In Classical times huge advances were made, particularly in Greece. Mathematics, astronomy and geometry were refined and some of the most important scientific principles were developed.

Atoms and causation

In the fifth century BC Leucippus and his pupil Democritus refused to accept the ancient supernatural explanations of nature and proclaimed categorically that every event had a natural cause. The two of them were proponents of a concept that all matter is comprised of tiny particles which were so small that they could not be broken up. These particles were called atoms, from a Greek word for "indivisible".

Aristotle: natural laws

Aristotle (384-322 BC) promoted the concept that observation of physical phenomena could ultimately lead to the discovery of natural laws governing those phenomena, though unlike Leucippus and Democritus, Aristotle believed that these natural laws were ultimately divine in nature. His was a philosophy of nature, an observational science based on reason. He has rightly been criticised for a lack of rigour (if not outright carelessness) in his observations. For example, he states that men have more teeth than women, which is not true. He did not use experiments to test and replicate his observations. Nevertheless Aristotle's science was hugely influential, indeed it dominated human understanding of the natural world prior to the eighteenth-century Enlightenment and some of his ideas have lasted, for example the classification of plants and animals into genera.

One of Aristotle's interests was the motion of objects. He asked basic questions such as "Why does a rock fall while smoke rises?", "Why does water flow downward while flames dance into the air?" and "Why do the planets move across the sky?" and explained these phenomena by describing the nature of the world. For Aristotle, all matter was composed of five elements (fire, earth, air, water and ether, a divine substance of the heavens). These elements interchange and relate to each other. The worldly elements (fire, earth, air and water) each had natural realms. For example, we exist where the earth realm (the ground beneath our feet) meets the air realm (the air all around us and up as high as we can see). The natural state of objects was at rest, in balance with the elements of which they were composed. The motion of objects, therefore, was an attempt by the object to reach its natural state. A rock falls because the earth realm is down. Water flows downward because its natural realm is beneath the earth realm. Smoke rises because it is comprised of both air and fire, thus it tries to reach the high fire realm, which is also why flames extend upward.

Aristotle understood natural objects in terms of four causes. Everything is made up of basic ingredients, which he called "material causes". For example, the material causes of an oak tree world be carbon, oxygen, hydrogen etc. These ingredients are brought together by "efficient causes", the actions and agents that cause the particular object to exist. For example, the efficient causes of our oak tree might be the acorn falling on the forest floor, a squirrel burying it, the action of sun, rain and wind etc. What makes the object what it is is its formal cause, that which makes something a tree and an oak rather than an ash, its recipe or DNA in modern terms. Ultimately all things aim towards a final cause, a reason for being, the fulfillment of their nature, flourishing. Aristotle's theory of causation brought together his scientific and ethical work. He saw that goodness exists in an object (or person) fulfilling their nature and so flourishing. We can understand human nature and what it is to be good in the same way as we can understand the nature of an oak tree, through observation and rational analysis. A full explanation of Aristotle's Ethics can be found under 'Natural Law' in the Ethics section of this site [link].

Aristotle did not attempt describe the reality that he observed mathematically. Though he formalised logic, he considered mathematics and the natural world to be fundamentally unrelated. Mathematics was, in his view, concerned with unchanging objects that lacked reality, while his natural philosophy focused upon changing objects with a reality of their own.

Archimedes - linking maths to science

Archimedes (287-212 BC) is known for several important breakthroughs. Voltaire remarked that "There was more imagination in the head of Archimedes than in that of Homer." He:

· outlined the mathematical principles of the lever, one of the oldest machines
· created elaborate pulley systems, reputedly having been able to move a full-size ship by pulling on a single rope

· defined the concept of the centre of gravity created the field of statics, using Greek geometry to find equilibrium states for objects - a task that would be taxing for modern physicists
· was reputed to have built many inventions, including a "water screw" for irrigation and war machines that helped Syracuse against Rome in the First Punic War.
· is attributed by some with inventing the odometer to measure distance during this time, though that has not been proven.

