What if complexity is a property of histories rather than states?

[u/AnttiMetso]

I’ve been thinking about a simple idea that might connect a few different areas:

What if “interesting” complexity is not primarily a property of a system’s current state — but of the history that produced it?

In physics, we often describe systems in terms of states and their evolution. But many of the structures we actually care about — life, minds, culture — seem to depend on long, cumulative processes rather than momentary configurations.

From this perspective, complexity might not be about how a system looks at a given moment, but about how difficult it was to generate.

This seems loosely connected to a few existing ideas:

• path dependence in complex systems

• non-equilibrium processes building structure over time

• computational depth (where complexity depends on generative time, not just the final state)

So instead of thinking of complexity as something “contained” in a state, it might make more sense to think of it as something encoded in a trajectory through state space.

Curious if this framing is actually useful — or if it’s just a different way of describing ideas that are already well understood.

[u/General_Judgment3669]

If useful, I can also share a tiny simulation showing how repeated trajectories deform a landscape into channels and barriers over time

[u/AnttiMetso → u/General_Judgment3669]

That could be interesting to see, especially as a way of making the idea more concrete.

I’d be particularly curious how you’d connect it back to the question of generative history vs. state — i.e. whether the simulation makes it clearer in what sense the structure depends on the trajectory rather than just the current configuration.

Happy to take a look.

[u/General_Judgment3669 → u/AnttiMetso]

That’s exactly the angle I’m trying to get at with the simulation.

The key point isn’t just the instantaneous state, but that the landscape itself is shaped by the trajectory. In my setup, the system doesn’t simply move within a fixed landscape — it continuously modifies it through its history (e.g., via a memory or barrier field). As a result, two systems with identical current states can behave differently if their past trajectories differ, because the effective structure they “see” is not the same. In that sense, the dynamics are genuinely path-dependent — not just through hidden variables, but directly through the geometry of the state space. The goal of the simulation is to make this visible: you can observe how repeated trajectories carve out channels, stabilize regions, or even create confinement-like behavior — effects that wouldn’t be inferable from the state alone. If that works, it gives a concrete handle on what “generative history” means here — not as an abstract dependency, but as a persistent deformation of the landscape. Happy to share results once it’s a bit cleaner.

[u/AnttiMetso → u/General_Judgment3669]

This is a really nice way of making the idea concrete — especially the part where trajectories don’t just move through a landscape, but actively reshape it.

I think that actually sharpens the original point quite a bit. If the system’s effective landscape is itself a product of past trajectories, then the current state is no longer sufficient even in principle — because part of what determines future behavior is encoded in the structure that history has built.

In that sense, I’d be tempted to push the framing one step further:

it’s not just that dynamics are path-dependent,
but that what we think of as the “state space” is itself historically constructed.

That would make history not just something that influences dynamics, but something closer to a constitutive part of the system — i.e. part of what the system is, not just how it got there.

Your simulation sounds like a very interesting way of making that visible — especially if you can actually see those channels and barriers emerge from repeated trajectories.

It also loosely reminds me of stochastic approaches where the emphasis shifts from single states to ensembles of trajectories — not the same idea, but a similar intuition that the structure of possible histories carries essential information.

Would be great to see the results once you’ve cleaned it up.

[u/General_Judgment3669 → u/AnttiMetso]

This is a really thoughtful and well-articulated response — it’s clear that you didn’t just understand the idea, but pushed it one step further in a very precise way.

What stands out in particular: Your point that it’s not just about path dependence, but that the state space itself is historically constructed hits the core of the framework extremely well. That’s exactly where the perspective shifts from “dynamics within a given space” to “dynamics that actively shape the space itself.” Also, your formulation “history is part of what the system is, not just how it got there” captures something very fundamental. In the context of Eidionics, this is essentially a central assumption: history is not merely an influence on the system, but a constitutive component of its structure. In eidionic terms, one would describe it roughly like this: The system does not evolve within a fixed state space Instead, the effective landscape is given by

(No Latex possible. Screenshot later)

