More on free will, and why quantum mechanics can't help you understand football

 

I’ve had some stimulating further discussion with Philip Goff and Kevin Mitchell on whether quantum mechanics can illuminate the free-will problem. Kevin has responded to our comments here; Philip’s have been on Twitter. Here’s where it all leaves me at this point.

First, here’s where I think we all agree:

(1) Events at the quantum scale can be adequately described by quantum mechanics – for our purposes, nothing more is needed.

(2) There’s no missing “force of nature” that somehow intervenes in matter as a result of “free will”.

(3) The future is not predetermined, because of quantum randonmess: at any given moment, various futures are possible.

Kevin’s argument is, as I understand it, that agents with free will are able to select from these possible futures.

Philip’s objection is that this is not how quantum mechanics works: those futures are determined by the probabilities they can be assigned from the Born rule.

I’m sympathetic to that observation: it isn’t at all clear to me how anything called free will can somehow intervene in a quantum process, however complex, to “select” one of its possible futures.

My objection to Philip’s point was, however, to the scenario he uses to illustrate it – where he decides whether or not to water his plant (called Susan). It seems to me to be ill-posed. I’m averse in general to thought experiments that don’t stack up in principle, and this seems to me to be one.

To calculate the Born probabilities for this situation, you would need to know the complete initial state of the system and the Hamiltonian that determines how its wavefunction evolves in time. Now, it is no good supposing we can define some generic “state of Philip confronted with thirsty Susan”. I’m not even sure what that could mean. How do we know what we need to include in the description to make a good prediction? What if Philip’s cell phone goes off just before he is about to water Susan, and calls him away on an emergency? How much of the world must we include for this calculation? And we’re looking to calculate the probability of outcome X, which quantum mechanics can enable us to do – so long as we know the target state X. But what is this? Is it one in which Susan stands in damp soil and Philip’s watering can is empty? But how do we know that he added the water of his own free will? What if in the initial state he know someone would shoot him later if he didn’t add the water? Does that still count as “free will”? I mean, he could in principle still refuse to water Susan, but it’s not what we would usually consider “free will”. But perhaps then our initial state needs to be one in which Philip has no such thought in his head. Had we better have a list of which thoughts are and aren’t allowed in that initial state? But whichever initial state we choose, we can never do the experiment anyway to see if the predictions are borne out, because we could never recreate it exactly.

My point is that we should not be talking about scenarios like this in terms of quantum states and wavefunctions, because that’s not what quantum mechanics is for. We can run an experiments many times that begins with a photon in a well-defined state and ends with it in another well defined state as it evolves under a well-defined Hamiltonian, and quantum mechanics will give us good predictions. But people are not like photons. Even though fundamentally their components are of course quantum particles obeying quantum rules, it is not just ludicrous but meaningless to suppose that somehow we can use quantum theory to make predictions about them – because the kind of states we care about (does Philip do this?) are not well defined quantum states, and the trajectories of any such putative states are not determined by well-defined Hamiltonians.

It seems to me the distinction here is really between quantum physics as a phenomenon and quantum mechanics as a theory. I don’t think anyone would dispute that quantum physics is playing out in a football match. But it seems to me a fundamental mistake to suppose that the formalism of quantum mechanics can (let alone should) be used to describe it, because that formalism does not involve the kinds of things that are descriptors of football matches, and vice versa. (Philip’s “watering a plant” scenario is of course much closer to a football match than to a Stern-Gerlach experiment.) It’s not just that the quantum calculations are too complex; the machinery of calculation is not designed for that situation. Indeed, we are only just beginning to figure out how to use that machinery to describe the simplest couplings of quantum systems to their environment, and these are probably probing the limits not just of what is tractable but what is meaningful.

Does all this objection, though, negate Philip’s point that free will can’t determine the outcome of a quantum process, as (ultimately) all processes are? In one sense, no. But my point is really that the answer to this is not legitimately yes or no, because I’m not sure the question has any clear meaning. The scenario Philip is depicting is one in which there is some massively complex wavefunction evolving in time that describes the whole system – him with watering can and potted plant – and somehow that evolution is steered by free will. But – and I think this is where I do agree with Kevin – I don’t believe this is the right way to describe the causation in the system.

 I don’t just mean it is not an operationally useful way to do that. I think it is fundamentally the wrong way to do it.

Here’s an example of what I mean. Imagine a tall tower of Jenga bricks. Now imagine it with one of the bottom brick removed, so that it’s unstable. The tower topples. What caused it to topple? Well, gravity and the laws of mechanics. Fine.

Now here’s the same tower, but this time we see what brought it to the state with the bottom brick removed: a child came along and took the brick. What caused it to fall? You could say exactly the same: gravity and mechanics. But we’re actually asking a different question. We’re asking not what caused the tower with the brick missing to fall, but what caused the tower with the brick still in place to fall – and the answer is that the child turned it into the unstable version. The child’s action was the cause.

When we try to speak of free will in terms of microphysics, we are confusing these two types of causal stories. We’re saying, Ah, the child acting is really just like the tower minus brick falling: physics says that’s the only thing that can happen. But what physics says that, exactly? Unlike the case of the tower falling, we can’t actually give an account of the physics behind it. So we just say, Ah, it’s somehow all there in the particles (why not the quarks? The strings, or whatever your choice of post-standard-model theory? But no matter), and I can’t say how this leads to that exactly, but if I had a really big computer that could calculate all the interactions, and I knew all the initial conditions, I could predict it, because there’s nothing else in the system. But that’s not a causal explanation. It is just a banal statement that everything is ultimately just atoms and forces. Yes it is – but at that level the true cause of the event has vanished, rather in the way that, by the time you have reduced a performance of Beethoven’s Eroica to acoustic vibrations, the music has vanished.

(This analogy goes deeper, because in truth the music is not in the acoustic waves at all, but in the influence they have on the auditory system of people attuned to hearing this kind of music so that they have the appropriate expectations. There is music because of the history of the system, including the deep evolutionary history that gave us pattern-seeking minds. So it makes sense to explain the effects of the music in terms of violations of expectation, enharmonic shifts and so on, but not in terms of quantum chromodynamics. You will simply not get a causal explanation that way, but just an (absurdly, opaquely complicated) description of underlying events.)

And you see that this argument has nothing to do with quantum mechanics, which is why I think quantum indeterminacy is a bit of a red herring. Free will – or better, volition – needs to be discussed at the level on which mental processes operate: in terms of the brain systems involved in decision-making, attention, memory, intention and so on.

The basic problem, then, is in the notion that causation always works from the bottom up, aggregating gradually in a sort of upwards cascade. There is good reason to suppose that it doesn’t – and that it is especially apt not to in very complex systems. Looked at this way, the microphysics is irrelevant to the issue, because the issue itself is not meaningful at the quantum level. At that level, I’m not sure that the matter of whether “things could have been otherwise” is really any different from the fact that things only turn out one way. (It could be interesting to pose all this in a Many Worlds context – but not here, other than to say I think Many Worlds makes the same mistake of supposing that quantum mechanics can somehow be casually welded onto decision theory.) Beyond quantum randomness, the notion that “things could have been otherwise” is a metaphysical one, because you could never prove it either way. Best, then, to jettison all of that and simply consider how decision-making works in cognitive and neurological terms. That’s how to make sense of what we mean by free will.

Does quantum mechanics rescue free will?

 

Philip Goff has challenged Kevin Mitchell’s interesting supposition that the indeterminacy of quantum physics creates some “causal slack” within which free will can operate. In essence, Kevin suggests (as I understand it) that quantum effects create a huge number of possible outcomes of any sufficiently complex scenario (like human decision-making), among which higher-level mechanisms of organismic agency can act to select one.

