  renders space as the set of, each unique sets of parallel lines (i.e. mobius  mirrored  parent strips and (parallel) looped chains) , in which in the set of spatially constrained  members, and  linked looped structures are parallel only by definition as a consequence of their relation to the center line  per frame of reference. A mobius strip that is parallel to all the strips in witness pairs becomes definable. This though renders an, at least, transiently existing parent strip to the (transient) witness pair,  suggesting the “chronic’ existence of a third (transient) point of  reference, and is very reminiscent of the assignation of a constant velocity of light in the special theory of relativity.  One might also find suitable analogy to this situation with the thought that the system state of proximals (i.e. witness pairs) reflects a third state that is a synergy of the two.  A box of red light and a box of blue light in proximity could be conceived to result in a box labeled “color’.  Whether  color is a suitable point of reference with respect to  blue and red does not seem  seem difficult to reconcile.  Whether ‘color ‘ can be defined by the same philosophy of  parallels and twisted contiguous surfaces (as in a mobius strip) comes to question about the nature of ‘color’, can it be described as  an energy that occupies a volume?  What of two human being conversing, is there a third witness ‘conversation/language’ concept, i.e. an ever present deity?.  One might approach this paradox  with the solution that it is an ever present logic that is valid to all frames of reference, to both physical construction and  interaction/propagation.  How does this though account for a third frame to witness pairs if by definition  witness pair implies only two entities.  One would have to conclude that the lines in witness pairs are parallel to the lines in a third reference frame, and  if he chooses not to stop at that point to claim  forth and  more frames, each greater with lesser curvature so that only sections of whole strips are involved as mirroring  entities with which to (approximate)  alignment  two sets of  parallels at once-  all descending  from the vast to the frame of witness pairs-as entities within.  What is, could be,  the location(s)  in space for  such perspectives ‘without’?  This is again reminiscent of the general theory of relativity that assigns the existence of mass-less gravitation-less though closed spaces and unsupporting of life requiring open space., though one might also remind himself of the above example of boxes of colored  light in which it is not an entity that is referred but a concept as the third reference.  A concept maybe considered a closed phenomenon, the concept of a concept also closed, the concept of a concept of a concept, so that all one can and does encounter in frames  beyond  beyond the witness pair is an ordered  library of  descending parallels that arrive at an example of witnesses in pairs that are parallel both to one another and  to all frames that exceed them.  Still again, though  where are these frames?  To account for them one must include the same notion of  physical coordinates that are lended to witness relations, unless one wishes to make a .separate case of them as they appear to be  distinct from entities in  the theories of general  and special relativity, though resembling the closed mass-less gravitation-less spaces of general relativity.   One might wish to claim an inherited set of proximities in order to give concepts location; why cannot a synergism of the energies of blue and red boxes of light have a location as well the  location assigned for that synergy and  location  assigned  to for example a synergy of  square and  round   have a location for the synergy of the two concepts.  One must claim somehow  that the concept and either or both together of  the parties in the entity ‘witness pair ‘ cannot form witness to it, to place concepts in a separate category ,possessing energy, ,   but not mass, again as in the general Theory of  Relativity ,though with physical coordinates that are  renderable from the plane geometry of Euclid, but with a twist and added demands to comply with a world that is not abstracted but confined to the constraints of physical reality. 

