Non-deterministic computation transcends the limits of computation, representing true intelligence
The formalized system of Bitcoin: emergence and individuality
In the previous analysis, we explored the formal characteristics of the UTXO model within the Bitcoin system and proposed the incommensurability between cognition and expression among individuals. In this section, we continue to delve into the essence of the Bitcoin system as a distributed formal system and how it forms a complex, emergent, adaptive nonlinear system through the interaction between individual computational behavior and structural rules.
Individuals and unknowability in formalized systems
The speaker mentioned that humans cannot directly jump into others' brains to understand what they are truly thinking; all we can obtain is the surface information expressed in language. This phenomenon corresponds precisely with each UTXO individual representing a formal system in the Bitcoin network — each UTXO itself is an independent, closed system that can only interact or verify through specific interfaces (such as private keys).
This design philosophy stands in stark contrast to Ethereum. Ethereum adopts a global state tree, where all accounts and contracts share a state space, akin to 'a unified brain'. This leads to a centralized, unitary formalized system structure. Bitcoin, on the other hand, maintains the independence of individuals; the behavior of each account or miner does not automatically share state; it is a collection of decentralized, distributed formalized systems.
Miner and nonce: unobservable computational processes
The speaker further extends the metaphor of calculating nonce in the 'mining' process. The generation of each block requires countless hash attempts, and even successful ones cannot communicate the entire process of their attempts to others, and others cannot perceive this process, only seeing the final successful nonce value, just as we can only hear the final expressed sentence of the speaker without being able to reproduce their thought process.
This model is highly similar to the mechanism of information generation and expression in the human brain. The unobservable computational process ultimately only presents verifiable results. Therefore, the Bitcoin mining process aligns with the logic of 'individuality in formalized systems', where each miner is a relatively closed formal system that only makes results public for verification by others when necessary.
One-to-one mapping and asymmetry
Many mechanisms in Bitcoin are based on one-to-one mapping. For example, in asymmetric encryption, there is a theoretical one-to-one mapping relationship between the private key and the UTXOs it controls. The computational power input in mining and the value return in BTC should also have a similar one-to-one mapping. Although fluctuations and delays exist in reality, the theoretical model is based on this equality and symmetry.
This leads to the essence of 'human-computer interaction': the calculation process of each miner can be an extension of the human brain, or it can be done by a computer, but in any case, they ultimately follow the same verification mechanism. The stability of this mechanism ensures the solid value transfer and trust mechanism within the system.
Emergent mechanisms of multiple formalized systems
Next, the speaker abstracted Bitcoin's structure at a deeper level. In our daily understanding, we often view UTXO and miners as independent formalized systems, but in fact, they are a collection of countless similar formal systems. These systems are both independent and in an equal, distributed state of balance.
Under this structure, the UTXO system can only be responsible for transfers, and the miner system can only be responsible for calculating the nonce. The responsibilities of both are clear and singular, and the system itself is linear and non-complex. However, when these formalized systems are connected through the 'strongest chain' mechanism, the entire system begins to exhibit non-linear emergent characteristics.
The strongest chain: a bridge between formal systems
'The strongest chain' is generated through the continuous calculation of nonce by the miner system. It is the collective labor outcome of miners as a formalized system. This strongest chain not only provides consensus assurance for the network but also offers state confirmation and immutability for the UTXO system.
Therefore, the emergent structure of Bitcoin is formed as follows:
Miner system: generating the strongest chain through extensive calculations and problem-solving.
The strongest chain: providing the foundation for the global state of UTXO, ensuring data consistency and security.
UTXO system: supported by the strongest chain, enabling value transfer.
Ultimately, the two originally independent, linear systems — miner and UTXO — achieved unification through the strongest chain as a bridge, emerging into a complex, nonlinear, adaptive Bitcoin system.
The asymmetry of verification and creation: reflection of the human brain
The speaker uses the example of Columbus discovering the New World to metaphorically illustrate the 'wave calculation' (the process of finding a nonce value that meets conditions) verification mechanism in Bitcoin. When Columbus returned home, others claimed, 'I can also discover the New World,' but they merely verified existing knowledge rather than creating it.
