Do you believe in miracles?

Tristan Casabianca has kindly drawn my attention to an article he published last year which discussed the case for the authenticity of the Turin Shroud – by which I mean the claim that it is not just an artifact made during the period traditionally ascribed to the life of Jesus Christ but that it was the cloth used to wrap his body between the Crucifixion and the Resurrection. It’s a thoughtful and provocative article, but I don’t agree with very much of it.

I won’t go into the evidence for and against the age and provenance of the Shroud here (see here instead). Suffice to say, it is still hotly contested, with several researchers arguing that the radiocarbon dating performed in 1988, which placed the Shroud in the 13th-14th century, was flawed in some respect or another. I’ve not seen convincing evidence to doubt that very careful study, but I do wish it could be repeated. I also think however that, based on the evidence we have to date, it is very hard to understand how the image of a bearded man was formed on the linen. It doesn’t seem to be painted on. It’s deeply intriguing, tantalizing question. In the interests of full disclosure, I don’t believe that Jesus of Nazareth was the resurrected son of God, and I find it extremely unlikely that this artifact which turned up in 14th-century France had anything to do with him. But that is just my opinion.

Casabianca’s article is concerned not so much with weighing up the arguments as with establishing the framework within which we should think about them. In particular, he takes issue with my comment in a 2008 column in Nature Materials that “the two attributes central to the shroud’s alleged religious significance – that it wrapped the body of Jesus, and is of supernatural origin – are precisely those neither science nor history can ever prove.” Casabianca in effect asks: really? Ever?

And in this much he is right: saying such and such can never happen is, when viewed philosophically, a contentious claim. It amounts to ruling out possibilities that we can’t be sure of. To take an extreme example: we might say that time travel contravenes the laws of physics as we currently know them, but can we really state as a philosophical absolute that there will never come a time when it becomes possible to travel back in time and witness at first hand the events that took place in Palestine around 33 AD? It sounds absurd to suggest such a thing (outside of Michael Moorcock’s splendid Behold The Man), but I’m not sure that a philosopher would accept such a ban as a rigorous principle, any more than we could deny the possibility that any other feature of (or indeed all of) our current understanding of the universe is utterly mistaken. I’m not sure that it is terribly meaningful to leave such possibilities open, though – in general when we say something is impossible, we mean it seems impossible according to our current understanding of the universe, and what more could we expect of such a statement than that?

But Casabianca is more specific. He says that of course we do come to accept some historical truths, even about the distant past. We accept that tomb KV62 discovered by Howard Carter is the tomb of Tutankhamen. So why should we consider it a theoretical impossibility that we could prove the Shroud to be the burial shroud of Jesus of Nazareth (even setting aside for the moment his theological status)?

Again, philosophically I don’t see how one could exclude that theoretical possibility. But could it ever happen, given what we have to go on? There is a possibility that Jesus of Nazareth was a real person – this seems rather likely to me, though I have no deep knowledge of the matter. How might we link this object to him? We could perhaps establish that the previous dating study was wrong, and find good reason to believe the Shroud was in fact made within, say, the two centuries bracketing the time Jesus is supposed to have lived. We might find pretty compelling evidence that it came from the Middle East, perhaps being able to localize it fairly well to Palestine, and also that it was probably used in a burial ritual. To be clear, none of this has been by any means proved right now, and some evidence argues against it – but in principle it seems plausible that it could happen.

What then? Casabianca offers no line of argument that could link this artifact to the person of Christ. Might we find his name inscribed on it somewhere? No, we will not. Might we be able to link the style of weaving to one specific to Nazareth at that time? If that were possible, surely it would have been done already. It seems to me that you have to think about what might be demonstrated historically in the light of the capacity of the artifact in question to hold the information required for that demonstration. I see no reason to think that the Shroud contains the kind of evidence needed to make such a definitive identification of provenance, and more than a random pot excavated in Birmingham can be linked to a specific Iron Age Brummie beer maker named Noddy. Whether one can exclude that as a “theoretical philosophical possibility” seems pretty irrelevant.

Casabianca goes on to point out that several historians do claim that there is good evidence for concluding that the Turin Shroud is the authentic burial wrapping of Jesus. And indeed they do. But it seems a very curious argument to say that it is valid to make this historical claim simply because some people do so. Simply, such claims are made; whether there are, or can be, adequate grounds for making them is another matter entirely.

Casabianca certainly goes too far, though, when he proposes that “to explain the image on the Turin Shroud, the Resurrection hypothesis is the most likely of all the hypotheses, even when compared with natural hypotheses.” There are several problems with this suggestion.

Casabianca suggests that it follows from “a historiographical approach (the ‘Minimal Facts Approach’)”, which I take to be some kind of Occam’s razor position. Even if you buy the usefulness in Occam’s razor for determining the preferred solution to a body of facts (and there is no philosophical or empirical justification for it), the idea becomes meaningless here. There is no calculus that allows you to make a quantitative comparison between a natural explanation of events that stays within the laws of physics and a supernatural explanation that does not. Is the explanation “God did it” economical because you can say it in three very short words? Or (as I think) does the idea that the laws of physics can be arbitrarily suspended by some unknown entity in fact incur an overhead of hypotheticals compared to which the demands of string theory look like a trifling concession? However you look at it, to afford supernatural explanations so casually doesn’t look like careful reasoning to me.

That’s all the more so given that there are so many unknowns and uncertainties about the Shroud image in the first place. Reports are contradictory and confused, technical issues are challenged, and quite frankly it has been pretty much impossible to perform careful, well checked science on this material at all, since the Roman church has made access to the samples so restricted. Put simply, we can’t be sure what facts we are proposing to explain.

