Classical Sorting Algorithms as a Model of Morphogenesis: self-sorting arrays reveal unexpected competencies in a minimal model of basal intelligence (2401.05375v1)

Abstract: The emerging field of Diverse Intelligence seeks to identify, formalize, and understand commonalities in behavioral competencies across a wide range of implementations. Especially interesting are simple systems that provide unexpected examples of memory, decision-making, or problem-solving in substrates that at first glance do not appear to be complex enough to implement such capabilities. We seek to develop tools to help understand the minimal requirements for such capabilities, and to learn to recognize and predict basal forms of intelligence in unconventional substrates. Here, we apply novel analyses to the behavior of classical sorting algorithms, short pieces of code which have been studied for many decades. To study these sorting algorithms as a model of biological morphogenesis and its competencies, we break two formerly-ubiquitous assumptions: top-down control (instead, showing how each element within a array of numbers can exert minimal agency and implement sorting policies from the bottom up), and fully reliable hardware (instead, allowing some of the elements to be "damaged" and fail to execute the algorithm). We quantitatively characterize sorting activity as the traversal of a problem space, showing that arrays of autonomous elements sort themselves more reliably and robustly than traditional implementations in the presence of errors. Moreover, we find the ability to temporarily reduce progress in order to navigate around a defect, and unexpected clustering behavior among the elements in chimeric arrays whose elements follow one of two different algorithms. The discovery of emergent problem-solving capacities in simple, familiar algorithms contributes a new perspective to the field of Diverse Intelligence, showing how basal forms of intelligence can emerge in simple systems without being explicitly encoded in their underlying mechanics.

• The paper demonstrates that classical sorting algorithms, repurposed with decentralized and error-tolerant operations, can model biological morphogenesis.
• The study employs Bubble, Insertion, and Selection sorts with localized decision-making, highlighting efficiency improvements and resilience amid disruptions.
• The research reveals emergent clustering and consensus behaviors in chimeric arrays, suggesting foundational principles for synthetic biology and decentralized intelligence.

An Analysis of Morphogenetic Competencies in Classical Sorting Algorithms

The exploration of emergent behaviors in minimal systems provides useful insight into understanding basal forms of intelligence and their implications for both biology and engineering. In the paper "Classical Sorting Algorithms as a Model of Morphogenesis: self-sorting arrays reveal unexpected competencies in a minimal model of basal intelligence," Zhang et al. present a compelling paper where they reinterpret classical sorting algorithms as models for biological morphogenesis processes. The authors challenge traditional views by investigating how these algorithms can simulate primitive cognitive competencies in decentralized systems and biological substrates.

Experimental Methodology and Model

The paper implements classical sorting algorithms, notably Bubble, Insertion, and Selection sorts, in a decentralized fashion where sorting decisions are made from the perspective of individual elements (cells). This approach departs from conventional top-down controlled models and introduces error-prone elements to simulate biological environments. By allowing elements to operate based on locally accessible information and interact with neighboring elements, the authors explore the ability of these algorithms to self-organize into ordered sequences, akin to biological morphogenesis.

Key Findings and Quantitative Insights

The paper reveals that even these simple algorithms display advanced competencies, such as error tolerance and the ability to navigate around defects (termed "Delayed Gratification"). Cell-view Bubble and Insertion sorts demonstrated significant improvements in efficiency compared to their traditional counterparts when accounting for both reading and acting steps. In contrast, the Selection sort was less efficient than its corresponding traditional implementation.

Error tolerance in the presence of Frozen Cells, representing malfunctioning elements that impede progress, highlighted the robustness of the cell-view sorting algorithms. Bubble sort, in particular, showcased superior performance in handling these disruptions.

Emergent Properties and Chimeric Arrays

One of the notable discoveries in this paper is the emergent clustering behavior in chimeric arrays, where different sorting policies (Algotypes) co-exist within the same array. Despite having distinct operational rules, elements exhibited a significant tendency to aggregate with similarly-behaving neighbors over the course of the sorting process. This suggests that emergent behavioral competencies can arise even without explicit encoding in the algorithm.

When contrasting cross-purpose sorting aims, i.e., where different components aim to sort in opposite directions, the system eventually reached a cooperative equilibrium. This phenomenon demonstrates the potential of distributed systems to achieve consensus despite conflicting local goals, paralleling some biological processes.

Implications

The results contribute to the fields of Diverse Intelligence and decentralized systems, emphasizing how even minimal and deterministic systems might harbor unseen competencies that form the foundation for more complex behaviors. The insights gleaned from these sorting algorithms provide a new lens through which to view regulatory morphogenesis, extending the dialogue regarding synthetic biology, regenerative medicine, and AI.

The paper reinforces the importance of exploring minimal models to uncover latent capabilities and problem-solving strategies that could inform the design of systems exhibiting both desired explicit behaviors and emergent properties. As researchers continue to incorporate these findings into practical applications, they might foreseeably advance our understanding of bio-inspired engineering and the design of robust, self-organizing artificial intelligence systems. Further investigation into the interaction of top-down controls with agential mediums, among other potential developments, offers an intriguing frontier for future research.