“The drum beats out of time…”

Far back in the mists of time, in those halcyon days when the Brexit referendum was still but a comfortably distant blot on the horizon and Trump’s lie tally was a measly sub-five-figures, I had the immense fun of working with Brady Haran and Sean Riley on this…

As that video describes, we tried an experiment in crowd-sourcing data via YouTube for an analysis of the extent to which fluctuations in timing might be a signature characteristic of a particular drummer (or drumming style). Those Sixty Symbols viewers who very kindly sent us samples of their drumming — all 78 of you [1] — have been waiting a very, very long time for this update. My sincere thanks for contributing and my profuse apologies for the exceptionally long delay in letting you know just what happened to the data you sent us. The good news is that a paper, Rushing or Dragging? An Analysis of the “Universality” of Correlated Fluctuations in Hi-hat Timing and Dynamics (which was uploaded to the arXiv last week), has resulted from the drumming fluctuations project. The abstract reads as follows.

A previous analysis of fluctuations in a virtuoso (Jeff Porcaro) drum performance [Räsänen et al., PLoS ONE 10(6): e0127902 (2015)] demonstrated that the rhythmic signal comprised both long range correlations and short range anti-correlations, with a characteristic timescale distinguishing the two regimes. We have extended Räsänen et al.’s approach to a much larger number of drum samples (N=132, provided by a total of 58 participants) and to a different performance (viz., Rush’s Tom Sawyer). A key focus of our study was to test whether the fluctuation dynamics discovered by Räsänen et al. are “universal” in the following sense: is the crossover from short-range to long-range correlated fluctuations a general phenomenon or is it restricted to particular drum patterns and/or specific drummers? We find no compelling evidence to suggest that the short-range to long-range correlation crossover that is characteristic of Porcaro’s performance is a common feature of temporal fluctuations in drum patterns. Moreover, level of experience and/or playing technique surprisingly do not play a role in influencing a short-range to long-range correlation cross-over. Our study also highlights that a great deal of caution needs to be taken when using the detrended fluctuation analysis technique, particularly with regard to anti-correlated signals.

There’s also some bad news. We’ll get to that. First, a few words on the background to the project.

Inspired by a fascinating paper published by Esa Rasanen (of Tampere University) and colleagues back in 2015, a few months before the Sixty Symbols video was uploaded, we were keen to determine whether the correlations observed by Esa et al. in the fluctuations in an iconic drummer’s performance — the late, great Jeff Porcaro — were a common feature of drumming.

Why do we care — and why should you care — about fluctuations in drumming? Surely we physicists should be doing something much more important with our time, like, um, curing cancer…

OK, maybe not.

More seriously, there are very many good reasons why we should study fluctuations (aka noise) in quite some detail. Often, noise is the bane of an experimental physicist’s life. We spend inordinate amounts of time chasing down and attempting to eliminate sources of noise, be they at a specific frequency (e.g. mains “hum” at 50 Hz or 60 Hz [2]) or, sometimes more frustratingly, when the signal contamination is spread across the frequency spectrum, forming what’s known as white noise. (Noise can be of many colours other than white — just as with a spectrum of light it all depends on which frequencies are present.)

But noise is most definitely not always just a nuisance to be avoided/eliminated at all costs; there can be a wealth of information embedded in the apparent messiness. Pink noise, for example, crops up in many weird and wonderful — and, indeed, many not-so-weird-and-not-so-wonderful — places, from climate change, to fluctuations in our heartbeats, to variations in the stock exchange, to current flow in electronic devices, and, indeed, to mutations occurring during the expansion of a cancerous tumour.  An analysis of the character and colour of noise can provide compelling insights into the physics and maths underpinning the behaviour of everything from molecular self-assembly to the influence and impact of social media.

The Porcaro performance that Esa and colleagues analysed for their paper is the impressive single-handed 16th note groove that drives Michael McDonald’s “I Keep Forgettin’…” I wanted to analyse a similar single-handed 16th note pattern, but in a rock rather than pop context, to ascertain whether Procaro’s pattern of fluctuations in interbeat timing were characteristic only of his virtuoso style or if they were a general feature of drumming. I’m also, coincidentally, a massive Rush fan. An iconic and influential track from the Canadian trio with the right type of drum pattern immediately sprang to mind: Tom Sawyer.

So we asked Sixty Symbols viewers to send in audio samples of their drumming along to Tom Sawyer, which we subsequently attempted to evaluate using a technique called detrended fluctuation analysis. When I say “we”, I mean a number of undergraduate students here at the University of Nottingham (who were aided, but more generally abetted, by myself in the analysis.) I’ve set a 3rd year undergraduate project on fluctuations in drumming for the last three years; the first six authors on the arXiv paper were (or are) all undergraduate students.

