psmv5: The inverted spectrum

In the course of chasing various Nicholas Humphrey flavoured hares, I arrived at reference 1, from where I picked up the phrase ‘inverted spectrum’. Reference 1 being a paper I first came across a few years ago, but have been reminded of its existence by an email from Academia of reference 2, useful people, even if they do make a profit and remain keen for me to contribute.

The inverted spectrum is described at some length at references 3 and 4 and addresses part of a problem – do we all see colours in the same way – that I have poked around from time to time over the years. With reference 4, from the Stanford philosophy department, being rather inaccessible to this layman.

Other parts of the problem include the various kinds of colour blindness, smaller differences between people in the colour receptors (cones) in the retina and the very small number of people who have four kinds of colour receptors, rather than the usual three. With my intuition on this part of the problem being that it would be possible for me to see as blue what you see as red, while agreeing on the names for what we see – an intuition which, for the moment, remains just that.

But, in any event, what follows is a rather different speculation to that offered about the inversion of black and white at reference 9.

The NCS bicone

In the past I have come across the spheroid of the Munsell system of colour of reference 6, a system which started out early in the twentieth century. Here we start with the slightly simpler bicone of the natural colour system of colour (NCS) of reference 5, from Sweden half a century later. Convenient here because the bicone can be rotated on itself.

A bicone which is traced by rotating the vertical triangle in the figure above on the axis of the horizontal hue circle, this last organised by the four primaries of red, yellow, green and blue. By the two pairs of opposites, red versus green and blue versus yellow.

White at the top of the triangle, black at the bottom, greys in-between.

In the example in the figure above, ‘Y30R’ is the hue, between red and yellow, the position on the circle, and ‘0570’ is called the nuance, the position on the corresponding triangle, that is to say the strength of the yellow (its saturation), the amount of white and black.

Another example, presented slightly differently and lifted from reference 5. Notice that black is labelled ‘S’ at the bottom of the triangle, the first letter of the Swedish for black, I think to avoid confusion with ‘B’ for blue.

All in all, much the same as the older Munsell system, but simpler.

Note that these hues appear in the same order as the colours on the CIE horseshoe (illustrated at reference 10), but with different spacing. And in the same order as the colours of the visible spectrum (illustrated at reference 9), barring the fading of blue and red to black and the absence of the red-blue mixtures in this last.

The proposition

Note that the forty hues on this NCS hue circle, modified from reference 5, have a natural order. A human subject can say, for example, that the hues P and Q are both between red and blue and that P is more blue than Q. Facts that I imagine that all human subjects with normal colour vision will agree on. But note also that a subject cannot usefully say that hues P and Q are both between red and green and that P is more green than Q, with neither being green at all. Red is adjacent to yellow and blue, but opposite to green. Bearing in mind the limits of discrimination, some of which are addressed at reference 10.

For present purposes, the circle represents the physiological facts on the ground. Roughly speaking, given a light signal arriving at a spot on the retina, using the composition of that light in terms of wavelengths, that signal can be mapped onto a position on the circle. This is no more than a matter of careful measurement. We can all agree on the results.

We suppose that, for most people (the normals), the subjective experience of that signal is adequately represented by the colours in the snap above. But that for some people (the abnormals), the experience of that signal is represented by rotating the hue circle by 180°, or rather differently, by reflecting the normal hue of red across the centre of the hue circle to green – this last being the inverted spectrum of the title of this post. Or perhaps rotating by some other amount. There are lots of maps which might do, some more complicated than others, but in what follows we stick with rotations.

Note that the concepts of identity, nearness and order are preserved by rotations: two colours which are identical for normals will be identical for abnormals and two colour which are near each other normals will be near each other for abnormals. One colour which is between two others for normals, will still be between two others for abnormals.

A thought experiment

We suppose that we have a good understanding of the path from the eye to the subjective experience of colour and that we are able to put electrical probes into that path.

We suppose that things are organised in roughly the way of LWS-R of reference 12. That the subjective experience, that consciousness, is the product of electrical activity in a small patch of cortex in the upper brain stem or lower brain. A particular location which one can probe for electrical activity, for evidence of consciousness, in this case for evidence of colour. That is not to say all kinds of tricky networked activity does not go into preparation, just that the last step to consciousness is the local activity in one small place.

The hypothesis that the experiment is testing is that the subjective experience of colour is qualified by a gene or genes which codes for something which we are calling phase, otherwise the starting position on the hue circle for any particular subject. We suppose that most people are normals, but that some people are abnormals.

framework of the experiment is that for a succession of subjects, both normals and abnormals, we present the eye with a succession of hues, running around the hue circle.

The signal arriving at the eye is S1(h) where h is the hue. The hue is expressed as a number modulo 2π. Alternatively we can say that h is in the half open interval [0, 2π). This signal is continuous in hue; that is to say the signal S1(p) is close to S1(q) where p is close to q. In particular, S1(h) tends to S1(0) when h tends to 2π from below. The signal for any one hue is pretty much the same for all subjects.