Philip responds that this won’t do the trick, because even though quantum mechanics can’t pronounce on which outcome will be observed for a quantum process with several possible outcomes, it does pronounce on the probabilities. He gives the example of his decision to water his dragon tree Susan (excellent name):

“Let’s say the Born rule determines that there’s a 90% chance my particles will be located in the way they would be if I watered Susan and a 10% chance they’ll be located in the way that corresponds to not watering Susan (obviously this is a ludicrously over-simplistic example, but it serves to make the point). Now imagine someone duplicated me a million times and waited to see what those million physical duplicates would decide to do. The physics tells us that approximately 900,000 of the duplicates will water Susan and approximately 100,000 of them will not. If we ran the experiment many times, each time creating a million more duplicates and waiting for them to decide, the physics tells us we would get roughly the same frequencies each time. But if what happens is totally up to each duplicate – in the radical incompatibilist sense – then there ought to be no such predictable frequency.”

It’s a good point, insofar as it needs an answer. But I think one exists: specifically, Philip’s scenario doesn’t really have any meaning. In this respect, it suffers from the same defect that applies to all attempts to reduce questions of human behaviour (such as those that invoke “free will”, a historically unfortunate term that deserves to have scare quotes imposed on it) to microphysics. The example Philip chooses is not “ludicrously over-simplistic” but in fact ill-defined and indeterminate. I don’t believe we could ever determine what is the configuration of Philip’s particles that predisposes him to water Susan. It’s not a question of this being just very, very difficult to ascertain; rather, I don’t see how such a configuration can be defined at the quantum level. We would presumably need to exclude all configurations that lead to other outcomes entirely – but how? What are the quantum variables that correspond to <watering Susan> or <not watering Susan (but otherwise doing everything else the same, so not cutting Susan in half either)>? What counts as “watering Susan”? Does a little water count? Is watering Susan before lunch the same as watering Susan after? This is not a simple binary issue that can be assigned Born probabilities – and neither can I see how any other human decision-making process is. (“Oh come on: what about ‘Either I press a button or I don’t’”? But no, that's not the issue as far as free will is concerned – it’s ‘Either I decide of my own volition to press the button, and I do it, and the botton works’ or not. And what then is the quantum criterion for ‘of my own volition’? How do we know it was that? What if I was bribed to do it?... and so on.)

Obviously such scenarios could go on ad infinitum, and the reason is that quantum mechanics is the wrong level of theoretical description for a problem like this. We simply don’t know what the right variables are: where the joints should be carved in an astronomically complex wavefunction for many particles that correspond to the macroscopic descriptions. And again, I don’t think this is (as physicists often insist) just a problem of lack of computational power; it’s simply a question of trying to apply a scientific theory in a regime where it isn’t appropriate. The proper descriptors of whether Philip waters Susan are macroscopic ones, and likewise the determinants of whether he does so. At the quantum scale they don’t just get intractably hard to discern, but in fact vanish, because one is no longer speaking at the right causal level of description.

This is, in fact, the same reason why Schrödinger’s cat is such an unhelpful metaphor. No one has ever given the vaguest hint at what the wavefunctions of a live and dead cat look like, and I would argue that is because “live” and “dead” can’t be expressed in quantum-mechanical terms: they are not well-defined quantum states.

I don’t necessarily argue that this rescues Kevin’s idea that quantum indeterminacy creates space for free will. I’m agnostic about that, because I don’t think what we generally mean by free will (which we might better call volitional behaviour) has any meaning at the quantum level, and vice versa. It’s best, I think, to explain phenomena at the conceptual/theoretical level appropriate to it. As Phil Anderson said years ago, it’s wrong to imagine that just because there’s reducibility of physical phenomena, this implies a reductive hierarchy of causation.

You’ll see very soon in Physics World why I’m thinking about this…

Is the UK ready for a Covid winter?

To prepare my article for The Guardian on whether the UK is prepared for a Covid winter, I spoke to many experts who gave a great deal of helpful information and advice. Only a small part of that could be fitted into the article, and I thought it would be helpful to put some more of it out there. So here is the longer version of that article.

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No one knows what Covid-19 holds in the coming months, but no one well-informed takes seriously Boris Johnson’s claim that it could all be back to normal by Christmas. With local outbreaks already prompting lockdowns in Leicester, Manchester and Preston, and cases rising at an alarming rate in Spain and Germany, it’s entirely possible that there will be grim days ahead. The faster spreading of the coronavirus and greater difficulty of maintaining social distancing as the weather gets colder, coupled to a return of schools and a desperate need to get the economy moving again, will increase the challenge of keeping a lid on the threat. So are we ready?

The good news is that some of what was lacking in March, and which led to such a disastrous outcome in the UK, is now in place. By no means all of that shortfall can be blamed on the present government; political leaders had for years ignored the warnings of specialists in infectious disease that a pandemic was a near certainty, the frightening lack of preparedness exposed by the 2016 Cygnus flu simulation was ignored while the nation was in the grip of Brexit-mania, the UK had no industrial infrastructure for generating testing capacity at short notice, and the NHS had been worn ragged by years of austerity. Besides, this was an entirely new virus, and little was known about how it spreads and harms the human body.

Significant headway has been made on some of those problems over the summer. The bad news is that it still might not be enough, and the outcome depends on many factors that are still all but impossible to predict. “We’ve got to up our game for the autumn”, says Ewan Birney, deputy director of the European Molecular Biology Laboratory, who heads its Bioinformatics Institute in Cambridgeshire. “We’ll be inside more. Universities and schools will be running. There will be a whole bunch of contacts that we don’t have now.”

“We can anticipate a lot more infections over the next few months”, says virologist Jonathan Ball of the University of Nottingham. The prime minister has advised hoping for the best and preparing for the worst, pledging that by the end of October there will be at least half a million tests for the virus conducted every day, and that the NHS will receive £3 bn of extra funding. But as Chris Hopson, chief executive of NHS Providers says, much more is likely to be needed in the next month or two to keep Covid-19 under control.

The nightmare scenario, he says, is a combination of a second surge of Covid-19 with a particularly difficult outbreak of winter flu, alongside the normal pressures that winter puts on health services, while they are trying to restart services put on hold during the crisis period – and all this being faced by an exhausted staff.

“The NHS would struggle if all of that came together at once”, Hopson says. “We struggle with winter pressures at the best of times, with insufficient bed capacity and community care capacity to deal with the levels of demand that we get”. Covid-19 creates a capacity loss because of the need to keep people infected by virus on separate wards from those who aren’t.

It’s not all gloom. The situation with personal protective equipment is now a lot better than in March, as is the availability of ventilators for severe cases (which turned out not to be so central anyway). What matters most, however, both for health services and for controlling the virus in the community, is the capacity for testing.

The lack of testing in the population was what largely hamstrung the response top the first wave – scientists and public health authorities were flying blind, not knowing how widespread the virus was or where it was concentrated. It was lack of testing that created the appalling spread of infection in care homes.

The situation now is very different. The UK is conducting tests as widely and as fast as most European countries: around 200,000 each day. Most of these are analysed in the Lighthouse Labs that were quickly set up for the task; repurposed academic labs throughout the country are also helping. “We’re in a much better position than we were at the start of the pandemic”, says molecular geneticist Andrew Beggs, who leads testing efforts at the University of Birmingham. “The government has massively increased the capacity for testing in a short space of time, and I’m more confident than I was two months ago that we’re got a really good chance of successfully testing people.”

What we need, says Ball, is “sentinel surveillance”: actively going out and working out where infections are occurring, particularly in high-risk populations such as hospitals and care homes, but also schools and universities. The Office for National Statistics is collaborating with other bodies in a pilot survey that will test a representative sample of households in the general population – up to 150,000 people a fortnight by October – to gauge the extent of infection.

Most testing uses swabs to collect samples that detect the presence of the virus, but it’s also possible to get an antibody test that reveals if you have had the virus without knowing it. Test results are almost always returned within 48 hours – much longer than that and they become of little value – and often within a day.

That’s important for several reasons. It alerts public health services and epidemiologists to dangerous hotspots of infections, so that they can be contained locally. It lets hospital staff know which patients can be safely kept on general wards, and whether they themselves are safe to be at work. Regular testing will be essential for frontline workers such as those operating public transport; at schools and offices it should not only tell people with suspicious symptoms whether they need to self-isolate but reveal whether the colleagues they came into contact with should do so.

