The Mathematics of Relationships
In prior articles we provided evidence to support the following claims: 1) Probability best characterizes the permanent and general features of fixed data sets. 2) The Living Algorithm best characterizes the changeable and individual moments of living data streams. As such, we have chosen to call the Living Algorithm math, the Mathematics of the Moment. Because of the way the Living Algorithm digests data streams, she also puts these moments in relationship to each other. Accordingly what happens at each instant in time has an effect upon subsequent developments. Let’s see how.
Living Algorithm transforms Instants into Moments
A. An Instantaneous Data Bit becomes a Moment
The Data Stream Mathematics of the Living Algorithm System specializes in relationships. This focus is due to the way in which the Living Algorithm digests information. She takes raw data (which we will call instants) and spreads them over time (which we will call moments). Graph A illustrates what happens when the Living Algorithm digests the number one (raw data/ instant) and transforms it into a moment.
Transformational Process gives Data a Meaningful Dimension
The instant is the point when the data enters the System. The impact is greatest when the data (instant) first enters the System. The effect of the impact on the System decays with each repetition of the process (iteration). This is why the measure of this diminishing impact is named the Living Average. In this case, it took about 60 repetitions (iterations) until the original impact faded to 'practical' zero. It could be said that the Living Algorithm transforms a one-dimensional entity into a two-dimensional entity. More simply put, the Living Algorithm gives Data a meaningful dimension by spreading its influence over time. As we shall see, raw Data is not in an accessible form for the organism, until it undergoes this transformation. Because moments are accessible, they provide the organism with meaning.
The Most Recent Moment is layered on top of the Preceding Moments.
B. The Accumulation of Moments
With each repetition of the process, a new data byte (instant) is digested in a similar fashion. The Data enters the System as a one-dimensional entity – in this case a one. The Living Algorithm then spreads the instant’s impact proportionately over time. This process transforms instants into moments. With each subsequent iteration, each moment is layered on top of what went before, i.e. the diminishing (decaying), yet influential, effects of the preceding moments (Graph B). Notice that the blue area in Graph A is an enlargement of the small blue sliver at the bottom left in Graph B. All of the colors in Graph B represent the layering and accumulation of moments.
Moments join forces to produce a Greater Impact upon the System
Graph A was produced by a data stream consisting of a single 'one', followed by a string of 'zeros'. A data stream consisting of 120 ones followed by 120 zeros produced Graph B. When there is just one data bit acting alone, its impact (the moment) on the system is quite small – its maximum only .06. However, when there are series of moments as in Graph B – specifically 120 of them, the total collective impact on the system is much greater – eventually rising to '1.0'. The collective force of the stream of ones has an impact on the overall System that is inevitably 16 times greater than a single ‘one’ acting alone. In short, there is a greater impact upon the System when the Moments operate together – moving in the same direction.
Interlocking Interactions between Data & Living Algorithm Measures
This type of interaction is additive (accumulative), which is certainly a valid form of interaction. Yet, there is another aspect of the Living Algorithm's method of digesting information that integrates the Data in an even more complex fashion. The above analysis only applies to the Living Average – the simplest measure generated by the Living Algorithm. When more complex measures are introduced, the resulting computational stew is an intriguing combination of interactions between data and measures. Without getting into mathematical details, Chart C below indicates the complex weave between the Data and the Living Algorithm's Measures that is required to produce the value of each new Measure. The columns of Xs without hats (the 2nd, 4th and 6th columns) represents the contributions of the Data, while the columns of Xs with hats represent the contributions of the Living Algorithm Measures.
C. Interlocking Interactions between Data & Living Algorithm Measures
Living Algorithm System: Moments only exist in Relationship, not as Independent Entities
We’ve seen two ways in which the Living Algorithm’s method of digesting data streams creates a relationship between the moments. There is one final way, perhaps the most significant for this discussion, in which the Living Algorithm produces an Interactive System. All the triangles in Diagram C above indicate change. As such, all the interactions in the Living Algorithm System are based in change, the differences between a complex mixture of Data and Measures. Accordingly no Moment exists as an independent entity in the dynamic System. Each Moment only exists in relation to the surrounding Measures and Data Points. Independent Existence is an Illusion. The only Reality is constant Change, at least in the Living Algorithm System.
Permanence leads to Definitive Patterns: Change leads to Suggestive Patterns
In Probability's System, the Reality is fixed and never-changing. This is why definitive predictions are possible. Permanence can be characterized by definitive patterns. The event horizon can be narrowed to a single point - just one alternative, based upon initial conditions and an equation. The mathematical functions (equations) of hard science epitomize this claim. In contrast, because the Living Algorithm System is founded in dynamic change, only suggestive predictions are possible. Evolving transience is best characterized by suggestive patterns. The event horizon can only be narrowed, not eliminated. Identifying these suggestive patterns is the Living Algorithm's specialty.
Living Algorithm Mathematics = the Mathematics of Relationships
In summary, the Living Algorithm's method of digesting Data Streams produces an Interactive System. This occurs in three significant ways. 1) The impact of individual data points accumulates to have a greater general impact upon the System. 2) The Measures and Data interact in a complex, interlocking fashion to produce derivative Measures. 3) The entire Living Algorithm System is based upon analyzing differences between Measures and Data. As such, each moment only exists, not as an individual entity, but in a dynamic relationship to the preceding moments. Accordingly, it seems fair to say that the Data Stream Mathematics of the Living Algorithm System could also be called the Mathematics of Relationships.
To see what other features that the Living Algorithm has in common with living systems, check out the next article in the stream Precision vs. Fungible Meaning.
To understand the nature of this ordeal, check out Can the Living Algorithm provide Life with Fungible Meaning?