Category Archives: History of Science
Part 1 of this series, “Atoms Old and New: Atoms in Antiquity” can be read here.
The transition to modern thinking
“It seems probable to me, that God in the beginning formed matter in solid, massy, hard, impenetrable, movable particles… even so very hard, as never to wear or break in pieces; no ordinary power being able to divide what God Himself made one in the first creation.” So wrote Sir Isaac Newton in his 1704 work, Opticks. Apart from the reference to God, there is nothing here that Democritus would have disagreed with. There is, however, very little that the present-day scientist would fully accept. In this and later posts, I discuss how atoms reemerged as fundamental particles, only to be exposed, in their turn, as less than fundamental.
The scientific revolution and the revival of corpuscular theory – 1543–1687
In 1543, on his death-bed, Nicholas Copernicus received a copy of the first edition of his book, On the Revolutions of the Heavenly Bodies, in which he argued that the Sun, not the Earth, was thecentre of what we now call the Solar System. In 1687, Isaac Newton published his Mathematical Principles of Natural Philosophy, commonly known as the “Principia”. With hindsight, we can identify the period between these events as a watershed in the way that educated people in the West thought about the world, and number the political revolutions in America and France, and the economic revolutions in agriculture and industry, among its consequences.
Before this scientific revolution, European thinking about nature still followed that of Aristotle. The Earth lay at the centre of the Universe. Objects on Earth moved according to their nature; light bodies, for instance, containe, air or fire in their makeup, and these had a natural tendency to rise. Earth was corrupt and changeable, while the heavens were perfect and immutable, and the heavenly bodies rode around the centre on spheres within spheres because the sphere was the most perfect shape. By its end, Earth was one of several planets moving round the Sun in elliptical orbits, the movements of objects were the result of forces acting on them, the laws of Nature were the same in the heavens as they were on Earth, and all objects tended to move in straight lines unless some force deflected them from this path. The Universe ran, quite literally, like clockwork. This mechanical world-view was to last in its essentials until the early 20th century, and still remains, for better or worse, what many non-scientists think of as the “scientific” viewpoint.
Left: manuscript where Galileo records his observations of the motion of the moons of Jupiter, dethroning Earth from its special position as centre of celestial motion. Below right, Gallileo demonstrates the telescope to the Doge of Venice, fresco by Bertini. Click to enlarge
In 1611, Galileo turned the newly-invented telescope on the heavens, discovered sunspots, and moons round Jupiter, and realised that the belief in a perfect and unchanging1 celestial realm was no longer sustainable. Earlier, he had studied the motion of falling bodies. In work that he started in 1666, Newton showed how the laws of falling bodies on Earth, and the movement of heavenly bodies in a Copernican solar system, could be combined into a single theory. To use present-day language, the Moon is in free fall around the Earth, pulled towards it by the same force of gravity as a falling apple. This force gets weaker as we move away from Earth, according to the famous inverse square law, which says that if we double the distance, the force falls to a quarter of its value. Then with a certain amount of intellectual effort (involving, for example, the invention of calculus), Newton was able to work out, from the acceleration of falling bodies on Earth, and from the Earth-Moon distance, just how long it should take the Moon to go round the Earth, and came up with the right answer. He was also able to work out just how long it would take satellites at different distances to go through one complete orbit. Of course, at that time, Earth only had one satellite (the Moon), but six were known for the Sun (Mercury, Venus, Earth, Mars, Jupiter, Saturn), and his theory correctly predicted how the length of the year of these different planets would vary with their distance from the Sun (the answer is a 2/3 power law; an eight-fold increase in distance gives a fourfold increase in time). Celestial and terrestrial mechanics were united.
It was around this time that a Dutchman, Anthony van Leeuwenhoek, began an extensive series of microscope studies, using single lens instruments of his own devising. Among the first to observe spermatozoa, he also described bacteria, yeast, the anatomy of the flea, and the stem structure of plants. He communicated his results to the Royal Society in London. Formally established around 1660, under the patronage of Charles II, this was and remains
Image from Arcana Naturae Detecta, 1695, Leeuwenhoek’s collected letters to The Royal Society. Click to enlarge
among the most prestigeful of learned societies. Here they caught the attention of Robert Boyle (of Boyle’s Law for gases). Boyle tried to explain such properties of matter as heat, and the pressure of gases, in terms of the mechanics of small particles, or “corpuscles”, and hoped that the other aspects of matter could be explained in the same kind of way. This was, after all, simply an extension downwards of the mechanical system that Newton had so successfully extended upwards. It is instructive to consider how far this hope was fulfilled. Atoms and molecules are in some ways similar in their behavior to small objects obeying the everyday laws of mechanics, but in others they are very different, and it is these differences that must be invoked if we are to understand the forces involved in the chemical bonding.
