Glossary A>F: definitions, descriptions and links of the diverse variety of terms employed throughout the multiple articles devoted to Behavioral Dynamics.
active pulse
The Active Pulse is the name that we have given to the first and last pulse of the Triple Pulse. The Active Pulse is the result when the Directional (one of the members of the Cell Equation's Family of Equations) digests a data stream consisting of an uninterrupted string of 120 ones. The graph below is a visualization of the Triple Pulse, which contains both the Active Pulse and the Rest Pulse. Experimentation combined with analysis has associated the Active Pulse with a creative session, consciousness, and attention.
algorithm
"In mathematics and computer science, an algorithm is an effective method expressed as a finite list for calculating a function. … In simple words, an algorithm is a step-by-step procedure for calculations. … Giving a formal definition of algorithm, corresponding to the intuitive notion, remains a challenging problem." (Wikipedia) The 'step-by-step procedures' we learn in elementary school to add, subtract, multiply, and divide large numbers are common examples of some simple algorithms.
The 'intuitive notion' of algorithm that we employ in our discussion of the Cell Equation has to do with a 'step-by-step procedure' for determining an answer. In mathematics and computer science this answer must be precise and unique - right or wrong. This includes the algorithm for determining the mathematical value of the Cell Equation. However, when the Cell Equation's algorithm is applied by living systems to make reasonable predictions the answer is necessarily fungible – close enough for practical purpose is acceptable. (For more details check out the article The Cell Equation Algorithm bridges Precise Math & Fungible Life.)
attention
The ability of more complex forms of life to focus awareness upon the world external to themselves - as opposed to simpler life forms whose response is entirely instinctual. Behavioral Dynamics claims that the mathematical model referred to as the Creative Pulse reveals the mechanisms of Sustained (conscious) Attention.
behavioral dynamics
A proto science devoted to the study of the dynamics of behavior from a mathematical perspective. Although intersecting with the orthogonal planes of physics, chemistry, biology, and psychology, it's theories are based solely upon the mathematics of the Cell Equation, sometimes referred to as fractal regeneration. This branch of the Mathematics of Behavior encompasses the Creative Pulse and Data Stream Momentum Projects.
The Individual Cell Equation
The General Cell Equation
The individual Cell Equation computes the Decaying Average (shown above right). The general Cell Equation (shown below right) is the foundation of the mathematics of Behavioral Dynamics (BD). (This general form is also referred to as the Cell Function).
The mathematics of the Cell Equation has many features in common with living systems. 1) Past Awareness. Both Life and the Cell Equation are self-referential feedback systems. Living systems have an awareness (whether conscious or not) of the past experience of the organism and the capacity for behavior that reflects that awareness. 2) Context Awareness. They are both sensitive to the present situation – a context sensitivity that incorporates the power to monitor and adjust. 3) Regenerative. They both require ongoing data input to sustain the momentum of a pattern, as the potential impact of the data on the ongoing average decays over time. 4) Composite Memory. They both, store memory as a synthesis of overlaying images, rather than exact replicas of events. 5) Fungible. They both must transform the precise details of data into averages in order to reveal patterns. 6) Recency Effect. While the potential impact of each data point decays over time, the most recent data points in the stream have the greatest potential impact on the Cell Equation’s ongoing averages. Similarly, the most recent events have the greatest potential impact on an organism’s current perceptions. Because both systems share these 6 characteristics, we argue that the Cell Equation is a powerful model of living systems.