Coming back to Casabianca’s contention, could science ever prove that the Shroud is of supernatural origin? Of course, scientists will rightly say that this is a semantic contradiction, since if new knowledge shows that what we have previously considered “supernatural” actually happens, it then just becomes part of the “natural”. But the real issue here is whether there could ever be incontrovertible evidence that such things as God, resurrections and divinely ordained virgin births may happen. Casabianca mentions the example of the stars spontaneously forming the sentence “God exists” in the sky. I for one am happy to say that, were that to happen, I would be given pause. My hierarchy of explanations would then be something like: It is a hoax or weird illusion; I have lost my mind; it is aliens; it is the Supreme Being saying hello. I have no problem of principle with working my way through that progression. Yes, I’m open to persuasion that God exists and that Christ rose from the dead and left his imprint in a cloth through supernatural means. Which rational person could not be?

But to accept such things on the basis of fuzzy and often rather poor science conducted on a jealously guarded scrap of old linen doesn’t seem terribly logical to me. To believe that a supreme being would have set us a puzzle of this kind, so hazily written and laced with red herrings, false trails and contradictions, to test our faith seems positively perverse. You would almost need to believe that He had set out not to challenge science but to traduce it. Such a God can’t be logically excluded from existence, but He does not interest me.

Killing the cat?

This graphic from New Scientist, and conversations last night at the Science Museum, got me thinking. Using Schrödinger’s cat as a way to illustrate the differences between interpretations of quantum theory is a nice idea. But it suffers from the flaw that challenges the entire thought experiment. In order to be able to talk about the scenario in quantum terms, we need to be able to express it in quantum terms. But we can’t, because “live cat” and “dead cat” are not well-defined quantum states.

What, you can’t tell a live cat from a dead cat? Nonsense! Well yes, it is; but that’s not we’re asking here. What quantum property is it, exactly, that characterizes the superposition state, and that will enable you, unambiguously and in a single shot, to distinguish the two classical states? Live and dead are not quantum variables, and I’m not at all sure that they can be correlated even in principle with quantum variables that can be placed in superposition states.

Schrödinger’s point was not, in any case, that these are two different states of a macroscopic object, but that they are logically exclusive states. The paradox lies not in “two states at once”, but in “two contradictory states at once”. He was pointing not to “weird behaviour” predicted by quantum theory, but to logical paradoxes.

And this is why the Many Worlds Interpretation doesn’t resolve the problem. Yes, it looks as though it does: both outcomes are true! As New Scientist puts it here, “The universe splits. Your cat is dead, but in a parallel world it remains alive.” (Or, as Rowan Hooper points out, vice versa.) But wait: your cat? Who is you? Whose cat is it in the other world?

Brian Greene, in The Hidden Reality, tells us: that is you too! They are both you. Oh, so that sentence reads “Your cat is dead, but your cat remains alive.” Greene isn’t troubled by the fact that this is not how “you” works. But nevertheless, this is not how “you” works.

David Deutsch and Max Tegmark say, ah language! What should we trust more, language or maths? Contingent sounds, or timeless equations? But here language is articulating something that underpins maths, which is logic. Schrödinger realized that, but his point seems to be forgotten (by some). I don’t have time to go into it here (my forthcoming book will), but individual identity is a logical construct. You can’t wish it away with fantasies about “other yous”. I am trying to resist the topical urge to suggest that the Many Worlds interpretation offers us “alternative facts”, but that is terribly hard to do. So folks, the second option here is far more problematic than it looks.

What about the first? Let me say first of all that in neither the Copenhagen nor the Many Worlds interpretation is the cat “simultaneously alive and dead”. Not only is there no way of expressing that in quantum mechanics (at least, no one has articulated one), but in any event the proper statement of the situation is that “We can say nothing about the state of the cat, other than that live and dead are both possible outcomes of an observation”. That might sound like a pedantic distinction, but it will not be possible to make sense of quantum mechanics without it.

Now, I would hesitate to call the Copenhagen interpretation the “standard” interpretation, since there is no consensus, nor even a majority view, about which is the correct interpretation of quantum mechanics, at least among those who think about foundational issues. What’s more, the “Copenhagen interpretation” is not a single thing: Heisenberg expressed it differently to Bohr, and Wheeler had his own view too, as did others. However, I think Bohr would have said something like this: after observation, we have acquired now information that has changed our view of the cat’s condition (assuming it can be expressed in quantum terms at all) from an indeterminate to a determinate one. Some Copenhagenists, such as Pascual Jordan, spoke of this in causative terms: our observations produce the results. In that view, it seems acceptable to say that “Your measurement killed the cat” (although since we cannot say that it was previously alive, we might need to say more strictly “Your measurement elicited a dead cat”). But I’m not at all sure that Bohr would have seen causation at work in the measurement, as if “wavefunction reduction” is a physical effect that kills the cat. (That’s really the third, “objective collapse” option, which is given the least problematic representation here.) I think Bohr might have said something along the lines that “Observation allows us to speak about the classical state of the cat. And look, it is a dead one!”

So, which way will you vote? Bear in mind, however, that there are other option available, not all of them mutually exclusive. And that you won’t be able to prove that you’re right, of course.

The EBS Club and how to blag your way in

Len Fisher is to blame for hooking me into the terrible narcissism that goes under the name of the EBS number. It’s the elite (pantomime boo and hiss!) version of the Kevin Bacon Game, or of the Erdős Number, by which you trace how many collaborations it takes to link you to actor Kevin Bacon (if you’re in the movies) or to mathematician Paul Erdős (if you’re in maths or some vaguely mathematical branch of science). There’s your E and B. The S is the fun one: how many links does it take to link you to doyens of Midlands heavy metal Black Sabbath? Your EBS number is the sum of the three.

Len explains the idea here. Elsewhere we’re told, rather flatteringly, that “To even have an Erdős-Bacon-Sabbath number puts you in quite an exclusive club” – one that includes the likes of Stephen Hawking, Richard Feynman and Brian May. Not surprisingly, it’s a club many will be keen to get into, and I sense a degree of fudging going on. Apparently as long as you’ve sat on a couch and chewed the cud with a film star, or been sampled in some portmanteau song, you can claim to have a B or an S. Or even a BS.