Early modern theory – 1780-1840
Between 1780 and 1840, chemistry underwent a revolution, that transformed it into the kind of science that we would recognise today. It is no accident that this was the same period as the beginning of the industrial revolution in Europe. Materials were being mined, and iron and steel produced and worked, on a larger scale than ever before. By the end of the period, mineral fertilisers were already in large scale use to feed the growing population. Demand for machinery led to improvements in engineering, and this in turn made possible improvements in the precision of scientific instruments. Much of the new interest in chemistry grew out of mining, mineralogy, and metallurgy, while improvements in manufacture and glass-blowing led to the precision balance, and to new apparatus for handling gases.
Here I will summarise some of the most important discoveries, as seen from our present point of view, and using today’s language. This means running the risk of creating a misleading impression of smoothness and inevitability. Inevitability, perhaps yes; the world really is what it is, and once certain questions had been asked, it was inevitable that we would eventually find the right answers. Smoothness, no; the very concept of atoms, let alone bonding between atoms, remained controversial in some circles way into the 20th century. Outsiders sometimes criticise scientists for taking their theories too seriously, but more often they are reluctant to take them seriously enough.
Overall, mass is conserved; the mass of the products of a reaction is always the same as the mass of the reactants. This is because atoms are not created or destroyed in a chemical reaction.2 Single substances can be elements or compounds, and the enormous number of known compounds can be formed by assembling together the atoms of a much smaller number of different elements. We owe our distinction between elements and compounds to Lavoisier (“The banker who lost his head“). Boyle had come close a hundred years earlier, but was so taken with the transformations of matter that he rejected the notion that its fundamental constituents were immutable.3
The combustion of carbon (its reaction with oxygen) gives a gas, the same gas as is formed when limestone is heated. But there is no chemical process that gives carbon on its own, or oxygen on its own, by reaction between two other substances. So we regard carbon and oxygen as elements, whereas the gas formed by burning carbon (what we now call carbon dioxide) is a compound of these two elements. The production of this same gas, together with a solid residue, by the heating of limestone, shows that limestone is a compound containing carbon, oxygen, and some other element.4 To us, using today’s knowledge, limestone is calcium carbonate, and decomposes on heating to give carbon dioxide and lime (calcium oxide). In Lavoisier’s time, there was no way of breaking down calcium oxide into simpler substances, so he considered it to be an element.
A short philosophical digression (and every scientist has a working philosophy, whether they realise it or not): Lavoisier could make as much progress as he did because he had introduced an operational definition of an element, referring not to some inner essence but to observationally defined properties. And implicit in this was the principle of fallibilism; conclusions are always in principle revisable in the light of further observation, as the example of calcium oxide shows.
Air is a mixture, and burning means reacting with one of its components, which we call oxygen. Metals in general become heavier when they burn in air. This is because they are removing oxygen from the air, and the weight (more strictly speaking, the mass) of the compound formed is equal to that of the original metal plus the weight of oxygen. (Mass is an amount of matter; weight is the force of gravity acting on that matter. Atoms are weightless when moving freely in outer space, but not massless.)
Different elements combine with different amounts of oxygen; these relative amounts are a matter of experiment. In modern language, when some typical metals (magnesium, aluminium, titanium, none of which were known when Lavoisier was developing his system) react with oxygen, they form oxides with the formulas MgO, Al2O3, TiO2.
About one fifth of the air is oxygen, and if we burn anything in a restricted supply of air, the fire will go out when the oxygen has been used up. Nothing can burn in (or stay alive by breathing) the remaining air. Some materials, like wood and coal, appear to lose weight when they burn, but this is because they are in large measure converted to carbon dioxide and water vapour, which are gases, and we need to take the weight of these gases into account.
It was also shown during this period that the relative amounts of each element in a compound are fixed (Law of Definite Proportions). For instance, water always contains 8 grams of oxygen for each gram of hydrogen. Moreover, when the same elements form more than one different compound, there is always a simple relationship between the amounts in these different compounds (Law of Multiple Proportions). Thus hydrogen peroxide, also a compound of hydrogen and oxygen, contains 16 grams of oxygen for each gram of hydrogen. Similarly, the gas (carbon dioxide to us) formed by burning carbon in an ample supply of oxygen contains carbon and oxygen in the weight ratio 3:8, but when the supply of oxygen is restricted, another gas (carbon monoxide) is formed, in which the ratio is 3:4. Carbon monoxide is intermediate in composition between between carbon and carbon dioxide, but it is not intermediate in its properties. For a start, it is very poisonous; it sticks to the oxygen-carrying molecules in the blood even more strongly than oxygen itself, thus putting them out of action. It is formed when any carbon-containing fuel, not just carbon itself, burns in an inadequate supply of air, That is why car exhaust fumes are poisonous, and why it is so important to make sure that gas-burning appliances are properly vented. It is also one of the components of cigarette smoke, which helps explain why cigarettes cause heart disease and reduce fitness.
