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"OH WATERS, TEEM WITH MEDICINE TO KEEP MY BODY SAFE FROM HARM, SO THAT I MAY LONG SEE THE SUN." - Rig Veda

Living things are low-entropy and energy-consuming, so they are unstable in the thermodynamic sense. Nevertheless, they can still be remarkably stable in the sense of persisting over time. Some replicating populations (certain bacterial strains, for example) have maintained themselves with little change over astonishing periods – millions, even a billion, years. They exhibit what we call dynamic kinetic stability (DKS). And, like entropy, DKS turns out to be driven by simple, powerful mathematics.

In fact, it rests on the mathematics of exponential growth. This is a pattern that we often see in self-replicating systems, and they don’t even have to be physical. Suppose you start with a dollar. Double it every week and, in well under a year, you’ll be the world’s richest person (assuming no one else discovers your secret). Keep going for another five years and you’ll have more dollars than there are atoms in the observable universe. Self-replicating molecular systems can, in the right circumstances, start off on the same explosive path. But there’s a twist: when they do, a new kind of chemistry emerges. Ultimately, it is this new chemistry that leads to what we term biology.

How could such a transformation come about? Why do replicating molecules give rise to replicating cells? In a word: evolution. Or, in four more: replication, variation, competition, selection.

Replicators do not always make perfect copies of themselves, and their variants have to compete with the originals for resources. Because both the originals and ‘bad’ copies share the same tendency towards exponential growth – because neither of them will stop unless they run out of resources – the more effective replicators end up driving the less effective ones into extinction. Accordingly, less persistent replicators tend to evolve into more persistent ones. Just like in the ‘regular’ chemical world, change in the replicative world is directed toward greater stability. Once again, it all comes down to the weight of numbers.

The second difference is a little harder to grasp. With entropy, the weight of numbers is always in the same direction. That keeps things simple: everything tends towards randomness and disorder. With DKS, on the other hand, stability is fickle. Some replicators are indeed astonishingly durable, but, crucially, DKS always remains circumstantial. Change the environmental conditions and the winner of the replicative race can change. In fact, that’s exactly what makes life so capricious and the evolutionary path largely unpredictable: the mathematics of replication forces it into a paradoxically restless search for rest.

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