Course 4 On The Substringular Vs. The Globally Distinguishable, Session 16, Last Test

1) What is the substringular?

2) What is the gloabally distinguishable?

3) How does phenomena differentiate relative to make the substringular appear as the globally distinguishable?

4) How fast does phenomena "circle" the ultimon?

5) Why is most physical phenomena a vacuum at any given moment?

6) When is a string a string? Describe an instanton.

7) How do point particles find heir way back to form a specific string?

8) How does spin effect the relationship between the subsringular and the globally distinguishable?

9) How does roll effect the relationship between the substringular and the globally distinguishable?

10) Describe point reformation.

11) How does point reformation effect he relationship between the substringular and the globally distinguishable?

12) Describe how point particles may form a vacuum when altered.

13) Describe how a vacuum may change into strings.

14) How does the multiaxial codifferentiation of a supersting effect its relationship to light.

15) Why must the multiaxial codifferentiation of a string be fully normalized in order for the associated superstring to be tachyonic?

16) When may a particle "catch up" with light?

17) Is the multiaxial codifferentiation of a "normal" superstring normal to or parallel with the general flow of point particles? Why?

Course 4 On The Substringular Vs. The Globally Distinguishable, Session 15, Part 2 (Two)

If the set of points will "bounce out" of the vacuum, then it will form a new string that will be of a different kind than before unless the initial conditions forming the string are the same. If the conditions are the same, then an identical string may be formed by the same set of points. If the vacuum is kept, then the design of this vacuum will be kept by the Lorentz-Four-Contractions of the given set of points. These contractions will be determined by the roll, spin, transformational motion, and pointal iteration of these given points relative to the basis of light. This is done since there is a lot of pointal motion of surrounding all of the strings. The pointal motion includes all of the points of the given set that we have discussed. As this set of points contains waves which interconnect with all waves and thence related strands of points, the differentiation of any set of points work on all other points. If something works on all other points, then it works on all light eigenstates. If something works on all light eigenstates, then its differentiation is done relative to light as a unit. Not only do these factors influence how a set of points or a string differentiates relative to light, yet also the axes of the strings and points relative to the ultimon influences this. Strings have a tensoric axis that goes in the direction of the width of the ultimon under normal conditions when the given superstring is in a completely holomorphic mode. The "axis" here is normal to point flow. When a tachyon is formed, the axis here is renormalized to go in the "length" direction of the ultimon -- majorized as it is. When a string has such an "axis," it may differentiate as a unit in a compactive manner at the speed of light, since the string is now nonabelian and may now flow in the direction of light eigenflow. (Singularized photon eigenbases flow 90 degrees to normal strings.) If a string had an axial that was in-between its basic axials in orientation, it may move faster than light, yet it would not be able to catch up with light when slower. This is since only by a stringular flow at the speed of light and in the direction of the flow of light may a string, which is constantly moving around the ultimon anyways, may a phenomenon move "toward" light. The ability or inability of a string to move toward light influences the appearance and detectability of the phenomenology of that string. This ability has a lot to do with the axes of the given strings. Such axes are controlled by the gravitational indices of the strings as these are propagated in space. This set of gravitational indices may be altered by swaying the region surrounding the strings. Such sway may be controlled via an electromagnetic/magnetic field delineation altered on a given superstring by changing the topological bases of the field through each layer that the given superstring is distributed within.

Course 4 On The Substringular Vs. The Globally Distinguishable, Session 15, Part One

As a string spins, rolls, and transversely moves along the ultimon, it also moves as an organization of individual points. These individual points not only move as a unit, yet these also reform many times in the process of going between any two locations. So, as a string breaks down into point particles in-between instantons, the individual point particles are constantly iterating and fading as entities in-between each locant that is in the size of a point. This started when time began, and will continue until time ends. As explained, points attempt to obey the Heisenburg Principle and the Pauli Exclusion Principles. Points also involve many waves. The density of a point may be described as condensed oscillation. When the points are pulled "forward," these will be noded out. This will make these to appear faded out. The process of points of a string in-between stringular iterations fading out, and iterating in relation to the behavior of the basis of light effects the ways in which the string iterates in terms of the related Lorentz-Four-Contractions. This is because the ways in which the waves that comprise the partial aspects of the given string differentiate in terms of where these are nodal and antinodal relative to the nodes and antinodes of all of the proximal light eigenstates in such a way so as to influence the way that the string will be measured, as a unit, relative to light, how the string will cohesively integrate relative to the measurements of an observer, and how the parameters that are measured that that given string will differ with where the string is to be localized as a phenomenon that is determined to be in a specific spot in the globally distinguishable. If this given string were to remain as simply a set of point particles that are not and will not reorganize as a string, then the ways in which the given set of points differentiate and the boundary conditions of the vacuum regions that this space will now iterate will form. I will continue with the suspense of this session later. Until then, you have a great day!
Later,
Sam.