Being unable to resist this prod to my competitive bone (gland, more probably), I started pondering. I can get to an EBS of 15 without too much of a stretch – and that is by considering actual co-appearances in a movie or playing together in a band onstage, not (for example) appearing in the same chat show. I haven’t done a great deal of work on the Erdős number, other than to note that my coauthor Jean-Marie Lehn (“Supramolecular chemistry”, The New Chemistry, ed. N. Hall; Cambridge University Press, 2000) has an EN of 5 – so that makes mine no more than 6. It may be that I could do better via my PhD supervisor Bob Evans, as he’s a theoretical physicist.

For my Bacon Number, I had the questionable honour of appearing in an obscure little movie called The Undertakers (in which I played a member of rock band Hot Nun) with my old school friend Suri Krishnamma, who went on to become a well respected film director who has worked with the likes of Albert Finney (→ Marisa Tomei → Kevin Bacon) and Ray Liotta (→ Ryan Reynolds → Kevin Bacon). So I get a BN of 4.



For my Sabbath number, I could bend the rules and claim an SN of 2 via veteran BBC producer Tony Wilson, who produced both my 1985 Radio 1 session and every other major rock band of the 1970s and 80s, including at least one Sabbath session. But I think it’s more in the spirit of the thing to cite a gig I played in the same year with session guitarist Bruce Roberts, a legend on the Southampton music scene (whose band used to rehearse in the flat upstairs from the one we rehearsed in – you wouldn’t have wanted to live in Cranbury Place in 1984-5). Bruce played in the Jess Roden Band, among many others (he supported the likes of the Who and Alex Harvey and played with Ben E. King and Bryan Ferry). So thanks to him, I’m off and running: Jess Roden sung with Paul Rodgers on Paul Kossoff’s solo album Back Street Crawler, Rodgers temporarily took the place of the late Freddie Mercury in Queen, and from Queen it’s an easy step to Sabbath. So there’s a SN of 5.



I did consider trying via Portishead guitarist Adrian Utley, with whom I played in a gig in Bristol. But Adrian moves on other circles, so it’s a circuitous route. I do, however, still have a recording of that gig, and so you can hear what happens when the ridiculously talented Utley steps up to a solo and wipes everyone else from the stage. It was breathtaking.

So there you are: what I’d claim is a bona fide EBS number of 15. And what does that mean? The answer, of course, is very little. Plenty of top scientists have an Erdős number bigger than mine. More to the point, even if my BN and SN are valid, they come from fleeting associations that really say nothing about any putative “polymathic” skills. My encounters with Bruce and Adrian taught me only the difference between a musician kind of competent enough to get away with playing in public, and one who will make an impact – even a small one, in Bruce’s case – on the music business. As for my dramatic prowess in The Undertakers, the less said the better. These metrics are really an exercise in clinging to celebrity by one’s fingertips. Or to put it more positively, they offer a fun excuse to return to some of the more curious avenues of one’s path through life.

At the same time, this little exercise supports what Mark Granovetter said in 1973 about “the strength of weak ties” in social networks. Granovetter pointed out that many social networks consist of strongly connected local clusters – a group of closely connected individuals – linked to one another via weak ties. It’s these weak ties between communities, he said, that join them into a single network. I can’t claim to be deeply embedded in the movie or music communities in the way that I am in science – but my connections to those other networks exist through rather fleeting, one-off and not particularly profound links (Suri is a lovely bloke, but I haven’t seen him for many years; Bruce, who died earlier this year, probably wouldn’t have known me from Adam a few weeks after that gig.)

And while EBS numbers are not at all of the same constitution as the infamous h-index and other metrics used to rank scientists, I can’t help suspecting that much the same applies to those: they can point to a varied and impactful career (see Hawking or May), but they can also rely to a fair degree on chance, happenstance, and being in the right place at the right time.

All the same, I just want Ozzy to know that I’m up for a jam. Anything to give me a smaller EBS number than Adam Rutherford.

More alternative heroes

It was fun to write this piece for Nautilus on who would have made some of the great discoveries in science if their actual discoverers had not lived. And very nice to see it is provoking discussion, as I’d hoped – there is nothing definitive in my suggestions. Here are two more case histories, for which there was not room in the final article.

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Fullerenes – Wolfgang Krätschmer and Donald Huffman

In 1985, British spectroscopist Harry Kroto visited physical chemists Richard Smalley and Robert Curl at Rice University in Houston, Texas, to see if their machine for making clusters of atoms could produce some of the exotic carbon molecules Kroto thought might be formed in space. Their experiments led to the discovery of hollow, spherical molecules called C60 or buckminsterfullerene, and of a whole family of related hollow-shell carbon molecules called fullerenes. They were awarded the 1996 Nobel prize in chemistry for the work.

Fullerenes had been seen before 1985; they just hadn’t been recognized as such. They can in fact be formed in ordinary candle flames, but the most systematic experiments were conducted in 1982-3 by experimental physicist Wolfgang Krätschmer at the Max Planck Institute for Nuclear Physics in Heidelberg, Germany. Krätschmer had teamed up with physicist Donald Huffman of the University of Arizona, for they both were, like Kroto, interested in the constituents of interstellar space.

Huffman studied dust grains scattered through the cosmos from which stars may form. He and Krätschmer began collaborating in the 1970s while Huffman was on sabbatical in Stuttgart, and initially they looked at tiny particles of silicate minerals. But Huffman believed that some of the absorption of starlight by grains in the interstellar medium could be due to tiny particles of something like soot in the mix: basically, flakes of graphite-like carbon.

