Is there colors that we can't see?

What a fascinating idea!
 
Sure it is, its a mix of red stimuli an green stimuli dominated by red, with little to no blue stimuli. I think it looks so different from yellow because that's where red cones start to dominate. But I'm not a color scientist so don't take my word for it.

Having finer distinctions then those I highlighted is possible, and happens with some colors. However, with 3 cones, you need at least 8 colors, for each option outlined above (including black, which I don't mention).

Actually you need only 2 "colors" (plus white or black) to sufficiently characterize most of the spectrum.

If you consider orange a color, then you cannot limit colors to only primary colors and 50/50 mixtures of them, as orange doesn't fit that. But with a new color the colors would only double if you use exactly that definition. If you conider only primary colors, then the colors would increase form 3 to 4, if you consider other mixtures then the colors would more than double.

By the way: The reason we see green, yellow, orange and red so differently, although they aren't much apart, is that the "green" cone and the "red" cone are very close together. This gives us the ability to decide between these colors.
 
I'm not only considering 50/50 mixtures. I'm considering what we perceive as separate colors: red, blue, orange, yellow, brown, magenta, ext. These aren't perfect categories as different languages have more or fewer groups. But they are widely agreed upon, and reflect the brains conceptual understanding of color.

"Categorizing the spectum" implies that we are talking about single frequency light again. With single frequency light, you are correct, as I said. But light can have multiple frequencies, and that's why having more receptors increases colors. Two overlapping receptors cannot identify light that is a mix of both high and low frequency, but not medium frequency. For that you need three receptors. This color for humans is magenta. With four receptors, more complex combinations of frequencies are detectable, each corresponding to new colors. Twice as many combinations, because it's each previous combination, plus the new color (plus the new color by itself, which can be seen as black+the new color).

Now it might be that insects see even more if there are evolutionary pressures to make finer distinctions, like we do with red and brown. But ceteris paribus, the number of colors would double.

For example, if a new cone were added between green and blue, we would be able to tell the difference between the combination 2 lights at 500 nm and 475 nm, and one light at 480 nm. Currently, assuming the right proportions for the two lights, this distinction is impossible.

Primary colors is an art term that doesn't have much to do with anything except that they are evenly spaced.

Light and dark have to do with intensity and are quite separate. Note that white is not the same as bright, since you can have a powerful red laser.
 
I'm not only considering 50/50 mixtures. I'm considering what we perceive as separate colors: red, blue, orange, yellow, brown, magenta, ext. These aren't perfect categories as different languages have more or fewer groups. But they are widely agreed upon, and reflect the brains conceptual understanding of color.

So you're measuring the number of colors by counting how many words someone has for them? The human brain can distinguish a lot of colors, no matter whether it has a name for it or not. (And people have a different amount of words for colors, women tend to have a lot more than men). There is a reason, monitors support more than 16 colors these days.


"Categorizing the spectum" implies that we are talking about single frequency light again. With single frequency light, you are correct, as I said.

Your argument makes no sense. If I consider only single frequency light and find that the amount of colors is mor ethan double and then I add a degree of freedom and also consider mixed frequencies, why the hell should the amount of colors decrease? :confused:

But light can have multiple frequencies, and that's why having more receptors increases colors.

Wrong. More receptors would also increase the colors of single frequency light.

Two overlapping receptors cannot identify light that is a mix of both high and low frequency, but not medium frequency. For that you need three receptors. This color for humans is magenta.

Why? If i have only blue and red cones, why shouldn't I be able to identify magenta? Both red and blue can be detected and differentiated against red and blue. The intermediate colors are the ones that would be missing (e.g. it might not be possible to tell the difference between green and cyan)

With four receptors, more complex combinations of frequencies are detectable, each corresponding to new colors. Twice as many combinations, because it's each previous combination, plus the new color (plus the new color by itself, which can be seen as black+the new color).

You're still only counting the combination of two colors. But as you said we have to consider the mixture of different frequencies. So you can also combine three, four and more colors. This would result in more than double colors.

For example, if a new cone were added between green and blue, we would be able to tell the difference between the combination 2 lights at 500 nm and 475 nm, and one light at 480 nm. Currently, assuming the right proportions for the two lights, this distinction is impossible.

