Does art compute?

A decade ago, a number of physicists and astronomers, an occasional mathematician, and even an interloping engineer or two (shhh…) here at the University of Nottingham started to collaborate with the powerhouse of pop sci (/pop math/pop comp/pop phil…) videography that is Brady Haran. I was among the “early adopters” (after the UoN chemists had kicked everything off with PeriodicVideos) and contributed to the very first Sixty Symbols video, uploaded back in March 2009. This opened with the fresh-faced and ever-engaging Mike Merrifield: Speed of Light.

Since then, I have thoroughly enjoyed working with Brady and colleagues on 60 or so Sixty Symbols videos. (Watching my hairline proceed backwards and upwards at an exponentially increasing rate from video to video has been a somewhat less edifying experience.) More recently, I’ve dipped my toes into Computerphile territory, collaborating with the prolific Sean Riley — whom I first met here, and then subsequently spent a week with in Ethiopia — on a number of videos exploring the links between physics and computing.

It’s this ability to reach out to audiences other than physicists and self-confessed science geeks that keeps me coming back to YouTube, despite its many deficiencies and problems (such as those described here, here, and here. And here, here, and here [1].) Nonetheless, during discussions with my colleagues about the ups and downs of online engagement, I’m always tediously keen to highlight that the medium of YouTube allows us to get beyond preaching to the converted.

Traditional public engagement and outreach events are usually targeted at, and attract, audiences who already have an interest in, or indeed passion for, science (and, more broadly, STEM subjects in general [2].) But with YT,  and despite the best efforts of its hyperactive recommendation algorithms to corral viewers into homogeneous groupings (or direct them towards more and more extreme content), it’s possible to connect with audiences that may well feel that science or math(s) is never going to be for them, i.e. audiences that might never consider attending a traditional science public engagement event. The comment below, kindly left below a Numberphile video that crossed the music-maths divide, is exactly what I’m talking about…


There’s still a strong tendency for a certain type of viewer, however, to want their content neatly subdivided and packaged in boxes labelled “Physics”, “Chemistry”, “Biology”, “Philosophy”, “Computing”, “Arts and Humanities Stuff I’d Rather Avoid” etc… Over the years, there have been comments (at various levels of tetchiness) left under Sixty Symbols, Periodic Videos, Computerphile etc… uploads telling us that the video should be on a different channel or that the content doesn’t fit. I hesitate to use the lazy echo chamber cliché, but the reluctance to countenance concepts that don’t fit with a blinkered view of a subject is not just frustrating, it narrows the possibilities for truly innovative thinking that redefines — or, at best, removes — those interdisciplinary boundaries.

Some physicists have a reputation for being just a little “sniffy” about other fields of study. This was best captured, as is so often the case, by Randall Munroe:

But this is a problem beyond intellectual arrogance; a little learning is a dangerous thing. As neatly lampooned in that xkcd cartoon, it’s not just physicists who fail to appreciate the bigger picture (although there does seem to be a greater propensity for that attitude in my discipline.) A lack of appreciation for the complexity of fields that are not our own can often lead to an entirely unwarranted hubris that, in turn, tends to foster exceptionally simplistic and flawed thinking. And before you know it, you’re claiming that lobsters hold the secret to life, the universe, and everything…

That’s why it’s not just fun to cut across interdisciplinary divides; it’s essential. It broadens our horizons and opens up new ways of thinking. This is particularly the case when it comes to the arts-science divide, which is why I was keen to work with Sean on this very recent Computerphile video:

The video stems from the Creative Reactions collaboration described in a previous post, but extends the physics-art interface discussed there to encompass computing. [Update 08/06/2019 — It’s been fun reading the comments under that video and noting how many back up exactly the points made above about the unwillingness of some to broaden their horizons.] As the title of this post asks, can art compute? Can a painting or a pattern process information? Can artwork solve a computational problem?

Amazingly, yes.

This type of approach to information processing is generally known as unconventional computing, but arguably a better, although contentious, term is lateral computing (echoing lateral thinking.) The aim is not to “beat” traditional silicon-based devices in terms of processing speed, complexity, or density of bits. Instead, we think about computing in a radically different way — as the “output” of physical and chemical and/or biological processes, rather than as an algorithmic, deterministic, rule-based approach to solving a computational problem. Lateral computing often means extracting the most benefit from analogies rather than algorithms.

