This week we hosted our second Leeds Colour Conference following the successful event in 2019. You can see details of the event here. We had two keynote speakers who didn’t disappoint. The second keynote was given by Ján Morovič from HP who spoke about how many colours there are. It was a brilliant presentation. Not surprisingly, there was no single answer. Rather, Ján’s talk discussed why this is a difficult question to answer and why there is probably no precise answer. But in doing this he covered so much ground in his usual engaging style. It was by far my favourite talk of the conference.
However, his talk reminded me of something I posted on quora a year or so ago. My post was not as sophisticated as Ján’s talk of course but covers some related topics. I reproduce it below for your reading pleasure:
HOW MANY COLOURS ARE THERE IN THE UNIVERSE?
This is a really interesting question but it cannot be answered without first stating what colour is.
I teach colour science at the University of Leeds. Whenever I have a new class I invariably start with the question: how many colours are there? (in the universe, is implied and sometimes I explicitly add, in the universe).
Within the first five minutes someone normally says that there are about 16 million; another person will say that there are an infinite number; and someone else will normally add that there are only three colours? Sometimes, I get someone who says that there are no colours (in the universe).
I then ask them how many countries there are in the world. Undergraduate students generally don’t know and to be fair I had to look it up. It turns out, of course, that the number depends upon whether you accept this or that country as being an independent country. However, the answer is about 186. Students normally give answers close to 186. Some may go as high as 300 and others as low as 150. But nobody says that there are as few as three. We don’t get answers to this question that range from 0 to infinity? Why?
The reason is because when we use the word country we have a good shared understanding of what the word means. When we use the word colour we do not. So that is where we need to start.
I think the two most logical answers are that there are zero or infinity. But let’s deal with 16 million and 3 first.
Those who say that there are about 16 million colours are aware that there are about 16 million different combinations of RGB on a typical emissive display. However, this is an arbitrary constraint of current technology, actually of commercial technology. When I was studying for my PhD (in the 80s I might add) I was not aware of any display that could provide 16 million combinations of RGB. We were happy with about 16. But in my lab today I have a display (actually the combination of a display and a graphics card) that can display about 1 billion different combinations of RGB. 24-bit colour displays (that can display RGB each with 256 values) are common. There doesn’t seem to be a consumer demand for displays with higher bit depth. But such displays certainly do exist and are used in research labs all over the world including in my own.
Those who say that there are only three colours in the world are referring to one of two ideas, both of which are fallacies. The first fallacy is that we can generate all colours by mixing three colours (called primaries) together. Of course, it has been known for a very long time that we cannot mix three colour primaries together to make all other colours. We cannot do this irrespective of whether we use additive or subtractive colour mixing. We can make all hues but hue and colour are not synonyms. If we try to make all colours by mixing three primaries we will find that we cannot match the chroma or saturation of some of the colours in the world. The second fallacy is that our visual system sees the world in RGB and creates all other colours from that starting point. This is ridiculous of course. Not only do we not see the world in RGB but it is not even true that we have three cones that are sensitive to just red, green and blue. I’m not going to provide a full explanation about this here but I have written about this quite a lot before. I will simply show the spectral sensitivity of the three cone types we have in our eyes.
Notice that the L cone class (which is sometimes referred to as the R or red cone) has sensitivity to (and therefore responds to) almost all of the visible wavelengths and that the maximum sensitivity of this cone is not even in the red region of the spectrum.
Now we can come to the idea that there are an infinite number of colours in the world. This idea is based on the belief that colour is a physical property of the world. According to this view, light at say 700nm really is red. It doesn’t just look red, it is red. This idea has been contested for a very long time. The earliest critique of this that I can find is by Democritus (460–370BC) who said:
For by convention colour exists, by convention bitter, by convention sweet, but in reality (there is only) atoms and the void.
