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In the Seed & Root Equation Notebook, we sought for & discovered a content-based equation that would determine the Directionals of a Live Data Stream in terms of the Raw Data alone. We called this equation the Seed Equation (page 28, Section II, Equation 1, S&R). Although this equation is small, concise, beautiful and precise, the Seed Equation needs to be unfolded, unraveled and unfurled to determine any Directional great or small. At the foundation of the Seed Equation we found a Root Equation (Page 4, Section II, Equations 10, S&R). This Fractal Root Equation, as we called it, feeds all the manifestations of the Seed Equation. This equation, too, is beautiful in its economy. But it is furled up and must be unfurled before it can determine any Directional.
A seed is a tiny particle, whose unfolding determines the nature of the plant. The roots feed the leaves and body of the plant. Although the Root feeds the Plant and the Seed determines its structure, they are disassociated with what is above the ground. Looking at an acorn, one has no idea what an oak tree might look like. Even looking at its root structure, knowing all about photosynthesis, one still couldn't predict what the branches and leaves would look like. The Root & Seed reveal many interesting elements of potentiality, but don't reveal the active manifestation. The Root & Seed indicate what type of plant it might be, that it is a plant, but indicate little about the individual workings out of destiny. Will the plant be subjected to drought or flood at a crucial stage in development? Will its leaves be eaten? Will its flowers be cut? Neither the Seed nor the Root can answer these questions.
In a similar way our Root & Seed Equations determine the structure of our phenomenon. The Seed Equation details the nature of its unfolding. The Root Equation determines how it gets its substance. But neither equation reveals much about the manifestation of our phenomenon. This occurs above ground, in the context of the environment. Although the Root & Seed Equations determine how our phenomenon deals with its content, it reveals very little about its response to its context.
What phenomenon are we talking about? The Phenomenon, we are discussing, are any Live Data Streams and their Directionals. Remember Live Data Streams are ordered, unfinished, inhomogeneous and unpredictable Data Sets. Many scientists don't believe in them. We do. We believe in Live Data Streams and we're not sure that we believe in Finished, Homogeneous, and Predictable Data Sets except on a Physical Material Level. So our Phenomenon are any data generation associated with Living Things. We define Life, not by carbon but by unpredictability, to be dealt with a little later on. Our Phenomena are Alive, not Dead. So our equations deal with the limits of Live phenomenon.
These two marvelous content-based equations, our Root & Seed Equations, reveal much about the general characteristics of our Phenomenon but reveal very little about our Phenomenon individually. We know that we have a Fractal phenomenon, but how does it manifest? These Equations are the Laws of our system. Our phenomenon cannot disobey these Laws. Out of these general laws come some individual laws from derivations, which will prove quite useful in computing individual Directionals. However, because of the unpredictability of our phenomenon, these Laws, general and specific, only determine the boundaries of possibility but do not determine the individual workings out of particulars.
The Law is the Constitution. The Congress and the Courts work together to put together individual laws, which don't violate the general law of the Constitution. But the people operate freely within these general laws to work out their individual destinies. The Law and its derivatives govern 200 million people but each of them has unique individual lives. Such are the Root and Seed Equations for the Directionals. They provide order but not motion.
The Laws provide the Static Order. They tell where the roads are. They are like a Map. Mechanisms guide the contextual response, but are not laws. If every time a road is taken, one hits a traffic jam, one tries other routes until he finds the most efficient route. He doesn't drive off the streets, but his route is in no way predetermined. In fact, it is determined by Experience, History, and Memory – a Contextual Response within a Content filled Environment.
Just as the Constitution is not used in local legal cases, the Root and Seed Equations are only used in general circumstances. The underlying structure that is revealed is quite illuminating in determining the context of motion. Where are the roads and where do they go? Yet outside of this structural mathematical context, we will never use these equations again. They are totally impractical on the individual level. They are concise in seed form but are incredibly complex unfurled and unfolded at even the most elementary levels.
For survival the organism is only interested in his context to his environment. The content of his environment is only important in the event that it influences the context. In the Derivative system developed above and in previous Notebooks, each Derivative is defined simply by an immediate context. The incredible complexity only occurs when the context is abandoned for the content. When the organism begins trying to store all the Data points, the content, and apply complicated formulas, quickly, it is in big trouble. When the organism is only storing practical and immediate derivatives, it doesn't carry unnecessary baggage and is able to immediately and easily calculate the Derivatives necessary to calculate the measures necessary to facilitate survival. One concept that we are developing is the facility of a context-based approach vs. the increasing complexity of a content-based approach when dealing with Data Stream derivatives.
Because we are interested in living organisms we will be looking primarily at the context-based derivatives in the studies that follow. The food, the Data, that feeds the Root Equation will be seen to be of utmost importance to the development of the Form. In the physical sciences the Form is predetermined by the function. With Living Data Streams the Form is only unfolded through the Living Data; there is no function to determine the Form. The Function is only to determine the Nature of the Unfolding, the way that the Data unfurls. In a Dead Data Stream the Function predicts the Data. In a Live Stream the Function only reveals the Nature, not the Form.
Below is a diagram, which illustrates what we are talking about. With Dead Data Streams, there is a feedback between Data and Function, whereby the Function is able to predict the Data, given only one point. These are very complex functions, but only need one piece of Data to determine the Form of the Data. With Live Data Streams, the Function and Data work together to determine the Form. The Function is simple, but all the Data is needed. For Dead Data Streams discovering the Function is everything. For Live Data Streams the Functions are predetermined and the workings out of the Data are everything.
Returning to our Map analogy, the Functions of the Dead Data Streams determine the exact path that any material substance will take. There is no variance. There is no choice. The Functions of Live Data Streams determine the possible roads but do not tell the way to take. There are a nearly infinite variety of different routes to take. There are myriad choices.
The complex functions of Dead Data Streams are written in the following archetypal form. Given any X one only need apply the function to determine Y. We will call these Descriptive functions because they describe how Y behaves as a function of X. This type of function has a marvelous number of physical applications. It operates very well upon Dead things. The higher derivatives can also be described by functions called Differential Equations. Again only one X and the function need be known to determine any differential. All the other Xs are inconsequential once the function is known.
With Live Data Streams, the functions are very different. The Root Function cannot determine Y from a given X. The Root Function needs all N of the previous Xs to determine the current YN. Any individual X has no meaning except in the context of all the Xs. Furthermore the Seed Function is a function of the Root Function. It determines all the higher Derivatives. Because it is dependent upon the Root Function, it too demands all the previous Data Points to determine the current derivative. Again, we must stress that, by definition no function exists that can describe a Living Data Stream or its derivatives. If a function is discovered that describes a Living Data Stream then the Living Data Stream has been killed and turned into a Dead Data Stream. In this study we are assuming that there exist Living Data Streams that can't be killed.