Monday, December 21, 2009

Solutions For Test#1 of Course 2

1)There is no ideal line. A one-dimensional superstring best describes a vibrating line.

Point particles form this vibrating line by interconnecting via mini-string in-between the associated point particles. These point particles form where these do because the globally norm conditions that surround these point particles cause the correlative need for supplementally globally ground conditions.



2)Every one-dimensional superstring that is not an encoder has one partition, or, aberration from vibrating linearity. Every two-dimensional superstring that is not an encoder has two partitions, or, aberrations from vibrating radiation in a hoop-like configuration. These partitions are necessary for the flexibility of the said superstrings so that these may vibrate along the homotopy of their topology.



3)A substring is a superstring is one set Laplacian iteration that is fully Lorentz-Four-Contracted. A globally distinguishable superstring is a superstring that is detectable at the Planck Length or the Planck Radius, is no existent over the mere Laplacian of one iteration, and has minimized Lorentz-Four-Contractions.



4)Superstrings fit in along the ultimon by being geometrically based on globally ground conditions.



For test solutions of 5) and 6), see handwritten solutions.



7)Real residue in terms of superstrings is residue that happens during iteration metrics that involves the phenomenal discharge of these superstrings and norm states. Such phenomenal discharge is the mini-string that is being pulled out of and into the said superstrings and the said norm states.



8)Imaginary residue in terms of superstrings is residue that happens during ultimon flow that involves the phenomenal discharge of superstrings and norm states.



9)Cassimer Invariance is the unchanging condition of the recycling of norm conditions among superstrings. It is not eternally invariant among tori-sector ranges that form black-holes. Yet, it may be eternally invariant in some tori-sector-ranges.



10)Imaginary residue is delineated upon superstringular phenomena in such a way that it effects the said phenomena over subsequent iterations.



11)Globally norm conditions effect the delineation of Imaginary residue, while globally ground conditions effect the delineation of Real residue.



9)Cassimer Invariance is

Sunday, December 20, 2009

Session 6 of Course 2, Test #1

1)Is these an ideal physical line? What phenomena best describes a vibrating line? How do point particles form this "ideal" vibrating line? Why do these points form where these do?





2)Describe the aberations in a string tht cause it to not be perfectly straight.





3)What is the difference between a substring and a globally distinguishable string?





4)How do string fit in along the ultimon as a general condition?





5)Draw a sketch of a rough pattern of long and short lines that converge. It must contain at least 10 lines.





6)Draw a sketch of a rough "pattern" of long and short lines that diverge. It must contain at least 10 lines.





7)What is Real residue in terms of a superstring?





8)What is Imaginary residue in terms of a superstring?





9)What is Cassimer Invariance? Is it eternally invariant?





10)What happens to Imaginary residue?





11)How do the norm conditions of point particles effect the type of residue that these obtain?

Saturday, December 19, 2009

Page 3 of Sessions 2,3,4, and 5(Residue Applied to 2-D strings

Now that we learned what is meant by Real residue, I will apply this concept to metaphorical vibrating circles, which represent two-dimensional strings. Take two circles. One has a small radius while the other has a large radius. The two circles are initially parallel to each other and are not touching. The two circles are actually thin hoops. The two circles propagate. These are not merely duplicated. In one of such an array, the pattern of small circle placewise differentiation and large circle placewise differentiation converges to a discrete symmetry. In another array as above, the pattern of small circle placewise differentiation to large circle placewise differentiation never converges to a discrete symmetry. You might say, "Well, if it's a pattern, then it is discrete." Not necessarily. If the pattern is anharmonic or if it is long enough, it may form sub-symmetries that diverge as the "pattern" ends its phenomenal discharge. By "ends its phenomenal discharge", I mean that the circles would stop moving around, and the pattern of all of the places that the circles were at would have a limitation. Such an erratic pattern has zero Weyl-Invariance, since invariance means that it doesn't change, and something that is erratic changes the eigenbasis of symmetry that would otherwise exist. If an eigenbasis of encodement due to discharged wave homotopy diverges in terms of wave commutation, while the divergent wave commutation (not divergent wave generation, which would do just the opposite), causing these waves to keep iterating in a string-like fashion that may be of different transversal, spin-orbital, and/or radial placements respectively, exists due to the same substringular operation, then the associated superstrings will always be within the same general locus of tori sector. Such waves that diverge during ultimon flow obey an odd function of wave residue in-between instantons, and thus bear an Imaginary Residue. Once the associated waves, along with the differentiating path operands that the "odd" waves propagate along, act upon the other correlative waves that have diverged from the initial said waves, the waves as a unit are then back into iteration mode, and thus bear residue that is said to be Real. Then their residue may be taken from the strings in a method I will later show, in order that norm conditions among substringular phenomena may have equilibrium. Imaginary residue that's already delineated stays within a general relative locus per iteration in spite of the fact that Imaginary residue is residue that is produced during ultimon flow, and ultimon flow is in-between instantons, and Imaginary residue causes Cassimer Invariant modes via certain motion of Planck phenomena related phenomena that I will describe in later courses.