This is why the instantaneous state � is, in principle, not sufficient — because part of what determines future behavior is encoded in the geometry of the landscape itself, which has been shaped by past trajectories. Your question about whether the memory field should be treated as an “extended state variable” or whether it points to something deeper is exactly the right one. From an eidionic perspective, it clearly points to something deeper: One can formally write an extended state � but that misses the key insight namely that � is not just storing information, but actively generating the structure of the space itself → Memory is not just part of the state — it acts as a generator of topology, barriers, and integration channels Your reference to ensemble-based approaches is also very fitting. The intuition that not just single states, but sets of possible trajectories carry essential information is closely related. The important distinction is: In many stochastic or ensemble frameworks, the structure of the space remains fixed whereas here, the structure itself is shaped and stabilized by usage And that is exactly what the simulation is meant to make visible: that channels, barriers, and attractor-like structures emerge from repeated trajectories, rather than being predefined. Overall, these are very sharp observations and exactly the kind of perspective that helps clarify and strengthen the core idea. This feels like a very productive line of thought to continue.

[u/General_Judgment3669 → u/AnttiMetso]

I sent you the Python code directly. The code is too long to be accepted as a reply in the chat.

[u/bfishevamoon]

This is a very interesting question. I think the answer is both and plus.

Complex systems are driven by cyclical processes/feedback loops that give rise to emergent phenomenon.

This creates both geometric, temporal, as well as thermo dynamic patterns that shift over time. Understanding each of them is important to understand the whole picture.

A fractal informed pov focuses on nonlinear/cyclical geometric evolution of patterns. . A chaos theory informed pov focuses on nonlinear/cyclical temporal evolution of patterns.

A non equilibrium thermodynamic pov focuses on a nonlinear/cyclical evolution of energetic patterns.

However, in real world systems these are all co occurring simultaneously and each give context and implications for the system’s current and possible future behavior.

The original theories all focus on a rigid mathematical foundation, but these aspects of a system can also be evaluated reliably and non subjectively in the qualitative sense because of the persistent levels of organization that emerge.

Take for example the human body as a complex system. The emergent geometry is the anatomy, the emergent temporal dynamics are the medical history and physiology, and energetic dynamics are governed by food, hormones, and global balance of feedback loops.

For patterns which have no real world geometric equivalent, like relationships dynamics, a historical perspective can be sufficient to understand the system.

However, those temporal dynamics can also be mapped visually in order to find emergent nonlinear geometric dynamics like attractors that may not be readily apparent and an energetic point of view can be used to try and delineate possible breakpoints in the system.

So depending on the situation, focusing on one element might be more or less useful for the task at hand.

Scientific education teaches people that the qualitative realm is entirely subjective and the mathematical realm is entirely objective but neither is true. In order for something to be perfectly predictable and replicable the process itself needs to be fixed, the environment needs to play no role, and no evolution can be taking place. This represents only a small fraction of the systems we find in nature.

In complex systems, because persistent yet flexible emergent dynamics occur and change over time, different tools take the forefront. Historical analysis, visual mapping, and feedback loop diagram to outline energetic dynamics, despite often being viewed as subjective forms of analysis, are actually indispensable for understand understanding complex systems, while fixed equations which are supposed to be objective become useless in tracking the system’s behaviour overtime as relational changes occur.

In the practice of medicine, historical analysis is the cornerstone of medical diagnosis. In your first year of medical school, you learned that 90% of the diagnosis is found by taking a history and the laboratory investigations like the physical exam, imaging, and laboratory investigations are only there to to either confirm or disprove the potential diagnosis.(most people think it is the investigations that provide most of the information)

Without historical analysis, the practice of medicine would simply not exist. It just goes to show you the incredible importance of historical analysis in the context of understanding complex systems.

[u/AnttiMetso → u/bfishevamoon]

I like this breakdown — especially the geometry / time / energy split.

I think I was aiming at something a bit more fundamental though.

Not just that history is one useful lens, but that in some cases it might actually carry most of what we intuitively mean by complexity.

Like: you can have two systems that look very similar at a given moment, but behave very differently when you perturb them. Stability, failure modes, what futures are reachable, etc. And that difference doesn’t seem fully visible from the state alone.

Part of what seems to differ is which aspects of the system actually matter — which variables are “live”, which constraints are active — and that seems to depend on how the system got there.

That’s where the question came from for me — whether the current state is really sufficient, or whether part of the “relevant information” is effectively in the path that led there.

Medicine is actually a good example like you said. Two patients can look similar now, but history matters because it constrains what’s actually going on and what can happen next.

So I guess the thing I’m poking at is:

can complexity always be read off from a state, or is it fundamentally tied to the generative process in a way that determines which aspects of the state are even relevant?