The union of the Cell Equation and a Data Stream also produces a Family of Averages (see below) that act as powerful predictors. Finally the Cell Equation is the ultimate in elegant and computational simplicity. Nothing more than basic arithmetic skills are required (note equation at the right). Due to these three features (similarity with living systems, powerful predictors, and simplicity) we argue that the Cell Equation is one of Life's primary algorithms – a computational recipe for processing data. In fact, this is a fundamental assumption of Behavioral Dynamics. (Check out the article Cell Equation for more details.)
cell equation family/ predictive cloud
The union of the Cell Equation and a Data Stream produces a family of ongoing averages (central measures) that characterize ongoing moments. Their relationships are shown below. As well as characterizing individual moments, these averages are powerful predictors, as well. These predictors provide crucial information about the next data point in the stream: 1) the most probable location, 2) the probable range of variation (like the standard deviation), and 3) the probable direction of the momentum (the recent tendencies). These 3 predictors generate a composite measure. We call this composite measure a predictive cloud due to its ongoing and evolving nature. Check out the Cell Equation Family for more information.
conscious, unconscouis, subconscious
These words have a simple meanings in the Cell Equation context. When an organism is conscious, it takes in information. When an organism is unconscious, it does not take in information. The organism's subconscious digests and organizes information. This process can happen or not during both the state of consciousness and unconsciousness.
creative pulse
The Creative Pulse is the name of a computer generated mathematical model based upon the one of the equations of the Cell Equation. The purpose of the Cell Equation’s Family of equations is to digest data streams. This classic image to the right represents the momentum of a data stream that contains 120 consecutive '1's. As the momentum of the uninterrupted data stream grows, the pulse rises to its maximum peak, gradually diminishes, and then ultimately zeros out. This model was chosen to represent an uninterrupted creative session - hence its name.
We remind the Reader that the pulse at right is the ideal representation of the Creative Pulse. It is produced by digesting a data stream consisting of an uninterrupted series of 120 1’s. The Experimenter sensed, from his own experience, that interruptions to his creative sessions seemed to have a disproportionate negative impact. We deem this the Interuption Phenomenon. To simulate interruptions to a creative session, he altered the ideal data stream by introducing interruptions in the form of 0s at a variety of locations along the stream. We called this series of manipulations the Creative Pulse Experiment. It turns out that this mathematical model reveals that interruptions to the data stream do have a disproportionate, negative effect upon the ideal dimensions of the Creative Pulse. The findings of these experiments are located in the Creative Pulse Notebook. The excellent fit between mathematics and experience inspired him to further explore the model. The Triple Pulse Experiments were one result of this exploration.
Other articles concerning the Creative Pulse include: Applications, Elements, and Creative Pulse Review.
creative pulse program
This Excel-driven, computer-generated program ties the 3 Creative Pulse 'experiments' together in a package. Each computer experiment employs this program to generate the all-important graphs. It is based upon the Directional's branch of the Cell Equation's Family. Below is the history of the program.
Discovery and Extensions
In our Data Stream Momentum phase we derived some central measures for a living data stream. Although related to standard deviations, they decayed as they were replenished. We called one of them a Decaying Deviation, or simply Deviation. We employed this measure in our discussions of Data Stream Momentum and the Boredom Principle. We called the other central measure a Directional. At the time of the discovery it was more of a curiosity – with no theoretical implications or practical applications.
Eight years later in 2002, in our quest to find a mathematical model that mimicked the Interruptions of a Creative Session, we created a computer program based upon the Deviation. This was ultimately unsuccessful due to the Deviation being a scalar, a sheer magnitude. Tweaked the program a little – basing it instead upon the Directional, a vector with a direction, hence the name. Plugged in the data – just a stream of ones – and, much to our surprise, out came the Creative Pulse. This turned out to be a great mathematical model for the Interruption Phenomenon. At the time we explored the extensions of the model – actually performing the Triple Pulse experiment, but didn’t really understand the implications of our discoveries. Eight years later in 2010 we employed the exact same program to investigate the insight he had concerning Quantized Behavior. Now it is nearly a year later and we are just beginning to write up the discoveries in intelligible form.
