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p. 182. The age of gravity – time for workfree

  • David Blockley

Abstract

‘The age of gravity — time for work’ looks at the development of the concepts of force and time, and how these affected the earliest tools which worked against the force of gravity. From prehistory up to Newton, science aimed to make sense of the world through the notions of mythos (stories which explained natural phenomena) and logos (rational thinking). These concepts were originally intertwined, but gradually separated. At the time of Newton, engineering began to emerge as a separate discipline. Mathematical developments led to the discovery of a link between force and acceleration, and the development of groundbreaking theories by Newton and Galileo.

What have a child's swing, a golf club, an opera singer, a flute, a radio, and a bridge got in common? The answer is timing – getting the best out of something with the least input of work. Imagine pushing the child's swing – you quickly learn timing, i.e. when to shove for maximum effect. In effect, you tune yourself to push the swing at what scientists call its natural frequency, i.e. the number of times it goes back and forth in an amount of time (usually minutes or seconds) when swinging freely. Your pushes are (an external stimulus) timed to produce resonance (a large amount of swing or amplitude of vibration) because you are pushing at a frequency close to the natural frequency of the swing.

A golf club has a natural frequency too. If a golfer, teeing up for a shot, can match his swing with the natural frequency of his club as it flexes in his hands, then he will have a ‘sweet’ shot – something all amateur golfers aspire to and talk about when it happens. He will use the elasticity of the club to transfer the energy of his back swing into the ball with maximum effect. The same phenomenon occurs when a baseball player or a cricket batsman finds the sweet spot on the bat. You will recall in Chapter 1 that we said that an opera singer can project his or her voice even in a large concert hall whereas a ‘pop’ singer has to have a microphone. Again, it's all about timing. A trained tenor can make the sound of his voice p. 19resonate through his head and chest cavities by altering the shape of his mouth, tongue, and lips, his breathing, and the movement of his larynx. When a flute player blows air into the mouthpiece of a flute, the air in the body of the flute resonates and produces a musical note – timing again. Different notes at different natural frequencies are made by fingering over the holes in different combinations. Stringed instruments rely on the resonance of vibrating strings of different length and mass. As we shall see later in Chapter 4, when you tune a radio to a particular radio station at a particular frequency, you are actually altering the electrical impedance (opposition to the electrical current) of an electrical circuit. You do this until the circuit resonates with (is in time with) the frequency of the electromagnetic radiation being received by your aerial from your chosen station.

These are all useful examples of resonance – but sometimes resonance is a dangerous nuisance and the best timing creates the least effect. Bridge designers must design their bridges so that they do not resonate when soldiers walk in step or the wind blows because the large vibrations can cause excessive damage. The Angers Suspension Bridge in France collapsed in 1850 as 500 soldiers were marching across and 220 were killed. We want a bridge and the wind blowing onto it not to be synchronous, i.e. out of timing. Perhaps the most famous commonly quoted example was the collapse of the Tacoma Narrows Bridge in 1940. However, modern wind engineers attribute that collapse to a different but related phenomenon, called self-excited flutter from the shedding of eddies or vortices.

So timing is important in the way most tools do work. Our own idea of work is familiar – exertion, effort, labour, or toil to make a living. It is every effort we make ranging from just moving around – like getting out of bed – to hard physical exercise such as running 10 kilometres. We work when we lift a heavy weight like a shopping bag. We work when we think hard about a problem. In more abstract terms, we work whenever we make a change of any p. 20kind. It is easy to see that when we push a child's swing, sing opera, or play a flute, we are doing work – but the kind of work being done in a radio or a bridge is not so obvious. In this and the next chapter, we’ll see how a bridge does work against gravity as it carries traffic over a river, and in Chapter 5 we’ll examine electromagnetic work in a radio.

In STEM (science, technology, engineering, and mathematics), work is defined precisely and objectively so that it is unbiased and independent of personal opinions. Work is the product of force and distance. So if you lift a mass of 1 kilogram (which has a weight of approximately 10 newtons) through 2 metres, then the work you do is 20 newton metres, or 20 joules. In the past, before the widespread adoption of SI units, the work that engines were capable of doing was compared with the work that horses could do – hence the term ‘horsepower’. Various people came up with various equivalences, but the modern agreed definition is that 1 horsepower is 746 joules per second or 746 watts. When we feel energetic, we feel ready to work – so energy is the capacity to do work and is also measured in joules. Power is the rate of expending energy or doing work. It is measured in joules per second or watts.