Saturday, December 12, 2009

Test#2 of Course 1, Session 12

1)Draw two hooks that catch each other. If these hooks are the same size and are tugging with the same force and in the supplemental direction, what could cause these to be released?

2)Explain how different directions of wave-tug may be advantageous or disadvantageous to pulling in the other hook.

3)Pretend that nearness is according to a polar diagram. When are two points near for sure, when are these very near, and when are these far?

4)Pictorially contrast two near particles with two far ones. State an example in which all four of these particles are relatively near as compared to that. State another example of two particles that are much more localized than any of those particles.

5)Name the ”neighborhood” of your writing utensil.

6)What are the local neighborhoods of a molecule of the air that you are breathing?

7)Relate the Pauli Exclusion Principle and the Heisenburg Principle to an electron. Name a flaw in this argument.

8)Relate the Pauli Exclusion Principle and the Heisenburg Principle to a string. What must be so in order to validate any conclusions as to how these principles function. (Use your imagination. I need to see effort and a development of truth based on our lessons.

Test 3 of Course 1 (Last Test)

1)Why must all "stuff in a spot" have angular momentum?



2)Give me an example of something actual that is not "stuff in a spot."



3)Why must strings be composed of smaller phenomena?



4)How is mass an energy?



5)How is electromagnetic energy related to mass?



6)How does a high voltage wire effect a creature that touches it?



7)How does a high amp/low voltage wire effect one that touches it? How much amps may kill a person?



8)Give an example of a harmonic wave.



9)What within an atom is the source of electromagnetics? What composes this?



10)What acts as waves? What are these waves composed of? How does this relate to superstrings?

Session 15 of Course 1, Energy, Matter, and Space

If something is a thing, then it can be pinpointed to a location. If a thing stands perfectly still by way of perception, then the energies that make up that thing are in static equilibrium. If the energies of a thing are globally in static equilibrium, then the thing is a form of matter.

Space is the range of spots where things can exist and change relative to one another. If things can't exist in a certain spot or rang of spots, then those spots are not of the classification to be named spaces. Spaces may also mean separations between things or members of space, yet, in order for the separation to be space, it must have the potential to have stuff in it. If the phenomena in a "space-hole" is not energy, yet a scattered lower form of point residue that leaves upon entry, then this spot or region of spots would definitely not be "space," since it can not contain energy. For instance, a string contains a region of spots that work together to form this function, while some point commutators associate with one such spot.

Space rearranges. It is altered in its shape, topology, and distribution. Energy is the redistribution of space as both an amplitudinal, morphological, and topological differentiation that diverges from one locale to another in at least one direction. So, the warping of space is simply an expression of a global amplitude in energy codifferentiation -- how two normal energies change the pattern of their spacial environment by the modulae of their amplitudinal, morphological, and topological distributions in the local regions in which these themselves change relative to one another. Everything that changes changes relative to every other change. Familiarity with definite patterns as to how these changes effect other things leads one to find clues as to how to develop a reliable scheme that has a high degree of probability. Playing out how these various forces interact through knowledge of your familiarity may lead you in the right direction of extrapolation and critical analysis. Through pseudo trials, one may be led to distinguish an applicable path.

