Dimensionality of Oribifolds

When a space that exists in the form of an orbifold moves through a discrete Lagrangian as a space that remains in the same general format of covariantly-based Real Reimmanian Gaussian symmetry, then, over the course of the corresponding Fourier Transformation in which such a given arbitrary space is moving over the eluded to time-frame, the said space is traveling consistently here in the same universe during the said duration. Yet, such a space as I have been discussing here may often enter perturbative fields in which the said orbifold may enter and/or leave levels of dimensionality that involve respectively more or less numbers of spatial dimensions. The genus of universe that a space or an orbifold is existent in does not work to define the number of dimensions that the said space is moving in as a specific condition in and of itself. Likewise, the genus of universe that a space or an orbifold is existent in does not work to define the specific format of dimensionality that the said space is moving in as a specific condition in and of itself. What genus that a given arbitrary space is moving in, over a specific given Fourier Transformation that here directly involves the timewise motion of an orbifold that is traveling through a Lagrangian in order to operate to perform a specific function, is based upon the format of the norm-based conditions of the directly corresponding discrete units of energy impedance that work to comprise the impedance of the said orbifold -- when in relation to the alterior formats of the norm-based conditions of the directly corresponding discrete units of energy impedance that work to comprise the impedance of the orbifolds that spatially surround the initially mentioned orbifold. This may not be a complete enough explaination for many to understand, yet, this is the beginning of a dialogue that we may work upon in order to better understand a solution to such questions. Sincerely, Sam Roach.

Manifolds of Superstrings That Act As Groups

The key to substringular phenomena moving together in sets or groups is the concept of orbifolds and orbifold eigensets. Superstrings tend to move together in groups that exist in membranes that may be described of as orbifolds. Orbifolds tend to exist in groups that may be described of as orbifold eigensets. Subatomic particles known of as quarks and leptons are comprised of certain basic orbifold eigensets. Such groups of membranes that are comprised of superstrings that work together for a common codifferentiable purpose act as sets of covariant interactive sets of substringular phenomena that work to fulfill their given respective operations. Often, in other cases, certain superstrings act to an extent alone in terms of an independant operator that is covariantly codifferentiable with its surrounding phenomena in order to fulfill a given arbitrary operation. Often, too, certain substringular phenomena other than superstrings work as sets in such a manner so as to fulfill other given arbitrary operations. Norm-States often tend to be comprised of multiple first-ordered point particles that work together as a group in order to permorm a certain operation. Norm-States often work in projections that operate as groups of norm-states that perform given arbitrary operations. Often, too, point commutators act in projections that behave as groups or sets of such said commutators in order to perform certain essential operations. All of the operations of the substringular act as a multiplicit covariantly codifferentiable group or set of smaller substringular phenomena that act in such a manner over time in such a fashion so that phenomena may coexist as a rather interconnected whole that allows the substringular to function. Enough for now.

Part One Of The Fourth Session Of Course Ten

Light-Cone-Gauge-Symmetry involves the differential chirality between the light-cone-gauge eigenstates that are attached to those one-dimensional superstrings that are a form of energy permittivity ,and, this symmetry also involves the differential chirality that exists among the light-cone-gauge eigenstates that are attached to those two-dimensional superstrings that are a form of energy permittivity.  This symmetry allows all of the superstrings to tend to travel at light-speed and below, in so long as the corresponding respective given superstrings obey Noether Flow.  Superstrings obey Noether Flow if these strings are orientable during either the Bette Action and/or during the Regge Action.  If a superstring is unorientable during both the Bette Action and also during the Regge Action, then, the said given arbitrary superstring will be tachyonic during the duration that exists in-between the initial iteration of instanton in which the said string was unorientable until the next corresponding iteration of instanton.  The mentioned general form of symmetry allows for all of the superstrings that are affiliated with the said tendancy of Noether Flow to travel through the general kinematics that are associated with "Ultimon Speed" during the course of that related Ultimon Flow that corresponds to the respective activity that happens in-between one iteration of instanton until the ensuing iteration of instanton.  The transveral components of any given first-ordererd-light-cone-gauge eigenstate pulls the whole respective said light-cone-gauge-eigenstate phenomenon around the Ultimon in a radial manner -- via the cross-sectional basis of the mentioned said light-cone-gauge eigenstate that is related to the initial Laplacian differential geometry that exists among both the respective second-ordered-light-cone-gauge eigenstates with correspondence to the initial Laplacian differential geometry that exists among the respective first-ordered-light-cone-gauge eigenstate during the course of that eigenmetric of BRST that exists during the iteration of instanton in which one is able to map the respective said "snapshot" of how such a mentioned differential geometry covariantly interacts with its local environment.  I have more to say about this later.
I will continue with the suspence later!  Sincerely, Samuel David Roach.    

The Third Part Of The Last Discussion

These semi-groups that here arbitrarily commute kinematically phenomenal discharge of those related superstrings, of one or more of the said orbifolds relative to one another, causes the spin-symmetries that become covariant here via wave co-axials that covariantly differentiate thru a Lagrangian that occurs over an arbitary Fourier Transform so as to curve with relative hermicity on account of the related Njenhuis wave-tug permittivity eigenforces and the related Njenhuis wave-tug impedance eignforces.  The Laplacian mapping of the path that relates to what I just described is what I am trying to convey here.  This happens in such a manner so that the Campbell/Hausendorf/Campbell Hausendorf and Zero-Norm Projections that are formed on account of this, here, arbitrarily forms a hermitian motion via the Greene Function known of as the Fujikawa Coupling.  In other related cases, such an activity may form other types of Yakawa Couplings.     
I will continue with the suspence later!  Sincerely, Samuel David Roach.