Unfortunately, the sound quality (and/or the duration) of many of the samples submitted in response to the Sixty Symbols video was just not sufficient for the task. That’s not a criticism, in any way, of the drummers who submitted audio files; it’s entirely my fault for not being more specific in the video. We worked with what we could, but in the end, the lead authors on the arXiv paper, Oli(ver) Gordon and Dom(inic) Coy, adopted a different and much more productive strategy for their version of the project: they invited a number of drummers (twenty-two in total) to play along with Tom Sawyer using only a hi-hat (so as to ensure that each and every beat could be isolated and tracked) and under exactly the same recording conditions.

You can read all of the details of the data acquisition and analysis in the arXiv paper. It also features the lengthiest acknowledgements section I’ve ever had to write. I think I’ve thanked everyone who provided data in there but if you sent me an MP3 or a .wav file (or some other audio format) and you don’t see your name in there, please let me know by leaving a comment below this post. (Assuming, of course, that you’d like to be acknowledged!)

We submitted the paper to the J. New Music Research last year and received some very helpful referees’ comments. I am waiting to get permission from the editor of the journal to make those (anonymous) comments public. If that permission is given, I’ll post the referees’ reports here.

In hindsight, Tom Sawyer was not the best choice of track to analyse. It’s a difficult groove to get right and even Neil Peart himself has said that it’s the song he finds most challenging to play live. In our analysis, we found very little evidence of the type of characteristic “crossover” in the correlations of the drumming fluctuations that emerged from Esa and colleagues’ study of Porcaro’s drumming. Our results are also at odds with the more recent work by Mathias Sogorski, Theo Geisel, Viola Priesemann (of the Max Planck Institute for Dynamics and Self-Organization, and the Bernstein Center for Computational Neuroscience, Göttingen, Germany) — a comprehensive and systematic analysis of microtiming variations in jazz and rock recordings spanning a total of over 100 recordings.

The likelihood is that the conditions under which we recorded the tracks — in particular, the rather “unnatural” hi-hat-only performance — may well have washed out the type of correlations observed by others. Nonetheless, this arguably negative result is a useful insight into the extent to which correlated fluctuations are robust (or not) with respect to performance environment and style. It was clear from our results, in line with previous work by Holger Hennig, Theo Geisel and colleagues, that the fluctuations are not so much characteristic of an individual drummer but of a performance; the same drummer could produce different fluctuation distributions and spectra under different performing conditions.

So where do we go from here? What’s the next stage of this research? I’m delighted to say that the Sixty Symbols video was directly responsible for kicking off an exciting collaboration with Esa and colleagues at Tampere that involves a number of students and researchers here at Nottingham. In particular, two final year project students, Ellie Hill and Lucy Edwards, have just returned from a week-long visit to Esa’s group at Tampere University. Their project, which is jointly supervised by my colleague Matt Brookes, Esa, and myself, focuses on going that one step further in the analysis of drumming fluctuations to incorporate brain imaging. Using this wonderful device.

I’m also rather chuffed that another nascent collaboration has stemmed from the Sixty Symbols video (and the subsequent data analysis) — this time from the music side of the so-called “two cultures” divide. The obscenely talented David Domminney Fowler, of Australian Pink Floyd fame, has kindly provided exceptionally high quality mixing desk recordings of “Another Brick In The Wall (Part 2)” from concert performances. (Thanks, Dave. [3]) Given the sensitivity of drumming fluctuations to the precise performance environment, the analysis of the same drummer (in this case, Paul Bonney) over multiple performances could prove very informative. We’re also hoping that Bonney will be able to make it to the Sir Peter Mansfield Imaging Centre here in the not-too-distant future so that Matt and colleagues can image his brain as he drums. (Knock yourself out with drummer jokes at this point. Dave certainly has.) I’m also particularly keen to compare results from my instrument of choice at the moment, Aerodrums, with those from a traditional kit.

And finally, the Sixty Symbols video also prompted George Datseris, professional drummer and PhD student  researcher, also at the Max Planck Institute for Dynamics & Self-Organisation, to get in touch to let us know about his intriguing work with the Giesel group: Does it Swing? Microtiming Deviations and Swing Feeling in Jazz. Esa and George will both be visiting Nottingham later this year and I am very enthusiastic indeed about the prospects for a European network on drum/rhythm research.