    It is at this notion of special and general, at the boundary of abstracted plan and tangible reality that I wish to conjecture a shared/common branching point or line to draw a parallel between the quantities of the radiation/propagation of  energy and mass as matter in a gravitational field, either filing volumes of space.  This parallel is dependant on the described geometry of the mobius strip.  Its center line has two potential roles, as delineator of length  to an endless surface if it framed with respect the quality of inside verses outside, and as a mirror  which has no dimension with respect to it as a concept, but is describable with physical coordinates.  The space containing these, entity and concept, filed exclusively with parallel lines generated from the center line of the mobius strip in which nothing can be defined as straight in  line, less for the occurrence of coincidences.   The longitudinal center line, a  mirror, is given a dual function as both a transverse a longitudinal element.  A long its length, it can be used to describe a path of propagation of energy, and transversely to describe the material, matter, mass in a gravitational field; in which its length is applied equally as a parameter in both directions to describe a volume that is a geometric product of an area times a distance, the area of a plane times the distance of a line.  On inspection, this description can be extended to account for many features of experienced space.   As radiation propagates in a planes and  mass in a line, the volume of any process may be described as the product of the two.  Matters of the longitudinal  propagation of energy aligned conceptually with the length of the center  line and matters of the possession of energy by matter aligned transversely across the mirror such that the path of propagation of a beam of light renders in a time dependant fashion distance and mass whose energy is embodied by the concept of  linked loops that are rendered from a divide to the center line., In a sliced viewed, a still frame,  mass is rendered, tentatively based on a threshold,  whose both, dimensions and mass parallel,  the length of the path of transit.  This pictorial also parallels  both description of light with transverse and longitudinal elements  as well as controversy over the nature of light as particle or wave.  Second, not present in the theory of  relativity or other descriptions,  is a potential accounting  for  the concept  of mass  as strictly physical existing weight as property of witness pairs, a single witness, non-proximity  not to exist, but the energy (of concepts) given a location along the line of  propogation,  a distance in relation to the distance of relations of parallel lines in witness pairs. Bearing no mass it has no potential witness relations with mass. 

    If one asks about the bending of light in gravitational fields, a fairly ubiquitously accepted phenomenon,  it might be  that the mass generated  transverse to light  propagation interacts with masses, or that it can be accounted for  in complex manner as facet of  vast distances of propagation along lines in which nothing but parallels exist to parent structures  and observers in a Euclid  like reference system, but which are modulated by both the physical constraints of  mass with respect to the long length and travel time along a center line. The curvature of space, not observed, impossible to observe by witnesses,  renders an observable  curved path  if other  entities (masses) are observable in the same frame, or both interpretations.  Otherwise, referral of the bending of light by mass,  as a ‘bent concept’ might seem appropriate to describe an  unusual circumstance in which an unusual event is born witness with the employment of scientific equipment  and given interpretation in terms of proximity that is construed in the witness frame of reference from a perspective of common naturally  perceived  proximity along a straight line, is ‘seen’ as if all events were tied in a straight line, to bend. In either case, mass that is manifest as weight, force, cannot be attributed to propagating radiation, potentially only as a manifestation  of its path, less one contemplate, in  this scheme, to assign physical weight to a concept.   The conceptual divisions assumed in order  to assign light both transverse and longitudinal  properties, particle verses wave properties can  be accounted for as totally longitudinal in nature, time not only active  in all frames but shared parametrically and not divisible among witness pairs or separable between masses(witnesses) and  paths of energy (or concepts).         

 

    Thus interpretation  with respect to witness or perception  becomes location/witness dependant as a kaleidoscope that renders different compositions dependant on witness location.  One might add an order to this scheme if he assumes this layout for all of space such that it is imposed as a constant facet to the intersection of energies transmitted through different spaces,  internal spatial changes within entitie, external changes, modulations  intersecting  with remodulations to produce  to coherent lines of change, motion (in vision for example)  that  are all compatible (with the same described coherent form of entities/ space)., as the basis of all relations/means of relation and inter relation of the kinds,  parallel does not mean straight as in the geometry of Euclid, but in this scheme  parallel in the Euclidean sense in any given  witness pair set unique  to each witness rendering the frames of each witness parallel; parallel is denoted only with respect to perspective defining center lines of defining mobius strips; things in nature can be made straight only with respect to the geometry of Euclid and with assumption/postulate that parallel  lines do not intersect.     

 

 

 

