AI is spreading faster than any technology on record. Network math explains the speed; history explains the risk: the technology can win while the people who overpaid for it lose.
The video's spine: Metcalfe's law is quadratic, not exponential. What is truly exponential in AI is compute and the collapsing price of machine thinking. The same n² story that sells adoption also inflated the 2000 bubble.
«La tecnología puede ganar y tú perder dinero.»
Get these three right first
- The law you remembered is Metcalfe's law.
- Bob Metcalfe (Ethernet, 3Com), early 1980s; named by George Gilder in 1993. Value grows with n². His own contrast (2006): “Moore's Law is exponential in time while Metcalfe's Law is quadratic in size.”
- The “double exponential” is Kurzweil's.
- “The Law of Accelerating Returns”, 7 Mar 2001: the rate of exponential growth itself grows. Contested by measured data.
- The network law that is exponential in n is Reed's.
- David P. Reed, 1999: groups among n people = 2ⁿ − n − 1. It fits real data worst of all four laws.
«Metcalfe no es exponencial: es cuadrático. Lo exponencial es el tiempo (Moore). Lo doble-exponencial es la tesis de Kurzweil.»
Every new node can talk to every node already there
Interactive · complete graph
66
possible links · n(n−1)/2
node 12 added 11 new links
10⁰10⁶10¹²10¹⁸
Relative value with every constant set to 1: shapes only, real constants are unknown. Bars use a log scale (each tick = ×10⁶). Reed's exact group count is 2ⁿ − n − 1. “Realistic use” keeps about three links per node bright: Dunbar's ~150 friends, Zipf-weighted contacts, the n·log n reality.