Bitcoin was the first decentralized consensus protocol, but it was different from traditional Byzantine fault-tolerant (BFT) protocols. Bitcoin prioritized decentralization and liveness over safety, allowing for forks and probabilistic finality. BFT protocols, on the other hand, prioritize safety and typically stop producing blocks in the event of a network split. Bitcoin's consensus is achieved through mining and the longest chain rule. Safety in consensus means that participants agree on a chain of blocks, while liveness ensures that new blocks can be produced. BFT protocols are of interest in the blockchain context due to Bitcoin's limited transaction capacity. In this part of the conversation, Mathieu explains the security and speed considerations in Bitcoin and BFT protocols. He discusses how increasing the size of blocks in Bitcoin can degrade security and the annoyance of probabilistic finality. He also highlights the high energy consumption of Bitcoin mining. Mathieu then explains the difference between crash-resistant protocols like Paxos and Raft and BFT protocols like PBFT. He discusses the assumptions made in BFT protocols and the trade-offs between safety and liveness. Mathieu also explains the different network models, including asynchronous, synchronous, and partially synchronous, and their impact on the protocols. Finally, he provides an overview of reliable broadcast and consensus protocols, including the role of leaders and the importance of certificates. The conversation explores the complexity of view changes in consensus protocols and the renaissance of asynchronous protocols. It discusses the use of leader rotation and locking values in consensus protocols. The conversation also delves into the concept of user chains and microchains in the Linear framework, highlighting the benefits of parallel chains for scalability and fast reading from the blockchain. It touches on the idea of consensus as a service and the potential applications of Linear as a layer 2 solution. The conversation concludes with a discussion on the need for consensus in blockchains and the use of FastPay for payments and atomic swaps.