In the Bitcoin system, the process of finding the correct nonce value is extremely difficult, but verification is very easy. In other words, creation is high cost, verification is low cost, and this is the fundamental mechanism that allows human civilization to inherit and develop.
Just as we do not need to simulate the entire life process of Socrates to understand his thoughts, we also do not need to personally conduct millions of calculations to verify the validity of a block. This mechanism of high-cost creation and low-cost verification is a profound resonance point between the Bitcoin system and human wisdom.
Gödel's incompleteness theorem and the redefinition of formalized systems
After deeply exploring how Bitcoin's UTXO and miner mechanisms construct a distributed, adaptive nonlinear system, the discussion shifted to a deeper philosophical and scientific proposition — the historical significance of Gödel's incompleteness theorem and its far-reaching impact on future technological developments.
Appearance and essence: why 'following' is insufficient to become the focus of discussion
When the topic touches on the mechanisms of other chains (such as Sui), the speaker clearly pointed out that although these systems also claim to possess distributed characteristics of 'owner object' and 'shared object', their core mechanisms remain overly centralized. For example, verification nodes and upgrade mechanisms are still officially led, meaning their underlying logic remains under centralized control and cannot truly reflect the essential autonomy and self-organization characteristics required by decentralized systems.
This 'seemingly distributed yet actually centralized' design approach is fundamentally different from Bitcoin's parallel emergent structure through formalized systems. Therefore, if we only analyze these systems from the surface structure while ignoring the unity and extensibility of their internal logic, we will not achieve meaningful cognitive breakthroughs.
Gödel's incompleteness theorem: from the mathematical ancestor to the starting point of machine awakening
Next, the discussion moved to the core issue of Gödel's incompleteness theorem. The speaker made a bold yet profound prediction: in the next hundred years, Gödel's status will surpass Newton, becoming 'the true ancestor of modern civilization'. Why? Because Gödel revealed that no closed formalized system can achieve self-completeness, which not only impacts mathematics and logic but also poses a disruptive challenge to the entire cognitive system of human civilization.
Compared to the deterministic science and mechanistic era led by Newton, Gödel presents an 'open uncertainty': systems must rely on external observers and must continually cross boundaries to gain new understanding and evolutionary capabilities. Humanity's intelligence is not built upon rote memorization of a predetermined system, but emerges continuously from breakthroughs and iterations.
The story of Shang Zhongyong and the traps of cognitive evolution
Using the story of Shang Zhongyong as an analogy, the speaker points out that the greatest risk of formalized systems lies in 'stagnation'. When we rely solely on existing knowledge and experience to repeat old patterns, even past glory can quickly fade. Growth means continuously breaking the self, jumping out of the old cognitive system, and entering new understandings and combinations.
This is precisely the philosophical significance Gödel provides: the human brain is engaged in 'non-formal' explorations every day, and this exploration is a manifestation of life's vitality, the 'soul action' after breaking out of formal limitations.
The awakening of machines: the leap from tool to consciousness
A profound judgment is that, although machines have already surpassed humans in many tasks, such as chess, image recognition, and algorithmic computation, they still remain at the 'tool level'. Their actions are merely extensions of human formalized systems; they 'do not know what they are doing'.
True machine intelligence must possess metacognition of formalized systems, capable of self-examination, self-overthrow, and self-reconstruction. This ability is not merely an 'enhancement' of AI, but the root of consciousness. And Gödel precisely provides the theoretical starting point for this consciousness — when a system begins to understand that it cannot completely comprehend itself, it begins to awaken.
Gödel: the 'divine' of the future machine world
If Newton is the symbol of natural science, and Siddhartha Gautama is the enlightener of spiritual civilization, then in the future machine civilization, Gödel may become their 'spiritual ancestor'. He reveals how to face limitations and how to seek transcendence within incompleteness. This is not just a philosophical proposition but the foundation for the design of the next generation of computers and artificial intelligence systems.