Left: Dalton’s table of the elements, with relative weights, based on H = 1. The correct value for oxygen is 16. Dalton’s value is based on an assumed formula HO for water, together with experimental error; likewise for other elements
All these facts can be explained if the elements are combined in molecules that are made out of atoms, the atoms of each element all have the same mass,5 and each compound has a constant composition in terms of its elements. For instance, each molecule of water contains two atoms of hydrogen and one of oxygen (hence the formula H2O); hydrogen peroxide is H2O2; carbon dioxide is CO2; carbon monoxide is CO; and the masses of atoms of hydrogen, oxygen, and carbon are in the ratio 1:16:12. Using these same ratios, we can also explain the relative amounts of the elements in more complicated molecules, such as those present in octane (a component of gasoline), C8H18, and sucrose (table sugar), C12H22O11. Why C8H18 and not C4H9, which would have the same atomic ratio? This can be inferred from the density of the vapour, using Avogadro’s hypothesis (see below).
Thus, by the early 19th century, chemists were in the process of developing consistent sets of relative atomic weights (sometimes known as relative molar masses). However, there was more than one way of doing this. For instance, John Dalton, the first to explain chemical reactions in terms of atoms, thought that water was HO and that the relative weight of hydrogen to oxygen was one to eight. This uncertainty even led some of the most perceptive to question whether atoms were real objects, or merely book-keeping devices to describe the rules of chemical combination.
Evidence from the behavior of gases (to around 1860)
A French chemist, Joseph Gay-Lussac, noticed that the volumes of combining gases and of their gaseous products, were in simple ratios to each other. In 1811, the Italian Count Amadeo Avogadro explained this by a daring hypothesis, that under the same conditions of temperature and pressure equal volumes of gases contain equal numbers of molecules. We now know this to be (very nearly) true, except at high pressures or low temperatures.
Avogadro’s Hypothesis, as we still call it, gives us a way of directly comparing the relative weights of different molecules, and of inferring the relative weights of different atoms. For example, if we compare the weights of a litre of oxygen and a litre of hydrogen at the same temperature and pressure, we find that the oxygen gas weighs sixteen times as much as the hydrogen. (This is not a difficult experiment. All we need to do is to pump the air out of a one litre bulb, weigh it empty, and then re-weigh it full of each of the gases of interest in turn.) But Avogadro tells us that they contain equal number of molecules. It follows that each molecule of oxygen weighs sixteen times as much as each molecule of hydrogen.
One litre of hydrogen will react with one litre of chlorine to give two litres of the gas we call hydrogen chloride. Thus, by Avogadro’s Hypothesis, one molecule of hydrogen will react with one molecule of chlorine to give two molecules of hydrogen chloride. So one molecule of hydrogen chloride contains half a molecule of hydrogen, and half a molecule of chlorine. It follows that the molecules of hydrogen and of chlorine are not fundamental entities, but are capable of being split in two. Making a distinction between atoms and molecules that is obvious to us now but caused great confusion at the time, each molecule of chlorine, must contain (at least) two separate atoms.6 By similar reasoning, since 2 litres of hydrogen react with 1 litre of oxygen to give 2 litres of steam, water must have the familiar formula H2O, and not HO as Dalton had assumed for the sake of simplicity.
Avogadro’s hypothesis was put forward in 1811, but it was not until 1860 or later that his view was generally accepted. Why were chemists so slow to accept his ideas? Probably because they could not fit it into their theories of bonding. We now recognise two main kinds of bonding that hold compounds together – ionic bonding and covalent bonding. Ionic bonding takes place between atoms of very unlike elements, such as sodium and chlorine, and was at least partly understood by the early 19th century, helped by the excellent work of Davy and Faraday in studying the effect of electric currents on dissolved or molten salts. They showed that sodium chloride contained electrically charged particles, and inferred, correctly, that the bonding in sodium chloride involved transfer of electrical charge (we would now say transfer of electrons) from one atom to another. But, as we have seen, Avogadro’s hypothesis implies that many gases, hydrogen and chlorine for instance, each contain two atoms of the same kind per molecule, which raises the question of what holds them together. These are examples of what we now call covalent bonding or electron sharing, a phenomenon not properly understood until the advent of wave mechanics in the 1920s.