In 1982 he visited Krätschmer to carry out experiments in which they heated graphite rods in a vacuum and measured the light absorbed by the sooty debris. They made and saw C60, which absorbs ultraviolet light at a particular wavelength. But they didn’t realize what it was, and decided their apparatus was just making unintelligible carbon “junk”.

It wasn’t until the duo saw the paper by Kroto and colleagues in 1985 that the penny dropped. But if it hadn’t been for that, the interest of astronomers in interstellar dust would probably have returned scrutiny anyway to those experiments in Heidelberg, and the truth would have emerged. As it was, the graphite-vaporizing equipment of Krätschmer and Huffman offered a way to mass-produce fullerenes more cheaply and simply than the Rice cluster machine. Once this was understood in 1990, fullerene research exploded worldwide.

Continental drift – Roberto Mantovani, or…

There are discoveries for the time seems right, and others for which it’s just the opposite. For one reason or another they are rejected by the prevailing scientific opinion, offering us the retrospective, appealingly tragic tale of the lone maverick who was spurned only vindicated much later, perhaps posthumously. That’s pretty much how it was for Alfred Wegener’s theory of continental drift. In the 1930s, Wegener, a German meteorologist (so what did he know about geology?), proposed that the Earth’s surface was not fixed, but that the continental land masses wander over time into different configurations, and were in the distant past disposed far from where they stand today. To doubt the evident solidity of the planetary surface seemed absurd, and it wasn’t until the discovery of seafloor spreading – the formation of fresh ocean crust by volcanic activity – in the 1960s that continental drift became the paradigm for geology.

In such circumstances, it seems rather unlikely that anyone else would have come up with Wegener’s unorthodox idea in his own era. But they did. Not just one individual but several others imagined something like a theory of plate tectonics in the early twentieth century.

The most immediate sign of continental drift on the world map is the suspiciously close fit of the east coast of South America with the west coast of Africa. But that line of argument, advanced by American geologist Frank Bursley Taylor in 1908, seems almost too simplistic. Taylor got other things right too, such as the way the collision of continents pushes up mountain ranges. But his claim that the movements were caused by the close approach of the moon when it was suddenly captured by the Earth in the Cretaceous period was rather too baroque for his contemporaries.

In 1911, an amateur American geologist named Howard Baker also proposed that the continents are fragments of an epicene supercontinent that was torn apart. His mechanism was even more bizarre than Taylor’s: the moon was once a part of the Earth that got ripped off by its rapid spinning, and the continents moved to fill the gap.

In comparison, the theory of Italian geologist (and violinist) Roberto Mantovani, first published in 1889 and developed over the next three decades, was rather easier to swallow. He too argued that the continents were originally a single landmass that was pulled apart thanks to an expansion of the Earth driven by volcanic activity. Wegener acknowledged some “astonishingly close” correspondences between Mantovani’s reconstruction and his own.

All of these ideas contain tantalizing truths: breakup of an ancient supercontinent (now called Pangea), opening of ocean basins, mountain building and volcanism as the driving force. (Even Baker’s idea that the moon was once a part of the Earth is now widely believed, albeit for totally different reasons.) But like a reconstruction of Pangea from today’s map, the parts didn’t fit without gaps, and no one, including Wegener, could find a plausible mechanism for the continental movements. If we didn’t have Wegener, then Mantovani, or even Taylor or Baker, could step into the same foundational narrative of the neglected savant. All intuited some element of the truth, and their stories show that there’s often an element of arbitrariness in what counts as a discovery and who gets the credit.

The Return by Hisham Matar: why it's a special book

These were my comments on Hisham Matar’s book The Return for the Baillie Gifford Prize award event on 15 November. The prize, for which I was a judge, was awarded to Hisham’s close friend Philippe Sands for his extraordinary book East West Street.

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When we produced our shortlist, and indeed our longlist, I felt pleased with and proud of it. But as my acquaintance with the shortlisted books has deepened, and perhaps particularly in the light of the political climate into which they emerge, I have felt something more than that. I’ve become passionate about them.

But it was passion that I felt about Hisham Matar’s book from the first reading. It tells of his quest to find out what happened to his father Jaballa in Libya during the Qaddafi dictatorship, after Jaballa was imprisoned in the notorious Abu Salim jail for his principled opposition to the regime. The Return of the title is Hisham’s return to Libya in 2012, 33 years after his family was exiled, when the Qaddafi regime had been overthrown. That was during what we now know to be a tragically brief period of grace before a descent into social and economic chaos created by the power vacuum.

Yes, the subject sounds difficult and bleak, but please believe me that this book is not that, not only that. It is wise and funny, it is perceptive to absurdity, to beauty and to friendship, as well as to terror and cruelty. Several times it was said in our judging meetings that Hisham’s book has a novelistic quality,

If this story were not factual, I would expect to see The Return on the Man Booker shortlist, and novelists could learn a great deal from Hisham’s impeccable handling of every scene, each of which unfolds at just the rate and in just the order it should, with precisely the words it needs and no more.

But calling the book novelistic could sound like a double-edged comment, as if to imply that perhaps the truth is sometimes held hostage to a nice turn of phrase. That is absolutely not the case. It feels hard to do justice to the brilliant construction of the book, the masterful handling of plot, suspense and intrigue, without seeming to reduce the magnitude of the subject to the dimensions of a thriller. But these aspects are really a mark of the achievement here, because even as they make the book a totally engrossing read, not once do they obscure the moral and artistic integrity of what Hisham has created.

Of course, he is an acclaimed novelist himself, but here he shows that there are qualities in literature far more significant than the apparent division between fact and fiction.

But it is factual. That is a sad and terrible thing, but it also makes The Return a sort of gift, an honouring of the history and suffering of individuals and a country.

There is something in it that brings to my mind Primo Levi’s testament If This is a Man. Like that book, this one can’t use art to expunge the awful, inhuman events that motivated it. But, in its quiet dignity, it shows us why we persist, and in the end, I think, why we prevail, in spite of them.