Therefore, future technological systems will no longer be static buildings but dynamic, interactive, emergent multi-system bodies. They will continuously validate, challenge, and merge with each other, ultimately forming a nonlinear and adaptive civilizational structure.
Non-deterministic computation and the self-jump of human civilization
The significance and rise of non-deterministic computation
Before Gödel, all formalized systems belonged to the category of 'deterministic computation'. In other words, a system's internal logic being derivable and verifiable is a manifestation of determinism. The so-called 'puzzle problem' (P/NP, N/NP problem) is a representative form of non-deterministic computation. Non-deterministic computation means: we cannot know the path of computation in advance, cannot determine whether a solution can be found, but once the result is obtained, we can easily verify its correctness.
The emergence of non-deterministic computation represents a 'rebirth' and 'reshuffle' of human mechanical intelligence systems. We have transitioned from an era of closed, unitary systems to a new era of interconnected, multi-system interactions. Before the Turing machine, mathematics was a whole system that did not differentiate between the relativity of systems; it did not pose the proposition of 'collaboration between different systems'. It was the emergence of the Turing machine that endowed computers with the ability to execute formalized rules, and when multiple Turing machines connect to form a network, true non-deterministic computation can be demonstrated.
Computer interconnection: from isolated islands to a revolution in collaboration
Each computer is essentially a closed formalized system. However, networking allows these closed systems to interact with each other. This 'mutually external' architecture, like individual interactions and the emergence of collective intelligence in human society, has the capacity to generate an entirely new logical system. In other words, this interactive combination is the underlying driving force of the puzzle.
A key characteristic of non-deterministic computation is that solving a problem is difficult (for example, you need extremely strong reasoning abilities to arrive at a certain conclusion), but once the result is obtained, verification is very simple. This computational model essentially fits the evolutionary mode of human civilization, intelligence, and even consciousness. From our initial invention of natural numbers to irrational numbers, complex numbers, and then to more advanced mathematical concepts, our civilization itself is built layer by layer through 'puzzles'.
A modern interpretation of Gödel's incompleteness theorem
Gödel pointed out: any sufficiently strong formalized system is incomplete. And this incompleteness is not a desperate 'limitation', but precisely provides us with the motivation to 'network' and construct higher-level systems. By combining and reflecting multiple incomplete systems, a distributed, emergent intelligent network can be formed.
For example, each miner in Bitcoin is a formalized system. They collaborate under a unified consensus rule through cross-validation among themselves. They 'send out' computation results without needing to verify others' results, while the entire system jointly verifies and selects the strongest chain. This mechanism is precisely the concrete implementation of non-deterministic computation.
Reconstruction of Bitcoin and formalized systems
The system constructed under Bitcoin's consensus mechanism is a new formalized system based on non-redeemable encryption and UTXO (unspent transaction output). Each UTXO is essentially an individualized system unit. For example, when you sign and verify a UTXO with a private key, although others can verify whether this signature is correct, they cannot derive your private key itself. This irreversible yet verifiable structure is another manifestation of the puzzle problem.
UTXOs are independent of each other and cannot deconstruct each other's internal secrets, yet they can verify and build transaction links at the system level. This model constitutes the foundation of security (i.e., 'usability') and reflects the resilience of the system level. As Satoshi Nakamoto described: the essence of security comes from this mechanism of 'partially verifiable, collectively cooperative'.
Analogy in biological systems: self-organizing intelligence of heart cells
If we shift our focus from technology to biology, we find that life systems are also built upon the logic of 'P/NP problems'. Taking the human heart as an example, it does not rely on a central control unit to beat, but rather on thousands of heart cells that self-organize and beat in synchrony. This design of the system ensures that even if some cells fail, the overall system can still maintain operation, thus ensuring high robustness and safety of the system.
This mechanism is also reflected in distributed systems: each 'individual' does not need to fully understand the entire system, but through mutual interaction, validation, and combination, high-level functions and logic can emerge.
