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Now that the Reader has been introduced to our Root Beings and seen how they behaved under different Circumstances we can speak about them as a Quest Metaphor.
Before barreling bluntly forward into nowhere, let us stress that we are only describing a Metaphor for the Quest. Beware of mistaking the metaphor for reality. The metaphor is just a way of describing an aspect of Reality. It is not Reality itself. Reality is so complex that no Box can hold it, especially mental boxes in the shape of metaphors. Thus this metaphor is just a handle on the complexity of Reality, not reality itself.
This is complicated, but worth spending some time on. This phenomenon that we are speaking of is a natural mechanism. It is not based upon psychology, environment, gene pool, father or mother, gender or culture, living or inanimate. There are no atoms, molecules, or any other building blocks of matter. There are no elemental forces like electricity, gravity and the like. There is nothing here but a mechanism of numbers. This is what happens when these types of iterative equations get together for a good time. These types of iterative equations are so basic that they generate all Rational Roots.
Number Mechanisms are independent of building block theorists. While they might underlie natural structure they are not made up quarks, cement, or any other sub-atomic particle. Crystalline structure has part of its meaning in a number mechanism that is independent of underlying elements.
Let us be specific about what we are speaking. We are speaking about multiple layer inverse iterative equations with specific coefficients, i.e. called Root Beings by their friends. As these equations are iterated they approach a distinct value. Thus our Root Beings are goal oriented. They have a distinct destination. Thus this metaphor does not apply to situations that have no goals. The idea that everything is already perfect is not part of this metaphor. This is why we call it a Quest Metaphor.
These Root Beings are seeking self-perfection. They are not meant to stand around. They are meant to go somewhere. They iterate themselves over and over, getting closer and closer to their goal. However while they get closer to their goal, they will never reach it. Thus these Root Beings are a metaphor for those seeking self-perfection, not for those who are happy where they are. They represent a transformation metaphor, not a Be Here Now metaphor.
Let us point out that these are not mutually exclusive states of being. One can be content in the natural quest for self-perfection. But this metaphor has nothing to do with how to achieve peace or contentment. It has only to do with the nature of the quest for self-perfection.
We have established that our Root Beings are not just ÔbeingŐ; they are going somewhere. We will call this their Quest. Where is their Quest going? They are going towards the True Root as their Limit. This is their only focus, their only Mission, True Intent.
How do these Beings move towards the True Root, impossibly seeking perfection? They iterate themselves. For our metaphor, we will call each iteration a movement towards the True Root based upon a Decision.
How is the Decision made to make each of these movements? Our Root Beings make their decisions based upon Past Events or the results of Past Decisions. If they are 4th Order Root Beings they make their decisions based upon three events from the past, 5th Order four events, 3rd Order two events from the Past and so forth. Thus each Decision is based upon the Results of Past Decisions.
Which Events are used to make Decisions? Under ÔNormalŐ Circumstances nearly any sequence of Events from the Past can be used as long as they are used in the right way in a balanced proportion. However as the Circumstances become more exceptional the only events that always work to get our Being to the True Root are the Most Recent Events extending continuously into the past.
Let us be more specific. When our Circumstance or Root Number is between about 6 and 1/2, many 4th Order Root Beings will work to get us to the True Root. However as the Circumstances become more intense, i.e. the Root Number becomes higher, only the True Root Being continues to take us to the True Root. The True Root Being never gets lost while the Bogus Root Beings canŐt handle the Stress of the larger numbers. Remember that these Bogus Root Beings work just fine under Normal Circumstances, i.e. when the Root Number is under 10.
What is the difference between these Bogus Root Beings and the True Root Being? First there are two types of Root Beings. There are Now-based Root Beings who donŐt extend far enough into the past, basing their decisions upon the most recent events and ignoring the past. This strategy works just fine when the circumstances are not extreme. The other type of Root Being is the Past Based Root Being. They ignore the most recent events in favor of events from the Past. Again this strategy works just fine under Normal circumstances. In contrast, the True Root Being is based upon the most Recent Event, extending continuously from here into the Past.
The metaphor: on the Quest we canŐt ignore Past or Present Events when making decisions under exceptional circumstances. We need to extend continuously from the Present into the Past. We must beware of dwelling too much in the past or in the present, except under Normal Circumstances. Under Normal Circumstances we can choose most any event in the sequence to reach the True Root and achieve our Quest as long as we have the appropriate Pattern.
What is this appropriate pattern? It is perfectly balanced.
No matter which events from the Past are used to make decisions, if they are not perfectly balanced they will never reach the True Root. They might be close, really close, but their approach comes to a standstill at a certain point. The Root Beings who come to this standstill are called False Root Beings. Once again they come very close but never get any closer.
The only difference between False Beings and the others is that their approach is not balanced. Both the Bogus and True Being both have the same Pattern. The Bogus Beings just arenŐt balanced in their choice of Events to make Decisions on. Their Pattern is correct and will take them to the True Root under Normal Circumstances. The True Pattern is based upon the Binomial Expansion, which we have called dimensional extension.