Perhaps Archimedes' greatest achievement, however, was to reconcile Aristotle's great error of separating mathematics and nature. As the first mathematical physicist, he showed that detailed mathematics could be applied with creativity and imagination for both theoretical and practical results.

Hipparchus, astronomer extraordinaire

Hipparchus (190-120 BC) was born in Turkey, though he was a Greek. He is considered by many to be the greatest observational astronomer of ancient Greece. With trigonometric tables that he developed, he applied geometry rigorously to the study of astronomy and was able to predict solar eclipses. He also studied the motion of the sun and moon, calculating with greater precision than any before him their distance, size, and parallax. To aid him in this work, he improved many of the tools used in naked-eye observations of the time. The mathematics he used indicates that Hipparchus may have studied Babylonian mathematics and been responsible for bringing some of that knowledge to Greece. Hipparchus is reputed to have written 14 books, but the only direct work that remains was a commentary on a popular astronomical poem. Stories tell of Hipparchus having calculated the circumference of the earth, but this is in some dispute.

Ptolemy's view of the universe

The last great astronomer of the ancient world was Claudius Ptolemaeus, known as Ptolemy. In the second century AD he wrote a summary of ancient astronomy (borrowed heavily from Hipparchus) which came to be known as the Almagest (the greatest). He outlined the geocentric model of the universe, describing a series of concentric circles and spheres upon which other planets moved. The combinations had to be exceedingly complicated to account for the observed motions, but his work was adequate enough that for 14 centuries it was seen as the comprehensive statement on heavenly motion. This view of the universe was almost universally accepted. Suggesting that the earth moved round the sun was at that time unthinkable, ridiculous.

Science in the Middle Ages

In Western Europe in the early Middle Ages, science was often seen as a way to reinforce theological beliefs rather than as a means of discovery in its own right. Many of the advances made in Classical times were lost and scholars had to make do with a limited and less-than-ideal selection of texts. Nevertheless, calling this period the "dark ages" is hardly warranted. The myth of early-medieval ignorance was reinforced by the humanists and their heirs, who often drew on the discoveries of earlier European scientists without acknowledging them in order to make their own achievements seem more remarkable. James Hannam in God's philosophers (2009) charts the development of science in Europe and shows it to have been a continuous process, extending from Classical times to the modern era, and demonstrates that the Church more often fostered scientific discovery than prevented it.

In the Islamic East the state of scientific scholarship in the early Middle Ages was better, with Islamic rulers sponsoring the translation of the Classical texts into Arabic and supporting the establishment of universities in cities such as Baghdad and Cordoba. Islamic advances in science from this time laid the foundations for many later Western advances. (The recent exhibition at the Science Museum, 1001 Inventions, charts this influence - the website and promotional film can be accessed here [http://www.1001inventions.com].)

One of the most important elements of the Islamic legacy was the development of Arabic numerals and the number 0. Using Arabic rather than Roman numerals made calculating things an awful lot easier. Mathematics developed quickly once Arabic ideas such as these filtered into Europe through the mixed societies of Moorish Spain and the Crusader Kingdoms in Palestine. Notably Al-Khwarizmi (Alghorismus, c780-c850) made huge strides in the use of algebra and invented the list of instructions for calculating a function that became known as an algorithm.

A Copernican revolution

In medieval Europe, Copernicus (1473-1543) read the work of Classical philosophers such as Aristotle and Euclid, as well as that of Islamic philosophers such as Ibn Rushd (Avveroes). He saw contradictions in the accepted model of the universe and developed his own, heliocentric, model of the universe (ie one in which the earth revolves around the sun), which was published shortly before his death.

Galileo - breakthrough and charge of heresy

According to Stephen Hawking, "Galileo [1564-1642], perhaps more than any other single person, was responsible for the birth of modern science." In 1610 Galileo began to champion the heliocentric model of the universe put forward by Copernicus and, in doing so, began a scientific revolution or paradigm-shift. In 1632, after a bitter battle with the Inquisition, Galileo published his Dialogue concerning the two chief world systems. This brought his opposition to the Church to a head and he was placed on trial and forced to retract his views and live under house-arrest until his death.

