Introduction: Why Living Organisms Must Be Large
The fundamental question of how physics and chemistry account for the events within a living organism reveals a striking paradox. While life appears to follow orderly and predictable patterns, the basic laws of the physical sciences are rooted in the chaotic and unpredictable movements of individual atoms. To understand why living things behave with such precision, one must first recognize that the laws of nature are not absolute dictates for single particles, but are instead statistical results that emerge only when vast numbers of atoms act in unison.
Erwin Schrödinger notes that this transition from chaos to order is the primary reason why atoms are so small and why human bodies must be correspondingly large. If our sense organs were sensitive enough to be triggered by the impact of a single atom, our lives would be a sensory nightmare of irregular and jittery movements. We would perceive no stability in the world because the unceasing heat motion of atoms would overwhelm any meaningful signal. For a brain to develop orderly thought, it must be composed of an enormous number of particles so that the random fluctuations of individuals cancel each other out.
This statistical foundation is best understood through a mathematical principle involving the square root of n. This principle states that the physical laws governing a group of n particles are subject to a relative error of approximately 1/√n. For instance, if a biological process relied on only one hundred molecules, the law governing that process would be inaccurate by about ten percent. Only when the number of molecules reaches into the millions or billions does the relative error drop low enough for the resulting behavior to become highly predictable.
Several physical phenomena illustrate this reliance on large numbers to create order. In paramagnetism, individual oxygen molecules act like tiny compass needles that are constantly knocked out of place by heat motion. It is only because there are trillions of molecules that a consistent and measurable magnetization emerges. Similarly, the process of diffusion is not driven by a purposeful force, but is the result of countless individual molecules moving randomly until a balanced distribution is reached.
The same limitation applies to scientific instruments used to measure the physical world. A torsional balance used to measure incredibly weak forces eventually hits a limit of accuracy known as Brownian movement. If the suspended part of the balance is too light, it begins to dance and tremble from the constant battering of air molecules. Human sense organs are essentially biological instruments, and if they were too refined, they would be as useless as a balance that never stops shaking.
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