Money as infrastructure
What is money? Is it a currency? An entry in a ledger? Asking that question is a bit like asking “what is water?”
Money is as integral to modern society as roads, electricity grids, water pipes or fiber optic cables. Modern life can’t exist without it. When we turn on the tap, water comes out. Although we take it for granted, tap water is the final output of a complex system. Water needs to be collected, purified and then transported. When we spend and use money, we also take for granted the complex infrastructure supporting it, a monetary system.
When we say that the goal of Shell Protocol is to create internet money, we don’t mean our goal is to create a currency. That would be like saying the goal of a water utility is to create water. Our goal is to create the infrastructure for a monetary system.
The purpose of this article is to explain how monetary systems are like fractals and how we can use that concept to design a protocol for internet money.
What is a fractal?
A fractal is any structure that is self-similar and scale invariant. That is, whether you zoom in really close, or zoom out far away, you will see the same pattern. I.e., the pattern doesn’t vary no matter the scale. It is easier to visualize fractals, so we will include several examples throughout this article.
Fractals are found everywhere in the natural world. An example is a tree. We start with a trunk. That trunk splits into large branches. Each of those branches in turn splits into smaller branches. And so on until the tree has split into narrow twigs. At each stage, the pattern is the same, regardless of the size of the branch.
Fractals can also be random. Real trees don’t always separate into evenly distributed branches. They are still fractal-like because when we take the average of their attributes, we find scale-invariant, self-similarity. On average a tree will branch out at regular intervals, even if there are specific instances where that doesn’t happen. Indeed, in computer graphics, trees are often generated from random fractals. Even if a structure doesn’t look exactly like a fractal, it can still have certain level of fractal-ness, especially when we look at the average features.
Networks are fractals too
We can distill the tree-branch pattern to an even simpler form: a graph. A graph is a way to represent entities and their relationships as a network. We have nodes (dots) connected by edges (lines). A familiar example is a social graph or social network. In Twitter, each node in the network is a profile. Each follow is an edge that connects profiles. Information travels through the network via tweets and retweets.
We can also represent a tree in the same way. Each split is a node and each branch is an edge. Visually, we can see that the resulting graph simplifies the structure yet preserves the relationships between branches. Hence the graph inherits the fractal-ness of the original tree. It is a fractal network.
Examples of fractal networks
Fractal networks are quite common. Social networks are fractals. They are hierarchical and self-similar (see above). Airline flight paths are also fractal-like. All the previously mentioned examples of modern infrastructure are fractal networks: roads, electricity grids, water pipes, fiber optic cables etc. Internet money is also a fractal network, or at least it should be.
The decentralized financial system on Ethereum is a fractal network. Each node in the network is a public address. Each edge is a transaction between the two addresses. The resulting graph has the quintessential properties of a fractal network: it is self-similar and hierarchical.
The ubiquity of fractal networks
Fractal networks are ubiquitous for three reasons:
Efficiency
Resilience
Simplicity
Efficiency
The hierarchical structure of fractal networks means that we can traverse the graph in very few steps. No matter which node we start on and which node we end on, there will be relatively few intermediate steps, even if the network is extremely large. For example, every actor in Hollywood is less than six degrees away from Kevin Bacon if we look at their IMDB profiles. This “small world” attribute of fractal networks arises because of the hub-spoke hierarchy.
The high level of interconnectedness, even for large networks, makes fractals highly efficient. Consider social media. Information on Twitter can spread rapidly because the network is so interconnected. There are very few degrees of separation between me and any other user of Twitter. In a monetary system, interconnectedness translates to efficiency because capital can flow from one node to another in few steps.
Resilience
Despite the hierarchy, fractal networks tend to be distributed. There are often many different paths connecting two nodes. Thus, if a random node in the network is compromised, the network can continue to function. This property makes fractal networks very resilient. If a water main breaks, that neighborhood will have their water shut off, but the rest of the city will be unaffected. Or if an airport is shut down, there will still be many possible flight paths to connect two cities in the world. A monetary system ought to be similarly fault-tolerant.
Simplicity
Perhaps the biggest strength of a fractal network is its simplicity. The network itself can be extremely complex, but the instructions to generate the network can be simple. One of the most famous mathematical fractals is the Mandelbrot set. It can be stated as a simple expression:
That’s compact enough to be a tattoo. Nonetheless, it generates a mesmerizingly complex pattern:
Fractals create complexity out of simplicity by taking a few basic building blocks and composing them into complex shapes. If we want to generate a fractal network for money, we don’t need to specify the system in its entirety. We just need to specify the right building blocks.
Lessons from Twitter
Social networks existed long before social media. However, Twitter created a new substrate for social networks that has changed the world. The platform has brought down dictatorships and undermined democracies. How did they do it?
Twitter defined a simple set of concepts that allowed a fractal network to organically form:
Profiles
Follows
Tweets
That’s it. Profiles are like nodes in the network. Follows are like edges. Tweets are the information that flows through the network. These three concepts are all it took to change society and alter the course of history. Twitter shows us that if you define the right concepts, you can supercharge a fractal network.
The internet money protocol
If we want to create internet money, we don’t need to build a fractal network from nothing. Decentralized finance is already a fractal network. Similarly, social networks were already fractal-like before Twitter. We just need to create simple building blocks. The internet monetary system ought to embrace the inherent fractal nature of money and harness it. If we build such a protocol, a highly efficient and resilient infrastructure for the flow of capital will grow organically, just as infrastructure for the flow of information grew on Twitter’s platform.
What is the fundamental building block of internet money? The answer lies in yet another fractal, shells. To learn why, stay tuned for the next installment.
GOOD