Wednesday, March 23, 2016

On the attack

One of the easiest ways to bring humour to music is with timbre. It’s cheap (literally) but still funny to play Led Zeppelin’s “Whole Lotta Love” or Richard Strauss’s “Also Sprach Zarathustra” on kazoo, as the Temple City Kazoo Orchestra did in the 1970s. Most things played on kazoo are funny. It just has a comical timbre.

Such performances inadvertently make a serious point about timbre, which is that it can matter more than the notes. This is overlooked when music is considered as notes on paper. Yet musicologists have largely neglected it, for the simple reason that we don’t really know what it is. One definition amounts to a negative: if two sound signals differ while being identical in pitch and loudness, the difference is down to timbre.

One feature of timbre is the spectrum of pitches in a note: the amplitudes of the various overtones. These are quite different, for example, for a trumpet and a violin both the same note. But our sense of timbre depends also on how this spectrum, and the overall volume, changes over time, particularly in the initial “attack” period of the first few fractions of a second. These are acoustic properties, though, and it might be more relevant to ask what are the perceptual qualities by which we distinguish timbre. Some music psychologists claim that these are things like “brightness” and attack, others argue that we interpret timbre in terms of the physical processes we imagine causing the sound: blowing, plucking, striking and so on. It’s significant too that we often talk of the “colour” of the sound.

Arnold Schoenberg thought it should be possible to write music based on changes of timbre rather than pitch. It’s because we don’t know enough about how the brain organizes timbre that this notion didn’t really work. All the same, Schoenberg and his pupils created a style called Klangfarbenmelodie (sound colour melody) in which melodies were parceled out between instruments of different timbre, producing a mesmeric, shimmering effect. Anton Webern’s arrangement of a part of Bach “The Musical Offering” is the most renowned example.

There’s one thing for sure: timbre is central to our appreciation of music, and if we relegate it below more readily definable qualities like pitch and rhythm then we miss out on a huge part of what conditions our emotional response. It would be fair to say that critical opinion on the music of heavy-metal band Motörhead, led by the late bass guitarist Lemmy Kilmister, was divided. But if ever there was a music defined by timbre, this was it.

Thursday, March 17, 2016

The Roman melting pot

Here's my column for the March issue of Nature Materials.


Recycling of materials is generally good for the planet, but it makes life hard for archaeologists. Analysis of ancient materials, for example by studying element or isotope compositions, can provide clues about the provenance of the raw materials and thus about the trade routes and economies of past cultures. But that business becomes complex, even indecipherable, if materials were reused and perhaps reprocessed in piecemeal fashion.

This, however, does seem to have been the way of the world. Extracting metals from ores and minerals from quarries and mines, and making glass and ceramics, were labour-intensive and often costly affairs, so that a great deal of the materials inventory was repurposed. Besides, the knowledge was sometimes lacking to make a particular material from scratch in situ. The glorious cobalt-blue glass in the windows of medieval French churches and cathedrals is often rich in sodium, characteristic of glass from the Mediterranean region. It was probably made from shards imported from the south using techniques that the northern Europeans didn’t possess, and perhaps dating back to Roman or Byzantine times. The twelfth-century monk Theophilus records that the French collected such glass and remelted it to make their windows [1].

In that instance, composition does say something about provenance. But if glass was recycled en masse, the chemical signature of its origin may get scrambled. It’s not surprising that such reuse was very common, for making glass from scratch was hugely burdensome: by one estimate, 100 kg of wood was needed to produce the ash for making 2 kg of glass, and collecting it took a whole day [2].

Just how extensively glass was recycled in large batches in Roman times is made clear in a new study by Jackson and Paynter [3]. Their analysis of glass fragments from a Roman site in York, England, shows that a lot of it came out of “a great big melting pot”: a jumble of recycled items melted together. The fragments can be broadly divided into classes differentiated by their antimony and manganese compositions. Both of these metals were typically added purposely during the Roman glass-making process because they could remove the colour (typically a blue-green tint) imparted by the impurities, such as iron, in the sand or ash [4]. Manganese was known in medieval Europe as “glassmaker’s soap”.

It’s the difficulty of making it that meant colourless glass was highly prized – and so particularly likely to be recycled. The results of Jackson and Paynter confirm how common this was. The largest category of glass samples that they analysed – around 40 percent of the total – contained high levels of both Sb and Mn, implying that glass rendered colourless by either additive would be separated from the rest and then recycled by melting.