Did the Qin emperor need Western help? I don't think so.

Did the First Emperor of China import sculptors from classical Greece to help build the Terracotta Army? That’s the intriguing hypothesis explored in an entertaining BBC documentary called The Greatest Tomb on Earth, presented by Dan Snow, Alice Roberts and Albert Lin. (See also here.)

If it was true, it would revolutionize our view of the early history of China. It’s widely assumed that there was no significant, direct contact between China and the West until the time of Marco Polo (although you would not have guessed from this programme that diffusion of artifacts along trade routes happened much earlier, certainly in Roman times around the first century AD).

But I didn’t buy the story for a moment. It turned out to be a classic example of building up a case by an accumulation of weak, speculative evidence and then implying that somehow they add up to more than the sum of the parts. Look at each piece of evidence alone, and there’s virtually nothing there. But repeat often enough that they fit together into a convincing story and people might start to believe you.

Archaeologist Albert Lin adduced evidence of the ancient road that connected that ancient capital of present-day Xi’an, near the site of the mausoleum of the Qin emperor Qin Shi Huangdi, to the West, perhaps via Alexander’s empire in India. Well, at least, it was claimed that “there was probably a road reaching [from the tomb] at least to Lintao” on the borders of the Qin Empire. Buy what Lin actually found was a short section of undated track – it looked maybe a kilometre or so long – heading northwest through farmland within the confines of the tomb complex in Sha’anxi. Lintao is almost 400 km away. Later in the programme Dan Snow claimed that on this basis “We have evidence of an ancient road network that could have brought Westerners to China”. No, they really don’t. (And why do we need to find an ancient physical road anyway, given that it does seem clear that trade was happening all the way from the Mediterranean region to China at least in Roman times?)

Another strand of evidence was the notion that large-scale, lifelike figurines suddenly appeared in the Qin tomb, looking somewhat like those of classical Greece, when nothing like this had been seen before in China. How else could this artistic leap have been made, if not with the assistance of Greek sculptors imported by the emperor? That, at least, was the case argued by Lukas Nickel of the University of Vienna, based solely on asserted coincidences of artistic styles. We were offered no indication of how the Qin emperor – who, until he became ruler of “all” of China extending more or less to present-day Sichuan, was king of the state of Qin in the Wei valley – how this emperor somehow knew that there were barbarians nigh on 2000 miles further west across the Tibetan plateau who had advanced sculptural skills.

There were some puzzles, to be sure. To make some of their bronze castings, the Qin metalworkers seemed to have used something like the so-called “lost-wax technique”, using reinforcing rods, of which examples are known in ancient Egypt. “It’s clear this process is too complex to stumble on by accident”, said Snow. But obviously it was stumbled on by accident – how else was it ever invented anywhere? Given the known metallurgical skills of the ancient Chinese – bronze casting began in the Shang era, a millennium and a half before the Qin dynasty, and some of the Shang artifacts are exquisite – how can we know what they had achieved by the third century BC? Besides, I was left unsure what was so exciting about seeing a lost-wax method in the Qin artifacts, given that we already know this technique was known in China by the 6th century BC. Still, Snow concluded that “We now have strong evidence of Western metalworkers in China in the third century BC”. No, we don’t.

Then a skull from the mausoleum site, apparently of a sacrificed concubine of the emperor, was said to look unlike a typically East Asian skull. Like, perhaps, the more Caucasoid skull types of the minority races in what is today Xinjiang? That’s consistent with the data – the skull is certainly not Western in its proportions, said Alice. It could come from further afield too, on the basis of this data – but there’s absolutely no reason to suppose it did. Still, we were left with the hint that the emperor might have employed workers brought in from far outside the border of his empire. There was no support for that idea.

We were also introduced to an apparently recent paper reporting evidence of DNA of Western lineage in people from Xinjiang. Quite apart from the fact that this says nothing about the import of Western artistic techniques in China during the Qin dynasty, it was very odd to see it offered as a new discovery. The notion that there were people of Western, Caucasoid origin in Xinjiang long, long ago has been discussed for decades, ever since the discovery in the early twentieth century of mummified bodies of distinctly non-Chinese – indeed, virtually Celtic – appearance, with blond to red hair and “Europoid” body shapes in the Tarim basin of Xinjiang. The existence of a proto-European or Indo-European culture in this region from around 1800 BC has been particularly promoted since the 1990s by American sinologist Victor Mair. DNA testing from the early 2000s confirmed that the mummies seem to have had at least a partly European origin.

What is particularly odd about the neglect of the Tarim mummies in the context of this programme is that Mair and others have even suggested that this Indo-European culture may have brought Western metallurgical technology from west to east long before the Qin era, by the usual processes of cultural diffusion. They think that the bronze technology of the Shang era might have been stimulated this way. Others say that ironworking might have been transmitted via this culture around the tenth century BC, when it first appears in Xinjiang (see V. C. Piggott, The Archaeometallurgy of the Asian Old World, 1999).

I enjoyed the programme a lot. It identifies some interesting questions. But the idea of West-East cultural influence in the ancient world is not at all as new as was implied, and to my eye the evidence for direct import of Western “expertise” by Qin Shi Huangdi to make his army for the afterlife is extremely flimsy at this point. It would make a great story, but right now a story is all it is.

Incidentally, several folks on Twitter spoke about the popular idea that the Qin emperor’s mausoleum contains lakes of mercury. You can read more about that particular issue here.

Making paint work: Vik Muniz's Metachromes

This is the catalogue essay to accompany the exhibition Metachromes by Brazilian artist Vik Muniz at Ben Brown Fine Arts in London, 6 October to 12 November.