Around about the time I started working with Brady on Sixty Symbols, our group was actively collaborating with Natalio Krasnogor and his team — who were then in the School of Computer Science here at Nottingham — on computational methods to classify and characterise scanning probe images. Back then we were using genetic algorithms (see here and here, for example); more recently, deep learning methods have been shown to do a phenomenally good job of interpreting scanning probe images, as discussed in this Computerphile video and this arXiv paper. Nat and I had a common interest, in common with quite a few other physicists and computer scientists out there, in exploring the extent to which self-assembly and self-organisation in nature could be exploited for computing. (Nat moved to Newcastle University not too long afterwards. I miss our long chats over coffee about, for one, just how we might implement Conway’s Game Of Life on a molecule-by-molecule basis…)

It is with considerable guilt and embarrassment that I’ve got to admit that on my shelves I’ve still got one of Nat’s books that he kindly lent to me all of those years ago. (I’m so sorry, Nat. As soon as I finish writing this, I’m going to post the book to you.)

This book, Reaction-Diffusion Computers by Andy Adamatzky, Ben De Lacy Costello, and Tetsuya Asai, is a fascinating and comprehensive discussion of how chemical reactions — in particular, the truly remarkable BZ reaction — can be exploited in computing. I hope that we’ll be able to return to the BZ theme in future Computerphile videos. But it was Chapter 2 of Adamatzky’s book, namely “Geometrical Computation: Voronoi Diagram and Skeleton” — alongside Philip Ball’s timeless classic, The Self-Made Tapestry (which has been essential reading for many researchers in our group over the years, including yours truly) — that directly inspired the Computerphile video embedded above.

The Voronoi diagram (also called the Voronoi tesselation) is a problem in computational geometry that crops up time and again in so very many different disciplines and applications, spanning  areas as diverse as astronomy, cancer treatment, urban planning (including deciding the locations of schools, post offices, and hospital services), and, as discussed in that video above, nanoscience.

We’ve calculated Voronoi tesselations extensively over the years to classify the patterns formed by drying droplets of nanoparticle solutions. (My colleagues Ellie Frampton and Alex Saywell have more recently been classifying and quantifying molecular self-assembly using the Voronoi approach.) But Voronoi tesselations are also regularly used by astronomers to characterise the distribution of galaxies on length scales that are roughly ~ 1,000,000,000,000,000,000,000,000,000,000 (i.e. about 1030) times larger than those explored in nanoscience. I love that the same analysis technique is exploited to analyse our universe on such vastly different scales (and gained a lot from conversations with the astronomer Peter Coles on this topic when he was a colleague here at Nottingham. )

As Cory Simon explains so well in his “Voronoi cookies and the post office problem” post, the Voronoi algorithm is an easy-to-understand method in computational geometry, especially in two dimensions: take a point, join it up to its nearest neighbours, and get the perpendicular bisectors of those lines. The intersections of the bisectors define a Voronoi cell. If the points form an ordered mesh on the plane — as, for example, in the context of the atoms on a crystal plane in solid state physics — then the Voronoi cell is called a Wigner-Seitz unit cell. (As an undergrad, I didn’t realise that the Wigner-Seitz unit cells I studied in my solid state lectures were part of the much broader Voronoi class — another example of limiting thinking due to disciplinary boundaries.)

For less ordered distributions of points, the tesselation becomes a set of polygons…


We can write an algorithm that computes the Voronoi tesselation for those points, or we can stand back and let nature do the job for us. Here’s a Voronoi tesselation based on the distribution of points above which has been “computed” by simply letting the physics and chemistry run their course…


That’s an atomic force microscope image of the Voronoi tesselation produced by gold nanoparticles aggregating during the drying of the solvent in which they’re suspended. Holes appear in the solvent-nanoparticle film via any (or all) of a number of mechanisms including random nucleation (a little like how bubbles form in boiling water), phase separation (of the solid nanoparticles from the liquid solvent, loosely speaking), or instabilities due to heat flow in the solvent. Whatever way those holes appear, the nanoparticles much prefer to stay wet and so are carried on the “tide” of the solvent as it dewets from the surface…


(The figure above is taken from a review article written by Andrew Stannard, now at King’s College London. Before his move to London, Andy was a PhD researcher and then research fellow in the Nottingham Nanoscience Group. His PhD thesis focused on the wonderfully rich array of patterns that form as a result of self-assembly in nanostructured and molecular systems. Fittingly, given the scale-independent nature of some of these patterns, Andy’s research career started in astronomy (with the aforementioned Peter Coles.))

