In this deterministic world, one of the most important sources of uncertainty is ignorance. In the Schrödinger’s cat thought experiment, we don’t know whether the cat is alive or dead. The source of that uncertainty at the macroscopic level is ignorance. The chamber is sealed and we can’t look inside of it.
From a macroscopic perspective, it’s no different from guessing what’s inside a sealed envelope or any other situation where some state of affairs exists but lack certain knowledge.
From a probability perspective, since we understand the physics of the cat in chamber system well enough, the probability of the cat being alive or dead is known. One could put that probability into a decision tree with a high level of confidence. If the probability of a decay event is 0.5, then the cat is not half dead and half alive, it has a 50 −50 chance of being alive. The event is determined, we just don’t know the answer until we open the box.
I want to completely blur past, present and future when it comes to ignorance since for decision making becaus it makes no difference. If the cat was unlucky enough to die in the first 5 minutes of being in the chamber, then the event occurred in the past we remain uncertain in the present. If we’re making a decision at the 30 minute mark the cat has a higher probability of being alive at present than if we make it at an hour just before opening the chamber, but since we won’t open the chamber until later, it doesn’t matter to us making the decision at 30 minutes. The event may or may not have occurred; ignorance obscures equally from the start to the finish. This is true of the future as well. If we substitute a coin flip to occur in an hour with the same 0.5 probability of success, the fact that the event occurs in the future makes no difference.
Let me also point out that knowledge without communication doesn’t dispel ignorance and thus has no influence on decision making. If we assume that the cat knows that it’s still alive inside the chamber, it makes no difference to us outside of the chamber. The outcome when the box is opened remains uncertain to us. Similarly, if I have a tape or transcript of an event in the past as long as I can’t time travel to influence those events my knowledge has no effect on decisions in the past. I know the text of Lincoln’s Gettysburg Address but that doesn’t affect the choices he had in writing it in 1863.
In the same context, consider the effect of an omniscient God who controls events in the world. Whether its a God that created a clockwork universe that plays out over time or a God that intervenes in events in the time stream, it makes no difference. Whether its a God who knows the full history of creation from the inception of the world to its end or a God that steers events with some ongoing intent also makes no difference. The knowledge and power of this God has no influence on our decisions unless knowledge is granted us about the world in the past present or future. Without knowledge, the veil of ignorance is itself enough to create conditions of uncertainty. As the world is presented to us, our ignorance requires us to make probabilistic decisions based on belief.
Knowledge has positive value in decision making. The more we approach the god-like state of knowing past, present and future, the better we can make decisions. Either probabilistic states can be made to collapse into certainty, like opening up the chamber and determining the state of the cat, or probability estimates can be refined, like checking on the cat halfway through its time in the chamber. Information that is irrelevant to the decision doesn’t help refine the probability estimate. Telling me its snowing outside can’t help refine the probability of whether the cat’s alive when the chamber is opened.
Making decisions under conditions of uncertainty is no different from making decisions under conditions of ignorance. Choosing ignorance over available knowledge is a completely different case
I’ve been following along here, and I think I’m inclined to object a bit on the Schrödinger analogy, but that’ll keep for another time.
I thought about your series a great deal yesterday during my 10 hour ordeal mediating a $4M lawsuit. Both sides were dealing with ignorance, uncertainty, communication, and prediction, trying to influence one another into making a more favorable decision.
Although we had documented damages of $4M, opposing counsel attacked the calculations, going so far as to construct a scenario where we had not been harmed, but actually benefited by their client’s negligence. (“I actually SAVED you money by running over your puppy! Future costs of vet bills, dog food, chew toys, etc.”)
The presentation of the calculations was designed to be as confusing, as a preview of what they would do to a jury.
So that was an effort to create uncertainty.
We were ignorant of the amount remaining on their client’s insurance policy, and the nature of the coverage. We learned the balance remaining, and that it was an erosive benefit. The erosive benefit was the critical piece of information, because that drove one element of the prediction of what we might be likely to recover at trial. (Policy limits – trial costs). That figure created our “floor.”
We were also ignorant of what the insurance adjustor’s top figure was in settling the case. A kibuki dance of offers and counter-offers, and then “brackets” ensues to indirectly communcate that figure.
The adjustor’s goal is to spend the least amount of money possible. Were we to go to trial, we’d likely recover our “floor,” but the adjustor would exhaust the policy in defending the case. There were also threats of “offers of judgment,” wherein the prevailing party, if their offer of judgment was rejected, could recover attorney’s fees – thus increasing each side’s potential risk. This is where you want good attorneys.
At the end of a 10 hour day, we seemed to reach an agreement, the insurance company is “considering” it and has a week to agree. The figure was our floor, plus $20K – likely our costs in the current month. And either $25K under or over what adjustor’s maximum was, based on his guidance – we remain uncertain about that. The kibuki dance revealed the figure he would not exceed, though that itself was more of an inference.
It was an interesting and generally unsatisfying exercise – I don’t recommend it to anyone. But all of the factors you discuss here were in play.
I think I like the cat only because its a quirky classical example of uncertainty. There’s been debate for over 100 years on the source of the uncertainty ranging from the physical equations to common sense. I find it interesting that it was originally proposed as a counter example to defend a naturalistic view of uncertainty and dispel the oddness of quantum theory.
You can create uncertainty in the clockwork universe of a computer. Its probably a better laboratory for understanding how uncertainty arises.
Your experience is one level up perhaps than what I’m writing about right now. When you starting adding in minds the uncertainty becomes compounded by the limitations we have in understanding ourselves plus the limitations in understanding other minds. Perhaps the most marvelous outcome of all of this is that we conscious humans can accomplish as much as we do.