Space is where the universes are acting. The activity of space is energy, and where these actions form a non-kinematic "actor" of "potential energy" is matter. Energy is kinematic change in phenomena. Phenomena is often such a change itself. Transformed space through charge delineation may form energy, and various energies balancing to form a static item is matter. Items that are not kinematism are matter and have mass.

Session 14 on Course 1, Pictorial Learning

1)Draw two points. Draw eight curves that connect these two given points. Now, draw a curve between the two given points that is an average of the other eight. Measure the length of this last curve, using a ruler and a protractor. How much shorter or longer is the curve than the eight other added curves? Measure the angle of the tangent that corresponds to the new curve as a mean wave (if smooth), if going from one point toward another, at one locus of the given curve. This is a central state wave. Moving this wave describes a harmonic vibration.



2)Draw an ordinary rectangle. Make points along it. Now, make a point above a plane of scattered points.



Let's discuss the above.



3)In "2", which array is globally norm?

Which array is globally ground?

Which array implies point commutation?

Which array describes strings?

Do these ever interchange?

Why?

Thursday, December 10, 2009

Session 13 of course 1, Stuff in a Spot

Pick any object into your thoughts. If the object is physical, it is stuff. In order for stuff to be real, it must exist in space. Anything that exists in space must be located at a certain spot.


Make a dot on a sheet of paper. If the paper stays still, then the dot remains in a certain spot relative to you. Certainly, the earth is moving, the solar systems moving, our whole galaxy is moving, and even the molecules of the dot that you made are vibrating. Yet, as far as your perception is concerned, the dot's spot doesn't change, or, in other words, the locus of your physical dot remains invariant.


Picture a bowling ball in its rollable area. Picture it moving or standing still, either way. If the bowling ball is moving, the ball is rolling as a weight that gains speed, or accelerates. A weight that moves has momentum. Any object has directions associated with its position. Interrelated directions associated with position describe angle. So, the bowling ball, when standing still still has direction associated with its position. The bowling ball has weight. Mass is energy in static equilibrium. So, the bowling ball is always energy. Everything with energy has a velocity associated with it. Even if that energy is the combined kinetic forces that apply to allow the bowling ball to not be outwardly kinetic itself. So, in so long as a phenomena has energy associated with it, it has momentum which is also acting in a certain direction. This is true even if the summed energies and their directions add up to the object or phenomenon globally remaining still. Thus, any phenomenon that is formed upon energy has at least some angular momentum associated with it.


If something is stuff, then it exists in a spot. Stuff that is energy or made up of energy will always bear a sense of locale, thereby being in a spot. Even if the stuff is moving in space, after each discrete unit of relative time, the stuff is in a specific location. Anything that can be called "stuff" is energy and/or made up of energy either as a kinetic form (normal energy) or as a potential (kinetic energy in static equilibrium). Any thing that exists in a spot has direction associated with it that interrelates to cause the objects position to be the way that it is in any given moment. Anything made up of energy has a momentum, since energy is a drive that has motion and is motion. Also, motion always has direction. Thus, anything that is stuff in a spot has angular momentum.


Energy can be broken down to the level of a string. Strings exist. Since these exist, these exist in a spot. So, any phenomena composed of strings has angular momentum. Things smaller than a string are gauge-actions that do not classify as energy. Things this small do not act as momentum particles, and instantaneously associate with all other point particles. Thus, these particles do not classically act as "stuff in a spot." If you went a universe of discrete lower than the superstring (which is level lower than the Planck level, which is 3*10^(-35)meters), you could attempt to justify that these point-like particles and states have angular momentum, yet you wouldn't, since such a level could never pinpoint one of these phenomena at a spot except with extremely technical probability equations. Yet, any string may be pinpointed to a relative locus by using a low level of discrete.