Part Two Of The Fourth Session Of Course Six

Well hello again world, this is Sam Roach here! I hope that I am keeping up with your attention span!

                     
So, the metrics of the substringular phenomena based on the past and future occurances that happen among such tiny particles and gauge-actions effect the metrics of the rest of the substringular arena that exists along the kinematically Fourier differentiation of phenomena that interacts from within and from outside the Ultimon. The main exception to the condition of metrics that do not have as much of a probability of effecting the surrounding metrics in a necessarily spontaneous way is when eigenstates of space that proceed within a series of space matrices are re-distributed to a sequence that functions as part of a different universe. (Parallel universes that are different do not necessarily have a directly corresponding spontaneous interaction with other universes during covariantly determined group intanton.) All of the parallel universes and time-potentials and sets of parallel universes are the fabric of the Ultimon. For an allegorical example, the earth appears flat, yet the earth is not flat. The direct fabric of the Ultimon appears completely topological and smooth, yet during certain metrics and submetrics that exist over the stretch of space and time, this is not always so. This means that after each duration of the Bases of Light, the flow of phenomena of the Continuum adjusts by one or more discrepancy interiorly on either side of its construction. This discrepancy is due to the fact that there is no such thing as a completely one or two dimensional phenomenon. The conditions that define certain phenomena as one or two dimensional are the Ward Conditions that define the spacial parameters that are used to scope the conformal dimensionality that is used to determine the inter-relationship of dimensionality itself. So, based on certain physical definitions that are used to extrapolate what determines something to be one, two,...to 32 dimensional has to do with discrete physical Ward Conditions. Remember, everything has length, thickness, and width. Accordingly, a tori-sector-range has phenomena on either side that curve relative to the prime given exterioralized phenomena by the radius of a discrete number of second-ordered point particles. A second-ordered point particle is the "skinnyest" type of phenomena that exists in free space. Third-Ordered point particles only exist where second-ordered point particles are at.

I will continue with the suspense later. Sincerely, Sam.

A Summary Of Part Two Of Session Five Of Course Six

Hi there people, this is Samuel Roach here!  I hope that you are doing fantastic!  I am here now to ellaborate as to some of what I meant when I typed out the second part of the fith session of Course Six.
                    
Think of this metaphor that is based on a reverse fractored tense relative to what I mean by parallel universes verses layers of reality.  Let us say that each life consistency that bears a soul was allagorical to a universe.  The various frameworks of their state of thought (the sets of general thoughts that each soul consistency imbued into their thinking) would be analogous to different layers of reality.  So, when a person "changes" their mind, each discrete set of such changes would here be analogous to a different layer of reality.  Correspondingly, many people may experience basically the same reality at the same time -- which is analogous to the concept that every universe shares certain "layers" of reality.  Often, the thoughts of many individuals and or the thoughts of an individual living creature may have the same thought pattern.  This is analogous to the condition that each type of universe is mirrored 9.1 million times, and there is 150,000 net layers of reality that each universe shares in total.

When multiple adjacent second-ordered point particles that are adjacet belong to the same layer of reality, then the sub-mini-string interconnections between these second-ordered point particles is going to tend to be tend to be based on a Semi-Laplacian-Based abelian differential geometry.  What I mean by an abelian differential geometry is that the interconnections between the said second-ordered point particles here bears a direct wave-tug that pushes and/or pulls the phenomena that it is covariantly interacting with through a unitary-based directoralized Lagrangian over the course of two consecutive instantons.
When multiple adjacent second-ordered point particles that are adjacent belong to a different layer of reality, then the sub-mini-string interconnecgtions between these second-ordered point particles is going to tend to be based on a Semi-Laplacian-Based non-abelian differential geometry.  What I mean by a non-abelian differential geometry is that the interconnections between the said second-ordered point particles here bears an indirect wave-tug that pushes and/or pulls the phenomena that it is covariantly interacting with through a multiplicitly-based directoralized Lagrangian over the course of two consecutive instantons.  The condition of the torsion that is applied to sub-mini-string, which is one level below discrete substringular field, works to define the condition as to whether such chord-like material is relatively jointal in nature (which is more relevant to abelian conditions), or as to whether such chord-like material is relatively smooth-curved in nature (which is more relevant to non-abelian conditios).
The other manner in which one may reffer to a "chord-like" phenomena in the substringular is that Planck phenoman related phenomena that are adjacent and of the same universe, since these bear more of an unborne tangency relative to one another, tend to bear more of an abelian interconnection with the other associated Planck phenomena related phenomena that I am here describing in this paragraph.
Such mini-string interconnection here that tends to be relatively abelian bears a direct wave-tug, even though the Lagrangian that is pulled through here does not necessarily bear a unitary directoralization in terms of the Lagrangian that the said phenomena pushes through.  Likewise, Planck-Like phenomena that are of different universes bear mini-string interconnection that tends to not bear as much direct wave-tug upon each other, and the said norm-conditions here do not have as much of an unborne tangency.
I will continue the suspense later!  Sincerely, Sam.