Establishing trust in a simulator. Consider the displacement of a spring due to the pressure of a gas (far left), or the time taken for a dropped ball to fall (middle left). Simple models can be proposed to describe either system. The former might be modelled as an ideal gas trapped in a box by a frictionless piston held in place by a perfect spring. The latter as a frictionless body moving with uniform acceleration. Calculating the quantity of interest within either system, displacement or time, respectively, reduces within the model to calculating a square root. We thus consider four methods to perform this simulation. Building an approximation to either model system; analogue simulation. Alternatively, using an abacus (middle right) or a calculator (far right); digital simulation.
With today’s knowledge, in the parlance used in this article, we would elevate the status of the latter two simulations to computations, because of the guaranteed accuracy with which each calculation reproduces the model. Meanwhile, the former two simulatiors are not so easily verified. Importantly, they are falsifiable, e.g. by comparing one to the other. This is similar to the state of analogue quantum simulators currently used to perform large-scale quantum simulations.
However, the confidence in each simulator is a matter of perspective. It is not objective. Many centuries ago, we would only have trusted the abacus to perform such a calculation, since its principles were well understood and square-root algorithms with assured convergence were known even to the Babylonians. Once Gallileo began the development of mechanics, we might have considered the method of dropping a ball. Confidence in the simulation could have been established by testing the analogue simulator against the abacus. Nearly two centuries ago, when we first began to understand equilibrium thermodynamics, we might have preferred the gas-piston-spring method. Nowadays, we would all choose the calculator or a solid-state equivalent. This confidence is partly a result of testing the calculator against some known results, but also largely because, after the development of quantum mechanics, we feel we understand the components of solid-state systems to such a high level that we are willing to extrapolate this confidence to unknown territory. In a century, our confidence could well be placed most strongly in another system.