As those holes expand, particles aggregate at their edges and ultimately collide, producing a Voronoi tesselation when the solvent has entirely evaporated. What’s particularly neat is that there are many ways for the solvent to dewet, including a fascinating effect called the Benard-Marangoni instability. The physics underpinning this instability has many parallels with the Rayleigh-Taylor instability that helped produce Lynda Jackson’s wonderful painting.

But how do we program our physical computer? [3] To input the positions of the points for which we want compute the tesselation, we need to pattern the substrate so that we can control where (and when) the dewetting process initiates. And, fortunately, with (suitably treated) silicon surfaces, it’s possible to locally oxidise a nanoscale region using an atomic force microscope and draw effectively arbitrary patterns. Matt Blunt, now a lecturer at University College London, got this patterning process down to a very fine art while he was a PhD researcher in the group over a decade ago. The illustration below, taken from Matt’s thesis, explains the patterning process:


Corporate Identity Guidelines™ of course dictate that, when any new lithographic or patterning technique becomes available, the very first pattern drawn is the university logo (as shown on the left below; the linewidth is approximately 100 nm.) The image on the right shows how a 4 micron x 4 micron square of AFM-patterned oxide affects the dewetting of the solvent and dramatically changes the pattern formed by the nanoparticles; for one thing, the characteristic length scale of the pattern on the square is much greater than that in the surrounding region. By patterning the surface in a slightly more precise manner we could, in principle, choose the sites where the solvent dewets and exploit that dewetting to calculate the Voronoi tesselation for effectively an arbitrary set of points in a 2D plane.


There’s a very important class of unconventional computing known as wetware. (Indeed, a massively parallel wetware system is running inside your head as you read these words.) The lateral computing strategy outlined above might perhaps be best described as dewetware.

I very much hope that Sean and I can explore other forms of lateral/unconventional computing in future Computerphile videos. There are a number of influential physicists who have suggested that the fundamental quantity in the universe is not matter, nor energy — it’s information. Patterns, be they compressed and encrypted binary representations of scientific data or striking and affecting pieces of art, embed information on a wide variety of different levels.

And if there’s one thing that connects artists and scientists, it’s our love of patterns…

[1] And that’s just for starters. YouTube has been dragged, kicking and screaming every inch of the way, into a belated and grudging acceptance that it’s been hosting and fostering some truly odious and vile ‘content’.

[2] On a tangential point, it frustrates me immensely that public engagement is now no longer enough by itself. When it comes to securing funding for engaging with the public (who fund our research), we’re increasingly made feel that it’s more important to collect and analyse questionnaire responses than to actually connect with the audience in the first place.

[3] I’ll come clean — the nanoparticle Voronoi tesselation “calculation” shown above is just a tad artificial in that the points were selected “after the event”. The tesselation wasn’t directed/programmed in this case; the holes that opened up in the solvent-nanoparticle film due to dewetting weren’t pre-selected. However, the concept remains valid — the dewetting centres can in principle be “dialled in” by patterning the surface.

“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:

[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



A Patter of Podcasts*

* Following extensive research — the best part of three whole minutes on Google — there shockingly appears not to be a collective noun for podcasts. Henceforth, I’m using “patter”. Given at least one OED definition of the word, I think it fits.

I’ve been very fortunate — if I were a religious man, I’d say “blessed” — to have had the support of not only the fantastic marketing team at Ben Bella (including, in particular, Lindsay Marshall) but a number of colleagues and friends when it comes to “plugging” that book I’ve recently written.