But most of those samples aren’t colourless. That’s because remelting tends to incorporate other impurities, such as aluminium, titanium and iron, from the crucibles, furnaces or blowing irons. The recycled glass may then end up as tinted and undistinguished as that made with only low amounts of Mn. As a result, while it is derived from once highly prized, colourless glass reserved for fine tableware, this high Sb-Mn glass becomes devalued and used for mundane, material-intensive items such as windows and bottles. Eventually it just disappears into the melting pot.

1. Theophilus, On Divers Arts, transl. Hawthorne, J. G. & Smith, C. S. (Dover, New York, 1979).
2. Smedley, J. W., Jackson, C. M. & Booth, C. A., in Ceramics and Civilisation Vol. 8, eds McCray, P. & Kingery, W. D. (American Ceramic Society, 1998).
3. Jackson, C. M. & Paynter, S., Archaeometry 58, 68-95 (2016). [here]
4. Jackson, C. M., Archaeometry 47, 763-780 (2005).

Tuesday, March 01, 2016

Many worlds or many words?

I’ve been rereading Max Tegmark’s 1997 paper on the Many Worlds Interpretation of quantum mechanics, written in response to an informal poll taken that year at a quantum workshop. There, the MWI was the second most popular interpretation adduced by the attendees, after the Copenhagen Interpretation (which is here undefined). What, Tegmark asks, can account for the robust, even increasing, popularity of the MWI even after it has been so heavily criticized?

He gives various possible reasons, among them the idea that the emerging understanding of decoherence in the 1970s and 1980s removed the apparently serious objection “why don’t we perceive superpositions then?” Perhaps that’s true. Tegmark also says that enough experimental evidence had accumulated by then that quantum mechanics really is weird (quantum nonlocality, molecular superpositions etc) that maybe experimentalists (apparently a more skeptical bunch than theorists) were concluding, “hell, why not?” Again, perhaps so. Perhaps they really did think that “weirdness” here justified weirdness “there”. Perhaps they had become more ready to embrace quantum explanations of homeopathy and telepathy too.

But honestly, some of the stuff here. It’s delightful to see Tegmark actually write down for once the wave vector for an observer, since I’ve always wondered what that looked like. This particular observer makes a measurement on the spin state of a silver atom, and is happy with an up result but unhappy with a down result. In the former case, her state looks like this: |☺>. The latter case? Oh, you got there before me: |☹>. These two states are then combined as tensor products with the corresponding spin states. These equations are identified by numbers, rather as you do when you’re doing science.

Well, but what then of the objection that the very notion of probability is problematic when one is dealing with the MWI, given that everything that can happen does happen with certainty? This issue has been much debated, and certainly it is subtle. Subtler, I think, than the resolution Tegmark proposes. Let’s suppose, he says, that the observer is sleeping in bed when the spin measurement is made, and is placed in one or other of two identical rooms depending on the outcome. Yes, I can see you asking in what sense she is then an observer, and invoking Wigner’s friend and so on, but stay with me. You could at least imagine some apparatus designed to do this, right? So then she wakes up and wonders which room she is in. And she can then meaningfully calculate the probabilities – 50% for each. And, says Tegmark, these probabilities “could have been computed in advance of the experiment, used as gambling odds, etc., before the orthodox linguist would allow us to call them probabilities.”

Did you spot the flaw? She went to sleep – perhaps having realized that she’d have a 50% chance of waking up in either room – and then when she woke up she could find out which. But hang on – she? The “she” who went to sleep is not the “she” who woke up in one of the rooms. According to this view of the MWI, that first she is a superposition of the two shes who woke up. All that first she can say is that with 100% certainty, two future shes will occupy both rooms. At that point, the “probability” that “she” will wake up in room A or room B is a meaningless concept. “She”, or some other observer, could still place a bet on it, though, right, knowing that there will be one outcome or the other? Not really – rational betters would know that it makes no difference, if the MWI holds true. They’ll win and lose either way, with certainty. I wonder if Max, who I think truly does believe the MWI, would place a bet?

The point, I think, is that a linguist would be less bothered by the definition of “probability” here than by the definition of the observer. Posing the issue this way involves the usual refusal to admit that we lack any coherent way to relate the experiences of an individual before a quantum event (on which their life history is contingent) to the whole notion of that “same” individual afterwards. Still, we have the maths: |☺> + |☹> (pardon me for not normalizing) becomes |☺> and |☹> afterwards. And in Tegmark’s universe, it’s the maths that counts.

Oh, and I didn’t even ask what happens when the probability of the spin measurements is not 50:50 but 70:30. Another day, perhaps.