Tests can also show how many people have now had the virus and are likely to have some level of immunity. Ball says that while its currently thought that perhaps 10% of the population have had Covid-19, some antibody results imply that the infection rater may have been much higher – as much as 50%. He suspects that actual number is somewhere in between. The more people have already been infected, the slower the virus might spread – and also, the lower the actual mortality rate is likely to be.

What’s more, new types of test being developed by British companies such as Oxford Nanopore and DNANudge could reduce the waiting time to a few hours, or less, from a procedure as simple as spitting into a cup. They can also be much more portable. “That gives you a lot more options for where you put the testing”, says Birney (who is a consultant for Oxford Nanopore). It could become routine to make a test part of airport flight check-in; commercial centres could have a testing facility where office workers get checked out at the start of the day. These options are still a long way off – and they depend on whether the promising initial results from the new methods stand up, as well as the companies’ unproven ability to scale up production. But “even if one technology doesn’t work our for rapid onsite screening, we have others in the pipeline”, says Beggs.

Another option is testing for the virus in sewage to keep track of infection levels in different parts of the country. From one test, you’re testing many thousands of people, says Birney. The Department for Environment, Food and Rural Affairs (Defra) has such a scheme underway, but it’s still too early to know how effective it will be.

Despite all this good progress, however, Hopson warns that there’s a lot to be done to create the testing regime that the NHS really needs. “Testing is one of the key issues we need to get right to prepare for winter, and there’s a long way to go to get to a fit-for-purpose operation,” he says. Both the number of tests and their speed will need to increase, and Hopson thinks that ideally we will need about a million tests a day by the end of December. “That’s a very tall order”, he says.

Tests will be crucial in health and care settings, where you need to know fast where a new patient should be put. For care homes, this information is vital to free residents from the need to be confined to the rooms. Epidemiologist Ruth Gilbert of University College London’s Institute of Child Health says that the loss of mobility and social interaction in care settings can accelerate mental and physical deterioration.

Equally crucially, the system needs to be joined up: a test result needs to go at once into people’s health records accessed by local GPs. And Hopson says there needs to be greater local control – at the moment the testing infrastructure is too nationally based.

“If you want to manage this risk, there’s a highly complex logistical operation with a complicated delivery chain”, Hopson says. “We need the funding to expand the capacity. We need the tests at volume. We need to set up the capacity close enough to where it’s needed. We need to get the computer systems joined up. It’s such a complex end-to-end process, from scientists developing tests to GP surgeries needing to see the care records, and local authorities, and it needs to operate at speed.”

It’s vital too that positive tests be followed up by effective contact tracing, so that others who might have been infected can self-isolate. “This is not working as well as it should”, says Hopson. “We’re losing too many people down that chain [of contacts].” The number of people being contacted and made to self-isolate is far lower in the UK than in other countries – and it’s not clear how much they are self-isolating anyway. “There has been no data published on it, and we know it’s not happening”, says Susan Michie, professor of health psychology at University College London.

This is as much a socioeconomic issue as a medical one. “People who are financially unable to self-isolate for 14 days need to be incentivized to do so”, says Hopson – their lost earnings need to be covered by the government. He points out that some places with high levels of outbreak tend to have higher percentages of ethnic monitory communities where English is not the first language, who are not always keen to interact with the state. This clearly needs sensitive handling – contact tracing must not seem “just a white middle-class operation”, he says.

Given the amount of preparation still to be done, many were alarmed by the news that Public Health England, the organization that overseas public healthcare within the Department of Health, is to be replaced by a new organization called the National Institute for Health Protection. This will bring the tasks of PHE under the same authority as NHS Test and Trace and the new pandemic data hub the Joint Biosecurity Centre.

“The last thing we need is reorganisation on top of this”, said Birney in response to the news, which came as a surprise to many like him who are involved in preparedness. “Even if this was the ultimately best chess move for a future pandemic preparedness, there is no way doing it mid-pandemic is sensible.” More than 200 public-health professionals signed a letter to The Telegraph in which they declared themselves “deeply disturbed by the news of another top-down restructure of the English public health system, particularly mid-pandemic, and without any forewarning for staff.”

But Hopson is more sanguine, saying that the move won’t involve large-scale restructuring of jobs. “I can see why everybody is jumping up and down”, he says, “but the leaders say to us that this is not a restructure.” Everyone will carry on doing their existing jobs – “it’s just that there’s a new interim team at the top level to link the parts together and create better coordination between them.” Having two different organizations doesn’t make a lot of sense. Putting them under one leadership team seems to us to make good sense.” Gilbert hopes that the new agency will make its data more widely available than PHE did, to help advance the science.

One of the biggest and most controversial issues for the autumn is the return of schools. While there is a broad consensus that getting pupils back must be a priority, this will inevitably raise the risk of spreading the virus. Although still too little is known about how readily this happens via children, there is some evidence now that secondary-school pupils can catch and pass on the virus much as adults do, and that primary-school children can do so even if they suffer only mild symptoms – probably about 15-20% of children infected have no symptoms, says Sanjay Patel of the Royal College of Paediatrics and Child Health.

There are encouraging signs that schools might not be a big source of infection, though. Sweden left schools open, and didn’t see lots of outbreaks or transmission, says Patel. Teachers didn’t have higher rates of infection either – lower than taxi drivers and supermarket workers.

“Schools have been working incredibly hard to try to get measures in place for opening in September”, says Patel. They will aim to keep pupils within small contact groups or “bubbles”, but this is much easier at primary than secondary level, where pupils change groups for different subjects and are less inclined to observe distancing rules. “If there’s an outbreak in a school, then sensible decisions need to be made about whether a bubble, a year, or a school needs to be closed”, says Patel.

He predicts that schooling “will be hugely disrupted for individual children and families, for bubbles and for year groups – there will be closures and outbreaks, and lots of children will be in and out of school.” Children of course get lots of coughs and colds over winter, and “those children will have to be excluded at once until they get a test result back. That means their parents will also have to isolate for that period.” But he hopes that regular seasonal viruses might themselves spread less because of the new measures.

“We have some really good plans in place for this winter”, he says. “We’ve learnt a lot from the first surge, and there’s absolutely no feeling of panic.”

But he adds that there’s no zero-risk option either. “The best way of protecting against outbreaks in school is to minimize the amount of infection in the community”, he says. This means compensating for school openings with restrictions elsewhere. At the moment, he says, it seems young people meeting in bars, pose a far higher risk of spreading than schools. So “do we prioritize our ability to go and have a drink in the pub, or the future education of our children?”

“The government has done a lot wrong, but generally we’re making progress”, says Beggs. “The natural British constitution is to be a bit gloomy about our ability to do things, but if we could share all the achievements we’ve done in a more optimistic way, I think people would be more reassured.”

Ah, there’s the rub. Beggs is right to warn about the danger of trying to present everything in the worst possible light in order to discredit a government that performed so dismally in the initial outbreak (about which I’ve written elsewhere). This would be unhelpful, as well as unfair to the many authorities, scientists, health professionals and others who have worked so hard to improve the prospects. Yet the fact remains that the good work done on preparedness stands in stark contrast to the very public and very damaging missteps the government has taken and continues to take. The messaging is still confusing, even misleading: ministers (and some chief medical advisers) seem intent, for example, on stressing the low risk that Covid-19 poses to young children returning to school (so stop worrying, parents!), whereas the true danger there is about transmission through the population generally. Announcements of local lockdowns have been woefully mismanaged. The alarm about the reorganization of PHE was deepened by the appointment of Dido Harding – who has no public health experience, a terrible track record with managing the Track and Trace system, and is married to a Conservative peer – as its head. While contracts do have to be awarded swiftly, without the delay of a drawn-out tendering process, in circumstances like these, too many seem to be going to companies with close contacts to government and its advisers. Blunders like the exams fiasco (and the refusal of government to accept blame or consequences) undermine even further public trust in our leaders.

