The cornerstone of today’s digital computing era is undoubtedly the Turing machine paradigm established by Alan Turing. This paradigm, by abstracting the computational capabilities of the human brain, proposed a universal computational model based on the core assumption that the human brain operates deterministically — that is, any process that “seems computable” can be systematically simulated on a Turing machine. This assumption greatly propelled the development of computer science and successfully constructed countless deterministic formalized tool systems, profoundly transforming all aspects of human society.
However, with the deepening of artificial intelligence research and the exploration of human intelligence itself, the limitations of the Turing computing paradigm are becoming increasingly evident. Its primary bottleneck lies in the fact that it is essentially a theory about a single deterministic formal system and is inadequate in explaining or simulating the non-deterministic elements found in the human brain — such as consciousness, emotion, intuition, and the complex sociocultural phenomena that emerge from them. As Gödel already noted during Turing’s time, the human brain may surpass pure computation, and dimensions such as consciousness and emotion are not fully covered by the assumptions of deterministic Turing computation.
Therefore, in order to break through the bottleneck of the current computational paradigm and build systems that are closer to human intelligence — or even possess some form of “self-awareness” — we need a revolution in computing paradigms. This revolution must go beyond the Turing framework, confront the challenges of uncertain computation such as consciousness, and draw inspiration from the cognitive and cultural co-evolution patterns of the human brain.
Observing the operation of the human brain, we find that it is not a single, centralized deterministic computational unit but rather a highly distributed complex system. The brain is composed of countless interconnected neurons, each performing relatively simple deterministic operations. Yet through complex network connections and dynamic interactions, highly sophisticated cognitive abilities emerge. Furthermore, individual brain cognition does not exist in isolation but co-evolves with human culture.
The relationship between individual cognition and culture is akin to that between a computer and the internet. The cognitive abilities of individual brains are the source of cultural innovation, while culture — through language, knowledge, tools, and customs — greatly expands and shapes the cognitive boundaries of the individual. Culture transmits the accumulated wisdom of generations, enabling individuals to explore the world’s rules without starting from scratch. At the same time, culture shapes individuals’ thinking patterns, values, and problem-solving strategies.
From the perspective of computational complexity theory, this evolution from individual cognition to cultural consensus can be likened to the P/NP problem. When facing a new problem, an individual’s cognitive process is often a complex and uncertain “solution-finding” process — akin to solving an NP problem that may require extensive trial and non-linear thinking. However, when the cognitive results of individuals are accepted by the social group and form cultural consensus, verifying this knowledge, norm, or practice becomes relatively easier — like verifying a solution to a P problem. Once cultural consensus is formed, such knowledge can be efficiently transmitted and applied, further shaping new individual cognition.
Therefore, the essence of human intelligence is not simply deterministic computation, but a complex, potentially uncertain process of exploration and solution at the individual level, culminating in a relatively stable knowledge system at the sociocultural level through mutual verification and consensus. This transformation from “hard to solve” individually to “easy to verify” collectively reflects a kind of nonlinear emergent intelligence, where the overall capability far exceeds the linear sum of individual capacities.
A new computing paradigm must build upon deterministic Turing computation while introducing mechanisms to handle uncertainty and complexity, with the goal of simulating advanced cognitive phenomena such as consciousness. This requires us to transcend the limits of a single formal system and explore emergent behaviors arising from the interaction among multiple formal systems.
Gödel’s incompleteness theorem states that any consistent axiomatic formal system capable of expressing basic arithmetic must necessarily contain propositions that can neither be proved nor disproved within the system. This implies an intrinsic limitation of formal systems and suggests that human rationality may exceed the boundaries of formal logic. Bringing this idea into the realm of computation implies that we cannot expect a single, fully deterministic formal system to simulate human intelligence entirely — especially phenomena like consciousness, which seem to involve self-reference and transcendence.
The P/NP problem, at the core of computational complexity theory, explores whether verifying a solution is easier than finding one. As discussed earlier, the complexity of human individual cognition may correspond to the difficulty of solving NP problems, while cultural consensus formation resembles P-type verification. Complexity science shows that complex systems composed of many simple units can exhibit unpredictable and difficult-to-understand macro behavior through nonlinear interactions. This provides a new perspective for understanding complex phenomena such as consciousness and culture — that they may be nonlinear emergent results from interactions among numerous deterministic or semi-deterministic micro-processes.