Saturday, December 5, 2009

Session 11 of Course 1, More About Relative Loci

Let me put it another way. Draw a point. Call it a spot. It is only a spot. A second spot near the first one is local to it, yet it is still separate from the first spot. If the two spots were to be at the same position and fill the same area, then these would be one in the same spot. So, if the spots were part of each other, these wouldn't be local, since these would be the same thing overlapping.

Likewise, if the second spot was smaller than the first, and occupied that first spot without causing any distinguishable change through detection, then the second spot would not be just local to the first spot, it would have indistinguishably replaced something of that first spot. The two spots would be an interdependent whole that would amount to no net change in either spot. Both spots would be inseparable increments of something that is just as it was and just where the first spot had been for some time. Local spots would be those near the first one.

Let's say that two spots overlapped. The area of the first spot would have remained intact, and the area of the second spot remained intact. The overlapped area would be dark, just as both the first and second spots were dark. It is likely that the area of overlap would be darker than either spot initially was. The new configuration would not have the same configuration as either initial spot.

Let us say that the spots were round.d Let's say that as prior the area of overlap caused indistinguishable replacement versus the darkened overlap that I mentioned in the last paragraph. The emitted area that was replaced is residue of the first and second spots, yet it is no longer a part of either spot. If the replacement was eased by the efficient removal of what is now residue, than the residue would be forced away from the new shape that has formed. thus, the new residue is no longer a part of the new configuration. You could now say that the second spot's parts that have remained unchanged are local to the first spot's parts that have remained unchanged, since these are unique and have a distinguishable identity that is different from either initial spot.

Earlier, when the overlapped area was darkened, both the maintained part of the first spot, the maintained part of the second spot, and the area of the overlap could be said to be local to the same thing.

Theoretically, anything may be broken down into parts that are unique from the original thing. Yet, certain things should never be tampered with. What determines what a unique "spot" is, that can not be broken down, nor any smaller parts found further down in scope, is your definitional context. A lepton may be thought of as a single thing when you consider it as a particle. An electron is made of leptons. An atom may be treated as a system that contains particles. Any system has components that are local to the mechanism of that system as a whole. Planck Phenomena and superstrings are discrete units of energy. This is because you can not have an energy that is a fraction of a Planck Phenomenon or superstring. For instance, a lepton system has Planck Phenomena and superstrings that are local to the very makeup of that lepton. Everything is locally interdependent on its interior and exterior.

Thursday, December 3, 2009

RE: Session 7 of Course 1‏

Two things interact in a situation. These objects or phenomena change relative to each other as both things associated in space and as two items that act as placeholders in both their individual relative time and their collective relative time. Suppose that each of these two items were a cane. Two canes. Both of these canes struck each other in many ways at the top of their structures, yet the canes never pulled each other to any significant sway, and thus only interacted as a static force that redistributed the ends of each other. Now let's say that the bottom of the canes were held by a highly powerful grip that had a leeway of some elastic modulae. In other words, the bottoms of the canes were held tightly, yet by a medium that was not rigid -- like a pair of hands. When the canes at their tops were to strike, these would be momentarily redistributed, while then returning to an approximation of their original spot. Like you can see, their differentiation would be static, and no significant net change would appear over any transient period of time in terms of the appearance of the scene. Yet, if you were to hook the ends of the canes, there would be a chance that one of the canes would pull the other. Even if both of the people holding the canes were of equal strength, depending on how the canes were twisted and/or torqued, could cause a net change in how these would be pulled.
Tug has to do with push-pull action. In order for there to be a push or a pull, there must be some static connection for at least one moment. For instance, you push a stone. In order for you to move it at all, your hand must have some interaction with the stone for at least one moment. If you tried to lift anything without interconnection, your hands would slip and you wouldn't be able to lift it. When something pulls something else, there is a significant static modulae that allows for the puller to pull. This interconnection is classically done when the two objects are hooked one onto another.
Waves tug, since these push and/or pull. The interconnection comes through electrostatics and/or hookable cusps in the morphology of the waves' structure. Strong electromagnetic fields pull in more wavelike phenomena, while strong electrostatic fields such as a high voltage fence will actually push out a person who tries messing with it. (High amps will pull you in and electrocute you, while a high voltage/low amperage situation will knock you away once the low amperage momentarily attempts to pull you in.) This is because amperage is charge per second, and a high amount of electrical charge flowing in a limited amount of time hooks any adjacent conductive material since this will balance the adjacent electrical band levels, and voltage is energy per charge, and if a wire has a lot of energy per charge, yet not much charge is flowing through the wire per time, then the low charge per time will barely attempt to pull the person while the wire's high energy will form a field that will repel the person as they are being shocked. Both examples of pull and push are examples of how interaction is a matter of wave-tug. General relocalization of particles is due to the various tendencies of wave-tug.