There are no such right proportions, that the distinctions would be impossible. If you have an absorption function Ab and Ag for the blue and green cone then you would have to find proportions such that:

q*Ab(500nm) + (q-1)*Ab(475nm) = p*Ab(480nm)
q*Ag(500nm) + (q-1)*Ag(475nm) = p*Ag(480nm)

With the further restriction that p and q are between 0 and 1. There is no reasons why there should be solutions for that, and there most probably aren't. I modeled it with Gaussian functions wth a FWHM of 100Thz, and there were no solutions. So you should be able to distinguish them with only two cones.

Primary colors is an art term that doesn't have much to do with anything except that they are evenly spaced.

I used it as a term for whatever colors you take to generate your color space, not matter whether its RGB or CYM or YUV or whatever.

Light and dark have to do with intensity and are quite separate. Note that white is not the same as bright, since you can have a powerful red laser.

But black is the same as dark.
 
So you're measuring the number of colors by counting how many words someone has for them? The human brain can distinguish a lot of colors, no matter whether it has a name for it or not. (And people have a different amount of words for colors, women tend to have a lot more than men). There is a reason, monitors support more than 16 colors these days.
It is reasonable to use mental categories for a purely mental construct. A color is a granular quantity if you consider it as a fuzzy set. That is you can assign a value of how orange, green, gray, etc. any combination of frequencies is. I am saying that the number of such perceived sets would double.

I suppose it might be useful to limit colors not to words, but to distinct colors that cannot be defined from other colors. If we do this I'm sure people will agree on a fairly small set of colors. This is still a mental definition with human dependent boundaries.

What definition of color do you use?

Your argument makes no sense. If I consider only single frequency light and find that the amount of colors is mor ethan double and then I add a degree of freedom and also consider mixed frequencies, why the hell should the amount of colors decrease? :confused:
Considering single frequency light would be as you describe, where no additional color is perceived, unless the visible spectrum is widened. But this is unrealistic, because everyone is used to seeing multi-frequency light.

Considering multiple frequency light would double the number of colors perceived, as I describe.

But light can have multiple frequencies, and that's why having more receptors increases colors. Wrong. More receptors would also increase the colors of single frequency light.
What distinct new colors would an additional receptor add, assuming it does not extend the visible range? you can already see all distinct frequencies of light. However, with multi-frequency light the colors would be increased (doubled).

Why? If i have only blue and red cones, why shouldn't I be able to identify magenta? Both red and blue can be detected and differentiated against red and blue. The intermediate colors are the ones that would be missing (e.g. it might not be possible to tell the difference between green and cyan)
You would not be able to tell the difference between green and magenta. red and blue cones do overlap slightly, so you would still be able to see what is currently in the green light region of the spectrum, but you would not be able to tell the difference between that and light in the extremities of the blue red range, like a combination of what is now red, and violet. They would look just like green. There is probably a kind of color blindness that exemplifies this.

And yes, you granularity of color perception would be reduced too. But that can be countered with more sensitive receptors.

You're still only counting the combination of two colors. But as you said we have to consider the mixture of different frequencies. So you can also combine three, four and more colors. This would result in more than double colors.
Don't confuse color and frequency. Megenta is surely a color, but it cannot be mapped to a single frequency.

Combining combinations of frequencies of more than two frequencies would result in non unique colors. For example a combination of single frequency light perceived as green and single frequency light perceived as red, can be made to be indistinguishable from single frequency light perceived as yellow. Adding a receptor between red and green would change this.


There are no such right proportions, that the distinctions would be impossible. If you have an absorption function Ab and Ag for the blue and green cone then you would have to find proportions such that:

q*Ab(500nm) + (q-1)*Ab(475nm) = p*Ab(480nm)
q*Ag(500nm) + (q-1)*Ag(475nm) = p*Ag(480nm)

With the further restriction that p and q are between 0 and 1. There is no reasons why there should be solutions for that, and there most probably aren't. I modeled it with Gaussian functions wth a FWHM of 100Thz, and there were no solutions. So you should be able to distinguish them with only two cones.
Fancy math, but it doesn't agree with experiment.

