It seems probable to me that God in the beginning formed matter in solid, massy, hard, impenetrable, moveable particles, of such sizes and figures, and with such other properties, and in such proportion to space, as most conducted to the end for which he formed them.

—Isaac Newton, Query 31, Book 3, Opticks (1704)

THE NEW WORLD OF SCIENCE

Historians still debate the causes of the dramatic upheaval in human thinking that took place in the seventeenth century called the scientific revolution. Some, a minority, even dispute that it was a revolution. The common wisdom is that the scientific revolution replaced the magical thinking and superstition of the medieval age, in which knowledge was primarily based on revelation and sacred authority, with rational thought founded on observation and experiment. However, most historians today say, as experts on anything always say, the truth is more complex.

The natural philosophy that originated in Greece continued into the Middle Ages, mainly in the Arabic empire.1 Meanwhile, most secular intellectual endeavor in Europe sank into decline. Still, medieval Europe was not totally absent of scholars who recognized the importance of observing nature. In my previous book I described how these scholars, notably Augustine of Hippo, viewed science as the handmaiden of religion by providing knowledge of God's creation.² Several modern historians, notably the French physicist and devout Catholic Pierre Duhem (1861–1916), claimed to see continuity between medieval scholarship and what is generally referred to as the “paradigm-shift” of seventeenth-century science.³

Some apologists have even gone so far as to argue that Christianity was the source of modern science.⁴ However, this hardly jibes with the historical fact that Greece and Rome were well on their way to science, as we know it today, until the fourth century, when the emperor Constantine (272–337) empowered Christianity and it became the state religion. The Catholic Church then proceeded to systematically eliminate alternative religions of every variety, including various polytheisms and any competing monotheisms. These were suppressed throughout the empire, along with any scintilla of freethinking.⁵

The Dark Ages roughly spanned the thousand-year period from 500 to 1500, when the Roman Catholic Church dominated the Western Empire. They ended only after the Renaissance and Reformation undermined the Church's authority. During the period of Church rule, science not only failed to advance but was also set back. Surely, this is no accidental coincidence; although there is no doubt the Dark Ages were a product of many other forces and not just Church dogmatism.⁶

Nevertheless, recent scholarship has confirmed that a few scholars in the fourteenth century had already developed several of the basic mathematical principles of motion that were later to be rediscovered and fully implemented by Galileo Galilei (1564–1642) and Isaac Newton (1642–1727). A French priest, Jean Buridan (ca. 1300–1358), introduced the concept of impetus by which a projectile remains in motion unless acted on by a contrary force. He defined impetus as the quantity of matter in a body multiplied by its velocity. Today we call this momentum (mass × velocity). However, Buridan regarded impetus as the cause of motion, while the mechanics of Galileo and Newton recognized it as a measure of motion that requires no cause.7

Also in the fourteenth century, a group of English scholars at Merton College, Oxford, called the “Oxford Calculators,” were developing the mathematics of uniformly accelerated bodies, including the law of falling bodies, that is usually attributed to Galileo.⁸ The Oxford Calculators made a distinction between dynamics, which is the cause of motion (or, as we now say, changes in motion), and kinematics, which is the effect. They also made a clear distinction between velocity and acceleration. The group included Thomas Bradwardine (ca. 1290–1349), who later became archbishop of Canterbury. Like Buridan, the Oxford Calculators were mostly churchmen.⁹

Some of the other factors that are normally attributed to the rise of science but were already present in medieval scholarship include: (1) the application of mathematics to physics and (2) the use of the experimental method.¹⁰

However, these advances did not have significant impact until Galileo pointed his telescope to the heavens and performed experiments on the motion of bodies that demonstrated the superiority of observation over revelation or pure reason. These observations, of the sky and in the laboratory, revealed a physical world that bore little resemblance to the commonsense notions of the rest of humanity. As early twentieth-century philosopher Alexander Koyré put it:

What the founders of modern science, among them Galileo, had to do, was not to criticize and to combat certain faulty theories, and to correct or replace them by better ones. They had to do something different. They had to destroy one world and to replace it by another. They had to reshape the framework of our intellect itself, to restate and to reform its concepts, to evolve a new approach to Being, a new concept of knowledge, a new concept of science—and even to replace a pretty natural approach, that of common sense, by another that is not natural at all.11

Koyré asserted that the modern attempt by Duhem and others to “minimize, or even to deny, the originality, or at least the revolutionary character, of Galileo's thinking” and to claim continuity between medieval and modern physics “is an illusion.”¹²

What Koyré refers to as “natural” above is not thinking materialistically, as we make the connection today, but rather thinking commonsensically. Common sense is the human faculty for forming concepts based on everyday experience, such as believing the world is flat. The everyday experiences humans had until the seventeenth century led them to view themselves at the center of the universe. The experience of looking through a telescope resulted in a radical new concept of the universe, one in which Earth moves around the sun and the universe has no center. If anything, the history of science is marked by the continual overthrow of common sense. Today, over a century after they were first proposed, we still have trouble reconciling relativity and quantum mechanics with common sense.

As we have seen, Aristarchus of Samos proposed the heliocentric model of the solar system two centuries before the Common Era, but this knowledge was largely forgotten in the Dark Ages. When reintroduced in the sixteenth century by Nicolaus Copernicus (1473–1543) and advanced by Galileo, it was not immediately established as any better than the ancient geocentric model of Claudius Ptolemy.

I need not repeat the oft-told story of Galileo's trial by the Inquisition in 1615.¹³ He had been ordered by Church authorities not to teach the Copernican model as fact but simply as a calculational tool. Convicted and sentenced to (a very comfortable) house arrest for life, and technically forbidden to do any further science, Galileo nevertheless proceeded to lay the foundation for Newtonian mechanics in his Discourse on the Two New Sciences, published in Holland in 1638.

GALILEAN RELATIVITY

Commonsense experience leads us to take for granted that we can tell when we are moving and when we are at rest. Galileo was questioned, quite reasonably, if Earth moves, why don't we notice it? His answer became one of the most important principles of the new physics: motion is relative.

A skeptical cardinal might have proposed the following experiment to Galileo: “Go up to the top of the Tower of Pisa and drop a rock to the ground. Using your own formula h = gt² / 2, where g = 9.8 meters per second per second (the acceleration due to gravity) and h = 57 meters (the height of the tower), the rock will take t = 3.4 seconds to reach the ground. [I have converted the units he would have used to the metric system]. If, as you claim, Earth is moving around the sun at 30 kilometers per second, then the rock should fall 102 meters away from the base of the tower because Earth will have moved that far in that time. The rock lands at the base, which proves Earth cannot be moving.”

Galileo would have insisted that, based on his telescopic observations, Earth moves (“Eppur si muove”) and, based on his experiments, the rock drops at the base of the tower. Thus, our theory of motion must accommodate those facts.

Here was perhaps Galileo's greatest contribution to the scientific revolution, establishing once and for all the superiority of observation over theory, especially those theories based on authority. Indeed, it is our reasoning—and not our observations—that is to be mistrusted, contrary to the teachings of medieval theologians who viewed observation as unreliable and Church authority as final.

So here's how Galileo solved the problem of why we don't notice Earth's motion. He introduced what we now call the principle of Galilean relativity. Let me state this principle in an updated, “operational” way that allows us to see exactly what it means and how it directly applies to the cardinal's proposed experiment.

The Principle of Galilean Relativity

There is no observation you can perform inside a closed capsule that allows you to measure the velocity of that capsule.

In the cardinal's experiment, Earth is essentially a closed capsule, since we are performing the experiment at the Tower of Pisa and not looking outside that environment. Thus, we cannot detect the Earth's motion by this experiment.

The principle of Galilean relativity implies that there is no observable difference between being at rest and being in motion at constant velocity. Today we have an advantage, not available prior to the 1950s, of flying in jetliners where we can hardly distinguish between being in motion and being at rest, except during takeoff, landing, and in turbulent air. In those exceptions, what we experience is a change in velocity—acceleration—and not motion itself.

