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Time, partitioning, and synchronization

Any time measuring method inevitably runs into the issues of partitioning and synchronization. Partitioning deals with the issue of dividing a larger measure into smaller measures, and combining smaller measures into a larger measure. Synchronization deals with the problem of how a set of devices can self-correct if some of them are corrupted. The two are fundamentally related because often a choice in one determines a choice in the other. A measure is often defined by a set of synchronization points, such as the radioactive decay of an element or the frequency of a crystal oscillator. Synchronization points can often be defined as a measure of a change in space, such as the revolution of a planet around a star, or the change in energy state of an oscillating structure. Fundamental to both is the notion of change. A synchronization event can only be defined if there is a unit of space in which a change is observed. And either the magnitude of the space is large (such as the movement of
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Individuality, creativity, and trust

Trust is an individual experience and a personal feeling. In a sense, trust only exists as a subjective experience. Objectively, the behaviors that manifest from trust are more akin to chemical reactions, where one's feelings of certainty in regard to one event trigger another event. The source of all trust is individual perception, and if one cannot trust their own senses, they can trust nothing. Fundamentally, the observation of natural events allows the mind to create an ordering. Such an ordering is often a direct reflection of the mechanical nature of the world. A feather falls when it is dropped. A pool of water evaporates in the sun. These certainties leave an impression on the human mind, and also set an expectation for human constructions. Subconsciously, individuals expect society to operate in a manner similar to nature. Just as a feather falls when it is dropped, they expect good deeds to be rewarded and bad deeds to be punished. One only has to observe a feather fallin

Awareness, power, and morality

There are few things as intoxicating as knowing something that other people do not know. Exclusive information is perhaps the oldest and most original binding force for cults and radical organizations. Is there anything that can more tightly hold a group together than an absolute certainty of their own conviction? The interpretation of right and wrong often takes dangerous turns and dives under the light of new information. Knowing becomes an addiction for the morally sensitive because the thrill of seeing the cards turned over has left a scar on their psyche. And perhaps cults are metaphorically like a den of addicts all seeking the same high. Society is like an onion, with many layers, and with each layer watching the layers below. It is only the certainty of an exclusive information that allows the formation of a meta-awareness, the formation of a new outer layer. Power structures can only be replaced if they are comprehensively understood, and power structures often employ their in

Availability, partition tolerance, and self-organizing maps

To construct a map, there must be an expectation of the environment. The CAP theorem lays out an abstract view of how agents can interact in an environment. The common utilization of a semantic interpretation of a response is what enables a map to be built. As an example, if the expectation of a response is that the responding entity must respond if it is non-failing, then a map can be built whereby the atomic expansion of the map happens all at once or not at all. Similarly, if the expectation of a response is that the responding entity may never reply at all, then a map can be built whereby the shrinking of the map happens partially all the time. In a sense, the semantic interpretation that is used to construct the map depends on the probability of error. If the probability of error is very low, then it is a reasonable expectation that every entity must respond if it is non-failing. If the probability of error is very high, then it is not a reasonable expectation that every entity mu

Causality, Interaction, and Complexity

In a highly chaotic system, such as a high temperature gas, it is not ideal to use an atomic causal model. Instead, the effective causal model is to approximate to what extent each atom is interacting with every other atom. If we increase the temperature, then the number of atoms each atom interacts with should increase. As the temperature decreases, the number of atoms each atom interacts with should decrease. If we were to randomly sample any atom, then on average, the atom should interact with a set of atoms of a certain size. Instead of thinking in terms of conditional probabilities and causal implications, we think in terms of sets of interconnected events. And this is because it is not computationally effective to analyze chaotic systems in a linear manner. We can apply the same line of reasoning to sampling. If a system has a particular sampling rate, the inputs to the system are batched according to the sampling rate. In other words, the system cannot discern the ordering of ev

Dual network with atomic learning rates

 

Recurrence relations and calculus