    When the mobius strip is flattened and arranged to form a circle it is clear that R/2 +R/2=R encompasses the maximum possible  width so, that as a result of the twist, greater widths would not overlap/intersect adjacent positions  physically, physical clearance from other parts of the strip potentially existing below this value and not above it.   If the center lines are confined to a plane in any reference frame, strips are constricted so that fractional divisions along the center length are made to correspond  in exact ratio to fractional divisions of the complete half turn embodied to the whole strip.  Thus widths of 0 to R/2, correspond to circumferences of 0 to C (C=2πR), for any particular strip and a correspondence of ½  of the whole ½, or ¼ turns.  To accommodate 360 degrees in the parent coordinate system a minimum of 4 strips of distinct orientation is needed ( 4 X 90 degrees).   A model comprised of all possible abstractions,  though has a maximum possible of ½ turn, at a width of R  and requires at least 2 strips  rather than  4 on order to encompass 360 degrees.  The difference in the number of strips need to encompass a whole turn might be translated to mean that a different number of parameters are required to describe space depending on whether one wishes to render  its core structure abstractly or confined  to the requirements of physical space.  Intuitively one would lean towards the simplest description with the least number of constituents.  The corresponding  models might be reduced in size  if the requirement for a 360 degree coordinate system is halved with the introduction  of a required plane of symmetry defined by the center line.  At this crossroads, in analogy,  todays’ science picks the less bulkier, but abstracted model that escapes the demands of physical reality at its core. For example, the value  c for the speed of light is held as a standard for the unit of distance- in the same breath, with the same dualistic ideology of arrangements of the parallel and series to render concepts  that descend from the same starting point, from  the senses of physical distance, proximity arriving at an identity  between  abstracted and  real values.

    However one other possibility exists that makes this conception, obsolete, lost to obsolescence  in the wake of a synergy that yields a holism of divides and symmetries that do not require mathematical degenerations –i.e. 4’s to 2’s to 1 in which space is described as a process catalyzed by the surface of the mobius strip translated from  its’ parent plane into the constrained volumes of space, neither its’ center line, plane, chained loops  physically existing, such that all that is abstracted is a geometrical form that can be tested against data and observation. In which the existence of dualisms, monisms, constants become second in importance to the assumption of a monism as a geometrical form that that can be suitably fit to elucidate volume and energy  I do not think this has been accomplished in light of the nature of the both open and closed spatial facets of the general and special theories of relativity. In the mobuis model presented all parameters can be given physical interpretation.  The  ½ in  Newtons laws of motion (1/2 mV^2) translates to align with the requirement for spatial constraint of figures (R/2) , c (the constant for light velocity) translates to a physical value for the velocity of propagation  along the mobius center line.  In the frame of a moving mass emitting radiation  in which mass and time can be given as state variables, one has :

E/m= R^2/2  + C^2

Volume =  R/2 C^2  

    In this case the existence of physical structure depends on the intersection of the tangible (plural mass with gravity-i.e weight)  with the intangible (geometrically constrained space)  energy as the constituents of motion. Though, the fabric of space conceived as a cloth weave might be accommodated  equally well by either situation, ,though one, the abstracted  one  ‘fits’ well within the proximities defined by the physical dimensions of the plane of  the drawing paper, and  naturally construed proximity, the restricted space model abstracted from it,  has  connections of both  parallel and non parallel lines  able to uniquely   fill space but not the plane of the drawing paper. The former general model in which all possible parameters for the mobius strip are included, fills the demand  for a physical coordinate system to account for volumes, though in the tangible world of processes,  this coordinate system  reduces in description to the mechanics of the motion picture.  It is at this paradox, to explain a contiguity of past to present that an analogy is  easily found to the motion picture studio, but  not so easily for actual processes of emergence. This paradox seems to resolve if credential is given to the existence of illogic, the converse of a  logic for processes.  The logically construed and created from assembled natural law, the movie theater as well as the logic of the physical processes that describe it,  maintained as a testimony to the logical construction of nature must be placed  into the class of illogic that also composes the constructions of dreams.  Dream content may contain even coherent descriptions of the Theory of  Relativity, Newtons’ Laws of Motion  or an exactly logical, comprehendible, and valid relation of human history or even nonsense.  It may contain a valid account of making movies but is no more bound  to the actualities realized of actual contiguity of time than either the Theory of Relativity or  Newtons’ laws of Motion. Physical theory of the world has progressed only from the conception of slices of nature to construe more slices of nature.   In the sense of a common logic of processes, the existence of life, viewed as a periodic intersection with logic, all is  encompassed into a category of  logic plus  illogic = illogic, that is put to explanation slice wise as neither a whole or part, ultimately is self defining and escapes the requirement for empirical investigation as the only source of grounding  for meaning, lingual meaning, much of  which  is not within the means of investigation.  The vain mathematical exploration of the physicist to render an ‘illogical’ mathematics such as the operation operation  in the Schroedinger wave equation, or the reorganizations achieved by the Lorenz transformation may be doomed by the absence  of coherent total perspective, the illogical can be captured only with the ‘logical’, common senses attributed to language which is by necessity grounded in the empirical. In this case a real meaning must be discerned for proximity; this I believed is only realized with the realization that the property hunter-gatherer can be applied only towards the economic and proximal tangibles of agrarian life that involve only land, food and the perception of volume as a source of energy related to physical size. The furthest conceptually that this may be extended is towards the bacterial flora in animals and soil but not to their internal constituents as a means of controlling energy flow, energy is but a concept, possessing no mass in this scheme, and is  not matter for consumption.    The case in the abstraction model given that renders one two or four distinct possible  uniquenesses seem to be, but are not  the only  alternative. Generally, processes that possess description involving geometrical progression or regression ubiquitously  elude to a reverse path that is construed from a present frame-i.e.-radio active decay.  It makes sense that the choice is not between cases of 2  or four varieties, whether to abstract or confine, maintain  symmetry, but that a whole ‘slice’ fitting empirical  interpretation  involves something other than a choice of  cases, but in  present models indicates  a single unique case with a unique focus resembling the  mathematical regression, i.e. a special situation of space that currently exists and is maintained  in which  simultaneity is maintained both longitudinally(i.e.-beyond the plane of the paper  and  transversely (within the plane of the paper)) as a general feature.  This might be conjectured  to be a common  (chronic)  temporal  influence of an unknown  phenomenon involving space, mass  and energy (Kirsh, 5 ).  It is not impossible to apply the presented model to study systems that are composed of both fast and slow propagations, e.g. agriculture  problems involving the movements of populations, and solar radiation, to create histograms and to compare them  physically to those generated mathematically, (e.g. Figure 4) in order to locate disturbances.  