According to this alternative view, perceptions such as colours, sounds, and smells do not exist in the world independently of us or other sentient beings. Imagine a world where there is no living sentient creature. A tree falls in the forrest. Does it make a sound? When the tree falls it generates a movement in the air called a pressure wave. It is only when that wave strikes the intricate structures of our ear that a physiological response is generated that ultimately results in our brains generating the perception of sound. Similarly, we touch a hot metal object. We experience pain. We would say that the pain is a property of the object. We experience the perception of pain which is our response to a physical property of heat. Sound is something that we experience as a response to a physical property (movement of air). Taking this view, we can say that colour is a response to sensing the physical property of light. Democritus is perhaps less well known than Newton who wrote something similar in the 1700s. He said:
For the rays to speak properly are not coloured. In them there is nothing else than a certain power and disposition to stir up a sensation of this or that colour.
According to Newton, light at 700nm is not red; it merely looks red to us. This might seem to be splitting hairs but the distinction is critical. It is why we sometimes disagree about a diagram similar to the one shown below.
The two small squares above are physically the same. You are probably looking at them now on a display. These two squares have the same RGB values. However, they don’t look the same. I quite like to use the terminology physical and perceptual colour (though I note that not every colour expert will agree with this classification). I would argue that the two squares are physically the same colour but perceptually different colours. The one on the right looks lighter, for example.
Some people will say that this is an illusion and they will say something like this.
The two squares are the same colour but they look different in colour because of the contrast with the respective backgrounds.
In fact, this is the view of most laypeople, I would argue.
However, it is my opinion that when they say something like this they are using two different definitions of the word colour in the same sentence without realising. I would modify their sentence to make this clear as shown below:
The two squares are the same (physical) colour but they look different in (perceptual) colour because of the contrast with the respective background.
They are some striking examples of this sort of illusion. For example:
In this image, the blue squares on the upper surface of the cube on the left are physically the same as the yellow squares on the upper surface of the cube on the right. By physically the same I mean that they have the same RGB values if you are looking at this on a display. If you print out this image and cut out the respective blue and yellow patches and view them out of context they will appear grey. In fact, the printer will have simply used a little bit of black ink in order to generate these blue and yellow patches. So where is the colour coming from?
I am happy to accept the terms physical and perceptual colour even though I have close colleagues who do not agree with me. They would argue that colour is perceptual and that there is no physical colour; there is only light. They would argue that light at 700nm, for example, is not red; it merely looks red. And they would have the likes of Democritus and Newton on their side.
If we accept for a moment that colour is a physical property then I think we could argue that the number of colours in the world is infinite. At least, for any practical purpose. I’m not an expert in quantum phenomena.
I have worked for my whole life to try to understand colour and to solve practical problems that arise in connection with colour. I work at the University of Leeds where I am Professor of Colour Science and Technology. In addition to my teaching and research I have undertaken consultancies with companies. These companies are concerned with textiles, automotives, food stuffs, cosmetics, dentistry, skincare, displays, printers, paints, inks to name but a few of the topics. You see, everything in the world that is manufactured is coloured and companies who manufacture those things invariably start to worry about how we communicate colours, how do we control colour, and how do we assess colour. And that is where I come in. In the 35-40 years of my professional career I have never come upon one instance of a company who cares about physical colour. They care about what colours look like. Because that’s what their consumers care about. Imagine a scenario where a consumer buys a suit and the jacket and the trousers don’t match. They look different in colour. And imagine that when they take the garment back to the store to complain the customer service agent says, “Don’t worry. They are the same physical colour. It’s just an illusion that they look different in colour.” It just won’t wash (pardon the pun).
Whenever I talk about colour or write about colour I am referring to perceptual colour. For me, if two things look different in colour, they are different in colour because that is how I define colour.
So finally we get to the people who responded that there are no colours in the world. They understand that colour is perceptual. They may even say that colours don’t really exist. However, I would disagree with them on this last point. To argue that colours don’t exist because they are perceptions is akin to arguing that pain is not real or that love does not exist. Not everything that exists in this world is explicitly physical.
