比特幣和網絡理論

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.

在上個月的分期付款中，我介紹了Power Law模型，該模型最初是由意大利物理學家Giovanni Santostasi引入的。為了快速回顧，如果您將比特幣價格的對數與時間對數進行了回歸，那麼您會得到很強的相關性，這表明比特幣的價格遵守了權力法。

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.

在與喬瓦尼（Giovanni）聊天並在他的研究周圍戳了一下之後，我發現比特幣地址也符合權力法。這表明價格不僅遵循了權力法，而且比特幣地址隨著時間的推移的積累也確實如此。

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.

喬瓦尼（Giovanni）關於權力法的最新發現有助於將網絡理論應用於模型比特幣的更廣泛趨勢。比特幣網絡在維持分散的共識中起關鍵作用。就像互聯網遵守梅特卡夫定律一樣，隨著網絡的擴展，比特幣的價值也會增加。

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.

有不同的方法來評估網絡的大小。傳統上，這是通過計算網絡中的節點的數量來完成的，該節點是指一個完整的節點是指存儲完整區塊鏈副本並在交易中通過網絡傳播時驗證的比特幣機。喬瓦尼（Giovanni）採用了對網絡的更廣泛的定義，將每個比特幣地址視為一個節點，地址之間的交易作為鏈接。這種擴展的觀點會導致大量的節點，因為從理論上講，比特幣地址的潛在數量是無限的。任何人都可以通過創建公私密鑰對來以無許可的方式生成比特幣地址。

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.

現在，在使用比特幣地址作為節點時，需要牢記一些考慮因素。某些行為可以使比特幣地址的數量膨脹，而不會真正增加比特幣的採用。例如，如果用戶將10個比特幣從單個地址傳輸到他們控制的10個地址，則每個地址都持有一個比特幣，則不會反映出採用的增加，但地址數量增加。同樣，使用將比特幣重新分配到新地址的混合服務並不表示更多活動的網絡使用情況，而是技術擴展了網絡的地址計數。

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.

除了此類邊緣案例外，比特幣地址的數量應作為比特幣使用情況的合理指示。儘管這種關係可能不是嚴格的線性，但通常，與比特幣網絡的更多參與應與隨著時間的推移隨著比特幣地址的增加相關。

Causation versus Correlation

因果與相關性

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.

就是說，權力法可以告訴我們比特幣價值的原因嗎？否。權力定律是一個減少形式的統計模型，該模型建立了比特幣外部指標（價格，時間，地址等）之間的關係。它沒有闡明影響這些指標的基本經濟因素。因此，儘管隨著時間的推移，比特幣地址的增加，但權力法並未澄清為什麼創建比特幣地址的原因。

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.

為了實現這一理解，經濟學家將需要比特幣的“結構性”模型，而不是像權力法這樣的“減少形式”統計模型。結構性模型將確定控制比特幣的買賣動態的基本經濟結構。比特幣的價格是通過供需定律在市場中確定的，類似於所有市場行為。因此，為了真正解釋比特幣的價值和價格，必須分解驅使個人購買比特幣的原因。

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.

為了說明不同的觀點，請考慮在過去幾年中分析NVIDIA的股票價格。您可以創建圖形，將價格，日誌價格與日誌時間，日誌價格與時間或其他各種轉換進行比較。儘管這些將提供價格的統計表示，但它們並不表示因果關係。我們認識到的真正因果因素是對神經網絡的需求。但是，計算神經網絡在回歸中與NVIDIA的股票價格的影響是一個複雜的過程。儘管如此，這並不會破壞神經網絡代表核心技術促進生成AI的現實，這又推動了對NVIDIA的專業計算能力的需求。對於比特幣，稀缺性體現了因果因素。

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.

儘管如此，有潛力。可以在更抽象的層面上構建比特幣需求的結構性經濟模型。想像一下將比特幣買家分為四類：短期交易者，長期持有人，公司和民族國家。這些類別中的每一個都有不同的目標，時間範圍，預算和風險概況。通常，長期持有人是第一個購買的人，其次是公司，然後是民族國家，短期交易員遍布整個過程。長期持有人可能會影響比特幣價格水平，例如180天移動平均線，而短期交易者則每週或每月要求波動。

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.

我樂觀地認為，更細微的基於代理的模型可以增強權力法提供的理解。這為研究與比特幣本身一樣的研究提供了令人興奮的領域。