The whole idea behind the just-noticeable difference is fundamentally flawed. The basic idea is that there is some minimum detectable difference in our perception before we can see the difference. So for example if I increase the brightness of a light by 0.001% it would be below the jnd and therefore you would be unable to detect any difference. I'm going to argue that this doesn't make any sense.

Assume that the jnd of temperature is 0.3K. Any difference below this in temperature would be unnoticeable. Therefore 30.2K feels the same as 30.4K and 30.4K feels the same as 30.6K. However, 30.2K does not feel the same as 30.6K because the difference in temperature is 0.4K which is above the jnd of 0.3K. Am I the only one who sees the problem here?

It's like saying a = b, b = c and a != c. It's obviously wrong, it leads to a logical absurdity. It breaks the transitive property of equality. The jnd cannot exist.

I think the reason the jnd has been formulated is a result of the way we use language. If I held up two sticks which were exactly 1.0m and 1.0000000001m in length and asked "Are there two sticks the same length?" the vast majority of people would say yes. However, everyone would realize that it's actually impossible for them to be the same length. The variations would result from their atoms vibrating differently due to heat - their lengths would be constantly changing by incredibly small amounts. Since it is impossible to completely remove the effect of heat from any system this effect will always be taking place.

The reason the people say "yes they are the same lengths" is because they interpret the question as "Is the length difference of these sticks less than 1mm (or some similar value)" or "Has the manufacturer of these sticks put a large amount of effort towards minimizing the difference in length of the sticks". We unconsciously interpret the question in a way different to its literal meaning. If we didn't do this automatically, communicating would be very difficult and take a long time.

This directly leads me to disliking the word "negligible" because its definition is essentially "quantities smaller than the jnd". So I do avoid using the term negligible.

The broken concept of jnd makes people not improve things which could could be improved. We say things like "There's no point in increasing the frames per second beyond 60 because the human eye cannot detect it as a 1/60th increase is below the jnd" or "We shouldn't increase the DPI of this screen because an increase is beyond the resolution of the eye (Retina Display)".

This belief that there is a jnd is holding back our progress in many technologies and we should do everything in our power to make it clear that jnd does not exist. If anyone would help to get the jnd article removed from Wikipedia it would be greatly appreciated.

Or the jnd exists, like all the research shows, and you're just ****ing up by assuming what you call equality (a sub-noticeable difference) is a transitive relation among things subject to jnd when it actually isn't.

The mistake is probably due to a rounding error.


PTB

Or it really exists (kind of, sort of) and your understanding is flawed. The key is understanding that your perception is somewhat granular and somewhat continuous in nature.

It is probably a bit of both (existing, you not understanding), but I can assure you that your body probably works well enough for you to navigate the world with sufficient precision that it doesn't make a whit of difference in any endeavor you should chose unless you decide that your best purpose is to be a human thermometer.

(and, it has nothing to do with how the question is phrased. The specific question asked is "which one is longer (hotter, whatever), or are they both the same length (temperature, whatever). It has nothing to do with manufacturing tolerances.)

Well this is just a sorites paradox.

There's no height such that we would say "X is tall", but if he were 1mm shorter, we would not say "X is tall". However, there are people who could not be described as tall.

A "just-noticeable difference" is not transitive

OP, maybe think about it this way: If you're right, and the whole A = B, B = C, so A = C argument works, then it can be extended to arbitrary-length chains, and to arbitrarily small distances, and you could conclude either that humans are capable of noticing literally every difference there is, or that they are capable of noticing no differences at all.

Does either of those results comport with your own experience of the world?

this thinking is so flawed.

the jnd is 0.3k.

the difference between 30.2k and 30.6k is > 0.3k so the difference is noticeable.

just because no difference is noticeable between 30.2k and 30.4k AND 30.4k and 30.6k does NOT mean it isn't noticeable between 30.2k and 30.6k.