Can a display with 16 million RGB combinations display 16 million colours? If you believe in the physical definition of colour you would presumably say yes. I would say no. Some of these combinations of RGB produce colours that are indistinguishable. According to my view of perceptual colour, if two stimuli (sorry to be technical at this point but if you have read so far I think you will allow me this) look the same colour, they are the same colour. And if two stimuli look different in colour they are different in colour. A while ago I published a paper that attempted to determine how many colours a smartphone could display. I ended up with an estimate of 2–3 million. I should declare that this work was supported financially by Samsung. But I still think the methods are interesting.
If you ask colour scientists in the world how many colours there are, most will say that this boils down to how many colours we can discriminate between. However, this is still a very difficult question to answer. And I have at least one close friend (who is a world expert in colour) who would argue that the question is ill-posed and cannot be answered. However, most estimates put the number somewhere in the range 3–8 million. My answer would be 3–5 million.
So there we have it: there are 3–5 million colours in the world.
You may agree or disagree with me. However, I hope – at the least – that you will agree that the question of how many colours in the world is an interesting and complex one. There is no easy answer that everyone agrees with. Certainly, it depends upon how you define the word colour. In my opinion, a lot of the disagreements that we see about colour stem from this problem that we don’t have a shared understanding of what the word even means. Some people, as I mentioned earlier, even conflate the words hue and colour and that is one of the many reasons why there are so many misconceptions around today about colour such as the fallacy that we can make all colours starting with three primaries.
Postscripts:
- I post a lot on quora – mainly about colour but sometimes about other subjects such as academic and chess. If you want to read any of that you can see my quora page here.
- Quora is free and I have no intention to ever participate in the quora program that monetises content. I really love quora as a platform. I have met some really nice (and incredibly knowledgeable) people there. The only thing that could make me leave quora would be if it becomes completely overrun with chatbots (thinking about it, that could be happening quite soon). But I do provide some paid content on a different site. A while ago I set up a patreon website where for a small monthly contribution you can get more focussed, detailed and intimate content. The idea behind this is to to generate ad curate high-quality content that will help people on their journey to understand colour.
- If the idea of people conflating terms such as hue and colour intrigues you and you are interested in more such misconceptions I really encourage you to visit the Colour Literacy Project webpage and particularly to view their new page on colour misconceptions.
Like some of your close colleagues, I am convinced by all the evidence that colour is perceptual and, as such, exists only in the mind; but I disagree with them when they subscribe to the prevailing sloppy notion, typified in the National Aeronautical Space Authority’s explanation, that only some light is perceptible:
The light we see, made up of the individual colours of the rainbow, represents only a very small portion of the electromagnetic spectrum. Other types of light include radio waves, microwaves, infrared radiation, ultraviolet rays, x-rays, and gamma rays — all imperceptible to human eyes.
(“What is the electromagnetic spectrum?”, hubblesite.org.)
Given that colour exists only in the mind and that lightness is one of colour’s three attributes (along with chroma and hue), then lightness exists only in the mind whereas all electromagnetic energy lacks lightness and, as such, exists only outside the mind in a physical world utterly devoid of lightness. This includes the electromagnetic energy the retinal capture of which in the retinas triggers vision. Thus the visible and physical worlds are mutually exclusive: insubstantial images of red balls exist only in the mind and substantial lightless balls exist, uncoloured and imperceptible, in the lightless, uncoloured and imperceptible physical world.
Quantum string theory agrees that this is so: “the three-dimensional world of ordinary experience … is a hologram …”. (See p. 298, “The Black Hole Wall”. Leonard Susskind, 2008.) Relativity theory, however, is based on the prevailing view that some electromagnetic energy is perceptible, even if it constitutes the merest sliver of just 0.0035% of the full spectrum of electromagnetic energy with the remaining 99.65% described as “invisible light” and, as such, exists, utterly imperceptibly, outside the mind. However the merest sliver of radiant energy is said to exist simultaneously both as imperceptible electromagnetic energy in the utterly imperceptible but substantial physical world and as insubstantial imagery in the full spectrum of three-dimensional colour contrasts in the insubstantial but visible world which exists only in the mind.
