Financial Magic with Network Math
Imagine a car that accelerates harder the faster you go. Exciting to think about, isn't it (better fasten that seat belt). The idea that such a thing could happen in real life (or at least, Wall Street's amazing simulation of real life) is based on the mathematical formula for calculating the number of possible combinations in a group of something: say, network nodes.
Now imagine this: you hold in your hand the world's only telephone. Oh by the way, please get out of the car first (if you can figure out a way to stop it). We don't practice unsafe cellular here at Business Buzz. Make your phone as fancy as you want – 2.4 GHz spread spectrum, multiple lines, built in digital answering machine, call waiting with Caller ID, the works. But, yours is the only one in existence. What could you do with it?
Right. Absolutely nothing, which makes a single network node good for exactly as much as war.
OK, let's "relax the constraints," as scientists like to say when they're conducting thought experiments (when you or I do this, it's daydreaming). Let's imagine one other person who has a phone identical to yours. Now you can call that person, and they can call you: two possibilities where none existed before. Did you imagine that other person was a very good friend? I hope so.
Add a third phone (or node) to the network: now each of the three lucky owners can call two other people. If conference calling was one of the features you imagined when you put your original solitary phone together, each of you could also make one call involving all three people on the network.
Get the idea? The more nodes on a network, the more things that can happen on that nework. The mathematical formula for the number of combinations of size p in a population of size n is:
n! ÷ n!(p – n)!.
The exclamation points stand for an operation called a "factorial" which involves multiplying a number by each number between it and 1. So, 1! = 1, 2! = 2 * 1 = 2, 3! = 3 * 2 * 1 = 6, 4! = 4 * 3 * 2 * 1 = 24.
As you can see, the factorial of a number starts to get really big really fast, just like the speed of the car that accelerates in direct proportion to its velocity. So do the number of combinations available on a network of n nodes: in fact, if you graph the total possibilities against the number of nodes in Excel, you get something that looks like this:
This graph only plots networks up to 14 nodes, and the peak of the Matterhorn represents 33,156,513 possible interactions.
Once the curve takes off, it's a skyrocket, but it takes a while to get going. There are already 85, 344 possibilities on a 9-node network, but that's such a piddly little number next to 33 million that the graph makes it look like zero.
This is what the business press calls "critical mass," a concept derived from nuclear physics (you can't get a chain reaction unless you have a critical mass of radioactive material). If there were two or more contenders for network supremacy, they'd be on a nearly level playing field until one of them reached critical mass. After that point, the added value of each new network node would rise so fast that (theoretically at least) there would be no way to catch up to the leader.
This graph may remind you of something else: the famous "hockey stick" model of revenues that was the basis for just about every dotcom "business model" (no one was so bold as to call them "plans"). Whether they were aware of it or not, all of them were based on the same mathematical model of network expansion. Now you can understand why pets.com would think it an excellent idea to spend $2 million on a 30 second Super Bowl spot featuring a sock puppet: they saw themselves in a race to critical mass (who were the other contenders: guppies.com? cyberfish.com?).
We all know how this played out over the last couple of years. You could say the "new economy" (aka the "network economy") stumbled over one difference between mathematical models and reality. It does you no good to have nearly infinite possibilities at your disposal if no one knows what any of them are.
One other thing to keep in mind when applying this model to network-based businesses: Critical mass applies equally to emerging new technologies and to established ones. For instance, if FireWire were to achieve critical mass in digital distribution of audio/video, it could overtake Ethernet/Cobranet practially overnight. So there is a down side to the new network economy, after all (as if we didn't know): the leader has to keep on accelerating just to stay in place.