This issue of trust will be crucial. Imposing local lockdowns to contain hotspots, identifying contacts of people who test positive, and persuading them to self-isolate, would be a challenge at the best of times, and hinges on whether people understand what they are being asked to do and why, and whether they trust those making the rules. Studies have shown that public trust in the government has already been badly eroded, both by the mishandling and poor messaging of the first wave and by what many see as the betrayal of Dominic Cummings’ lockdown breaches. Scientific and public health systems can do all they can to prepare, but in the end so much will depend on leadership and execution. I have been encouraged by what I have heard about the former; about the latter, I fear I remain gloomy.

Music in lockdown

The images of people in Italian cities singing to one another from their balconies during the lockdowns to cope with the Covid-19 pandemic seem to come now from another, kinder era: before the enormity of the international crisis was fully apparent, before the death toll approached a quarter of a million and the sense of social unity had begun to fragment as politicians and others used the situation to sow and exploit division.

Here in Britain we considered that footage of balcony serenades to be gloriously Italianate, feeding into a romantic national stereotype (even if it later happened too in Germany, Spain and Switzerland). But there was in truth something universal about this impulse to turn to music in times of crisis and catastrophe. It has happened everywhere as people struggle to cope with the fears and constraints of the pandemic, offering a cathartic release much as Leonard Slatkin, chief conductor of the BBC Symphony Orchestra, turned to Samuel Barber’s Adagio for Strings to express the right sentiment at the usually celebratory Last Night of the Proms following the 9/11 terrorist attacks in 2001.

What makes music a good vehicle for this role? “In crises”, German musicologist Gunther Kreuz has said, “music has a very strong function to balance people, and show them there is light at the end of the tunnel.” During the pandemic, he says, there were also initiatives involving small ensembles playing in front of care homed for elderly people. One obvious advantage music has in this respect is that it works very well as a socially distanced medium: a kind of communication and contact that remains effective from a distance.

But there is more to it than that, some of which surely relates to the global use of music in ritual and worship. Unlike conversation, music is designed to be broadcast to groups: it allows everyone who hears it to feel addressed individually. That can be true to some extent for the spoken word too – the recital of a poem or sacred text, for example. But the deep value of music for promoting a sense of community, sacredness and emotional connection is precisely that it has no words – or perhaps, for those of us listening to the Italian balcony arias without understanding a word, that the words needn’t matter. Because music shares a great deal with spoken language – the rhythmic and pitch variations, the nested and episodic structure of phrases – it seems to carry meaning without actual semantic content. Each of us is free to create the meaning for ourselves.

At the same time, it penetrates directly to the emotions, in part by a kind of mimicry of human emotional expression but also by stimulating the neural reward pathways that respond to our subconscious anticipation of pattern and regularity. It is this powerful capacity of music for expression of what lies beyond words that led cultural critic Walter Pater to declare that “all art constantly aspires towards the condition of music”. In an age of catastrophe, music becomes more indispensable than ever.

Three colours: Yellow

Jan van Huysum’s Flowers in a Terracotta Vase (1736) is a riot of floral colour, the equal of anything else by the Dutch flower painters of the seventeenth and early eighteenth centuries. But some of it looks decidedly odd. The leaves spilling out from among the bright blooms don’t look at all healthy, or indeed natural: they are more blue than green.


Jan van Huysum, Flowers in a Terracotta Vase (1736).

This is neither by intention nor mistake. Simply, the yellow pigment that Huysum mixed with blue to create his greens has faded. It was a common problem noted even at the time: the English chemist and writer Robert Dossie wrote in his Handmaid to the Arts (1758) that “The greens we are forced at present to compound from blue and yellow are seldom secure from flying or changing.”

Because artists did not then have a particularly vibrant green pigment that approached the colour of fresh vegetation, they often needed to resort to this mixing of primaries. But unless your primary pigments are bright and pure, such a mixture may become a little murky. Among the brightest of yellows were lake colours, meaning that the pigment was made from a water-soluble organic (plant- or animal-based) substance – basically a dye – fixed to the surface of fine particles of a white powder like chalk or ground eggshell. But organic dyes don't last well when exposed to light: the rays break up the colorant molecules, and the colour “flees”. (Even today pigments and dyes that are not colourfast are said to be “fugitive”.)

Technically these yellows were not exactly lakes, but pinks. Yes, it’s confusing: the word “pink” originally referred not to a pale reddish colour but to a class of pigments similar to lakes but made without the need for an alkali in the recipe. In the seventeenth century there were yellow pinks, green pinks, and light rose-coloured pinks. It is only because the last of these stayed in use for the longest that the term today denotes a hue.

The colorant used for yellow pinks was typically an extract of weld, broom or buckthorn berries. But one used these materials – as Huysum discovered – at one’s own risk.

It’s not that artists didn't have alternative, more stable yellows available. But as with any colour, not all yellows are equal. Those that could be made from minerals or inorganic compounds produced artificially might last longer, but some were rather dirty or pale in their tint.

There was, for example, yellow ochre: a yellowish form of the iron oxide mineral that also came in reds and browns. But if ochre today conjures up a brownish earth colour, that’s because yellow ochre was in truth more like that: fine for tawny hair, but not at all the thing for tulips or satin robes.

Then there was Naples yellow, as it was known from the seventeenth century: a pigment of rather variable composition but which was generally made from synthetic compounds of tin, antimony and lead. The ancient Egyptians knew how to combine lead with antimony ore to make a yellow, and in fact a natural mineral form of that compound (lead antimonite) was also used as an artists’ material. It could be found on the volcanic slopes of Mount Vesuvius, which is how it came to be associated with Naples. Other recipes for a yellow of similar appearance specified mixing the oxides of lead and tin. The ingredients weren’t always too clear, actually: when Italian medieval painters refer to giallorino, you can’t be sure if they mean a lead-tin or lead-antimony material, and it is unlikely that the painters recognized much distinction. Before modern chemistry clarified matters from the late eighteenth century, names for pigments might refer to hue regardless of composition or origin, or vice versa. It could all be very confusing, and from a name alone you couldn’t always be sure quite what you were getting – or, for the historian today, quite what a painter of long ago was using or referring to.


The chemise of Jan Vermeer’s The Milkmaid (c.1658-61) is painted with a lead-tin yellow.

In some respects that’s still true now. A tube of modern “Naples yellow” won’t contain lead (rightly shunned for its toxicity) or antimony, but might be a mixture of titanium white and a chromium-based yellow, blended to mimic the colour of the traditional material. There’s no harm in that – on the contrary, the paint is likely to be not only less poisonous but more stable, not to mention cheaper. But examples like this show how wedded artists’ colours are to the traditions from which they emerged. When you’re talking about vermilion, Indian yellow, Vandyke brown, orpiment, the name is part of the allure, hinting at a deep and rich link to the Old Masters.

One thing is for sure: you won’t find the gorgeous orpiment yellow on the modern painter’s palette (unless perhaps they are consciously, and in this case rather hazardously, using archaic materials). It is a deep, golden yellow, finer than Naples and lead-tin yellows. The name simply means “pigment of gold”, and the material goes back to ancient times: the Egyptians made it by grinding up a rare yellow mineral. But at least by the Middle Ages, the dangers of orpiment were well known. The Italian artist Cennino Cennini says in his handbook, written in the late fourteenth century, that it is “really poisonous”, and advises that you should “beware of soiling your mouth with it.” That’s because it contains arsenic: it is the chemical compound arsenic sulphide. (A different form of the same compound, also found as a natural mineral, furnishes the pigment realgar, the only pure orange colour available to painters until the nineteenth century.)


Natural orpiment (arsenic sulphide).

