“Digital Physics” in Full-Chain Games

A few months ago, before joining Lattice, I joked to Ludens (the Lattice founder) that the team should publish an article called "Why Your Protocols Need Physics." This article is part philosophical discussion, part marketing propaganda (and maybe part nonsense), and it will explain why automated market makers (AMMs), decentralized lending markets (DeFi), and blockchain Layer1 and Layer2 Their protocols should be made physical** by implementing concepts such as spatial coordinates, velocity, etc. Incorporates light, energy conservation, and other physical principles into its underlying smart contracts and architecture.

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The foregoing was inspired by comments Ludens made to me (also expressed in podcasts and talks) about the current computational limitations of blockchain and its irreconcilability with universal physics. Ethereum has only one dimension: time, therefore, EVM-compatible chains can only process transactions sequentially. The universe has four dimensions: three-dimensional Euclidean space (x, y, z) and time, which means that events occur in parallel in the universe. Blockchain events are time-ordered, and the rate of information dissemination is determined by the rate at which validator nodes package transactions. Events that occur in the universe are affected by the theory of relativity, and the speed at which information travels is limited only by the speed of light.

Can we simulate phenomena that exist in Universal Physics and Relativity by “giving” smart contracts coordinates (locations) on the blockchain and limiting interactions with specific contracts to specific locations? This would eliminate global state (since information travels at the speed of light) and essentially parallelize the EVM by "cheating" how state is propagated across the blockchain network.

If Alice trades with Bob in one area of space, it has no effect on whether Charlie can trade with Dave a million miles away. Although the EVM needs to sequence this transaction, physically enforced smart contracts do not because they have the concept of spatial coordinates. From the perspective of the blockchain network, there is no longer a need for global block producers, only local block producers that ultimately coordinate transactions on a global scale.

Other phenomena can also be unlocked through spatial coordinates, not just hacky implementations of EVM parallelization. Examples of this can be found in the design of zkDungeon, a game that predates MUD (Lattice's on-chain application operating system), as well as OPCraft and Sky Strife (our first two games built on MUD). zkDungeon is a cross between a board game and an on-chain battle royale game where players can build and mine territories on the map, summon creatures, and trade resources like gold and souls.

Like the hypothetical EVM above, the contract has a defined coordinate on the map. Unlike the hypothetical EVM, coordinates are not mandated for the purpose of transaction parallelization, they exist to encourage "emergent" behavior, such as players establishing trade routes, sea kingdoms, all of which will appear in defined "physical" locations of automated market makers (AMM). Through local contracts, we can quickly insert trading markets into the game and incentivize new curious player behavior to use them.

Screenshot of zkDungeon

Something as simple as defining contract coordinates in metric space can have huge impacts, from creating new types of player-for-hire behavior to helping the EVM transition from today's serial computers to higher-performance computing models. We call these simple prescriptions "Digital Physics", I would like to think of Digital Physics as the fundamental law of on-chain systems and it is possible throughout the stack (from application layer to infrastructure layer) produce resonance.

There are other examples of digital physics in well-known on-chain games. In Dark Forest, players can choose how to uncover the game's fog of war map. They can use Dark Forest's standard in-browser single-threaded Java miner to calculate hashes and thus reveal the map. Or they could devote more CPU cores to computing hashes by using a simple drop-down module. There are also custom miners written in Rust that allow for faster map discovery, or if players want to outsource mining, they can use a remote miner running on a server or Raspberry Pi. One player got attention for implementing this on a 96-core AWS instance (which probably cost around $3 per hour).

This behavior can be difficult to understand if you don't know the other plugins players have built for Dark Forest. As a game with dozens of license-free plug-ins, players can also buy and sell equipment, planets, and even planet coordinates (in a world with incomplete information in the fog of war, information itself can become a commodity in the game market, and even the most valuable goods). Suddenly, mining in the Dark Forest universe becomes a completely rational economic behavior, similar to mining any valuable resource in the physical world.

The valid inputs you choose to accept can have huge consequences and directly affect the digital physics of your system. Imagine that the map exploration speed in Dark Forest is static, and players cannot customize the speed at which they want to explore the map. This would make the total universe size in Dark Forest a linear function of player count and game time, rather than a function of those two factors, plus the cumulative resource cost of mining. Games between players will be simpler: The strongest players will be those who spend more time in the game, or spend more real-world money buying map coordinates. The actual current version of Dark Forest allows for a third variable, based on how much money players are willing to spend to uncover the computing resources of the universe. In other words, by taking hashrate as an input, users have greater control over how big they want the universe to become, increasing the likelihood of more dynamic behavior in the future.

The autonomous world is an ideal petri dish for "digital physics". There are no best practices for what "strong" digital physics looks like, it will depend on the on-chain world you are designing. Not every world needs to be restricted to operations performed within the confines of a grid, or within a universe that expands at the same rate as your computing power. The most important thing about digital physics is the resonance it can generate.

We believe autonomous worlds are emerging from a primitive state. Like the universe we inhabit, they require in-depth research to complement product-level experiments and technical documentation. We hope to organize the ideas, intuitions, mistakes, and insights we gain while building autonomous worlds to make the truth more accessible to anyone exploring with us.