    It is at this point of argumentation that I believe an addition might be made to the concept of emergence, emerging concept of nature that is arrived from  a sense of an ‘’emerging nature’ in contrast  to a nature containing emerging objects.  Mankind, tending to model nature, not in likeness to himself, but to his problems that are seated  in conceptions of nature with respect to behavior, to feed and care for, in an organized way, a growing population that is hunting and gathering. Hunting and gathering  the internal constituents of cells, chromosomes, etc. is not the same as hunting and gathering food and resources.

The logic of natures’ construction, mans’ own logic he reserves for himself with which to render interpretation, is but, as in my rendition of movie making or dreams,  a necessarily illogical slice of a grand illogic erected from non energy containing, non-emerging volumes on the flat surface of paper, when unaware, diffused to fill spaces that are not defined and have come to evolve in description into a general encompassing case for which conflicting data from empirical test is beyond the  real means and philosophical assumptions that are assumed by science. A bullying of  nature around has occurred to suit circumstances.

    I wish to build a special case ascribable to the world from the above rendition of logic and illogic, which obviously both exist in nature if man construes himself as part of nature.  In this manner the only logic ascribable is that of an absolute renderable contiguity of the identity of the kinds with time; the present as an emergence product of the past, which has no definition with which to build a grounding.   This fact must held true for all aspects of the world.  It must be though, a special product of emergence , a special case , as man with his own hands can create situations of logically comprehendible emergences; but which are only slices.  The world here, to be accounted for logically in rendition, is examined with respect to the concept of proximity, the past as a transparent component, the construed present as an apparent, meaning witnessible and testable , component.  It would seem, does seem, that in constructions, in existing endeavors, that an escaped fact common to the folds of the past as they relate to the present both baffles and threatens that our science is unsound.  As a result a compulsive and manic thirst involving exploration and data collection seems to be underway. Once considered scientifically unattainable, materially unfeasible, science fiction,  computer systems can be found commonly in house holds.  Science appears to have progressed to  a state that endorses  strongly its tenets, emerges stage to stage sometimes to draw attention for explanation  and study to encompass mans own assembled creation, as in a quick, yet  enduring marriage with a projected lasting in which self discovery is perennially at the door step, but as described above for the relation of man and machine, taken as a  logical facet of his relationship with the environment, it is really no more than an addition to the set of illogical compositions of the world that comprise the unexpected as a certain partner to life processes.  To include  the facets of physical invention within a set ascribable to an understanding might be analogous to the process of boring holes with ones’ own self created drill and to boast that he knows the dimensions of the hole bored.  