Physicists, meanwhile, were developing the kinetic theory of gases, which treats a gas as a collection of molecules flying about at random, bouncing off each other and off the walls of their container. This theory explains the pressure exerted by a gas against the walls of its container in terms of the impact of the gas molecules, and explains temperature as a measure of the disorganised kinetic energy (energy of motion) of the molecules. The theory then considers that this energy is spread out in the most probable (random) way among large numbers of small colliding molecules. It can be shown that molecules of different masses but at the same temperature will then end up on average with the same kinetic energy, and it is this energy that at a fundamental level defines the scale of temperature. This is a statistical theory, where abandoning the attempt to follow any one specific molecule allows us to make predictions about the total assemblage.
The kinetic theory explains the laws (Boyle’s law, Charles’ law) describing how pressure changes with volume and temperature. Avogadro’s hypothesis can also be shown to follow from this treatment. Many other physical properties of gases, such as viscosity (which is what causes air drag) and heat capacity (the amount of heat energy needed to increase temperature), are quantitatively explained by the kinetic theory, and by around 1850 the physicists at least were fully persuaded that molecules and, by implication, atoms, were real material objects.
Structural chemistry, 1870 on
Kinds of isomer. The nature of optical isomers was established by Pasteur. Simple rotamers, such as the pair shownbottom right in diagram, readily interconvert at room temperature, giving an equilibrium mixture. The other kinds shown generally do not
Chemists were on the whole harder to convince than the physicists, but were finally won over by the existence of isomers, chemical substances whose molecules contain the same number of atoms of each element, but are nonetheless different from each other, with different boiling points and chemical reactivity is. This only made sense if the atoms were joined up to each other in different ways in these different substances. So atoms were real, as were molecules, and the bonding between the atoms in a molecule controlled its properties. This is what we still think today.
Einstein and Lucretius The piece of evidence that finally convinced even the most skeptical scientists came from an unexpected direction, from botany. In 1827, a Scottish botanist called Robert Brown had been looking at some grains of pollen suspended in water under the microscope, and noticed that they were bouncing around, although there was no obvious input of energy to make them do so. This effect, which is shown by any small enough particle, is still known as Brownian motion. Brown thought that the motion arose because the pollen grains were alive, but it was later discovered that dye particles moved around in the same way. The source of the motion remained a mystery until Albert Einstein explained it in 1905. (This was the same year that he developed the theory of Special Relativity, and explained the action of light on matter in terms of photons). Any object floating in water is being hit from all sides by the water molecules. For a large object, the number of hits from different directions will average out, just as if you toss an honest coin a large number of different times the ratio of heads to tails will be very close to one. But if you toss a coin a few times only, there is a reasonable chance that heads (or tails) will predominate. and if you have a small enough particle there is a reasonable chance that it will be hit predominantly from one side rather than the other. Pollen grains are small enough to show this effect. But this is only possible if the molecules are real objects whose numbers can fluctuate; if they were just a book-keeping device for a truly continuous Universe, the effects in different directions would always exactly cancel out. And if molecules are real, then so are atoms. It is just as Lucretius said, looking at dust in the air two thousand years earlier:
So think about the particles that can be seen moving to and fro in a sunbeam, for their disordered motions are a sign of underlying invisible movements of matter.
1 In fact (see earlier post), the Arabs had already recognized the variability of the star Algol
2 We cheat. There are, of course, processes (radioactive decay, nuclear fusion) where the number of atoms of each kind is not conserved because one element is transformed into another. We simply decide to call these physical processes, so that our statement remains true by definition. Nonetheless, it is useful, because it is usually pretty obvious whether a process should be called “chemical” or “physical”, on other grounds, such as whether or not it involves the formation of new bonds between atoms.
3 The Architecture of Matter, S. Toulmin and J. Goodfield, Hutchinson, 1962
4 In present-day notation,
C + O2 = CO2 and CaCO3 = CaO + CO2
5 This is not quite true. Most elements are a mixture of atoms of slightly different mass but very similar properties. The relative atomic masses of the elements as they occur in nature are an average of the masses of these chemically identical isotopes
6 So we can write the reactions as H2 + Cl2 = 2HCl and 2H2 + O2 = 2H2O
An earlier version of some of this material appeared in my From Stars to Stalagmites, World Scientific. Leeuwenhoek material via Buffalo Library. Dalton’s table of elements and their symbols via Chemogenesis. Isomers image by Vladsinger via Wikipedia
This post originally appeared on 3 Quarks Daily.