Orpiment was one of those gorgeous but costly pigments imported to Europe from the East, in this case from Asia Minor. (In the early nineteenth century there were also imports from China, so that orpiment was sold in Britain as Chinese Yellow.) Such alluring imports often arrived through the great trading centre of Venice, and orpiment was hard to acquire up in Northern Europe during the Middle Ages and the Renaissance – unless, like the German artist Lucas Cranach, who ran a pharmacy, you had specialist connections to exotic materials. Some orpiment was made not from the natural mineral but artificially by the chemical manipulations of alchemists. This type can be spotted on old paintings today by studying the pigment particles under the microscope: those made artificially tend to be more similar in size and have rounded grains. From the eighteenth century it was common to refer to this artificial orpiment as King’s Yellow. Rembrandt evidently had a supplier of the stuff, which has been identified in his Portrait of a Couple as Isaac and Rebecca (often called The Jewish Bride), painted around 1665.

If Dutch painters wanted a golden yellow like orpiment without the risk of poisoning, the Age of Empire supplied another option. From the seventeenth century, Dutch paintings (including those of Jan Vermeer) begin to feature a pigment known as Indian Yellow, brought from the subcontinent by the trading ships of Holland. It arrived in the form of balls of dirty yellowish-green, although bright and untarnished in the middle, which bore the acrid tang of urine. What could this stuff be? Might it truly be made from urine in some way? Lurid speculation abounded; some said the key ingredient was the urine of snakes or camels, others that it was made from the urine of animals fed on the yellow Indian spice turmeric.

The mystery seemed to be solved in the late nineteenth century, when an Indian investigator making enquiries in Calcutta was directed to a village on the outskirts of the city of Monghyr in Bihar province, allegedly the sole source of the yellow material. Here, he reported, he found that a group of cattle owners would feed their livestock only on mango leaves. They collected the cows’ urine and heated it to precipitate a yellow solid which they pressed and dried into lumps.

The cows (so the story goes) were given no other source of nutrition and so were in poor health. (Mango leaves might also contain mildly toxic substances.) In India such lack of care for cattle was sacrilegious, and legislation effectively banned the production of Indian Yellow from the 1890s.


J. M. W. Turner was one of the nineteenth-century artists who made much use of Indian yellow.

There has been debate about how much of this story is true, but the basic outline seems to stand up – the pigment has a complicated chemical make-up but contains salts of compounds produced from substances in mango leaves when they are metabolized in the kidneys.

While artists were having to rely for brilliant yellows on fugitive plant extracts, deadly arsenic-laden powers and cows’ urine, one might fairly conclude that they would welcome better yellows. So, then, it’s not hard to imagine the excitement of the French chemist Nicolas Louis Vauquelin when at the start of the nineteenth century he found he could make a vibrant yellow material by chemical alteration of a mineral from Siberia called crocoite.

This stuff was itself red – it was popularly called Siberian red lead, since there was truly lead in it. But in 1797 Vauquelin found there was something else too: a metallic element that no one had seen before, and which he named after the Greek word for colour, chrome or chromium.


“Siberian red lead”, a mineral source of chromium.

The name was aptly chosen, because Vauquelin soon discovered that chromium could produce compounds with various bright colours. Crocoite is a natural form of lead chromate, and when Vauquelin reconstituted this compound artificially in the laboratory, he found it could take on a bright yellow form. Depending on exactly how he made it, this material could range from a pale primrose yellow to a deeper hue, all the way through to orange. Vauquelin figured by 1804 that these compounds could be artists’ pigments, and they were being used that way even when the French chemist published his scientific report on them five years later.

The pigment was expensive, and remained so even when deposits of crocoite as a source of chromium were discovered also in France, Scotland and America. Chromium could also supply greens, most notably the pigment that became known as viridian and which was used avidly by the Impressionists and by Paul Cézanne.

The chromium colours play a major role in the explosion of prismatic colour during the nineteenth century – evident not just in Impressionism and its progeny (Neo-Impressionism, Fauvism and the work of van Gogh) but also in the paintings of J. M. W. Turner and the Pre-Raphaelites. After the muted and sometimes downright murky shades of the eighteenth century – think of Joshua Reynolds’ muddy portraits and the brownish foliage of Poussin and Watteau – it was as if the sun had come out and a rainbow arced across the sky. Sunlight itself, the post-Impressionist Georges Seurat declared, held a golden orange-yellow within it.

For their sun-kissed yellows, the Pre-Raphaelites and Impressionists did not need to rely on chromium alone. In 1817 the German chemist Friedrich Stromeyer noticed that zinc smelting produced a by-product with a yellow colour in which he discovered another new metallic element, named after the archaic term for zinc ore, cadmia: he called it cadmium. Two years later, while experimenting on the chemistry of this element, he found that it would combine with sulphur to make a particularly brilliant yellow – or, with some modification to the process, orange. By the mid-century, as zinc smelting expanded and more of the byproduct became available, these materials were offered for sale to artists as cadmium yellow and cadmium orange.


The artificial pigment cadmium yellow.

The cadmium colours have always stayed rather expensive, though. Nothing really beats cadmium red, a variant that went on market only around 1910. But it is typically around twice the price of other comparable reds, and the same goes for cadmium yellow. In that respect things have not changed so much since an artist in the Renaissance had to weigh up the worth of acquiring expensive orpiment as opposed to the drabber but much cheaper Naples yellow.

There’s a lesson in the cadmium pigments that applies to all colours, through all ages: they have often been byproducts of some other chemical process altogether, often discovered serendipitously as chemists and technologists pursue other goals – to make ointments, say, or soap, glass or metals.

It’s no different now. If you buy a tube labeled “Indian Yellow”, you can be sure no mangos or urine went into its making. Chances are, it will contain a yellow pigment that goes by the unromantic name of PY (pigment yellow) 139 – no mineral or metal salt, but a complicated organic molecule, meaning today that it is carbon-based and resembles molecules found in some living organisms. Chemists will say that it is a “derivative of isoindoline”, but the key point is that at its core is a ring of six carbon atoms joined into a so-called benzene ring.

That’s a clue to the true heritage of these modern organic pigments. Pure benzene, as well as other molecules closer still in their shape and structure to those of PY139, was first isolated in the early nineteenth century from a substance called coal tar, the black tarry residue left over from the industrial extraction of natural gas from coal for gas lighting. Coal tar has a pungent smell – think of the traditional coal-tar soap, which contained some disinfectant compounds distilled from coal tar. This is because it is full of molecules with benzene rings at the core, which tend to be aromatic. (Chemists use that word simply to signify that benzene rings are present, irrespective of smell itself.) In the mid-nineteenth century, German chemist August Hofmann, the leading expert on aromatic coal-tar compounds, set his young English student William Perkin the challenge of trying to make the anti-malarial drug quinine from coal-tar extracts. Perkin didn’t succeed, but instead he found he had made a rich purple substance that he called aniline mauve and began to sell as a dye. That was the beginning of the synthetic-dye industry, which gave rise to the modern era of industrial chemistry: by the early twentieth century, dye manufacturers were starting to diversify into pharmaceuticals and then plastics.

This is the world from which PY139 comes, along with a host of other organic pigments that mimic the old traditional colours with safer, cheaper compounds – many of them used also as food colorants, dyes and inks. One of the first offshoots of the aniline dyes was a yellow, simply called aniline yellow and belonging to an important class of colorants called azo dyes; it was sold commercially from 1863. There is a good chance that, when you see yellow plastic products today, they are coloured with azo dyes.


Winsor and Newton’s azo yellow.

It seems a deeply unglamorous way to brighten the world today, compared to the age of King’s Yellow, saffron and Indian Yellow. It could feel that what is saved in the purse is sacrificed in the romance. Maybe so. But artists are typically pragmatic people, as eager for novelty as they are attached to tradition. There has never been a time when they have not avidly seized on new sources of colour as soon as those appear, nor when they have not relied on chemistry to generate them. The collaboration of art and science, craft and commerce, chance and design, is as vibrant as ever.

Three colours: Blue

This is the second of theree essays on colour commissioned for the catalogue of a now-cancelled exhibition on colour at the Musée d’Orsay in Paris.

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In 1954, French artist Yves Klein said that “I believe that in future, people will start painting pictures in one single colour, and nothing else but colour.”