I don’t want to turn Symptoms… into a series of adverts for ‘Uncertainty to 11′ — and I won’t. Promise. I’ve got a stack of non-book-related posts coming up if I can ever find time — but I’ve done a series of podcasts and interviews recently that I’ve enjoyed so much I wanted to say a public thank you to all those involved (including Lindsay for setting up and coordinating the majority.) I’ve already blogged about The Aussie Pink Floyd pinkcast and The Death Hangout, and there are a few other podcasts to be uploaded/broadcast in future that I’ll blog about (briefly) in due course, but for now…

The Unmade Podcast

Unmade…” is the brainchild of Brady Haran, with whom I’ve worked just a little over the last decade or so, and Tim Hein. The premise is that they chat about ideas for podcasts that might get made, but probably never will. Occasionally, they invite a guest or two on to join in the conversation and come up with their own ideas for podcast themes. Not only did Brady and Tim let me do that — although, as I noted in the podcast, I can’t claim credit for all of the suggestions I made — but they very kindly let me waffle on at length about that bloody book…


Although the Ikonokast podcast with Greg Laden and his co-host Mike Haubrich started off on that Spinal Tap-inspired theme, we diverged from there quite quickly and chatted about a much broader variety of academic (and non-academic) concerns than just the metal-quantum interface…

Coincidentally, that piece of metal that opens up the Ikonokast conversation (and closes the Unmade podcast) is something called The Root Of All Things that I recorded a while ago as background music for a video. I’m hoping to find time to expand this short piece, with the help of a few musician (and scientist-cum-musician) friends, to a full-blown nano-themed sci-fi metal track over the course of the next year or so. (After all, there’s EPSRC funding to do so.) For now, however, that piece has found its place as backing music for some of Pete McPartlan’s wonderfully quirky animations and art…

The Quantum Podcast

height_90_width_90_15817639_1066803776798865_1271 The Uncertainty Principle and Metal

Maria, the host, is a second year undergraduate physics student who explains a variety of topics covered in her degree via her podcast. We had a fun time discussing everything from Devin Townsend to string theory and the state-of-the-art in theoretical physics. The latter is a theme I’m going to return to very soon here at Symptoms… (and elsewhere) in the context of Sabine Hossenfelder‘s impassioned, sharp, and brilliant critique of the state of 21st century physics, “Lost In Math“. If you have any interest at all in physics, you owe it to yourself to go get Hossenfelder’s book.


I spent most of this podcast trying to stop laughing. Byrne and Wade, your genial hosts, are both very funny guys. Unfortunately, when tasked, I failed spectacularly to come up with a musician joke on the spot. Usually I fall back on one of the drummer classics — “How can you tell a drummer’s at the door? The knocking speeds up” — but it was clearly too early in the morning and/or insufficient caffeine had been imbibed.

A big thank-you to Brady, Tim, Greg, Mike, Maria, Byrne, and Wade for the invitation to join them for a natter.

Metallizing and Melodifying Phi

Apologies for the radio silence on the blog of late. I’ll be posting more regularly in the coming days/weeks. For now, this one is a bit of a blast from the past. Over six years ago (gulp), Brady Haran and I collaborated with the talented and prolific Dave Brown (boyinaband) on a suitably metallized rendition of a fundamental constant — the golden ratio, otherwise known as φ

MoriartyAs I’ve said during various talks about the metal-maths-physics interface (including this) over the years since that video was uploaded , some people buy a Porsche for their mid-life crisis. Mine involved attempting to reconnect with my — substantially less follicularly challenged, see image to right for pictorial evidence — halcyon heavy metal days…

At the time of uploading the video, I wrote the first blog post below. It’s been loitering at Brady’s, now discontinued, original blog for quite some time. I’m reblogging it here, along with another post from many moons ago on a more sedate rendering of φ (and its cousin τ).

Metallizing Phi

13 July 2012

Here are all the gory details for the musicians amongst you…

Guitar tuning: Bb F Bb Eb G C

(This is traditional “drop D” tuning, i.e. D A E D G B E, dropped two tones in order to approximate the math metal/Djent sound without a seven string guitar.).

We stick almost exclusively to riffs derived from the Bb harmonic minor scale (although the chorus is based around the natural Bb minor scale)

I used Guitar Rig to record the riffs (both clean and effected) which I then sent to Dave who used his studio wizardry and musical acumen to arrange and structure the song. This involved quite a number of e-mail exchanges to hone the structure of the song during which Dave had to rein in my old school metal tendencies on more than one occasion…


0:00. We kick off with a clean picked piece which looks like this:


The digits of phi are “embedded” in the notes played on the 4th string. I make use of octaves and finger picking to embellish the riff.