The 10th Session of Course 1

Two things interact in a situation. These objects or phenomena change relative to each other as both things associated in space and as two items that act as placeholders in both their individual relative time and their collective relative time. Suppose that each of these two items were a cane. Two canes. Both of these canes struck each other in many ways at the top of their structures, yet the canes never pulled each other to any significant sway, and thus only interacted as a static force that redistributed the ends of each other. Now let's say that the bottom of the canes were held by a highly powerful grip that had a leeway of some elastic modulae. In other words, the bottoms of the canes were held tightly, yet by a medium that was not rigid -- like a pair of hands. When the canes at their tops were to strike, these would be momentarily redistributed, while then returning to an approximation of their original spot. Like you can see, their differentiation would be static, and no significant net change would appear over any transient period of time in terms of the appearance of the scene. Yet, if you were to hook the ends of the canes, there would be a chance that one of the canes would pull the other. Even if both of the people holding the canes were of equal strength, depending on how the canes were twisted and/or torqued, could cause a net change in how these would be pulled.
Tug has to do with push-pull action. In order for there to be a push or a pull, there must be some static connection for at least one moment. For instance, you push a stone. In order for you to move it at all, your hand must have some interaction with the stone for at least one moment. If you tried to lift anything without interconnection, your hands would slip and you wouldn't be able to lift it. When something pulls something else, there is a significant static modulae that allows for the puller to pull. This interconnection is classically done when the two objects are hooked one onto another.
Waves tug, since these push and/or pull. The interconnection comes through electrostatics and/or hookable cusps in the morphology of the waves' structure. Strong electromagnetic fields pull in more wavelike phenomena, while strong electrostatic fields such as a high voltage fence will actually push out a person who tries messing with it. (High amps will pull you in and electrocute you, while a high voltage/low amperage situation will knock you away once the low amperage momentarily attempts to pull you in.) This is because amperage is charge per second, and a high amount of electrical charge flowing in a limited amount of time hooks any adjacent conductive material since this will balance the adjacent electrical band levels, and voltage is energy per charge, and if a wire has a lot of energy per charge, yet not much charge is flowing through the wire per time, then the low charge per time will barely attempt to pull the person while the wire's high energy will form a field that will repel the person as they are being shocked. Both examples of pull and push are examples of how interaction is a matter of wave-tug. General relocalization of particles is due to the various tendencies of wave-tug.