creative pulse project
A series of computer experients surrounding the Creative Pulse graph (above) and her manipulations. The Creative Pulse Project has 3 branches: 1) the Creative Pulse ‘experiments’, which explored the impact of interruptions on the creative process, 2) the Triple Pulse ‘experiments’, which investigate the impact of sleep interruptions on the following day, and 3) the Quantized Behavior ‘experiments’, which examine the potentials and dangers of behavioral overdrive. The Creative Pulse Project is one of the 4 main branches of the Mathematics of Behavior (which includes Behavioral Dynamics). Two elements bind the 3 experiments together as a project. The same Excel-run computer program is employed throughout. And the Creative Pulse Graph is employed as the ideal standard of comparison for the other graphs generated by the program. For a more detailed description, check out the article on the Creative Pulse Project.
data set & data stream
A Data Set consists of a static number of clearly defined data points. Data Sets are the substance of the mathematics of Probability. Probability utilizes fixed and invariable central measures, such as mean average and standard deviation, to characterize data sets. In contrast a Data Stream is a growing set of ordered Data points. This distinguishes it from a Data Set, with its static set of Data points. In order to process a data stream Probability must treat it as a fixed data set.
Only the Cell Equation treats the data stream, not as a fixed set, but as a living set. The Cell Equation does so by articulating a Decaying Average – a weighted, temporal relationship between points, which is constantly subject to change. For a more thorough discussion check out Data Stream Momentum Notebook.
data stream momentum
Data stream momentum is a mathematical method for determining the momentum of a flow of information and the attendant inertia to changes in that data stream. In other words, the method examines the pattern of energy in a series of moments as a way of analyzing the strength of a habit. As such, it is a way of quantifying the energy or strength of habits. Data Stream Momentum is also the name of an entire notebook devoted to the mathematical development of the concept. Because of the presumed importance of this notion, a collection of notebooks from the Author's creative obsession of 1994 was given this same title.
decaying average
The Decaying Average is a context-based central measure of a data stream, as contrasted with the content-based central measure of a data set. A data stream is alive in that it is characterized by an ongoing flow of information, while a data set is static in that it is definitive and unchanging. While a data set produces a mean average, a data stream produces an ongoing average. This averaging of the ongoing flow of information weights the most recent data points more heavily, while proportionately diminishing the weight of past data points. We call this measure the Decaying Average.
The Cell Equation generates the Decaying Average. This equation is shown above right. It utilizes the Xs with subscripts (XN) and bars (
) to identify the Decaying Average. Subscripts indicate the Decaying Average's place in the data stream and the bar indicates that she is an average rather than an individual data point. We’ve characterized the Decaying Average as the Mother in the Cell Equation’s family of equations. Her offspring equations, also ongoing averages, determine the range and relative direction of the data stream.
The algorithm for computing the Decaying Average is a simple procedure.
- 1) Determine the difference between the most recent data point and the existing Decaying Average.
- 2) Scale this difference proportionately.
- 3) Add or subtract the scaled difference to the existing decaying average. We add if the data point is larger than the existing Decaying Average; and we subtract if the data point is smaller than the Decaying Average.
This simple procedure turns the existing Decaying Average into the previous Decaying Average and, in so doing, produces the next Decaying Average in the data stream. This process continues with the input of each new data point, relegating each Decaying Average into a proportional part of the past Decaying Average. Check out the Decaying Average Notebook for more details, including basic applications and fundamental rationale.
directional
A measure of directed information acceleration. She is the daughter of the decaying average. They are both manifestations of the Cell Equation. She and her descendents are the core measures behind the Creative Pulse Project. Her transformations include the Creative Pulse and the Triple Pulse. When positive in this context, experiments have suggested that she is associated with the ability to think, consciousness, and attention. When negative, she is associated with unconsciousness, not thinking, and non-attention. It has further been postulated that attention is irresistably drawn to her as an acceleration, and that their union generates a child which is the Creative Pulse. Her children are the Liminals.
discovery
In the context of this paper the word 'discovery' means something new to oneself, as in the 'discovery' of a new restaurant, a new hiking spot, or ‘discovering’ something new about oneself.