Adding green and red light will result in a perceived yellow color just as readily as using a pure yellow frequency range source. This is best demonstrated with stage lights. (500nm and 475nm are actually green and blue, but the principle is the same)

I used it as a term for whatever colors you take to generate your color space, not matter whether its RGB or CYM or YUV or whatever.
Right. Well, you would need 1 additional primary color if you add a receptor.

But black is the same as dark.
I could nitpick and disagree with your words, but I suspect by and large we agree on the big picture here.
 
Wrong. More receptors would also increase the colors of single frequency light.
Err, hold on. When you say increase the amount of colors of a single frequency, what do you mean by that? How can a single frequency produce different colors without modifying brightness? Even still, won't that be the same color, except less intense/darker?

Or do you mean more receptors that respond to that specific frequency?
 
Err, hold on. When you say increase the amount of colors of a single frequency, what do you mean by that? How can a single frequency produce different colors without modifying brightness? Even still, won't that be the same color, except less intense/darker?

Or do you mean more receptors that respond to that specific frequency?
We're talking about the amount of colors generated by the whole spectrum of single frequency light. That is the whole spectum of visible EM radiation, when each frequency is detected in issolation.
 
It is reasonable to use mental categories for a purely mental construct. A color is a granular quantity if you consider it as a fuzzy set. That is you can assign a value of how orange, green, gray, etc. any combination of frequencies is. I am saying that the number of such perceived sets would double.

I suppose it might be useful to limit colors not to words, but to distinct colors that cannot be defined from other colors. If we do this I'm sure people will agree on a fairly small set of colors. This is still a mental definition with human dependent boundaries.

If you do that, you get 3 or 4 colors. All other colors can be expressed through those. And adding another receptor would increase this by exactly one, not double.

What definition of color do you use?

If one considers patches with the same brightness and can spot a difference between one patch and all others that have been designated as colors, it's a new color.

Considering single frequency light would be as you describe, where no additional color is perceived, unless the visible spectrum is widened. But this is unrealistic, because everyone is used to seeing multi-frequency light.

[...]

What distinct new colors would an additional receptor add, assuming it does not extend the visible range? you can already see all distinct frequencies of light. However, with multi-frequency light the colors would be increased (doubled).

If the visible spektrum was not widened (e.g. because a new cone was added between green and blue), we still would be able to percieve new single frequency colors. We can easily tell the difference between green, yellow orange and red, although they're close together, because of the green cone. As it is, between blue and green there are not many colors we can easily tell the difference between. If another cone would be added there, this would change, and people would start assigning whole new colors between green and blue.

And this would not be unrealistic, as you can easily create monochromatic light.

You would not be able to tell the difference between green and magenta. red and blue cones do overlap slightly, so you would still be able to see what is currently in the green light region of the spectrum, but you would not be able to tell the difference between that and light in the extremities of the blue red range, like a combination of what is now red, and violet. They would look just like green. There is probably a kind of color blindness that exemplifies this.

Yes, but the green colors would be missing, that would be missing, not magenta. You'd still be able to tell the difference between all sorts of combinations of red and blue, but in the region that would now be green, there wouldn't be many colors.

Don't confuse color and frequency. Megenta is surely a color, but it cannot be mapped to a single frequency.

Yes, that's the point. In general you cannot map a combination of two frequencies to a single frequency. That's why you need to consider at least three color combinations, leading to more than double the colors if you add another cone.

Combining combinations of frequencies of more than two frequencies would result in non unique colors. For example a combination of single frequency light perceived as green and single frequency light perceived as red, can be made to be indistinguishable from single frequency light perceived as yellow. Adding a receptor between red and green would change this.

Actually if you mix two single frequencies, it would result in a unique color with three cones. Only once you start mixing three or more unique frequencies you are getting non-unique colors. With a new cone this would increase to four single frequencies that are needed to get non-unique colors.

Fancy math, but it doesn't agree with experiment.

Adding green and red light will result in a perceived yellow color just as readily as using a pure yellow frequency range source. This is best demonstrated with stage lights. (500nm and 475nm are actually green and blue, but the principle is the same)

Only if that green and red light is already a mixture of frequencies. If you do the experiment with single-mode lasers, there would be no combination of two lasers that would exactly reproduce the color of one laser.
 
