Like so many aspects of our digital economy, Bitcoin is a network that depends for its success upon scale. When only one person owns Bitcoins and is willing to exchange them for goods and services, they are useless. But every extra person who agrees to own and exchange Bitcoins adds to the value of that network. Crucially, they add to the value not in a linear but an exponential fashion. One plus three equals 16.
When social networks scale rapidly, as with Instagram, we tend to look askance at the value they suddenly command. Instagram was bought by Facebook last year for $1bn (£650m). As many pointed out at the time, the firm had just 13 employees. But what mattered was the scale of its network – its app had been downloaded 27m times since launch at the end of 2010, and its active user base was both highly engaged and growing.
The reason these numbers matter to the astute buyer can be found in two mathematical properties of networks. Metcalfe’s law observes that the number of possible connections between any two individuals in a network grows in proportion to the square of the number of members. Reed’s law adds that, as a network grows, the number of subnetworks that can be formed from its members grows even faster (we could think of fan page Facebook communities, or specialised communities of commercial exchange within Bitcoin). This may be even more important than Metcalfe’s law, because the raw number of possible connections overstates the human tendency to associate in small groups.
Take these effects together and each additional Bitcoin user adds vastly more value to the Bitcoin community than our linear-thinking minds expect. The case can be made that, as media attention grows and more people buy in, Bitcoin’s non-linear price increases accurately reflect its non-linear growth in value.
Bitcoin is an imperfect example. Its economy owes much to hoarding and speculation. Still it reminds us that we live in an age where the value of connection is paramount. Digital innovation is disrupting our lives, challenging even national currencies. Yet we do not stop to think about what this really means.
As one guru of the disrupted economy Seth Godin has pointed out, we are experiencing a change in the nature of scarcity. The internet and its social networks provide more people than ever with the chance to innovate at very low cost. What is scarce now are meaningful and lasting connections. Bitcoin, like the rest of us, must build those links if it is to fulfil its ambitions.
Marc Sidwell is managing editor of City A.M.