What’s remarkable is that all of this collaborative effort stemmed from Sixty Symbols. Public engagement is very often thought of exclusively in terms of scientists doing the research and then presenting the work as a fait accompli. What I’ve always loved about working with Brady on Sixty Symbols, and with Sean on Computerphile, is that they want to make the communication of science a great deal more open and engaging than that; they want to involve viewers (who are often the taxpayers who fund the work) in the trials and tribulations of the day-to-day research process itself. Brady and I have our spats on occasion, but on this point I am in complete and absolute agreement with him. Here he is, hitting the back of the net in describing the benefits of a warts-and-all approach to science communication…

They don’t engage with one paper every year or two, and a press release. I think if people knew what went into that paper and that press release…and they see the ups and the downs… even when it’s boring… And they see the emotion of it, and the humanity of it…people will become more engaged and more interested…

With the drumming project, Sixty Symbols went one step further and brought the viewers in so they were part of the story — they drove the direction of the science. While YouTube has its many failings, Sixty Symbols and channels like it enable connections with the world outside the lab that were simply unimaginable when I started my PhD back in (gulp…) 1990. And in these days of narrow-minded, naive nationalism, we need all the international connections we can get. Marching to the beat of your own drum ain’t all it’s cracked up to be…

Source of cartoon: https://xkcd.com/1736/

[1] 78. “Seven eight”.

[2] 50 Hz or 60 Hz depending on which side of the pond you fall. Any experimental physicist or electrical/electronic engineer who might be reading will also know full well that mains noise is generally not only present at 50 (or 60) Hz — there are all those wonderful harmonics to consider. (And the strongest peak may well not even be at 50 (60) Hz, but at one of those harmonics. And not all harmonics will contribute equally.  Experimental physics is such a joy at times…)

[3] In the interests of full disclosure I should note that Dave is a friend, a fan of Sixty Symbols, Numberphile, etc.., and an occasional contributor to Computerphile. He and I have spent quite a few tea-fuelled hours setting the world to rights



Science Rhymes (and resonates)

So, on April 29th this is happening:

My colleague Gerardo Adesso, who leads the Quantum Correlations group here at Nottingham — who have a very clever logo indeed, it must be said — is a man of many talents and has been writing poems and limericks to accompany each Physical Review Letter he publishes. He’s decided to extend that poetry challenge to other scientists via the Science Rhymes event described in the tweet above.

Gerardo was kind enough to relax the rules ever so slightly for yours truly — I was given special dispensation to write a song rather than a poem for “Science Rhymes”. I’ve been banging the drum for the importance of bridging the STEM-arts & humanities gap at every available opportunity so leapt at the chance when Gerardo asked if I could contribute. The song I’ve written, (un)certain, is embedded below (via SoundCloud), followed by the lyrics. The theme is resonance, which is at the core of the dynamic force microscopy technique we use in our research (as described in this video; at about the 3:04 minute mark into (un)certain, I’ve sampled the sound of the force microscope signal.) There’s also a heavy dose of quantum mechanical allusion mixed (none so subtly) into the lyric — we work with single atoms and molecules (and, indeed, single chemical bonds) so are very definitely in the quantum regime.

“Resonance” is, of course, used in a much wider sense than just its technical physics (and engineering) context: “in tune with…“, “on the same wavelength…“, “in harmony…” all describe how we connect — how we resonate — on a very human level. (un)certain is about the certainty of that type of resonance. Think of it as a quantum love song…



a time and a place

in our reciprocal space

closer than close

yes, we resonate…

entangled webs we weave

our universe is calling

a matter of phase or faith?


…and as the waves come crashing down

we collapse into this state

uncertainty fades

we’ve finally found our way


worlds apart

and we lucked out


for Lori

15 minutes of…

Quite why it’s taken me so long to discover this Tim Minchin gem, I don’t know. It was released back in January. Aeons ago. But it’s not just Minchin’s signature clever lyrics — case in point,

Pick up your pitchfork and your torch. We’ll go hunt the monster down. But keep an eye out for uneven ground.  We’ll turn on you if you stumble.

— his quirky vocals, and his wonderful “earworm” melodies that have had me playing “15 Minutes” on an infinite loop. It’s also about the closest to new Jellyfish music we’re ever going to get ever since that transcendent band went to the great gig in the sky. (Well, OK, let’s not be over-dramatic. They just split up; the band members are still with us. It still felt like a bereavement to me, however, because “Belly Button” and “Spilt Milk” have been constant companions.)

