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Thank you.. I think so too, because we can argue the point all day long ad-infinitum, but we will never get past this.. 
..until we can answer that.
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Putting it through an LLM might yield some interesting results.
Nothing is impossible but things can be highly improbable.
The longer you flip a coin the closer you will get to 50/50 heads and tails. If thats not the case, you have something influencing your throws. Thats simply how statistics work.
Zero correlation? But… they have 100% correlation. That’s the premise of the thought experiment. That they’re perfectly correlated.
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I didn’t consider it to be a different person flipping the coin. I read the OP as, I’M the one flipping the coin. If I flip the coin, and I choose when to stop flipping, and I already know that I’m not a meteorologist or consciously controlling the weather myself in any way, then… all that went into my answer.
When you look at the scenario as it being a coin you’re personally flipping, does that affect your take on the situation?
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Oops, you’re right, my mistake.
Let’s replace it with some version of self-deception. Maybe the weather segment is on the radio every day when my alarm goes off, so I hear the next day’s forecast without consciously registering it, and subconsciously choose to stop flipping on a flip that correspond with what I heard.
I think that’s unlikely, and could easily accept a 5-10 flip coincidence. 20-30 flips and it seems like the reasonable alternative to a weather-predicting coin. And it would still require non-coin evidence to disprove.
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It would seem so on the surface.. what we see is happening, but the correlation between them is illogical, for scientific reasons.
..unless the fair coin is made from a weather-modifying material. 
lol
Correlation is what’s on the surface. Correlation is a surface level observation. Every time you see a, you see b. Every time you don’t see a, you don’t see b. That’s correlation. If it’s what you see on the surface, then that’s correlation.
The coin and the weather are correlated in the given scenario. We don’t know why they’re correlated, we don’t know how, we don’t know if they’ll continue to be correlated. We don’t know if they have a casual link. But what we do know is they are correlated.
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Difficult to pinpoint but at about 97% confidence or 2.2 sigma. Too lazy to calculate know how many days that is.
LLM agrees with me on what it means for something to be correlated:
First of all I thank you all for having this back and forth
Ok, fair enough! You then can’t discount it is a fair coin (nor have good reasons to believe it is not a fair coin)
The problem with that is that “likelihood” is less precise than what was previously written. It can have several different meanings (like belief, certainty, trustworthiness, all different).
What do you mean by that? Do you suppose we are bound to find some explanation?
The point is that there is nothing fishy in the example. You are adding stuff which is fishy (for example, a person), which obviously is liable. Now, you assert that you think someone is lying when that someone is not lying (since that is not in the hypothesis). Do you mean that in practice you would call a non liar a liar? But then… to make it even more obvious, you can change the weather for the output of a Stern-Gerlach experiment (50% each) and you’d be in way worse waters. In fact, you are dissecting a different hypothesis.
@MagsJ I still don’t understand what you meant. What did you mean before? Are you supposing there is a mechanism where there isn’t? The correlation is illogical as how? Both the statistics of weather there (to simplify it) are 50% and both can be correlated yet not one causing the other nor having both a mutual cause
Then you fall into the problem of probability being only surely applied to thought scenarios (not practical ones), it being subjective and so on. You seem to hold the frequentist view of probability (the longer you flip a coin…). From the set of all fair coins, most will land 50/50 but others will land some N number heads. They’re not most fair coins, for sure, but some will. Maybe a better example is that a coin that lands exactly heads then tails then heads then tails then heads then tails all along can be a fair coin (with no influence), and an unfair coin too. For example, the basic thing of a fair coin is that each throw has the same probability as the prior, so it can land heads any N amount, all in a row.
You seem to be confusing statistics and probability - they’re not the same. Statistics gives data about measured stuff. Probability, as much as solid ground we can step on, is about thought scenarios.
I would think it’s a fair coin. A fair coin that also has this added extra property of predicting, or possibly even causing, the weather.
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But then… is it a property of the coin?
Yes, if it predicts rain correctly 99 times out of 99, it is a magic coin.
But is it a fair coin, then? Is it a magic fair coin?
Did it get rain right 99 times out of 99?
For 99 days this happened: The last flip of some day fell heads. The day after that, it rained.
Now, if the coin was in some sort of very windy place, with nobody to watch if it fell heads or tails the last time of the day… even if the next day rained when it was heads… did in that case that coin predict the weather?
I would at some point think it is, if it’s correct enough times in a row about raining. Obviously it’s a stipulation of the situation that it isn’t.
I think maybe you’re confused about the fact that sometimes it can be justified to believe something that’s incorrect. I’m saying I would BELIEVE that it’s a property of the coin in some way, and that it would even be rational to believe that, because of what I see, even if it’s incorrect. You can have rational beliefs that are nevertheless incorrect.
Rationality doesn’t guarantee 100% rate of correctness, rational people are just more often correct, or less drastically wrong, than irrational people.
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..and my mind instantaneously told me that they are not, because.. there is a correlation for you/others, but not for me/other others.
[the confusion seems to lay, in that I have not changed my initial position, but you have failed to see that]
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I know what it means, I just don’t agree with it.
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There are known mechanisms with regard to Astrology, specifically regarding the birth-season <—> personality aspect.. mine is ‘psychopath’. 
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I’m supposing there isn’t a mechanism where there should be one, in order to make sense of the coin as predictor of rain.
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Because there lacks a mechanism, to connect the coin to it raining.
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Indeed.