You have as best of a fair coin as you can have. You flip it, it falls heads and you notice the next day that it rains in your town. You flip it some amount of times that day, and the last time you flip it, it falls tails. The next day it doesn’t rain.
You continue flipping the coin, and each time you do it, the same pattern happens.
Now, after how much days are you convinced that the coin can predict rain?
Are you never convinced? Are you always convinced?
Would the owner of the coin, being skeptical, come to believe it predicts the weather, ever? Would the owner never believe it? Would any of those make sense?
This is a thought experiment (but that is possible), that tries to point out at the arguments like ‘lack of evidence is evidence of lack’ and questions about skepticism.
I’d love for you to tell me what you think about it
Since a fair coin can land in any pattern whatsoever (even heads,tails,heads,tails,heads,tails,heads,tails always alternating) and so on for any finite amount of times… wouldn’t induction lead you to say that coin predicts the weather?
Convinced of what exactly?
I’d be convinced that there is a pattern as long as the pattern holds. But as you stated: Each time i do it, the pattern will repeat.
So the pattern existing is not a matter of whether or not i am convinced. The pattern is there and i am observing it.
What the relationship of the pattern is with rain, nature, reality, me… now those are very open ended questions and work off of assumptions. Does it cause the rain or does it predict it? Will it rain if i decide to never flip it again?
But asking whether or not i am convinced of the pattern once you stated that it will occur 100% of the time… that kinda makes no sense to me.
If the pattern is accurate 99 times i will assume it to be correct the 100th too if thats what you are asking.
Clearly there is some kind of anomaly going on because whats happening is highly statistically improbable.
The only thing i can be sure of is the fact that i am observing an anomaly.
Whether that anomaly is actually linked to weather or just one of my mate’s pranks with somekind of trick coin… i donno.
The coin, its heads or tails probability, and the weather for tomorrow, have zero correlation between them.. no matter how you want to reason it, to be so?
You are just negating the hypothesis. The point being that there is a coin that has correlation of 100% with if it rains tomorrow.
You seem to be confusing correlation with cause.
Not at all: there is no evidence of anomly, since it is possible. If, when something possible you disregard it, you are then altering the probabilities. For example, completely (even ideally) fair coins can land heads any continuous number of times.
You are observing something you don’t expect, for sure, but since it is a fair coin, and it rains (you can choose a place where the statistics is that it rains half the days of the year, even), it is to be expected.
It is not a prank nor a trick coin. It is a fair coin, and there’s nobody making any prank - that’s the point. You cannot conclude such is the case
what? I didn’t understand you. The coin you have there mostly never falls heads, which is way more surprising yet it is a fair coin and the day it rains (about once per 5 years), it certainly falls heads the day before, tho it is a fair coin
Great question. I don’t think the answer is, “After 3 days we can assume the coin predicts the weather”.
But I also don’t think the answer is, “no matter how many times it gets the right answer, we can never be justified in thinking it predicts the weather.”
Being right 3 times in a row is a one in 8 chance. So… not really all that rare. But by the thousandth day correctly predicting, I think it would be foolish not to think there’s at least the possibility of something there. I know some people would say they would never accept that as a possibility, but if we were met with such a coin, and it did keep getting it right, then even without any known mechanism for how this coin is predicting the weather, we have to accept there’s some possibility that it really is.
One way of phrasing the question is, in all possible worlds, what percent of them have a coin like this that looks like it can predict the weather, and it’s actually predicting the weather?
Vs what percent of possible worlds have a coin like this, but it’s only “predicting” correctly by random chance?
If it’s only 5 flips correct, which is something like 1/32 chance, I think it’s fair to say there are a lot more possible worlds with coins that are only random that just coincidentally look like they’re predictive. But eventually, if the number of correct flips gets high enough, it’s going to flip. Eventually it would be reasonable to say, there are more possible worlds where the coin actually predicts the weather, than possible worlds where it got it right by pure chance. I don’t know how many consecutive correct flips it takes, but I do think there’s a number.
The problem, tho, is that it is a fair coin and it predicts yet, yet predicts it by pure chance.
I think this is just an example of anything that we humans collectively came up with an explanation such as a cause-effect. Another problem is that because it is a fair coin, the amount of previous flips has no effect on the next flip, so the “Nth time” is the same as the first time.
There is a related thing, too: A fair coin can land heads any finite amount of times consecutively. If we have two bins in which we put fair coins on one, and “unfair” coins in the other, when we drop that fair coins which land heads every N times in the “unfair” bin, we are messing up the statistics of the fair coins (since we remove the throws of that actually fair coins). Plus, there are unfair coins that would land in the fair coin bin too
We only know what we see. I don’t SEE that it’s fair, I see it flipping heads and tails at an approximately equal rate, and apparently random, which kinda looks fair. And I see the final flip correlating with whether it rains every day.
Telling me what it IS doesn’t help hypothetical me decide what to believe about it. Hypothetical me looking at the flips can only choose what to believe based on what I see.
I agree with FJ’s question about possible worlds, but I would phrase it differently (though I think they are equivalent): I would ask, what is the likelihood of the alternative hypothesis? I agree there’s some level of coincidence at which I’m going to believe the coin is predicting the next day’s weather even without an alternative, but in practice we’re going to reach parity with the likelihood for some alternative hypothesis much sooner. And once we get there, no amount of additional flips will move us towards the hypothesis that the coin predicts the weather.
For example, here I notice that the coin is being flipped throughout the day, and it’s only the last flip that counts. If the owner of the coin has some other reliable way of predicting the weather, then she could choose to stop slipping on a flip that corresponds to whatever that other prediction says, and lo, the coin is as reliable as the other way of predicting the weather.
Suppose we know her to be a reasonably honest person, so for a few flips we think it’s coincidence. After about 10 correct predictions, we get suspicious, but maybe we still trust her and think coincidence is more likely (1/1,024). After 20 we’re calling bullshit (1/1,048,576), we think she’s lying.
Notice that the next flip doesn’t increase the likelihood that the coin predicts the weather. Instead, it increases the likelihood that the flipper is lying. Now, we need non-coin evidence to rule out that possibility. There’s no number of additional flips that would move us any closer to the hypothesis that the coin predicts the weather, because each flip supports a different hypothesis instead.
So, if we assume that the only possible explanations are coincidence or prediction, I agree with FJ that there is a number of flips after which we should conclude prediction. But in practice many other explanations will become more likely than prediction much earlier, and after that point the flips add no additional evidence of weather prediction.