Course 4 On The Substringular Vs. The Globally Distinguishable, Session 14, Part Two

Charge needs some sort of voltage, whether Diraced or Reverse-Diraced, because if electrons didn't spin at all, they could not rotate at all yet alone orbit. (Majoranas are built into atoms, since space is curved at this level, since it involves gravity at a level greater than that of a string.) After the iteration of the ultimon, every particle must not only bear angular momentum, yet also spin-orbital-interaction. As said before, this has to do with tangency. Everything that exists exists, and is tangent to something. As implied before, tangency produces spin, spin produces radial and transversel motion, and radial and transversel motion produces orbits. Strung out waves are like magnetism. Magnetism is related to spin and orbit. the relation is that spin and orbit give off waves as we would think of waves. these waves may be viewed of as at least some sort of energy or impetus. Points are condensed oscillation, or stuff in a relative spot. Stuff that is in a spot has a density. A density that is tantamount to a point spins and orbits. What spins and orbit is the thing that gives off waves. Stuff that gives off waves exists in a direction has some sort of motion relative to its surroundings, and the given thing moving has a drive in the given direction. Anything that has a direction is at some sort of angle. Angular drive is tantamount to angular momentum. As the waves and points move thru stuff, they may either end up directly connected, or relatively separated. So, as strings reiterate in such a way that their waves remain connected, not only do the strings build up a relation to their surroundings, yet the waves that connect these strings also build up a relation. This relation may metaphorically like a "Backgammon Game." As the stuff reiterates, it may be more or less bound to a certain relative locus. If the "opponent" wins your spot, then these strings will no longer iterate with such interconnection. Yet, since change is reality, there is always motion. Some principles of space and time are constant, since there is existence. So, no one may ever "block out" another "player" entirely. Everything is a kinematic relation. Nothing is stagnant. If motion ended, there would be no reality. Yet, we're here. So there. So, wave iteration is like a very long "Backgammon Game" with many players and a twist that bends us back to the beginning. Yet, there are only so many "sides to a di." Eventually, entropy worked more and more. Entropy is disorder. Disorder slows down reality (material). The slow down of reality brings chaos with eventual harmony.

Course 4 on The Globally Distinguishable Vs. The Substringular, Session 14, Part One

So, nuclei particles and electrons are composed of smaller particles. These smaller particles in the subsringular are actually sequences of strings that exist in individual parts of a tori sector. As these sequences iterate and reiterate, these effect the stuff that they interact with. These sequences also have direct wave connections with other of "such types" of sequences. Simplify to two stringular sequences. These are connected by wave during one quaternionic-instanton-field-impulse-range. Once the strings of these sequences leave the range of the instanton field, the point particles associated with these strings move out of a line formation and into a more scrambled formation. There is still at least some wave connection between some of the waves that existed not only between the points of the individual strings, yet also between the points of each string toward each other. As a matter of fact, if these strings end up reiterating in the same general relative locant, there will be some wave connection between all of the points of both strings during the whole transit of the strings as points around the Continuum. Not only will the condensed oscillations or points effect the stuff that it goes through, yet the strung out waves will also effect the stuff that these encounter on their way around the ultimon (Continuum). As a matter of fact, points have fields, as said before. Two things con not occupy the same spot at the same time. So, points tend to rely on strung out waves, in the substringular, to produce effects. I will continue with the suspense of this session later. Until then, have a phenomenal day!
Sincerely,
Sam.

