Part Two Of The Seventeenth Session Of Course Ten

As I was discussing, as the discrete units of the directorals that here correspond to the prior eluded tensors are considered over an arbitrarily given Fourier condition that inter-relates the related superstrings that work to comprise the assoicated said traits, residue that is here delineated over a relatively brief metric works to transversally and vibrationally commute a certain degree of "tingling" that lubricates the kinematic association that covariantly binds the two said traits.  The coupling that happens over the course of the prior mentioned brief metric is an arbitrary given example of a Yakawa coupling that here involves indices that works to allow a variance that translates a tense of Weyl covariance that tends to conform to the corresponding Ward Caucy conditions that work to define the physical boundaries of the said traits in all of the Fourier-based derivatives that involve the overall dimensional scope in which the superstrings that work to define the said traits exist in.  The corresponding Cassimer Invariance that will happen here -- if the related Yang-Mills supersymmetry is to here take hold -- will then attain a spontaneous metric that here involves a parity and dual chirality that will work to even out the loci of the settings over the duration in which each associated encodement is quantized.  Yet, if the corresponding Yang-Mills supersymmetry that we are to consider were to not be attained here, then the associated holomorphic residue will flow over the duration of the brief metric that inter-relates this second possible scenario -- after each reiteration that would thence happen between the homotopic indices of the said traits.  The prior mentioned metrical condition would cause the metaphorical-based "fluid" flow that I had initially mentioned in my last post to become perturbated in terms of its displacement over a tightly-knit Fourier Transformation in which the traits mentioned earlier will, in this case, not be as superconformally invariant as these otherwise would be.  Under the conditions of such a perturbation of what would otherwise be more delineatorial-based stable, the inter-related fractal of magnetic coupling that could be extrapolated here would involve an increase in magnitude as well as an increase in terms of the corresponding fractal of charge.  The "fluid" would then snap and recoil in terms of its delineation over the course of the prior mentioned tightly-knit Fourier Transform.  If the associated holomorphic index that would then exist under the directly prior mentioned conditions were to now increase in terms of action intensity over the course of the kinematics that would involve the covariance of the related eigenstates that are comprised in part by the superstrings that work to form the prior mentioned said traits, then the recoiled sections of "amorphous" quantitative topology may -- after the coure of the proper sequence of iterations and the proper series of wave discharge -- slip in terms of its positioning of local distribution as a folded manifold to where it would go back into a connection that would here exist in-between the hyperstates of the said traits in so that the exterior counterpoise that would here be physically present, as well as the corresponding hypnostates of the related holonomic ground-states, would then differentiate through time in a singularized manner in so that the given phenomena would then act as a theoretical homotopical-based eigenbasis.  Such an eigenbasis would here be partially codifferentiable in terms of the inter-relation of the covariance of the two said traits over a related Fourier Transformation in such a manner so that the related activity would work to draw in the quanta of a re-convergent norm projection. I feel that I am burning the candle at both ends.  I will continue into course 11 when my sanity lets me.  I will continue with the suspence later!  Sincerely, Sam Roach.

