Solutions To Test Two of Course One

1)(For Initial Two Pictures, See Handwritten test solutions.)

                   
If these hooks, due to the lack of rigidity between these, slipped along the borne

tangential surface that interconnected them, then these hooks would dually slide off of

each other along the shared topographical region of borne tangency.



2)Wave-Tug in the direction of the hooks’ individual changes in the second derivative of

curvature, taken individually yet dually, that appertains to a topographical dual position

where there is an actual limit of curvature along the touching surfaces of the hooks,

particularly if the reverse directional pull pulled these hooks upon each other, would be

advantatious toward keeping the hooks together.

Wave-Tug that is directed away from the actual change in the second derivative of the

curvature of the hooks, which would slide the hooks’ tips toward each other, particularly

if there was a torsional three-dimensional force that produced a lack of borne tangency,

would be disadvantatious to keeping the hooks together. Additional force of one hook

upon another would increase the chance of the second hook to be pulled in the first

hook’s direction. Additional force of the second hook upon the first hook would increase

the chance of the first hook to be pulled in the second hook’s direction



3)In a polar diagram, when two points are within the same ellipse yet not touching, these

points are relatively near. With the same polar diagram, if these points were complete

yet touching, these points would be very near. If these points are of two totally different

ellipses, then these points are far.



4)(For correlative pictures, See Handwritten Solutions.)

If there were two particles that were 50 ellipses away, that would make all four points in

A and B near.

If two particles were complete yet touching, that would make all four of the points of A

and B appear far.



5)The “neighborhood” of my writing utensil is the paper I am writing on, my hand I am

writing with, and the air existent that touches my writing utensil.



6)The local neighborhood of a molecule of the air I am breathing are the other molecules

of the air I am breathing, my body that absorbs the air, and the superfluous dust in the air

I am breathing.



7)Electrons spin antisymmetrically so that these may be at different spots at the same

time. That is the Pauli Exclusion Principle. You can not find with an expectation value

of “1” (pure certainty) where an electron as at and what it is giving off at the same time.

The Pauli Exclusion Principle is always true, yet, via extrapolating substringular activity,

one may basically have a good idea of where an electron is at and what it is giving

off at the same time. Syncronous electrical flow may provide an expectation value to

determine this with virtual certainty.



8)Adjacent superstrings oscillate antisymmetrically so as not to intrude upon each

other (Pauli Exclusion Principle). You can not pinpoint a superstring’s position and its



scattering and requantification at the same time (Heisenburg Principle). Superstings

constantly change in differential clause per group metric, and superstrings recycle

on account of the activity of ultimon flow. Superstrings, even though these reverse

fractorially form a tense of inertia, are never inert both during and in-between instantons.                                        

More About On-Shell Mass

A two-dimensional superstring has a three-dimensional field associated with it. When                                                                                                
                        
a relatively knit Fourier Transform that is highly Laplacian forms a torroidal structure

with an annulus at its central coniaxial, the whole Majorana-Weyl supercharge associated

with the operation of the associated superstring’s conformally invariant kinematism

is delineated, after the group metric that forms the basically Gliossi-Sherk-Olive field

described, at the outer shell general locus of that given M-field that is associated with

the described kinematic differentiation of the given two-dimensional superstring’s three-

dimensional field. This considers the fact that every superstring, whether it partakes

of mass or not, has a mass index. Such an on-shell supercharge as taken thru a Fourier

Transform that alters the spin-orbital and angular momentum distribution, delineation,

and directoralization of the associated three-dimensional field toroidal structure converts

the Yau-Exact indices transport in such a way as to form a discrete unit of mass as

to the M-field structure that I have conveyed. This is tantamount to that a spherical

shell with a physical charge in its center delineates all of the energy of its charge along

the topography of its associated shell. Likewise, the norm state Ward conditions of

the annulus of a toroidal 3-D field of a 2-D superstring delineates all of the angular

momentum and spin-orbital distribution indices at the outer shell of that given toroidal

3-D structure. Likewise, the “figure-eight” twisted toroidal structure created by certain

fermionic superstrings forms the point mass of electrons and neutrinos. This mass

of certain fermions is created by this: The norm state conditions when considering

the Ward conditions of the annuli of the two relatively Mobius ends of the “figure-

eight” described have angular momentum and spin-orbital momentum that transfers

their distribution and directoralization indices outward to the outer topology of the

given “figure-eight-like” structure. The kinematic differentiation of the Yau-Exact

indices of the “figure-eight” structure as a whole causes the given phenomenon to

translate, thru the Fourier Transform of the given M-field thru a Minkowski or Hilbert

Lagrangian, its mass indices into an integration of Hamiltonian eigenstates that allow

the Kaluza-Klein phenomena, as with 3-D fields of 2-D superstrings, to convert and/or

maintain as a mass. The abelian geometry of the light-cone-gauge of such Yau-Exact

structures causes the E(6)xE(6) gauge-bosons related to form Schwinger indices that

keep the M-fields oriented to coalesce their Noether indices into a conformally invariant

manner that has to be orientable per general locus in order to translate to a proceeding

general locus as long as the mass indices associated are limited. Since any M-field needs

a limited Lagrangian distribution in order to delineate its Majorana-Weyl indices over a

group metric that is based on a harmonics or anharmonics that may not coincide with a

group directoralization of Noether flow unless the associated superstring is unorientable,

Kaluza-Klein mass is always under light speed, per iteration, and mass must become

Yang-Mills as in a worm-hole or Yang-Mills also, if otherwise tachyonic, which is true

when mass bears unorientable yet finely directoralized motion via a Ward polarizable

dark matter holomorph. Unorientable superstrings may only be as such temporarily when

in a large group even if Reverse-Lorentz-Four-Contracted. Mass may become Yang-

Mills and tachyonic if its field delineation is majorized.                                                                                                                                                                                                                    

Test Three of Course One

1)All “stuff in a spot” must have angular momentum because a discrete physical entity                                                    

                           
always bears a presence in a direction with a scalar magnitude.



2)Something actual that is not “stuff in a spot” would be the “space-hole,” since this is a

metric that happens in-between instantons.



3)Strings must be composed of smaller phenomena since strings vibrate and curl. The

presence of oscillation in the topology of a phenomenon indicates the presence of smaller

phenomena.



4)Mass is energy in static equilibrium.



5)Electromagnetic energy is energy that is formed by an electron, once thought to be a

point mass, dropping an energy level.



6)A high voltage wire tends to pust one away from the wire.



7)A high amperage/low voltage wire will hold one upon the wire until the current is

released. One tenth of an amp may kill a person.



8)A smoothly vibrating sinusoidal wave is an example of a harmonic wave.

An opposite wave of energy, when the initial wave of energy is applied toward

the “opposite wave” would cancel the energies of these waves, yet such an occurrence

could not destroy discrete homotopic unit of condensed oscillation that exists on a

smaller scale.



9)The electron is the source of electrostatics. Three leptons of a charge of (-1/3) each

glue together to form an electron (which has a charge of (-1).



10)Curves that change in at least the first two derivatives along the ontour of these curves

are waves. These waves are composed of energy that either staticly and/or kinematically

is distributed along the topography of the curves that comprise the given waves.

Superstrings act as open strands and closed loops that vibrate as topological waves that

comprise a Planck related length/circumference respectively.