If you do that, you get 3 or 4 colors. All other colors can be expressed through those. And adding another receptor would increase this by exactly one, not double.
Not really. All colors are a mix of 3 or 4 primary colors, but that's a physical result. Mentally pink is not perceived as whitish-red, for instance. Imagining red and imagining white would not lead to an imagining of pink. On the other hand, imagining brown and white, will lead to beige. This is in some way even more subjective then the first definition.


If one considers patches with the same brightness and can spot a difference between one patch and all others that have been designated as colors, it's a new color.
Yeah, this is more or less the combination of Hue an saturation on an HSI scale. Adding a color receptor would eliminate the possibility of having hue as a single variable, for the reasons I describe. But the new degree of freedom would be bounded, and it's difficult to describe exactly how.

But the real problem I have with this definition, is that it doesn't separate the granularity of color, and the existence of new colors previously non existent. In creasing granularity can be done by increasing the sensitivity of detectors, without adding more. But adding more detectors will add more colors not distinguishable on the HSI scale.

I'm willing to consider other definitions, but bear in mind that since I'm making the claim, we use my definition of color.
If the visible spektrum was not widened (e.g. because a new cone was added between green and blue), we still would be able to percieve new single frequency colors. We can easily tell the difference between green, yellow orange and red, although they're close together, because of the green cone. As it is, between blue and green there are not many colors we can easily tell the difference between. If another cone would be added there, this would change, and people would start assigning whole new colors between green and blue.

And this would not be unrealistic, as you can easily create monochromatic light.
I agree that we would be able to make finer distinctions, I disagree that this necessarily means new names, since we can still call the colors greenish-blue. It's not like art students name every color they mix on a palette. Note that I'm assuming that we are talking about someone being born into our culture, not some other race that evolved with 4 color cones.


Yes, but the green colors would be missing, that would be missing, not magenta. You'd still be able to tell the difference between all sorts of combinations of red and blue, but in the region that would now be green, there wouldn't be many colors.
No, because you could still see single frequency light in the green range. So it still makes sense to call it green, because every body else calls it green, and it's in the rainbow. But colors that would otherwise be magenta would look just like green.

So what I'm suggesting is that colors in the rainbow keep their names. And the color not in the rainbow (megenta) be the name we omit.


Yes, that's the point. In general you cannot map a combination of two frequencies to a single frequency. That's why you need to consider at least three color combinations, leading to more than double the colors if you add another cone.
Depends on what you mean by "in general". Any two combinations of frequencies will match to a single frequency as long they are on the same half of the visible spectrum. the half way point being where green is dominant. So if false roughly 50% of the time counts as not being false in general, then you are wrong.

Actually if you mix two single frequencies, it would result in a unique color with three cones. Only once you start mixing three or more unique frequencies you are getting non-unique colors. With a new cone this would increase to four single frequencies that are needed to get non-unique colors.
Well if you mix frequencies that are close together, then it doesn't matter how many cones there are, because you're only stimulating two of them. It's when multiple cones are stimulated that having more frequencies means more colors.

So red+yellow+green=red+green=yellow, but red+green+blue=white.

That's the crux of the matter really. More cones implies twice as many combinations that are perceived distinct.

Only if that green and red light is already a mixture of frequencies. If you do the experiment with single-mode lasers, there would be no combination of two lasers that would exactly reproduce the color of one laser.
What the hell gave you that idea? Sure filters arn't as perfect as lasers, and may let some mixed light though, but thats not the main reason why mixing colors works the way it does. If you mix green and red light you will get yellow. It doesn't matter if the source is lasers or filtered light. I can find you plenty of sources that tell you that green+red=yellow, and none of them say anything about it not working with lasers.
 
There are no such right proportions, that the distinctions would be impossible. If you have an absorption function Ab and Ag for the blue and green cone then you would have to find proportions such that:

q*Ab(500nm) + (q-1)*Ab(475nm) = p*Ab(480nm)
q*Ag(500nm) + (q-1)*Ag(475nm) = p*Ag(480nm)

With the further restriction that p and q are between 0 and 1. There is no reasons why there should be solutions for that, and there most probably aren't. I modeled it with Gaussian functions wth a FWHM of 100Thz, and there were no solutions. So you should be able to distinguish them with only two cones.
I thought about this more and I think the correct equations are:

q*Ab(500nm) + r*Ab(475nm) = C*Ab(480nm)
q*Ag(500nm) + r*Ag(475nm) = D*Ag(480nm)

Where C and D are constants, representing the degree of stimuli percieved by each cone for the 1 frequency light.
q and r are the intensity of the green and blue light.
 