And on a similar theme to that of “15 Minutes”, there’s also this criminally over-looked recent classic by Shattered Skies…

“To be seen, to be scene, to be seen…”

Photonic Rock

This is an invited post by Johnny Russell, who contacted me some time ago about an intriguing “photonic” guitar he’s been developing, as demonstrated in the video below. (Subscribe to Johnny’s channel if you want to find out more.) I’m always intrigued by new approaches to music technology so I’ve been keeping an eye on what Johnny’s been doing.

Over to you, Johnny…

Just imagine you had a choice, between hail or snow; for one hour everyday for the rest of your life, regardless of the actual climate, it would hail or it would snow. Which would you choose? Easy decision, right?

Hail is interesting, exciting and even scary when it does come, but snow… snow is beautiful and magical, each snowflake a unique and fragile mathematical pattern that suggests some deeper and profound meaning of the universe in which we exist.

But actually I’m going to talk about music, so why the snow or hail metaphor?

Well it seems in the last ten or so years popular music has become exactly the choice we wouldn’t make – constant hail, every single day. You see, just as water can take on the spatial structure of hail and snow, sound can take on the temporal structure of electronic dance music or Beethoven’s 5th Symphony. Just as the spatial structures of hail and snow have different formation processes, so too does the temporal structure of music, but with music the distinction is quite easily defined: was the temporal structure generated by a computer or created by a human.

And what is one thing missing from computer generated music? Groove.

Music is fundamentally one of the most important aspects of culture. And from the bird’s song to the very heartbeats that give our bodies their constant rhythm, all of it follows mathematical patterns that give rise to groove. These fractal patterns are called long-range correlations, the mathematical name that describes the respective spatial and temporal structures of both snowflakes and groove music.​ These groovy patterns have existed all throughout the history of evolution, as they are an intrinsic part of the universe in which we live. But, for the first time in human history, as the music industry aims for “perfection” and producers have taken the role of musicians, these patterns have largely been removed. The vast majority of music on the radio mathematically contains little groove, resulting in melodies that don’t remain with us as there is little human fluctuation, no groove that we can inherently and fundamentally relate to; hail.

A big part of this trend is that with music tech, there remains one last problem; the guitar, the number one rock star instrument cannot be made to produce MIDI in real time to create these fractal patterns. This problem has been around for decades, but for each attempted solution, something has to be sacrificed from a true guitar style to achieve this. The problem here is simply because string dynamics are complicated, there are many frequencies bouncing around at any instant. To know the frequencies you then have a problem which is analogous to the quantum mechanical Heisenberg uncertainty principle: the more accurately you know position, the less accurately you know momentum.

With string dynamics the trade-off is that to know the fundamental frequency node of the note on the vibrating string, you need time; the more time you have, the more precisely the frequency can be calculated. This is done by a mathematical process called a Fourier Transform. This is what current systems work with, which means that the MIDI note can’t be calculated and played without some latency. The other approach is to redesign the guitar completely, but these systems lose the subtlety and speed of the string dynamics themselves. The one consistent thing across all these systems is that they are completely electronic.

The Russell Photonic Guitar is the first REAL guitar to produce chords, note slides, hammer-ons and pull-offs with MIDI sound in line with the natural or electric sound coming out of the guitar, simultaneously, in the moment. Finally, a next generation instrument that can sync with the flow of human emotion. With this, not only will electronic and rock music have a new tool in which to explore the vast MIDI landscape, but also classical music will have piano that can also do all the unique guitar string tricks, and here also new musical landscapes will be opened up for musicians to explore, and everyone to enjoy.​

Lastly, and possibly most importantly; contrary to music dividing people due to the attachment of egos or identity to so many separate splintered genres, music still has an overwhelming power to bring different people together. It all has to do with groove. A remarkable scientific discovery on the power of groove is outlined in this paper, in which the authors studied beat fluctuations between two musicians, and, to quote, “…the next beat played by an individual is dependent on the entire history (up to several minutes) of their partner’s interbeat intervals.” Which means that two people can be locked into the same groovy fractal pattern.

Why is that so significant? Well, do you know how if you look at the stars, due to the finite speed of light, you are looking into the past? The same thing happens on a much smaller scale if you are interacting with a fellow human being; you’re interacting with a moment that has already gone. We are all islands of isolation separated by the finite speed of light, the speed of causality. So how can we bridge our islands of isolation? If we essentially all get on the same groove (sometimes referred to colloquially as a “groove train”) by way of fractal patterns, we are temporally locked, and isn’t that truly experiencing the same moment together? If that is the case, then that is truly Zen.

This is the power of groove, and why the Russell Photonic Guitar will be so significant for all of music.