Klein did not wait for the future – he began painting monochromes in the 1940s. But it was only in the late 1950s that he truly found what he was looking for: a blue so glorious, so lustrous and deep, that it spoke for itself, and said all that Klein wanted to express. “Blue is the invisible becoming visible”, he said.


Yves Klein, IKB 79’ (1959).

It is not always easy to interpret Klein’s remarks, but I believe this one is not so hard to fathom. Blue has always spoken to something beyond ourselves: it is a colour that draws us into the void, the infinite sky. “Blue is the typical heavenly colour”, said Wassily Kandinsky – and who would doubt it after seeing the ceiling of the Arena Chapel in Padua, painted by Giotto around 1305, a vault coloured like the last moments of a clear Italian twilight? Some cultures don’t even recognize the sky as having a hue at all, as if to acknowledge that no earthly spectrum can contain it. In the ancient Greek theory of colour, blue was a kind of darkness with just a little light added.

There’s a strong case to be made, then, that shades of midnight have always been the most treasured of artists’ colours. One of the earliest of the complex blue pigments made by chemistry was virtually an ancient industry in itself. The blue-glazed soapstone carvings known now as faience produced in the Middle East were traded throughout Europe by the second millennium BCE. Faience is typically now associated with ancient Egypt, but it was produced in Mesopotamia as long ago as 4500 BC, well before the time of the Pharaohs. It is a kind of glassy blue glaze, made by heating crushed quartz or sand with copper minerals and a small amount of lime or chalk and plant ash. The blue tint comes from copper – it is of the same family as the rich blue copper sulphate crystals of the school chemistry lab, although faience could range from turquoise-green to a deep dusk-blue. These minerals were typically those today called azurite and malachite, both of them forms of the compound copper carbonate. It’s not at all unlikely, although probably impossible to prove, that the manufacture of glass itself from sand and alkaline ash or mineral soda began in experiments with firing faience in a kiln somewhere in Mesopotamia.


Egyptian faience: a statue of Isis and Horus, c. 332-30 BC.

Similar experimentation might have given rise to the discovery of the trademark blue pigment of the Egyptians, simply known as Egyptian blue or frit. The recipe, at any rate, is almost the same: sand, copper ore, and chalk or limestone. But unlike faience glaze, this material is not glassy but crystalline, meaning that the atoms comprising it form orderly arrays rather than a jumble. Producing the pigment requires some artisanal skill: both the composition and the kiln temperature must be just so, attesting to the fact that Egyptian chemists (as we’d call them today) knew their craft – and that the production of colours was seen as an important social task. After all, painting was far from frivolous: mostly it had a religious significance, and the artists were priests.

Azurite and malachite make good pigments in their own right – the first more bluish, the second with a green tint. They just need to be ground and mixed with a liquid binder. In the Middle Ages that was generally egg yolk for painting on wooden panels, and egg white (called glair) for manuscript illumination. Good-quality azurite wasn’t cheap, but there were deposits of the mineral throughout Europe. To the English (who had no local sources) it was German blue; the Germans knew it as mountain blue (Bergblau).


The mineral form of the blue pigment azurite (hydrated copper carbonate).

A cheaper blue was the plant extract indigo, used as a dye since ancient times. Unlike most organic dyes – those extracted from plants and animals – it doesn’t dissolve in water, but can be dried and ground into a powder like a mineral pigment, and then mixed with standard binding agents (such as oils) to make a paint. It give a dark, sometimes purplish blue, sometimes lightened with lead white. The Italian artist Cennino Cennini, writing in the late fourteenth century, described a “sort of sky blue resembling azurite” made this way from “Baghdad indigo”. As the name suggests – the Latin indicum shares the same root as “India” – the main sources for a medieval artist were in the east, although a form of indigo could also be extracted from the woad plant, grown in Europe.

But the artist who could find a patron with deep pockets would be inclined towards a finer blue than any of these. When the Italian traveller Marco Polo reached what is today Afghanistan around 1271, he visited a quarry on the remote headwaters of the Oxus River. “Here there is a high mountain”, he wrote, “out of which the best and finest blue is mined.” The region is now called Badakshan, and the blue stone is lapis lazuli, the source of the pigment ultramarine.

Cennino shows us how deeply ultramarine blue was revered in the Middle Ages, writing that it “is a colour illustrious, beautiful, and most perfect, beyond all other colours; one could not say anything about it, or do anything with it, that its quality would not still surpass” [Cennino Cennini, Il Libro dell’ Arte (The Craftsman’s Handbook) (c.1390), p. 37-8. (Dover, New York, 1960)]. As the name implies, it came from “over the seas” – imported, since around the thirteenth century, at great expense from the Badakshan mines.

Ultramarine was precious not just because it was a rare import, but because it was extremely laborious to make. Lapis lazuli is veined with the most gorgeous deep blue, but grinding it is typically disappointing: it turns greyish because of the impurities in the mineral. Those have to be separated from the blue material, which is done by kneading the powdered mineral with wax and washing the wax in water – the blue pigment flushes out into the water. This has to be done again and again to purify the pigment fully. The finest grades of ultramarine come out first, and the final flushes give only a low-quality, cheaper product, called ultramarine ash. The best ultramarine cost more than its weight in gold in the Middle Ages, and so it was usually used sparingly. To paint an entire ceiling with the colour, as Giotto did in the Arena Chapel, was lavish in the extreme.


Lapis lazuli, the source of ultramarine.

More often the medieval painter would use ultramarine only for the most precious components of a painting. That seems to be the real reason why most altarpieces of this period that depict the Virgin Mary show her with blue robes. For all that art theorists have attempted to explain the symbolic significance of the colour – the hue of humility or virtue, say – it was largely a question of economics. Or, you might say, of making precious materials a devotional offering to God.


Duccio’s Maestà altarpiece (1308-11). The Virgin’s robes are painted in ultramarine.

But materials make their own demands. When, during the Renaissance in the fifteenth century, artists began to use oils rather than egg yolk to bind their pigments, they found that the switch both enalbed and demanded new techniques. The colours dried more slowly and so could be blended into subtle shadows and highlights, enhancing the realism of the work in line with the emerging humanist philosophy. But the artists also had to cope with the fact that some pigments look different when bound in oils; ultramarine was one of them.

This is largely a matter of physics: light is bent and scattered to different degrees in the two binding agents, and the result is that ultramarine looked more transparent. Painters were then forced to compromise the purity of precious ultramarine by mixing it with a little lead white to keep it strong and opaque. Its mystique waned accordingly, and artists began to feel more free to use a whole range of lighter blues in their works. The art historian Paul Hills says that “Blue by the fifteenth century was moving away from its association with starry night, the vault of the heavens, to the changeful sky of day.”

You can compare azurite and ultramarine side by side in Titian’s explosion of Renaissance colour, Bacchus and Ariadne (1523). Here is that starry vault, indeed turning to day before our eyes, and it is painted in ultramarine. So too is Ariadne’s robe, which dominates the scene. But the sea itself, on which we see Theseus’s boat receding from his abandoned lover, is azurite, with its greenish tint.


Titian’s Bacchus and Ariadne (1523). Ariadne’s robe, and the sky, are painted in ultramarine.

Over the centuries, artists accumulated a few other blues too. Around 1704 a colour-maker named Johann Jacob Diesbach, working in the Berlin laboratory of alchemist Johann Conrad Dippel, was attemtping to make a red lake pigment when he found that he had produced something quite different: a deep blue material. He had used a batch of the alkali potash in his recipe, supplied by Dippel – but which was contaminated with animal oil allegedly prepared from blood. The iron used by Diesbach reacted with the material in the oil to make a compound that – unusually for iron – is blue in colour. By 1710 it was being made as an artist’s material, generally known as Prussian blue.

It wasn’t entirely clear what had gone into this mixture, and so for some years the recipe for making Prussian blue was surrounded by confusion and secrecy. In 1762 one French chemist declared that “Nothing is perhaps more peculiar than the process by which one obtains Prussian blue, and in must be owned that, if chance had not taken a hand, a profound theory would be necessary to invent it.” But chance was a constant companion in the history of making colours. At any rate, Prussian blue was both attractive and cheap – a tenth of the cost of ultramatine – and it was popular with artists including Thomas Gainsborough and Antoine Watteau. It comprises some of the rich blue Venetian skies of Canaletto.