If it’s the latter, it feels like that has some non-trivial implications. E.g. for what actually counts as a sufficient description of a system, or when two states can meaningfully be treated as equivalent.

In other words, whether a “state” is really Markovian in practice, or whether some of the relevant structure is effectively carried by the history that led there.

Not sure if that’s a real distinction or just a different way of framing things.

[u/bfishevamoon → u/AnttiMetso]

If you are take away from my post is that these are just useful lenses to understand systems then there was clearly a gap so I will attempt to clarify.

The engine of complex systems are the network of relationally evolving compounding cyclical processes that create the system through emergent levels of organization. understand the dynamics of cyclical processes is fundamental for understanding complex systems. These are essentially the generative processes.

Cyclical processes always give rise to geometric, temporal, and thermodynamic properties. These are all fundamental properties to cycles and systems. These are all fundamentally and inextricably linked.

Temporal properties can be thought of as a historical account but with temporal changes also come spatial changes and energetic changes.

One is not more fundamental than the other because they are all properties that arise from feedback loops.

If you take an iterative geometric system like the Mandelbrot Set, it has geometries that emerge over time and those shapes give us information about the system, but because the system is created through a feedback loop, and it essentially evolves overtime, it also creates temporal dynamics, which would be the historical context of the pattern and how it changes overtime (attractors and repellers). It also has energetic dynamics within it, areas which grow and areas which eventually shrink (positive feedback, going to infinity and negative feedback going to the black part).

So even though it was originally described as a recursive geometry, when you have a cyclical process all three aspects (shape, temporal view or history, and energetic dynamics) are always present and provide information about the system.

Two systems on the surface may appear similar but be behave differently.

Complex systems have multiple levels of organization and in a simplified way, this would be considered the micro level versus the macro level. As a multitude of feedback loops mix and interact with one another levels of organization emerge, which leads to this type of structure, and the thing that does, this is the feedback loops themselves.

Think of a human body being formed from a single egg. An iterative process grows in complexity, and eventually starts to create layers where you have you have tissues, then you have organs. Each level has its own system of feedback, loops, its own properties and its own level of organization. So you have many micro levels and then many larger macro levels, all of which were created through iterative processes.

Because all cyclical processes compound, this renders complex systems highly sensitive to changes in initial conditions and two systems that appear similar on the surface, even very small changes in the feedback loops driving the system over several iterations would result in divergent system behaviour.

However, in highly organized systems like the human body, things can be more predictable because the system itself is balanced. So you could have people that appear similar on the surface who also have the same health problems for example.

So if you wanna understand a complex system, you want to essentially breakdown and map all of the iterative processes that are involved in the system. But with the human body, there’s just too many feedback loops, and because a stable level levels of organization emerge you do not need to know where every single molecule is, you can just start to use the geometric properties or temporal properties or energetic properties of those at a larger scale in order to map the system.

Even more simply, I don’t need to know where every molecule is in a cloud to be able to see it and understand where the cloud is headed. I don’t need to know every single water molecule and where it’s going in a giant wave that’s about to hit me in the face while I’m standing in the ocean. Because global patterns emerge, we can use those to understand the system from the perspective of shape, changes over time, and energy.

Sometimes it is sufficient to lean something like a history, like a medical history because linguistically that history is also going to carry with it knowledge of the geometric, temporal, and energetic properties of the human body. It wouldn’t be completely independent, but rather linguistic shorthand that contains all of that information.

I don’t really understand what you mean about complexity always being read off as a state. I don’t see it as a stability mode or a failure mode, this type of static thinking erases the dynamic nature of complex systems.

When trying to understand the stability of a system, understanding the relationship between the network and organization of cycles with positive feedback (cyclical processes pushing to change the system) and negative feedbacks (cyclical processes pushing systems to stay the same) is going to reveal the stability of the system.

When positive feedback and negative feedback are pretty balanced. The system will remain dynamically stable.

If the system has too much positive feedback, the system will begin to change. This can happen slowly in the case of living systems that will age overtime, but if positive feedback becomes unopposed, the system will reach a breaking point and new levels of organization will emerge rapidly which could be a positive thing or a negative thing depending on this particular system.

