Structured Communication and Collective Cohesion Measured by Entropy by Arlin Cooper and Rush Robinett III Albuquerque, New Mexico   Page:  1 | 2 | 3 As an illustration of unique signal entropy metrics, a communication channel that carries information in bits, and has the same number of zeros and ones, has unity entropy . However, for a communication channel that carries three times as many zeros as ones (or vice versa), the communication entropy of the channel is . This maps to a trivial requirement on unique signals that the numbers of zeros and ones must be equal. Extending this concept to binary patterns requires defining a number of n-character “entities,” indexed by i, that can be single bits or groups of bits. The probability of each of these entities (which can overlap) is derived from the maximum potential probability, corresponding to matching the frequency of appearance of the entities. For example, consider the 24-bit pattern given in Equation 6: (6) The pattern has 12 0s and 12 1s, so p1 = p2 = 1/2, resulting in unit bit entropy rate. There are 6, 6, 6 and 5 transition pairs (i.e., 0 followed by 0, 0 followed by 1, 1 followed by 0, and 1 followed by 1), so there are four possible entities, and they have a bit-pair entropy metric of  Note that this also minimizes statistical dependence of one bit on the next (first-order dependence). Since there are eight transition trios (two occurrences of 00 followed by 0, three occurrences of 00 followed by 1, etc., resulting in trio counts of 2, 3, 3, 3, 3, 2, 3 and 3) in the example pattern, the bit-trio entropy metric is 0.994. This minimizes second-order dependence. The above metrics are the highest that can be achieved, which contributes to a near-optimum 24-“event” unique signal pattern. This concept can be extended to the remaining bit lengths and to non-uniform bit lengths, but there are many other considerations in choosing effective unique signal patterns [Ref. 10]2.  An interesting aspect of the relations of unique signals to interpersonal communication is that apparent communication isn’t always representative of the real thinking of one or more of the communicators. Frequently, an improved picture is obtained over a period of time by asking questions in different ways and observing responses to other verbal and non-verbal stimuli. A high-entropy pattern can be established over time that comes closer to a true picture by combining random-appearing information in the same manner that a high-entropy sequential unique signal pattern can be used to distinguish random inputs from an unambiguous “intent” input. From an interpersonal communication standpoint, this means, for example, that communication should not be one-sided (it is helpful to avoid transmission dominating reception, or vice versa), queries should not encourage unipolar responses (it is helpful to avoid multiple questions where the most “acceptable” response is always the same; e.g., “Yes”), and information should be transmitted and received in ways that appear near-random (using various approaches, such as probing for responses, observing situational responses, and adapting to the communication target, all the while maintaining the goal of random-appearing communication mode). Communication Entropy Encoding In establishing the entities for communication, a “coding” strategy must be derived in order to represent the entities most effectively. This can also be measured using entropy. Considerable work has been done on data compression as a communication entropy-enhancing encoding technique. Shannon-Fano coding (now obsolete, but an important foundation) was developed by Shannon and Robert Fano [Ref. 11]. This was essentially a top-down approach that assigned ranked (high to low) probabilities to sets of symbols. For binary coding, the set was divided into an equally probable high group and low group. The first set was assigned the first bit value (e.g., 0) and the second set was assigned the other bit value. The process then continued until all bit assignments had been made. This procedure offered an important development impetus and was useful for a while, but was provably less than optimal. In 1951, a Fano student at the Massachusetts Institute of Technology, David Huffman, developed a bottom-up technique that was provably optimal for integer numbers of encoding bits [Ref. 12]. An example of Huffman coding is shown in the appendix to this article. Huffman coding gives minimum information entropy (maximum information transfer) consistent with maximum efficiency (maximum communication entropy). The message for interpersonal communication is that the most immediately important messages should be expressed the most efficiently. Subjective Entropy Probability metrics imply objective information. For example, Shannon entropy and Huffman coding are based on the assumption that the information statistics are measurable and stationary. When use frequencies can only be estimated subjectively, modifications to the objective entropy measures are necessary [Ref. 13]. One reason for this is that probabilities are objective measures. Subjective estimates are more appropriately handled through possibilistic concepts, such as fuzzy mathematics [Ref. 14]. The most basic description of the difference between probability and possibility is that the probabilities of all possible outcomes must sum to one. Possibilistic numbers are uncertain, forcing a weaker condition: the ranges of possibilistic uncertainty can sum to less than or more than one, although the probabilistically objective outcomes within the ranges (when and if known) would precisely sum to one. Semantic Information Entropy Some communication is intended to transmit information, some to receive information, and some to exchange information. Semantics are important because the information needs to be meaningful, but indirect communication may be optimal. Subtle messages can sometimes better avoid causing hurt and can discourage the establishment of defensive barriers. Effectiveness is an issue where influence or action is desired. The time frame is a consideration, since some effects are intended to be immediate and some must be established over a long term. Latent effects (influence of previous background on current communication effects) show that information conveyed is dependent on history and context. The mode can be detached or in close proximity. The participants can be two or more peers, or can be in the “leader/follower” context. Once the actual entities of a potential communication and the likelihood of each entity have been established, semantic information entropy (henceforth simply termed “entropy”) can provide a metric that helps determine whether the information is near random (high entropy) or contains real contribution (low entropy). Entropy metrics can also be used to track trends and illuminate interpersonal response dynamics. A core of these nuances is selected for development in the remainder of this article.   "In establishing the entities for communication, a 'coding' strategy must be derived in order to represent the entities most effectively." In addition to transmitted information and communicated information, received information is important. In other words, information intended for transmission must be understood by the recipient. When one sends information that is not understood or is understood to lack meaning, the semantic content is low and the entropy metric should be high. An example of the former is words spoken in a language that is not understood by the listener. An example of the latter is a vacuous greeting such as “Hi, how are you?” From a communication entropy viewpoint, the channel is mostly wasted. However, when people communicate, the prior establishment of a common context can facilitate semantic understanding. This illustrates that there are compelling social and bonding values to preliminary exchanges, as a common basis for understanding is built. When a semantically important message is to be sent, following establishment of a common context, it should be expressed concisely so it will receive high attention and there will be no misunderstanding due to obfuscation. Examples are “Listen!” and “You’re fired!” If prior context has been established, the meaning is unlikely to be missed. Where messages are intended mostly for establishing a common social context, conventional entropy appears high when viewed in the short term. However, this type of entropy must be measured with the objective over time in mind, also recognizing that an up-front investment is made with the expectation of a long-term payoff. With these considerations, the eventual value of context-oriented exchanges can be consistent with low entropy. This is because social-entropy effort can form a basis over time for more efficient conveyance of low-entropy messages that are basic to semantic communication. For example, carefully constructed social relations in a marriage can lay a foundation for unmistakable information through something as simple as an arched eyebrow. Measuring the intent of such targeted exchanges requires a low-entropy metric. Stimulus/Response Strategies There are various forms of stimulus/response interactions. When one person questions another and listens to the answer, this is straightforward, but the information obtained may not be optimum. For example, a manager might ask an employee, “What do you really want to do in your job?” If the answer is, “Whatever you want me to do,” or “Anything,” the interchange is not particularly productive. These types of responses are likely caused by fear about how the information might be used (lack of trust). Similar to the concepts outlined in the previous section, high-social-entropy communication can be used to create a trust background for a communication stimulus for which the response has a high semantic value when associated with the stimulus. Another type of stimulus/response is to observe the response to an external stimulus. A situation might force a response from an individual that is more informative than a question might be. For example, one person might ask another, “Do you trust me?” and receive “yes” as an answer. Alternatively, the respondent might be discovered trying to hide information from the questioner, which would display a lack of trust. In the latter case, the stimulus might have been inadvertent, but the action can be more informative and honest than the response of “yes.” This is an illustration of “actions speak louder than words.” Latent Effects Entropy Relations The actual interpersonal communication experience is generally a combination of the previously discussed modes. Combining these in a way amenable to quantitative analysis requires use of a modeling decomposition. A latent-effects decomposition [Ref. 15] is of particular interest because it demonstrates a cascading series of effects. An example is shown in Figure 2 below. This is a simplified structure with a single feedback path and no time dynamics, but it illustrates some important points. Working from lower left to upper right, the first module represents groundwork for a long-term relationship, establishing a common context and building trust. The second module represents information gathered that helps create a background portrait. The third module represents information and guidance that are to be conveyed. The fourth module represents imperatives of importance to be unambiguously given, where there are latent-effects influences from the three earlier modules. The feedback path accounts for learning, adaptation and strategy changes. Figure 2 — Example Latent-Effects Entropy Structure. There are primary inputs to each module, and secondary inputs from one module to the next. In the Figure 2 example, there are 4 modules shown, with 13 primary inputs and 4 secondary inputs (y1 used twice). Not shown are mirror-image negative inputs corresponding to each of the inputs in Figure 2. This is necessary to establish a computational balance. The inputs are denoted as ei. The primary input values (range [0, 1]) represent effectiveness for the specific information entity used. The primary inputs are proportional to enhanced communication. Values for all inputs can have uncertainty (e.g., possibilistic). Module outputs (the y1) represent the entropy-related result of the process indicated by each module. It is desirable for both these outputs and the secondary inputs to represent the module contribution to the interpersonal communication process, with higher values representing greater contribution. Since this is the additive inverse sense of the entropy (greater entropy is less valuable), the conversion from inputs to outputs requires intermediate representations for the possibilistic entities. The first intermediate step is to derive quality-related entities that are analogous to probabilities, but which are possibilistic. We term these entities “qualitivities” here. These must sum to one for an entropy-related calculation, just as the probabilities in objective entropy sum to one. Since there are 2n inputs (including the mirror-image inputs), the maximum-entropy value for each would be 1/2n. This corresponds to an entropy metric of one. Increasing effectiveness of communication reduces entropy by forcing the inputs away from the equally likely value, while assuring that they still sum to one. We choose to let positive input eis increase the numerator of the qualitivity linearly from 1 toward n. The mirror-image balancing negative inputs decreases the numerator of the qualitivity linearly from 1 toward zero. In order to assure that the sum of the qualitivities (which are analogous to uncertain possibilities) must be one, and in order to associate outputs with the quality of communication, there are two basic steps (Equations 7 and 8). The first step accounts for deviations (positive or negative) from equi-possible reference points. The structure in Equation 7 ensures that the sum will be one. Calculations for the example will use an interval limit of the possibilistic functions, meaning that only a lower and upper bound will be indicated, although the extension to more general possibilistic functions is straightforward [Ref. 14]. ____________________ 2 Higher-order unique signal independence is maximized using non-entropy metrics for reasons given in Ref. 9.   « PREVIOUS PAGE     NEXT PAGE »