the first thing school students of chemistry learn is that it is all about weighing things. So many grams of this added to so many grams of that: no wonder it so often seems like cookery.
There is nothing obvious about this need for quantification in the study of matter and its transformations. There is little evidence of it in the philosophies of ancient Greece, which sought to explain nature in terms of vague, qualitative propensities and tendencies, affinities and aversions. For Aristotle, things fell to earth because they possessed a natural ‘downward’ propensity. Empedocles claimed rather charmingly that the mixing and separation of his four elements to make all the bodies of the world were the result of the forces of ‘love’ and ‘strife’.
This is not to say, of course, that quantification was absent from the ancient world. Of course it wasn’t. How can you conduct trade unless you know what you are buying and selling? How can you plan a building without specifying the heights and proportions? Throughout the ancient cultures of the Middle and Near East, the cubit was the standard measure of length: the distance from the point of the elbow to the tip of the middle finger. The dimensions of Solomon’s Temple are listed in great detail in the Bible’s first Book of Kings: an illustration of how much quantification mattered in the court of ancient Israel. Double-pan balances are depicted in Egyptian wall paintings from around 2000 BC, and precious materials were weighed out in grains and shekels. (Because the number of grains to a shekel varied from one country to another, a merchant in the Mediterranean would have to carry several sets of standard stone weights.)
And artisans knew that if you wanted to make some useful substance by ‘art’ – which is to say, by chemistry, which was then indistinguishable from alchemy – then you had to get the proportions right. A Mesopotamian recipe for glass, recorded in cuneiform script, specifies that one must heat together ‘sixty parts of sand, a hundred and eighty parts of ashes from sea plants [and] five parts chalk’. In Alexandria such prescriptions were collated and recorded in alchemical manuscripts, where they began to take on a new character. No longer content with a purely practical, empirical science of matter, the Alexandrian alchemists sought the kind of unifying principles that Greek philosophy extolled. And so one finds tracts like Physica et Mystica (as it was known in later Latin translation) by the Egyptian sage Bolos of Mendes, who flourished around 200 BC, in which the recipes are accompanied by the cryptic comment ‘Nature triumphs over nature. Nature rejoices in nature. Nature dominates nature.’
Not all of Hellenistic practical science took on this mystical mantle: Archimedes and Hero conducted ingenious and quantitative experiments without conjoining them to some grand theory of nature. Yet for chemistry, the pragmatic and the numinous remained wedded for centuries. When the Arabic philosophers encountered Alexandrian texts during the Islamic expansion in the seventh century AD, they embraced all aspects of its alchemical philosophy. The writings attributed to the Muslim scholar Jabir ibn Hayyan, which were most probably compiled by various members of the mystical Isma’ili sect in the late ninth and early tenth centuries, expounded the idea that all metals were composed of two fundamental ‘principles’: sulphur and mercury. These were not intended as replacements for the classical Aristotelian elements – Aristotle’s philosophy was revered by the Arabs – but they added another layer to it. ‘Philosophical’ sulphur and mercury were not the elemental substances we now recognize; rather, they were elusive, ethereal essences, more like properties than materials, which were blended in all seven of the metals that were recognized at that time.
Despite their pseudo-theoretical veneer, the Jabirian writings are relatively clear and straightforward in so far as they provide instructions for preparing chemical substances. The great tenth-century Arabic physician Abu Bakr Muhammad ibn Zakariya al-Razi (Latinized as Rhazes) also offered recipes that were very precise in their quantities and procedures:
Take two parts of lime that has not been slaked, and one part of yellow sulphur, and digest this with four times [the weight] of pure water until it becomes red. Filter it, and repeat the process until it becomes red. Then collect all the water, and cook it until it is decreased to half, and use it.
This prescription produces the compound calcium polysulphide, which reacts with some metals to change their surface colour – a process that would have seemed to be related to the transmutation of one metal to another, the prime objective of later alchemists.
These quantitative recipes, relying on careful weighing and measuring, were copied and adopted uncritically by Western alchemists and artisans in the early Middle Ages. But alchemy was not respectable science: the scientific syllabus at the universities was largely confined to geometry, astronomy and the mathematics of musical harmony. And so while alchemy propagated quantification and motivated the invention of new apparatus, it was indeed largely a kind of cookery learnt from books, and the measurement it entailed did not become a regular part of scientific enquiry. As often as not, old errors of quantification were simply retained. A medieval recipe for making the bright red pigment vermilion from sulphur and mercury – a transformation of obvious alchemical interest – specifies far too much sulphur, because it is based on the Arab alchemists’ theoretical ideas about the ‘proper’ ratio of these substances rather than on their ideal proportions for an efficient chemical reaction.
Only a bold and extraordinary individual would have realized that one’s knowledge of the world could be increased by measuring it. The German cardinal Nicholas of Cusa (1401–1464) was such a man. He is one of the great forgotten heroes of early science, an iconoclast who was prepared to make up his own mind rather than taking all his wisdom from old books. In his book On Learned Ignorance (1440) (a title that reflected the penchant of scholars for presenting and then synthesizing opposing hypotheses) he argued, a hundred years before Copernicus, that the earth might not be at the centre of the universe. It is a sphere rotating on its axis, said Nicholas, and is larger than the moon but smaller than the sun. And it moves.
For his investigations into natural philosophy he used fine balances and timing instruments such as sand glasses. He suggested that one might observe the rate at which objects fall by dropping them from a tall tower, and cautioned that in such an experiment one should account for air resistance. This demonstrates not only that Nicholas thought to ask quantitative questions (everyone knew that objects fell to earth, but who worried about how fast they fell?) but also that he was able to idealize an experimental test: not just to take its outcome at face value, but to think about factors that might distort the result.
To Nicholas’s contemporaries, all manner of natural phenomena, such as the weather, were dictated by the influence of the stars. But he laughed at the astrologers, calling them ‘fools with their imaginings’, and suggested instead that the weather might be forecast not by charting the motions of the heavens but by testing the air. Just leave a piece of wool exposed to the atmosphere, he said – if wet weather looms, the increased humidity will make the wool damp. And what is more, you can put numbers to that: you can figure out how much more humid the air has become by weighing the wool to measure the moisture.
He also had a bright idea for investigating the mystery of how plants grow. The notion of growth from a seed was a central emblem of the mystical philosophy of Neoplatonism, from which most of the medieval ideas about magic and alchemy sprung. But Nicholas saw that this was a problem that could be addressed by quantitative experiment:
If a man should put an hundred weight of earth into a great earthen pot, and should take some Herbs, and Seeds, & weigh them, and then plant and sow them in that pot, and then should let them grow here so long, until hee had successively by little and little, gotten an hundred weight of them, hee would finde the earth but very little diminished, when he came to weigh it again, by which he might gather, that all the aforesaid herbs, had their weight from water.
It was a fine suggestion; but the experiment was not carried out for another two hundred years.
The troublesome recluse
Nicholas’s
