Capacities Multiply

Systems that last — cells, firms, markets, ecosystems, machines that learn — are usually analysed by adding up their strengths. This paper proposes that their capacities multiply instead. A weak capacity then caps the whole, however strong the others are. The gain from coupling and the risk of collapse both live where capacities meet, and additive methods are blind to both. The paper calls the space of such coupled capacities Pattern Space. It proposes five coordinates for it: structure, dynamics, growth, feedback and direction. Under named assumptions it gives a bound on the expected gain from analysing coordinates together, and it suggests readings that show a multiplicative state approaching collapse while there is still time to act. Each claim is graded as shown, consistent with the evidence, or open. The evidence so far is summarised, including tests that failed. It ends by setting out the kind of test that would tell a product apart from a sum or a threshold.