[Technical note: the terms speed and velocity are often used interchangeably in normal discourse. In physics, the velocity v is the time rate of change of position and is a vector. That is, it has both a magnitude and direction and requires three numbers to specify. We use boldface type to designate familiar three-dimensional vectors. The speed v is the magnitude (or length, when drawn to scale on paper) of the velocity vector, indicated conventionally in italic script.]

When we are flying in an airplane, we are said to be in the plane's frame of reference. Someone standing on the ground is in Earth's frame of reference. We will have much occasion as we move the discussion into modern physics to talk about frames of reference.

Observers in different frames of reference often see things differently. If you are on a boat moving at constant speed down a river and you drop an object from the top of the mast, you will see it fall straight down to the base of the mast. Someone standing on shore, in a different reference frame, will see the object fall along a parabolic path. However, note that the two of you will still witness the same result, namely, the object landing at the base of the mast. In the time it took the object to fall to the deck, the boat will have moved ahead a certain distance; so, to the observer on shore, the object has a horizontal component of velocity exactly equal to the velocity of the boat. To the observer on the boat, that horizontal component is zero.

We can see how this follows from the principle of Galilean relativity. Suppose that instead of standing on deck, you are below in the hold, which has no portholes. You are not aware if the boat is moving or not, so you decide to find out by dropping a coin from your hand to the deck of the hold. If the coin does not land at your feet but some distance away, you will have detected that the boat is moving by an observation made solely inside the hold. This would violate Galileo's principle. You would have detected your motion inside a closed capsule. Instead, the coin will drop to your feet exactly as it would if the boat were tied up at the dock, verifying the principle of Galilean relativity.

THE PRINCIPIA

The heliocentric model was eventually accepted based on Galileo's telescopic observations but also because it proved superior to the Ptolemaic model once the data improved, thanks to Tycho Brahe (1546–1601) and Johannes Kepler (1571–1630). Kepler inferred from his own careful observations and from those of Brahe that the planets move around the sun in ellipses rather than circles. He proposed three laws of planetary motion.

Kepler's Laws of Planetary Motion

1. The orbits of planets are ellipses with the sun at one focus.
2. A line from the sun to the planet sweeps out equal areas in equal times.
3. The square of the orbital period is directly proportional to the cube of the semi-major axis of the orbit.

In January 1684, physicist Robert Hooke (1635–1703) was sitting in a London coffeehouse along with architect Christopher Wren (1632–1723) and astronomer Edmund Halley (1656–1742). They started talking about gravity. Halley asked if the force that keeps the planets in orbit could decrease with the square of distance. His companions both laughed. Wren said it was easy to reach that conclusion, but it was quite another thing to prove it. The boastful Hooke said he had proved it years ago but never made it public. Wren challenged Hooke to produce the proof in two months, but Hooke never did.14

Impatient with Hooke's failure to provide his proof, that summer, Halley went to visit Isaac Newton in Cambridge, whom he barely knew at the time, and asked the Lucasian Professor what the curve of a planetary orbit would be if gravity were reciprocal to the square of its distance to the sun. Newton responded immediately that it would be an ellipse, as Kepler had observed. Halley asked Newton how he knew that, and Newton replied, “I have calculated it.”¹⁵ Newton rummaged around, but he could not find the proof among his papers and promised to work it out again.

Unlike Hooke, Newton kept his promise. Three months later he sent Halley a nine-page treatise presenting the proof. This so impressed Halley that he personally funded the publication on July 5, 1687, of the greatest scientific work of all time, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). (Maybe you think Darwin's On the Origin of Species was greater, but let's not argue about it.)

Principia presented Newton's laws of motion and his theory of universal gravitation, from which Newton derived Kepler's laws of planetary motion. But Principia did much more. It provided the framework for the remarkable scientific achievements that followed. Perhaps the most remarkable was Halley's comet. Halley had determined that the comets that appeared historically in 1456, 1531, 1607, and 1682 were the same body, and he used the new physics to predict that it would reappear in 1759. When it did, after Halley's and Newton's deaths, few could any longer dispute the enormous power of the new science.