Course Four on The Globally Distinguishable Vs. The Substringular, Session 13, Part 2 (Two)

As to instantons, the metric co-differentiation of strings thus happens relative to the basis of light. So, as strings interact with each other, this happens relative to the recycling of action or the interchange of action. For instance, whenever strings interact, these interchange information. So, the metric relations between strings influences the detectability of the given strings relative to one another, since direct interaction creates a sense of nearness. This direct interaction is influenced by not only those wave-tugs that connect the strings, yet also to the ways in which these interconnections exist and change relative to the differentiation of light. The differentiation of light is how the recycling of differential geometries change. The general process remains the same, yet the details of intra and inter specific instanton-quaternionic-field-impulse-ranges and their eigenmeter kernels (in-between the ranges) changes will vary transporationally. This relative change in wave-tug will not only effect the individual eigenmetrics of the strings and their differentiation, yet also the placement of the phenomena. This will effect the relative parameters and the delineations of the phenomena of the associated universe in the substringular as well as in the globally distinguishable.

Course 4 on The Globally Distinguishable Vs. The Substringular, Session 13, Part One

Existence is primordially action and its result. The result of action is stuff. The result is space that obtains relative change in the given action. As said before, light is the result of the recycling of differential geometries. Differential geometries are real because they are shown by the results of action. Actions are recycled by the recycling of the geometries that are obtained by those particles that comprise the universe on the substringular scale. Light is the source of detection. Detection is the source of perception. So, how light is formed and how it differentiates effects the parameters we perceive and our world view of them. Light in the substringular bears wave-tug with strings (one- and two-dimensional). This wave-tug influences the metric in which the strings related to a common eigenbasis of light interacts and transpires. Meter, as said before, is successiveness in action. The successiveness of action in terms of superstrings in a tori-sector-range is allowed by a quaternionic-instanton-mode. Each eigenstate of such a mode allows for each subsequent instanton, and each instanton is an iteration of Real time for the space-time-continuum. The integration of instantons is time. I will continue with the suspense of what I am leading up to later. Until then, you have a great day.
Sam.

Course 4 on The Globally Distinguishable Vs. the Substringular, Session 12, Part One

So, protons are bigger than electrons. This is true both in terms of size and in terms of mass. Since a proton has more mass than an electron, it has more two-dimensional superstrings associated with its mass than an electron does. Each fundamental particle just under the level of the proton is a certain thing that describes a three-dimensional delineation in the globally distinguishable. In the subsringular, these "packages" that are here have such delineations that are actually sequences of one- and two-dimensional strings. Each of such sets is in an order in a majorized plane. Each of such stringular encodements is just a segment of its correlative substringular string. (I'll explain this later.) The order of such a set is a thin band of strand-like phenomena and hoop-like phenomena that are very limited in side-to-side transversel sway besides the basic vibration of the said superstrings. It is limited by the Caucy Ward conditions of the given world-tube that is affiliated with the said superstrings. The whole set of such sets that comprises the proton is an association of substringular sequences that exist on separate parts of a tori-sector-range (one of such per part). The symmetrism of these sequences bears a wave-tug that is mini-string that goes from not fully compactified to fully compactified once its surrounding pressure is exerted upon it in an abelian way in a manner that is like a "party whistle" that acts thru any holomorphic operand that is vacant. (Stuff with a perturbative symmetrism will push the described mini-string into an anharmonic mode.) Please wait for the physical example that I will describe to you during the second post of this session so that you will have a better feeling for the concept that I am trying to let you know.
You have a phenomenal day!
Sam.

Course 4 on The Globally Distinguishable Vs. The Substringular, Session 9, Part 2(Two)

The globally distinguishable has no infinite changes in the position of an object between two direct moments of where that object is. -- In other words, in the globally distinguishable, if an object is at one spot in one nanosecond in the globally distinguishable, it cannot appear to exist at the other end of the Continuum during the next nanosecond unless it enters the SUBSTRINGULAR. In the globally distinguishable, every particle that appears near each other is near each other. Particles that we view of as far away from each other are far away from each other. Basically, the globally distinguishable assumes that the reality that we observe is as is. It assumes that the three-dimensional delineations that we observe actually define the basis of interaction, when, in fact, these do not do that. Newtonian physics works based on the conclusions reached with the globally distinguishable. Most "logical" conclusions of physics based on matter interplay involves all stipulation as derived from the workings of the globally distinguishable. How can one say that the globally distinguishable is ever wrong? Anomalous singularities alone proves the fact that the globally distinguishable is not the ultimate in perception. When the interacting physical limits define the basis of an object to be interspersed in space and time, then it can be proven that the locus of an object is not completely isolated, and inevitably that all energies interact within very, very brief periods. Thus, no objects are only closely isolated for what we would term of as even the briefest time period. The briefest time that is actually time is 10^(-43) of a second.