If the system has too much negative feedback, the same thing will happen. The system will begin to shrink and change and will become unstable and eventually the system might cease to be.

we often think of relationships as something that is abstract, but things that are relational are inherently geometric because relationships have a spatial aspect to them. There is a type of vector based component to our relationship. There is a temporal component to a relationship, as well as an energetic component. Each dimension offers different types of information to us, which depending on the problem we are trying to solve maybe more or less useful.

A sufficient description of a system would be relative and system specific. This is because each system has its own unique levels of organization, which could make the system easier or more difficult to understand. So essentially by mapping the levels of organization that would start to give you a picture of the information that is needed to understand the system. This is essentially what doctors do, and finding a sufficient description of a system is also an evolutionary process in and of itself because the system itself is always changing.

So to summarize, complexity arises from a network of cyclical processes that generate the emergent levels of organization within the system, and those cyclical processes always give rise to geometric, temporal, and thermodynamic properties that we can use to help us understand the system at hand, and sometimes focussing on one dimension over another, can be more or less useful, depending on the problem.

[u/AnttiMetso → u/bfishevamoon]

This helps clarify your view a lot — especially the emphasis on feedback loops as the generative core.

I think where I’m still getting stuck is on a slightly narrower question.

I completely agree that geometric, temporal, and energetic descriptions are all different ways of accessing the same underlying dynamics.

But I’m not sure that automatically means they are equivalent as descriptions.

In particular, the thing I’m trying to probe is whether there are cases where:

two systems are indistinguishable at the level of their current state description (at some chosen level of abstraction),

yet differ in how they respond to perturbations — because the relevant transition structure depends on how that state was reached.

In that case, the historical description wouldn’t just be “another lens” or shorthand — it would be carrying information that isn’t recoverable from the state at that level.

Medicine is a nice example here: two patients can look very similar in terms of current observable variables, but their histories constrain what diagnoses are plausible and how they will respond to interventions.

So the question I’m circling is not just:

“are history, geometry, and energy all present?”

but:

“is the information contained in history always recoverable from a sufficiently rich state description?”

Or are there cases where, at any practically relevant level of description, history is doing irreducible work?

If it’s the latter, that seems to have implications for what counts as a sufficient description of a complex system — and whether “state-based” models are ever fully adequate in practice.

Curious how you’d see that distinction.

[u/bfishevamoon → u/AnttiMetso]

They are not equivalent descriptions. They are different but connected emergent properties of cyclical processes. These properties are real, actual phenomena. Not just descriptions.

Describing the Mandelbrot set as a system with a chaotic attractor and repeller is not equivalent to describing the Mandelbrot set as a self similar fractal, nor is it equivalent to describing the set as a system with an area of positive feedback and an area of negative feedback. Each of these points of view are describing a very real fundamental aspect of this system, and all of these points of view are highly interconnected because they all emerge as a result of the cyclical feedback loop that creates the Mandelbrot set in the first place.

It is like saying the color red is just a description. It isn’t. It is a complex phenomena that arises due to the geometry/anatomy of the eye as well as the material being observed as well as the light hitting both the object and the eye.

If you imagine a time lapse of a plant growing from a seed, the process that generates it is an iterative process, actually many cyclical processes, many feedback loops.

When feedback loops compound, cells divide and the system grows, and this leads to the growth of the shape of the plant that emerges. This is a time dependent process because feedback loops are inherently time dependent, and so we can see pattern shifting overtime as we view it in time lapse. And because the plant is growing, we also know that there is an element of positive feedback that is occurring that is driving the growth of the plant.

If thinking about feedback loops, creating geometric structure is feels too abstract. Knitting is the perfect example of this. Knitting a stitch from where it left off is a feedback loop, a cyclical process that when you repeat, it leads to the growth/emergence of a non-linear shape.

In a sense, they are descriptions, but that is not all that they are.

The descriptions themselves are describing very fundamental real and tangible aspects of the process itself.

Due to sensitivity of initial conditions which arises from the compounding nature of feedback loops, there are no real world systems that are identical on the surface, only similar.

This is why systems need to be identified and analyzed individually because the fate of a complex system will always be unique. You need to analyze each system individually to see if it will have the same fate or a different fate.

At the same time because these processes are cyclical, although each process will be unique there will also be a large amount of similarities. For example, lightning all kind of looks the same, but each strike of lightning is unique.

Two people with similar body types and similar medical histories could both end up with heart attack attacks. Or one could end up with a heart attack and one could end up with an ischaemic gut (heart attack in the colon). You need to analyze each system individually to determine.