Three hundred years after it was glimpsed by Jean Buridan, another fundamental principle was carved in stone by Newton.

The Principle of Inertia

A body in motion with constant velocity will remain in motion at constant velocity unless acted on by an external force.

Usually this is accompanied by a similar statement for a body at rest, but by the principle of relativity there is no difference between being at rest and being in motion at constant velocity: rest is just “motion” at zero velocity in some reference frame (you can always find such a frame). So the added statement is redundant.

The law of inertia is the first of Newton's three laws of motion. All three boil down to another, more general principle, that is, the principle of conservation of momentum.

The Principle of Conservation of Momentum

The total momentum of a system of particles will remain fixed unless acted on by an outside force

where force is defined as the time rate of change of momentum in Newton's second law. Newton's third law, “for every action there is an equal and opposite reaction,” also follows from conservation of momentum.

As just noted, the momentum p of a particle is its mass m times its velocity v, that is, p = mv.16 Momentum is a vector whose magnitude is mv, where v is the speed, and whose direction is the same direction as the velocity vector. The total momentum of a system of particles is the vector sum of the individual particle momenta. Particles in a system not acted on by an external force can collide with one another and exchange momenta, as long as the total momentum remains fixed.

PARTICLE MECHANICS

Newton correctly inferred that gravity was not important in the mutual interaction of corpuscles and that other forces, such as magnetism and electricity, came into play there. He rejected the primitive notions of hooks or any “occult” quality holding atoms together to form composite bodies. He wrote:

I had rather infer from their cohesion, that their particles attract one another by some force, which in immediate contact is extremely strong, at small distances performs the chemical operations above-mentioned, and reaches not far from the particles with any sensible effect.¹⁷

The principles of mechanics originated by Galileo and Newton are, as is all of physics today, most easily rendered in terms of particles. Note I am not saying that the “true” objective reality is particles. I have already emphasized that we have no way of knowing what that true reality is. My point here is that the particle model is the easiest way to understand and describe physical phenomena.

In this model, a system of particles can be compounded into a body whose momentum is the vector sum of the momenta of its constituent particles, whose mass is the sum of the masses of the constituents, and whose velocity is the total momentum divided by the total mass (not the sum of particle velocities!).

Furthermore, nothing stops us from peering deeper into the nature of “particles” to find out if they can be best described as composite bodies in their own right. This is the reductionism given to us by the ancient atomists, which is the best model of the material world that physics has in the present day.

In 1738, Swiss mathematician Daniel Bernoulli (1700–1782) showed how the pressure of a gas could be understood by assuming the gas is composed of particles colliding with one another and the walls of a container. As we will see, a century later this became known as the kinetic theory of gases and, despite intense opposition, constituted one of the earliest scientific triumphs of the atomic model of matter.

I would like to point out an advantage of the particulate view of matter that is not always recognized and exploited. Most people have difficulty understanding the physics that underlies everyday phenomena. However, the observations we make in normal life are easily understood if you think in terms of particle interactions. We can't walk through a wall because the electrons in our bodies electrostatically repel the electrons in the wall. Our hands warm when we rub them together because we are transforming the kinetic energy in the motion of our hands to kinetic energy of the particles in our hands, thereby raising their temperature. An electric current is the flow of electrons from point to point. When we talk, the vibration of our vocal cords causes a pressure wave that passes through the air to set a listener's eardrum vibrating. That pressure wave is composed of a series of regions where the density of air particles is alternately higher and lower that moves from the mouth to the ear.

And, of course, as we will see, light is not some occult force but the passage of particles called photons from a source to a detector such as the eye.