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Why did so many artists abandon painting over the course of the twentieth century? There is no point looking for a single answer, but among the ones we might consider is that painters lost their trust in paint. It’s something rarely talked about, this relationship of painters to paint – or at least, it is rarely talked about except by painters themselves, to whom it is paramount. Paint represents the graft and the craft of painting, and for that very reason it is all too often neglected by art critics and historians, who have tended to regard it merely as a somewhat messy means to a sublime end. But many leading artists since Matisse have been making art not with paint but about paint, and in the process displaying their uneasy relationship with it.

No one put this better than Frank Stella: “I tried to keep the paint as good as it is in the can.” Two things leap out here, as British artist David Batchelor suggests in his book Chromophobia. First, for Stella paint comes in cans, not in tubes (it is an industrial mass product). Second, it looks good in the can. Indeed, perhaps it looks better in the can than it will once you start trying to apply it. The challenge of a blank canvas is familiar: it demands that the painter find something to fill up that blankness, something that will have been worth the effort. Blankness means it’s up to you. But paint in a can is a challenge of a different order. Here it is, already sensual, beautiful and pure – qualities that the artist might hope to retain in the finished work, but the paint sitting in the can says ‘you think you can do better than this?’ Probably not.

Paint had become too perfect. Anyone who has tried to make paint the way a Renaissance master (or more probably, his apprentices) would have done will know that it emerges as unpromising stuff: sticky, gritty, oily. It was the artist’s task to wrestle beauty from this raw earth, which must have seemed a noble and mysterious thing. In the Middle Ages there was barely time even to take note of the paint: blended from pigments and egg yolk, it dried in minutes, so you had better get to work and not sit there admiring it in the dish. But industrialization changed all that. Pigment was machine-ground with the power of horses or steam until the powder was fine and smooth. It was mixed with oils and additives in great vats like those one can still see in the factories of artists’ suppliers such as Winsor and Newton: an almost obscene orgy of viscous colour. Cheaper pigments and new binding media led to the production of colour by the can, made not for daubing onto canvas but for brushing in flat swathes over walls and ceilings. These were no longer the rust-reds and dirty yellows of Victorian décor, but deep pinks, azure, viridian, the colours of sunsets and forests and named for them too.

That makes it sound as though artists were spoilt for choice, and in a sense they were: the range of colours expanded enormously, and most of this rainbow was cheap. But not all the colours were reliable: they might fade or discolour within weeks or years. Instability of paint is a problem as old as painting. But in the past painters knew their materials: they knew what colours they could mix and which they should not, which are prone to ageing and which withstand time. From the early nineteenth century, however, painters became ever less familiar with what was in their materials. These were substances made in chemicals factories, and not even the paint vendors understood them. Even if the technical experts (then called colourmen) guaranteed them for five years, how would they look in fifty? At first, paint manufacturers had little idea about such matters either, and they did not seem to care very much. Disastrous errors of judgement were made at least until the 1960s, as anyone who has seen what became of Mark Rothko’s Harvard murals will attest: valued at $100,000 when completed in 1962, they were in too embarrassing a state to remain on display by 1979.

But it was not just this lack of technical understanding that led painters to distrust paint. Every medium had its message, and the message of oil paint was now deemed a bourgeois one, to be disowned by any self-respecting artistic radical. It “smacked of garrets and starving artists”, according to British artist John Hoyland. Any sign of a brushstroke spoke of painterly traditionalism, and was to be avoided at all costs. The impassive matt finish of acrylics was the thing: it gave the artist a neutral colour field to play with, unencumbered (so they liked to think) by history. For some, this embracing of new paint media arose out of economic necessity: commercial paints bound in synthetic resins were cheaper, especially if you planned (as many did) to work on a colossal scale. For others, new media offered new styles: Jackson Pollock needed a “liquid, flowing kind of paint”, Stella seized on metallic radiator paints to step beyond the prismatic rainbow. But paints made from plastics also spoke of modernity. Nitrocellulose enamel spray paints are used on cars and toasters, so why not, as Richard Hamilton decided, use them for paintings of cars and toasters? “It’s meant to be a car”, he said, “so I thought it was appropriate to use car colour.”

The idea, then, was that the artist would no longer try to hide the materials in the manner of a nineteenth-century French academician like Ingres, but was constantly referring to them, reminding the viewer that the picture is made from stuff. That’s true even of the flat anonymity of the household paints used by an artist like Patrick Caulfield, which at first seem to be concealing their identity as ‘paint’ at all: they’re saying ‘this is only a surface coated with colour, you know’ – or as Caulfield puts it, “I’m not Rembrandt.” The paint is not pretending to be anything else.

Part of the pleasure of Vik Muniz’s works is that they often do pretend to be something else, but so transparently that you notice and relish the medium even more. “Oh, those are diamonds! That’s chocolate, that’s trash, those are flowers.” His Metachrome series is particularly rich in allusion, because the works confront this issue of the material of painting in ways that highlight several of the problems of paint, which have vexed and in the end sometimes inspired painters. They leave the medium – pastel sticks – literally embedded in the work, and not as accidental remnants but as constructive elements. On the one hand this creates a Brechtian sense of ‘here’s how it was done’, a denial of illusion. These become not just images of something, but works about creating art. It reminds us of the disarming honesty of French painter and sculptor Jean Dubuffet’s remark: “There is no such thing as colour, only coloured materials.” By reconstructing the paintings of famous artists with the pigment-saturated tools still visible, Muniz demystifies the original objects. And art itself then becomes more humble, but also more valuable: not an idea, nor a commodity, nor an icon, but a product of human craft and ingenuity.

This wouldn’t count for so much if the aesthetic element weren’t respected either. The solidity and chromatic depth of these pieces of coloured material are richly satisfying. We can enjoy them as substance, source and subject. They seem to invite us to pluck them up, and to start making marks ourselves.