Course 4 on The Globally Distinguishable Vs. The Substringular, Session Nine, Part 1

Where something is depends on what you are trying to pinpoint. Let's say, for instance, that you are trying to find a boat on the ocean. The boat may or may not be moving, at least of its own accord. If you knew the exact latitude and longitude of the ship to the nearest second at a certain instant (the selfsame minute), you would then have a neighborhood with which to look in that might be sufficient enough to help you find the boat. A boat is what we would call an object. An object that is tangible to our world is three-dimensional and moves in three-dimensional space. Any object as we just called it is a phenomenon that is perceived by us as a three-dimensional delineation in the GLOBALLY DISTINGUISHABLE. I term it as such because our direct perceptivities are in a universal encoding that our physical senses can detect or distinguish. Such an encodement of perception gives us completion in our ability to unify actual occurrences and things as an entity that is global. Another way of looking at this is that our general reality as we view it and live in it as a physical entity is the globally distinguishable. The laws of physics that are the most commonly associated with normal, everyday occurrences as we would normally think of them is the condition of reality that is thus termed globally distinguishable. So, based on this, where a person goes is where they are, not only in terms of their whole body, yet, also in terms of every particle that comprises that person -- no only at the outside of the journey, yet during the whole journey. I will continue with the suspense of this session later. Until then, you have a phenomenal day.
Catch you two!
Sincerely,
Sam.

Course 4 on The Globally Distinguishable Vs. The Substringular, Session 8, Part Two

Consider the spinning to be holomorphic relative to the surface area of the paraboloid. Consider the rate of the spinning to be maintained at a constant speed. Of course, since you are spinning, your direction is always changing so that you are constantly accelerating. Think of the trans location of phenomena besides yourself, whom is staying put, that was at one point touching the parabola, from the surface area of it, as proportional to the differentiation in the speed of the sway spinning. This would mean that discharge from the surface would be transferred at a constant rate. Since this is true for the whole topology given, it is certainly true for the potential at which you would be at. You are in line with a potential discharge of residue from the surface of the paraboloid, which would be a trans location of surrounding phenomena. This would mean that the norm vector of each point along the surface would be constant in magnitude, although constantly changing in direction. Wouldn't this then mean that the norm conditions of the surface area of the given paraboloid would constantly alter part of its Caucy norm conditions, while constantly maintaining the others? Now, this is saying that the point is relatively stationary. It is going nowhere to a non moving observer. Now say that the paraboloid was just setting there. It is not necessarily a sphere, although it could be a sphere. It has a position since it has a shape. Anything that has a position exists at an angle. Now, let's say that the object rolled down the table. Its angle of position at each increment of motion along the table works to define its coexistence with its environment, including the table. The rolling of the object is like a spin. The change of the object's norm conditions as it rolls is the physical action of the object that brings it to the new positions which create the object's motion. The driving force of the object in whatever direction it is pressured into also causes motion by allowing a positional drive of the object. So, change in norm conditions in both radial translation and positional drive work together to form the basic building blocks of regular motion.

Course 4 on The Globaly Distinguishable Vs. the Substringular, Session 8, Part 1

As told already, an electron's spin works to determine its magnetic field. This is because the magnetic field of an electron is normal to its electric field, and an electric field is based on the angular momentum of the given electron. Angular momentum is based on the directoral impetus of the electron in any series of locants, as implied before. In order for something to spin, the phenomenon has to go around. That's what spinning is. This means that the surface area of any object that spins must have radial translation after every discrete metric in which that object does indeed spin. Whenever something exists, it exists in some sort of space. Anything that exists in space is touching something, and at every spot in which it exists. Whenever there is touch, there is tangency. So, everything that exists involves tangency. The condition of tangency is normalcy. This is because wherever there's a tangency point, there is a norm vector. So, anything that exists has some sort of normalcy that is associated with whatever topological surface that you may wish to discuss. Normalcy may not always be associated with Real space, yet it is always associated with some sort of medium through which points or indices may be relayed or at least temporarily transferred. whenever radial motion happens, there is always at least a potential of spinning of either the object in radial motion or the indices that it translocates. Radial motion that differentiates homotopically through a metric always involves actual spinning. Let's say that you are a small point. You are on the surface of a smooth paraboloid. The paraboloid spins. Remember, you are touching the paraboloid. As the paraboloid spins, you spin with it. You are staying put on the relative spot of the paraboloid, now. So, you are in tact with a constantly differentiating norm vector that is kept in the sequential pattern of the spinning of the paraboloid. I will continue with the suspense of this session later. Until then, I hope that you are having a phenomenal day.
Catch you two!
Sincerely,
Samuel

