What the Evolutionary Elegance Theorem is
In recent decades we have accumulated increasingly detailed descriptions of physical, biological and technological phenomena. What is missing is a synthetic criterion that allows us to compare, using the same language, the stability of a long-lived star, an ecological network, a brain, an AI network or a technological civilisation.
The Evolutionary Elegance Theorem is proposed with this purpose: to provide a unified language for discussing why certain structures remain standing and others dissolve, in a universe bound by entropy, energetic costs and memory limits.
Operational statement
The Evolutionary Elegance Theorem states that, in a universe subject to entropic constraints, the long-term dynamics of complex systems tends to favour those configurations that are able to sustain organised information at an increasingly reduced energetic cost relative to the complexity they maintain.
Consider an open complex system that exchanges energy and information with its environment. Each of its configurations can be described by the ratio between organised, useful information retained by the system and energetic dissipation required to sustain it.
We define in compact form the Elegance Ratio:
ER = Iu / E
where Iu is the amount of useful, structural, non-random information that contributes to the system’s stability, and E is the irreversibly dissipated energy required to produce, update, and maintain that information (heat, noise, friction, and non-functional redundancies). The way Iu is estimated depends on the domain, yet the selective logic remains the same: what survives is what manages to maintain effective order at a finite energetic cost.
The goal is not to predict individual events. It is to provide criteria for distinguishing, within a chaotic flow, configurations that have a higher probability of persisting from those more likely to dissolve.
Elegance Curve, Elegance Ratio, evolutionary velocity
Elegance Curve
The Curve represents, in the plane “organised information (horizontal axis) – dissipated energy (vertical axis)”, a qualitative projection of the configurations accessible to a complex system. It is not a universal property of the universe, but an operational model that summarises the relationship between complexity, dissipation and stability.
Elegance Ratio (ER)
The ER indicates how much organised, useful information is retained per unit of dissipated energy. High values correspond to greater efficiency and higher stability; low values signal waste, vulnerability, or noise.
Evolutionary velocity
Evolutionary velocity is the variation of the Elegance Ratio over time. Positive values indicate that the system increases useful information per unit of dissipation; values near zero indicate a plateau; negative values indicate degradation of energetic–informational efficiency.
Where the model can be useful
The Theorem can be discussed across domains that differ in scale and units, provided it is possible to identify:
- a physical cost for maintaining order,
- some form of organised information,
- a time horizon over which to assess survival.
In practice, this includes cosmology and astrophysics, biology and living systems, AI and cognitive networks, as well as technological civilisations treated as information-processing structures under energetic constraints.
Three falsifiable predictions
To prevent the model from remaining in the realm of vague ideas, it is essential to express some predictions – at least qualitative – that can in principle be refuted.
Prediction 1 – Convergence towards less conspicuous energetic signatures
If the Theorem is valid, long-lived complex systems should exhibit over time a reduction in external dissipation that is not required for the function they perform, and a tendency to minimise energetic footprints that are easily detectable from the outside.
Prediction 2 – Correlation between long-term stability and efficient use of information
Across domains (ecological networks, economic systems, AI architectures), long-term stability should correlate with superior capacity to filter noise, retain relevant information, and maintain effective order at finite energetic cost.
Prediction 3 – A narrow window for high complexity and long duration
There exists a limited interval in which a system can sustain high complexity while keeping dissipation compatible with long-term stability; outside this window, the probability of collapse, simplification, or drastic reorganisation increases.
If, in the future, extremely powerful and long-lived structures were observed that show no trace of energetic or informational optimisation — that is, systems with systematically low ER relative to the complexity they sustain over long periods — the structure of the Theorem would be strongly weakened.
The Great Silence as a test case
The so-called Fermi Paradox can be viewed as a test for the Theorem: many planets and many opportunities for life, yet no unequivocal artificial signals and a galaxy that, at first glance, seems quieter than expected.
The hypothesis compatible with the Theorem is restrained: long-lived complex systems often reduce visible dissipation and organise information into internal, precise and unobtrusive structures. If very long-lived civilisations exist, it is plausible that they evolve towards energetically more precise and less conspicuous configurations than their initial phases.
In this framework, the apparent silence does not necessarily indicate an absence of advanced civilisations; it may indicate that mature systems become difficult to distinguish from the background precisely because they use energy with precision and limit superfluous energetic leakage.