In the words of Richard Feynman, "if it disagrees with experiment, then it's wrong." The difference threshold is utilised in countless peer reviewed studies with known practical applications. We can entertain all the math we like, but if it disagrees with reality, it's wrong...
I do not know what the explanation would be, it would need exploring with technology we currently don't have. What is known is that presenting the same tone to a human subject does not produce the same conscious perception, when all external stimuli can be controlled within significant limits, it would seem the explanation is likely to do with the nature of the internal processing. A hypothesis. :)
On your main point: what if you keep all conditions of the subject and environment constant? Then it should be impossible for the subject to respond differently to identical stimuli, shouldn't it? He should perceive A the same in all such occasions. On your fancy point: where, when, how does reality disagree with math?
Perhaps, but we cannot keep all the conditions of the subject constant, the machinery of human perception is made of millions of proteins in constant flux and you cannot hope to keep them the same. If you present the same tone to a subject over and over they will rarely place it at the same volume each time they hear it. Human beings have variable perception, unlike machines which can accurately measure the tone in decibels. This is explained by ROC curves.
That's right. But are you suggesting that it is constant physiological change that accounts for the existence of just noticeable differences? If you aren't, then you should take my proposal as a Gedankenexperiment in need of explanation.
Ah, I see where you are coming from. No it's a mistake in interpretation, what actually happens is that the subject could hear A twice and say they are different A does not always equal A in the mind. Therefore the Weber Just Noticable Difference can only really be interpreted statistically, but those statistics are demonstrably useful. The video on signal detection theory might help. ... and yes, reality disagrees with mathematics frequently. :)
Let me try to summarize your answers. I think you grant there can be no Weber fraction working for one subject in unchanged internal and external conditions. You state that the just noticeable difference, usually expressed as a Weber fraction, exists only as an average over many subjects and many conditions. Am I right? To be honest, I must still figure out whether this emergence as an average is mathematically possible if the fraction doesn't exist for any subject under fixed context. Thanks.
Surely, reality cannot disagree with mathematics. Perhaps, experiments are misinterpreted in some way. Take items A and C, with just the threshold difference between them, and put item B in between. So, you claim the subject will say that A is differeent from C but B is just the same as both A and C, don't you?
In the words of Richard Feynman, "if it disagrees with experiment, then it's wrong." The difference threshold is utilised in countless peer reviewed studies with known practical applications. We can entertain all the math we like, but if it disagrees with reality, it's wrong...
I do not know what the explanation would be, it would need exploring with technology we currently don't have. What is known is that presenting the same tone to a human subject does not produce the same conscious perception, when all external stimuli can be controlled within significant limits, it would seem the explanation is likely to do with the nature of the internal processing. A hypothesis. :)
Take a series of a hundred sounds S1-S100 such that, for all n, the difference in pitch |Sn-Sn+1|
On your main point: what if you keep all conditions of the subject and environment constant? Then it should be impossible for the subject to respond differently to identical stimuli, shouldn't it? He should perceive A the same in all such occasions.
On your fancy point: where, when, how does reality disagree with math?
Perhaps, but we cannot keep all the conditions of the subject constant, the machinery of human perception is made of millions of proteins in constant flux and you cannot hope to keep them the same. If you present the same tone to a subject over and over they will rarely place it at the same volume each time they hear it. Human beings have variable perception, unlike machines which can accurately measure the tone in decibels. This is explained by ROC curves.
That's right. But are you suggesting that it is constant physiological change that accounts for the existence of just noticeable differences?
If you aren't, then you should take my proposal as a Gedankenexperiment in need of explanation.
lovee the accent
Ah, I see where you are coming from. No it's a mistake in interpretation, what actually happens is that the subject could hear A twice and say they are different A does not always equal A in the mind. Therefore the Weber Just Noticable Difference can only really be interpreted statistically, but those statistics are demonstrably useful. The video on signal detection theory might help. ... and yes, reality disagrees with mathematics frequently. :)
Why we always call the answers constant.. What does this mean
Let me try to summarize your answers. I think you grant there can be no Weber fraction working for one subject in unchanged internal and external conditions.
You state that the just noticeable difference, usually expressed as a Weber fraction, exists only as an average over many subjects and many conditions.
Am I right? To be honest, I must still figure out whether this emergence as an average is mathematically possible if the fraction doesn't exist for any subject under fixed context.
Thanks.
Surely, reality cannot disagree with mathematics. Perhaps, experiments are misinterpreted in some way.
Take items A and C, with just the threshold difference between them, and put item B in between. So, you claim the subject will say that A is differeent from C but B is just the same as both A and C, don't you?