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Randi is a kook because he is a tv personality with a profitable image to preserve.
Think.
A few hours ago it was quite clear from what you posted here that you had no idea how Randi's $1 million challenged even operates. Now here you are calling Randi names. You don't know anything about the man.
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Regarding your questions about how to determine if psychic abilities are real or not, let's run with an example.
Suppose I notice that sometimes when I'm out walking at night, streetlights mysteriously turn off as I walk under them. I suspect I may have a special magical aura that causes street lights to turn off when I walk near them.
What if you had experiences that could be reproduced, how many times would you have to reproduce it on your own before you understood it was real?
With my streetlight ability, I'd want to test it out a reasonable amount. For example, I wouldn't go walking along the same street every night at the same time, walking under the same lights. Maybe they're on timers. I'd look silly if I called the papers and claimed I could turn off streetlights just by walking near them, and I couldn't.
So, what I'd do is I'd walk down lots of different streets. I'd walk under lots of streetlights. I'd start making records of how many of the lights I walked under turned off in my presence. I'd note the details. Do they turn off after I walk under them, or before, or does it vary? What delay is acceptable before I might put it down to another cause? Suppose I walk under a light and 10 minutes later it turns off (maybe I get a friend to follow me around 10 minutes later to check the lights). Is it still fair to say that my power caused the outages?
How many lights need to turn off to confirm my mysterious power in my own mind? Is 1 in 10 enough? 1 in 50? 1 in 100? Or at least 1 in every 2 or three? I mean, maybe my power doesn't absolutely work every time, but if it works 2 times out of three, that's still fairly convincing.
At what point would you share this reproducable experience?
At the point where I was confident that it was truly reproducible.
At that point I might front up to James Randi and say "I have thoroughly checked my powers, and I assert that 3 times out of every five times I walk under a streetlight it will turn off." That's a solid, definite, testable claim. Note that my power doesn't have to work every time to verify my claim.
With whom would you share it?
Once I was really confident, I'd share it with everybody. I'd become famous as the guy who can turn off lights just by walking under them. Freaky!
What if it didn't work when you tried to reproduce it for an audience, but worked again when you were alone?
Then I'd begin to suspect somebody was playing tricks with me, or that I was mistaken, or mad. I'd try to get a few close friends, relatives or associates to come on one of my walks and witness my power for themselves. That would be a good check on whether I was crazy or not. Of course, I probably would have done that in the first place, before I started making claims in front of an audience.
Would you discontinue your investigation?
I'd continue investigating until I determined whether I was mistaken, deluded or the subject of a prank.
Would you try to find out why it only worked when you were alone and nobody knew what you were doing?
Naturally.
Premonition is certainly useless in most cases, there is very little to look to other than mental projection, but how would you study it?
Keep a diary of your premonitions, for a start. Do it for a reasonable time. For example, if you get one premonition a week, do it for 6 to 12 months. Then look back over what you wrote down. How many premonitions came true, and how many did not? Once you've convinced yourself that you're really getting premonitions, go to somebody else and let them keep your diary and do the checking. Then you have an independent witness.
Remember to be specific about your predictions. Don't write down "I will see a cat in the next month". Write down "I will see a white cat with a damaged ear crossing West 22nd street at 3 pm next Tuesday." Check to see if it comes true.
What controls would you use?
For what? A formal test?
Suppose I wanted to demonstrate my streetlight ability. I'd get independent testers to randomly open a page of the street directory and select a random street. Then, we'd all go down there at night and I'd walk down the street, taking care to walk under each streetlight. The formal testers would note how many of the streetlights turned off as I walked along, and check against my claims of how many I thought would be affected.
Note: I would have to be clear with my claim up front. If I told the testers that the streetlights would turn off within 10 minutes of me walking under them, then if it was suddenly reported two days after the test that all the streetlights in that street had mysteriously failed for some unknown reason that wouldn't confirm my abilities. You can't change the rules after failing the test you said would be fair.
What if it didn't fit your structure out of ignorance?
Then I'd make an effort to learn more.