Randomness and Logic

Randomness

If you consider the classical example of a random event, a coin toss, you will realize that this event is not fundamentally random. It is governed by the laws of Physics. Given the initial states, like the coin mass, air density, the force of the flip and anything you can think of, the result of the coin toss can be predicted in theory. What we call random here is just a practical ignorability.

Logic

Logic is an abstract concept. But consider how you would implement logic in the physical world. Like a logical AND gate. The implementation of the AND gate although results in a practically deterministic behavior of it, fundamentally it is probabilistic due to how quantum particles behave.

Quantum particles

Quantum particles like photons and electrons behave randomly. But this an oversimplification. Take the famous double slit experiment for example where if you shine a light (or photons) through a slit, it creates an interference pattern behind the slit. So when we observe the light it behaves like a particle, but had it behaved like a particle all along it shouldn’t have produced a pattern. So the measurement results here are probabilistic suggesting the event had some randomness. A side note is that there are a few, and rather stunning interpretations, of this event which we do accept to be fundamentally random. For example, the Many-Worlds interpretation goes into the idea of multiverse where our measurement brings us to a single reality, where the unobserved outcome happened in a different reality.

Duality

To me the coin toss and the logical AND gate seem like the two sides of the same coin (pun not intended). And that coin is philosophically a gap in our understanding of this mysterious region between reason and chance. The coin toss seems practically random but fundamentally deterministic, while the AND gate seems practically deterministic but fundamentally random. Or may be not.

My naive brain thinks that only one of these is ultimately true. It’s either all fundamentally governed by reason or it’s all fundamentally random. And we will very very likely never know which one it is.

But this gap between the universe being completely deterministic or probabilistic is where life is - we are caught between what we can predict and what we can’t, trying to making the most of both.