比特币和网络理论

In the previous month's installment, I covered the power law model, which was initially introduced by Italian physicist Giovanni Santostasi. To quickly recap, if you regress the logarithm of bitcoin’s price against the logarithm of time, you get a strong correlation, which indicates that bitcoin’s price adheres to a power law.

在上个月的分期付款中，我介绍了Power Law模型，该模型最初是由意大利物理学家Giovanni Santostasi引入的。为了快速回顾，如果您将比特币价格的对数与时间对数进行了回归，那么您会得到很强的相关性，这表明比特币的价格遵守了权力法。

After chatting with Giovanni and poking around his research a bit more, I discovered that bitcoin addresses also conform to a power law. This suggests that not only does the price follow a power law, but the accumulation of bitcoin addresses over time does as well.

在与乔瓦尼（Giovanni）聊天并在他的研究周围戳了一下之后，我发现比特币地址也符合权力法。这表明价格不仅遵循了权力法，而且比特币地址随着时间的推移的积累也确实如此。

Giovanni’s latest findings on the power law contribute to a broader trend of applying network theory to model bitcoin. The Bitcoin network plays a pivotal role in maintaining decentralized consensus. Much like the internet adheres to Metcalfe’s Law, so does bitcoin’s value increase as the network expands.

乔瓦尼（Giovanni）关于权力法的最新发现有助于将网络理论应用于模型比特币的更广泛趋势。比特币网络在维持分散的共识中起关键作用。就像互联网遵守梅特卡夫定律一样，随着网络的扩展，比特币的价值也会增加。

There are different ways to gauge the size of a network. Traditionally, this is done by counting the number of nodes within the network, where a full node refers to a Bitcoin machine that stores a complete blockchain copy and validates transactions as they spread through the network. Giovanni adopts a broader definition of the network, considering each bitcoin address as a node, with transactions between addresses as links. This expanded viewpoint results in a vastly greater number of nodes, as the potential quantity of bitcoin addresses is theoretically infinite. Anyone can generate a bitcoin address in a permissionless manner by creating a public-private key pair.

有不同的方法来评估网络的大小。传统上，这是通过计算网络中的节点的数量来完成的，该节点是指一个完整的节点是指存储完整区块链副本并在交易中通过网络传播时验证的比特币机。乔瓦尼（Giovanni）采用了对网络的更广泛的定义，将每个比特币地址视为一个节点，地址之间的交易作为链接。这种扩展的观点会导致大量的节点，因为从理论上讲，比特币地址的潜在数量是无限的。任何人都可以通过创建公私密钥对来以无许可的方式生成比特币地址。

Now, there are some considerations to keep in mind when using bitcoin addresses as nodes. Certain behaviors can inflate the number of bitcoin addresses without genuinely increasing bitcoin’s adoption. For example, if a user transfers 10 bitcoin from a single address to 10 addresses they control, each holding one bitcoin, it doesn’t reflect increased adoption, yet the number of addresses rises. Similarly, using a mixing service that redistributes bitcoin to new addresses doesn’t signify more active network usage but technically expands the network’s address-count.

现在，在使用比特币地址作为节点时，需要牢记一些考虑因素。某些行为可以使比特币地址的数量膨胀，而不会真正增加比特币的采用。例如，如果用户将10个比特币从单个地址传输到他们控制的10个地址，则每个地址都持有一个比特币，则不会反映出采用的增加，但地址数量增加。同样，使用将比特币重新分配到新地址的混合服务并不表示更多活动的网络使用情况，而是技术扩展了网络的地址计数。

Excluding such edge cases, the count of bitcoin addresses should serve as a reasonable indication of bitcoin’s usage. While the relationship might not be strictly linear, in general, greater engagement with the Bitcoin network should correlate with an increase in bitcoin addresses over time.