Doctor Flow
We're applying this apropos nickname to Dr. Mihaly Csikszentmihalyi. This esteemed man spent his entire career investigating the human phenomenon that he deemed Flow - even writing a national bestseller of the same name. Flow is an important process that humans must participate in to have those 'optimal experiences' that make life worth living. Other researchers have shown that these optimal experiences are part of a complex process-called 'intrinsic motivation'. According to the theory, this is a basic need that must be fulfilled for a human to be happy, productive, and motivated. The Flow process is related to, if not the same as, the Creative Pulse. Although we know the doctor's name is pronounced 'chick-sent-me-high', this is impossible to discern from the letters, which are even more difficult to spell. Hence the accessible and descriptive nickname.
dumb kid syndrome
In a scientific sexperiment students were first asked to evaluate their writing skills. They then graded each others papers. In the final stage of the experiment they evaluated their skills again. In general grading the papers helped correct everyone's self perception. For instance: although the smart kids initially undervalued their skills, they raised their self evaluation after grading the papers of others. However a certain subset of the dumb kids continued to over value their skills despite being shown papers of obviously superior quality. This is the Dumb Kid Syndrome: to overestimate one's skills despite being shown evidence to the contrary. This is a particularly difficult illusion to surmount as the individual or group isn't perceptive or smart enough to evaluate the contrary information properly. This syndrome applies to anyone who continues to maintain a theory, belief or self perception despite being shown or experiencing copious amounts of evidence that contradicts their stance.
elegant simplicity
A feature of good science. If constructs are too messy or complicated
scientists continue to search for simplicities. Because of frequent validations over the centures it
is believed that this a feature of natural systems. Copernicus rejected Ptolemy's
geocentric model of planetary motion because it lacked simplicity. For more on this
topic check out Copernicus and Elegant Simplicity.
evo-emergence
Nearly everyone agrees that evolution occurs regularly on the micro-level. However there are big problems on the macro-level. This is the area most often attacked by those who don't believe in gradual evolution. How did the elements of the earth gradually evolve from matter to life, from no senses to the sense of smell, from one sex to two sexes, etcetra. Some scientists have suggested that two complimentary processes are occuring instead of one - the other being emergence. Emergence is when something has properties that are not contained in its component parts. Molecules generally have emergent properties that are not predictable from the atoms that make them up. This is why chemists are forever experimenting to discover new and useful features of unusual molecular compoounds. Two hydrogen and one oxygen atom do not predict the features of water. The increasing complexity of matter yields emergent forms. Of course emergence has an unpredictable, almost divine, component that many scientists resist. To sidestep these thorny issues we will refer to macro and micro evolution together, as evo-emergence. Whether pure evolution, mathematical emergence due to increasing complexity, or divine intervention, doesn't really matter. The process is the same.
fractal regeneration
A system of mathematics based upon self referential (iterative) equations which simultaneously decay and are replenished - just like any living system. The Cell Equation is the foundation of the system. Due to its systematic self referential nature the system's structure is fractal in nature - hence the name. Its features are very different from the decay of inanimate objects - which aren't replenished (with glaciers a notable exception to this rule.) Fractal regeneration is the mathematical structure that supplies the theoretical foundation for the science of Behavioral Dynamics.
fractal scientist
A real scientist is professional. Not just an amateur, a fractal scientist is an individual who theorizes and does research completely outside the framework of the Scientific Establishment. The results of a fractal scientist don't become real until ratified by real scientists. However a fractal scientist might create a proto science.
fungible
Fungible is a legal term that allows for an acceptable range of imprecision in the application of law. For instance, a baker is not found criminally liable if his loaf of bread is not exactly the same weight as advertised. The term recognizes that perfect accuracy of prediction is impractical, if not impossible. In this same sense, we suggest that fungible is a term that aptly applies to all living systems.
Living systems require a certain tolerance for imprecision (ambiguity) in both interpreting and responding to the constant flow of information. In order to recognize patterns, organisms must frequently overlook precise details in order to make rough (read practical) comparisons. ‘One can’t see the forest for the trees’ is a common metaphorical expression that recognizes how precise details can obscure patterns. It seems that living systems must have some mechanism whereby they can overlook extraneous details of sensory input to focus upon pattern. This mechanism gives precise details a fungible (approximate) meaning.