Another blue from the Renaissance and Baroque periods went by the name of smalt, which is not so very different from the cobalt-blue glass of Gothic cathedrals such as Chartres, ground to a powder. Its origins are obscure, but may well come out of glass-making technology; one source attributes the invention to a Bohemian glassmaker of the mid-sixteenth century, although in fact smalt appears in earlier paintings. Cobalt minerals were found in silver mines, where their alleged toxicity (actually cobalt is only poisonous in high doses, and trace amounts are essential for human health) saw them named after “kobolds”, goblin-like creatures said to haunt these subterranean realms and torment miners. Natural cobalt ores such as smaltite were used since antiquity to give glass a rich blue colour, and smalt was produced simply by grinding it up – not too finely, because then the blue becomes too pale as more light is scattered by the particles. As a result of its coarse grains, smalt was a gritty material and not easy to use.

Some art historians make no distinctions between this “cobalt blue” and those that were given the name in the nineteenth century. But the latter were much finer, richer pigments, made artificially by systematic chemistry. In the late eighteenth century the French government asked the renowned chemist Louis-Jacques Thénard to look for a synthetic substitute for expensive ultramarine. After consulting potters, who used a cobalt-tinted glassy blue glaze, in 1802 Thénard devised a strongly coloured pigment with a similar chemical constitution: technically, the compound cobalt aluminate. Cobalt yielded several other colours besides deep blue. In the 1850s a cobalt-based yellow pigment called aureolin became available in France, followed soon after by a purple pigment called cobalt violet – the first ever pure purple pigment apart from a few rather unstable plant extracts. A sky blue pigment called cerulean blue, a compound of cobalt and tin, was a favourite of some of the post-Impressionists.


The water in Renoir’s Boating on the Seine (La Yole) (c.1879) is painted in cobalt blue.

But what artists craved most of all was ultramarine itself – if only it wasn’t so expensive. Even by the mid-nineteenth century it remained costly, which is why the Pre-Raphaelite Dante Gabriel Rossetti caused much dismay (not to mention added expense) when he upset a big pot of ultramarine paint while working on a mural for Oxford University.

By Rossetti’s time, however, artists did at last have an alternative – it’s just that several of them had not yet learnt to trust it. As chemical knowledge and prowess burgeoned in the early nineteenth century, bringing new pigments such as cobalt blue onto the market, it seemed within the realms of possibility to try to make ultramarine artificially.

It was a prize well worth striving for, because pigment manufacture had become big business. The manufacture of colours and paints wasn’t supplying artists; there was now a taste for colour in the world at large, in particular for interior decoration. Factories were set up in the nineteenth century to make and grind pigments. Some sold them in pure form to the artist’s suppliers, who would then mix up paints for their customers from pigment and oil. But some pigment manufacturers, such as Reeves and Winsor & Newton in England, began to provide oil paints ready-made; from the 1840s these were sold in collapsible tin tubes, which could be sealed to prevent paints from drying out and could be conveniently carried for painting out of doors.

Mindful of the importance of the pigment market, in 1824 the French Society for Encouragement of National Industry offered a prize for the first practical synthesis of ultramarine. It is a complicated compound to make – unusually for such inorganic pigments, the blue colour comes not from a metal but from the presence of the element sulphur in the mineral crystals. This composition of ultramarine was first deduced by two French chemists in 1806, offering clues about what needed to go into a recipe for making it. In 1828, an industrial chemist named Jean-Baptiste Guimet in Toulouse described a way to make the blue material from clay, soda, charcoal, sand and sulphur, and he was awarded the prize (despite a rival claim from Germany). In England this synthetic ultramarine was subsequently widely known as French ultramarine, and Guimet was able to sell it at a tenth of the cost of the natural pigment. By the 1830s there were factories making synthetic ultramartine throughout Europe.

Artists looked upon this substitute with considerable caution, however. Ultramarine still retained some of its old mystique and majesty, and painters were reluctant to believe that it could be turned out on an industrial scale. Perhaps the synthetic variety was inferior – might it fade or discolour? Actually synthetic ultramarine is (unlike some synthetic pigments) very stable and reliable, but J. M. W. Turner was evidently still wary of it when, in the mid-century, he was about to help himself to the ultramarine on another artist’s palette during one of the “finishing days” at the Royal Academy, where artists put their final touches topaintings already hung for display on the walls. Hearing the cry that this ultramarine was “French”, Turner declined to dab into it.

But by the end of the century, synthetic ultramarine was a standard ingredient of the palette: small wonder, given that it could be a hundred or even a thousand times cheaper than the natural variety. Synthetic ultramarine is the pigment in Yves Klein’s patented International Klein Blue, which he used for a series of monochrome paintings in the 1950s. But ultramarine never looked like this before – at least, not on the canvas.

Klein noticed that pigments tend to look richer and more gorgeous as a dry powder than when mixed with a binder – another consequence of how light gets transmitted and refracted – and he sought to capture this appearance in a paint. In 1955 he found his answer in a synthetic fixative resin called Rhodopas M60A, made by the Rhone-Poulenc chemicals company, which could be thinned to act as a binder without impairing the chromatic strength of the pigment. This gave the paint surface a matt, velvety texture. Klein collaborated with Edouard Adam, a Parisian chemical manufacturer and retailer of artists’ materials, to develop a recipe for binding ultramarine in this resin, mixed with other solvents.


Yves Klein, Venus Bleue (1962).

Even in the modern era, then, some artists were still depending on chemical assistance and expertise. Despite the profusion of new pigments with complicated and recondite chemical formulations, the intimate relationship of painters to their materials has not been entirely severed.

Three colours: Red

This is the first of three essays on colours that were to be included in the catalogue for an exhibition at the Musé d'Orsay in Paris this year, which has been cancelled. So I'm putting them here for your delectation. Each essay focuses on the pigments developed and used through time for one of the primary colours.

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One hundred thousand years ago, the last Ice Age covered much of northern Europe with glaciers several kilometres thick. Small groups of Homo sapiens coexisted with other, now extinct human ancestors: Neanderthals and Denisovans. Life was nasty, brutish and short. Yet in a cave in what is today South Africa, humans found the time and inclination to mix red paint.

Their tools have been found in Blombos Cave on the Southern Cape coast: grindstones and hammer-stones for crushing the pigment, and abalone shells for mixing the powder with animal fat and urine to make a paint that would be used to decorate bodies, animal skins and perhaps cave walls. The red colour was made from ochre, a natural, soft, iron-rich mineral chemically similar to rust.


A piece of engraved ochre from Blombos cave in South Africa.

The evolution of complex ways of thinking and socializing seems only to have happened fifty thousand years later – and yet even at the dawn of human culture it seems that the urge to adorn our surroundings and ourselves with colour was deeply felt. It was done in the colours of nature: black charcoal, white chalk and ground bone, and the brownish-red of ochre. It’s no wonder that a word for “red” seems to be one of the earliest colour words to appear in languages across the globe, after those for black and white. The cave paintings made 15-35 millennia ago in Chauvet, Lascaux and Altamira attest to the genuine artistry that early humans achieved.

Red ochre is still on the artist’s palette today: a “dirty” red, some might say, but an honest, humble one, and cheap too. It’s iron that gives the mineral this hue. Like many metals when chemically combined with other elements, it absorbs light within a characteristic band of the visible spectrum, soaking up the blues and greens but reflecting the reds. That red is purer in the colour of blood, where an iron atom sits at the heart of the protein haemoglobin and ferries oxygen around our bodies. The bloody hue is reflected in the technical name for ochre-like minerals: haematite, literally “blood-stone”, which is iron oxide.

