Quote from: marcus_of_augustus on March 27, 2014, 12:50:46 AM

Quote from: SlipperySlope on March 26, 2014, 10:51:33 PM

Quote from: ThirdRenaissance on March 26, 2014, 10:14:42 PM

Quote from: SlipperySlope on March 26, 2014, 09:08:20 PM

Therefore it is reasonable to suppose that small-world effects will disconnect the bitcoin price relationship from transaction volume, in that the future whole Bitcoin network will not be uniformly well connected but rather be clusters of well connected nodes.

I don't see how this applies to Bitcoin. One of its fundamental properties is the decentralized consensus, as long as this mechanism works all nodes must be in the same state. By definition there can't be any clusters that behave differently and connectivity is not an issue as long as there is a connection to the network. Unless you are assuming that forks could exist alongside each other in completely disconnected networks, but then Bitcoin has failed as a whole.

Sorry that I was not sufficiently clear. By way of example lets look at the worldwide email system. Every email client can reach any other email client by email address - just like Bitcoin. But if China was suddenly subtracted from the email system, it would not make my email service worth a lot less because I cannot communicate in Chinese. The worldwide email system has small world effects in that well connected nodes, i.e. nodes that might send messages to one another, are partitioned by natural languages that the users understand.

By well connected, I mean that a node has a reasonable probability of reaching another node in the network - not that it merely possible to reach that node.

But if everybody on the network can speak Bitcoin ....

Well yes, all peers on the network can speak Bitcoin. My hypothesis is that when considering the likelihood of connections between peers, i.e. the likelihood of a transaction between two addresses, the entire future Bitcoin network will be partitioned somewhat into clusters of addresses more likely to participate in transactions. For example, walk-in local merchants will have transactions with local walk-in customers, but are much less likely to participate in transactions with far away customers.

If someone can convince me that within 7 years Bitcoin entails the economic version of the Singularity, please do so. Otherwise I believe that Metcalfe's Law must eventually disconnect from explaining bitcoin prices given daily transaction quantity and addresses quantity.