Structural Limitations of Central Planning

In contemporary leftist and futuristic discourse, there is a strong tendency that can be described as "technological fetishism of planning." It is based on the deterministic assumption that the historical failures of planned economy models (such as the Soviet GOSPLAN) resulted almost exclusively from the lack of computational power and digital data transmission at the time. According to this hypothesis, the implementation of modern technologies—including supercomputers and AI—is a sufficient condition to solve the problem of economic calculation.

From a cybernetics perspective, this view is incorrect. It assumes that the economy is a static and fully deterministic system that can be "solved" with sufficient processing power. However, this ignores the fact that the complexity of socio-economic systems grows exponentially faster than the possibilities of their central modeling. There are hard, mathematical limits to controllability that cannot be overcome by technology alone. To understand these structural barriers to centralization, we must turn to two fundamental laws of control: Ashby's Law of Requisite Variety and the Markov Brothers' Inequality.

Material Foundations of System Diversity

W. Ross Ashby formulated a principle that, for cybernetics, has an ontological significance comparable to the law of value in Marx's political economy: "Only variety can absorb variety" (Law of Requisite Variety).

In the analysis of complex economic systems, the concept of "environment" encompasses all social interactions: consumer preferences, variability of natural conditions, technological innovations, and unpredictable geopolitical factors. This environment generates a set of states with extremely high entropy—this is the variety of the environment ($V_o$). Opposite this complexity is the control system (central planner, optimization algorithm, bureaucracy), which is characterized by its own, finite regulator variety ($V_r$).

A necessary condition for maintaining stability, controllability, and survival of the system is satisfying the fundamental inequality:

$V_r \ge V_o$

In cases where $V_r < V_o$, the system inevitably loses the ability to control effectively. Ashby, however, points to two ways to restore balance, which are often confused in political practice:

1. Strengthening the variety of the regulator ($V_r \uparrow$): Increasing computational power, employing more planners, using AI.
2. Suppressing the variety of the environment ($V_o \downarrow$): Simplifying the system being controlled.

In a market economy, the reduction ($V_o$) occurs in a spontaneous and destructive manner—through the anarchy of production, cyclical destruction of productive forces (bankruptcies), and waste of capital and labor (unemployment). In historical socialism, the reduction of $V_o$ often occurred through forced standardization. However, it should be noted that not every reduction of $V_o$ is a failure of the system—technical standardization (e.g., charger formats, network voltage) is a desirable reduction of entropy. The problem arises when reduction is forced by a lack of $V_r$ where society expects choice (e.g., in consumer goods).

A central supercomputer, despite its enormous $V_r$, still constitutes an informational "bottleneck" compared to the infinite complexity of social life. If the system relies solely on one central unit, it must either possess divine omniscience or drastically limit consumer choice to "fit" reality into the model.

Approximation and the Cost of Dynamics

Assuming that the economic system is dynamic, central planning encounters a mathematical barrier. Although modern methods (e.g., neural networks) are not directly polynomials, the Markov Inequality for polynomials serves here as an excellent heuristic model for the broader problem of the stability of universal approximators.

Let $f(t)$ denote the actual, time-varying function of social needs, and $P(t)$ the planning model. The inequality for the first derivative takes the form:

$\max |P'(t)| \le \frac{2 \cdot n^2}{w} \cdot \max |P(t)|$

Where:

• $P'(t)$ – the rate of adaptation of the plan to an external shock.
• $n$ – the degree of complexity of the model (in neural networks, the equivalent is the depth of the network/number of parameters and the associated risk of overfitting).
• $w$ – the width of the time window.

Dialectical Contradiction of Parameter "n"

The above relationship reveals a fundamental contradiction present in every control method (from polynomials to deep neural networks):

• Ashby's Imperative (high $n$): To accurately reflect reality, the model must be complex. A neural network must have billions of parameters to capture the nuances of demand.
• Stability Barrier (low $n$): Highly complex models are mathematically prone to instability with sudden changes in input. In polynomials, this is the Runge effect; in neural networks, these are so-called adversarial examples or the problem of exploding gradients.

A supercomputer can calculate that to optimize production with a 1% change in demand, a sudden maneuver (high $P'(t)$) must be performed. For the algorithm, this is just a number. For the physical economy, it is a catastrophe.

Inertia of Matter

Political economy, as a materialistic science, must consider the physical limitations of the productive base. The plan operates on matter, which has inertia.

The Markov Inequality for higher derivatives points to the problem of so-called "jerk." The limit for the second derivative (acceleration) increases proportionally to $n^4$.

$|P''(t)| \sim n^4$

Conclusion: Even with immediate recalculation of the plan by AI, the inertia of production processes is a barrier. Factories require time to retool. Attempting to control the economy with an algorithm of excessive complexity ($n$) leads to the disruption of the continuity of processes not due to calculation errors, but due to excessive variance in control signals (high frequency of decision changes).

Structural Solutions in Socialist Cybernetics

The solution to the control dilemma does not lie solely in escalating computational power, but in system engineering that combines three strategies:

1. Recursive Decentralization (Increase in Effective $V_r$)

Instead of one global model with extremely high $n$, we use a system of local models. A historical example is the Chilean Cybersyn project and the VSM (Viable System Model).

Thanks to the autonomy of lower-level units, complexity is solved locally. The center (Metasystem) does not have to process every bit of information, which protects it from overload. This is not the only way, but in systems of high social complexity, it is the most resistant to errors.

2. Conscious Shaping of $V_o$ (Standardization as Choice)

Instead of treating $V_o$ as a force of nature, socialism can consciously reduce unnecessary complexity of the environment. This does not have to mean "one pair of shoes for everyone." It can mean, for example, the unification of chassis platforms in transportation, modularization in construction, or API standards in logistics.

This is a strategic suppression of variety that frees up computational resources ($V_r$) to handle those areas where variety is socially desirable (culture, science, individual expression).

3. Reduction of the Time Horizon ($w$)

Shortening the time window of planning allows for lowering the requirements for complexity. A fast feedback loop allows for small, frequent corrections instead of rare, revolutionary shocks.

VSM and the Question of "Anarchy of Production"

Is VSM decentralization a return to market anarchy? VSM proposes a homeostatic planning system, eliminating the opposition between indicative and directive planning.

1. Coordination Mechanisms (System 2 and 3)

   • System 2 (Coordination): Dampens oscillations between units (e.g., schedules), preventing conflicts over resources.
   • System 3 (Control): Has insight into the whole. If the autonomy of a unit threatens the homeostasis of the whole, System 3 intervenes directly.

2. Algedonic Signals

   • A key element is algedonic signals (pain/pleasure)—automatic alarms when safe ranges are exceeded.
   • Here, a key political problem often omitted in technical descriptions arises: Who sets the pain thresholds?

In a bureaucratic system, these thresholds are susceptible to manipulation by local managers. The question remains open: who and how often should redefine the "safe range"? In the Cybersyn project, the creator proposed using social opinion meters in every household, which was to enable real democratic control.

Technology provides a signaling mechanism, but it is politics (people) that must define the objective function. Without democratic control over the system's parameters (meta-control), VSM can degenerate into a technocratic dictatorship or a certain federation of corporations.

Summary

The belief that technology alone will solve the calculation problem is idealism.

Ashby's Law teaches us that we must balance between increasing computational power and wisely reducing the complexity of the environment.

The Markov Inequality warns that overly complicated central plans are unstable when confronted with physical reality.

Cybernetic socialism is not a "central computer," but a distributed nervous system where stability results from the balance between autonomy (low $n$) and coordination.