I don’t think you could get up to 99.99% confidence for assertions like “53 is a prime number”. Yes, it seems likely, but by the time you tried to set up protocols that would let you assert 10,000 independent statements of this sort—that is, not just a set of statements about prime numbers, but a new protocol each time—you would fail more than once.
If you forced me to come up wit 10,000 statements I knew to >=99.99% I would find it easy, given sufficient time. Most of them would be probability much much more than 99.99% however.
Here is a sample of the list:
I am not the Duke of Edinburgh.
Ronald Mcdonald is not on my roof
I am not currently in a bath
I am currently making a list of things I believe are highly likely
Eliezer Yudowsky is not a paperclip maximising AI
I am not the 10,000th sentient being ever to have existed.
The Queen is not a cockerspaniel in disguise.
I am not a P-zombie.
53 has no prime factors other than itself. (this is much greater certainty; as I can hold in my mind the following facts “the root of 53 is less than 8. 53 is not in the 7 times table. 53 is not in the 5 times table. 53 is not in the 3 times table and 53 is odd” simultaneously. For 53 not to be prime would require, as for 2+2 not to equal 4, that I be very insane. My probability of being that insane is less than 1 in 10,000, and of having that specific insanity is lower still.)
The difficult part is in finding 10,000 statements with precisely 1 in 10,000 odds; not finding 10,000 statements with less than 1 in 10,000 odds.
If you can make a statement every two seconds, you could actually stand up and do this. If I could get sponsorship to offset existential risk, I’d take this challenge on to actually stand up for the best part of a day and make 10,000 true statements with nary a false one.
I would however go for less variety than you if I wanted to be confident of winning this challenge. “My teeth are smaller than Jupiter. The Queen is smaller than Jupiter. A Ford Mondeo is smaller than Jupiter...”
Those statements aren’t even approximately independent though, if Jupiter turns out to be really small, they’re all true. That’s why mine were so weird, the independence clause.*
*(they still aren’t actually independent, but I’m >99.99% sure you couldn’t make a set of statements that were)
However, it’s possible to make a set of statements that are mutually exclusive, which might actually be a superior task “I am not the 11,043rd sentient entity ever to exist. I am not the 21,043rd sentient entity ever to exist, etc.”
I perceive the intention of the original assertion is that even in this case you would still fail in making 10.000 independent statements of such sort—i.e., in trying to do it, you are quite likely somehow make a mistake at least once, say, by a typo, a slip of the tongue, accidentally ommitting ‘not’ or whatever.
All it takes to fail on a statement like “53 to be prime” all it takes is for you to not notice that it actually says ’51 is prime’ or make some mistake when dividing.
Any random statement of yours has a ‘ceiling’ of x-nines accuracy.
Even any random statement of yours where it is known that you aren’t rushed, tired, on medication, sober, not sleepy, had a chance and intent to review it several times still has some accuracy ceiling, a couple orders of magnitude higher, but still definitely not 1.
If you forced me to come up wit 10,000 statements I knew to >=99.99% I would find it easy, given sufficient time. Most of them would be probability much much more than 99.99% however.
Here is a sample of the list: I am not the Duke of Edinburgh. Ronald Mcdonald is not on my roof I am not currently in a bath I am currently making a list of things I believe are highly likely Eliezer Yudowsky is not a paperclip maximising AI I am not the 10,000th sentient being ever to have existed. The Queen is not a cockerspaniel in disguise. I am not a P-zombie.
53 has no prime factors other than itself. (this is much greater certainty; as I can hold in my mind the following facts “the root of 53 is less than 8. 53 is not in the 7 times table. 53 is not in the 5 times table. 53 is not in the 3 times table and 53 is odd” simultaneously. For 53 not to be prime would require, as for 2+2 not to equal 4, that I be very insane. My probability of being that insane is less than 1 in 10,000, and of having that specific insanity is lower still.)
The difficult part is in finding 10,000 statements with precisely 1 in 10,000 odds; not finding 10,000 statements with less than 1 in 10,000 odds.
If you can make a statement every two seconds, you could actually stand up and do this. If I could get sponsorship to offset existential risk, I’d take this challenge on to actually stand up for the best part of a day and make 10,000 true statements with nary a false one.
I would however go for less variety than you if I wanted to be confident of winning this challenge. “My teeth are smaller than Jupiter. The Queen is smaller than Jupiter. A Ford Mondeo is smaller than Jupiter...”
Those statements aren’t even approximately independent though, if Jupiter turns out to be really small, they’re all true. That’s why mine were so weird, the independence clause.*
*(they still aren’t actually independent, but I’m >99.99% sure you couldn’t make a set of statements that were)
However, it’s possible to make a set of statements that are mutually exclusive, which might actually be a superior task “I am not the 11,043rd sentient entity ever to exist. I am not the 21,043rd sentient entity ever to exist, etc.”
I perceive the intention of the original assertion is that even in this case you would still fail in making 10.000 independent statements of such sort—i.e., in trying to do it, you are quite likely somehow make a mistake at least once, say, by a typo, a slip of the tongue, accidentally ommitting ‘not’ or whatever. All it takes to fail on a statement like “53 to be prime” all it takes is for you to not notice that it actually says ’51 is prime’ or make some mistake when dividing.
Any random statement of yours has a ‘ceiling’ of x-nines accuracy.
Even any random statement of yours where it is known that you aren’t rushed, tired, on medication, sober, not sleepy, had a chance and intent to review it several times still has some accuracy ceiling, a couple orders of magnitude higher, but still definitely not 1.