I see. It seemed to me that it was about the experimental method which did not fit to a mathematical statement.
I understand the possibility of being mistaken. I was mistaken many times, I am not sure with some proofs and I know some persuasive fake proofs…
Despite this, I am not very convinced that I should do such things with my probability estimates. After all, it is just an estimate.
Moreover it is a bit self-referencing when the estimate uses a more complicated formula then the statement itself. If I say that I am 1-sure, that 1 is not 1⁄2, it is safe, isn’t it? :-D
Well, it does not matter :-) I think that I got the point, “I know that I know nothing” is a well known quote.
Please, be more specific. I am not sure exactly what are you responding to.
Do you mean that a math proof (or knowledge of it) can be considered as experimental method in some sense?
I don’t think you’ve responded to my linked comment. But OK, looking up a result in a math book could count as an experiment, as could any method by which you might learn about dyslexia or whatever you suspect might be confusing you. If you don’t believe anything like that could happen to you, either you made that judgement based on experience and science or you are very badly misguided.
To be honest, your comments confuse me. I knew about the link but I didn’t see a connection between the link and experimental method and where the citations in the link came from. I am not sure what you mean by “anything like that” in your last comment and I am not very interested in it.
But I prefer to keep the original problem: If looking up a result in a math book could count as an experiment what is the (broader) definition of an experiment, then?
I think that I got the point, “I know that I know nothing” is a well known quote.
It’s actually a somewhat different point he’s trying to make (it’s spaced out over several blogposts) - the idea is not to say “all knowledge is fallible.” You should be very confident in math proofs that have been well vetted. It’s useful to have a sense of how certain your knowledge is. (like, could you make 100 similar statements without being wrong once? 1,000? 10,000?)
(i.e. “the sun will rise tomorrow” is a probability, not a certainty, and “Ghosts could be real” is a probability, not a certainty, but they are very different probabilities.)
If you’re interested, I do recommend the sequences in more detail—a lot of their points build on each other. (For example, there are multiple other posts that argue about what it’s useful to think in probabilities, and how to apply that to other things).
I see. It seemed to me that it was about the experimental method which did not fit to a mathematical statement. I understand the possibility of being mistaken. I was mistaken many times, I am not sure with some proofs and I know some persuasive fake proofs… Despite this, I am not very convinced that I should do such things with my probability estimates. After all, it is just an estimate. Moreover it is a bit self-referencing when the estimate uses a more complicated formula then the statement itself. If I say that I am 1-sure, that 1 is not 1⁄2, it is safe, isn’t it? :-D Well, it does not matter :-) I think that I got the point, “I know that I know nothing” is a well known quote.
Ahem. I can think of many ways that some broadly defined “experimental method” could come into play there.
(I think this may have came across a bit more confrontational than was optimal)
((Also, on that note, mirefek, if I came across as more confrontational than seemed appropriate, apologies.))
Please, be more specific. I am not sure exactly what are you responding to. Do you mean that a math proof (or knowledge of it) can be considered as experimental method in some sense?
I don’t think you’ve responded to my linked comment. But OK, looking up a result in a math book could count as an experiment, as could any method by which you might learn about dyslexia or whatever you suspect might be confusing you. If you don’t believe anything like that could happen to you, either you made that judgement based on experience and science or you are very badly misguided.
To be honest, your comments confuse me. I knew about the link but I didn’t see a connection between the link and experimental method and where the citations in the link came from. I am not sure what you mean by “anything like that” in your last comment and I am not very interested in it.
But I prefer to keep the original problem: If looking up a result in a math book could count as an experiment what is the (broader) definition of an experiment, then?
It’s actually a somewhat different point he’s trying to make (it’s spaced out over several blogposts) - the idea is not to say “all knowledge is fallible.” You should be very confident in math proofs that have been well vetted. It’s useful to have a sense of how certain your knowledge is. (like, could you make 100 similar statements without being wrong once? 1,000? 10,000?)
(i.e. “the sun will rise tomorrow” is a probability, not a certainty, and “Ghosts could be real” is a probability, not a certainty, but they are very different probabilities.)
If you’re interested, I do recommend the sequences in more detail—a lot of their points build on each other. (For example, there are multiple other posts that argue about what it’s useful to think in probabilities, and how to apply that to other things).