Recommended Reading
The Position of Chemistry
amongst the Other Sciences & Mathematics
When I was studying in the Sixth Form for my three A-Levels, Maths/Phys/Chem, I was undecided which to follow at university. I already had my own chemistry laboratory at home, so I thought that if I applied to read mathematics, I would be able to continue with chemistry as a hobby. As it turned out, I was offered a chemistry place at Oxford, and most of my best friends there were mathematicians. The best of both worlds, perhaps.
My maths friends used to try to wind me up, saying that the physical sciences were just a branch of applied mathematics, and that maths itself was more akin to languages. The argument was along the lines of “My father is bigger than yours . . .”. If you are currently in the Sixth Form, you may be experiencing similar arguments between the Arts and Science students. However, the maths people did have a point: all sciences use mathematical models in order to explain their experimental observations.
Similarly, some physics undergraduates used to say that all of chemistry could be explained in terms of their discipline. Again, they have a point. Chemistry is related to the valence electrons in atoms, ions, molecules, and other species. The behaviour of electrons is well established. To a first approximation, the classical model of point electrical charges, in an electric field, may be applied; i.e. classical electrostatics. To a second approximation, more detailed analysis requires quantum mechanics to explain some of the deviations from classical behaviour. Both classical electrostatics and quantum mechanics are considered to be under the Physics banner, which uses Mathematical models to explain behaviour. In addition, Chemistry is often divided into Physical, Organic, and Inorganic, underlining the connection between he two sciences.
Some chemists have gone as far as to say that all of Biology can be explained in terms of Chemistry, but that the former has not advanced far enough from the phases of classification, taxonomy, etc.
These extreme views are often put forward with a certain degree of tongue-in-cheek, and in playing devil’s advocate. They also display hindsight rather than history, i.e. ignoring how mathematics and the different sciences have fed off, and developed alongside, one another. Using a top-down approach, the protagonists portray a Venn diagram, with mathematics encompassing all sciences, physics embracing the other sciences, chemistry encircling biology, which is a subset of them all. Poor biologists! If the physicists think that they are so much better, why do they have such a host of so-called fundamental particles (including 36 quarks) in their Standard Model, with a possible equal number again as their supersymmetric partners in string theory?
Another point, often conveniently ignored by mathematicians and physicists in their arguments, is the Three-Body Problem. The mathematical model of the Earth orbiting the Sun (or more strictly, them both orbiting their centre of mass) is that of the two bodies being represented by point masses, and the gravitational force between them following the inverse square law. The equations for this can be solved exactly, so that at any given time, you can predict their exact positions and velocities, from Newton’s Laws of Motion. If you bring the Moon (the Third Body) into the model, exact solutions become impossible. [Note that this is without even taking into account Heisenberg’s Uncertainty Principle, and Einstein’s Theories of Relativity.] To a large extent, this does not make a great difference to us in the real world. Approximations (using perturbation theory) can predict the tides, forthcoming eclipses, how to send rocket missions to the Moon, etc, with sufficient accuracy.
Applying the same principles to chemistry, the behaviour of an electron in a hydrogen atom (2-body problem: 1 proton + 1 electron; classical electrostatic inverse square law attraction) is well defined mathematically. Solutions of the maths equations exactly match experimental observations in e.g. spectroscopy. Any additional particles result in insoluble equations, i.e. the chemistry cannot be predicted. In practice, what happens is that the experiments are performed to produce the quantitative results, and the approximate solutions to the equations are obtained in an iterative fashion (perturbation theory), until the values become close. It is then said that theory and experiment are in agreement. Extended theoretical work can then plug experimental values into the equations, with the possibility of making further predictions. Until a fully defined TOE (Theory of Everything) is produced, this is the way that things must proceed: theory and experiment leapfrogging, feeding off one another. With a TOE, the numbers should just drop out of the equations (e.g. mass and charge of the electron; the universal gravitational constant; the speed of light). However in science, you can never prove a theory, only disprove it. You can never know when a new experiment, or a thought, will throw up something unexpected, which does not fit in with what is currently held to be true.
Two of my maths friends have mellowed with age and experience, and have become less insular in their view of their subject. They stayed on in academia. One is now professor of mathematical biology, i.e. using mathematical models to explain biological systems. The other, in this age of worry about climate change and global warming, is applying partial differential equations to explain the flow of glaciers.
When we look at the sciences and mathematics, we bring our own point of view, perspective, prejudices, baggage, etc, with us. It is good that some scientists become so engrossed in their own branch of a subject, that they pursue it to the greatest depths. Equally, it is good that others are able to take a broader perspective, forging links between strands in different areas. The development of maths and science goes hand in hand as communication is maintained between various areas. Any thoughts of going into these fields could take you on a journey of many twists and turns, never quite knowing where you might end up.
Bon voyage!
