Defining Uncertainty

Let’s think about the nature of uncertainty and try to get an understanding of the different ways something can be ‘uncertain’ and establish some terms to clearly define what we mean. Generally speaking, there’s at least 2 ways to use the word in this philosophical context; The casual way that it is normally used and understood in every day conversation, and the technical way that I’m going to explain here.

The casual use of the word is subjective and sometimes rather unspecific. Here are some examples of uncertainty used in the casual sense:

“I’m uncertain whether I locked the door this morning when I left the house.”

“The fate of mankind is fraught with uncertainty.

“How many grains of sand are in the world is a question that will always be uncertain.

All we can say for sure about this usage is that the subject making the statement cannot reliably predict something. The uncertainty may or may not apply to anybody other than the subject.

The technical use of the word, which I will capitalize to denote this special definition from now on, is much more specific. Something that is Uncertain in the technical sense isn’t merely unknown, but is in principle unknowable. An event is Uncertain if, given every physical fact relevant to the event, there remains more than one possible outcome. Usually, but not always, the Uncertainty of macroscopic events is negligibly small, since all Uncertainty of this type comes about during the individual quantum events that occur on only the smallest scale. Here’s an example of Uncertainty used in the technical sense that also highlights how it doesn’t always apply only to the microscopic world:

“It is Uncertain whether the cat will still be alive after spending an hour in Schrodinger’s diabolical box.”

The Uncertainty here isn’t merely based on ignorance; even a being cognizant of every physical fact could at best only predict what the odds were that the cat would make it.

A key difference I want to stress here is that uncertainty based solely on ignorance has only one possible result, regardless of appearances to the contrary. I may be uncertain whether I remembered to lock my door, but the fact is, I either locked it or I didn’t. Let’s say I did lock it when I left and just forgot. Subjectively, there are 2 possible outcomes to the event of me checking the door; locked, or unlocked. Nevertheless, when I check it, the only possible outcome is that I find it locked. There was no chance whatsoever for it to be unlocked, despite my uncertainty.

On the other hand, let’s say somebody secretly rigged my door’s lock with a box much like the one theorized in Schrodinger’s thought experiment but instead of either doing nothing or killing a cat it either does nothing, or it changes the locked status on the door (if it was locked it unlocks it and if it was unlocked it locks). Subjectively, there’s no difference to me personally since I’m unaware somebody tampered with my lock. Just like the first time, there are 2 possible outcomes to the event of me checking the door, but unlike last time, there really are 2 possible outcomes to the event. What, if anything, does this signify? Despite 2 possible outcomes, the event can only occur 1 possible way. If it just so happens that I did lock it and the box didn’t unlock it so when I check it, it’s locked isn’t that exactly what happened in the first example? How is an event that might occur but doesn’t different from the event not occurring at all? I don’t even have an inkling what the answer is. Spinning my mental wheels on thoughts like these just makes me want to lie down and take a nap. It seems to me there should be some difference, maybe in the level of entropy or in the number of possible alternate universes; who knows.

Another tricky area is mentioned in the sample sentence about the number of grains of sand in the world. Subjectively, this is obviously uncertain. Not only that, but it’s pretty safe to say nobody is certain about this, and it may even be the case that it is physically impossible to ever figure out the number because even if you could build a machine to count sand particles, say, by the time you finished counting the number of particles would be different than when you asked because the amount of sand changes more or less continuously. So we could reasonably claim that a question like this is unknowable. Does this mean it’s Uncertain in the technical sense? The answer is no. Whether you, I, anybody else, or God himself is capable of counting fast enough, the fact is that at the exact time in question, there is only 1 possible correct answer. The fact that nobody knows the answer doesn’t suddenly transform a deterministic set of facts into quantum chaos. The number of sand grains is predetermined, even if nobody’s around to do the predetermining.

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~ by jneuhaus on June 10, 2008.

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