“Network effect” is a term that is used to describe the characteristic of a certain good whose value to the buyer depends on how many other people use the product.

This term is often applied to the use of fax machines, the benefit of using one operating system over another, and the use of social networking sites, such as Facebook or MySpace, where users benefit from each new member added to the network.

In the early 1980s, Robert M. Metcalfe used the concept of network effects to advertise his invention, Ethernet, to big businesses.  Specifically, Metcalfe said that “customers needed their Ethernets to grow above a certain critical mass if they were to reap the benefits of the network effect.”  Furthermore, he said that while the cost of the product was proportional to the number of cards bought, the benefit was proportional to the square of this number:

“The network effect says that the value of that Ethernet card to the person on whose desk it sits is proportional to the number, N, of other computer users he can connect to. Now multiply this value by the number of users, and you have a value for the whole operation that is roughly proportional to N ².”

This phenomenon—that the value of a network is proportional to the square of the number of users—is called Metcalfe’s Law.

In his Forbes article, Robert M. Metcalfe applies his famous law to yet another network: the brain’s neural network.  Metcalfe argues that although the speed of transistors in electronic networks is exponentially faster than the speed between neurons, the abilities of electronic networks cannot compare to those of neural networks.  What is it about the brain that “makes even the most advanced supercomputers look pitifully stupid?” is the question behind this article.

Here is Metcalfe’s answer to this question which I will include for the sake of demonstrating the theory that the network effect is proportional to the square of the number of its parts:

“The brain does its intelligent computing with 10 ¹¹ neurons, interconnected in a very complicated network of roughly 10 ¹⁶ electrochemical connections, called synapses. Neuron synapses tick along relatively slowly, at about 10 ³ times per second.

So, the brain and SC5832 both have 10 ¹¹ computing elements. But the transistors run 10 ⁶ times faster than the neurons. We might therefore easily assume, using round numbers and neglecting the network effect, that the SC5832’s network of transistors is 10 ⁶ times as intelligent as the brain’s collection of neurons.

 Not so. Kurzweil estimates that the human brain’s networked intelligence produces the equivalent of 10 ¹⁶ computations per second. This is 10 ⁴ times more than the computational power of the SC5832. In other words, the brain is 10 ⁶x10 ⁴, or 10 ¹⁰, times smarter than it should be, just counting computing elements and multiplying their speeds.…

Each transistor in SC5832 processor chips connects directly to one, two or maybe three other transistors. By contrast, each neuron, with its incoming dendrites and branching axons, forms 10 ⁴ to 10 ⁵ electrochemical synapse connections with adjacent neurons. Estimates are that the brain of a child has 10 ¹⁶ synapses (alas, the number goes down with age). So, the connections among transistors in the SC5832 are on the order of 10 ¹¹, while connections among neurons in the brain number 10 ¹⁶.

But more connections mean greater value–in this case, intelligence. How much greater is the whole than the sum of its connected parts? The brain ends up not 10 ⁶ less intelligent than the SC5832, as we were tempted to think, but 10 ⁴ more intelligent. This is the network effect, surprising us by a factor of 10 ¹⁰.

How might we have predicted such a large effect? Metcalfe’s Law predicts that value is roughly proportional to N ². Try squaring the connection advantage of the brain over the SC5832, which is 10 ⁵, to get 10 ¹⁰.”

In his conclusion, Metcalfe goes on to say that the internet is, in a way, just like a synapse between two neurons; it spreads ideas from one person to another, connecting one brain to the second.  If Metcalfe’s Law is indeed true, then as the internet continues to reach new corners of the earth, one should expect a surge of new ideas, one that is equal in size to the square of the number of internet users on earth.