    The  process of creating ones own contiguities with an assumption that involve the  conception of  a mirror for his study of  the contiguities of the world to which we are born, by definition , ”born into”, pre-existing  seems at the least unwise, as the past in inaccessible and basically unknown. .  At the root of these misconceptions seems to be a false construction that embodies the notion of ‘proximity’ as physical closeness, and although the theory of relativity approaches this issue, temporal proximity is included into slices divided into concepts of transverse and longitudinal that are a single issue of the longitudinal.  The world is framed in this unreal manner past to present as logically assembled.’. A tangible conceptual scheme can be made with assumptions in the form of a thread, emergence to emergence,  as inherited proximity involving  all entities  and  decreasing complexity to the whole in order to account for an energetics of evolution, birth of life, instead of from perceptions of a rendered statistically ordered, less diverse, inert element, to lend to these (inert elements) a greater complexity and diversity than is assumed simply from their arrangements, and witnessable distribution rather than complexity of structure; to consider arrangements and complexities of structure in a temporal order as one contemplates emergences; to consider  the grand expanses  of the cosmos   down to the micro world of atoms,  molecules, the biochemical composition of living entities and to construe that the human being, even his appearing advanced cognitive processes, new in evolution, are arrived at from a state of higher complexity and diversity.  In this view form might be construed to take president  in a different manner than what is ordinarily construed.  If one considers the examples discussed of the mobius strip it might be possible to construe a universal holism in the form of a logic centered on it as a mechanism to find explanation, employing it to structure all states, past and present to an emerging open system  of matter- energy,  and empirical  fact.   

    Figure 1 shows a square in which three sides are consttued to construct the present/transverse element; the forth  side is derived from longitudinal/temporal,  propagations from that  preceding as energy is born witness to the other three sides by means of inherited proximity.  The sides of the square, which may as well be represented by a triangle or other figure, but in actuality is an emerging circle (or egg shape) defined by contributions from both the transverse (witnessible) and the longitudinal (past , unwitnessible) .    as a geometry of lengths that are conjectured to function at the root of all natural fittings. Form is reduced to a matter of lengths rather than velocity and mass  such that the fitting of parts, longitudinal and transverse, is accommodated more as matter of the assembly of a (3-dimensional) picture puzzle than as rules governing the energy of chemical and  physical processes.  The geometrical structure of the mobius strip as catalyst is made to account for the inherent energy of  matter   as the consequence of a torque energy and a mirror symmetry along the dividing line of parent mobius strips with a ½ twist  It is proposed to be an inherent and indivisible  aspect of the properties of matter, that is witnessed conceptually as the generation of untwisted looped pairs from, parallel to length  longitudinal cuts of parent strips. The uracil molecule found in RNA of the cytoplasm of cells and not in the DNA of the nucleus or other organelles, seeming to act as a the delineator of biological identity has a mirror symmetry that is unrenderable  in test tube experiment as it has been found not to be synthesizable from it chemically synthesized mirror halves.  It’s biological function and specificity to RNA seem to be a factor of the contortion ability of its planar configuration to fit in o the structure of DNA verses RNA.  Space is conjectured to be shaped and embodied in all aspects with respect to the contour of the mobias strip, such that it is by no means straight geometrically with respect to proximity, either of matter or of energy-the energy attributed to concepts verses the witnessible..  DNA can be construed in this scheme as a piece of physical path , physical and energetically active memory defined in relation to its previously existing state of energy possessing parametrically a unique path and velocity (Figure 2).  ΔC is proposed to be the topic of constructions and is translated in magnitude to fit the square puzzle piece as a manifestation of  proximal spaces to form a synergy product of volume (with the other three sides of the square in Figure 3). A unique description, one case results in which  linear motion is represented as the case of mechanical constraint  (i.e. limit of strip width=R/2) and the propagation of the energy of radiation energy is represented from the case of bidirectional propagation (area = (distance of propagation) ^2) . All is encompassed beyond the plane of the paper (as an applied parallel property of contours, mechanical constraint, mirroring,  and halving of stips to change their conformations)   in which a geometrical  form only is maintained in all frames of reference. 