The Thirteenth Session Of Course 10

What ramifications as to energy flow are due to those permutations in the radial tensors of a set of one and two-dimensional superstrings that quantify to form the phenomena of an arbitrary given physical trait which is covariant whith another arbitrary given physical trait?  A sequence of one and two-dimensional superstrings wobble in the scenario that I am beginning to enfold.  The given arbitrary wobbling that I just mentioned happens in regions which centralize locally toward their respective substringular neighborhoods as a kinematic eigenmatrix of reiterations which expel harmonic wave residue.  This happens after the convergence of each corresponding series of itertating superstrings in such a manner so as to form an output of the related superstrings.  The delineation of such an output distributes homotopic residue in the given arbitrary substringular local region in which what I have just described is happening.  The ghost anomaly-related residue here renormalizes in conjunction with the directly related point commutators which here act as eigenstates.  This happens in such a manner so that the related Imaginary radial tensors (Njenhuis tensors) that most directly correspond to the Real Reimmanian-based transversal anharmonic nodal indices interact in a Yakawa manner that is not Gliossi in this case.  This Yakawa-related coupling interacts with the directly associated Fock Space that is involved with the associated given arbitrary superstrings that are being discussed here.  As the mentioned superstrings wobble as I have been mentioning, the anharmonic nodal indices converge upon a harmonic wave delineation at a discrete measure in the substringular so as to bear an interaction during the multiplicit iterations of instanton.  This happens over a discrete metric that here involves an integer number of instantons that happen over a sequential series.  (The discrete metric here happens over a discrete period of what one would here describe as a discrete amount of Real Reimmanian-based time.)  This metric acts to Dirac the quaternionic-based reiterative substringular metric in respect with the associated given arbtirary superstrings that are involved here in so that the sequential compactifying that may be described over the duration of such an activity happens in a euclidean manner that involves a reverse-Clifford Expansion that is not euler in terms of the decrease in Hodge Volume over time.  What was first here a reverse-expansion will then stretch back in respect to the relativel locally-related superstrings which are most directly associated with the partial encodement of one of the respective covariant traits in relation with the other related trait.  As the metric that is directly associated with the prior mentioned wobbling superstrings relapsess, the related Poincaire generators, which here distribute that partial integration of such associated parameters, so that when such parameters are varied in distribution, this will cause the occurance of the activity of substringular pheonomena that is directed in each related separate variable of one of the given traits in covariance with the other one.  This happens in such a manner so that the given related superstrings of one of the mentioned traits may then be able to differentiate in a Fourier manner as a whole relative to those superstrings that appertain to the other mentioned trait so as to form a substrate that normalizes the corrrelative critical cusps of each associated jointal singularity that was previously separated by the harmonic discharge of the corresponding field propagation in the given substringular region in which such activity is happening.  The related Poincaire interaction that one may thereby entail may involve what I just mentioned because of the prior Fock Space encodement that works to help cause the prior mentioned activity.  This described form of compactification and decompactification that toddles back-and-forth causes the delineatory-bases of membranes that are described as orbifolds, which, via the related parity-based and vibration-based modes, works to delineate operands that have the nature to allow the time-based flow of topological phenomena that other phenomena may be distributed into in order to allow discrete energy-based holonomic entities to flow over a sequential series of multiplicit related instantons that are covariant so that energy may exist at all.  I will continue with the suspence later!  Sincerely, Sam.    

The Eleventh Session Of Course Ten

When a second-ordered light-cone-gauge topology is plucked by a gauge-boson, the activity of such plucking is known of as a light-cone related gauge-metric, and, the vibration of such a gauge-metric is known of as a second-ordered Schwinger Index.  The individual mini-string links between a superstring and its associated Fadeev-Popov-Trace are known of as second-ordered light-cone-gauge eigenstates.  The whole general holonomic field topology of these links that exist in-between a superstring and its corresponding Fadeev-Popov-Trace is known of as a first-ordered light-cone-guage eigenstate.  The sum of the vibrations that are formed by a first-ordered light-cone-guage eigenstate is known of as a Schwinger Index (first-ordered).  A second-ordered Schinger-Index may be delineated through an arbitrary given Rarita Structure eigenstate with a tense of orphoganal Yakawa gauge activity, and thus bear a harmonic wave propagation along the said associated Rarita Structure eigenstate.  Or, a second-ordered Schwinger-Index may be delineated with a tense of assymetric multiplicit (in terms of directorals) Yakawa gauge activity, and thus bear an anharmonic wave propagation along the same general type of associated Rarita Structure eigenstate.  When a gauge-boson (E(6)XE(6)) that plucks a second-ordered light-cone-gauge eigenstate does not bear a tense of borne tangency in terms of the associated homotopic Ward directoralization -- the gauge-boson as a whole is not orphoganal as a unit upon the given second-ordered light-cone-gauge eigenstate, the said  E(6)XE(6) string that forms the perturbation here in the proximal locus of the given arbitrary Rarita Structure eigenstate causes an anharmonic wave metric-gauge that, in and of itself, tends to move in the direction of the course of propagating an eventual Wick Action.  A Wick Aciton is the most important form of a Hausendorf Projection.   

