10.1.2—
Chemistry

A second example can be supplied by chemistry, which experienced distinctly separate stages of progress towards mathematical and connective maturity. There was a time when chemistry was largely independent of physics. In fact, chemistry attained a remarkable degree of mathematical maturity with very little help from physics, and it is possible to learn large portions of chemistry with little or no knowledge of physics. (Indeed, I believe it is still the practice in teaching chemistry in the schools

first to present a chemistry that involves little or no physics before moving on to those parts where physics becomes crucial.) For there was substantial progress in understanding basic laws governing combinations of the elements before there was any underlying physical theory about what sorts of microstructure might account for these laws. The periodic table (Mendeleev around 1869), the notion of valence (Frankland in 1852), and a remarkable set of laws governing combinations of elements (as early as Lavoisier's work published in 1787) were developed long before these notions were further grounded in a theory of subatomic particles in the twentieth century. With the development of the periodic table, the notion of valence, and laws of combination, chemistry achieved a significant degree of mathematical maturity. In this respect, the age of Lavoisier made a significant step beyond the procedures and wisdom of previous chemists and alchemists, however great their technical skill, because there was, for the first time, a rigorous and systematic description of how the elements reacted in combination.

The major progresses in theoretical chemistry since the time of Mendeleev have been in the connections, the border marches, between chemistry and other disciplines such as physics and biology. In order to understand reactions between large molecules, for example, it was necessary to understand something of their physical structure. The propensities of molecules to combine in certain ways (some of which seemed anomalous) called for an explanation in terms of underlying structure, an explanation supplied by such notions as electron orbitals, ionic and covalent bonding, and the postulation of charged and uncharged subatomic particles. In the process, chemistry became increasingly connected to physics. At the same time, it became evident that many biological phenomena could be accounted for by chemical explanations: the bonding between hemoglobin and oxygen accounts for the transport of oxygen through the circulatory system to cells throughout the body (and hemoglobin's preference for bonding with carbon monoxide explains the ease of carbon monoxide suffocation); important parts of processes such as the Krebs cycle are chemical in nature; and of course the basic element underlying genetics, the DNA molecule, is typified by a particular molecular structure. With the advent of discoveries such as these, chemistry—which already had a high degree of mathematical maturity—acquired a large amount of what we might call connective maturity as well. It is worth noting, however, that most of these connections were not made until the latter half of the twentieth century, more than a century after

chemistry had gained significant mathematical maturity. Some things take time.

It seems safe to say that sciences tend to become both more powerful and more firmly established as they become more intimately connected with one another. Chemistry raises questions that physics has to answer, and provides answers to questions raised by biology. Astronomy provides a lab for physics to study things that cannot be reproduced here and now, and physics provides a lab for testing hypotheses about things that are too far away to investigate firsthand.