Not really. All colors are a mix of 3 or 4 primary colors, but that's a physical result. Mentally pink is not perceived as whitish-red, for instance. Imagining red and imagining white would not lead to an imagining of pink. On the other hand, imagining brown and white, will lead to beige. This is in some way even more subjective then the first definition.

I don't know about you, but if I imagine red and white, I'd certainly imagine pink (the rosy pink, not the magenta pink)

But the real problem I have with this definition, is that it doesn't separate the granularity of color, and the existence of new colors previously non existent. In creasing granularity can be done by increasing the sensitivity of detectors, without adding more. But adding more detectors will add more colors not distinguishable on the HSI scale.

But it does. On the edges of the spectrum it's obvious: I cannot tell the difference between 780nm near-infrared light and "normal" red light. And colors the in green range are look more similar than colors in the green-yellow-orange red range, if the ranges are of the same size. Adding a new receptor would change all that. With more information, the brain would be able to distinguish more colors in the range of that receptor.

I'm willing to consider other definitions, but bear in mind that since I'm making the claim, we use my definition of color.
The problem I have with your definition is, that is is too subjective, too reliant on language. Everyone will describe colors a bit differently, so basing a definition on that description is on shaky grounds. I don't even know how many colors there are, if we go after your definition.

I agree that we would be able to make finer distinctions, I disagree that this necessarily means new names, since we can still call the colors greenish-blue. It's not like art students name every color they mix on a palette. Note that I'm assuming that we are talking about someone being born into our culture, not some other race that evolved with 4 color cones.

The description will probably the same. But for someone like that, blueish-green and yellowish-green might have similar names, but he percieve it as totally different colors, like yellow and orange.

No, because you could still see single frequency light in the green range. So it still makes sense to call it green, because every body else calls it green, and it's in the rainbow. But colors that would otherwise be magenta would look just like green.

So what I'm suggesting is that colors in the rainbow keep their names. And the color not in the rainbow (megenta) be the name we omit.
That's just discussing on the description and that has little relevance on how we actually percieve the colors.

Depends on what you mean by "in general". Any two combinations of frequencies will match to a single frequency as long they are on the same half of the visible spectrum. the half way point being where green is dominant. So if false roughly 50% of the time counts as not being false in general, then you are wrong.

"In general" means that you can say that for every case. 50% wrong counts as "not true in general"

Well if you mix frequencies that are close together, then it doesn't matter how many cones there are, because you're only stimulating two of them. It's when multiple cones are stimulated that having more frequencies means more colors.

So red+yellow+green=red+green=yellow, but red+green+blue=white.

But you're only stimulating two cones if you are in the fringe red range. In the blue range, the red and the green cone have about the same response. And the blue cone can be stimulated up to the red range (Although the response is very weak. But that's just a question of the light power)

What the hell gave you that idea? Sure filters arn't as perfect as lasers, and may let some mixed light though, but thats not the main reason why mixing colors works the way it does. If you mix green and red light you will get yellow. It doesn't matter if the source is lasers or filtered light. I can find you plenty of sources that tell you that green+red=yellow, and none of them say anything about it not working with lasers.

You will get something that looks like yellow. But it might not correspond to any spectral yellow.
 
EDIT: removed not really related text.

I don't know about you, but if I imagine red and white, I'd certainly imagine pink (the rosy pink, not the magenta pink)
Yeah it's subjective.

The problem I have with your definition is, that is is too subjective, too reliant on language. Everyone will describe colors a bit differently, so basing a definition on that description is on shaky grounds. I don't even know how many colors there are, if we go after your definition.
Well we can't exactly read peoples minds. Language is the only tool we have to understand the mental categories our minds make.

Knowing how many colors there are does not change the fact that they double.

You will get something that looks like yellow. But it might not correspond to any spectral yellow.
I have never seen or heard of a color that a monitor cannot display. Monitors make yellow by mixing red and green, and no shades in between. It therefore seems that monitors can display any spectral colors, by mixing red and green as outlined.
 