Despite the Church proclaiming the heliocentric (sun-centred) view of the universe "false and contrary to Scripture", it soon became the dominant view among scientists and gave rise to an explosion in scientific ideas which led to the Enlightenment. By the mid-eighteenth century the Church had stopped opposing Galileo and by 1939 Pope Pius XII said that Galileo was one of the "most audacious heroes of research ... not afraid of the stumbling-blocks and the risks on the way, nor fearful of the funereal monuments." In the 1990s both Pope John Paul II and Cardinal Joseph Ratzinger (now Pope Benedict XVI) expressed regret over how the Church reacted to Galileo.

Enlightenment: the world as a predictable machine

During the Enlightenment scientists developed a view of the universe as an orderly, vast and complicated but predictable machine. Newton, Kepler, Pascal, Halley, Herschel and Hooke contributed to a more and more complete understanding of the world; indeed by the nineteenth century scientists were speculating how long it would take them to find out everything and so do themselves out of a job.

Doing God out of a job

The mechanistic view of the universe was at once a blessing and a threat to religion. On one level, science confined itself to discovering how things worked and religion supplied the why. Nevertheless, the more that science provided a "theory of everything", the less need there was to believe in God, particularly a God who has any meaningful role in the universe. Deism (the belief that God created the universe but is distant, not interested in us) or atheism, was a natural conclusion of scientific research in this paradigm.

Towards Darwin

Certainly, scientific research revealed the glory of God by displaying the mind-bending complexity and order and apparent purpose, but it also suggested that "nature is red in tooth and claw" (as Tennyson wrote), that human beings may not be the favoured masters of all creation and that supposing a purpose for the universe may be crude and simplistic. Many of the scientists of this period were religious - indeed, there was a high proportion of clergymen amongst their ranks, using their scholarship and leisure time to advance the boundaries of knowledge of the natural world. However many soon had to face difficult questions as a result of their research. Charles Darwin was just one such. He delayed publication of his On the origin of the species (which eventually appeared in 1859) for many years, perhaps for fear of alienating his devout wife. His own scepticism advanced slowly; he found Paley's Natural Theology (1802) convincing when preparing for holy orders at Cambridge but after the loss of three children and years of botanical study he could no longer hold to a faith in an all-powerful, loving God.

Darwin's theory of evolution by natural selection was not an entirely new idea. Darwin did however provide the evidence to support the theory, making it a convincing argument. That did not mean that his ideas were accepted without resistance however. Famously his supporters were mocked for seeing human beings and apes as descendants of a common ancestor. The theory did not gain widespread acceptance until the mid-twentieth century and, in America, there are still huge numbers of people who refuse to accept the theory of evolution and campaign for it not to be taught in schools.

Evolution vs a design argument

The theory of evolution by natural selection is based on inductive reasoning; it is an a posteriori, strong, argument which in this shares characteristics with both cosmological [link] and teleological [link] arguments. The difference is the weight of evidence on which the conclusions are supported; today there is a very great weight of evidence supporting Darwin's argument. The statement "species evolve to suit the prevailing conditions through a process of natural selection" is verifiable. Some critics have suggested that it might be falsified, however, with particular reference to the theory's inability to account for phenomena such as the irreducible complexity of natural systems, the existence of specified complexity in nature, the existence of incredibly beautiful or complex organisms such as the human eye, or certain behaviour patterns such as love and altruism. Proponents of versions of the design argument for the existence of God [link] tend to be the loudest critics of Darwin.

Dawkins' arguments

Richard Dawkins has made a spirited effort to fight back, to state the evidence in support of evolution, to argue that it is so persuasive that Darwin's theory is all but a fact and to refute alternative arguments. In The blind watchmaker (1986), Dawkins argues that natural selection is "blind". An "unconscious automatic process", it has no aim, no purpose. "Evolution has no long-term goal. There is no long-term target, no final perfection to serve as criteria for selection ... The criteria for selection is always short-term, either simply survival or, more generally, reproductive success. The "watchmaker" that is cumulative natural selection is blind to the future and has no long term goal."

