It's possible that I'm not considering something about certain types of experiences, but Smith were to have...a set of coincidences play out in his life, it seems as though Smith could convey those experiences to Jones at least well enough for Jones to understand them and evaluate what the most likely cause was, just as Smith can. In other words, it doesn't seem like access to the qualitative aspect of these experiences is required in order to evaluate these experiences. That seems to be the important point here.
OK. I'm Smith, you're Jones and this is real, not a hypothetical example.
I used to be a skeptic, until a period of intense and transformative experiences about 13 years ago, after which I am best described as a mystic of no specific religion. I'm reluctant to say "I'm a theist", because everybody has different ideas about what the word "God" means, but I'm definitely a supernaturalist. The central theme of those experiences was synchronicity. Big ones.
I'm getting married in three weeks. When I met my fiancee, at the end of 2012, she was entirely agnostic regarding such things. She had no strong religious beliefs and no strong atheism/skepticism either. I talked to her about what had happened to me, and at the end I said to her "just watch out for synchronicity."
Then something happened on my birthday in September 2013. I don't really do birthdays - I've spent years telling people not to send me cards. Only my mother persisted in sending them, so it was normal for me to recieve only one card. But my fiancee also decided to give me a card - which she drew by hand a few days before my birthday. On the day of my birthday I got a card in the post from my mother. It had some mice on it, preparing for a party, and a cat, and a balloon. I put it on the mantelpiece. When my fiancee (then girlfriend) got home from work, still having not yet seen my mother's card, she gave me hers. She'd made me some pickle and some jam as presents, and inside the card it said "you're the pickle on my cheese, the jam on my scone" and on the front was a picture of pickle going on cheese, and jam going on scone. I put it on the mantelpiece next to the other one, but the wrong way round (the picture was sideways). She told me to put it the right way up, so I moved it through 90 degrees.
A few minutes later, as I sat on the sofa drinking a glass of wine, I noticed something strange about the pictures. Firstly it was obvious that in both cases there was a lump of cheese in the bottom left corner. A slight co-incidence - how often do you get two birthday cards with a lump of cheese in the same corner, especially when you only got two cards in total? But I had now also noticed that in both cases, in the top right hand corner there was a red circle with something dangling down from it. 2 co-incidences on the cards? I pointed this out to my girlfriend, and just as she was saying "oh, that's a bit strange, isn't it" she stopped in mid-sentence and said "Geoff, look in the top left corner!" The body of the cat on my mother's card was drawn from behind, as a circle. And it was a tabby cat (I have a tabby cat), so it was multi-coloured, with black lines curving round on a grey background. And on my girlfriend's card? In the same corner was the pickle, which just happened to be a grey circle with black blobs in it, sort of going round in a circular effect. By now you'll have guessed how the story ends. There was only one corner left. In the bottom right hand corner of my girlfriend's card was a scone. And on my mother's card? A cake.
At this point my girlfriend was completely freaked out, although not in a frightening way. She knew she hadn't "cheated" - it was her who drew the card, after all, and she had no way of knowing what card my mother was going to send. For her, it was conclusive proof that I was for real, and I think it was probably a turning point when she decided she wanted to stay with me - that I was the one. It was also conclusive proof in the reality of synchronicity. She says it is the strangest thing that has ever happened to her. It's a long way short of the strangest thing that has ever happened to me, but it's in the same category.
Now...assuming I am not just lying to you, and that my girlfriend wasn't lying to me....that these co-incidences are real...is it enough to convince
you?
Because I've posted this on a skeptics' website, and I can tell you that a grand total of zero skeptics believed there was anything even remotely spooky about this. In fact, for them it was just evidence that people will believe any old tripe. And yet when I look at those cards, it is as obvious to me as the day it happened that this was synchronicity - or "mind reading" - at work. It's an almost perfect example, and as good an example as you could hope for to test your own theory out.