My point is that when two things are not noticeably different, that is not the same as mathematically equal. Therefore, your transitivity point is not valid.

Do you have a point which does not rest on the transitive property? If yes, then please restate it for me. If no, then we are done.

Equal. If you interpret it as being indistinguishable then you'll end back at sorites paradox because "indistinguishable" is a vague term - its definition contains the word negligible. There is no reason to introduce vague terms when discussing jnd.

Then why does the wikipedia page begin with "This article needs additional citations for verification"?

This belief that the jnd exists really is holding back technology. Just today I read an article on engadget titled BBC shows off 33-megapixel Super Hi-Vision Olympic footage, we ask: why? It then goes on to say that 33-megapixel technology is pointless since "8K is the maximum the human eye can understand".

just because it's the maximum the human eye can understand does not make it useless.

i'm certain there's some technological fields where it will prove beneficial. eg. take a picture of something with an 8mp, enter the data into a computer. take the same picture with a 33mp camera, and enter it into the computer. software analysis will be vastly different between these pictures.

that's like saying everything at CERN is pointless because the human eye can't see it.

You're wrong, it is not saying equal. Once you fix this incorrect thought, I think your whole issue goes away. Note that no one but you is saying that jnd=equality, so you should probably consider that you're wrong. I don't see this leading to the paradox either, so all's good.

Are you claiming jnd isn't generally accepted as true?

So what are we missing out on?

Bingo.

/thread

Let me clarify further and say that when we say 2 things differ by less than the jnd but by more than 0, we are saying that they are in fact NOT equal, but we simply can't perceive the difference.

Two things can be different and we cannot notice the difference. But they are still different.

Sometimes the difference between the two things really is insignificant (in a suitable context), in which case it doesn't matter that the two things are very slightly different. This property is called continuity in a suitable continuous framework, and you can demonstrate continuity by thinking about the effects of small variations in such a framework.

Continuity is a key concept in a wide variety of subjects.

That's a great article. So is Aether Theories, with the quote from Nobel Laureate Robert Laughlin:

"The word 'ether' has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. . . . Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry. [..] It turns out that such matter exists. About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with 'stuff' that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo.”

Probably because it needs additional citations. Wikipedia is not about what's true, it's about what can be verified in what they consider acceptable sources. (Trust me on this one, please - I have thousands of wiki edits and have been involved in discussions about this. Officially and unofficially, they will choose what's sourced over what's true, if it comes down to it. )

But that has nothing to do with the issue. You accept that at least some people advance this concept, and are claiming it's flawed. But your claim is based on the idea that it's logically impossible, when it is not susceptible to logical disproof: it's just how people perceive things. They've tested and found, unsurprisingly (in fact, inevitably) that people don't notice infinitely small differences; given that, and that they do notice big ones, there's a minimum, which they then test to find.

I don't understand how this can possibly be hard to understand.

It would be if that sufficed to make the matter disappear. It isn't a math problem, so much as a how people work problem.

You cannot distinguish between 1 yoctogram and 1 microgram, even though there is a huge percent difference between them.

The idea is that there are limits to your ability to measure crap using your eyes, skin, ears, etc. JND works in understanding your ability to measure crap.

It is a problem of how people work, not a math problem. I doubt that you are bothered that your odometer measures distance in tenths of a mile even though you can turn left at intervals of "whenever you feel like turning."

My argument doesn't rely on people interpreting it to mean equal. If you interpret it as statistically indistinguishable then you give rise to circular reasoning, as follows:

jnd is the smallest value at which a person will pick the longer of two lines which differ in length by the jnd no more often than random chance (ie 50%). Two lengths which differ less than the jnd are classed as statistically indistinguishable. The definition of statistical indistinguishability is "when the statistical distance between the two distributions is negligible". Now in this context the definition of negligible is 'less than the jnd'.

Now you can see the circular definition. If you can find a definition of negligible which doesn't contain the phrase "less than jnd" and which isn't vague then please tell me.

That's my point. My point was that ganstaman was saying jnd was accepted, but surely if this was true the Wikipedia article would have more citations.

It is susceptible to logical disproof. The jnd itself is not a subjective matter, it's objective. Just to make it clear: the jnd is not concerned with what the subjects consciously noticed. The only thing which matters is the probability of the subject picking the longer of two lines (or whatever the stimulus is) i.e. the ratio of them picking the correct versus the incorrect answer.

There is no such thing as an infinitely small difference - no number has the property of being the smallest number greater than 0.

The fact that I logically disproved jnd implies that there must be something wrong with the experiment. And there is. Here is the page describing the experiment. The fundamental problem is that the experimenters use a fixed finite number of trials. In this case it is 240. The problem with this is that this number is not enough to reliably determine when the subjects rate of picking the longer of two lines is 50.01%. It would be within the margin of error of the 50% null hypothesis so the statisticians just say "the person is just as likely to pick either".

The probability that a person picks the longer line approaches 50% (from 100%) as the difference between the lines decreases. I could run an experiment to show that a person more often than not will pick the longer line for any arbitrarily difference in length but it may require an extremely large number of trials for a small difference in length.

Yes it does. You claimed it was equality and then applied the transitive property of equality to show the concept was invalid. If we aren't talking about equality, then we don't have reason to think the relationship is transitive and your whole argument is reduced to nothing. There's no need to address any more of your post if you're now taking back your initial argument.

Did you actually read the article?

There's nothing circular coming from here.

THIS!!!

Just in case this isn't clear, this is exactly what it means. Nothing more, nothing less. It is a description of human perception.

It is just a description of the difference between "looks the same to me" and "doesn't look the same to me."

Doesn't matter whether kangareth likes it or not. It describes what it describes and does so quite well.

This thread is such a train wreck, no wonder you have trouble finding people who agree with you on other topics