eli5 When it comes to probabilities of past events

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When someone says “wow there was only a 30% chance of that happening!” But wouldn’t it be 100% because it DID happen and due to an (probably) infinite amount of unseen variables? In this way would this mean the universe is deterministic?

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Probabilities are usually a stand-in for uncertainty. Usually when someone says something had “a 30% chance of happening”, they actually mean “given the limited information”.

But that stops being true when you get to quantum mechanics, as far as we can tell. There, there are true probabilities. There is no “more information” you could know that would allow you to know which measurement outcome would happen.

This is still potentially deterministic if the many worlds interpretation of quantum mechanics is true, since then all possible outcomes do happen. The evolution of the wave function is deterministic and the statistical nature of measurement outcomes arises from self-locating uncertainty about which branch of the wave function you’re on.

Some things are deterministic. E.g. if you built a sufficiently accurate machine to flip a coin in the exact same way multiple times in a row, it could get the same face every time.

But there are some physical phenomena, particularly at the quantum level, which do appear to be truly probabilistic. Perhaps we simply lack understanding of how the universe really works.

Roll a 6-sided die. You have a 1/6 chance to roll a 6.

You rolled a 1! You had a 1/6 chance to roll a 6; it just didn’t happen.

Roll again. You rolled a 6! You had a 1/6 chance to do that, and sure enough, it happened!

“The past has a probability of 100%” is a statement that helps avoid getting too into this argument (for better or worse). It can mean “the past has happened, and probability no longer has any effect on it”, which is where you seem to be coming from. We shouldn’t base too many of our decisions on the theoretical chance of something specific happening if the chance of it happening is already in the past (sunk cost fallacy, as an example).

But probability is fun! And even if we can’t change the past, looking at the theoretical probabilities can give us appreciation for how special the present is by examining how special the past was. So when somebody talks about a past event with a probability, they are talking about theoretical events that didn’t happen, not the 100% of the past. They are talking about how special the current state of things are, and how randomness can measure the theoretical chances.

It’s misused fairly often (so what if my combination of genes has a small chance of existing, I’m me and even if I was different I’d just be a different me that also had a small chance of existing), but generally thinking of “past random chance” as “how special past events are” instead will probably help you understand what people are talking about.

>“wow there was only a 30% chance of that happening!”

The operative word here is “WAS”. Yes now that it has happened, there is a 100% chance that that’s the outcome that happened. But before that, there WAS a 30% chance that that outcome would be the one that happened. When people say “there was only a [%] chance of that happening”, they mean that’s what the probability was before the event happened, given only the information available at the time.

If you flip a coin and get heads, there *was* a 50% chance of that happening – because before the flip, the odds of heads *was* 50%.