Session Seven Of Course Ten On The Light-Cone-Gauge

What are the ramifications of Yakawa Couplings in terms of how these, in certain circumstances, effect light-cone-gauge eigenstates?  This here is going to be something similar but different from something that I wrote for Course Nine.  Let us say that there are here two sets one-dimensional superstrings and also two sets of two-dimensional superstrings that codifferentiate over a Fourier Transformation in a covariant manner in the scenario that I am about to discuss.  One of the said sets of one-dimensional superstrings along with one of the sais sets of two-dimensional superstrings are in the process of going through a significant perturbation, when one is to compare what these two sets of superstrings are going through over a given arbitrary duration that involves a sequential series of timebound iterations that are consecutive and Caucy Ward Bound over the whole Fourier Transformation that I am relating in this case.  Each of the said two groups of superstrings that are relatively interbound in terms of being both covariant -- as well as going through a relatively significant perturbation --  also bear a certain degree of covariant codifferentiation over the same general duration of Fourier Transformation with the other two sets of superstrings that I initially mentioned near the beginning of this scenario, except, the other two sets of superstrings involved here are not going through a relatively significant perturbation when compared with the initial two  mentioned groups of superstrings.The two-dimensional stringular groups that I initially mentioned  bear a kinematic homotopic residue, in spite of the condition that one of these groups here is altering in terms of its relative Ward-Caucy condtions while the other substringular groups is not.  Such a kinematic homotopic residue involves a propagation of a sequential series of Laplacian-based differential symmetry between the point-fill, spin, and roll superfield tensors whic quantify as a homogeneous wave permittivity that is bidirectoral in terms of the resulting kinematic operation of such superstrings over a deffinitive Fourier Transform.  The relatively invariant stringular groups bear a deffinitive inter-relationship with each other in spite of the conditon that two of  these groups is going through a perturbation in their Ward-Caucy bounds while the other two groups are relatively unperturbated in their Ward-Caucy bounds over a duration that involves the motion of the said supeerstrings over a discrete period of time.  The more that a Wilson Line develops -- alligning the parity between those strings which would converge the holonomic discharge of wave interaction between the two said altering groups with the two said relatively unperturbated groups -- the more that the conformally invariant stringular groups that I had metioned earlier that are being altered will be one of the superstringular groups of its corresponding tori-sector that will eventually dissociate from having a direct correspondence with the groups of superstrings that are here not being altered as I previously described.  This is partially on account of the condition that the Polyakov Action and the activity of the light-cone-gauge eigenstates is altered when two relatively less related superstrings are brought into too much allignment with two relatively more related superstrings.  This is considering here that the condition of the perturbation in the said two said substringular groups that I had mentioned involves the same general format of alteration in Ward-Caucy bounds.  But here, the said homotopic residue of each stringular group that undergoes such a change will maintain its generation as it propagates along the Ultimon.  This is so that the previously mentioned homogeneous wave permittivity that is involved here will respond in such a manner so that the commutation of spin symmetry via the indices that are local to both sets of stringular groups at one metric or another on their way around the Ultimon will here differentiate with a basis of chirality that hermitianly distributes the substringular residue as it vibrates in proportionality to the norm-conditions that relate to the transition of the angular momentum of each segment of the related residue.  As bi-local stringular encodements converge their trait-based residue ("traits" here referring to the residue of their intrinsic vibrations) in proportion to the even distribution of their wave propagation, the described semi-groups isometrically commute their mentioned kinematic phenomena-based discharge in a manner that bears a symmetric parity.  The spin symmetries that become covalient via "wave-axials" of the kinematically differentiating respective Ward-Caucy curvatures here are then the action of Yakawa Couplings that bear some sort of cohomological inter-relaion with the light-cone-gauge in terms of the respective Gliossi interactions that happen over time.  Sincerely, Sam 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.

