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Zero Probability

“It isn’t. I think it isn’t…”

This is my translation of “Pravděpodobnost nula”, a beautiful meditation in mathematics and philosophy by Petr Klán.

It isn’t. I think it isn’t.

I am walking through the sum of the harmonic series, <$ \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \ldots $> Far into infinity. It is not that this sum is unbounded that fascinates me; it is the incredible slowness of its growth. Around the ten-thousandth term the sum is only a little over nine. Changes are visible neither far behind nor far ahead. Thinking of timelessness, I am surprised by Plato walking in the opposite direction. He says: “You see the timelessness. You are walking in the right direction. Towards the discovery of timeless mathematical objects isomorphic with the history of the Universe. They existed before us and will exist after us.” Fantasy beautiful and near, I muse.

At the 100,000th term the sum is just twelve. I. Newton suddenly appears and speaks boldly. “I do not believe in timelessness but in one clock showing absolute time. It gives sense to the motion in the Universe and its laws, even though I do not know where exactly the clock is.” Fascinating courage and reason, I muse.

At the millionth term where the sum is but little over fourteen I overhear R. Descartes and G. Leibniz excitedly discussing the multiplicity of time, the consequence of things and processes of the real Universe. Ambling soon after them is A. Einstein who brings this idea to fulfillment. I am trying to understand what he is saying. “Absolute time? Every observer has their own time. Yet laws of motion make sense. But there is timelessness in equations.” A stage with amazing, rhythmic performance, I muse.

I am speeding up, I would like to reach the sum of one hundred today. At the unimaginably “timeless” term of fifteen followed by forty-two zeros. A large screen outside by the path tells me that I am approaching the present. It is showing “What is real is real only in the given moment. A moment is one term in a sequence. The future is not known, it is open, with infinity of possibilities. Only a small number of them will be realized.” Zero probability does not exist in unimaginable timelessness, I muse.

Tired, I walk to the nearest telescope to observe future moments which I do not know. The telescope can see all the way to the sum of one thousand somewhere around the term of 175 followed by 432 zeros. Moments in which it is difficult to predict events are different here, “longer” than moments in which certainty is assumed. Past the sum of one thousand is the horizon of the harmonic seriesʼ visible timelessness. Despite my weariness I am amazed to observe something strange. A being appearing in mutually incongruous states. Alive and dead at the same time, with clock going forward and back in the same moment. Moments are simultaneously short and long, events are certain and uncertain. A nice future is one that is imaginatively uncertain and socially certain, I muse.

I am falling asleep. In the real time, with unknown future. I had to age that day to live longer. Timelessness does not bring zero probability with it. When I woke up in the morning refracting rays were embracing a rose not yet awakened. In the infinity of possibilities and the finitude of time they had.

May 21, MMXIII — Philosophy.