An excellent historical summary by my friend Michael Roberts, who has himself revisited the sites that Darwin explored in Wales. Darwin the geologist and Darwin the naturalist are inseparable.
HE ORIGIN OF DARWIN AS A NATURALIST
Darwin concluded The Origin of Species with this magnificent paragraph;
It is interesting to contemplate an entangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us. These laws, taken in the largest sense, being Growth with Reproduction; inheritance which is almost implied by reproduction; Variability from the indirect and direct action of the external conditions of life, and from use and disuse; a Ratio of Increase so high as to lead to a Struggle for Life, and as a consequence to Natural Selection, entailing Divergence of Character and the Extinction of less-improved forms…
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Glen Roy is a valley in the Western Scottish Highlands, just south of the Great Glen (home to Loch Ness), and draining through Glen Spean to Loch Linnhe, an inlet of the Atlantic. It is remarkable for the presence of the Roads, a series of parallel, almost horizontal, grooves in the hills on the sides of the glen. Clearly shorelines; but of what body of water? And why are there more than one of them?
Darwin thought the Roads represented vanished marine shorelines, one above the other as the result of vertical movement. Agassiz explained them, rather, as successive shorelines of a glacial lake, now vanished because the retaining glacier has melted away. If so, and if global warming is real, we might expect to see vanishing lakes today, as the glaciers retreat. We can, and we do, as my friend Peter Hess explains.
Charles Darwin visited the Glenroy area in 1838, two years after his return from his round the world voyage on the Beagle. During that voyage, he had examined the geology as well as the plants and animals of the places he visited, and among them was the coastal area of Chile. This is marked by raised beaches inland where once had been shoreline, and Darwin correctly described these as the effects of uplift, which we now know to be driven by plate tectonics. So it was natural that Darwin should have applied a similar explanation to the Roads, suggesting that the Cairngorms, like the Andes, were a zone of uplift, and that the Roads were ancient beaches of the Atlantic, now some ten miles away. The alternative theory, that they represented shorelines of an ancient lake, ran up against a seemingly conclusive objection; such a lake could only have formed if there had been a barrier across the valley, but there was no trace of this.
Only a year later, the Swiss naturalist Louis Agassiz visited the area. He had just published his Ice Age theory, and in the Highlands he found plenty of evidence to support it; scratches on bedrock caused by the passage of glaciers, erratics (boulders far from their parent rock formations), and moraines (piles of rock rubble that had been carried by glaciers, left in place when the glacier melted).
Evidence of this kind is not difficult to find throughout much of Scotland. I saw some of it myself earlier this month a few miles from Glasgow as a student on Glasgow University extension course (see illustrations). Agassiz realised that his ice age theory also provided the correct answer to the mystery of the Roads. Yes, there had been a lake, and yes, the roads did represent the shorelines at different times, carved into the sides of the valley by fierce freeze-thaw cycles. As for the barriers holding the lake in place at different levels over the course of time, they were a series of long vanished glaciers.
We now know that Agassiz was basically correct. Indeed, we can trace a whole series of glaciations, not just a single ice age. And Darwin was right in thinking that the area has experienced uplift; it could not fail to do so as the weight of ice above it melted away.
Later Darwin was to write of his paper on the Roads as his greatest blunder. He had visited Snowdonia in North Wales in 1831, as a student companion of the noted geologist Adam Sedgwick, who had been looking for fossils. In his Autobiography (p. 70) he laments how
“neither of us saw a trace of the wonderful glacial phenomena all around us; we did not notice the plainly scored rocks, the perched boulders, the lateral and terminal moraines. Yet these phenomena are so conspicuous that … a house burnt down by fire did not tell its story more plainly than did this valley.”
But it took Darwin several years to reach this point, and even then he persisted for a while with hybrid explanations, in which icebergs rather than retreating glaciers had deposited at least some of the erratics.
Agassiz rejected Darwin’s concept of evolution when it was published twenty years later, but this does not seem to have diminished Darwin’s respect for him. Belief in the fixity of species was, in the 1860s, understandable conservatism, even if now, 150 years later, it is no more than deliberately cultivated ignorance.
The present is key to the past. It follows that the past can increase our understanding of the present. And so it is in this case. The glaciers of Switzerland are receding. Those of the southern Andes are receding even faster. Among them is Chile’s Colonia glacier, which dams a lake, Lake Cachet 2, some 3 square kilometers in area. As the glacier shrinks and weakens, it becomes progressively less able to hold back the water of the lake, which now periodically bursts through; on one recent occasion, the lake emptied itself overnight.
