What is a Random Event?

Naive approaches to randomness associate random events to outcomes that cannot be predicted precisely.  Then, the argument is that lack of prediction is in turn due to lack of knowledge of initial conditions and as a result true randomness does not exist. The conclusion then is that probability does not exist in the world. However, this is the formal logical fallacy of denying the antecedent.

In the following video an unfounded claim is being made right from the start to setup a strawman argument against randomness. The claim is that if we knew the initial conditions of a coin when it is tossed, then we would know the face that will show up and, as a result, a coin toss is not a random process:

However, the above claims involve the following unsupported hidden premises and possibly more:

  • Our physical theories are true descriptions of reality
  • We can measure all of the initial conditions to sufficient accuracy
  • There are no hidden variables that cannot be measured

In the case of a simple coin, it may be possible to model its dynamics and make accurate predictions that are 100% correct for small distances and initial impulse forces (tossing force). However, imaging tossing a coin from a jet flying at supersonic speeds and at high altitude. The following question arises:

Can we know all of the initial conditions and forces that will affect the coin trajectory falling to the ground so that we can predict the outcome of the toss?

Some may argue that in principle we can know the initial conditions but are they all  knowable? If every condition that can affect the coin trajectory is knowable, can we still argue that the trajectory will be known and as a result the face that will show up when the coin reaches the ground?

To start with, I have trouble with the concept of knowbility as it may depend on the ultimate nature of reality. However, the more crucial issue here is whether the equations of motion (A) exist for this kind of trajectory and (B) can be solved without triggering a chaotic mode. These questions must be answered before one can make ludicrous claims of omniscience of dynamical trajectories.

Let’s go back to the formal logical fallacy. I have claimed before that randomness is a sufficient condition for probability but not the other way around, as non-omniscience can force us to deal with deterministic phenomena in a probabilistic way. Therefore, denying randomness to deny probability is the formal fallacy of denying the antecedent.

So what is a random event? A random event is an outcome of a probability space.  Think of a deck of cards. Ask someone to draw a card from it. Theoretically, you can assume that if you know all of the initial conditions of this experiment, including the motion of the molecules in the subject’s brain and how they can manifest her free will (if something like this exists) to decide which card to select, i.e., you have a model for that, you could predict the outcome. I am not convinced however that the assumption is correct but this is not the main issue here. The main issue is that  there is a science, called probability theory, that tries to deal with these experiments from a randomness perspective, i.e., that the selection of the subject will be random and as a result, the probability of picking one particular card is 1/52.  Those that believe that probability theory and its notion of “random events” is an attempt to assign randomness to physical reality are confused the same way that people were confused when Newton defined forces and they rushed to assign to them a real existence. Let us recall what Newton said in his reply (Principia)”

I likewise call attractions and impulses, in the same sense, accelerative, and motive; and use the words attraction, impulse or propensity of any sort towards a centre, promiscuously, and indifferently, one for another; considering those forces not physically, but mathematically: wherefore, the reader is not to imagine, that by those words, I anywhere take upon me to define the kind, or the manner of any action, the causes or the physical reason thereof, or that I attribute forces, in a true and physical sense, to certain centres (which are only mathematical points); when at any time I happen to speak of centres as attracting, or as endued with attractive powers. (Emphasis added)

I rephrase Newton’s statement to apply to randomness and probability:

I use the words randomness and probability considering those notions not physically, but mathematically: wherefore, the reader is not to imagine, that by those words, I anywhere attribute randomness or probability, in a true and physical sense, to reality.

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