What if we could test the stability of very different systems without beginning with their real-world names? A forest, a company, a transport network and a digital information system may look unrelated. Yet each can be represented, at an abstract level, as nodes, connections, dependencies, capacities and points of vulnerability.
The Applied Force Model is a proposed way of exploring this possibility. Strip away the labels, retain the structural properties that matter, apply hypothetical disturbances, and observe how the network responds. The aim is not to claim a universal law in advance, but to develop a repeatable way to ask where a system is resistant, where it is vulnerable, and how local changes might spread.
1. Represent the system without its name
Begin with a network. Nodes represent entities or functional units. Connections represent relationships, dependencies or channels through which effects can travel. Nodes may have different sizes, weights, capacities and strengths; connections may differ in strength and direction. Branches, loops, hubs and clusters describe the network’s topology.
At this stage, a node need not be called a person, plant, machine or institution. Its real-world identity can be set aside while the properties relevant to the experiment are retained. This abstraction is useful only to the extent that those retained properties actually govern the behaviour being tested.
This representation builds on our Neural Network Infographic (NNIG) design concept, which encodes node importance and relationship strength through visual properties such as size, line weight, connection thickness and topology. For the underlying design principles, see AI–Human Assisted Design: A New Protocol for Infographics.
2. Nodes act like variable resistors
A key idea in this model is that each node has a resistance profile rather than one universal strength value. Resistance means the degree to which a node withstands, absorbs, redirects or remains unaffected by a particular disturbance. It depends on the type of disturbance and on the node’s current state.
Consider a weather model. A plant node may respond positively to mild rain, yet suffer when waterlogging damages its roots. A person node may experience little direct physical effect from mild rain, so for that specific test it could be represented as relatively insensitive to the disturbance—almost like a rock-like node. But the person may still be affected indirectly if rain floods a road, damages a home or disrupts food supplies.
These are functional analogies, not claims that people are literally made of rock. The model asks which properties are relevant to the selected force. A person-node could be relatively resistant to mild rain but sensitive to extreme heat; a plant-node could respond differently to both. The same node may therefore need a different response profile for each disturbance class.
3. Resistance can change
Resistance need not remain fixed. Metal may be largely unaffected by light rain, yet lose strength or deform at sufficiently high temperatures. A component that withstands pressure in its original state may fail after heat has weakened it. Some systems recover after a disturbance; others retain damage or undergo a lasting transformation.
This means that the order and history of disturbances can matter. Heat followed by pressure may produce a different outcome from pressure followed by heat. Repeated small disturbances may accumulate, while a single large disturbance may cross a threshold immediately. The model should record the node’s state after each step, not simply mark it as permanently strong or weak.
4. Apply different forces and combinations
The imagined force is a testing input. It might represent mechanical pressure, wind, heat, rain, an electrical field, a change in demand, a loss of resources or a disruption to information flow. In an abstract simulation, these need not be literal physical forces; they can be defined as disturbances with specified intensity, direction, duration and reach.
Test one disturbance at a time, then combinations. A network may tolerate each disturbance separately but fail when they occur together. A directional force may expose a weak branch that a uniform force misses. Repeated exposure may gradually reduce resistance. A failure in one node may redistribute load or disruption to neighbouring nodes, triggering further failures.
Connections also need response properties. A strong connection can preserve coordination, but it can also transmit a disturbance efficiently. A weak connection may be a vulnerability in one context and a useful point of containment in another. The effect depends on what the connection carries and on the rules governing the network.
5. Observe the network, not just the first broken node
The result of a test is more than a binary answer—stable or broken. Record which nodes change state, which connections fail, whether effects spread, how much of the network remains functional, whether the system recovers, and how sensitive the outcome is to the disturbance’s magnitude or direction.
This also requires care with terminology. Structural failure, fragility, resilience and dynamical chaos are related questions, but they are not identical. A network can fail predictably without being chaotic. A system can behave chaotically without physically breaking. The Applied Force Model can investigate these outcomes, but should not treat them as interchangeable.
6. Can results transfer to similar models?
Suppose a model reveals that a highly connected central node is a critical point of failure. Could the same insight apply to a different network with a comparable structure? Perhaps—but resemblance alone is not enough. The mapping must preserve the properties and response rules that determine how disturbances travel and how components fail or recover.
A useful research programme would group models into families with comparable topology, node-response profiles, connection rules and constraints. Tests on one model could then generate predictions for other members of the family. Those predictions would need to be checked rather than assumed. If they repeatedly transfer, the model may reveal general structural principles that are not tied to a single real-world domain.
7. The proposed “Chaos Constant”
The working name “Chaos Constant” refers to a possible quantity or compact profile that might help describe how a model responds to disturbances. It should remain a placeholder until experiments show what can be measured reliably. One number may not be enough: resistance thresholds, cascade size, recovery time and sensitivity to perturbations may need to remain separate measures.
The first task is therefore not to announce a universal constant. It is to define the experiment clearly enough that different people can run it, compare results and discover whether a smaller set of quantities captures the behaviour of many network families.
8. A practical first protocol
- Build a small network with explicitly defined nodes, connections and dependencies.
- Assign each node a response profile for the chosen disturbances, including thresholds and recovery behaviour.
- Specify each disturbance’s type, intensity, direction, duration and sequence.
- Run single-disturbance tests, then combined and repeated tests.
- Record local changes, cascading effects, total functional loss and recovery.
- Repeat with small changes to the network and test whether the outcomes remain predictable.
- Compare structurally similar models to see which findings transfer.
Conclusion: from representation to experiment
The Applied Force Model begins with a simple shift in perspective: represent a system by the properties that govern its behaviour, rather than by its name. Nodes have different and changeable resistance profiles. Connections transmit, limit or redirect effects. Disturbances can act alone, in combination or over time. The network’s response can then be observed and compared with that of structurally similar models.
This is an exploratory framework, not yet a validated general theory. Its value will depend on whether its abstractions can be defined precisely, whether experiments produce reproducible results, and whether predictions transfer beyond the model in which they were first discovered. The immediate goal is modest: build a testable model, learn from its failures, and let the evidence determine how far the idea can go.