We will start our examination of engineering in depth by looking at some of the earliest tools that have to work against the forces of gravity, and as we do we will see how the special role of the engineer evolved. Figure 3 is a timeline to help you keep track of the order in which things happened. In Chapter 3, we will look at modern examples together with how we use heat to do work and work to make heat, and in Chapters 4 and 5 we will explore how we use electromagnetic work to process information.

It is impossible to know just how the first humans conceived force and time. Clearly, they would have a common sense notion of work and effort, and they would have noticed the regular movements of the Sun, Moon, and stars. The weather patterns, p. 21

3. Timeline

p. 22including thunder and lightning, must have seemed beyond humankind, sometimes welcoming (warm sunshine) and other times threatening (thunder and lightning). So they began to make up stories about natural events. Their need to feel safe from these other-worldly events drove an activity of creating stories which were the objects that served as explanations or knowledge. Such stories were mythos.

These regularities were practically useful. The nomadic hunter-gatherers needed to find food and would have modified their hunting activity as they saw how the behaviour of animals and plants was related to the movements of the Sun in the daily cycle, the Moon in the lunar cycle, and the seasons in the annual cycle. At first, they probably relied on judging the position of the Sun in the sky or shadows on the ground. By sharing that knowledge and cooperating in the hunt, they learned to be more effective at tracking animals and finding water. They learned to control fire and, as caves couldn’t be moved, they began to make tools, clothes, build huts of tree branches, leaves, straw, stones, and animal skins – objects.

Perhaps the first farmers (settled farming dates from around 10000 BC – domestication of animals around 8500 BC) used the length of shadows or a stick in the ground (gnomon) as a primitive sundial. As they began to barter their goods, they needed to know when to sow, when to harvest, when the rivers may flood. They needed to estimate the size of their fields and their crops. By 7000 BC, large buildings, or ‘longhouses’, up to 30 metres long were being built across northern Europe.

During the 4th and 3rd millennia BC, metals were obtained from ores, melted, cast, and hammered. Textiles began to be woven from flax and wool. Writing came about 3500 BC, as did the first recorded sundial found in Mesopotamia (now south-eastern Iraq). Arithmetic was being developed by 3000 BC in Egypt. The Sumerians who lived between the Rivers Tigris and Euphrates p. 23

4. Weighing scales, Luxor Temple, Egypt, 5000 BC

began to irrigate their fields with canals and ditches. In order to set these out, they needed to understand the likely water flows from these rivers to their crops.

To help all of this activity, five basic types of machines were developed in antiquity – the wedge, the lever, the wheel (including the winch and the gear or toothed wheel), the pulley, and the screw. The wedge was perhaps derived from the axe – one of the first Stone-Age tools. It was used for splitting wood and cutting stone slabs from quarries. Levers date back to prehistory and were used then, as now, for moving large objects and, for example, as hoes for cultivation, spades for excavation, and oars for rowing. Around 5000 BC, the lever, as a simple balance, was used for weighing (Figure 4). The date of the first wheel is unknown, perhaps also around 5000 BC. The winch or capstan is a wheeled drum or shaft that can be turned, by hand, using radiating spokes or handles. A heavy load is pulled by attaching it p. 24to a rope or chain wound around the drum. The ease with which a handle can be turned, relative to the heavy load being pulled, is called the mechanical advantage. In other words, it is the ratio of the output force (the heavy load) to the input force (the force needed to turn the handles) and is equal to the ratio of the radius of the spoke handle to the radius of the drum. Examples of cranes, catapults, and tread mills based on the winch date back to the 5th century BC, and improvements in the mechanical advantage of the machines were sought intuitively.