Well we can't exactly read peoples minds. Language is the only tool we have to understand the mental categories our minds make.

I don't think so: Consider the following experiment. You take a bunch of colors and tell the subject to group them into as many groups as he thinks are appropiate. No naming of the colors necessary.

Knowing how many colors there are does not change the fact that they double.

Yes it does: To make any assertion about whether colors double, triple or whatever, you need to define first, how exactly you count the colors. Something uncountable cannot double.

I have never seen or heard of a color that a monitor cannot display. Monitors make yellow by mixing red and green, and no shades in between. It therefore seems that monitors can display any spectral colors, by mixing red and green as outlined.

:lol: There are a lot of colors that a monitor cannot display:
http://en.wikipedia.org/wiki/Gamut
 
I think your missing the point, in that colour doesn't actually exist. Different wavelengths of light enter our eye and the brain decodes this as a colour sensation.
For example, a wavelength of approx. 700nm usually indicates the colour violet. That particular wavelength has nothing to do with the colour violet, except that the brain happened to assign that specific colour to that specific wavelength.

Colours are not limited by the number of light wavelengths or how good the receptors in the eye are, they are limited by the lack of the brain to create any more.
 
I think your missing the point, in that colour doesn't actually exist. Different wavelengths of light enter our eye and the brain decodes this as a colour sensation.

That is more a philosophical question. Do ideas exist? If they do, then so do colors.

For example, a wavelength of approx. 700nm usually indicates the colour violet. That particular wavelength has nothing to do with the colour violet, except that the brain happened to assign that specific colour to that specific wavelength.

Err...no...700nm is red, as is 720nm, as is 680nm. That's the whole point. The brain cannot distinguish these, because it lacks information. Only if a new receptor was added in that range, the brain could assign different colors to those wavelengths.

Colours are not limited by the number of light wavelengths or how good the receptors in the eye are, they are limited by the lack of the brain to create any more.

If there were more, or better receptors, the brain would have additional information and would use this increased information to create more colors.
 
All 'm saying is that if another reseptor were added, then the effect of adding a receptor is that all present colors can now be mixed with the new color. The mixture will not be mappable to single a previously recognizable, but instead to two previous colors.

Therefore our current list of recognized mental color categories must at least double to accommodate the stark differences now apparent.
 
The description will probably the same. But for someone like that, blueish-green and yellowish-green might have similar names, but he percieve it as totally different colors, like yellow and orange.
This discussion is kind of tangent, because my point is not about single frequency colors.

But you're only stimulating two cones if you are in the fringe red range. In the blue range, the red and the green cone have about the same response. And the blue cone can be stimulated up to the red range (Although the response is very weak. But that's just a question of the light power)
Yes, but in the red-green range, the green cone perception goes up as the blue cone goes up, the blue doesn't add new frequency information. Same for red in the green-blue range. I admit, I'm not 100% certain of this. If you have a source, please link it.

I don't think so: Consider the following experiment. You take a bunch of colors and tell the subject to group them into as many groups as he thinks are appropiate. No naming of the colors necessary.
So choose the colors that an artist chooses to use in an all-purpose digital pallet? I suppose that could work. Yeah, I'll say it: such an artist would choose to double his pallet, if his audience and him were granted a third receptor.

Now there are anomalies with this method, such as if an artist likes to use a particular color in his work a lot, then he may have more tones of near that color. With time an artist may come to prefer more or less of the new color, and would adjust his pallet accordingly (even though it is his universal pallet).

Yes it does: To make any assertion about whether colors double, triple or whatever, you need to define first, how exactly you count the colors. Something uncountable cannot double.
It's not uncountable, there is just a lot of uncertainty in the count. And I have suggested a way to count colors.

:lol: There are a lot of colors that a monitor cannot display:
http://en.wikipedia.org/wiki/Gamut
The article discusses limitations on the shape of the gamut, but no colors are mentioned as being impossible to display in the middle. Obviously the middle is limited by discretization, but since that can be programmed arbitrarily, it can be picked such that any specific color is possible. So I maintain that a monitor can be made to match the color of any low intensity laser perfectly.
 
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