"Theater" is the English term for a place where actions are represented when used for communication purposes, initially religious, as in the Festival of Dionysus, where the notion of theater was formalized in Greece, and psychological (catharsis). In modern warfare, theater is used to describe the area of operations in which force can be applied. In all cases, theaters are communal in that they require at minimum at least two participants, an actor and an observer in the most reduced case. The key distinction of theater in warfare can involve physical outcomes, actor/observers may be in conflict, and observers acted upon may have no capability to themselves take actions with meaninfdul physical outcomes. In performance art the observer is acted on only psychologically, with the goal of producing a chemical (emotional or instinctial) response to influence behavior (which in most cases is to assure future ticket sales;) Showbiz!

Deep analysis of the nature and use of Modern Martial Arts requires n-dimensional thinking through the filter of Claude Shannon and a generalized theory of information.

The simplest way to understand this is from the standpoint of preseration of the arts: how to failthfully transmit a signal through all the noise.

Observing dozens or hundreds of distinct styles within a family of systems, such as the various branches of Chinese boxing, one will notice various movements appearing consistently in more instances.

Repetition of a symbol is the fundamental insight that launches the field of Information Theory. They needed to be able to ensure our instructions to our satellites could be read through interference.

A second example arises from a General Theory of Games, rooted in Dilemma Problems, where participants communicate via actions only, in a binary mode of "cooperate or defect"

We see this fundamental decision problem as the basis for everything from nuclear detante to hand-to-hand-combat.

A third communicative element is the performative aspect. We can trace sword dances with resonable confidence via records to the Han Dynasty. Martial performance has been an element of Chinese martial art throughout recorded history, and therefore provides what is likely the most robust body of work for analysis.

This type of communication arises in sparring in the form of "tit for tat", bringing similar force back on an opponent that then bring at you. Players can escalate or de-escalate. The power of a punch is a form of signal between contenders.

Discussing the subject of Modern Martial Arts in a formal way will require a formal taxonomy and definition of terms. Because natural language can be imprecise, formal statements may be attempted from time to time. Application of martial arts, from mechanics to strategy, is grounded in the mathematics of physics and game theory, luckily the basic math is very very simple. As an example, even children can understand Shannon's concept of repeating a symbol (letter, number, etc.) to that if parts of the message are lost in transmission, the meaning of the message can be faithfully reconstructed by the redundancy.

We all have to be engineers, phycisists, mathematicians, historians, mythographers, scholars, and ideally artist and true philosophers.

Bow Sim Mark described strong martial choreography as a function of "sentences" and "phrases". An individual movement is a "word", a sequence of letters or brushstrokes that produce a recognizable symbol, and an entire routine may be but a paragraph in a larger narrative. This kind of thinking was shared by the influential film choreographer Yuen Woo-ping, who gained iniaial popularity due not just to the clarity of his jung fu fight sequences, but the clear narrative contained within these sequences.

Meaning is conferred upon symbols in natural languages through an informal process of consensus driven by use. In formal languages such as arithimetic, logic and computer code, which is all ultimated rooted in irreducible functions used to define higher-level aggregate functions or outcomes (values) which have concrete meaning in their defined, formal systems.

In formal systems, chains of functions can be represented with a single symbol, as in use of Greek and other non-numeric representations in human-readble mathematics. In automated processes such as electronic computation, chains of functions can be represented with a single symbol that connotes a numeric address, and "called", which then allows the program to utilize ("run") that aggregate function.

All formal systems can be thought of as **"mechanics"** in the sense of Euler, especially post-theory of computation. Algorithms are algoritms.

In this way a word, sentence, paragraph or narrative can be a symbol, and even represented with more compact sybols such as "titles", used for quick reference.

Dance and martial arts have a distinction in representational systems in that, although rooted in the natural world, the functions represented are physical movements that have observable and tangible outcomes. In computation, where even a numeric result requires a specific application of electric charge and storage and representation of that result in electric, magnetic form or mechanical form. in dance and martial art, the results are physical and must be consistent.

See Godel's Incompleteness Theorem which proves even formal systems can either be complete or consistent but never both. Choreography is an example of an informal system that requires consistency, and ideally, is "complete" in regard to capability in all relevant domains of application. We might term such systems "quasi-formal". Such a systems can never be wholly complete or consistent, but the results can be measures and studied as in any form of clinical science.

Choreographic routines have practical, physical outcomes. This can be as simple as when a dancer leaps, and has to utilize a natural analysis of physics in order to land in the correct location and posture, even were a dancer may have no formal math. In both dance and martial arts the outcomes can also be goals such as physical conditioning, strengthening specific muscle and tendon groups and building muscle memory, or application of force in conjunction with another body.

Note that even where we create an algebraic stucture to utilize numeric values, those numeric values are the products of logical functions.

Two-person choreographic sequences are algorithmic processes based on a chain of input and response (output). Category theory would likely be sufficient for formal definitions and statements within the finite set of practical physical sequences that comprise any given system of martial art, which is more bounded than dance due to it's fundamentally partisan structure. "Partisan" is here used in the sense of Game Theories, indicating adversariality, even where the adversiality is simulated, as with Judo and Tai Chi "players" in free communication of a sporting match and in choreography with the partner.

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2023.7.20

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