The inadequacies of sundials would have become obvious – they don’t work at night or in the shade. So by around 1400 BC, water clocks were being used. Water was drained slowly from one container to another and the water levels shown by marks on the containers used to indicate the time. A gear or toothed wheel, made in wood, is first mentioned in Egypt around 300 BC and was used as one of the ways to improve water clocks. A float was connected to a notched stick which through a gear tooth wheel turned a hand that pointed to the time.

5. Using pulleys to lift a weight

p. 25The idea of a pulley was perhaps inspired by throwing a single rope over a tree branch. A single pulley, used in ships, water wells, and the like, is shown in an Assyrian relief from 870 BC. The compound pulley (Figure 5) is often attributed to Archimedes and was given detailed treatment by Vitruvius. A screw inside a pipe used for raising water may have been part of a pump for Sennacherib, King of Assyria, for the water systems at the Hanging Gardens of Babylon and Nineveh in the 7th century BC. However, it is more commonly ascribed to Archimedes (Figure 6) but probably invented by the Pythagorean Archytas of Tarentum. Wooden screws were commonly being used by the 1st century BC in, for example, oil and wine presses. A shipwreck found near the island of Antikythera in 1900 revealed a complex analogue device of more than 30 finely tuned bronze gear wheels for calculating time and astronomical cycles, built around 100 BC, probably in Rhodes.

6. An Archimedean screw used to move grain in a flour mill, Derbyshire, UK

p. 26The period from 900 BC to 200 BC has been called the ‘Axial Age’ because it was pivotal to human development, not just spiritually but intellectually and practically. During this time, in four distinct regions, the world's great traditions came into being: Confucianism and Daoism in China, Hinduism and Buddhism in India, monotheism in Israel, and philosophical rationalism in Greece. The frontiers of human consciousness were pushed forward. It became essential to test everything empirically against personal experience. Religion was a practical matter – it was about how you behaved not what you believed. Technological developments were not simply the result of guesswork and luck. People showed a highly developed ability to observe and to learn from experience. They may have expressed their deepest thoughts in terms of mythos but their intellectual awakening enabled them to progress as need drove activity.

The ancient Greeks were deep thinkers and polytheists. From around the 8th century BC, they began to tackle the higher needs of esteem and self-fulfilment. One of their first great thinkers was Thales, born in the 7th century BC. He was a man of many talents – statesman, engineer, businessman, philosopher, mathematician, and astronomer. He suggested that the way to live a righteous life is to refrain from doing what we blame in others. He was practical – he helped an army cross a river by diverting the stream. He went to Egypt and brought some of their ‘geometrical facts’ back to Greece. He estimated the height of a pyramid by observing the length of the shadow of a pyramid at the same time as his shadow was the same length as his height. The Egyptians had rules for calculating areas of fields and volumes of crops and so on, but they had no concept of geometry as a systematic way of seeing relationships. Geometry was a Greek invention. The seeds for Western science were being sown. Bertrand Russell said that Western philosophy began with Thales. Geoffrey Lloyd said that there was a discovery of nature and the practice of rational criticism and debate. Traditional explanations that story-tellers p. 27had passed on without any real criticism now were in competition as people looked for the best explanations.

Where earlier thinkers had attributed material substances as primary things, about 50 years after Thales, Pythagoras established an esoteric sect (activity) who thought the patterns (objects) they discovered in numbers were the route to the divine (knowledge). For example, they discovered that musical harmonies depend on numerical ratios in the length of a string. The Pythagoreans thought that by concentrating on pure abstractions, they could ‘wean themselves away from the contaminations of the physical world and get a glimpse of divine order’.

The Sophists, such as Hippias of Elis, emphasized common sense and techne, a technology that would make them more effective here and now. They wanted ordinary people to take full advantage of their own potential – to forget the old fairy tales and think for themselves. Detailed and methodological observations were valued. They sought to distinguish between people with medical knowledge and magicians, quacks, and charlatans. Greek surgeons set broken limbs using a winch.

