The theory is the foundation of application. Isn’t discovering fundamental laws the biggest contribution to our time? […] The study of the deep structure of matter is the foundation of the foundations of all other sciences.
—Excerpt from The Three-Body Problem by Liu Cixin
The mat is the canvas and we are the protons. The mat unfolds as a cosmos of strategy, physicality, and intellect, reminiscent of the famed Three-Body Problem — a challenge that has perplexed scientists with its chaotic and unpredictable dynamics — the interactions between BJJ competitors unfold in complex patterns, often defying straightforward predictions. This intricacy forms the crux of our exploration, laying the foundation for Graphling, a pioneering project designed to illuminate the strategic depths of BJJ. Leveraging principles of model design, Graphling aspires to offer a solution to BJJ’s own Three-Body Problem. Through the application of system design models, it aims to transform the chaotic interplay of grips, control, and maneuvers into a navigable map of possibilities with newfound clarity and precision.
A Continuous Dance Defined by Discrete Moments
When you first encounter a BJJ match with no background in submission grappling or wrestling, you would be puzzled to see two players colliding like trucks at one time, then turn into snake noodles in a spiral the later, only to be finished in a split second: it takes nuance of ergonomics to have a good grasp of what’s going on. Due to the sports’ dynamic properties, swift movements are sometimes chained with another, and rigid control follows the other. As observers, however, we can set certain axiomatic qualities to simplify the common phases of the sport:
- Players start standing, which requires them to travel to ground (via takedowns or pulling guard).
- A control position is established with a top player and a bottom player, laced with attempts to either submit the opponent, or transition to another advantageous position that leads to more submission opportunities/risks.
- Sometimes you rinse and repeat until the match reaches the end, scored by dominance, or a player submission.
No matter how long and complex, we can frame BJJ as a blend of continuous motion between discrete decisive moments that opens the players to other opportunities. It is imperative to identify these illuminating moments that guide us in this spaghetti.
Embedded Systems Design Principles: A Guiding Framework for BJJ Modeling
Graphling proposes a two-layered translation approach. First, it aims to translate the core dynamics of BJJ — positions, transitions, techniques, and strategies — into relevant system design properties and models. Secondly, it seeks to map those system models and elements into practical software development practices for a tangible user-facing product.
The first translation layer, which we will primarily explore in this article, involves identifying system properties in BJJ dynamics through embedded system design models. Embedded systems design, which deals with creating highly efficient, reliable, and predictable systems within strict resource constraints like smart home devices and autonomous driving, offers valuable principles for modeling dynamic systems like BJJ. Once we have these linchpin elements of highly capable systems, the second layer translates the abstract into features that allow moonshot objectives like computer vision capabilities to be within reach.
This multi-layered translation approach provides a foundation to model BJJ’s intricate cosmos while paving the way for an innovative, data-driven platform. Through insights gleaned from structured models and cutting-edge visualizations, Graphling aims to empower practitioners to master the chaotic dynamics of combat within the palm of their hand.
The Discretization Problem: Breaking Down the Sport into Manageable Elements
The essence of discretization lies in converting complex, continuous phenomena into a series of discrete elements. This process is crucial for our first translation layer in defining system properties in an applicable manner from intricate dynamic flows of BJJ. By breaking down the fluid and often unpredictable sequences of BJJ into smaller, teachable components, practitioners can more effectively study, learn, and refine their techniques. For instance, a guard pass, a fundamental yet seemingly complex maneuver, can be deconstructed into three identifiable stages no matter its variation, according to BJJ Mental Models:
Disentangle: Defeat your opponent’s attempts to get dominant grips.
Control: Stabilize the position to deny your opponent movement.
Pass: Complete the actual passing technique.
Discretization offers valuable analytical insights, but preserving the fluid essence of BJJ requires a bit more attention to detail because the sport is not inherently discrete. BJJ also focuses on leverage, timing, and momentum, demanding a balance between discrete analysis and honoring its continuous, dynamic interaction which requires continuous time signals. In developing Graphling, this balance is pivotal; the system must allow for a granular breakdown of techniques without losing sight of the holistic, dynamic nature of the sport. Ensuring this balance requires a nuanced understanding of both the technical and artful aspects of the sport.
This process mirrors the methodical approach of embedded systems, where models provide predictability and control in applications requiring nuanced interaction with the physical world. By applying these principles to BJJ, the first layer of translation aims to map out the sport’s inherent chaos into an ordered system of positions, transitions, and strategies. Just as embedded systems leverage deterministic models to ensure reliability and efficiency, Graphling seeks to apply a similar methodical lens to BJJ, offering practitioners a novel way to visualize and strategize their path through the sport’s complex landscape. It is within this framework that we bridge the gap between the physical mastery of BJJ and the analytical prowess of system design, setting the stage for the subsequent translation into software development and other powerful features.
Syntax & Semantics: The Rules of Engagement
Chaos is merely order waiting to be deciphered.