0:08 Dave comes in with sixteenth note “chugs” (on Bb) which are timed to match the digits of phi (as explained in the video).

00:16 All hell breaks loose. Same idea as for ‘chug’ pattern starting at 0:08, except this time  matched by kick drums. (All drum programming by Dave – visit his website for tutorials on how he lays down those impressive drum tracks).

00:40 The riff for verse 1 is basically power chords given by the digits 161803398, as follows (where ^ represents a higher octave):

1 – Bb

6 – Gb

1 – Bb

8 – ^Bb

0 – ^Db

3 – Db

3 – Db

9 – ^C

8 – ^Bb

8 – ^Bb

00:55 The chorus is a similar idea but this time in Bb minor (not harmonic minor).

1 – Bb

6 – Gb

1 – Bb

8 – ^Bb

0 – [rest]

3 – Db

3 – Db

9 – ^C

8 – ^Bb

8 – ^Bb

7 – Ab

1:11 Here we switch to ‘encoding’ the [1 + sqrt (5)]/2 representation of phi in the riff. It’s a much more old school metal riff  and involves lots of use of the open sixth string (first note of the Bb harmonic minor scale) to incorporate ‘1’.

The digits of sqrt (5) are then encoded as shown in the tablature below.

I wanted to get a somewhat Mastodon-esque feel here so used lots of octaves (and slides into octaves).

I tried to down-pick as much as possible to ‘drive’ the riff . The ½ of (1+sqrt(5))/2 is built in as half-time on the drums.


1:27. I very much wanted to have a heavily Tool-influenced riff in the song. Tool are math metal  pioneers and, as many of those who have watched the “Golden Ratio – Making a Math Metal Anthem” video have pointed out, their song Lateralus has lyrics which are based around the Fibonacci sequence. So, the following is my ‘homage’ to Tool…


The digits of phi are encoded in the notes on the sixth and fifth strings and I ‘pedal’ around Bb notes on the third, fourth, and fifth strings.

2:15 As explained by Dave in the video, his riff here is also derived from (1 + root 5 )/ 2.

Sqrt (5) is embedded in the number of chugs again and the drums are half time. The “1” is a sustained and ringing Bb note.



Real but uncountable


At the root of the problem

Patterns will!

Emerge from the equation

Golden Angle!

Sprials out of control


Chorus: The proportion is divine, you’ll find your way

To Phi (to Phi) (to Phi)

The ratio defined, you can’t deny

It’s Phi


The five-fold way

Forbidden symmetry

Crossing points define

Demonic  geometry

[Verse 1 is fairly self-explanatory.Verse 2  above is a little more obscure. It refers to the pentagram which, of course, is a key piece of metal ‘iconography’. The verse refers to five-fold symmetry which is directly linked to phi.].

Phi = root(1 + Phi = root(1 +Phi = root(1 +Phi = root(1 +…

[This stems from the equation φ = sqrt (1 + φ) which, of course, is recursive – hence the looping lyric). 




The Tau of Phi

To accompany Numberphile’s Tau of Phi video…

The music is here:

For some unfathomable reason, not everyone is a fan of heavy metal so I thought it might be helpful to compose a piece of ‘mathemusic’ which didn’t involve growling, screaming, and/or distorted, detuned guitars. If nothing else, I thought it might win Brady back a few  of those subscribers who unsubscribed from Numberphile in protest when our Golden Ratio Song was uploaded.

There are, of course, a number of great pieces of music out there whose composers have used fundamental mathematical constants as their basis (long before we decided to ‘metallize’ phi in the way we did). ViHart’s “A Song About A Circle Constant” and Michael Blake’s “What tau sounds like” are great examples and highly recommended. And both Tool (with ‘Lateralus’) and After The Burial (with “Pi”) have written songs directly inspired by constants in Nature. (More on Tool below).

But what do we get if we mix melodies and riffs based around a number of different constants? This was one of the motivations for the “Tau of Phi(bonacci)” piece. I was intrigued as to how a piece inspired by the digits of both tau and phi would sound.

