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.
The clock is one of the oldest human inventions,
meeting the need to
consistently measure
intervals of time shorter
than the ‘natural’ units:
the day, the lunar
month, and the year.
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 Water power was superseded by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.