I'm pretty sure "accepted as fact" isn't a requirement for an article on Wikipedia. If it were, here's a short list of articles that need to be removed before "just noticeable difference":

Luminiferous aether
Plum pudding model
Any number of articles on cosmology
Any number of articles on psychology
etc.

I just realized what JND meant

You're saying if a trees falls in the forest and no one is around to hear it then it DOES make a sound.

Yes, but if we can't tell the difference between a jar with 1,000,000 jelly beans in it from one with 999,999 jelly beans in it, then logically we can't tell one with 2 jelly beans from one with 1 jelly bean.

In case this sounds like I am backing kangaroo, I am not. His take on it is silly.

JND exists in a certain manner but is not a complete view of perception. It isn't meant to be the whole theory of perception. It has limitations. Those limitations have been examined in great detail through experiment. It is a problem of just learning about how people actually work than a logical problem.

Equality is a transitive relation. The transitive property of it applies to anything you use with it, including the jnd which is a constant. If the equality relation is shown to not work with jnd then its the jnd which is invalid not equality because equality is defined rigorously.

It's not. Sorites paradox is the result of the poorly defined term "heap".

Equality is transitive. The constant k is defined as ΔI / I. So it is simply a number. You can't say "oh well logic doesn't apply to this number because it's special".

The truth is that you are both looking for a relation similar to equality but which does not have the property of transitivity. There is actually such a relation and its name is "approximately equal to". ≈ Often in everyday language we mean ≈ instead of = for example when saying "That egg's mass is 100g" we don't mean mass = 100g, we mean mass ≈ 100g. I think it's this loose use of language that contributes to rise to the belief that a jnd exists.

Look at an example such as a digital camera. It takes photos and outputs a 1000 by 1000 image with each pixel taking a value from 0 0 0 (black) to 255 255 255 (white). I take the camera to a pitch black room and get out my photon firing machine. My machine can fire an exact number of red photons specified by the user. I set it up to fire 1 photon at a particular pixel on the camera's CMOS sensor then take a photo. The photo is still completely black. I keep incrementing the number of photons fired by 1 until there is a difference in the image. This occurs when I fire 21 photons. The output photo now has the top left pixel with value 1, 0, 0.

It would be tempting to say that the jnd of the camera is 21 photons. But the fact is that changing the number of photons by just 1 can potentially change the output of the camera. If it changes from 0 to 1, the output does not change but if it was changed from 20 to 21 it changes.

This does not seem right.

Equality is transitive certainly. If a=b and b=c then a=c.

But indistinguishability is not transitive. Given a ind b and b ind c, it does not follow that a ind c. You can see that in the statistical analysis of experiments or measurements. Equality and indistinguishability are not necessarily the same thing.

This is not quite right either. That is not how sensors work. There is a chance that the detector will produce a signal even in complete darkness due to the inherent energy of the electrons in the sensor. The warmer the sensor the higher that dark current. The detectability is a function of the statistical likelihood of random chance producing a signal. I think you really need to consider the effect of the statistics of measurement and error more in this discussion. I think that would change your point of view.

jnd is better expressed as a % rather than a fixed number.

It's a good that we aren't talking about indistinguishability then. I found this pdf which explains Statistical Indistinguishability but you will see it uses the term "negligible". This is a term which I outlined in my first post as problematic as it is essentially a synonym of jnd.

I am aware that my example was very simplified. But adding in random chance does nothing to disprove anything I said. Each increase of a single photon would still increase the probability that the output will change.

When we say that 2 things differ by less than the jnd, are we saying they are equal or indistinguishable to us?

As a more general note, you are taking an interesting tone itt. Jnd seems like an accepted concept. If I didn't feel it made sense or was inaccurate, I would come to the forum to try to understand where my thinking was wrong. After all, I'm not so special that I think I can overthrow an already accepted concept. But you seem so convinced you're right that you come across as mean to anyone trying to explain why you're not.