If I generate a statement at the same confidence level as “I have toenails” every day for a century, I’d be unsurprised to get a few wrong just because my brain glitches every once in a while, I’d be surprised if I got as many as ten wrong, and I’d be only slightly surprised to get them all right.
So call that .99998 confidence. Which in practice I refer to as certainty. Of course, better-designed brains are capable of higher confidence than that.
Is there anything that anyone can be more certain about than your belief that you have toenails, or is .99998 the upper bound for confidence in any prediction?
My confidence that I have toenails is more certain than my confidence that there is no accurate claim of a confidence of exactly 1.
is .99998 the upper bound for confidence in any prediction?
Not at all. For example, as I already said, better-designed brains are capable of higher confidence than that.
There may also be other classes of statements for which even my brain is capable of higher confidence, though off-hand I’m not sure what they might be… perception and recognition of concrete familiar objects is pretty basic.
Thinking about it now, I suppose the implication of ownership adds some unnecessary complexity and correspondingly lowers MTBF; my confidence in “there are toenails on that foot” might be higher… maybe even as much as an order of magnitude higher. Then again, maybe not… we’re really playing down at the level of organic brain failure here, so the semantic content may not matter at all.
My confidence that I have toenails is more certain than my confidence that there is no accurate claim of a confidence of exactly 1.
You can get pretty darn high confidences with negation and conjunctions. I can say with great confidence that I am not a 15 story tall Triceratops with glowing red eyes, and I can say with even greater confidence that I am not a 15 story tall Triceratops with glowing red eyes who is active in the feminist movement.
(Incidentally, now you have me wondering how “Linda is a Triceratops and a bank teller” would work in the classic conjunction fallacy example.)
So, as a matter of pure logic, you’re of course correct… but in this particular context, I’m not sure. As I say, once I get down to the 5-9s level, I’m really talking about brain failures, and those can affect the machinery that evaluates negations and conjunctions as readily as they can anything else (perhaps more so, I dunno).
If I made a statement in which I have as much confidence as I do in “I am not a 15 story tall Triceratops with glowing red eyes” every day for a hundred years, would I expect to get them all correct? I guess so, yes. So, agreed, it’s higher than .99998. A thousand years? Geez. No, I’d expect to screw up at least once. So, OK, call it .999999 confidence instead for that class.
What about “I am not a 15 story tall Triceratops with glowing red eyes who is active in the feminist movement”? Yeesh. I dunno. I don’t think I have .9999999 confidence in tautologies.
Within noise of 1. I couldn’t list things that I am that certain of for long enough to expect one of them to be wrong, and I’m bad in general at dealing with probabilities outside of [0.05,0.95]
In one of the ancestors, I asked if there was an upper limit <1 which represented an upper bound on the maximum permissible accurate confidence in something. (e.g. some number 0<x<1 such that confidence always fell into either (1-x, x) or [1-x, x].
I’m happy to say “within noise of 1” (aka “one minus epsilon”) is the upper limit for maximum permissible accurate confidence. Does that count as an answer to your question?
I don’t know any way to put a number to it; for any given mind, I expect there’s an upper limit to how confident that mind can be about anything, but that upper limit increases with how well-designed the mind is, and I have no idea what the upper limit is to how well-designed a mind can be, and I don’t know how to estimate the level of confidence an unspecified mind can have in that sort of proposition (though as at least one data point, a mind basically as fallible as mine but implementing error-checking algorithms can increase that maximum by many orders of magnitude).
I’d initially assumed that meant I couldn’t answer your question, but when you gave me “within noise of 1” as an answer for your confidence about toenails that suggested that you considered that an acceptable answer to questions about confidence levels, and it was an accurate answer to your question about confidence levels as well, so I gave it.
I’m not sure how I could tell the difference between two upper bounds of confidence at all. I mean, it’s not like I test them in practice. I similarly can’t tell whether the maximum speed of my car is 120 mph or 150 mph; I’ve never driven above 110.
But, to answer your question… nope, I wouldn’t be able to tell.
What do you suppose that upper bound is?
