Humans are often described as “language animals”, implying that the ability to communicate linguistically makes humans unique. Big-Tech giants are pushing artificial intelligence (AI) and deep learning technologies to build machines capable of talking and writing to a such a level to be indistinguishable from humans. However, at least for now, human vision abilities seem to remain a much more difficult hurdle for AI. The widespread use of visual CAPTCHAs to protect web hosts from automated (“bot”) fraudulent access, tells that for a computer it is still much more difficult to reproduce human vision abilities, compared to language skills. Further, the role of psychology in our visual processing cannot be underestimated, the eye being in all respects a prolongation of our brain, capable of straightforwardly converting light energy into a cognitive process.

In the late 1660s, Isaac Newton started experimenting with his celebrated Phaenomena of colours. At the time, people thought that colour was a mixture of light and darkness, and that glass prisms were responsible to make the light coloured. Robert Hooke was a proponent of this theory of colour, and had invented a scale that went from brilliant red, which was pure white light with the least amount of darkness added, to dull blue, the last step before black, which indicated the complete extinction of light by darkness. Newton realised that this theory was false. He set up a prism near his window, and projected a beautiful rainbow spectrum onto the far wall. Then, to prove that the prism was not “colouring” the light, he placed a second prism on the optical path of the light and mixed the colours back together in a single white light.

Despite taking several wrong turns, it was however Johann Wolfgang Goethe who reformulated the topic of colour in an entirely new way, by writing a 1,400 pages treatise on the subject (Zur Farbenlehre, 1810). Newton had viewed colour as a purely physical problem, involving light rays from a source bouncing off objects and entering our eyes. Goethe realised that the sensations of colour reaching our eyes are also shaped by our brain, that is by the mechanics of human vision and by the way our brain process information. Therefore, according to Goethe, what we see of an object depends upon the object, the lighting, and our perception.

Looking up at the night sky with a basic telescope, or even with a good binocular, you will see stars to shine mostly around white light. However, after some practice you could start seeing also reddish-orange, or shining-blue stars. But no matter how carefully you look, you will never see a green star (and to a good extent, no purple ones either). Sure there are lots of green objects in the night sky, for example by looking a little below the Cygnus constellation in summer you may spot the Dumbbell nebula; in the winter sky, on the left of Orion and above Canis Major, you may see (but you need at least an amateur telescope) the Seagull nebula. However, the green in these objects is of chemical origin, it comes from clouds of doubly-ionised oxygen that are excited by UV radiation from nearby stars. The colour we see a star is instead thermal in origin: the star core is at temperatures of hundreds of millions degrees, and when the thermal energy reaches the star surface it has cooled down to about 3,000 to about 10,000K. The radiation corresponding to such temperature range mostly falls in the “visible electromagnetic spectrum”, meaning visible by our human eyes. Because of the steady-state radiative conditions, any star is glowing as an almost ideal blackbody at its given temperature. This is the colour we eventually see with our eyes. And no green nor purple is there.

Try to go on Google and search for something like: why there are no green stars? You will get a number of answers, unfortunately most of them wrong, or only partly correct. The most frequent explanation would be that the temperature only tells you the peak frequency of the emitted light, whereas the star actually emits a lot of energy also at frequencies above and below. Hence, when a star has a surface temperature around 6,000K, thus peaking in the green, we rather see it white. But then, you may ask why the same does not happen also with red- or blue-peaked stars? (And you start suspecting it kinda happens, since most stars indeed look white.) The answer, as Goethe correctly deduced, lies in our visual perception rather than in the star light-emission. All colour perception is created by the brain of the observer. As such, no star really has any colour at all: colour is not a fundamental physical property, it is made up in the brain of the observer. 

Our retina, as (nearly) everybody knows, contains three types of receptors (cone cells) sensitive to different regions of the electromagnetic spectrum that we humans call “visible”. This three-colour based system (or trichromacy) can translate into many independent, equivalent colour schemes. If one of the parameters is mapped to the absolute intensity of light, or luminance, then the other two variables, usually called hue and saturation, can be used to rigorously define any colour in our subjective perception scale (HSL scheme). The diagram that is obtained in this two-variable plane resembles a fingernail inclined to the left (see image attached, left), and is called a colour space. A perfectly equivalent diagram can be obtained by sticking to the red-green-blue (RGB) scheme, it will look somewhat deformed compared to the HSL one, but it works perfectly as well. 