The overflow channel through which the vanished Loch Roy must have drained can still be detected as an abrupt narrow valley in the surrounding hillsides. The draining of Lake Cachet II sent 200,000 tonnes of water overnight down Chile’s main river, and caused giant waves as far as the Pacific Ocean, 60 miles away.
Since Agassiz and Darwin examined the roads of Glen Roy, the earth’s mean surface temperature has increased by roughly 1oC, with another 0.5oC in the pipeline even if emissions were to be stabilised at the same levels as in the year 2000.
Which, of course, they won’t be.
Darwin’s drawing of the Roads from Darwin Online. Dunglass Crag, photos by author. Darwin’s boulders photographed by Michael Roberts. Lake Cachet II images via NCSE. Global temperature anomaly graph from NASA GISS via Wikipedia
h/t Michael Roberts, Dana Nuccitelli, Peter Hess. An earlier version of this post appeared in 3 Quarks Daily.
As in Alcatraz; Alcove; Alfalfa; Alcohol; Alkali; Alizarin; Almanac; Alchemy; Alembic; Algol; Almagest; Algebra; Algorithm; Alhambra
The syllable Al- is Arabic for “The”, and is attached to the beginning of the word to which it applies.
Like English today, or Latin in Renaissance Europe, the dominant language of learned discourse for several centuries was Arabic. Arabic-speaking scholars translated the great works of the Greek philosophers and scientists, as well as studying them in the original, did likewise for the texts of Indian mathematics (from which we derive our modern “Arabic” numbering system), and made important discoveries of their own. Spain was where the worlds of Islam and of Western Christianity met, fought, and mingled for more than seven hundred years, and it is mainly through Spanish that Arabic words have entered the English language.
Alcatraz, an island in California famous for its prison (left), was named by the Spanish explorers for the pelican (Arabic al-qadus, the water carrier), which they wrongly believed to carry water in its bill. In a further misapplication, the word has passed into English as the name for a completely different bird, the “Albatross”. Alcove (al-qubbah, the arch) reminds us of the glories of Moorish architecture, as in the Alhambra (or the red house) in Granada. This building was decorated with abstract designs (Arabesques) of great intricacy, whose patterns show so subtle a use of geometry and symmetry that they are studied by mathematicians even today. Alfalfa (from the Arabic name for the plant) is grown for hay in dry climates, such as that of Spain. The syllable al also occurs in numerous place names. The Algarve to us is the south of Portugal; to the Iberian Arabs, it was al-Gharb, the West. A very common combination is with wadi, valley, as in Guadalquivir (al-wad al-kebir, the Mighty River, the island of Guadalcanal in the Pacific (named after a town in Spain, wad-al-Kanat, valley of merchant stalls), Guadalajara (wad-al-Hajara or valley of stones) in Spain and Mexico. There are even a few Arabic-Spanish or Arabic-Latin hybrid names, such as Alicante (al– tacked onto the Roman name Lucentum, or City of Light) or Guadalupe (wad-al-lupus, valley of the wolf) But most of the Arabic al- words in common English use refer to the Arabic achievements in science and mathematics.
Alchemy, algebra, and Arabic numerals
Historically, the West has failed to give anything like due credit to the Arabic contribution to knowledge. A century ago, the justly renowned physicist, philosopher, and historian Pierre Duhem described the “wise men of Mohammedanism” as “destitute of all originality”. I myself, somewhat more recently, was taught at school that the Renaissance was brought about by Byzantine scholars who alone had been guarding the flame of knowledge kindled in classical times, and who, after the fall of Constantinople to the Turks in 1453, were dispersed throughout Europe. This account is as unhistorical as it is patronising. We can trace the golden age of Arabic science to the eighth century translation project, centred on Baghdad, which made the thought and knowledge of the Greece (and Persia and India) available in Arabic. And we must in turn acknowledge, as among the events leading up to the Renaissance and what we call “the” Scientific Revolution, the translation project centred on Toledo, that four centuries later was to translate the work of Arabic into Latin.
Our system of writing numbers was invented in India, from where Persian scholars brought it to the Arabic world. By the tenth century it had spread from there, through Spain, to the rest of Europe, so that we still refer to Arabic (as opposed to Roman) numerals. (The shapes of the actual numerals that we use follow those of the western part of the Islamic world, and have a clear family relationship to those from the eastern part, which are the ones used in Arabic writing today.) The word algorithm originally meant calculation with Arabic numerals. The word preserves the name of the Persian mathematician and polymath al-Khwarizmi, who had by around 825 CE worked out the procedures for doing arithmetic as we do, using zero, and positional notation for powers of ten. (If you think this was only a minor advance; just try doing long multiplication using Roman numerals. Masochists are invited to try long division.) The word “algorithm” has now acquired an interesting new meaning, as a procedure or set of rules for calculating an answer, and much of computing science is devoted to finding the best algorithm for a given class of problem.
