The Secret Spark, Part 2

Let’s examine the issue of the emergence of life more formally for a moment. Let me begin with a claim: Life is a binary quality. In other words, it is either on or off, 1 or 0. Life is digital. The only other option is that life is analog, moving in a continuous progression up from nothingness to a point where we recognize it as life.

Let me obviate the discussion of where that point might be by demonstrating that the cases are equivalent. First we have to start with an assumption. Let’s call it an axiom.

Life exists.

Too obvious? Without accepting this statement at the outset, we put ourselves in a difficult position. We may not know the best way to define life, but we should at least agree that there is a difference between what is alive and what is not alive. That difference is the quality we’ll define as life, and we will assume that we can tell the difference between something that is alive and something that is not. Even this assumption has its trappings, but we have to draw the line somewhere.

Now let’s consider a continuous function f that describes a thing’s degree of being alive at time t in the interval [0,1], with 0 representing something that is not alive and 1 representing something that is totally alive, whatever that may mean to us. We’ll say, for instance, that a rock has a value of 0 and a human being has a value of 1. Organic compounds changing and developing into future life will make the transition from 0 to 1, however slowly.

Now let’s define a delta function, similar in spirit to the Kronecker delta. We’ll define it as follows:

δ(t) = 0 if f(t) = 0; 1 if f(t) ≠ 0

The significance of this delta function is that it tells us when a thing has risen above the axis that forms the border between the nonliving and the living. It therefore states that the degree to which something is alive is unimportant as long as it is nonzero. This delta function therefore reduces any evaluation of life to a binary representation, which was to be demonstrated.

Now let’s examine this function for a nascent life form over an arbitrary interval of time, let’s say between t = 1 and t = 5: δ(1) = 0; δ(2) = 0; δ(3) = 0; δ(4) = 1; δ(5) = 1. We notice the change of state between t = 3 and t = 4. We therefore partition the interval t = [3,4] into regular subintervals and reevaluate. The most practical algorithm is a decimal approach, dividing the interval into ten equal subintervals, thus adding one decimal place of precision to the result.

Let’s say we find a change of state between t = 3.4 and t = 3.5. We would then subdivide that interval into ten more parts and continue the analysis. The goal is not to find the precise time the change occurred, but rather to get a precise result for the width of the interval in which it occurred.

What we’ll find if we follow this algorithm ad infinitum is the infinitesimal. In other words, the interval of time begins to resemble a mathematical point, and the emergence of life becomes like a line intersecting an axis at that point.

When dealing with time, there is a point at which it becomes meaningless. In physics, that interval is known as Planck time, equivalent to roughly 5.391 ×10^-44 seconds. The laws of physics don’t do much for us at intervals smaller than Planck time, and it corresponds to the time a photon takes to travel the Planck distance, which is the interval of length at which the quantized, digital nature of gravity becomes theoretically evident.

Perhaps we are indeed microcosms, little universes whose very existence and power of contemplation is a mystery on the order of the universe itself. But whatever we learn, and for whatever answers we find for every what and when and how, there will remain a why.