Test Solutions For Test One of Course 4 on the Globally Distinguishable Vs. the Substringular, Part Three, by Samuel Roach

11) A point particle generally travels in the "current" of a majorized plane of multiplicit Minkowski space. A majorized plane has four dimensions as a minimum. A Fock point particle is 10,000 times from being completely condensed, and a stringular point particle is two times away from being completely condensed. 10^4 = 10,000. So, a Fock point particle exists in its whole region by iterating in 10,000 different spots per 10,000 radial motions of the said point particle as it travels through iteration and Ultimon time (the "time" in between iterations). This means that a stringular-based point particle exists throughout its neighborhood by a factor of 5,000 per 10,000 radial motions of the said particle as it travels through iteration and Ultimon flow.



12) Waves are expelled and brought in by first-ordered point particles to allow for the differentiation of mini-string, or, in other words, to allow for the motion of substringular fields. If substringular fields did not move, strings wouldn't move and would cease to exist.



13) The computer is an example. IF THEN ELSE statements.



14) The motion and holonomity of point particles as part of superstrings during discrete units of time is detectable by discerning the activity of the said superstrings over the course of a Fourier Transformation.



15) Electrons exist in D-fields, which are six-dimensional. These have six-dimensions that they exist in because an electron, in order to have both angular momentum and spin-orbital momentum that are crossed relative to each other by the "right-hand-rule" must exist in a double supremumized kinematic differentiation relative to the first-ordered point particles that comprise the superstrings of the said electrons.

Test Solutions For First Test of Course 4, Part 2

6) The "dance" of energy is Fourier translated discrete Planck phenomena related phenomena. The "dancer" of energy is Fourier translated superstrings. Fock energy is the Fourier translated norm states that consist of point commutators. A single unit of Planck energy is an eigenstate of energy. The actual motion of discrete Planck phenomena and superstrings is their gauge-metrics, or, in other words, their activity that exists both per iteration and also within discrete units of time.

7) Electrons surround nuclei at a relatively fast rate (close to light speed). We normally encounter matter, which is made up of atoms. Atoms, with the exception of H+ ions, are composed of electrons orbiting their nuclei.

8) If the electromagnetic energy interacting with an electron was controlled, one would have a higher probability of "pinning" down an electron's position and what it is giving off at the same time. If you traced the given electron down to its path of kinematically differentiating locus, if no energy was added to the given electron, and if the given detection had no aberrations both in terms of angle of inspection and the directoralization of the inspection, one could better detect an electron with a higher probability.

9) An ideal line is straight with no aberrations. A one-dimensional superstring is a very thin vibrating strand that would be almost like an ideal line if it wasn't for the exterior forces acting upon the given one-dimensional superstring.

10) A point particle exists as a mesh of mini-string in a locus. The substance of this mini-string that is in this locus is the point particle itself, while the whole locus of where the point particle extends is the neighborhood of the said point particle.

Test One Solutions To Course Four, Part 1

1) The Heisenburg Exclusion Principle holds true foremost because electrons are constantly bombarded by incoming electromagnetic energy that tends to associate with the described electrons in a random manner. Electrons are a relatively point mass that exists as particle, wave, and energy all at the same time. So, even if you were to have selective electromagnetic energy to interact with an electron, once you were to identify the given electron as a particle, the electron's wave and energy qualities would alter your ability to detect the given electron. This is particularly since an electron always needs to move at close to light speed in order to be an electron.

2) Any sort of identification of an electron at a locus of region would indicate that the spin, orbit, and angular momentum of that electron as it moves transversely forms a surface area of the given electron that relatively tends to orthogonally "throw" off phenomena that attempts to interact with the said electron in a directoralization that is existent in a given manner when one includes the overall Fourier Translation of the given electron through its kinematically based Lagrangian in space and time.