Relativity theory’s assumption is based on the fact that rays of electromagnetic energy emitted from two far-distant events which reach one observation point simultaneously and will reach some other observation points one after the other. From this fact, the theory infers that the two earlier events took place simultaneously with respect to the first observation point, whereas the same two events took place one after the other with respect to the other observation point. This ignores the fact that the radiant energy from sequential effects will also reach some points simultaneously and other points sequentially: physical simultaneity is imperceptible because it pertains to the earlier occasion when invisible distant events emit invisible radiant energy, not to the later occasion/s when some of that earlier-emitted invisible energy gets to be absorbed in an observer’s retinas thereby triggering her perception of the imagery of visible events apparently taking place in their colourful, three-dimensionality only in her mind.
The inference’s obvious invalidity arises from the fact that, instead of relying on the facts of physical mechanics, relativity theory relies on the perceptual experiences of two observers, one of whom is based midway between two very distant
simultaneous events and the other of whom is moving along the straight line between the two events. Thus the stationary observer gets to see two apparently simultaneous events and the moving observer gets to see one event happening somewhere up ahead of her before she gets to see a second event happening somewhere back behind her. In short, the visible relativity of simultaneity is a perceptual phenomenon and, as such the relativity is with respect to the observer, not with respect to the completely invisible physical world. (See my seperate paper on Chapter IX, Part 1, of Albert Einstein’s “The Special and General Theories of Relativity”.)
This is confirmed by the fact that events are seen to take place, not in the earlier invisible order in which they actually took place, but in the later order in which those events’ radiant energy reaches the viewer. For example, imagine a solar flare taking place seven minutes before an electromagnetic event takes place on the Moon. By this time the solar rays are 7 minutes, and 7/8ths of the way, into their flight to Earth, so the Suns’s rays are one minute away from Earth right now. The rays from the lunar surface go on to reach Earth one and a quarter seconds later, followed by the solar rays reaching Earth one and a quarter seconds short of another minute later again. Thus the observer on Earth gets to see the image of a lunar event taking place over one perceptible minute in her veridical perception of her body’s steady progress through the one-way flow of physical time before she gets to see the image of a solar flare. Her visual system fabricates this perceptible substantial flow of time by transforming the rays’ later local impact on her retinas into looking like their earlier widely-separated invisible emissions. This leaves her with the perceptual experience of an insubstantial image of two insubstantial visible events taking place in the insubstantial but visible distance in the reverse order to the invisible but substantial order in which the earlier imperceptible physically distant events, which triggered her insubstantial perception, actually took place in the substantial but invisible world. Her visible system also transforms the seven-minute external but imperceptible flow of external physical time in from the invisible but substantial solar event to the invisible but substantial lunar event into a visible one-minute (minus one and a quarter seconds) flow of physical time out from the image of a visible but insubstantial nearby invisible lunar event to the image of an insubstantial but visible solar event in the visible but insubstantial visible distance apparently only now taking place in the insubstantial but invisible distance. This is in the opposite to the imperceptible earlier external physical flow of time of seven minutes between the two substantial but invisible events.
The visual system resorts to this trick because its reach into its physical environs is fully confined to the virtually two-dimensional layer of photo-absorbent molecules in each retina. Those two layers cannot somehow reach back though time and space because all that each layer registers is no more than the fleeting digital pattern of where it captures and then analyses every captured photon’s characteristics, annihilating each photon there and then in the process. Captured photons are thus colourless and invisible because they are destroyed on the visual system’s threshold and so do not exist in the mind thereby confirming that all radiant energy exists only outside the mind..
And the photons are destroyed without revealing their age. From that meagre two- dimensional physical input, the visual system sets about fabricating a visible surrogate image of a corresponding colourful three-dimensional visible world appearing to stretch deep into visible but insubstantial three-dimensional space. In the process, the visual system resorts to transforming the later timing of each captured photons’ annihilation on one of two two-dimensional photon-absorbent layers in the retina into looking like the earlier time at which the original event took place in the distance of three-dimensional space, in the process emitting radiant energy, all utterly invisible. Thus the visual system’s actual input is colourless, substantial but invisible electromagnetic energy and its actual output is colourful but insubstantial visible light.
