上個月，我審查了意大利物理學家Giovanni Santostasi首次提出的Power Law模型。回想一下，將比特幣價格的對數與時間對數進行回歸，這會產生緊密的貼合性，這與遵循權力法的比特幣價格一致。
Bitcoin addresses follow a power law, just like the price and time. This means that the number of bitcoin addresses increases over time at a rate that is proportional to the total number of addresses. This is consistent with the idea that bitcoin is a network technology, and the value of the network increases with the size of the network.
比特幣地址遵循權力法，就像價格和時間一樣。這意味著比特幣地址的數量隨著時間的推移增加，與地址總數成正比。這與比特幣是一種網絡技術的想法一致，並且網絡的價值隨著網絡的規模而增加。
There are several ways to measure the size of a network. The traditional method is to use the number of nodes on the network. In the case of Bitcoin, a full node is a bitcoin machine that keeps a copy of the full blockchain on disk and validates all transactions as they propagate through the network. However, Giovanni uses a broader notion of the network, with a bitcoin address as the node and transactions between addresses as links. This more generalized approach will have many more nodes, since the number of bitcoin addresses is theoretically infinite. Anyone can create a bitcoin address in a permissionless way by generating a public-private key pair.
有幾種測量網絡大小的方法。傳統方法是使用網絡上的節點數量。就比特幣而言，完整節點是一台比特幣機器，可在磁盤上保留完整區塊鏈的副本，並在通過網絡傳播時驗證所有交易。但是，喬瓦尼（Giovanni）使用該網絡的更廣泛的概念，比特幣地址作為節點和地址之間的交易作為鏈接。這種更廣泛的方法將具有更多的節點，因為從理論上講，比特幣地址的數量是無限的。任何人都可以通過生成公私密鑰對來以無許可的方式創建比特幣地址。
Using bitcoin addresses as nodes has consequences that need to be carried in mind. There are some behaviors that increase bitcoin addresses without actually increasing bitcoin adoption. For example, suppose a single user with 10 bitcoins in a single address sends that bitcoin to 10 addresses that he controls, with one bitcoin each. This would not increase bitcoin adoption, but would increase the number of addresses. Similarly, using a mixing service that recycles bitcoin by sending it to new addresses would also not represent an increase in the usage of the network, but would technically increase the size of the network if it is measured in addresses.
使用比特幣地址作為節點的後果需要牢記。有些行為可以增加比特幣地址，而不會實際增加比特幣的採用。例如，假設單個地址中有10個比特幣的單個用戶將該比特幣發送到他控制的10個地址，每個地址都有一個比特幣。這不會增加比特幣的採用，但會增加地址的數量。同樣，使用將比特幣發送到新地址來回收比特幣的混合服務也不代表網絡使用情況的增加，但如果在地址中測量網絡，則可以從技術上增加網絡的大小。
Aside from edge cases like these, the number of addresses should be a rough proxy for the usage of bitcoin. The relationship may not be one-to-one, but it should be in the right direction, where more usage of the Bitcoin network leads to more bitcoin addresses over time.
除了這樣的邊緣案例外，地址的數量應該是使用比特幣的粗略代理。這種關係可能不是一對一的，但是應該朝著正確的方向發展，隨著時間的流逝，更多使用比特幣網絡會導致更多的比特幣地址。