— O Homem Duplicado (“The Double”) by José Saramago
Mapping the Mat: Finite State Machines
At its core, the progression of a BJJ match can be likened to a computer program or finite state machine (FSM), where each position represents a distinct state, and every transition is triggered by clearly defined techniques or actions within expectation. Here, we can introduce determinism to our framework, where we assume that the same initial conditions will always lead to the same result. Much like how a program moves between different operating states based on inputs, a guard player transitions to the mount position by executing a perfect sweep.
As a mathematical model, a deterministic FSM can be represented as a quintuple of variables consisting of (States, Inputs, Outputs, update, initialStates), where
- States is a finite set of states: the myriad of control positions encountered in BJJ (e.g. Half Guard, Side Control, Mount);
- Inputs is a set of inputs: the techniques or actions executed (e.g. sweeps, guard passes);
- Outputs is a set of output: the immediate consequences (e.g. successful guard pass to another state, submission, counter);
- updates: States × Inputs → States × Outputs is an update function, mapping a state and an input to a next state and an output (n×m indicates the Cartesian Product of n&m, which is the set of all possible pairs of n&m);
- initialStates is the initial state: the starting points for matches or drills providing the baseline for analysis and learning
For example, imagine a BJJ match as a series of decision points, much like navigating through a complex maze. Each decision (input), whether it’s attempting a sweep or defending against a pass, leads the practitioner to a new position (state). For instance, a practitioner in the ‘guard’ position (initial state) decides to attempt a ‘sweep’ (input). If successful, this action transitions them to a ‘top control’ position (output via update), altering the dynamics of the match (new state).
These deterministic models map out the potential outcomes that could unfold from any given input or initial state (BJJ position or technique). However, the adaptive nature of combat sports and the resistance from the opponent introduce an inherent level of nondeterminism, where the same initial conditions can lead to different outcomes, that must also be accounted for.
Embracing the Unpredictable: Nondeterministic FSMs
The unpredictability of an opponent’s reactions is where nondeterministic models shine. Unlike deterministic systems with unique outcomes, nondeterminism allows for multiple potential next states based on the current inputs and conditions, like One-To-Many relationships.
From the side control position, for instance, an opponent might attempt to regain guard, try to escape to a neutral posture, or even make a submission play of their own. Nondeterministic Finite State Machines can capture these branching possibilities, reflecting the true complexity of the grappling environment with a resisting opponent.
In a mathematical model, Nondeterministic FSMs is also represented by a quintuple similar to FSMs, except for its update variable (States, Inputs, Outputs, possibleUpdates, initialStates):
Flows and Jumps: Hybrid Systems & Mode Transitions
The dynamics of BJJ exist in a constant interplay between discrete decisions and continuous, fluid movement as we mentioned in the discretization problem. A Hybrid system integrates both aspects, representing the discrete transitions between positions while also modeling the continuous flow of movement and technique execution within each mode or state, i.e. a system that flows and jumps.
Consider the rear-naked choke from the back mount position. The initial transition to secure the back could be modeled step by step. But once there, the practitioner must fluidly adjust grips, shift weight, and apply pressure — continuous dynamics captured by differential equations within that choke mode, until a threshold of which discrete transition occurs: either locking in the submission or being forced to switch positions.
Divide and Conquer: Hierarchical Modeling & Composition
Even simple BJJ techniques comprise nested components. An armbar from the guard, for example, might include grip fighting to establish dominant grip while getting rid of the grip of the opponent, securing the major joints of the arm (wrist, elbow, and shoulder), and finally levering into the submission. These elements could all be represented as respective finite state machines on their own.
Hierarchical models facilitate breaking down these complex, high-level behaviors (superstate) into modular sub-components (substates) connected through well-defined relationships. This compositional approach allows systematic analysis and refinement of each individual element, enhancing overall skill acquisition.
While we’ve explored several powerful models, the true potential lies in translating these abstract models into tangible software implementations. With these core system modeling concepts explored, representing the intricate dynamics of BJJ through embedded systems design principles, we have painted the first translation layer. This lays the foundation for the second translation layer — mapping these abstract system models into product features. This will also put computer vision integration and other advanced capabilities into a closer reality. Imagine real-time match analysis that track different states, identify pivotal moments, and provide data-driven feedback.
Reading Between the Layers: From Ideas to Product
The path to mastering BJJ lies in understanding the interwoven lattices of technique, strategy, and dynamic interaction with certain compromise. By systematically translating higher dimensions into the user’s reality, Graphling charts a new frontier — one where design meets the complexity of martial arts.
This modeling process is an ongoing endeavor of learning and refinement, both on the mats honing physical skills and in the skies of expanding our systemic comprehension. With each iteration, the essence of the art becomes clearer while the insights derived from structured analysis grow sharper. Therein lies the heart of Graphling’s potential: enhancing performance through scientific principles, while preserving and celebrating the rich tradition of Brazilian Jiu-Jitsu as a holistic mind-body practice.
I couldn’t have dived into systems design in a short period of time if it wasn’t for Introduction to Embedded Systems by Edward Ashford Lee & Sanjit Arunkumar Seshia and as always BJJ Mental Models gives provides an comprehensive framework for systematically internalizing BJJ.
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