The Aristotle Clock is a novel clockwork mechanism whose fundamental principles of operation are based on the physics of Aristotle and the Classical (“Apollinian”) world rather than those of Galileo and Newton (“Faustian”).1 Whereas Faustian mechanics assumes frictionless operation in the vacuum of space, Aristotelian physics practically requires immersion in a viscous medium.2
The purpose of any mechanical clock is to produce a repeatable event that takes the same amount of time even as the quantity of energy in the system varies. It’s possible to build a clockwork that obeys none of the principles of Faustian physics and operates effectively only when immersed in a fluid medium. Water clocks and hourglasses create events of a fixed duration without relying on Galilean physics, but they do not allow for the repetition necessary to measure indefinite periods of time.
The Aristotle Clock works by leveraging buoyancy and viscosity (which are completely absent in a vacuum) to turn a small change in the density of a body into a motion with a predictable velocity (generally the terminal velocity of that body in the medium). A slightly negatively buoyant body is immersed in a fluid (such as water), sinking at a constant rate. When it reaches a certain depth, its weight depresses a valve which allows for a compressed, less-dense fluid (e.g. air) to enter into the body, which causes the body to expand. The density of the body decreases as the body expands (to a fixed volume), such that the body is now slightly positively buoyant. The body begins to rise at a predictable rate—when it reaches a certain height, its buoyancy depresses another valve which allows the compressed, less-dense fluid to escape the body, and springs pull the body back to its original volume, at which point it begins to sink again, and the cycle repeats. The Aristotle Clock is recharged (the way that a traditional clock is wound) by increasing the pressure of the less-dense fluid, for instance using a compressor (Fig. 1).
Conventional mechanical clocks rely on small oscillations about a local minimum in the potential energy of the system, such that the restoring force of the mechanism is proportional to the distance of the system from that minimum (since at a minimum the linear term of the Taylor series expansion of an arbitrary potential energy function vanishes, so the lowest-order term that varies is quadratic in position, and F = −dU/dx = −kx, the solution to which is a sinusoid with a constant oscillatory period). With such clocks, fluid resistance disrupts the operation of the mechanism and generally reduces accuracy, since in the presence of this resistance the restoring force depends on the speed of the mechanism rather than merely the displacement from equilibrium. Indeed, most clocks are designed to operate in an environment as close to a vacuum as possible (and the clock is designed to minimize this effect, for instance in the aerodynamic shape of a swinging pendulum).3
The clock’s timing varies mainly with the time the body takes to reverse direction and to fill or empty. It is a strict requirement of the design that the less-dense fluid be much less dense than the surrounding medium: then the change in the buoyancy won’t depend on the energy source (the pressure of the compressor, etc.). The time taken in the sinking and the rising must be significantly longer than the time taken for the body to reverse direction, which is inherently more variable. But as a pendulum clock may be made more accurate by increasing the length and mass of the pendulum, the Aristotle Clock may always be made more accurate simply by increasing the distance through which the floating body moves.
Fortunately, Aristotle tells us that the speed of the “natural motion” of a body is, within a certain physical regime, constant, increasing with the body’s weight in the fluid and decreasing with the fluid’s resistance.4 With near-neutral buoyancy, the floating body 1) moves slowly and 2) changes direction quickly and easily (e.g. with inelastic collisions). An object immersed in a dense and viscous fluid will accelerate due to its buoyant force until the fluid resistance—which grows with speed—balances it out. In such a fluid, the “terminal velocity” of a rising/sinking body is soon reached, and the body will travel at a constant speed.5 The smaller the net buoyant force, the slower the speed of operation and the smaller the clock may be while maintaining a given standard of accuracy.
A variation in the design of the Aristotle Clock, developed by Carl Boyer, increases the accuracy significantly by employing two cylinders linked so that when one reaches the bottom, it releases the other to sink (Fig. 2). Each cylinder rises and then waits at the top, so the period is set only by the time each takes to sink, and variations in rising, filling and venting don’t affect it.