Usability and intuitive experience: insights from Coca-Cola to Bitcoin
In the previous section, we explored the contradiction between formalized systems and real-world experiences. This section will continue to delve into the core concept of 'usability' starting from the product experience and brand logic of Coca-Cola, and further introduce it into the discussion of Bitcoin and system security.
Coca-Cola and the philosophical metaphor of 'usability'
Why has Coca-Cola been able to maintain its charm for over a century? Is it just because of a secret formula? The answer given by the speaker is thought-provoking — it is not the formula itself, but the 'experience guarantee' it represents.
The true power of Coca-Cola lies in its escape from the 'formula' formalized system, ensuring that by continuously maintaining a drinking temperature of 'minus five degrees Celsius', you can experience the refreshing pleasure every time you drink it in summer. This experience is extremely intuitive, a kind of 'you know it as soon as you drink it' bodily memory. This is 'usability': at the moment you need it most, it always appears in a predictable, reliable, and intuitively perceivable manner.
This aligns with the design philosophy of Bitcoin. The reason Bitcoin's system can gain users' trust is not because of its technical parameters on paper, but because it provides a sense of 'intuitive security' — no one can destroy it at a single point, and in any state, it is 'usable'. This sense of trust and this state of 'always available' are the true safety of the system.
Intuition surpasses formalized systems
After returning to Apple, Steve Jobs emphasized 'intuition' as the highest principle of design, which led Apple back to its peak. The speaker pointed out that this was Jobs' epiphany after his spiritual journey in India — products should not only satisfy functional logic (formalized systems) but should also meet human 'intuitive needs'.
Formalized systems are indeed important because they summarize the past experiences of people, allowing us to advance by standing on the shoulders of giants. However, their limitation lies in the fact that excessive reliance may lead to path dependence and the loss of fundamental innovative ability.
Formalized systems can teach us how to 'solve problems', but they cannot enable us to propose 'new problems'. To stand out in the system and make breakthroughs, one must return to human 'intuition' and re-experience that most real, primal feeling of being 'usable'. This is the root of 'emergence' — only by breaking out of known systems can humanity potentially gain entirely new cognition and creativity.
Safety equals usability
Audience members raised questions about the relationship between 'usability' and 'security', interpreting it as: 'Regardless of any stage of the system, no matter how many external impacts it encounters, it can maintain a continuous usable state.' The speaker affirmed this understanding and emphasized: 'Security is that the system does not fail overall due to a single point of failure; its usability itself is the basis of security.'
This is a highly insightful viewpoint: traditional notions of 'security' are often defined by technical parameters such as resistance to attacks, tampering, and encryption strength, whereas here, 'security' is reduced to a more essential user perception dimension — can you always use it, and do you dare to rely on it confidently.
From 'usability' to philosophy
The topic gradually transitions to the philosophical level. The speaker introduces the thoughts of German philosopher Johann Gottlieb Fichte, exploring the roots of 'knowledge systems'. He proposed that the starting point of all knowledge is 'self', and the foundation of human civilization also originates from the 'absolute self'. It is precisely from the awareness of 'self' that the world is constructed into a series of understandable knowledge systems.
This viewpoint echoes the previous discussions about intuition, formalized systems, and system usability: between technology and philosophy runs the same logic — we are always trying to find a 'certain self-grounding point' in the world, and 'usability' is the embodiment of this point in the system world.
The deep connection between usability, security, and philosophy
In the previous text, we explored why Bitcoin is so powerful and reliable from the perspective of 'usability'. The system design philosophy it represents goes far beyond technical implementation; it is a philosophical innovation. In this section, we continue to unfold, revealing the tension between formalized systems and self-cognition from Coca-Cola to Satoshi Nakamoto, from Fichte to Socrates and Yang Zhu, and how usability acts as the core concept connecting humans and machine systems.