Socrates had a mission to bring his fellow Athenians to a better understanding of themselves. Almost all we know of Socrates is through the writing of Plato (around 400 BC). Plato picked up on the Pythagorean focus on abstraction through his ‘theory of forms’. A form is an archetypal essence of something beyond any actual manifestation of a reality – an abstract object. A circle is a good example since its definition is abstract and perfect, but every circle actually produced is inevitably imperfect – even if only very slightly. Over the door of Plato's academy was the motto ‘Let no one unacquainted with geometry enter here’. The ideals of mathematical form were divine. The real world was untidy – only the world of forms was perfect (knowledge). It was a dimension of reality that transcended normal experience but was entirely p. 28natural. For example, Plato's description of beauty was, as Karen Armstrong notes, similar to what others called God or the Way – absolute, unique, eternal – but beauty was only part of the Good. But Plato's aim was not religious – he wanted a rational cosmology. It was a powerful vision that when later merged with monotheistic religion would influence Western thought profoundly.

Aristotle was Plato's most brilliant pupil, who brought philosophy down to earth. Instead of seeking meaning in the immaterial world, he found it in ‘change’. Change was a universal striving for fulfilment. He explained time in terms of change and not vice versa. Human well-being lay in intelligent, clear, rational thinking – this was the way man linked with the gods and grasped ultimate truth. It was logos.

Aristotle maintained that everything is moved by something else – so there must be an unmoved mover – God. Reason demanded that a chain of cause and effect must start somewhere. Aristotle believed that the natural state of an object is at rest and that it won’t move unless acted on by a force. The earth is at rest and so a heavy body would fall to earth faster than a lighter one. He thought that velocity is proportional to the moving force and inversely proportional to the resistance, but there was no concept of velocity as magnitude as we understand it today. Motion to Aristotle was a bridge between the potential and the actual.

Aristotle, or his pupil Straton of Lampsakos, wrote the oldest known textbook. It was called Mechanika or Mechanics and talks about gear wheels, levers applied to weighing balances, and galley oars. It gropes towards an explanation of how a ship can sail into the wind and asks questions about the breaking strength of pieces of wood of various shapes. He used a primitive form of virtual velocities later explained by Hero (1st century AD) as ‘the ratio of force to force is inversely the ratio of time to time’.

p. 29In 300 BC, Euclid produced his book of geometry called The Elements, arguably one of the most important mathematical texts ever written. In it, he brought together many previous ideas and integrated them into a single system of axioms from which theorems could be proved. After Euclid, division lines of considerable accuracy could be drawn on sundials and water clocks. From Euclid to the European Renaissance, geometry was to be the only theoretical language available. In effect, geometry was the mathematical ‘spectacles’ through which, until Galileo and Newton, people made sense of the world around them. It was the theoretical language of STEM.

One of the first engineers was Archimedes (c. 287–212 BC), although that is not how he is generally remembered and he wrote little of it. Plutarch, in the 1st century AD, wrote:

Yet Archimedes possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge, that though these inventions had now obtained him the renown of more than human sagacity, he would not yet deign to leave behind him any commentary or writing on such subjects; but repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life ….

But this disapproval was from Plutarch (who was no engineer but a well-to-do country gentleman) not Archimedes himself. Indeed, Geoffrey Lloyd says Plutarch may have fabricated it.

Of course, Archimedes is well known as a scientist – chiefly through the story of him jumping out of his bath and shouting ‘Eureka’. His famous principle is that a body when immersed in water is subject to an upward force equal to the weight of water displaced – called its buoyancy. We have already mentioned the screw but perhaps his most impressive invention was the p. 30compound pulley. Plutarch reported that Archimedes boasted to King Hiero that he could move any weight. So the King and many passengers sat in one of the King's boats and challenged him to pull them along – which he did. Whatever technique Archimedes used to pull King Hiero's boat, he clearly understood the concept of mechanical advantage. Figure 5 shows a modern explanation of how a weight W can be lifted using only one-quarter of W, but Archimedes reasoned about this in an entirely geometric way. Thomas Heath described him as ‘the greatest mathematical genius the world has ever seen’. He proved the balanced lever by geometrical symmetry, and his work on the quadrature (finding areas) of curved plane figures gave birth to the calculus of the infinitesimal later perfected by Kepler, Fermat, Leibniz, and Newton.

