In the realm of decentralized technologies, Bitcoin's blockchain stands as a pioneering example of how complex systems can operate without centralized control. In a recent paper, Bitcoin: A Non-Continuous Time System, the author delves into the fascinating aspect of this system: the concept of time. Unlike physical systems and even our own subjective experience, where time is continuous and linear, Bitcoin's blockchain operates on a discrete and probabilistic timeline. This feature enhances security and efficiency of the network but also challenges our conventional understanding of time in digital and physical systems.
In order to understand non-continuous (discrete) time, we must understand that Bitcoin's blockchain diverges from the traditional notion of time in computing that treats time as a continuous variable, where events unfold in a predictable sequence, by introducing randomness and unpredictability into its temporal sequence. The creation of a new block is a probabilistic process, since although the average of a block creating is 10 minutes, this time can vary significantly due to the inherent randomness of the mining process. The non-continuous nature of time in the blockchain is also reflected in the occurrence of forks and rollbacks. When multiple miners simultaneously produce valid blocks, the network temporarily splits into multiple chains. This creates ambiguity in the blockchain's history, disrupting the continuity of time. The network eventually resolves this by adopting the longest chain, discarding shorter branches and reversing transactions in them. This process might seem chaotic,and can be thought as a temporary discord in the symphony, where different sections of an orchestra momentarily play different melodies. Eventually, the orchestra comes back together to play in harmony. This process at the end of the day settles a logical structure and maintains the integrity and security of the blockchain.
The transactions are also a non-linear process of confirmation that messes up with the notion of linear time. When a user initiates a transaction, it is broadcast to the network and included in a block after it is validated by miners. But the transaction is not immediately final, since it requires multiple confirmations, typically 6 blocks, to be considered confirmed and irreversible. Then the confirmation process is subject to delays due to the random nature of block generation and network propagation. The time it takes for a transaction to be included in a block is influenced by the transaction fee, as higher ones increase the likelihood of quicker inclusion in a block. Until a transaction receives enough confirmations, it is vulnerable to being reversed if a rollback occurs. Then a transaction's finality is uncertain until sufficient confirmations are received, and this includes a layer of discontinuity in the system, as the transaction can be reverted during the process of block reorganization.
The effects of this non-continuous time for decentralized systems are multifaceted. This non-continuous time model enables Bitcoin to function efficiently in a decentralized environment. By breaking time into discrete blocks, Bitcoin is able to process transactions in a way that does not require constant synchronization or real-time processing, which allows it to maintain network scalability. Since each block represents a step in time, the system is not bound by real-time constraints and can process transactions at its own pace. This model is then more adaptable than continuous systems since it doesn't require constant update and synchronization. It also reduces the computational overhead associated with maintaining real-time accuracy, and allows the network to grow without the limitations of synchronous timekeeping. The model also ensures that all participants follow the same sequence of events, even when those events are not perfectly synchronized across the system. Then, decentralized networks achieve consensus without relying on synchronized global time.
Although time in classical physics is treated a continuous variable flowing predictably, certain phenomena still require to be modeled by Bitcoin's blockchain time model. One of this phenomena is quantum mechanics. Quantum systems challenge classical notions of continuous time through abrupt state changes. During measurements, the wave function collapse instantaneously "jumps" a system into a definite state, bypassing smooth transitions. Discrete-time models, such as quantum walks (analogs of classical random walks), also use stepwise evolution to describe particle behavior. Additionally, some interpretations of quantum gravity propose spacetime itself as quantized at Planck scales, suggesting time's fundamental granularity. What if time is quantized at a microscopic scale, and the passage of time is fragmented and probabilistic, in the same way as it occurs in a blockchain?
The concept of granular time can also be found in cellular automata model systems, where time progresses in discrete, uniform steps. Each cell in a grid updates its state synchronously based on predefined rules and the states of its neighbors. For example, in Conway's Game of Life, cells transition between "alive" or "dead" states at each time increment, creating complex emergent patterns. This stepwise evolution allows cellular automata to simulate natural phenomena -- like fluid dynamics or biological growth -- using simplified, granular time. Non-continuous time here enables computational tractability and reveals how simple rules can generate intricate behaviors over iterative cycles. What if we were able to encode cellular automata systems into the passage of time of any blockchain, converting it from an analogy to a real merge of both ideas?
Discrete time is not merely a computational convenience in technology but might be a hidden feature of nature, worth of being explore in more depth.