A Little About Substringular-Based Traits

What ramifications as to energy flow are due to permutations in the radial tensors of a set of one and two-dimensional strings that quantify to form the phenomena of a trait which is covariant with another one?  A sequence of one and two-dimensional superstrings wobble in a region which centralizes locally to their respective neighborhoods as a kinematic eigenmatrix of reiterations which expel harmonic wave residue.  This happens after the convergence of the series output of the related superstrings, of which delineates homotopic residue.  The ghost residue renormalizes in conjunction with the directly related point commutators which act as eigenstates to the Imaginary radial tensors of the transversal anharmonic nodal indices.  This bears Yakawa Couplings with the mentioned superstrings' Fock Space.  As these strings wobble as described, the anharmonic node indices converge upon a harmonic wave delineation at a discrete measure in the substringular, bearing an instanton interaction of a discrete metric.  This said metric acts to Dirac the quaternionic reiterative strings' metric, while then sequentially compactifying to a euclidean measure, after which stretching the relatively local strings which are associated with that partial encodement of the associated given covariant trait.  As the metric of the wobbling strings relapses, the Poincaire generators, which distribute the partial integration of such associated parameters, varies in terms of each separate variable of the given trait.  This happens in order to:  1)  Get a given substringular trait to differentiate as a whole in a Fourier manner relative to another given substringular trait.;  & 2)  To gen a substringular association to act as a strung-out substrate that normalizes the correlative critical cusps of each jointal singularity that was previously seperated by the harmonic discharge of the corresponding field propagation in the substringular.]  The Poincaires that are related as such in this case can do this because of the prior mentioned Fock Space encodement.  This type of compactification that I just described causes substringular membranes, which, via the associated angular momentum that is associated here, delineates substringular operands thru which the said topological phenomena may be distributed into in order to allow discrete energy to flow -- so that energy may exist at all.
When I find the test questions that I have for the end of Course Nine, I will submit a post for that.
I will continue with the suspence later!  Take Care.   Sincerely, Sam Roach.  

Course 6, Session 5, Part 2, The Toroidal Nature of Superstrings

Well hello again world, this is Sam Roach here! 
First of all, I would like to elaborate as to what I mean by a "chord."  The interconnections that exist in-between all of the second-orderred point particles taken per individual connection of all 91*10^(81) universes of a tori-sector-range that equally involves forward and backward moving time are flush between each individual of such second-ordered point particle and the interconnective one on either of its sides.  Yet, the interconnections that exist in-between all of the second-ordered point particles taken per individual connection of all of the universes of the rest of the tori-sector-ranges do not involve such a flush interconnection in-between the described individual succeeding flow of Laplacian-based second-ordered point particles.
Another way of looking at the concept of a "chord" is that the corresponding interconnections of Planck phenomenon related phenomena that involve the same tori-sector-range tend bear a mini-string connection that tends to be more abelian in Yakawa Gliossi based differential geometry than the corresponding interconnections of Planck phenomenoon related phenomena that involve different tori-sector-ranges.
So, what did I mean by the "moment" that I was just describing near the end of the post that I wrote for part 1 of session 5 of course 6?  If three people were to view the whole substringular Ultimon at once, and  they simultaneously were to observe three tori-sector-ranges -- oneperson viewing each tori-sector-range at once, what each person would describe to each other afterwards would different if they accurately described their persception.  This is because no two tori-sector-ranges are exactly the same, plus, the position and distance from where one observes something effects what your observation is, based from the general concept of Lorentz-Four-Contractions.  The "chords" you would be observing would actually be segments of reiterating group substringular relations of activity, since these would interconnect to each other, and these would all interconnect to other chord-like segments that would interconnect until these would circle around the Ultimon in-between each instanton.  This integration of chord-like segments form a hoop-like majorized surface that exist withing a main world-tube.  Each of such hoops is right beside another single hoop, and there is a world-tube relatively "above" or "below" each main world-tube. Their is also a corresponding world-tube to the relative "right" or "left" of each main world-tube.  This rectange of world-tubes represents a tensoric state of dimensionality, since we are here talking about the main world-tubes of one set of parallel universes, and, each of such hoops has the dimensional potential of exhibiting 32 spacial dimensions plus time.  Each of such "rectangles" forms a ring-like shape.  This "ring" interconnects to two other of such rings.  These three rings form the instanton-related basis of the Ultimon.  Each of such "rings" actually has a basis of three dimensions, though.  Each ring needs the other two in order to have the basis of the three dimensions that life-forms are able to generally perceive in day-to-day living.  The adjacent main world-sheets or world-tubes represent the fact that every dimension has two sides.  The inner/outer world-tube geometric general Ward Conditions represent the fact that time goes both forward and backward simultaneaously in the Ultimon, yet only evenly when under the globally distinguishable terms of the predominant substringular tori-sector-range.  So, each ring-like entity that I just described has a basis of three dimensions, in spite of the ability of each of these to exhibit 32 spacial dimensions plus time, yet each of such "rings" require the other two rings to allow an existence of 96 spacial dimensions plus time, and this ability allows for the fact that we as life-forms observe three spacial dimensions that each have two general sides -- not to mention that the iteration of the substance of these world-tubes allows for the dimension of time.  This should be enough food for thought for right now.  I will continue with the suspense of the third part of this session later. 
In the meanwhile, ponder this.:  How does the inter-relation of energy in terms of discrete permittivity and discrete impedance get effected by what I just wrote?  I will help with this later.  Sincerely, Sam.