Geometry enabled craftsmen to formulate ‘rules of thumb’ for proportioning structures. Most of our knowledge of Roman time is due to Vitruvius; his ten books of architecture were probably written in the 1st century AD. He splits Roman architecture into three parts – the art of building, of making time pieces, and the construction of machinery. He mentioned a number of different types of sundial. The books are like an early engineer's handbook. A rule for the columns of a Forum reads:

Make the upper columns smaller by one-fourth than the lower, because when it comes to bearing stress, the lower columns should be more substantial than the upper. Do this also because we should imitate the nature of growing things, as in the case of tapering trees.

Vitruvius presented in considerable detail machines such as pulleys, cranes, and methods for pulling large blocks. Of course, military war engines were very important to the Romans. A Roman legion had an architectus – master builder; mensor – surveyor; hydraularius – water engineer; and a ballistarius – catapult/artillery-maker.

p. 31After the fall of the western Roman Empire in the 5th century, much of ancient learning was protected by the eastern Romans or Byzantines. During this period, Europe was dominated by the Church. The pagan Greek attitude had been that manual work was degrading. The Christian religious view, led by St Benedict and St Augustine in the 6th century AD, was that work was an obligation. That didn’t stop the monasteries from using more and more machines to release time for contemplation. The light ploughs used in the drier soils of southern Europe were no use in the heavier soils further north. The wheeled heavy plough had a sharp blade to cut a furrow, a share to slice under the sod, and a mould board to turn it over. Eight oxen were needed but were eventually replaced by the horse. The ox harness pressed on the throat and not the shoulder blades of the horse and so the poor beasts were unable to work efficiently. It wasn’t until the 6th century that the breast strap was introduced, and the padded horse collar around the 8th century. Horseshoes were needed in the wet soils of the north. The stirrup was unknown to the Greeks and Romans. Lynn White wrote: ‘Few inventions have been so simple as the stirrup, but few have had so catalytic influence on history.’ The stirrup gave the horserider lateral support and revolutionized his ability to fight on horseback. It was important in the development of feudalism with a new nobility that challenged the power of the Church. Other improvements included the three-field system of agriculture. One field lay fallow whilst the crops in the other two were used. The next year, the uses were rotated. Yields increased by as much as 50%. The water clocks and water wheels described earlier by Vitruvius were improved, as were windmills, canal locks, and mining. In the UK, by the time of the Domesday Book in 1086, 5,624 water mills were recorded south of the Rivers Trent and Severn.

In the meantime, by the 7th century, much of the Mediterranean was taken by the Arab Muslims. The result was an Islamic golden age or renaissance which lasted from around the 8th century to the 13th century and beyond. Centres of learning were established and p. 32Greek texts were copied into Arabic. There was a melting-pot of numerous cultures with important developments in the arts, agriculture, economics, industry, law, science, technology, and philosophy. The library at Cordoba had 600,000 titles by AD 900. Empirical experimentation was not frowned upon. Although religious belief was strong, mythos and logos were compartmentalized in a way that was to the advantage of practical life. Many of our modern words, such as algebra (Arabic al-jabr) and alcohol (al-kuhl), derive from this time. The Arabs developed gunpowder and paper (from China), the horse collar, windmill, water wheel, and Arabic numerals. Thinkers such as al-Kindi, al-Biruni, Avicenna, Avernpace, and Averroes introduced Greek ideas into Arabic and developed them. The Muslim thinkers realized Aristotle's physics was inadequate and proposed new ideas which sowed the seeds for work in the 13th century to explain the acceleration of freely falling bodies and the continued velocity of projectiles. For a variety of complex reasons, the Muslim golden age faded and the initiative shifted to northern Europe.

Adelard of Bath had translated Euclid from the Arabic in 1120, though there is evidence that some of the work was known in Europe from the 9th century. No one entering one of the famous Gothic (beginning in 12th-century France) cathedrals, such as the one in Gloucester, could fail to be impressed by the sheer magnitude of the structure. The numerical rules of proportion were formulated as a result of trial and error, taking note of structural success, and perhaps more importantly, of failures. John Fitchen pointed out three-dimensional models were also used during the construction of cathedrals. The architect, the structural engineer, and the contractor were one. Apprentices were trained through the guilds and the more capable became master builders. They were really masters of all phases of the work but, with only a few exceptions, had modest social standing.