Maths In Action

Just back from London where I had a fun — and ever-so-slightly daunting — time talking about the beauty of maths in music and physics for an audience of 700 GCSE students at the “Maths In Action” conference. The venue was stunning…


Just about visible at the front of the cavernous auditorium is the speaker before me, Hugh Hunt (Engineering, Cambridge), doing a remarkable job of entertaining and engaging the audience with his demonstration-packed talk on angular momentum, gyroscopic precession, and all things spin-y. Hugh’s talk was an impossible act to follow — he set the bar exceptionally high indeed. I did my usual spin on the quantum-metal interface but tilted it towards a discussion of the role of mathematics in physics. (I had to come clean right at the start and confess to the students that I am most definitely not a mathematician.)

The students were great throughout — they certainly were not shy to shout out answers to the questions I asked (and to sing musical notes back to me, occasionally even in tune). An extra big thank you to Korbyn — and my sincere apologies if I’ve got the spelling wrong — for coming up on stage to play the opening riff to Black Sabbath and help me introduce the concept of the diabolical flattened fifth.

And, of course, I have to say a huge thank you to David Matthews, coordinator of the event (and Maths Programme Manager for The Training Partnership, who run a very broad series of GCSE events of this type)  for both the invitation to speak and for such an impressively organised day. As someone who too often struggles to manage just two teenagers*, attempting to coordinate 700 would bring me out in a cold sweat…

* I’m joking, Niamh and Saoirse. You’re great.

“Science on Saturday” Goes to 11

This weekend I had the honour and privilege of being the first speaker for the 2019 Ronald E Hatcher Science on Saturday series of lectures held at, and organised by, Princeton’s PPL (Plasma Physics Laboratory).  I’ll let PPPL themselves explain what Science On Saturday is all about:

Science on Saturday is a series of lectures given by scientists, engineers, and other professionals involved in cutting-edge research. Held on Saturday mornings throughout winter, the lectures are geared toward high school students. The program draws more than 300 students, teachers, parents, and community members. Topics are selected from a variety of disciplines.

Named after the late Ronald E Hatcher, who ran and hosted the series for many years, Science on Saturday is a fun way to bring physics (and other lesser sciences) to the general public(s) and other scientists alike. I was bowled over by the enthusiasm and engagement of the audience, who braved a bracing Saturday morning to hear about the connections between Sabbath, Stryper, and Schrödinger.  (The free bagels and coffee before the talk were, I’m sure, not entirely incidental in attracting the audience. I certainly can vouch for the quality of the pre-lecture consumables.) The Q&A session at the end ran for over an hour, with many insightful questions from the audience, whose age range seemed to span ~ 9 to 90 years young!

A number of those who were in the audience e-mailed me after the talk to ask for a copy of the slides. I’ve uploaded them to SlideShare (sans videos, regrettably) to make them publicly available here:


Andrew Zwicker has been the energetic and entertaining host for Science on Saturday for, if I recall correctly, more years than he cares to remember. In parallel with his career in physics, Andrew has successfully forayed into politics, as outlined at his Wikipedia page. Before the lecture he told me about an exciting scheme to encourage more early career researchers into politics. I thoroughly understand the reticence of many scientists to get involved with the political sphere — my involvement with the Royal Society MP-Scientist pairing scheme a number of years ago was an eye-opener in terms of the mismatch that can exist between political and scientific mindsets — but we need to bite the bullet and dive in*, especially in an era when hard scientific evidence is so readily dismissed as “fake news”. (Apologies. Make that “FAKE NEWS” and add any number of exclamation marks to taste.)

On the day of my Science on Saturday lecture, a white supremacist march had been mooted to be held in Princeton (not the most likely of venues, it fortunately has to be said, for that type of hatemongering.) In the end, the basement dwellers never turned up — they claimed that it was a hoax. But the counter-protesters attended in their heart-warming hundreds…

I’d like to offer a very big thank you both to Andrew for the invitation to speak at “Science on Saturday” and to DeeDee Ortiz, the Program Manager for Science Education at PPPL, for organising the visit. A similarly massive thank you to Lori for all of her help and organisation, including providing the key musical “props” used during the lecture.

*Excuse the mixed metaphor. I love mixed metaphors. This, taken from Leon Lederman’s “The God Particle” as an example of writing by one of his PhD students, is my very favourite: “This field of physics is so virginal that no human eyeball has ever set foot in it.” (That quote tickles me so much that I use it as part of the introduction to the final year Politics, Perception, and Philosophy of Physics  module here at Nottingham.)