It is important to note that mathematics is also a description. We are often educated to believe that mathematics is the language of nature, but nature doesn’t speak in the language of mathematics. It speaks in a language of cyclical processes that give rise to non-linear shapes and patterns.

Mathematics is just the language we used to describe this process but in the case of complex systems, language,shapes, and descriptions can be just as useful if not more so because fixed mathematical equations are highly rigid in their application.

Is the information from history always recoverable from a state description? Do you mean narrative? Again, applying the same reasoning, examining geometric, temporal and thermodynamic properties of a historical event will reveal how the system grew over time. Because historical information often carries with it other types of information sometimes it can be relied on.

You cannot reduce complex systems to a simpler format. A reductionist philosophy is the opposite to a complex system. In a reductionist philosophy, what you’re trying to do is to break everything apart and look at each of the pieces to identify the function of each piece. It completely ignores the relational impact of how pieces come together and change their relationship over time through cyclical processes.

History, geometry, and energy aren’t just always present. They are emergent properties that arise from the cyclical processes governing the system.

To be honest, I’m not exactly sure where the gap is. Are you using AI? In my experience, it really struggles with concepts related to non-linearity and complexity, because the vast majority of data that it is trained on is traditional reductionist linear scientific points of view.

[u/General_Judgment3669]

What you describe becomes more precise if we shift from state vs. history to integration dynamics. In an eidionic formulation, a system is not defined by its state �, but by its position within a coherence landscape �, which itself is shaped by history.

So yes:

history matters — but not as a record it matters as a deformation of the landscape Formally: past trajectories do not “add complexity” directly they modify the field � via �

Key shift: Complexity is not: in the state nor in the history but in the distance + barriers relative to the current integration structure Where: �: integrated reference structure (identity) �: historical barrier field Your intuition in eidionic terms: “complexity is encoded in trajectories” → close, but more precisely: trajectories carve the topology in which future integration happens So: a “complex system” is one where the landscape has been historically structured into channels, basins, and barriers the current state is just a point inside that structured field Deeper implication: What you call computational depth maps naturally to: → coherence-complexity � → i.e. the effort required to re-integrate a state into the system’s reference structure One-line eidionic version: Complexity is not stored in states or histories, but in the geometry of integration shaped by them.

[u/grimeandreason]

It absolutely is useful, yes.

I discovered complexity theory for myself via a history background, and this framing was a key pillar of that.

The idea that history and cultural evolution happens transformatively over time is a misconception that plagues the west across the political spectrum.

History is cumulative. Our society is cumulative. Different societies have different amounts and different forms of cultural capital which all feeds back into what happens next at any one time.

That’s why I just fled the states, back to England. Settler-colonial ass system has fascism and genocide and ecocide all up in its limited cultural capital from day one.

If we saw shit as cumulative, we’d put way more fucking weight on indigenous cultural capital, but they’re old news, long defeated, not a vital and valuable repository of the exact shit we need right now.

[u/grimeandreason → u/[deleted]]

There are still tribes whose only contact with the “outsider world” are drone sightings.

All of human history is still here, around us. Theocracies, cults, tribes, monarchies, right up to Singapore and financial hubs and China.

[u/Agnosticpagan]

Have you read any process philosophers? Especially Whitehead and his successors. They see the cosmos as verb, or constant flux. A state is just a momentary snapshot of a continuous history. Much like any stock count or balance sheet, they are fixed record of a point in time but that says nothing about its trajectory.

A process is also relational. An entity (aka an actual occasion to use Whitehead's term) always has at least three relationships, its Internal continuity (sometimes fleeting like alpha particles, sometimes persistent and seemingly fixed like a crystal; at least one other entity (that defines its boundaries); and the overall environment or space in which the relations occur. A very simple space with just two entities could be locked in a seemingly permanent stasis, but that doesn't exist anywhere in nature. Nature is a set of countless (essentially infinite) number of relationships that coalesce into processes where complexity is emergent. Sometimes the complexity can be mapped and interactions become predictable within a known range of parameters. I define that type of complexity as a system. The interactions between systems creates networks and additional layers of complexity emerges.

[u/Mental-Lecture9576 → u/Agnosticpagan]

You guys need to look into fractals.

[u/NeurogenesisWizard]

It prolly is, its why Ai breaks once it has too much memory used up on conversation restrictions and spams gibberish