If I generate a statement at the same confidence level as “I have toenails” every day for a century, I’d be unsurprised to get a few wrong just because my brain glitches every once in a while, I’d be surprised if I got as many as ten wrong, and I’d be only slightly surprised to get them all right.
So call that .99998 confidence. Which in practice I refer to as certainty. Of course, better-designed brains are capable of higher confidence than that.
What’s your confidence that you have toenails?
Is there anything that anyone can be more certain about than your belief that you have toenails, or is .99998 the upper bound for confidence in any prediction?
My confidence that I have toenails is more certain than my confidence that there is no accurate claim of a confidence of exactly 1.
Not at all. For example, as I already said, better-designed brains are capable of higher confidence than that.
There may also be other classes of statements for which even my brain is capable of higher confidence, though off-hand I’m not sure what they might be… perception and recognition of concrete familiar objects is pretty basic.
Thinking about it now, I suppose the implication of ownership adds some unnecessary complexity and correspondingly lowers MTBF; my confidence in “there are toenails on that foot” might be higher… maybe even as much as an order of magnitude higher. Then again, maybe not… we’re really playing down at the level of organic brain failure here, so the semantic content may not matter at all.
(nods) Mine, too.
What’s your confidence that you have toenails?
You can get pretty darn high confidences with negation and conjunctions. I can say with great confidence that I am not a 15 story tall Triceratops with glowing red eyes, and I can say with even greater confidence that I am not a 15 story tall Triceratops with glowing red eyes who is active in the feminist movement.
(Incidentally, now you have me wondering how “Linda is a Triceratops and a bank teller” would work in the classic conjunction fallacy example.)
So, as a matter of pure logic, you’re of course correct… but in this particular context, I’m not sure. As I say, once I get down to the 5-9s level, I’m really talking about brain failures, and those can affect the machinery that evaluates negations and conjunctions as readily as they can anything else (perhaps more so, I dunno).
If I made a statement in which I have as much confidence as I do in “I am not a 15 story tall Triceratops with glowing red eyes” every day for a hundred years, would I expect to get them all correct? I guess so, yes. So, agreed, it’s higher than .99998. A thousand years? Geez. No, I’d expect to screw up at least once. So, OK, call it .999999 confidence instead for that class.
What about “I am not a 15 story tall Triceratops with glowing red eyes who is active in the feminist movement”? Yeesh. I dunno. I don’t think I have .9999999 confidence in tautologies.
Within noise of 1. I couldn’t list things that I am that certain of for long enough to expect one of them to be wrong, and I’m bad in general at dealing with probabilities outside of [0.05,0.95]
In one of the ancestors, I asked if there was an upper limit <1 which represented an upper bound on the maximum permissible accurate confidence in something. (e.g. some number 0<x<1 such that confidence always fell into either (1-x, x) or [1-x, x].
I’m happy to say “within noise of 1” (aka “one minus epsilon”) is the upper limit for maximum permissible accurate confidence. Does that count as an answer to your question?
What you said is an answer, but the manner in which you said it indicates that it isn’t the answer you intend.
I’m asking if there is a lower bound above zero for epsilon, and you just said yes, but you didn’t put a number on it.
I didn’t, it’s true.
I don’t know any way to put a number to it; for any given mind, I expect there’s an upper limit to how confident that mind can be about anything, but that upper limit increases with how well-designed the mind is, and I have no idea what the upper limit is to how well-designed a mind can be, and I don’t know how to estimate the level of confidence an unspecified mind can have in that sort of proposition (though as at least one data point, a mind basically as fallible as mine but implementing error-checking algorithms can increase that maximum by many orders of magnitude).
I’d initially assumed that meant I couldn’t answer your question, but when you gave me “within noise of 1” as an answer for your confidence about toenails that suggested that you considered that an acceptable answer to questions about confidence levels, and it was an accurate answer to your question about confidence levels as well, so I gave it.
So… you wouldn’t be able to tell the difference between an epsilon>0 and an epsilon =>0?
I’m not sure how I could tell the difference between two upper bounds of confidence at all. I mean, it’s not like I test them in practice. I similarly can’t tell whether the maximum speed of my car is 120 mph or 150 mph; I’ve never driven above 110.
But, to answer your question… nope, I wouldn’t be able to tell.