MECHANICAL PHILOSOPHY

Historian David Lindberg describes how Aristotle's physics remained unchallenged in the later Middle Ages until the rival physics of Epicurean atomism became known through the rediscovery of Lucretius's De rerum natura. Atomism contributed to the “mechanical philosophy” that, by the end of the seventeenth century, had become dominant. The key figures were Galileo in Italy, Descartes and Gassendi in France, and Boyle and Newton in England, with many others also contributing.

All except Descartes adopted the picture of atoms and the void. Instead, he viewed the universe as a continuum of matter filling all of space and described the motion of planets as being moved by rotating bands of matter called vortices. So while it was not the model of the solar system that survived, Descartes's model was the first attempt to provide a mechanical explanation. And so, the organic universe of medieval metaphysics and cosmology was routed by the lifeless machinery of the new materialists.18

The physics of atomism presented no problems for Galileo, Newton, and other theists of the time, nor does it today. They simply reject the cosmological and metaphysical implications. Atomism, as originally presented, posits an infinite universe of eternal, uncreated material particles acted on by impersonal, nonliving, mechanical forces. Most religions imagine a finite, created universe containing not only material particles but also immaterial souls, acted on by personal, vital, supernatural forces.

The Christian atomists of the seventeenth century accepted the particle aspects of atomism, but they rejected the notion that reality is nothing but atoms and the void. They all saw what happened in 1600 to Bruno (see chapter 2), who preached not only that everything was made of atoms but also the atomist doctrine of an infinite universe, although his particular teaching was not atheistic but referred to an infinite God. Gassendi also argued that atoms and God can coexist. Galileo never questioned the spiritual authority of the Church, and his atomism seems to have played no part in his trial for teaching heliocentrism.19 Newton, although accepting the existence of corpuscles and the void, did not view his own theory of corpuscular motion as complete and talked about God continually acting in moving bodies around to suit his plans. In Principia, Newton wrote about the atomists of antiquity:

They are thus compelled to fall back into all the impieties of the most despicable of all sects, of those who are stupid enough to believe that everything happens by chance, and not through a supremely intelligent Providence; of these men who imagine that matter has always necessarily existed everywhere, that it is infinite and eternal.²⁰

PRIMARY AND SECONDARY QUALITIES

Despite Newton's objections to the impiety of atomism, the Newtonian mechanistic scheme implied a distinction between two types of physical properties that was first proposed by Democritus and is inherent to the atomic model. Recall from chapter 1 that Democritus was quoted as saying, “By convention sweet, by convention bitter, by convention hot, by convention cold, by convention color; but in reality atoms and the void.”

According to philosopher Lawrence Nolan, as science gradually developed into a field separate from philosophy, it became characterized, especially after Galileo, by the reliance on sensory observation and controlled experimentation as the primary, if not the only, reliable sources of knowledge about the world.²¹ Nolan notes that a distinction between primary and secondary properties was fundamental to the mechanistic model of the universe developed in the seventeenth century.

The new model sought to explain all physical phenomena in terms of the mechanical properties of the small, invisible parts (atoms) that constitute matter. These are primary. They are all that is needed to explain how things work. Secondary properties, such as color or sound, play no role in that explanation. As Nolan puts it, “The color of a clock or the sound it makes when it chimes on the hour are [sic] irrelevant to understanding how a clock works.” All that matters are the size, shape, and motion of its gears.22

A major objection to this view, going back to Aristotle, is that the primary properties are unobservable while the so-called secondary properties are what we actually detect with our own two eyes and other senses. The distinction is perhaps less important today, where we can use our scientific instruments to measure the mass, energy, and other primary properties of particles. The main difference we now recognize is that many secondary properties are, as Democritus noted, “conventions” that we use to describe the subjective reactions we mentally experience as our brains process what our senses detect. For example, I might find an apple tastes sweet, while you find it tastes sour.

However, not all secondary properties are simple, subjective artifacts of the human cognitive system. Recall the discussion in chapter 1 about wetness. This is a property of water and other liquids that results from the arrangement of the molecules of the liquid and is not a primary property present in the molecules themselves. Today we call such properties emergent. While it is true that wetness is something we sense when we touch water, the property of wetness can be objectively registered with instruments independent of direct involvement of any human sensory apparatus.