Points of colour

One thing brought to mind by Metachromes is the specks and lumps of colour and crystal seen in cross-sectional micrographs that art conservators use routinely to study the multilayered techniques of the Old Masters. Those images reveal that the colour may be surprisingly dispersed: sometimes the grains are as sparse as raisins in a fruit bun, so that it seems a wonder the paint layer does not look patchy or translucent. (The effect may be cumulative: in Titian or van Eyck the bold colours come from the painstaking application of layer after layer.) But what these micrographs also reveal is colour unmixed: greens broken down into blues and yellows, flesh tones a harlequin jumble of hues mixed with white and black. They remind us that the rich hues of the Old Masters are an optical illusion conjured from a very limited palette: they had only a few greens to play with, their blues were sparser still. The illusion is sustained by scale: the flecks are so small that the eye can’t distinguish them unaided, and they blend into uniformity. When this optical mixture produces so great a perceptual shift as yellow and blue to green, the effect seems like alchemy. We get accustomed to this method of making green in the nursery, but still it seems odd to be confronted by such stark evidence that our eyes are deceiving us, that there is only yellow and blue at the root of it all.



Colour mixing is genuinely perplexing. Isaac Newton explained it in 1665, but the explanation made no sense to artists. Yellow, he said, comes from mixing red and green. Add blue and you get white. This was clearly not the way paints behaved.

Newton’s experiment is commonly misunderstood. He did not show for the first time that sunlight could be split into the rainbow spectrum; that had been known since time immemorial, for all you needed was a block of clear glass or crystal. Some suspected, however, that this colouration of sunlight might be the result of a transformation performed by the prism itself. Newton showed that if one of the coloured rays of the spectrum – red, say – is passed through a second prism, it emerges unchanged: these are, he said, “uncompounded colours”, irreducible to anything else. And if the entire spectrum is squeezed back through a focusing lens, it reconstitutes the original white ray. Colour, then, comes from plucking this rainbow, extracting some rays and reflecting others. Black objects swallow them all, white objects reject them.

According to Newton, the colours we see are in the light that conveys them. Goethe (whose antipathy to Newton I have never really fathomed) spoke for many when he said that thanks to Newton “the theory of colour has been forced to enter a realm where it does not belong, to appear before the judgement seat of the mathematician.” Dyers, he says, were the first to perceive the inadequacy of Newton’s theory, because “phenomena forcefully confront the true practitioner, the producer of goods, every day. He experiences the application of his ideas as profit or less.” And so he knew much better than to waste valuable dyes by attempting to make yellow from red and green.

Goethe’s largely misconceived theory of colour continues to exert a strange appeal, but what he did not appreciate is that there are two kinds of colour mixing. One works for dyes and pigments, and it involves the removal of prismatic wedges from sunlight: take away the reds and violets, and you are left with green. This is subtractive mixing. The other works for light rays, and it involves a gradual reconstitution of the spectrum from its component rays. The retina tickled with red and green light, for example, reports back to the brain in just the same way as it does when struck by pure yellow light. This is additive mixing. The Scottish physicist James Clerk Maxwell explained this in 1855, and his discoveries quickly filtered down in popularized forms to painters, some of whom dreamed of finding within them a prescription for filling their canvases with sunlight.

Additive mixing can be achieved in various ways. In television screens, trios of light-emitting pixels in the additive primaries – crudely speaking, red, green and blue-violet – are juxtaposed at too small a scale for the eye to resolve from a normal viewing distance, and their light is blended on the retina. Maxwell showed that he could achieve the same thing with pigments by painting segments of disks and spinning them at great speed, something that the polymathic Englishman Thomas Young had also done at the beginning of the nineteenth century. The Impressionists took away the message that all visual experience is constructed from spectral colours, so that these were the only ones they should use – no more ochres or umbers. They tried to banish black from the palette, and while white remained indispensable, their whitewashed walls and snow were broken up into bright primaries. When Claude Monet needed browns and blacks to depict the smoky train station at Saint-Lazare, he mixed them from primaries, although you would never guess it.

Paul Signac and Georges Seurat went further. They hoped to do away with subtractive mixing entirely, seeing that it almost inevitably degraded the brightness of the colours. Instead, their pointillist style, with small dots of pure pigments placed alongside each other like meadow flowers scattered among grass, was intended to let the colours mix optically, on the retina rather than on the canvas, when viewed from the right distance. These Neo-Impressionists believed that this would give their works greater luminosity.

Curiously, Newton himself had described something akin to this. He said that a mixture of dry pigment containing yellow orpiment, bright purple, light green and blue looked at a distance of several paces like brilliant white. The scattering of coloured grains in Muniz’s pictures hint at the same thing. There are places where the colour seems uncertain, treacherous, on the verge of shifting: it depends on where you’re standing, and might change as you step back.

But for the Neo-Impressionists, pointillist optical mixing did not really work. Partly this was because they had only a hazy grasp of the new colour theory, corrupted by an old notion about the yellow-orange colour of sunlight. Partly they were inconsistent in applying the technique, varying the size of their tache strokes. Signac admitted his disappointment with the experiment: “red and green dots make an aggregate which is grey and colourless” – although this pearly sheen is now an aspect of what we enjoy in the atmosphere of their peinture optique. As it drifted from its scientific origins, pointillism became just another mannerism, a style rather than an experiment. It’s a style that Muniz plays with here, the strokes and marks of the artist sometimes playfully but effectively substituted by the pastel sticks themselves. They are Titian’s grains of colour writ large, confessing their illusionism – but still performing it anyway, if we let them.

Work with dirt

“Sometimes we want to know how things are made. Sometimes we don’t,” says Muniz. Metachromes forces us to confront the fact that painting is made from what Philip Guston called ‘coloured dirt’. It is not smoothed flat or artfully raised into ridges by brush or knife: the dirt is simply there, heaped and glued onto the surface, and provoking us to wonder what this stuff actually is.