More About Yakawa Couplings

The most common Yakawa couplings are the Fujikawa and the Reverse Fujikawa couplings. The next most common couplings that are Yakawa are the cohomological bindings of M-State shells that either appertain to one-dimensional superstings' integrative fields over a relatively small group metric Laplacian which can be described as a tightly knit Fourier Series integration that defines an open string and its field over a conformal set of iterations OR two-dimensional superstrings' integrative fields over a relatively small group metric Laplacian which can be described as tightly knit Fourier Series integration that defines a closed string and its field over a conformal set of iterations. Let's say that two conformal fields of either one-dimensional superstrings or of two-dimensional superstrings that iterate taken individually in a relatively tight location so as to define either two thin Hilbert figure-eight morphologies or two toroidal morphologies taken respectively that bind at a locus that is defined by the conipoint and coniaxial norm conditions of both subspaces in conjunction with the interaction of either two norm Campbell Projections, or, two norm Hausendorf projections, that are brought together via the propagatorial norm conditions of the neighboring Schwinger Indices which form a pertinent Gaussian gauge-metric and directoralization, because the local Schwinger Indices are formed by the local vibrations of first and second-ordered light-cone-gauge eigenstates that are from either the same core region of the associated superstrings, or from proximally regional superstrings that bear the same Planck phenomena normalcy as projected in a euclidean directoralization relative to one another, (The given Hodge Projection defines the same tense of substringular impedance orphoganation.), the associated substringular M-Fields, when completely unperturbated and therefore also Noether here, when covariant upon a supplementally norm tensorism, will bind together at the designated locus or loci until these are scattered upon or made tachyonic or acted upon by a supplementally norm Chern Simmons holonomic singularity in a spontaneous manner. Such a binding is accomplished by the hyperbollically tangent tying of intermingling mini-string or substringular field integration that involve an interactive commingling due to the sub-impedance and sub-permittivity eigenstates that sway toward each other in the given manner due to the fractoring of the Gaussian Ward conditions that are present. Such a tying happens one binding cite at a time per BRST instanton as the whole cohomology is eventually bound over a relatively small group metric. In-Between each instanton, the superstrings go thru ultimon flow, and are encoded to tie and rety more and more over the course of relatively few iterations that involve Real time. Once the cohomological unit is tied and obtains a Chan-Patton or Clifford Caucy Ward conditionality, the associated structure is stable under a tense of conformal invariance, until either it is scattered upon by a holonome or by a state of Majorana-Weyl invariant tensorism to where it becomes at least partially tachyonic, or is interfered with by a Chern-Simmons singularity or set of singularities that are directorally distributed by a propagated holomorphic or antiholomorphic holonome that goes from being a Njenhuis tensor to being a tensor that is displayed on the Real Reimmanian plane.