In The selfish gene (1976) Dawkins claims that human beings only act so that their genes may survive. All we are is mechanisms to pass on our genes in competition with other species. We are simply the mechanisms used by our genes to replicate themselves: "We are survival machines - robot vehicles blindly programmed to preserve the selfish molecules known as genes."

He argues that human beings have evolved to meet the conditions available; there is no purpose and no meaning to our existence. We are simply what evolved; our ability to understand our place in the universe is remarkable and fills Dawkins with awe. He understands human beings strictly in terms of biology - we have about 5 billion cells each containing 46 chromosomes and 23 base pairs. Each chromosome contains tens of thousands of genes. Dawkins describes DNA as follows:

"It is raining DNA outside. On the banks of the Oxford canal at the bottom of my garden is a large willow tree and it is pumping downy seeds into the air ... not just any DNA, but DNA whose coded characteristics spell out specific instructions for building willow trees that will shed a new generation of downy seeds. These fluffy specks are literally spreading instructions for making themselves. They are there because their ancestors succeeded in doing the same. It's raining instructions out there. It's raining programmes; it's raining tree-growing, fluff spreading algorithms. This is not a metaphor, it is the plain truth. It couldn't be plainer if it were raining floppy discs."

Dawkins' assumptions about believers - a false dichotomy

Dawkins' arguments are very persuasive, but one issue that could undermine his position is the naïve impression that he has of what most religious people actually believe. He attacks Christians for taking a literal view of the Bible and for holding that God created the universe literally in seven days, yet no serious theologian or philosopher in Britain thinks this and few enough ordinary Christians either. Would it be reasonable for a theologian to attack science on the grounds of what a few ordinary people think is what science claims about evolution, without referring to what experts actually say?

Most hold that the creation stories are myths, metaphors which point towards a truth beyond which is difficult to talk about in everyday terms. It is clear that myths, metaphors and symbolic language can convey deep and important truths and indeed some critical realists have pointed to the fact that science itself often uses these forms of language when normal words and grammar is inadequate to convey realities beyond normal experience.

Dawkins and some scientists, who see science as necessarily opposed to religion, set opposing arguments up as if there are only two possible explanations for the universe: either the universe was created through a Big Bang and life evolved through a process of natural selection or an old man with a white beard said "let there be light" one Sunday morning about 4,500 years ago. This is a false dichotomy. It is possible that neither explanation is right - or that elements of both explanations are true.

Can one be open-minded when it comes to matters of truth? Scientists would point to the reams of evidence in support of the theory of evolution by natural selection and would find the idea of questioning the theory and teaching the stories of primitive civilisations in laboratories offensive. However, as historians of science such as Kuhn and Feyerabend have pointed out, it is a recurring feature of science to be committed to one paradigm to the extent that it causes opposing evidence to be excluded and the progress of knowledge to be slowed. What is the best way forward? There are certainly some things that evolution struggles to explain.

How many million years?

One is the timescales for change. As we can observe it, natural selection takes much longer to achieve the evolution of species than the fossil record indicates such change actually took. Further, we cannot observe any case of natural selection leading to one species transforming into another, only of changes taking place within biological classifications. Scientists argue that it is only a matter of time before such detail is filled in by researchers, but those opposed to evolution argue that something else is needed to explain these phenomena, namely God. Groups such as Answers in Genesis [link] employ experienced teachers who tour schools sharing their creationist perspective and pointing out to young people all the things that evolution cannot explain. They suggest that God may have created creatures of each genus and then started a process of evolution to refine his creations within a dynamic world. In Britain some new academy schools have been founded by creationist groups who choose to teach evolution only as one theory alongside alternative theories such as divine creation in science lessons. Needless to say, this remains extremely controversial.

Einstein's legacy

Albert Einstein (1879-1955) was an unlikely candidate to change the course of science, a Swiss patent-clerk who couldn't get a job as a teacher. Nevertheless, his work caused another paradigm-shift and opened the door for splitting the atom, quantum mechanics and technologies from the moon-landings to the mobile phone. In 1905 Einstein published his doctoral dissertation and four more papers, which made his reputation as one of the most important minds of his generation. He called 1905 his annus mirabilis.

