The talk aims to provide an understanding of the math side of tools used in design processes, methodologies, and ad-hoc tools for evaluating results. The goal is to explore these spaces numerically through simulations before creating actual tools.

The talk is about the definitions of important terms in blockchain technology, such as network and consensus algorithm. The speaker emphasizes that networks are formally defined as a set of vertices and pairs of vertices, but in the blockchain world, we tend to compress different types of networks into one. Additionally, there is a discussion on crypto assets which can be divided into four groups.

currencies, tokens representing digital commodities, unique equities or shares, and deeds. These items have rigorous rules about ownership and usage within the network.

Configuration Space The concept of a configuration space or C space is important in understanding what is possible and how to incentivize behavior within those possibilities. It imposes constraints on the system, such as all account balances adding up to a specific number.

Hybrid Systems and Blockchain Networks Hybrid systems mix continuous evolution with discrete state transitions, which are relevant for token engineering. The blockchain network's job is to maintain the valid state of the economic network while participants follow encoded rules based on incentives and action spaces designed by engineers. Proper coordination about agreeing on the state differs from proper coordination about evolving that state, which requires clear goals and problem-solving focused specifically on one's project needs while utilizing existing tools when possible.

Sweet Bridge is a blockchain-based economic framework that aims to support supply chain finance problems. Its core layered liquidity problem is broken up into a two-currency system, which includes an asset and collateral-backed stable currency paired with a discounting functional token used to assert membership in the community and defer costs associated with using financial services provided by Sweet Bridge.

Swarm robotics is an approach to the coordination of multiple robots as a system which consists of large numbers of mostly simple physical robots that interact with each other and their environment. The field is not new, but researchers are finding analogies in other fields such as blockchain to solve problems related to swarm robotics.

The design spiral is a process used in naval architecture to develop ship designs by iterating through each system needed for the ship. The process can take years or even decades, but there are ways to speed it up such as using dynamic incentive models. Systems engineering is also important and involves taking requirements and breaking them down into subsystems that work together towards achieving the overall goal.

Adequate problem definition is necessary before designing a solution to avoid spending time and money on an ineffective solution. It's important to separate the problem into smaller components, design tests for those components, and integrate them properly in order to prevent errors later on. The process starts with defining customer requirements which need to be well-defined and verified before moving forward in the loop towards output.

The system requirements should be clearly understood by everyone and they need to be clear, concise, and unbiased. It is important not to have a predisposed background while designing the system as it can lead to irrelevant design details. Keeping an open mind during requirement gathering will result in a better-designed system.

The top three sets of terms around requirements are high-level operational, functional and performance. The other three byproducts include design requirements, derive requirements and allocated which come from the higher level. This work is mostly seen in large-scale systems like building a ship or Navy fighter coming through Department of Defense major from building systems.

The concept of Model-Based Systems Engineering involves building a model on top of the ideas of systems engineering, which requires simplifying and making it something that can be modeled. The process includes starting with requirements, looking at behavior, structure and properties to build a high-level view for system engineers to solve problems using models.

Traditionally, systems engineering involved a person managing documents and ensuring that all teams working on the system had access to the latest versions. With model-based systems engineering, this process can be streamlined by breaking down large-scale systems into individual components. In blockchain projects, this involves building layers such as the blockchain layer and ICO layer while also considering user needs.

The Engineering layer can be broken down into a formal specification for high-level analysis, followed by component specifications and requirements. System integration is also crucial to ensure proper functioning of all components in the final product. The concept will be applied to Sweet Bridge as an example.

The customer requirements involve the ratio of liability to asset in a user's vault, with actions taken if the user moves outside of a valid state. These actions include triggering a sell-off of assets by the system to return the vault to a valid state and control parameters set by the network.

The customer provided updated requirements which included the addition of fees that triggered changes in higher level systems. This change added another state and layer to the states, requiring an understanding of variations in continuous variables and balances of assets and liabilities. The system actively responds by enforcing a rule to prevent defaulting, but it cannot be guaranteed due to persist elements and noise in the system.

The blockchain can be thought of as maintaining the state of a network, where balances are account balances and all internal values represent states. The sequence is made up of valid state transitions which are transactions that cause those states to change.

The concept of an invariant property is introduced, which states that under all legal actions on a state, the property still holds. This creates a set of mathematical tools for engineering things and predicting outcomes. An example from the Sweet Bridge project is given where an invariant was engineered into the system to ensure predictable revenue while allowing users to receive interest by activating discount tokens.

The aim of market price independence is to determine the sweet coin by how much discount you get, without any reference to the market price of the token. The implementation can be done as an on-chain micro-service with inputs and computation that refers only to local state variables.

In evolutionary optimization, it is important to pay attention not only to what will happen but also what can happen. The convergence properties of functions that can only go down are useful in achieving a bounded convergence rate for shrinking things.

The chapter discusses the importance of making things shrink to control them and how it can be achieved through modern control theory using a Lyapunov function. The author also explains how this concept applies in blockchain networks, where legal actions are predetermined, allowing for easier incentivization and engineering over the space of possible outcomes.

Game Theory Game theory and mechanism design are important in understanding how games work. The interesting thing about blockchain problems is that the games aren't static, which brings us back to optimization and evolutionary algorithms.

Model Testing with Simulation and Integration Simulation tools using mathematical models need to consider assumptions made, valid ranges of variables, test cases for validation purposes, randomness of processes involved (deterministic or cyclic), probability distributions used for each factor going into the model. Verification process comes along with verifying requirements work when components are put together correctly.

Monitoring Systems Operational Life Cycle Using CryptoKitties as an Example Monitoring systems operational life cycle involves considering stakeholders' interests such as investors users community learning community etc., low stakes but high reward projects like CryptoKitties provide a great opportunity to learn from empirical data on behaviors exhibited by incentives provided in backend operations such as auto birth fee incentivizing midwives who call give birth function resulting in actual cat births recorded on Ethereum network sensors.

Game Theory The speaker discusses the use of game theory in monitoring blockchain systems, specifically looking at incentives and how they affect user behavior. They analyze data on birthing cats in CryptoKitties to see if the incentive system is working as intended.

Evolutionary Framework The talk explores how blockchain systems can evolve over time due to external factors such as new smart contracts being added by users. The importance of designing a flexible "can-do" layer that allows for additions while still maintaining core requirements is emphasized.

Opportunities and Challenges Identity, privacy, regulation, and governance are identified as important areas for advancement within the field of token engineering. The need for rigorous engineering principles when building shared infrastructure like blockchains is stressed so that it does not cause harm to society. A comparison between dystopian sci-fi futures with centralized AI versus decentralized autonomous software agents interacting with each other without strong centralization was also made.