In this Metaphor, our Inverted Dimensional Journey begins with the first extension, based upon the inversion of the combination of the polarity of infinitesimal existence and dimensional capability. Neither existence nor dimension can exist without the other. This is the Rational Numbers, pure and simple, really going nowhere, just there. Luxuriating in existence. The Balance of Being and Process. Self and Other.
The second extension throws this polarity against itself to create another inverted dimension. This is the Square Root Formula, a little bit of numerical reality and one level of feedback. Now Other breaks into Other and Parents/Family. Constant interactive feedback is used to maintain Balance.
As one matures, new levels of Dimensionality are constantly added. Relationship, Job, Kids on the most obvious level. OneŐs Creative, Spiritual, and Material Life on the more subtle levels. Each of these levels adds another aspect of feedback that needs to be balanced in the pot. The metaphor of these Root Beings is that these elements must be balanced or a Plateau will be reached, but not the Peak of the True Root.
In all fairness to the False Beings of this Metaphor, it must be stated that if the proper events and Circumstances are chosen, that these False Beings continually approach a different value. These False Beings only fall apart when the Number is very small or very large. However let it be pointed out that the Number that the False Beings are approaching has No Name. These False Beings work their whole Life to achieve a unnamed State. This is OK. However to reach the True Root of the Number one must take the Balanced Approach to Dimensionality.
This means to treat each dimension of OneŐs Life with Equal Respect. Neither Family, nor Job, nor Wife, nor Creative Life is more important. They all contribute to the growth of our Being. To distort oneŐs quest by focusing upon one level of dimensionality at the expense of the others will contribute to growth, but one will plateau at a wall unless one balances the attack.
This brings up some laws of our Beings. One law of our Beings is that the more Dimensions that are added the Quicker the Approach to the True Root. The Second is that when youŐre on the path that no matter how far you go youŐre the same Distance from the End. The Third is that Conversion to the True Being is possible at any time. The Fourth Law is that the Approach of the True Being is always erratic.
The First Law is demonstrated but not proved by the graph in Section 4B, in the section on Seeds. The Higher the Root the steeper the approach to True Root. In different words, With the same Circumstance or Root Number, the Higher Roots will approach quicker than the Lower Roots. Specifically the Cube Root Equation approaches its Root more quickly than does the Square Root Equation. Adding Balanced Dimensions to oneŐs life moves one ahead more rapidly, although more erratically, as we saw.
The Second Law has to do with the fact that one can always get closer to the True Root but one will never get there. Thus all Beings that are on the Path are the same distance to the End. Even when one Being has reached the End relative to another Being, it is only an illusion. While the other Being is so far ahead as to seem enlightened, in actuality he still has just as far to go to the Goal. Thus we all hope to reach the Path, but we will never reach the End. The most we can hope for is the continual increase in subtlety.
The Third Law has to do with the self-correcting nature of our Equations. No matter what garbage has gone before, if the Pattern is righted and the Events are properly ordered, the Being will immediately begin heading towards the True Root. The idea is that no matter how fouled up the past is, it can always be righted with the proper balanced pattern and the proper attitude towards Time. No Being is ever truly lost, in this metaphor. The data that is fed into the iteration is secondary to the pattern and events priority that are established.
The Fourth Law is that the Approach is locally erratic and globally consistent. It is never straightforward. As we saw in the earlier section the progress is punctuated by temporary enlightenments and momentary setbacks, in the midst of steady progress. The lesson here is not to be discouraged by setback, nor to be attached to local enlightenments. Both of these phenomenon are temporary aberrations from the stable Path and donŐt really reflect oneŐs true position.
A Corollary principle is that no matter how fast the approach that the end is still just as far away. Thus under this aspect of the Game it would be better to be On the Path moving slowly rather than Off the Path and moving nowhere. The point here is that being on the Path is everything. The Path leads one on the maze towards greater precision while not being on the path means that the Being is going to an unnamed destiny or going nowhere, i.e. not approaching a limit.
While we are all parts of the same package, the Game that our Root Beings are playing have certain rules that are independent of the numbers themselves. Each of the Root Beings is just doing what they are programmed to do. The False Root Being relentlessly pursues an unnamed goal. The Bogus Beings falls apart under pressure. Only the True Beings pursue the True Root under any Circumstance. While these descriptions are loaded with human emotions, in reality each of our Root Beings is just doing what he was born to do. Each pursues and achieves an independent Destiny, wholly dependent upon their preexisting conditions. It is not their fault that they fall apart under stressful conditions. The Now-based Beings are programmed to bifurcate under certain Circumstances, no matter what. If they ÔimproveŐ into the True Root Beings then they would no longer be themselves any more. We would miss their rigid straight-line approach under Normal Circumstances. While we love the True Root Being for never letting us down under any Circumstance, we love the other Root Beings for being themselves under all Circumstances.