Many art historians and critics don’t care much for that. They will talk of ‘cobalt’ as a shorthand for a strong blue, as though they think this is the hue of that silvery metal itself – and never mind the fact that the blue cobalt-based pigment of van Dyck had very little to do with the cobalt blue of van Gogh – the latter a nineteenth-century innovation that the artist called a “divine colour”.

Paint disguises this grainy minerality. Seeing it restored in Muniz’s images, you can’t help but wonder about the chemistry. Colours like this are rare in the earth, for even gorgeous gems such as sapphire and ruby turn pale and disappointing when finely ground. When geology alone supplied the palette, reds were rusty and yellows were tawny, both of them ochres. Malachite, a copper ore, gave a pleasant bluish green, but not the vibrant green that light-harvesting chlorophyll brings to grass and the leaves of flowers. Of purple there was almost nothing – a rare manganese mineral, if you were lucky; or dyestuffs that blanched in the light. For orange you took your life in your hands with realgar, the highly toxic sulfide of arsenic.

Blue alone is well served by nature: it could be extracted, at immense cost and labour, from lapis lazuli, a mineral mined in Afghanistan, and brought across the seas – or as the name has it, ultra marina. Mere grinding wasn’t enough to turn lapis into this midnight blue: the blue component (called lazurite) had to be extracted from the impurities, which otherwise made the powder greyish. This was done by mixing the powder with wax into a dough and kneading it repeatedly in water to flush out the blue. The best ultramarine cost more than its weight in gold, and was reserved only for the most venerated of subjects; skies made do with cheaper blues, unless you were Giotto. When Johannes Itten, the mercurial colour theorist of the Bauhaus, insists that blue connotes meekness and profundity in medieval images of the Virgin, he forgets that to the medieval artist symbolism embraced the material too: the ultramarine robes of the mother of Christ honour her through their vast expense.



Wetness transforms

Today ultramarine is produced by the tonne – not from lapis lazuli, which is still very costly, but as an industrial chemical made in a furnace from soda, sand, alumina and sulfur. This was a triumph of nineteenth-century chemistry. Some of the leading chemists of that age were assigned the task of finding good synthetic substitutes for ultramarine, and they succeeded with cobalt blue; but it did not match the real thing. In 1824 the Society for the Encouragement of National Industry in France offered a prize of 6000 francs to anyone who could devise a way of making ultramarine synthetically. Its elemental constituents had been deduced in 1806, but the curious thing is that, unlike most pigments, ultramarine does not derive its colour from the presence of a particular metal in its crystal lattice (iron, copper, lead, mercury, chromium, cobalt and zinc are among the usual sources). Here, sulfur is the unlikely origin of the rich blue, and to understand it properly you need quantum chemistry.

The prize drew plenty of charlatans, but within four years it was claimed by the colour-maker Jean-Baptiste Guimet from Toulouse – a claim that was challenged, with justification but without success, by a German chemist at Tübingen. ‘French’ ultramarine offered Giotto’s glories for a fraction of the cost, although at first artists could not bring themselves to believe that it could be as good as the natural material.

The ultramarine you will buy in the tube today is made with this synthetic product, and it is probably better than the gritty grindings Titian used. But you should see the pigment before it becomes paint. It seems to emit a glow just beyond the visible range, it has a depth and velvety lustre that the liquid binder can only diminish. It is a colour to gaze on for long moments. Here is Frank Stella’s dilemma redoubled: if you think the paint looks good in the can, you should see pigment before it becomes paint.

That was what bothered Yves Klein in the 1950s. “What clarity and lustre, what ancient brilliance”, he said of raw pigments. But the touch of a binding medium is fatal to this texture: “The affective magic of the colour had vanished. Each grain of powder seemed to have been extinguished individually by the glue or whatever material was supposed to fix it to the other grains as well as to the support.” What goes wrong? The way light bounces off the pigment particles is modified by the medium, even if it is perfectly transparent, because light entering it cannot but be refracted, the rays bent as they are in water. This effect of the medium depends in its refractive index – a scientific measure, if you like, of its ray-bending power. So the same pigments may look different in different media: vermilion mixed with egg yolk is a rich orange-scarlet, but when Renaissance painters began mixing it with oils the result was less impressive, and soon they turned to other reds, to the crimsons and magentas of red lakes.

By the 1950s, painters already had several alternative binders to oil at their disposal – nitrocellulose, acrylics, alkyds, most of them petrochemical-based resins. Was there a binder, Klein wondered, that would fix the pigment particles in place without destroying their lustre? This was a chemical matter, for which the artist needed technical assistance. He got it from his architect friend Bernadette Allain, and most importantly from a Parisian manufacturer of paint, Édouard Adam. In 1955 they found that a resin produced by the chemicals company Rhône-Poulenc, called Rhodopas M60A, thinned with ethanol and ethyl acetate, had the desired effect. In Klein’s words, “it allowed total freedom to the specks of pigment such as they are found in powder form, perhaps combined with each other but nevertheless autonomous.”

Klein used this binder with the pigment that best deserved it: ultramarine. He premiered his brilliant blue sculpture-canvases in Milan in 1957 with an exhibition called ‘Proclamation of the Blue Epoch’. This blue became his trademark: coating blocks, impregnating sponges, covering twigs and body casts. It was International Klein Blue, patented to preserve its integrity in 1960, two years before the artist’s untimely death.

Another solution was to simply refuse to degrade the pure pigment with any kind of binder. In his Ex Voto for the Shrine of St Rita (1961), Klein encases ultramarine powder along with a synthetic rose pigment and gold leaf in clear plastic boxes. In Metachromes, Muniz offers a homage to Klein’s pigment triptych, this celebration of raw, synthetic “coloured dirt”.



Like Klein’s works, Metachromes poses the question: when does the material “leave the can” and become a work of art? It’s not a question that needs an answer. It’s there to remind us that “what is made” should require us to consider too “how it is made” and “what it is made of” – that we are not merely Homo sapiens but Homo faber, and that it is because we are both that we survive.