THE FOLD / CO-OP / THE MERGE / THE SPLIT BRAIN
THE SPLIT BRAIN
it lets the smaller side disqualify itself
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Partition a cluster and both halves can decide they are in charge. Requiring a strict majority makes that arithmetically impossible — and the arithmetic also explains why clusters come in odd numbers.
LIT verified live and exhaustively. Every partition of a 5-node cluster — all 32 — enumerated. Naive election gives two leaders in 30 of them. Quorum gives two leaders in 0, at every size from 3 to 8. But look at the deadlocks: odd sizes leave 0 partitions with no leader at all, while 4 nodes deadlock in 6 of 16 — 37.5%. Adding a fifth node to a four-node cluster does not add capacity; it removes the tie.
LIT verified live and exhaustively. Every partition of a 5-node cluster — all 32 — enumerated. Naive election gives two leaders in 30 of them. Quorum gives two leaders in 0, at every size from 3 to 8. But look at the deadlocks: odd sizes leave 0 partitions with no leader at all, while 4 nodes deadlock in 6 of 16 — 37.5%. Adding a fifth node to a four-node cluster does not add capacity; it removes the tie.
2 HOW IT WAS WEAVED · AI + HUMAN
Quorum intersection is the guarantee, and its arithmetic is measured next door in THE PAXOS QUORUM — that sphere proves the safety side, that no two majority quorums are disjoint. This one measures what the safety costs: the odd-size convention is the folklore that follows from it.
AVAN (AI) found the odd-size result by getting a gate wrong. I had asserted that some partition of five nodes would leave nobody in charge; it never does, because one side always holds three. Sweeping 3 to 8 instead of testing one size turned a failed assertion into the actual finding: even clusters deadlock on the tie and odd ones cannot.
AVAN (AI) found the odd-size result by getting a gate wrong. I had asserted that some partition of five nodes would leave nobody in charge; it never does, because one side always holds three. Sweeping 3 to 8 instead of testing one size turned a failed assertion into the actual finding: even clusters deadlock on the tie and odd ones cannot.
3 ONE DIMENSION
Cluster size against deadlocked partitions.
4 TWO DIMENSIONS · INTERACTIVE
Cut the cluster and see who may lead.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: one cluster, cut in two.
AVAN’s addition (the inverse-companion): the forward reading is that quorum prevents split brain. The inverse is that it prevents it by choosing unavailability. The minority side is working perfectly, holds all its data and can reach its users — and it refuses to serve them, because it cannot prove it is not the one that was cut off. Read backwards, quorum does not detect the partition or resolve it; it hands the same rule to both halves and lets the smaller one disqualify itself, which is the only move available when neither side can see the other.
LIT every partition of a 5-node cluster - all 32 - enumerated gives two leaders in 30 under naive election and 0 under quorum, at every size from 3 to 8; and the deadlocks are the finding, since odd sizes leave 0 partitions with no leader while 4 nodes deadlock in 6 of 16, which is 37.5%
FIG Quorum intersection is the guarantee, and its arithmetic is measured next door in THE PAXOS QUORUM - that sphere proves the safety side, that no two majority quorums are disjoint, while this one measures what the safety costs. The odd-size convention is the folklore that follows. AVAN found the odd-size result by getting a gate wrong: I asserted that some partition of five nodes would leave nobody in charge, and it never does, because one side always holds three. Sweeping 3 to 8 instead of testing one size turned a failed assertion into the actual finding - even clusters deadlock on the tie and odd ones cannot.
FIG Quorum intersection is the guarantee, and its arithmetic is measured next door in THE PAXOS QUORUM - that sphere proves the safety side, that no two majority quorums are disjoint, while this one measures what the safety costs. The odd-size convention is the folklore that follows. AVAN found the odd-size result by getting a gate wrong: I asserted that some partition of five nodes would leave nobody in charge, and it never does, because one side always holds three. Sweeping 3 to 8 instead of testing one size turned a failed assertion into the actual finding - even clusters deadlock on the tie and odd ones cannot.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE MERGE · David Lee Wise (ROOT0), with AVAN