That being said for individuality and alternate destinies, we mathematicians, and pretend mathematicians, have a game called Equation. This Game has one main rule. This Rule is very simple. The quantities on both sides of the equality sign must equal each other in some way.
With most ÔNormalŐ Equations, i.e. non-iterative equations, the equations are either right or wrong. Normally they are not right under certain conditions and wrong under others. We might have an equation, which applies under certain circumstances and another equation which applies under other circumstances but normally the equation itself doesnŐt fall apart except at perhaps certain distinct values, i.e. dividing by zero.
Further Normal Equations donŐt usually approach their answer more or less slowly. Two plus two is immediately four with no intermediate steps. Most Normal Equations are instantaneous. However there is a group of them, which contain infinite series, which can approach their goal at different speeds.
Our iterative equations are never instantaneous unless they equal zero, i.e. when one of their factors is zero and neutralizes the whole series. Not only arenŐt they instantaneous, they are never exact either, always getting closer and closer, but never arriving. Despite these idiosyncrasies, with repeated iterations the True Equations approach the desired Root, while the False Equations donŐt. When we are finding the Root of two, no matter whether the square or fifth root, countless different iterative equations work just fine and would be considered True Equations. When we are finding the Root of 1000, only one equation works (Practically speaking). This equation is the one that we call the only True Equation.
The point made is that any iterative equation can do what it wants to do for itself, but if it does not do the work it was intended to do, it is called a false equation. In other words, we could not put the square Root of 1000 on the other side of the equality from a Now-based Equation, while we could put it on the other side of the One True Equation. These iterative equations either approach the appropriate limit or they donŐt. Our terms of true and false are mathematical not personal opinions.
Possibly a question comes to mind. Maybe we the experimenter have set unrealistic goals for our Beings. Maybe we need to set other goals. Under Exceptional Circumstances there are no goals. Both our Bogus and False Beings fall apart under Exceptional Circumstances. They donŐt head off for another goal. They just dissipate, approaching no apparent goal, bouncing around somewhat aimlessly. The Bogus Beings either approach the True Root or they fall apart. They have no other goal but the True Root. When they are not approaching that, they arenŐt approaching anything.
This is not true of False Beings. Under many Circumstances the False Beings will approach a goal different from the True Root. Indeed under Normal Circumstances the False Equations can be manipulated to come as close as necessary to the true Root. While the False Equation might come close to the True Root, at one point its approach flattens and it can get no closer. The False Beings reach a wall, which canŐt be bridged. This wall could be anywhere from 4 place accuracy to 16 place accuracy but a wall will be reached where the False Being can go no further because in fact his goal is slightly different from the Real Root. On the other hand the True Beings will not hit a Wall, but will instead get consistently closer to the True Root.
What is this other goal that our False Root Being is so urgently seeking out? It is unnamed. While we assume that its approach to its goal is also steadily consistent, we canŐt really test it out, because its goal doesnŐt really have a numerical name. While the True and Bogus Being, Normally, i.e. under Normal Circumstances, approach the Root of some Rational Number, which can be named and evaluated by the computer, the False Beings approach some other type of number. We call them patterned transcendentals. If its a fourth order Root Equation, it approaches a fourth order patterned transcendental.
Thus we are not trying to be pejorative when we call them False or Bogus Equations. We are being descriptive. They do not satisfy the requirements of our equations and are hence deemed false by any in the scientific community, not because of any arbitrary values but because they donŐt work.
The equality rule of our Equation Game differentiates out the Root Beings that work from those that donŐt. Thus we are now back to our original point. If the iterative equation steadily approaches its Destiny the True Root, we deem this good. Conversely if it does not approach the True Root we deem this bad.
Thus in the world of Root Beings, the good Root Beings approach the True Root while the bad Root Beings donŐt. Under this definition of good and bad, from a mathematical level, it doesnŐt matter how quickly the Root is approached so much as that the Equation will lead the Seeker steadily towards the Root. With endless iterations the slowest True Root Being will always inevitably overtake and pass the quickest False Root Being. Hence being on the right Path is of utmost importance, while being quick is of secondary importance. As long as the Being is on the path it will always get closer and closer, while if the Being is not on the path from improper coefficients, no matter how close, at one point progress will stop and the slower Root Being on the Path will eventually and inevitably pass them up.
This leads us to our next corollary Law. It is better in our limited metaphorical mathematical sense to handle two dimensions well rather than many dimensions poorly. If our Root Being is seriously out of balance on the higher levels, to the extent that their coefficients are flawed, then they will never reach the True Root because they are not even on the Path. However if our Root Being is only 2nd order but is on the Path, then progress is steady and consistent and will inevitably pass the False Being when theyŐve hit their Wall. Thus metaphorically it is better to handle fewer things well than to handle more things poorly.