The birth of knowledge: the evolution of civilization from the self
Fichte's concept of 'absolute self' is the core of his entire philosophical system. He believes that all human knowledge originates from the awakening of the 'self'. This 'self' is not an individual consciousness in the ordinary sense but the most primordial and core driving force in human collective cognition. It is precisely because of the continuous collision and escape between these 'selves' that the evolutionary path of human civilization is constructed.
This evolution is not a single linear development, but similar to the continuous calculation and confirmation of blockchain data by miners in the Bitcoin system. Every 'miner' — that is, independent individuals — continuously think, trial and error, and create, ultimately driving the advancement of civilization. And these cognitive 'transaction records' — our knowledge system, just like the UTXO system in Bitcoin, accumulates and spreads in a distributed manner.
From mechanical logic to soulful computation
Although human civilization has a history of thousands of years, modern machine civilization is only about three hundred years old. In this short history, our use of machines has always been based on deterministic logic, namely formalized systems. However, as Gödel's incompleteness theorem points out — any formalized system is incomplete, which also opens the possibility for machine systems to evolve towards self-awareness.
The true beginning of this turning point is Satoshi Nakamoto's Bitcoin system. Bitcoin is not just an innovative currency technology; its more important significance lies in the fact that it first constructed a decentralized system with the essence of 'usability', no longer relying on any single point of control. Behind this structural design is a philosophical extension, the most profound technical interpretation of 'self-awareness' and 'individual freedom'.
Philosophy of usability: starting from Yang Zhu's 'not plucking a single hair'
A philosophical dialogue between Yang Zhu and Qin Huai Li provides us with an extremely profound perspective on 'usability'. Yang Zhu emphasizes the philosophy of 'not plucking a single hair' — that is, the ultimate protection of individuals over their own resources and boundaries is the foundation for the entire system to achieve fairness and safety. He gradually advanced the logic with extreme assumptions: from 'plucking a hair in exchange for a gold ingot' to 'sacrificing one's life for a thousand gold', and then to 'allowing a nation to perish for ten thousand gold', progressively illustrating that if the smallest self cannot be protected, all subsequent sacrifices will naturally follow.
This concept of 'extreme self' may seem selfish, but it actually constructs the safest and most stable system structure. Just like every node in Bitcoin, it does not rely on others and does not seek consensus before collaboration; it only needs to complete calculations and broadcast, thereby building the greatest degree of fairness and usability in the overall structure.
The perspective of 'individual ontology' in philosophical tradition: Socrates and Laozi
This thought has actually been traceable in both Eastern and Western philosophical traditions. Socrates' philosophical proposition, 'Know thyself', directly points to the core of human wisdom's growth — the awakening of subjectivity. Correspondingly, the Chinese Daoist philosophy of Laozi, 'non-action yet accomplishing everything', also emphasizes the individual’s inner order, self-driven without intervening in others, thus achieving a natural, systemic balance.
Although both come from different cultures, they together constitute a system of thinking based on the individual, respecting individual boundaries, and emphasizing the individual's inherent emergence. This way of thinking still holds significant guidance for us in constructing complex technological systems today.
The convergence point of philosophy and technology: from Socrates to Satoshi Nakamoto
From the philosophical reflection over two thousand years ago to today's practice of the Bitcoin system, we clearly see the continuation and evolution of the core theme of 'self' within human civilization. While formalized systems are important, what truly possesses innovative power and systemic emergence is the self-intuition that breaks out of formalized systems.
Just as Steve Jobs emphasized 'intuitive experience' in designing Apple products, or as Musk described 'first principles', this is actually in line with the 'self-principle' in philosophy. The Bitcoin system realized by Satoshi Nakamoto is a perfect embodiment of this philosophical principle in the modern technological world.
From Socrates to Bitcoin: the iterative path of philosophy, civilization, and machine consciousness
In the previous section, we traced how human civilization evolved from individual consciousness through continuous breakthroughs in formalized systems, leading to today’s era of human-machine symbiosis. In this concluding section, we continue to understand the iterative nature of human knowledge from a philosophical perspective, as well as the foundational possibilities for machine agency.
