Bitcoin and Technology

Last month, I reviewed the power law model, first proposed by the Italian physicist Giovanni Santostasi. Recall that regressing the logarithm of bitcoin’s price against the logarithm of time generates a tight fit, and this is consistent with bitcoin's price following a power law.

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.

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.

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.

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.