Ailnolth (1157–90) was one of the first men to be called an engineer. French was the language of the upper classes in p. 33England, so he was called an ingeniator. ‘He was a versatile man – a craftsman of technical training … accustomed to making the great war engines which preceded the use of gunpowder.’ By the time of the reign of Edward III (1312–77), the men who looked after the firearms were known as artilators or ingeniators.

The Renaissance marked the beginning of a new era, with an immense change in attitudes. Men such as Brunellesco (1377–1446), Alberti (1404–72), Michelangelo (1475–1564), and Leonardo da Vinci (1452–1519) were typical of the versatile men of this period. They were artist-engineers – people who started studying, learning Latin and mathematics – becoming cultivated. Leonardo da Vinci was one of the first to be appointed as an engineer. He was Ingenarius Ducalis (the Duke Master of Ingenious Devices) to the Duke of Milan, and Ingenarius et Architectus to Cesare Borgia. Leonardo was the archetype of the Renaissance man. He is one of the greatest painters of all time and his talents covered science, mathematics, anatomy, sculpture, botany, music, and writing. Paolo Galluzzi, Director of the Istituto e Museo Nazionale di Storia della Scienza in Florence, said that between the end of the Roman Empire and before Leonardo the role of the technical worker was generally anonymous. Beautiful buildings were made but the name of the builder wasn’t recorded. The intellectual and social distinctions were strong – being trained in the mechanical arts meant that someone who worked with their hands was fit only to work under the direction of someone who was better educated. By the 14th century, people started to use their brains and their brawn.

But still the only theoretical language available was geometry. It is difficult for us in the 21st century to realize that there was no concept of velocity as a magnitude – even by the 14th century. To the Greeks, a magnitude could only come from the proportion of two like quantities such as the ratio of two distances. Velocity and speed involves a ratio of unlike quantities – distance and time. The defect of Aristotle's physics was its failure to deal with p. 34acceleration. Thomas Bradwardine and others at the University of Oxford in the 14th century made explicit the ratio of unlike quantities and hence paved the way for velocity and acceleration. They argued that a body moving with uniform velocity travels the same distance as a constantly accelerating body in the same time if that uniform velocity is half of the final velocity of the accelerating body. Nicole Oresme at the University of Paris showed how these ideas could be represented on a graph with time on the horizontal axis and speed on the vertical axis so that distance is the area of a rectangle or triangle. Jean Buridan, also in Paris, suggested the idea of impetus, which he said was the quantity of matter multiplied by its velocity – an anticipation of the modern concept of momentum. Both of these ideas influenced Galileo.

Galileo Galilei (1564–1642) has been called the father of modern science both by Albert Einstein and Stephen Hawking. One of his first pieces of technology was the telescope. He didn’t invent the idea, but he did develop it and then proceeded to look at the heavens. The moons of Jupiter weren’t fixed but seemed to be orbiting around the planet. Galileo saw what was implicit in the earlier ideas from Oxford and Paris that the distance travelled during a uniform acceleration starting from rest is proportional to the square of the elapsed time. He rolled balls down an inclined plane and timed them using a water clock. He used geometry to conclude that objects move at a given velocity unless acted on by a force – often friction. This was against Aristotle's idea that objects slow down and stop unless a force acts upon them. Galileo stated: ‘A body moving on a level surface will continue in the same direction at constant speed unless disturbed.’ This was later incorporated by Newton in his first law of motion. Galileo got very close to distinguishing between weight and mass but was unable to make it clear since weight was still seen as an intrinsic downward tendency not depending on an external relationship with another body – an idea that was later to be generalized by Newton in his theory of universal gravitation. Galileo did decide p. 35that what persists in motion is the product of weight and velocity which he called impeto or momento – our modern idea of momentum.

In 1635, Galileo suggested using a pendulum to keep the time, and in 1656 Christian Huygens in Holland built one. These pendulum clocks were much more reliable, so that by the 1700s clocks were beginning to replace sundials. They didn’t require sunny skies but often had to be reset from a sundial.