RE: Session 6 of Course 1, Jointedness‏

Picture the frame of a warehouse as it is being built. Certainly, all of the materials used to build the building are not going in the same direction. If this were to happen, the pieces used to make this building would either be laying on top of each other and/or laying side by side and/or connected in a long line that would not be able to form a building. Some parts of the building would need to be connected at the side of other parts.
If you are going down a road, and you come to a stop, after which immediately turning right, you would have made a ninety degree turn. The same would be true in such a case if you were to turn left. Ninety-Degrees looks like an "L" or a backwards "L." Ninety-Degrees is also the change from the side of a circle to its top, and is the phase difference between sine and cosine. When you draw a sine wave correctly, it is a smooth curve. When you draw a cosine wave correctly, it is a smooth curve. If you draw a terraced structure correctly, it makes some immediate direction changes either when going from up to across and from across to up or when going from across to down and from down to across.
Let us examine a curve that is smooth from our perception. Its change in direction has no erratic differences along the swipe of the curve. You can't draw any lines between any three points of the curve from the perspective at which the curve is smooth. Yet, if you were to observe the curve from a smaller scale -- perhaps down to individual molecules that make up the writing that formed the drawing of that curve, you would notice jointedness at this or some smaller level. Likewise, if you took monkey bars at an elementary school, and you looked at these at some smaller level, there would be a point where you could see a smoothness to the curvature. This would be a perspective of the apparently jointal object to where it would no longer appear jointal, yet smoothly curved.
So, jointedness is a function of all phenomena, as well as smooth curvature is a function of all phenomena. If you look at phenomena at a small enough basis, any change in position is a ninety-degree alteration of space relative to some other phenomenon. Yet, if you look at things from a large enough or a small enough basis, all curvature has some smoothness. For instance, with the monkey bars, if you make a one sided map of the area of the monkey bars at a distance, and localized these, the monkey bars would appear as a thin structure of lines, or, if observed from a further distance, these may appear as a dot or a thin line. It would not appear as a jointal composite here, yet as a smooth and tiny structure. Yet, if you observed certain molecule's curvature from within the monkey bars themselves, again, the monkey bars would appear as a smooth structure and not as jointal. Certainly, observing the monkey bars for their intended purpose would make them appear quite jointal.
Ninety-Degrees means immediate change in direction. In order for anything to happen in space, direction must change immediately from some perspective. Yet, in order for change to have any organization, there must be smoothness. Thus, jointedness and smooth curvedness.

Session 6 of Course 1, Jointedness‏

Picture the frame of a warehouse as it is being built. Certainly, all of the materials used to build the building are not going in the same direction. If this were to happen, the pieces used to make this building would either be laying on top of each other and/or laying side by side and/or connected in a long line that would not be able to form a building. Some parts of the building would need to be connected at the side of other parts.
If you are going down a road, and you come to a stop, after which immediately turning right, you would have made a ninety degree turn. The same would be true in such a case if you were to turn left. Ninety-Degrees looks like an "L" or a backwards "L." Ninety-Degrees is also the change from the side of a circle to its top, and is the phase difference between sine and cosine. When you draw a sine wave correctly, it is a smooth curve. When you draw a cosine wave correctly, it is a smooth curve. If you draw a terraced structure correctly, it makes some immediate direction changes either when going from up to across and from across to up or when going from across to down and from down to across.
Let us examine a curve that is smooth from our perception. Its change in direction has no erratic differences along the swipe of the curve. You can't draw any lines between any three points of the curve from the perspective at which the curve is smooth. Yet, if you were to observe the curve from a smaller scale -- perhaps down to individual molecules that make up the writing that formed the drawing of that curve, you would notice jointedness at this or some smaller level. Likewise, if you took monkey bars at an elementary school, and you looked at these at some smaller level, there would be a point where you could see a smoothness to the curvature. This would be a perspective of the apparently jointal object to where it would no longer appear jointal, yet smoothly curved.
So, jointedness is a function of all phenomena, as well as smooth curvature is a function of all phenomena. If you look at phenomena at a small enough basis, any change in position is a ninety-degree alteration of space relative to some other phenomenon. Yet, if you look at things from a large enough or a small enough basis, all curvature has some smoothness. For instance, with the monkey bars, if you make a one sided map of the area of the monkey bars at a distance, and localized these, the monkey bars would appear as a thin structure of lines, or, if observed from a further distance, these may appear as a dot or a thin line. It would not appear as a jointal composite here, yet as a smooth and tiny structure. Yet, if you observed certain molecule's curvature from within the monkey bars themselves, again, the monkey bars would appear as a smooth structure and not as jointal. Certainly, observing the monkey bars for their intended purpose would make them appear quite jointal.
Ninety-Degrees means immediate change in direction. In order for anything to happen in space, direction must change immediately from some perspective. Yet, in order for change to have any organization, there must be smoothness. Thus, jointedness and smooth curvedness.