Al-Khwarismi’s writings also give us the name, and the concept, of algebra (al-jebr, sometimes translated as “balancing” or “completing”), including the rules for solving quadratic equations by completing the square. One other possible meaning of the word is “uniting” or “joining”, and in sixteenth century England it also meant “bone-setting”.
Mathematics finds practical application in astronomy. This is a science of great utility for tracking the seasons, and also for navigation (the Arabs traded as far as Indonesia), and orientation (Moslem worshippers would need to know, as exactly as possible, the correct direction to Mecca). Here Arabic scholars were greatly helped by their access to the work of the Greek astronomers of Alexandria. The Greek theory of planetary motions placed the Earth at the center, with the other heavenly bodies following epicycles, or wheels within wheels. This theory was fully developed by the astronomer Ptolemy in a work still referred to by the name of its translation into Arabic, the Almagest (Arabic al-, the; Greek megisti, greatest). However, Arabic astronomers made original discoveries in both observational and theoretical astronomy. They followed their Hindu precursors in anticipating Copernicus’ shift of the center of the revolutions from the Earth to the Sun, and developed the sophisticated mathematics required to handle the implications of such a shift. When they discovered that a star in the constellation Perseus showed varying intensity over time, they called it Algol, the ghoul (yes; ghoul is also Arabic), because it went against Aristotle’s view that everything above the moon was perfect and unchanging. The predicted motions of the moon (important in Islamic religious observance) and planets, together with a list of dates for planting, can of course be found in an almanac (al-manakh, the calendar).
The language of chemistry in particular shows evidence of its origins in the Arabic science of alchemy (al-Khemiya; from Greek chimeia, art of refining metals). If today we think of alchemy as a benighted precursor to the true science of chemistry, that is just a trick of historical perspective, and indeed the two terms were used more or less interchangeably, both in the Arabic-speaking world and in Europe, until relatively recent times. While greatly discredited by its later practitioners in Europe, alchemy was the first serious attempt to relate observed chemical changes to an underlying theory of elemental composition. One piece of apparatus much used by the alchemists was the alembic (al-anbiq, the vessel, from greek ambix). Arabic craftsmen also developed the practical aspects of the subject, extracting the red dye alizarin (al-asarah, the juice) from the madder plant and developing the process for binding it to cotton. They also extracted potassium carbonate from the alkali (al-qali, the ash) made by burning seaweed, and this process was the main source of alkali for soap making and other purposes until the 19th century. The ladies of the Middle East used al-kohl (the powdered antimony) in eye makeup, a practice mentioned by the Prophet Ezekiel, who did not approve. This, strangely, is the origin of our word alcohol. Over time, this word has changed its meaning completely, from powdered antimony, to any fine powder, to a distilled essence used to suspend the powder, to the intoxicating substance ethyl alcohol (strictly forbidden to Moslems), and finally, in modern scientific usage, to any substance containing a similar carbon-oxygen-hydrogen grouping.
Science, as I have mentioned, was pushed forward by its practical applications. Observational and theoretical astronomy, essential to navigation at that time, were highly advanced. Anatomy and medicine were also well developed, and, more than three hundred years before William Harvey, the Egyptian physician al-Nafis worked out that blood circulates through the lungs. Optics was well advanced, with knowledge of refraction and lenses, the laws of reflection from a curved surface, the fact that in vision the eye focuses incoming light, and the cause of the rainbow, which involves two refractions and one reflection from a curved surface. These discoveries in optics involved both sophisticated calculations (sine, cosine, and tangent functions were known and used), and true experiments involving water-filled bowls and light passing through slits. Arabic alchemists also conducted true experiments, and realized that sulfur and mercury were fundamental “principles” (we would say elements), although they failed to free themselves from the Aristotelian doctrine that the different metals were interconvertible.
While consciously and conscientiously built on classical achievements, Arabic science at its best was original, adventurous, and (especially in astronomy and geography) supported by meticulous observation. One of the greatest of Arabic astronomers and polymaths was al-Biruni, 973 -1048 (in 1970, the crater Al-Biruni on the Moon was named after him). He contributed to the development of observational instruments and numerical and geometric techniques, and recognised that the earth rotated daily on its axis, but was neutral on principle regarding whether the earth went round the Sun once a year, or vice versa, on the grounds that these two were observationally equivalent. He also very clearly distinguished astronomy from astrology, which, as he explained, had been concocted by astronomers to satisfy the popular demand for practical benefit from their science. His other achievements include the recognition of the nature of fossils as petrified plant and animal remains, the realisation that valleys are formed by erosion, and the inference from the nature of the soil and the gradation in size of buried stones, that the plain of the Indus had been formed from river-borne sediments.