So I will make a distinction between secondary properties and secondary qualities that I have not seen made by philosophers writing on the subject. The physical detectability of wetness is a secondary property that is independent of human involvement, while the conscious sensation of wetness is a secondary quality that involves the human cognitive system.

A long-standing controversy exists among philosophers about the perceiver dependence of the secondary quality color, which Democritus listed as one of his conventions, along with bitter, sweet, hot, and cold.23 Whether something tastes bitter or sweet, or feels hot or cold, is clearly subjective, dependent on human sensory perception. Similarly, color, such as the redness of a tomato, is a qualitative experience and so is a secondary quality. But each of these phenomena is also associated with objective properties. Hotness and coldness are related to what you read on a thermometer. The color “red” is the name we apply to the way our brains react when our eyes are hit with photons (atoms of light) in the energy range from 1.8 to 2 electron-volts.

Considering the role of the human cognitive system in describing secondary qualities leads us into a discussion of the brain and the still-controversial question of whether matter alone is sufficient to explain the subjective experiences we have, such as pain, which are called qualia. However, this is not a subject for this chapter and will be deferred until chapter 13.

OTHER ATOMISTS

Another important, believing scientist who helped spread the gospel of atomism was chemist Robert Boyle (1627–1691). Boyle's law says that the pressure and volume of a gas are inversely proportional when the gas is at a fixed temperature. Bernoulli was able to derive Boyle's law from the kinetic theory of gasses, as mentioned previously. Boyle made no original contributions to the atomic model itself and, like most of his contemporaries, imbued them with divine purpose.²⁴ However, his experiments did get people thinking again about the void.

Richard Bentley (1662–1742), chaplain to the bishop of Worcester, was also an ardent atomist and anticipated that the universe was mostly void. But he could not see how purposeless matter could account for the ordered structure of the world.²⁵

The noted philosopher John Locke (1632–1704) also supported atomism but expressed skepticism that theory alone, without observations, can elucidate the fundamental nature of things. However, recall that atomism was based not just on thought but also on observations. Locke also followed other Christian atomists in rejecting the notion that “things entirely devoid of knowledge, acting blindly, could produce a being endowed with awareness.”26

This view was widespread as science developed further in the eighteenth century. Indeed, it was a problem that concerned philosophers in Europe and in the Arabic-speaking world during the Middle Ages. One solution was to imbue atoms with life and intelligence of their own. A non-supernatural duality was envisaged in which two types of matter existed: organic and inorganic. The French philosophers Pierre Louis Maupertuis (1698–1759) and Denis Diderot (1713–1784) promoted this doctrine.²⁷

Animate atoms made it possible to eliminate the need for a divine hand in assembling them into living things, especially thinking humans. Diderot made this suggestion along with Paul-Henri Thiry, Baron d'Holbach (1723–1789), both firm atheists at a time when there were few around. They collaborated in assembling the colossal thirty-five-volume Encyclopédie.²⁸

French physician Julien Offray de la Mettrie (1709–1751) provided what was perhaps the first fully materialist, atheist philosophical doctrine. He argued that the human body is a purely material machine and that there was no soul or afterlife.²⁹ Like others of his era, he could not see how chance could produce the world as we see it. However, he also rejected God as the source and said the world results from the operation of natural laws that remain to be discovered.

MORE ANTIATOMISTS

The antiatomists of the seventeenth and eighteenth centuries were motivated by their Christian beliefs and used religious rather than scientific arguments to support their positions. These included Descartes, who, although a proponent of mechanics, was deeply wedded to the duality of mind and body and could not believe that everything is reducible to atoms.30

Another great philosopher of the period who objected to physical atoms was Gottfried Wilhelm Leibniz (1646–1716). In their place, he imagined metaphysical atoms called “monads,” little immaterial soul-like objects that formed the substance of existence.³¹ He never explained how we would be able to demonstrate their existence. But, then, the concept of empirical verification, introduced by Galileo, had not yet taken hold.