Test #1 For Course #1, Session 8‏

1)What are the six keys that I gave to logical organization?

2)List an example of each of the previous keys.

3)Draw a two-dimensional axes. Draw an identity function from it. Draw a line that is (-1)*the identity function.
Label the quadrants. Circle the labels of the quadrants that corresponds to the identity function.

4)Make a cartoon of the identity function moving as a swipe of one full circle going counterclockwise.

5)Draw lines that go jointedly from one spot to another.
Next, draw a smooth curve that approximates this path.

6)Draw a circle. Circle its top. What function is maximized there? What function is zero there? Put a square at the bottom of the given circle. What function is minimized there? What function is zero there?
Put a triangle on the left side of the given circle. What function is minimized there? What function is zero there? Put a rectangle of the right side of the given circle.
What function is maximized there?
What function is zero there?

7)Why can't change be constantly jointal?

8)Why can't change be constantly smooth?

9)What does the Heisenburg Principle amount to?

Test #1 For Course #1, Session 8‏

1)What are the six keys that I gave to logical organization?

2)List an example of each of the previous keys.

3)Draw a two-dimensional axes. Draw an identity function from it. Draw a line that is (-1)*the identity function.
Label the quadrants. Circle the labels of the quadrants that corresponds to the identity function.

4)Make a cartoon of the identity function moving as a swipe of one full circle going counterclockwise.

5)Draw lines that go jointedly from one spot to another.
Next, draw a smoothe curve that approximates this path.

6)Draw a circle. Circle its top. What function is maximized there? What function is zero there? Put a square at the bottom of the given circle. What function is minimized there? What function is zero there?
Put a triangel on the left side of the given circle. What function is minimized there? What function is zero there? Put a rectangle of the right side of the given circle.
What function is maximized there?
What function is zero there?

7)Why can't change be constantly jointal?

8)Why can't change be constantly smooth?

9)What does the Heisenburg Principle amount to?

Session 6 of Course 1, Jointedness

Session 6 of Course 1, Jointedness

Tuesday, December 1, 2009

SESSION 5 OF COURSE 1

What kind of planar curvature is equally distant from its center at all times? A circle. If the top of a circle were anywhere where you arbitrarily determine it to be at, where would the circle be maximized at? At that top. A maximum position indicates the location of its highest value and the top of something is higher than its bottom. This depends on whatever you arbitrarily called the "top." This generalization depends on if the "top" were the highest point of the circle, and if, depending on your context, the maximization of the circle's structure were to also be at one with whatever you may also arbitrarily call the maximization of the circle. For instance, not as a trick question, the maximum position on the earth would more likely be the magnetic north pole rather than the magnetic south pole. In trigonometry, the sine function is maximized at pi over two. This is at ninety degrees, and is at the top of the circle. If you looked at the circle upside down, the top of the circle (actually, the bottom) would appear to be 3pi over two. Here is where the sine function is minimized. If you choose an orientation that is fixed, and pi over two is at a location mathematically at least, then, by this orientation, that position is always the top of the circle. Here, we are talking about a unit circle, so when the sine function is maximized, it equals one. And when it is minimized, it equals negative one.

How does one come up with what the sine and cosine functions are? In a unit circle, what's the closest distance from the x-axis to the top of the circle? One. Likewise, what's the closest distance from the y-axis to the right side of the circle? One. What's the closest distance from the x-axis to the right side of the circle? Zero. What's the closes distance from the y-axis to the top of the circle?Zero. Likewise, the sine function is maximized at the top of the circle (pi/2) and the cosine function is maximized at the right side of the circle (0pi). The sine function is zero at 0pi, and the cosine function is zero at pi/2. What does this indicate? It shows that the sine function is more of an indicator of how things change in nature. For instance, a toy rocket starts from "scratch", not accelerating or decelerating. You shoot it out. It goes from zero to an accelerated speed. Soon, the rocket slows, rapidly decelerating. Once it falls, it will accelerate toward the earth (the earth's acceleration upon this toy rocket being constant)