    The manifestation of proximity is intuitively suggested to be a function of the inverse of  parametric values of  distances that translate to the values of energy contained to volumes, approximated to Δc such that it is a necessary property of the universe that a congruency exist with respect to appropriate acceptable sizes of masses and their formation energy with respect to interpretation in which energy is translated to distance/length...  Inverse plots of the egg (Figure 4) from a construction of space involving light emitted in plane transverse to the  direction of propagation  of a moving mass, from the mass as a traveling point on a line fit both the scale and shape of starting plots though independent parameters of angle align very differently in the rendition of form. Inverse values of c (1/(3 X10^8) m/s, ,about .3 meters per year ) are within explanatory range of  gestation time and size of the gametes of mammals.  The universe births egg shapes structures, either mass or volume in this scheme in which only increments of change and ratios are considered.

    This conceptualization  of emergence is very similar to the physics of crystal growth in a medium which supplies the energy and resources for growth from a seed, e.g.an ordered arrangement of volumes in an energy supplying medium. .  Recent research reports (Sowerby et al., 6) on mechanisms of the origin of life suggest that the genetic code might emerge from layers of nucleosides generated under artificially created  conditions that are postulated to have existed in the past.  This evaluation, though lesser in scope than the presented model does not preclude it. Recent  assessments (Danchin et al., 7) relate the spatial constraints necessary to account for the physical structure of the cell wall from the   arrangement and composition of the gene sequences responsible to encode for its’ constituents  This creative  holistic approach in analysis concurs with the presented representations of  proximity and the existence of physical/spatial constraints that are arrived from a translation of linear geometry in which constraints exist as a special case (i.e. pre-existing in DNA) and are  translated to be characteristic of the physical content of space(s). In a broader view DNA is postulated to obey the same physics with respect to emergence, structure and function.  The interpretation from observation of a genetic language is suggested to arise  by induction (Kirsh,4) that excludes self/internal and external relation and is given classification, as presented,  as a general case.        

    The geometry of Euclid can be envisioned to graduate conceptually from the  set of the illogical sets of slices of the world to a set  of logical wholes, with a simple twist that inverts inside with outside. made to Euclids’  plane geometry that yields physical intersections to conceived  parallel lines . Most important to the pursuits of civilization, science can possess  a ‘logical’ concept for proximity that bears it’s truth more in philosophically found aspects of the world rather than from strictly within  views erected from the wishes, wants and frustrations of civilization as hunter-gathers.

    Important to this is the concept of a natural ethic that encompasses a whole rather than slices of nature  lingually oriented as a malleable form rather than mathematically oriented as a rigid structure, embodied mathematical logic to the innately illogical, as it relates to topics of the economy of space is a growing population with limited resources.  On inspection of plane geometry and the spatial arrangement presented, the accepted  (general case ) description entails the utilization of space at a much greater rate than the arrangement of mobias strips in which  the class number of sets in the latter is reduced by a maximum of ½, and is (the general case) reflected in the false assumption of proximity to objects that in reality exceed the classification as tenable objects of  hunting/gathering behavior from which the natural world has been  organized scientifically.  Space is not used economically, but spend thriftily from a reserve perceptually perceived to be infinite to unnaturally cause a lessening that is hardly perceived distinctly from the effects of overpopulation.    

Conclusion

 

Scientific method can be limited by either experimental serendipity, philosophical short comings or both. It is suggested in the enclosed  manuscript that nature is  misconstrued as a result of  false ideations of proximity.  Representations of the proximities of entities are suggested not to be apparent from the perspective of sensory based human perception, but more realistically organized not as the world is perceived to be structured but as routes of emergences actually occurred.

   The theory of relativity is proposed, in part, to be the product of an overlooked, unavailable to the senses,  emergence of a force to the environment of the earth over an extended longitudinal time period with respect to humanly constructed,  transverse slices over intervals appropriate to the human life time.