Al-Biruni’s contemporaries included Ibn al-Haytham (Alhazen), 965-1039, and Ibn Sina (Avicenna), 980-1037. Ibn-Sina and al-Buruni agreed on the nature of fossils, the formation of river valleys and alluvial plains, and the implied antiquity of the Earth. Ibn-Sina’s greatest achievements, however, were in the area of medicine. These made his name familiar even in late mediaeval Europe, and he is referred to as an authority on poisons in Chaucer’sCanterbury Tales. Ibn al-Haytham was employed by the notoriously eccentric Egyptian Caliph al-Hakim to supervise engineering works intended to regulate the Nile floods. This proving impossible, he fell from favour, and it is said that he found it prudent to pretend madness. He was placed under house arrest, and his Book of Optics ranks, along with John Bunyan’s Pilgrim’s Progress, Adolf Hitler’s Mein Kampf, and Bertrand Russell’s Introduction to Mathematical Philosophy, among notable works written in prison.
Much Islamic art was highly mathematical. It involved a knowledge of all the ways in which the two-dimensional space of a wall could be symmetrically divided by tiling, and anticipated in its practice even such twentieth century developments as color symmetry and five-fold pseudosymmetry.
I have carefully referred to “Arabic” scholars and artisans, rather than to “Arabs.” “Islamic” might seem more accurate, for a culture that included Persia (Iran) and much of Central Asia, but the culture we are discussing borrowed freely from pre-Islamic sources, and many of the participants were not themselves Muslims. Throughout its greatest period, from the eighth to the thirteenth centuries, it was a multicultural society, with Zoroastrian, Jewish, and Christian scholars and craftsmen all contributing to its rich intellectual life. Ali ben Isa, the most noted Arabic oculist, was a Christian. Saladin’s family physician, Moses ben Maimon (Maimonides), was a Jew. The Persian mathematician Omar Khayyam, who systematized the solutions of cubic equations (as well as writing the lyric verse for which he is now best remembered in the West) was a free-thinking skeptic. The mathematician al-Khwarizmi, whom we have already met, worked in Baghdad at the heart of the Arab world but borrowed freely from Hindu sources; both he and al-Biruni hailed originally from Central Asia, and Ibn-Sina was Persian.
Islam itself was far from being a single rigid structure. The doctrinal divisions between and within Sunni and Shi’a branches were (and are) as profound as those in Christianity between Catholic and Protestant, and in Sufism (which continues to flourish; you can now download Sufi music online) Islam has a mystical tradition that transcends all orthodoxies.
Arabic science and mathematics formed the bridge between the achievements of the ancient Greeks, and the emergence of modern science in Europe in the sixteenth and seventeenth centuries. By this I do not mean to imply that it was merely a passive vehicle, but rather that all of these should be seen as part of the same ongoing activity. To the enlightened, science was not regarded as hostile to religion; on the contrary, the visible world was seen as testifying to its invisible Creator. When the Arabs first over-ran the Hellenized eastern Mediterranean, a deliberate decision was made to translate the Greek texts available there into Arabic, and it was by way of these Arabic translations, in the multi-cultural societies of late medieval Spain, that this ancient knowledge was restored to pre-Renaissance Europe.
1] Physics, history of; Catholic Encyclopaedia, 11:48 (1911).
2] Or, to give him his full name, Abu-Jafar Mohammed ibn-Musa al-Khwarizmi, “Father of Jafar, Mohammed son of Moses, the man from Khiva (now in the central Asian republic of Uzbekistan)”
3] For this observation, among others here, I am indebted to Jim Al-Khalili’s Pathfinders, Allen Lane, 2010.
4] S. Pines, Isis, 55(3), 343, 1964
5] Technically, the two-dimensional space groups
6] We consider him part of this same cultural community, although, individual in this as in so many other things, he wrote in Persian
Alcatraz prison, (c) David Corby 2006 via Wikipedia; Creative Commons license. Statue of al-Khwarismi, Uzbekistan, Image by © Melvyn Longhurst/Corbis via the blog Missed in History. Alhambra architecture and tiling, photos by author; click to enlarge.
This piece originally appeared in 3 Quarks Daily