Consciousness requires the raw data of sensory input. However, this data is only useful if it has meaning. Some mechanism must process the raw data for it to make sense to the organism. The ongoing processing of information is an ongoing way of making sense of sensory experience. The Cell Equation’s method of information processing transforms the precise details of sensory data into ongoing averages. These ongoing averages provide some rough (fungible) approximations as to the location, range and tendency of any flow of information. Even though these averages are just rough approximations, they provide the basis for the tentative working hypotheses that organisms require for survival. And because we’re moving through time, these approximations are moving through time as well. Accordingly the Cell Equation’s method of averaging creates an ongoing relationship between data points. In creating this ongoing relationship, patterns are revealed. These patterns provide essential meaning to the organism. Due to the inherent imprecision of the process these patterns have a fungible characteristic that living systems require. (For clarification of these points check out the article: Cell Equation's Fungible Meaning vs. Hard Science's Precision.)
The Rest Left to Avoid Tedious Linkage Changes
maven
A Jewish word for someone who is impelled to assist others by pointing out good monetary deals on goods and services due to extensive information gathering. In The Tipping Point by Malcolm Gladwell he uses the word to indicate a personality type that is essential to the spreading of social trends. They are characterized as those who want to help others out by disseminating useful information that they have accumulated with no reward in mind.
orthogonal
A mathematical term referring to perpendicular dimensions. These dimensions only intersect and interact along a single line - an infinitesimal amount of their entire surface area. Similarly physics and psychology only interact to influence behavior within a limited zone. Otherwise they are independent of each other - with their own laws and principles. This notion of orthogonal planes is why the science of physics will never be able to determine the behavior of of any living organism. It is also the reason that Behavioral Dynamics is independent of the physical and psychological realms, while simultaneously interacting with these other disciplines.
proto science
A logical system of thought which has no rigorous empirical evidence to back it up. It is waiting for testing to validate the theories. This is different from a pseudo science, which has been tested repeatedly with no conclusive results. As Behavioral Dynamics has not been tested rigorously by real scientists it is still a proto science. After testing it becomes either a pseudo or a real science.
pseudo science
A logical system of thought which has no rigorous empirical evidence to back it up. For instance astrology is based upon an elaborate system of correspondences between time of birth, personality, planetary interactions, and earthly events. Although an uncountable number of books have been written over millenia regarding these connections it is not considered a science because no experiements executed with repeatable scientific rigor have verified the validity of any of these correspondences. This does not disprove astrology, just leaves it in the realm of a pseudo science. Similary until Newton's laws were verified through observation his was but a pseudo science. This holds true for Behavioral Dynamics as well. Until repeatable experiments can be performed which validate specific theories, the logical structure of correspondences remains a proto or pseudo science.
sustained attention
The ability of complex forms of life to focus consciousness upon a certain topic of interest for an extended length of time. A predator focusing consciousness upon prey to obtain food – the male focusing upon the female of the species for reproductive purposes – the artist focusing upon a painting to produce beauty - or even a mob focusing upon a perceived injustice to wreak revenge – are all examples of this type. Behavioral Dynamics claims that the Creative Pulse reveals the mechanisms of Sustained Attention.
syllogism
"the logical form of an argument consisting of three statements, two premises and a conclusion. The conclusion of a valid syllogism follows logically from the premises and is true if the premises are true." (Desk Encyclopedia)
In the classic writings of Aristotle and his followers, the syllogism was more specifically defined as being of 3 types: categorical, hypothetical, and disjunctive. However Aristotle gave this meta-definition of a syllogism. "A syllogism is a discourse in which, certain things being posited, something else follows from them by necessity." This is the essence of deductive reasoning. Although we will attempt to stick to the two premise form, sometimes we will use the word syllogism to refer to a deductive argument of any length.