The human brain and human society are both essentially highly distributed systems. Neurons in the brain process information in parallel, while individuals in society interact and collaborate through complex networks. Distributed systems and multi-agent theory study how multiple autonomous entities can achieve global goals or exhibit emergent behavior through local interactions without centralized control. This offers important tools for building new computational paradigms — namely, by designing multiple interacting computational units (formal systems) with different functions and interaction rules to simulate the complexity of the brain and society.
To more clearly understand the features of the new computing paradigm, the following table compares the traditional Turing machine paradigm with the proposed new paradigm:
Based on the analysis above, the new computing paradigm can be envisioned as a distributed hybrid architecture based on the principles of P/NP. It no longer focuses solely on a single deterministic formal system but emphasizes the collaborative operation and dynamic evolution among multiple formal systems with different characteristics.
These systems resemble the formation and verification processes of cultural consensus, aiming to efficiently and reliably validate and disseminate existing knowledge and solutions. They may be based on mature deterministic computational models like the Turing machine and use distributed consensus algorithms (e.g., blockchain consensus mechanisms) to ensure the accuracy of information and system stability. Such systems excel at processing structured data, logical reasoning, and precise computation — forming the foundation for building reliable knowledge bases and executing deterministic tasks.
These systems aim to simulate complex individual cognitive processes, focusing on large-scale, potentially highly parallelized searches and trials to discover new solutions or patterns. They may also rely on deterministic Turing-machine-based computation but are characterized by the need to explore vast computational spaces — akin to solving NP problems. They can adopt various search strategies, optimization algorithms, and biological mechanisms (e.g., evolutionary algorithms, reinforcement learning), allowing the system to autonomously learn and adapt within complex possibility spaces. These systems excel at handling unstructured data, uncovering latent patterns, engaging in creative reasoning, and solving complex problems — serving as the engines for generating new knowledge and solutions.
In the case of Bitcoin:
The key to the new computing paradigm lies in effectively connecting the verification-oriented and solution-oriented distributed formal systems to form an organic whole capable of emergent higher-level intelligent behavior. We can draw from Bitcoin’s longest-chain mechanism and see it as a kind of distributed “oracle” that provides feedback and guidance for the solution-oriented systems.
Bitcoin, designed by Satoshi Nakamoto, can be seen as an early and enlightening case of hybrid architecture. It is not a fully deterministic tool but rather a complex system exhibiting self-organizing intelligence through the collaborative operation of multiple distributed formal systems of different natures.
Bitcoin’s success demonstrates that by effectively combining distributed formal systems of different natures and connecting them through a mechanism similar to a distributed oracle, one can build a complex system that surpasses traditional deterministic tools—featuring self-organization and learning capabilities. Although Bitcoin was not intended to simulate human consciousness, the P/NP-style collaborative thinking embedded in its architecture provides valuable inspiration for building more advanced artificial intelligence.
The current Turing computation paradigm has achieved great success in constructing deterministic formal tool systems, but its limitation lies in the difficulty of explaining and simulating the non-determinism and emergence found in human intelligence. A new computational paradigm needs to go beyond the constraints of a single deterministic system, drawing on the patterns of human brain cognition and cultural co-evolution to explore the complex behaviors that emerge from the interaction of multiple formal systems of different natures.
From the perspective of the P/NP problem, we can construct a hybrid architecture that combines systems good at deterministic verification with systems adept at complex search and trial-and-error, connected through mechanisms akin to distributed oracles, simulating the evolutionary process of human intelligence from individual exploration to cultural consensus. Bitcoin, as an early attempt, showcases the potential of this hybrid architecture.
Future research directions will include:
The new computational paradigm is not meant to completely abandon the Turing paradigm but to extend and deepen it—introducing perspectives of uncertainty, complexity, and evolution. The ultimate goal is to build the next generation of intelligent systems that not only solve problems efficiently but also learn autonomously, adapt to their environment, and even exhibit a form of “self-awareness,” ushering in a new era of adaptive consciousness.