Here’s how the piece of music works. (I used Audacity for all of the recording, effects, and mixing).

0:00 – 0:17. Opens with a gently looping piano melody derived from the first eight digits of tau mapped onto a Bb harmonic minor scale. (The same scale as we used for the math metal song). The sound in the background is a combination of strings and a crescendo involving Bb octaves which I then time-reversed. The strings throughout the piece are based on the digits of tau.

0:18 – 0:43. The tau riff continues to play. The chords underlying this are an interpretation on piano of the opening of the math metal Golden Ratio song. I take some ‘liberties’ here, however, and first play the sequence: “1…6…1” three times in a row, (starting at 0:18, 0:27, and at 0:36). That is, I repeat the first three digits of phi three times. This adds to the overall ‘atmosphere’ of the piece. (What’s important, I feel, is to use the constants to inspire the composition, rather than to slavishly reproduce the sequence of digits. Music and maths (and physics!) are all about creativity.)

0:45 – 0:51. Chords represent the “8” and “0” of phi.

0:52 – 1:00. …and then the “3..3..9..8” of phi.

1:02 seconds (and ~ 0.8 of a second!) – “Reprise” of opening tau riff on guitar and piano..

1:09 Tool’s “Lateralus” riff (downtuned to Bb and played on electric piano, rather than guitar). There were very many comments about “Lateralus”, and its relationship to the Fibonacci series, under the video for our golden ratio song. I felt it only right to ‘allude’ to Lateralus here. Timing of riff not coincidental (for Tool aficionados…).

1:20 ViHart, in her wonderfully crystal-clear vocal tones, sings 6..2..8..3..1..8..5..3. [Lots of delay and reverb courtesy of Audacity’s standard effects base].

I sampled the numbers from Vi’s “Oh No,  Pi Politics Again” video.

…except for the “6”. Unfortunately, she didn’t sing the digit “6” in that video so I add to resort to sampling her rendition of “6” from her tau song. But in her tau song, she’s singing along with a guitar. This meant quite a bit of manipulation of the frequencies of the sample to attempt to isolate the vocal.

[Warning – ‘tech-y’ musical bit:

ViHart sings the notes in her songs/melodies in the key of C major. But the music in the “Tau of Phi(bonacci)” is based around Bb minor. My first thought was to transpose ViHart’s vocals down two tones (i.e. from C to Bb major). But she ended up sounding not too unlike Barry White.

Not good.

So I instead transposed her vocals up a semitone to C#. C# major is the tonic major key of Bb minor so shifting Vi’s vocals up a semitone (a) doesn’t modify her overall vocal tone too much, and (b) works harmonically (in principle!).]

1:28 – 1:37. Piece fades out with tau riff gently looping on guitar.


A few years later I collaborated with another exceptionally talented musician (and physics teacher), Alan Stewart, on this piece of maths-influenced instrumental prog rock. (I learnt so very much from Alan about how melody and harmony work.)

Alan’s original version without my everything-one-louder-than-everything-else guitar on top (and with a full explanation of the links to the maths) is here:


Brady Haran, Doctor of Letters

A short blog post to say just how delighted I am that Brady Haran was awarded an honorary degree by the University of Nottingham earlier this week. It’s been my great pleasure to work with Brady on Sixty Symbols (and a number of his other channels) over the past seven years. Despite — no, make that because ofour occasional tête-à-tête on just how to put across a piece of physics for a broad audience, I always look forward immensely to Brady (+ camera + bag of accessories) appearing at my door.

Brady’s work, and his remarkable work ethic, have put Nottingham on the map — and then some — when it comes to public engagement and communicating science. As Mike Merrifield describes in the video below, Brady’s ever-expanding portfolio of videos has topped 400 million views./ That’s nearly 2 billion minutes’ worth of viewing worldwide. All of us at the University of Nottingham owe Brady a huge debt of gratitude and it’s wonderful that this has been formally recognised by the award of Doctor of Letters.

Brady is his usual modest self in his acceptance speech (starting at around the 6 minute mark below), but it’s no exaggeration to say that he has fundamentally and radically changed my approach to explaining science and, by extension, my teaching.

I have learnt so much from him over the years.

Thank you, Brady, and congratulations.