When Galileo was forced to recant, during the Inquisition, his book favouring the Copernican theory that the Sun, not the Earth, was the centre of the universe, he turned his attention to mechanics and published Two New Sciences. In it, he considers the tensile strength of a bar, the strength of a cantilever, a beam on two supports, and the strength of hollow beams. Naturally, his solutions are important, but not correct. He assumes, for example, that the stress distribution across the root of the cantilever is uniform, and because he has no concept of elasticity he assumes a constant distribution of stress across the section, right up to the point of collapse. However, he does come to the correct conclusions about the relative importance of the breadth and width of the rectangular cross-section.

Sir Isaac Newton (1643–1727) was the man who really connected time and work. He is arguably one of the most influential men in history. His name is synonymous with classical mechanics. He described universal gravitation and three laws of motion which dominated the scientific view of the physical universe for three centuries. He stated the principles of conservation of momentum. He built the first practical reflecting telescope and developed a theory of colour based on his observation that a prism decomposes white light into the colours of the visible spectrum. He formulated an empirical law of cooling and developed differential and integral calculus at the same time as Leibniz. Newtonian mechanics came to be regarded as the most perfect p. 36physical science, and an ideal towards which all other branches of inquiry ought to aspire.

So here at last, we have the relationship between time and work that has served engineering on Planet Earth since Newton and will continue to do so unless we are ever called to build anything that will travel at a speed approaching the velocity of light. From bridges and buildings to aeroplanes and space rockets, Newton's laws are the basis of everything that we have done and much of what we have yet to do.

Three observations are pertinent. Firstly, from pre-history to Newton, science was about trying to make sense of the world around us – it was both mythos and logos. Between Augustine (5th century) and Thomas Aquinas (13th century), truth became not a reflection of God as much as a relation of things to each other and to man. Their relationship to God was left to theology. Men such as the Venerable Bede showed practical curiosity. By the 12th century, Robert Grosseteste was writing that it was not possible to arrive at absolutely certain knowledge of cause and effect, but it was possible to approach a truer knowledge by making deductions from theories and then eliminating those whose consequences were contradicted by experience. A gradual separation of mythos and logos had started with the Greeks but was never complete – but nevertheless, the seeds had been sown. After Galileo and Newton, as we will see in the next chapter, science turns into the much more modern idea of ‘making sense of the world through systematic rational thinking, observation and experiment in order to understand and make testable predictions’.

Secondly, by this time engineering was emerging as a separate discipline. Many of the great figures from Thales, through Archimedes, to Galileo and Leonardo were driven not only by a need to understand but also to help with practical requirements – military and agricultural. But the separation of technics and science was never as complete as sometimes is p. 37supposed. Francis Bacon writing in 1605 said that the mechanical arts had flourished because they were firmly founded on facts and modified in the light of experience. The Middle Ages saw some remarkable technical progress, with new methods for exploiting animal, water, and wind power, inventions such as the mechanical clock and improved magnifying lens. All were in response to clear human needs. The telescope, microscope, thermometer, and accurate clock were later indispensable for the testing of new ideas. The notion that the purpose of science was to gain power over nature was being expressed.

Thirdly, until the 14th century, the theoretical language of mathematics was arithmetic and Euclidean geometry. Only ratios of like quantities were admitted. So, for example, Archimedes, who was arguably the most successful at using mathematics in experimental inquiry, relied on the symmetry of ratios to analyse the balanced lever. Jordanus de Nemore in the 13th century very clearly used virtual displacements but with geometry. The Aristotelian notion of power, velocity, and resistance could not be modelled. As soon as ratios of unlike quantities were used to model velocity and acceleration, a new mathematics of change and motion began. The realization that force was related to acceleration led quickly to Galileo's inertia and Newton's gravitation theory.

In articulating Archimedes’ disdain for ‘mere trade’, Plutarch had reflected the Greek philosophers’ (particularly Plato's) attitude that derived from the search for perfection. Two major consequences followed. Combined with monotheism very powerful religions emerged. Science came to be regarded as mere discovery and clearly separated from the individual creativity of art.

But how have these three laws formulated by Newton enabled us to engineer big bridges and send rockets into space? That is the story of modern engineering which we now move on to in the next chapter.