The American Psychological Association Dictionary describes illusion as “a false sensory percept. Illusions of the senses, such as visual illusions, result from the misinterpretation of sensory stimuli.”. All that a viewer sees, then, in her colourful visible world is nothing but illusion arising from the visual system’s structural misinterpretation of the later time when some radiant energy from invisible external sources ends up being captured in the virtually-two-dimensional layer of photo- absorbent molecules at the back of each retina.
While the distortionary effects of the visual systems’s transformations of external substantial but invisible space/time relationships across deep space into very different visible but insubstantial space/time imagery are obvious at astronomical scales, they are not obvious locally. For example, radiant energy emitted/reflected within 3 kilometre from the viewer hits her retinas within 1/100,000ths of a second. This is well below a threshold which is high enough to make a movie film projected at 24 frames a second look like flicker-free continuous movement. The visual system thus presents the viewer with imagery whose coarseness enables a virtually real illusion of an extended visible “roughly Now” whereas the imperceptible physical Now is strictly “right now”, all of which is invisible because radiant energy takes time to reach any retinas. The visible “roughly Now” serves everyday visual purposes well. The viewer gains nothing from the fact that an invisible very short split second actually separated two physical events whose radiant energy triggered her later perception of the image of two simultaneous events. But the differences are of fundamental significance to the scientist.
Science has long accepted that the image of both the Moon and the Sun tracking across the sky from east to west is an illusion, as is the image of the rising Moon’s contraction as it rises above the horizon. That science persists in mistaking illusionary imagery for the actually invisible world of matter and energy is testimony to the power of the illusion. (The illusion works only because literally we cannot see past it into a totally invisible physical world, including the two retinas’ physical connection to the brain, all of which exists entirely out of our visual reach.) Thus science continues to fathom a universe in which, it calculates, we see just a 0.0035% sliver of the spectrum of otherwise unseeable but detectable electromagnetic energy and that about 68% of the universe’s energy is undetectably dark along with about 28% of matter, leaving less than 5% which is detectible. (See “Dark Energy, Dark Matter”, NASA Science, nasascience.com.)
The visual system has a whole box of tricks to bolster the visible world’s apparent veridicality, in its visible but wholly illusional colourful three-dimensionality. One such trick compensates for the time-lag from when an invisible external physical event takes place to when a corresponding surrogate image appears in the observer’s visible world by fabricating an image in which a moving object is seen to be ahead of its visibly static background. (See, for example, “Flash-lag Effect: Visual Illusion 3D”, YouTube – eijwat, 2 November 2011.)
Relativity theory is incoherent because it relies on colourful illusionary imagery to justify the notion that the relativity of physical simultaneity is determined, after the event, by when some electromagnetic energy is absorbed in an observer’s retinas and where she is in three-dimensional space when that energy is captured in her retinas. Thus visible but insubstantial imagery of simultaneity is very different from invisible substantial physical simultaneity. In contrast, quantum string theory’s Holographic Principle recognises that the colourful visible world of visual experience is nothing more than an illusional perceptual experience: “the three- dimensional world of ordinary experience … is a hologram …”.
However, the principle adds, in Susskind’s words, that “reality” (which I take to mean the physical world) exists as coding on a distant two-dimensional holographic surface. Thus, while recognising the world of visual experience is all illusion, the principle fails to recognise that there is not one distant two- dimensional encoded surface but two very local two-dimensional encoded surfaces — the photo-absorbent retinal layers inside the viewer’s head which are encoded with the continuously-refreshed pixillated patterns of fleeting dots, each dot briefly marking the capture of a single photon at particular spot on one of the two retinas. Thus the principle fails to recognise that the physical world exists, not in the form of distant two-dimensional surface pixillation, but in its colourless invisible three-dimensional state, including the two pixillated retinal layers, which envelops each viewer’s visual experiences of the illusional imagery of a colourful visible world, all actually existing only in her mind.