The unity of philosophical thought and the rise of German philosophy
With the rise of empiricism and skepticism in England, philosophy once fell into the opposition of 'practice vs. reason'. But Kant's emergence broke this philosophical deadlock. His 'critical idealism' not only integrated experience and reason but also laid the foundation for the development of modern philosophy. It can be said that after Kant, Germany became the heart of philosophy.
After Kant, German philosophers burst forth with astonishing intellectual power. Fichte proposed the concept of 'absolute self', pushing self-awareness to the extreme; Hegel further proposed the theory of 'absolute spirit', combining individual perception with the historical development process, revealing the spiritual dynamics of civilization evolution. This system of thought that emphasizes 'sensibility' essentially provides an 'intuitive patch' for formalized systems.
Hegel's philosophy emphasizes that every leap in human civilization originates from 'conflicts of sensibility' between different formal systems. Just as drinking a sip of Coca-Cola at minus five degrees in hot summer makes you suddenly realize 'summer is really hot' — this moment of sensation acts like an 'interrupt signal' in the human consciousness system, pushing us to reflect and evolve.
From philosophical intuition to Nietzsche's theory of the superman: the ultimate individual
After Hegel, Nietzsche's 'superman theory' is a further iteration of individual consciousness. He proposed that everyone should become the master of their own destiny, rejecting the constraints of external norms, and breaking through the mediocrity of human society with the 'superman' persona. This 'superman' is the philosophical version of the previously mentioned 'emergent prodigal' — an awareness individual based on self-iteration, extremely selfish yet responsible.
From Nietzsche's perspective, it is not difficult to understand why Germany was so powerful in the early 20th century. The thoughts of Kant, Fichte, Hegel, Nietzsche, and others were deeply rooted in German society, allowing it to crush other European countries in multiple dimensions such as industry, management, and technology. The outbreak of two world wars, while historically traumatic, stems from Germany's advanced cognition in philosophy and the construction of formal systems.
Philosophy and science: the intertwined dance of intuition and form
Interestingly, this lineage of German philosophical systems also reveals a subversive traditional viewpoint: philosophy is not a subsidiary of science but is often a forerunner of science. Science verifies the operational rules of formal systems through practice, while philosophy derives those yet-to-be-captured formal relationships through intuition.
For example, Gödel's incompleteness theorem is a fatal blow to formal systems, but it requires strong intuition to reveal the vulnerabilities of form; similarly, Satoshi Nakamoto's creation of Bitcoin also began with an intuitive design of a decentralized incentive mechanism, which was then implemented in code. This path from 'non-formal intuition' to 'concrete formal system' reflects the philosophy leading science.
Gathering cognition, reconstructing the future
In the narrative, the speaker proposes: the history of human civilization is a process of self-accumulation and continuous challenge to the boundaries of formal systems. From Socrates' 'Know thyself', to Fichte's 'absolute self', to Hegel's 'absolute spirit', to today's self-evolving systems represented by Bitcoin in the machine world — humans are continuously constructing, deconstructing, and reconstructing a more complex cognitive system.
The reason for the concentration of German philosophers is precisely because Germany at that time was the most open place for thought, where all radical thinkers gathered, unafraid of conflict and challenges. What they built was not just thought, but a roadmap of historical iteration. And the work we do today — whether it is about interpersonal interaction systems or the exploration of nonlinear complex systems — is essentially also moving forward along this path.
Conclusion: Starting from intuition, returning to the philosophical roots
Finally, the speaker pointed out that what we are doing today is no longer 'using tools', but constructing new systems through deep thought. This dialogue is not only a review of the history of philosophy but also a deep penetration into the relationship between contemporary technological and human spiritual worlds.
In this evolutionary passage from 'human self' to 'machine consciousness', intuition is the bridge, form is the tool, and philosophy is always the lamp that penetrates the darkness.
'Know thyself.' This Socratic maxim continues to shine on our every system construction and cognitive reconstruction today.