Years ago I wrote and self-published for fun the book So, You Think You’re Psychic? You can download a free PDF of it on the Books page.
There’s nothing wrong with the book—except that now I would do all the probability tables differently. None of them in the book are wrong. But I wrote the explanations when I was still a p-value believer, as all fledgling statisticians were trained to be. And still are. That has to stop. But that’s a subject for another day.
I also wrote it back in my atheist days, when I was a mistaken believer in materialism. That means the discussions about physical mechanisms of purported psychic phenomenon are incomplete, and in part flawed.
Except for these weaknesses, the rest of the book stands up pretty well. It badly needs updating, of course, and if I find myself with unexpected free time, or lucrative financial incentive, I’ll do so.
For now, let me answer an email I recently received from a person with the wonderful name of Swapnil Kamble.
I have read your book ‘so you think you are psychic?’. Its a great book. I am not very good at statistics. I had a question.
1) If try guessing numbers from a pool of 1 to 100, using (pseudo)RNG app on my mobile or pc, what is the probability of getting it right 3-4 times in a session of 100 guesses?
2) Does it mean am i psychic?
3) Also if i guess 99 out of 100 times, then am i psychic?
4) in context of guessing the numbers, at what point will i be called psychic, i mean what is the minimum probability that will prove that there is some extrasensory phenomenon involved?
1) The probability of guessing a number from 1-100, when all you know is that the number will be 1-100, is 1%, or 0.01. The probability of getting k = 3-4 right in a session of n = 100 is had by a binomial calculation. For k = 3, it’s 0.061 and for k = 4 it’s 0.015. That means getting 3 or 4 right is 0.076.
That’s not so small. Especially if you consider you might repeat the session. The probability of getting 3 or 4 right if you repeat the session just once, for a total of 2 sessions, is 0.15. If you do 3 sessions, the probability is 0.21 that at least one of the 3 sessions you’ll get 3 or 4 right. By the time you repeat it just 10 times, the probability is 0.55, or 55% that at least in one session you’ll get 3 or 4 right. Better than a coin flip!
2) Now 10 sessions isn’t a lot if you consider more than one person around the globe has done them. If just 2 people did 10 sessions, the probability at least one of them sees at least one session with 3 or 4 right is 0.79. For 3 people it’s 0.91, for 4 it’s 0.96%, and for 5 it’s 0.98, or 98%! I certainly sold more than 5 copies of the book, so maybe at least this meany sessions were completed.
You can see it’s really easy for at least one “successful” psychic session to be reported using these criteria as a “success.” Even if people are just guessing—by which I mean not using any psychic powers.
In order to prove psychic ability using these criteria, you’re going to have to do a lot better. Guessing only 3 to 4 in 100 is indicative of very weak powers. What’s stopping you from guessing all 100? Or something in the high 90s?
One answer is that you’re a very weak psychic. Hey, not every ball player hits 400, so this is possible. Now if you can consistently hit 3-4 in every session, then you might be on to something. You must keep careful, careful track, not forgetting any sessions, or partial sessions, and you must not allow yourself any excuses about why a failed session (or partial session) “doesn’t really count.” Ball players don’t get those excuses, and neither do you.
3) The probability if guessing 99 out of 100 is about 1 times 10 to the negative 197. A very, very, exceptionally small number. So, yes, if you can in test conditions, under the watchful eye of people like myself, who can spot mistakes (people often fool themselves with sensory leakage), then I’d say you’d have psychic powers.
4) This is an excellent question. There is no excellent answer. The problem is that no session of the types you are attempting are ever considered in isolation. We have had long experience of people cheating, and amazing reports come under immediate suspicion. That’s why testing under controlled conditions are mandatory.
Then some paranormal powers don’t need probability at all. Like coming back from the dead. Or turning water into wine. Do these things and we’ll know you’ve got something.