# 2.2: Role of theory

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From its early days, ecology has been in part a theoretical– mathematical science, and it is now also a computational science. Mathematical theory arises where systems are relatively simple. In our modern era, computation can address somewhat more complex systems, though creating computations on complex systems that satisfy the basic tenets of science is still problematic. For very complex systems, narrative is all we have available.

Examine the levels in Figure 2.1.1 to think about where theory applies. Subatomic particles and atoms are the realm of quantum mechanics, one of the most sublime and successful theories. Theory applies nicely to the hydrogen atom, a two-particle object. And while it applies to larger atoms, the raw mathematics becomes too complex as the number of particles grows, so computation comes into play. At higher levels like the molecular one, theory is harder to apply. Organic chemistry, for example, is not a strongly mathematical science, and at the level of protoplasm and cells there is no comprehensive mathematical theory or computational equivalent. This level is far too complex—with minuscule molecular machines running along tubules and carrying mitochondria on their backs at high speed relative to their size, it is more complex than any industrial factory. At the level of tissues and organs systems, we have only narratives to guide our understanding.

What happens, then, at the level of organisms, at the entry to ecology? Individual organisms are exceedingly complex. There is no complete mathematical theory for the internal operation of individual organisms. But externally, organisms behave as a unit and populations become simpler than individuals—glossing over heartbeat, neuron firing rates, white blood cell replication, and so on, with all their enormous complexity. Details disappear. Populations can be described with basic mathematics. Communities are more complex, but are still within the reach of mathematics and, particularly, within the reach of computation. And ecosystems are complex, but with some unifying properties.

The whole earth thus begins to be simpler, and at the level of planets and solar systems, things once again become nicely mathematical. This is the level where, with Newton, modern science was born. In part, this emerging simplicity is because levels of detail again merge together. At the level of planetary orbits, it does not matter that dinosaurs once dominated the planet or that Mozart ever wrote any concertos.

At larger scales still, solar systems are completely describable with computers, although the mathematics becomes difficult, and as we move out into galaxies and the entire universe the descriptions become difficult again.

Changing scales thus involves the successive movement in and out of simplicity. Where is the complexity in the universe greatest? It turns out to be at about one meter. In other words, at our scale. A great spike in complexity appears just where we and other forms of life arose.

That is no accident. A philosophical idea called the weak anthropic principle suggests that any part of the universe that can sit around and contemplate itself and the larger universe must itself be complex. We are constrained to live at a scale of great complexity, or not to exist at all. That is worth some reﬂection.

But we try to find simplicity among this complexity, to let us feel we understand, and to let us predict what can happen.