除了此类边缘案例外，比特币地址的数量应作为比特币使用情况的合理指示。尽管这种关系可能不是严格的线性，但通常，与比特币网络的更多参与应与随着时间的推移随着比特币地址的增加相关。

Causation versus Correlation

因果与相关性

That said, can the power law tell us the cause of bitcoin’s value? No. The power law functions as a reduced-form statistical model that establishes a relationship between external metrics of bitcoin (price, time, addresses, etc.). It does not elucidate the underlying economic factors that influence these metrics. Thus, despite the increase in bitcoin addresses over time, the power law does not clarify why there has been a rise in the creation of bitcoin addresses.

就是说，权力法可以告诉我们比特币价值的原因吗？否。权力定律是一个减少形式的统计模型，该模型建立了比特币外部指标（价格，时间，地址等）之间的关系。它没有阐明影响这些指标的基本经济因素。因此，尽管随着时间的推移，比特币地址的增加，但权力法并未澄清为什么创建比特币地址的原因。

To achieve that understanding, economists would require a “structural” model of bitcoin rather than a “reduced-form” statistical model like the power law. A structural model would pinpoint essential economic constructs that govern the buying and selling dynamics of bitcoin. The price of bitcoin is determined in markets through the laws of supply and demand, similar to all market behaviors. Hence, to genuinely explain bitcoin’s value and price, one must break down what drives individuals to purchase bitcoin.

为了实现这一理解，经济学家将需要比特币的“结构性”模型，而不是像权力法这样的“减少形式”统计模型。结构性模型将确定控制比特币的买卖动态的基本经济结构。比特币的价格是通过供需定律在市场中确定的，类似于所有市场行为。因此，为了真正解释比特币的价值和价格，必须分解驱使个人购买比特币的原因。

To illustrate a different perspective, consider analyzing Nvidia’s stock price over the past few years. You could create graphs comparing price to time, log price to log time, log price to time, or various other transformations. While these would provide statistical representations of price, they are not indicative of causality. The true causal factor we recognize is the demand for neural networks. However, calculating the impact of neural networks in a regression alongside Nvidia’s stock price is a complex process. Nevertheless, this does not undermine the reality that neural networks represent the core technology fueling generative AI, which in turn drives the demand for the specialized computing capabilities Nvidia delivers to the market. For Bitcoin, scarcity embodies that causal factor.

为了说明不同的观点，请考虑在过去几年中分析NVIDIA的股票价格。您可以创建图形，将价格，日志价格与日志时间，日志价格与时间或其他各种转换进行比较。尽管这些将提供价格的统计表示，但它们并不表示因果关系。我们认识到的真正因果因素是对神经网络的需求。但是，计算神经网络在回归中与NVIDIA的股票价格的影响是一个复杂的过程。尽管如此，这并不会破坏神经网络代表核心技术促进生成AI的现实，这又推动了对NVIDIA的专业计算能力的需求。对于比特币，稀缺性体现了因果因素。

Nonetheless, there is potential. It might be possible to construct a structural economic model of bitcoin demand at a more abstract level. Imagine categorizing bitcoin buyers into four groups: short-term traders, long-term holders, corporations, and nation-states. Each of these categories possesses distinct objectives, time horizons, budgets, and risk profiles. Typically, long-term holders are the first to buy, followed by corporations and then nation-states, with short-term traders interspersed throughout. Long-term holders may influence the bitcoin price level as measured by, say, a 180-day moving average, while short-term traders dictate fluctuations on a weekly or monthly basis.

尽管如此，有潜力。可以在更抽象的层面上构建比特币需求的结构性经济模型。想象一下将比特币买家分为四类：短期交易者，长期持有人，公司和民族国家。这些类别中的每一个都有不同的目标，时间范围，预算和风险概况。通常，长期持有人是第一个购买的人，其次是公司，然后是民族国家，短期交易员遍布整个过程。长期持有人可能会影响比特币价格水平，例如180天移动平均线，而短期交易者则每周或每月要求波动。

I am optimistic that a more nuanced agent-based model could enhance the understanding provided by the power law. This presents an exciting frontier for research intertwining physical and social sciences, much like Bitcoin itself.

我乐观地认为，更细微的基于代理的模型可以增强权力法提供的理解。这为研究与比特币本身一样的研究提供了令人兴奋的领域。