   Instead of strict mathematical translation of perception of nature into natural law. a universal geometry existing beyond  linear constructions made on drawing paper, based on the geometry of the mobuis strip and a visit to the Plane Geometry of Euclid and his Parallel Postulate is proposed.  It is decided that  straight lines on the plane of paper exist in a real space in which parallels can intersect and nothing might be  straight or determinable to exist purely that way. Space is postulated to be egg shaped by virtue of the available coincidences of change needed to produce coherent structure involving the linear motion of masses and the planar propagation of radiation or energy. An ever-present logic involving simple mathematical operations and ratios is proposed to pervade all-i.e. internal physiological construction and function as well as sensory discrimination and energy states responsible for the existence of concepts and cognition, all are postulated to be mirrored from a primordial form existing in nature that is differentiated from it by means of the possession of different routes of emergence, inherited proximity.  Major implications of this scheme are a natural ethic and the unfeasibility of other means for the arrangement of space e.g.-multiple universes, the closed spaces entailed by general relativity, etc. The universe as the topic of human study is restricted to exclusive  definition, a mutually  shared nature with  the human mind as the instrument of test by means of  mutual witness; as  tribute to their sameness with respect to their  means of existence. It is the contrast of  sameness and differential path of inheritance towards apparent proximities that presents the paradox of inertia to account for motion, constitution and property differentiation of different spaces/entities with respect to frame of reference, simultaneity, memory and consciousness in living organisms. Quantum theories of brain function and consciousness are suggested to be, in one frame, a milking of the stone in search of  mathematical enumerations of proximity relations that are ubiquitously derived, in part, from unwitnessible past events;  and in another frame a search for explanation of a beginning in lieu of granting an external (to ?) funding source for the orders and diversities of nature that are accomplished by the  inheritance of proximity, and the absence of non proximity such there are no feasible loose-ended abstracted exceptions to common logic.   It is proposed to be  this frustration, at the doors of unresolved  paradox  and failed experimental serendipity to unearth  appropriate physical parameters to oppose escaped  theoretical abstractions generating rationalized parallels of environmental, agrarian in origin, tools for survival with  equipment that penetrates the interiors of observed structures, that  universals of spaces and volumes have become  the victim of accessibility, frustration  from the mallets of physical scientific-social  machinery.    

 

 

Literature Cited

 

1)    Einstein, Albert Physics and Reality Journal of the Franklin Institute 221:3 359-382 March 1986

2)    Heath, Thomas, L. The Thirteen Books of Euclid’s Elements, Cambridge University Press 1908

3)    Kirsh, Marvin, E. Induction, Space, and Positive Ethics Ludus Vitalis, vol. XVI, num. 30, 2008, pp. 225-228.

4)    Heath, Thomas, L. The Thirteen Books of Euclid’s Elements, Cambridge University Press 1908

5)    Kirsh,  Marvin E., Einstein and Mythology : The Lengthier  the Relations in a Myth the Greater Its’ Mass.  (in review : http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1422742)

6)    Sowerby, S.J., Heckl, W.M., The Role of Self-Assembled Monolayers of the Purine and Pyrimidine Bases in the Emergence of Life, Origins of Life and Evolution of the Biosphere, Volume 28, Number 3, June 1998 , pp. 283-310(28)

7)    Danchin A., Guerdoux-Jamet P., Moszer I. , and Nitschké P. Mapping the bacterial cell architecture into the chromosome Philos Trans R Soc Lond B Biol Sci  v.355(1394); Feb 29, 2000.

 

 

 

Figure 1   Representation of Transverse and Longitudinal Components in Entities

 

 

 

       

               

Figure 2  The Form of DNA possessing the quality of memory is derived from the general from of space as an inverted surface.  Distances are along the length of the inversion; volumes are areas of surface multiplied times distance.  A model composed of inherited proximities are proposed as a spatial necessity for the feasibility of living entities.

 

Figure 3 Geometry of the Mobius Stip

 

 

Figure 4       A graphical representation of an egg made from an equation (Equation 2).  On the right is its’ inverse (1/R)(black) supper imposed on the non inverted form (green).  Both the inverted and non inverted forms occupy comparable  volumes and shapes, may represent a fitting of transparent  energies/geometries to form a ‘logic’ of the universe  

                                       E/m=  Velocity^2/2 + Light Velocity^2 (C (Speed of light) is applied as a variable                                        R(a)Sin @ = Velocity       R(a) Cos @ = Velocity of light                                                                 Radius/Radius(a) = [[(sin theta)+2 (Cos theta)]^2(2 Cos phi)^2]^1/2