A hue is objectively defined by the reflectance spectrum derived from a standard sample. There are a couple of example of such spectra to be found at reference 7. While it can be seen from reference 8 that the definition of reflectance is not trivial mathematically – but it is, nevertheless, an objective definition, not subject to the vagaries of brains and their subjective experiences. Remembering that the subjective appearance of that objectively defined hue will vary with the ambient lighting.

We have a function N1(h) which gives the standard name for a sample of the hues in the range [0, 2π). A sample which we suppose to be evenly spread across that range. With hue circle illustrated above representing a sample of 40, ten for each of the four primary colours.

The hue named by the subject is N2(s, h). For all subjects and all hues we have it that N1(h)=N2(s, h). That is to say, all the subjects agree on the names of hues. They all agree on the name of the colour of a wooden brick – noting here that the number of brick colours is generally quite small, say less than ten – and that most people would have trouble putting a name to a lot more colours. The subjects have all been trained since infancy to name their hues in this way, perhaps including the options of combinations like ‘greenish-blue’ and qualifiers like ‘light’, ‘dark’ and ‘very’.

At some point along the processing path, preferably near or at the point of projection into consciousness, the signal has become S2(s, h), where s is the subject and h is the hue. These signals do vary with the subject.

But we find that, for the S2 signals, the population falls into the two segments, the normals and the abnormals. So that S2(a, h)=S2(b, h+ α), where a is a normal subject, b is an abnormal subject and α is the phase angle for abnormals, in the range [0, 2π).

From which we might reasonably deduce that the hues experienced by the abnormals are offset by α radians from the hues experienced by the normals. Otherwise put, the hue circle of abnormals has been rotated by α radians with respect to that for normals.

Other configurations are possible. We might find segments of the population with small but reliably detectable offsets. We might find segments of the population taking one of a small number of large offsets. But, provided they all agree on the names, this might be difficult to detect.

Detection?

But having got this far, the argument at reference 4 is that colours are not as neatly arranged as the NCS would suggest with its simple bicone, with the problem nicely exposed by the rather irregular sphere of the Munsell colour system of reference 6, which shows first that humans can distinguish more saturation levels for yellow than they can for blue and second that yellow appears to be brighter than blue. So renaming blue yellow and vice-versa would likely have side effects which could be detected. And which have not so far been detected.

I should add that I have yet to think through where exactly in the processing path suggested above on should look for these effects.

But to all of which my response is so what? People’s perception of colour varies in detail for all kinds of reasons, variation which does not figure in everyday life. What does the man in the street care for saturation levels? He can name a dozen colours, more if you allow a few qualifiers like ‘dark’, and that is good enough for him. And some cultures make do with very few words for colour. So why should evolution object to more or less values for saturation for some particular hues?

Odds and ends

Inversion is attractive with colour as we have the circle of hues which can be rotated and flipped, seemingly preserving at least some of the important properties of colour.

So what about sound, when we might treat the octave in the same way as the colour circle? Maybe pitch is a reasonable analogue of brightness and timbre is a reasonable analogue of saturation. But I have not come across any attempt to map sound onto anything like the NCS bicone, so maybe it does not work or maybe it just doesn’t help.

The other senses such as smell, taste and touch are not obviously amenable to this sort of thing, not having, to my knowledge, a core circular component.

The Canford people snapped above do not tie into a recognised colour scheme, choosing to do their own thing. Including a numbering scheme which I have yet to work through. Furthermore, the card called Burgundy is No.09 while the corresponding ink from the Daler-Rowney parent is No.013. All very confusing. Daler-Rowney is to be found at reference 11, with Rowney being a leading name in coloured crayons and the better sort of paint boxes when I was small, while Daler, of whom I had not previously heard, did boards. And since 2016, Daler-Rowney has been part of the Italian Fila family of reference 13. Maybe the Brexit crew want to unpick all that.

Perhaps I ought to take a look at what the Dulux paint people do.

Conclusions

I have speculated about a phase shift mechanism whereby the perception of colour might vary between genetically defined groups of individuals. I have speculated about how that perception might be looked at objectively, that is to say from the outside rather than from the inside.

The possibility of such a phase shift remains, for me anyway, a possibility.

PS: and flipping the bicone, top to bottom, switching black and white, as at reference 9, still looks like an option.

References

Reference 1: How to solve the mind-body problem - Nicholas Humphrey – 2000.

Reference 2: https://www.academia.edu/.

Reference 3: https://en.wikipedia.org/wiki/Inverted_spectrum.

Reference 4: https://plato.stanford.edu/entries/qualia-inverted/.

Reference 5: https://ncscolour.com/.

Reference 6: https://munsell.com/.

Reference 7: https://psmv5.blogspot.com/2022/01/on-grasssmann.html. Some background material.

Reference 8: https://en.wikipedia.org/wiki/Reflectance.

Reference 9: https://psmv5.blogspot.com/2021/12/on-seeing-colour-some-science-fiction.html.