Such colour maps allow to establish a quantitative link between the spectral wavelength of light and human colour perception. In the example colour space shown in the figure, the absolute wavelengths of ideally monochromatic light are distributed along the upper perimeter, from left (λ=380 nm) to right (λ=700 nm). Any points inside the diagram indicate mixed colour palettes. You may also notice the three points lying somewhere in the full blue, green, and red regions. The triangle they delimit covers only a part of the entire colour space, and is the so-called gamut. This region is the actual set of colours that can be represented by a given device, such as a TV screen or a printer. Many different gamuts exists, for example the ones defining the PAL or SECAM systems, or the Adobe workspace. (Note that you are probably seeing this figure with a sRGB-calibrated screen, therefore the colours you see are not the real ones the figure was meant to display.) 

Due to the heterogeneous distribution of cone cells in the retina, the three values, HSL or RGB or other, depend also on the observer’s field of view. To eliminate this variable, the International Commission on Illumination (CIE) defined a color-mapping function called the Standard (colorimetric) Observer, to represent an average human’s chromatic response within a 2-degrees arc inside the fovea, the most sensitive part of the eye’s retina. This is known as the CIE 1931 2° Standard Observer, mathematically characterised by three colour-matching functions, x(λ), y(λ) and z(λ), often approximated by Gaussians. And here comes the trick that makes green stars forbidden from the night sky. The stimulus variables, for example RGB, are a convolution of the three colour-matching functions with the spectral radiance L(λ) of the light source, integrated over the whole spectrum of wavelengths λ. As we said above, a star emits an almost ideal blackbody spectrum. Now, if you use the Planck’s blackbody distribution for L(λ) you obtain the “Planckian locus”, a curve that puts on the diagram the apparent colours matching blackbody temperatures, as they appear to the human eye (or better, to the Standard Observer). This is the thick black curve plotted in the middle of the figure: as you can see, it goes from blue to red passing through white, but it does not touch the green or purple regions of the diagram. In other words, when we look at a blackbody emitter our eyes are unable to see it green.

Chromaticity mixes the physics of light with brain physiology, to build up an objective specification of colours. However, strange things can still happen. For example, imagine to pull one of the points making the gamut triangle outside the perimeter of the colour space. This will originate imaginary colours outside the colour space, which could not be displayed by any physical object nor viewed by any animal eye, but are mathematically possible. A chimerical colour is one such imaginary colour that can be seen temporarily, for example by looking steadily at a strong colour until some of the cone cells become fatigued, thus temporarily change their colour sensitivity, and then looking at a markedly different colour. 

The checker shadow illusion is an optical illusion published in 1995 by Edward Adelson, professor of vision science at MIT. The image (see attached, right) depicts a checkerboard with light and dark squares, partly shadowed by another object. The optical illusion is that the area labeled A appears to be a darker colour than the area labeled B. However, within the context of the two-dimensional image, they are of identical brightness, i.e., they would be printed with identical mixtures of ink, or displayed on a screen with pixels of identical colour. You can convince yourself that this is absolutely true by opening the image with any image-editing program, such as GIMP. Then, with the eraser tool, cancel all of the image except the A and B squares… magic! 

Our brain has the capacity to perceive the lightness (or reflectance) of a surface as invariant, even when the intensity of incident light varies from point to point. In the checker shadow illusion, the brain perceives that the image is lit from a source coming from the right. Supposing that the shadow on the checkerboard makes the squares in its path darker, our brain tries to restore the colour pattern on the basis of the logical alternance suggested by the symmetry of the image, rather than using the physical values of light intensity.

It all seems to depend on those three little, stupid functions x(λ), y(λ) and z(λ), for our eyes to transfer physical information to the central processing unit. Researchers like Alejandro Parràga spent a life trying to explain (see e.g. Curr. Biol. 10 (2000) 35) how our human eye has been shaped by evolution to follow these three weird, almost-Gaussian filters, by which we see, live and love. Bees have eyes sensitive to UV radiation. Cats and dogs have only blue and green cone cells, so they have a hard time with objects in shades of red. I wonder whether my cat sees a green star when she looks up in the starry summer nights.

Green stars and grey squares

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