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Showing posts from July, 2024

Logical operators on complex values

Traditionally, computers define logical operators on real values: AND 0 0 | 0 1 0 | 0 0 1 | 0 1 1 | 1 OR 0 0 | 0 1 0 | 1 0 1 | 1 1 1 | 1 XOR 0 0 | 0 1 0 | 1 0 1 | 1 1 1 | 0 I believe a similar construct can be made for complex values except that logical equivalency could maybe have two interpretations: either the magnitude is the core comparison value or the frequency (radian representation of the complex value in the unit circle) is the core comparison value. From a magnitude perspective, we could say that X AND Y for two complex values X and Y is itself if and only if both X and Y lie on the same circle.  In a sense, this is establishing a primitive group structure because the value of the operator depends on whether or not an item belongs in a set. Likewise, we could define an XOR operator the same way, just in the inverse, that both X and Y do not belong to the same circle. From a frequency perspective, we could say that X AND Y for two complex values X and Y is itself if and only

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

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