3) A sports related ball that spins, orbits, and moves transversely in a circular path will tend to throw off the air that interacts with the said ball in a multiplicitly orthogonal manner when considering the overall translation of that ball in time and space. The prior would only exist with an integer number of sports related balls. So, you couldn't have 1 and 1/2 balls doing this, since the balls here are considered discrete phenomena.

4) The angular momentum of an electron forms its electric field, while the spin-orbital momentum of an electron forms its magnetic field. J = L cross S. This means that the momentum of an electron equals its angular momentum cross its spin-orbital momentum.

5) The momentum of electrons (J) is formed in part by the attraction of the electrons with protons. As the electrons have a momentum given to them that is a drive in a direction (angular momentum) that also spins in two relative orthogonal manners so as to counter intruding forces (magnetic field produced by spin-orbital momentum), the holomorphic directoralization of this overall momentum pulls the electrons around the nuclei in a circular propagation.

Course 4 on The Globally Distinguishable Vs. the Substringular, Session 7, Test 1

1) Why can't electrons be measured at a specific spot, while what these are giving off is measured, simultaneously?

2) Describe briefly the surface area of an electron as it is identified in a specific locant slice.

3) What parallels to the situation in "2?" Describe this reasoning to the example conceptually. (Describe this discussing the discreteness of the given general phenomena.)

4) Describe how electric and magnetic fields interrelate to the "2" of electrons.

5) Describe how the "J" of electrons causes their propagation.

6) What is the difference between what we call energy, the Fock energy of any given phenomenon, the eigenstate of the phenomenon, and the action of the of the basis of that energy. Please provide just the simple concepts relating.

7) Besides the fact that electrons work to form light, and we encounter light, what makes electrons the phenomena that we as living beings tend to always encounter otherwise.

8) Describe how you could accurately detect an electron at a given locant Without overt perceptive errors.

9) Relate the concept of an ideal line to the actual existence of a string.

10) What is the relationship between a point particle and its neighborhood?

11) Why is their a field density to a point particle?

12) Why are waves expelled from point particles? (Please use the example that I gave in my previous writings.)

13) What physical invention of the last 200 years relates to the sequences and series of stringular iterations? Describe.

14) Describe the "detectable' field density of a point particle.

15) What dimensional aspects of the space-time-continuum define the reason for "4", including the fact of the continual transpiring of the Space-Time-Continuum?

Course 4 on The Globally Distinguishable Vs. the Substringular, Sessin 6, Part Two

Now, back to my discussion that describes superstringular activity in terms of metaphorical springs.
Consider what I wrote in Part one of this session. Likewise, condensed oscillation "springs", among the interacting points of the Continuum, the individual points forward as well as working to propel and spring the other points of the Continuum. And as said before, the ordering of point particles (neighborhoods) are strings. Strings are things, Not mere translation. What we depict as energy, as said, is made up in part by superstrings. Yet motion and energy are conceptually equivalent, and motion is why as objects are translated -- these go from one spot to another. The actual translation of the given strings through space is what is termed of as an action that is sometimes called a gauge-metric. The sequences of strings that are reassorted to form a given increment of what we normally call energy is an energy eigenstate. The strings themselves which comrprise such sequences are the energy itself (what we would define it as). And the surrounding activity to the "energy" that works along with it to allow it to happen is termed of as the Fock energy. Fock energy is the direct environment to a string, and involves more waves than those waves that superstrings directly have in the locus of their direct placements. (See Earlier Lesson) So, it always involves a lot more stuff than just the Real Reimmanian Gliossi field of superstrings. (As compared and contrasted to the Gliossi-Shirk-Olive field of superstrngs.) Energy is comprised of superstrings that are inter bound to their direct field trajectory that exists as such throughout all of Real Reimmanian time and most of Ultimon time. Such a field trajectory is always existent during iteration at a placement that is relatively reverse holomorphic to the positioning of a given superstring. Such energy is known as the impedance contribution to the Planck phenomenon related phenomena. Such discrete units of energy impedance that are associated as one discrete unit per discrete superstring are known as Fadeev-Popov-Traces. Superstrings act as the "dancers" of the substringular, while their associated Fadeev-Popov-Traces act as the "dance" of the substringular.
Please, if you have any questions, I am more than willing to answer any of them that I can.
I am here to serve. I will add to the suspence of this course later.
Sincerely,
Samuel David Roach.