The Byzantine Generals Problem was first proposed by Leslie Lamport, Robert Shostak, and Marshall Pease as part of research being conducted at NASA. The problem deals with how to define how to direct a network of disconnected units in a leaderless situation. It has been somewhat adapted to the problem of Bitcoin for this description however the original paper can be found here.
The problem defines how generals can issue commands without a centralised communication structure while remaining robust in the face of bad actors who might try to issue malicious commands to the army.
The Byzantine army is encamped outside a city broken into divisions, each controlled by a general. Generals have no means to communicate other than through messengers. There are traitorous generals in the army who will try to issue commands that prevent the loyal generals from reaching agreement on a reasonable plan forward, so the messaging protocol must ensure that message receivers can know that they are from a loyal general.
Anyone can present a message to a general claiming it to be from another general so the protocol must have a means for generals to know with certainty that any proposed moves are from another general. A cipher that demonstrates the message is from a real general is needed. In Bitcoin, Proof of Work demonstrates a node’s authority to write blocks to the ledger. This is a core element of Nakamoto Consensus.
The army sometimes becomes divided when two generals find valid moves at around the same time. It takes a short period of time for orders to be propagated so the generals may end up following divergent moves.
If the army starts moving apart, generals in the group that falls behind the front will stop what they are doing and catch up. This is what happens in a network Re-org, with the abandoned move creating an Orphan Block.
The need for generals to always be at the front of the army incentivizes the best generals to form direct lines of communication with each other leading to much faster communication. In Bitcoin, this incentive drives miners to find the best way to connect to each other, driving the Bitcoin Core Network members into forming a Small World Network with large highly connected systems. This core trends towards a Nearly Complete Graph where all nodes are connected to almost all other nodes.
Finding valid solutions to proof of work is generally limited to 6 nodes an hour so the center of the mandala trends towards a size maxima constrained by Metcalfes law. As more nodes join the competition, it becomes more expensive to maintain connections, so miners will instinctively cut ties with non-performing miners to connect with newer, more powerful nodes. This element of constant building to maintain position can be described as a Red Queen’s race where participants must continuously accelerate in order to maintain their position in the field.