Einstein is best known for the formula e=mc2, his theory of special relativity, but this is just one of his advances. He developed a theory of general relativity, put forward new ways of looking at thermodynamics and photons, advocated the use of a priori principles in physics and advanced quantum mechanics. He also directed his discoveries towards cosmology, asking what they could tell us about the nature of the universe as a whole. Einstein made sense of the universe by hypothesising a "cosmological constant", and using this supposed that the universe could be an eternal static sphere.

Einstein's static universe was an accepted paradigm for much of the twentieth century. Physicists such as Fred Hoyle hung onto this theory even when most others had accepted the Big Bang theory of an inflationary universe with a beginning and an end. The Big Bang Theory gained acceptance in the 1960s, once evidence from astronomy (Hubble) and radio interference (Penzias and Wilson) had been produced to support its claim to truth. British physicists Stephen Hawking and Roger Penrose were instrumental in making the case for the Big Bang at this time. The BBC docu-drama Hawking [link] explores this and is available on YouTube. Some of Einstein's other theories have stood the test of time much better.

Quantum reality

Quantum mechanics has thrown new light on the way the universe works on the smallest level, how matter and energy interact. Bohr, one of the fathers of quantum science, famously remarked that if you claim to understand quantum physics, you don't, and Richard Feynman said, "I think I can safely say that nobody understands quantum mechanics!" The mathematics behind quantum mechanics is abstract and its implications are non-intuitive; things don't behave as we would expect them to on a sub-atomic level and this throws into question "certainties" about the universe that most of us take for granted. For example, "quarks" can be in two places at the same time and can both exist and not exist simultaneously, and they are influenced by the process of observation. Basic principles of logic and scientific research are challenged by the world quantum research describes.

Room for doubt

The influence of this new uncertainty can be seen in the writings of critical realists and has been particularly well-received by believers, who felt threatened by scientific pretentions to explain everything and who find the new, more mysterious world that science is suggesting might leave room for God and faith. These include John Polkinghorne and Alister McGrath.

Physicists such as Max Planck, Werner Heisenberg and Neils Bohr advanced quantum theory during the 1930s and 1940s but many of its implications are still being worked out today. One of the differences between quantum physics and classical physics is that quantum only provides a range of possibilities and probabilities, not definite conclusions. If, as Wittgenstein observed in the Tractatus, "the universe is all that is" and Quantum qhysics demonstrates there are a range of possibilities, perhaps multiple universes must exist - to enable all the possibilities that exist to coexist when in our world things must either exist or not exist, and cannot do both or neither despite the science suggesting that they must ... These "multiverses" would never be accessible to us and are really no more than a logical hypothesis, but the influence of this way of seeing reality can be seen beyond science in the philosophy of religion [link], in the work of Plantinga and Swinburne, for examples, both of whom hypothesise about the existence of multiple universes containing all possible states of affairs and then try to reason back to why God would create this world rather than any other.

God and the Big Bang

The Big Bang theory is less of a threat to religion than the theory of evolution through natural selection. Indeed, it seems to support the idea of a temporal creation and is probably compatible with the Cosmological argument [link]. The singularity that caused the big bang about 13.7 billion years ago could truly be said to be "neither something nor nothing" as Aquinas described God. Stephen Hawking in A brief history of time (1988) was satisfied to say that if this is what people meant by God then he could accept that the cause of the Big Bang could be God. He has since changed his mind however, in his 2009 book The grand design.

Professor Alister McGrath, along with several other high-profile and well qualified scientists who are also believers, argues that it is a good scientific principle that if a postulated explanation is simpler and has greater explanatory power than alternatives, then it should be taken seriously. They suggest that it is more credible to say that God caused the precise conditions necessary for the Big Bang to produce our universe than to say that it is just an unbelievably improbable fluke. This is not a proof that God exists - but it does point to God as being a hypothesis that needs to be taken seriously.