During the Industrial Revolution, chemists perfected a method for making iron oxide artificially, so that the red colour could be more precisely controlled. It was an offshoot of the manufacture of sulphuric acid, an important ingredient for textile bleaching. This red substance was sold to artists as “Mars red”, an echo of the old alchemical term for iron compounds. The planet Mars was long associated with redness. It has that hue even to the naked eye, for its surface is covered with iron oxide minerals.

But the classic red pigments of the artists don’t rely on iron minerals, the hue of which is not the glorious red of a sunset, or indeed of blood, but of the earth. For many centuries, the primary red of the palette came from the compounds of two other metals: lead and mercury.

Lead is something of a chameleon metal. By combining the raw metal with various other substances – vinegar, carbon dioxide, air – alchemists and artisans knew since the time of the ancient Egyptians how to obtain white, yellow and red materials. Red lead was the finest of these colours, made by heating “white lead” in air. It was known too in ancient China from at least the fifth century BCE. Roman and Greek painters used it, although the Roman writer Pliny in the first century AD was wary of artists who used bright colours like this too lavishly – the sober artist, he insisted, deployed a more muted palette, with reds of ochre.

To Pliny, any bright red was called minium, and red lead was a slightly second-rate version: minium secundarium. But by the Middle Ages minium had become more or less synonymous with red lead, which was used extensively in manuscript illumination. That art came to be described by the Latin verb miniare, “to paint in minium”, from which we get the term “miniature”: nothing to do, then, with the Latin minimus, “smallest”. The association today with a diminutive scale comes simply from the constraints of fitting a miniature on the page.


A miniature painted in red lead from c.1300.

Pliny’s best minium was a different red pigment, called cinnabar. This was a natural mineral: chemically, mercury sulphide. It was mined in the ancient world, partly for use as a red colorant but also because the liquid metal mercury could easily be extracted from it by heating. Mercury was thought to have almost miraculous properties: ancient Chinese alchemists in particular used it in medicines.

By the Middle Ages, alchemists and craftspeople knew how to make mercury sulphide artificially by combining liquid mercury and yellow, pungent sulphur (available naturally in mineral form) in a sealed vessel and heating them. This process, which was described in a craftsman’s manual of around 1122 by the German monk Theophilus, can give a finer quality of red pigment. It was a procedure of great interest to alchemists too, as the Arabic scholars of the eighth and ninth centuries had claimed that mercury and sulphur were the basic ingredients of all metals – so that combining them might be a route to making gold. Theophilus, however, had no such esoteric arts in mind; he just wanted a good red paint.

“Artificial cinnabar” became known by the name vermilion. The etymology is curious, and shows the confusing and treacherous flux of colour terms in an age when the hue of a substance seemed more significant than vague, pre-scientific notions of what its chemical identity was. It stems from the Latin vermiculum (“little worm”), since a bright red was once extracted from a species of crushed insect: not a paint pigment but a translucent dye of scarlet colour, arising from an organic (carbon-based) substance that the insects produce. Such dyes were also known as kermes, the etymological root of “crimson”. Because the insects that made it could be found on Mediterranean trees as clusters encrusted in a resin and resembling berries, the dyes might also be called granum, meaning grain. From this comes the term “ingrained”, implying a cloth dyed in grain: the dye was tenacious and did not wash out easily.


Vermilion is used abundantly in Masaccio’s Saints Jerome and John the Baptist (c.1428-9), in the National Gallery, London.

Vermilion is by no means the only close link between the reds of textile dyes and the reds of paint pigments. The former are translucent and dissolve in water, and are generally organic substances extracted from animals or plants – such as cochineal, an extract of New World beetles that became popular with cloth dyers in the sixteenth century. But paint pigments must be opaque and long-lasting, whereas dyes tended to fade as they were washed out or as sunlight broke down the delicate organic molecules.

Red dyes were associated with majesty, opulence, status and importance: they were the colours used for cardinals’ robes in the Middle Ages and Renaissance. Painters needed fine reds to render on board and canvas these dignitaries whose portraits they were increasingly commissioned to paint. Red lead and vermilion served well enough in the Middle Ages, but the increased demand for verisimilitude in the Renaissance highlighted the difference between the orange hue of the pigments and the crimson of the dyes.

One way to capture the quasi-purple magnificence of those dyes was to fix the colorant molecules onto solid, colourless particles that could be dried and mixed with oils like a regular pigment. This process involved some challenging chemistry, but even the ancient Egyptians knew how to do it. The basic idea is to precipitate a fine-grained white solid within a solution of the dye: the dye sticks to the particles, which dry to make a dark red powder. In the Middle Ages this process used the mineral alum, which can be converted to insoluble white aluminium hydroxide. The pigment made this way was called a lake, after the word (lac or lack) for a red resin exuded by insects indigenous to India and southeast Asia.

One of the best red lakes of the late Middle Ages and the Renaissance was made from the dye extracted from the root of the madder plant. As lake manufacture was perfected, artists such as Titan and Tintoretto began to use these pigments mixed with oils, giving a slightly translucent paint that they would apply in many layers for a deep wine-red tint or would wash over a blue to make purple. In this as in much else we can see the constant exchange in materials and knowhow between dyers and pigment-makers.


There is abundant, rich red lake in Titian’s Portrait of the Vendramin Family (1543-7).

A popular source of a luxurious, blood-red lakes in the late Middle Ages was the dye called cochineal, harvested in eastern Europe from a species of beetle that encrusted the perennial knawel plant with a resinous crust. The colour comes from organic compounds made by the insects themselves, which are killed, dried and crushed. According to one estimate, about 70,000 insects were needed to make one pound of this so-called carmine lake. The plant was harvested around midsummer, and if the crop failed, the price of carmine soared. After the discovery of the New World, however, cochineal for dyes and pigments gained a more reliable (if scarcely cheaper) source as an import from the Spanish colonies in the Americas.

The existence of strong red pigments was vital to the evolution of the palette. According to the art historian Daniel Thompson, the invention of a method to make synthetic vermilion transformed the nature of medieval art:
“No other scientific invention has had so great and lasting an effect upon painting practice as the invention of this colour… Given abundant vermilion, the standard of intensity in the painter’s palette automatically rises. Equally brilliant blues and greens and yellows were required to go with it… If the Middle Ages had not had this brilliant red, they could hardly have developed the standards of colouring which they upheld; and there would have been less use for the inventions of the other brilliant colours which came on the scene in and after the twelfth century.” (D. V. Thompson, The Materials and Techniques of Medieval Painting, p.106. Dover, New York, 1956.)

Aside from the creation of red lakes, rather little about the painter’s reds changed from the Middle Ages until modern times. The Impressionists in the late nineteenth century made avid use of the new yellows, oranges, greens, purples and blues that advances in chemistry had given them, yet their reds were not really any different to those of Raphael and Titian.

It wasn’t until the early twentieth century that a vibrant and reliable new red entered the repertoire. The discovery of the metal cadmium in 1817 immediately produced new yellow and orange pigments, but a deep red was made from this element only around the 1890s. The yellow and orange are both cadmium sulphide; but to get a red, some of the sulphur in this compound is replaced by the related element selenium. It wasn’t until 1910 that cadmium red became widely available as a commercial colour, and its production became more economical when the chemicals company Bayer modified the method in 1919.

Cadmium red is a rich, warm colour – it is arguably the painter’s favourite red, except for the price. That was certainly true for Henri Matisse, for who red held a special valence - as his interiors in La Desserte (aka The Red Room, 1908), Red Studio (1911) and Large Red Interior (1948) attest. Of the second of these, art critic John Russell said “It is a crucial moment in the history of painting: colour is on top, and making the most of it.”


Matisse’s The Red Studio (1911) is painted in cadmium red.

Colour is on top. That was that way in went in the twentieth century, from the strident chromatic statements of the Fauves (Matisse at their head) to the stark primaries of Ellsworth Kelly and the hypnotic maroon colour fields of Mark Rothko (whose experiments with new reds made from synthetic and fugitive dyes did not end well). Colour went from being the artist’s medium to being the subject. In that shifting of the agenda, red led the way.