ES1210: Learning from the Renaissance

Week 6: On Clocks, Analogues, Algebra, and Algorithms.

Definition: a clock is an instrument used to indicate, keep, and co-ordinate time.

meeting the need to consistently measure intervals of time shorter than the ‘natural’ units: the day, the lunar month, and the year.

The clock is one of the oldest human inventions,

The earliest devices for measuring time were sundials, supplemented variously by candle ‘clocks’, incense sticks, variations on the hourglass idea, and water clocks. Many of the mechanisms associated with the earliest Renaissance clocks were first developed in sophisticated water clocks.

The accuracy of the water clocks, even those using gearing as developed by Greek and Roman makers, was variable and subject to deterioration through the rapid wear of predominantly wooden moving parts. Usually calibrated by reference to a sundial whenever this was possible, they were mainly used for ceremonial, religious, and astronomical purposes. Despite these problems, a number employed an escapement mechanism and remained the most accurate means of measuring fixed lengths of time until the invention of pendulum-based clocks following Galileo’s discoveries.

Taken together, the water clock and the pendulum clock effectively bracket the Renaissance period in Western Europe, i.e., from the last third of the 1300s to the last third of the 1500s.

The first mechanical clocks were employed as a means to regulate the ringing of bells, and with some accuracy. Even those introduced during the late 1300s typically lost no more than some 15 minutes a day. Water power was superseded by the use of weights, but an additional mechanism was needed to regulate the speed with which the escapement operated. Initially, this was achieved either by using weights or ‘fans’ at the two ends of a centrally pinioned ‘foliot’ which rocked back and forth, slowing the rate at which the escape wheel turned. Locally, the best surviving example is the Salisbury clock (1386), recently repaired and now on show near the entrance to the cathedral.

(See also the short video on the module outline.) At Salisbury, as elsewhere, the possibility of moving the weights was used to adjust the length of the canonical hours to match the changing hours of daylight – time flowed faster in the winter.

Apart from signalling the time for ceremonial and religious services, this clock mechanism was soon adapted to drive two additional forms of analogue model: moving automata which often accompanied the ringing of the bells, and models of the solar system. The latter, initially at least, simply automated the movement of the metal plates used in astrolabes – widely used devices for measuring the timing of astronomical events.

(Richard of Wallingford’s clock of 1336 had a large dial based on an astrolabe design showing the sun, the moon’s phase, a star/planet map, a wheel of fortune, an indicator of the tide level at London Bridge, and bells which rang every hour, the number of strokes indicating the hour.)

The earliest mechanical clocks, even if they did have a dial to ‘tell’ the time, did not give any indication of minutes or seconds. But by the end of the 1400s such features became more common. Springs began to be used to drive the mechanisms of smaller, domestic and portable clocks. These involved a further mechanical refinement to maintain the accuracy of time measurement while the motive power transmitted by the spring declined as it unwound.

So much for the mechanical history – but our interest in the Renaissance rests on the identification of general principles that informed subsequent developments within culture, and the educational domains these entailed. Physics in general, and metallurgy in particular, were an essential part of the story; but so was the huge shift in social economics which occurred during this period. At its start the working day was fixed by the seasons and the passage from day to night, at its end time was money, and man-made time had started to supersede ‘natural’ time. Again, at its start, time only existed locally, within the nearest abbey cloister, at its end, the idea of a single, universal time was conceived.

The educational domain featured in the rest of this presentation is, generally, that embodied in all of these devices: mathematical logic, which leads in turn to the science which underpins the modern development of computing.

At the start of the Renaissance, only a few representations of number had survived the centuries of monasticism; by its end, algebra and the use of our present system of arabic numerals had spread throughout Europe. Analogue mathematical models could now be represented systematically and algorithms used to describe their operations, i.e., the necessary conceptual foundations for later science were laid.*

* Réne Descartes published his La Géométrie in 1637, in so doing introducing analytic geometry and a modern algebra, but this work rested on that of the Arab scholars – so where did they get their algebra? In part, they generated it themselves, but at the height of their expansion they were able to pool the resources of a number of other civilisations – mainly as a result of their extensive trading practices. The discovery of a way of representing indeterminate relational structure can be traced as far back as the Babylonians. Scholars in Greece and India extended these findings (trading again featured) – towards a geometric algebra in Greece, and a means to solve quadratic equations in India. Persians also contributed new techniques and, via the Silk Route, there were also links with Chinese

mathematics.

By way of a transition, consider the following abstract generalisation of a clock’s function provided by Wikipedia:-

The older clocks relied on a continuous process – the movement of the sun, the emptying of a reservoir of water, etc. All modern clocks use repetitive oscillatory processes.

All modern clocks have analogous parts:-

They have an object that repeats the same motion over and over again, an oscillator, with a precisely constant time interval between each repetition.

Attached to the oscillator is a controller which sustains the oscillator’s movement by replacing the energy it loses to friction and converts its oscillations into a series of pulses.

The pulses are then added up in a chain of counters to express the time in units.

An indicator displays the results in human-readable form.

To continue, see the webpages attached to the module outline featuring Max Black and David Harel. The prospect of science at the end point of the Renaissance is clear. Parallel to the development of an abstract, flexible language – a revised mathematics – there was a growing respect for facts that had been established by valid experiments – and parallel to this there was also a growing proficiency in forms of public address that could accurately communicate these findings. The Novum Organum of Francis Bacon, together with his utopian fantasy, A New Atlantis, look forward to the early modern period – a period in which science and technology increasingly modify the form and conduct of social life.