As I’ve done in the past, I thought I’d share a photograph of some of the books I’ve been using as “research material” – one of the most enjoyable things about writing for this series! Unlike the previous two books, the unifying theme of this one has more to do with style than subject-matter, so it may not be obvious from the photo. So you’ll have to wait until Springer formally announce the new book – hopefully some time in the first half of next year.
Just out – my second book in collaboration with Paul Jackson, following on from Weird Wessex a few years ago. Like its predecessor the new book is “a tourist guide to strange and unusual sights” – but this time they’re right in the centre of London.
There’s an Egyptian Goddess in Mayfair and Karl Marx in Soho, a tiny police station in Trafalgar Square and an 18-inch-wide alley in Covent Garden (careful you don’t get stuck!). Alongside the iconic landmarks that the regular guidebooks tell you about, central London has an impressive assortment of quirky and unusual sights, from art installations in the form of human body parts to hundred-year-old advertising signs and a forgotten tube station. This book gives you a guided tour of all these sights and more – without straying far from the places you were going to see anyway, like Big Ben and Buckingham Palace, the Tower of London and St Paul’s Cathedral, the museums of South Kensington and the entertainment hotspots of the West End.
Like Weird Wessex, Random Encounters on the London Tourist Trail is packed with full-colour photographs. With improved paper and print quality, the colours really stand out in this one too. You can get it from Amazon UK or any other Amazon store. There’s also a Kindle version (although that won’t give you colour pictures if you use an ordinary monochrome Kindle reader).
When Eric Morecambe mangled Grieg’s Piano Concerto on a TV special in 1971, he insisted he was “playing all the right notes, but not necessarily in the right order”. That’s a valid point, because there aren’t that many different notes on a piano and the only thing that distinguishes one tune from another is the order in which you play them.
To a mathematician or computer programmer the situation is crying out for quantitative analysis. The diagram above shows the “transition matrix” for one specific Beatles tune (using the MIDI standard where middle C is C5). It’s clear there’s a lot of order here. One thing that jumps out is that there’s only one “black” note, G#5, and it’s always followed by A5. In fact A5 is a very popular note, cropping up after no fewer than 8 different pitches. On the other hand, G#5 itself is very rare, only ever coming after D6, and then only 6% of the time.
As well as analysing the original tune, this allows us to write a new tune of our own using the same transition matrix. The result (as the aforementioned mathematicians and computer programmers will recognize) is a first-order Markov chain. Producing an algorithm of this type from scratch would be rather tedious (as indeed the initial analysis would be), but fortunately there’s some free software called OpenMusic which includes built-in Markov functions that make the process much simpler.
Of course, there’s more to a tune than the pitch of the notes – there’s the duration of a note too. But that can be analysed and reproduced by exactly the same method. I experimented with an algorithmic composition of my own, based on the Beatles song analysed above. As a first step, I used the OpenMusic Markov functions to generate a series of tune-fragments for both the “right hand” and “left hand” of the piano. Then, to give the composition some structure, I arranged the fragments in a rough approximation to classical sonata form.
I won’t say what the original song was, because I want to see if anyone can guess it. As a hint, I’ve inserted a brief quotation from the original at the mid-point of the piece. Here it is on YouTube:
My second contribution to Springer’s Science and Fiction series is out now – Rockets and Ray Guns: The Sci-Fi Science of the Cold War. It’s in a similar style to Pseudoscience and Science Fiction, and even includes some pseudoscience of its own (e.g. UFOs, ESP and mind control) as well as the more obvious topics such as nuclear weapons, guided missiles and space warfare.
The Cold War saw scientists in East and West racing to create amazing new technologies, the like of which the world had never seen. Yet not everyone was taken by surprise. From super-powerful atomic weapons to rockets and space travel, readers of science fiction had seen it all before.
Sometimes reality lived up to the SF vision, at other times it didn’t. The hydrogen bomb was as terrifyingly destructive as anything in fiction, while real-world lasers didn’t come close to the promise of the classic SF ray gun. Nevertheless, when the scientific Cold War culminated in the Strategic Defence Initiative of the 1980s, it was so science-fictional in its aspirations that the media dubbed it “Star Wars”.
This entertaining account, offering a plethora of little known facts and insights from previously classified military projects, shows how the real-world science of the Cold War followed in the footsteps of SF – and how the two together changed our perception of both science and scientists, and paved the way to the world we live in today.
The book has already received a couple of nice reviews:
- By Tom Reale (“a work that will delight science, history, and SF buffs alike”) on the AIPT website
- By Brian Clegg (“a solid contribution to the history of science fiction and its relation to the real world”) on his Popular Science blog
I mentioned musical set theory in a previous post, and now that I understand it better I’m getting very enthusiastic about it. It’s a really powerful technique for analysing and composing music. The mathematical connection may give the impression that it “dehumanizes” music by imposing mechanistic constraints and artificial rules – but the exact opposite is true. It’s traditional music theory that forces arbitrary rules and constraints on you – set theory liberates you from them. It’s a framework for organizing your own creativity – with no rules whatsoever.
I’ll explain how it works in a moment, but first a few words about my sources. The bible of the subject is Allen Forte’s The Structure of Atonal Music, which is divided into two roughly equal parts. The first is packed with useful stuff, although the second part was much too advanced for me. But Forte’s book is really about musical analysis, and what I was interested in was composition. On that front, I found a great little book by Stanley Funicelli called Basic Atonal Counterpoint (which is a CreateSpace book, but very professionally done). I also found a lot of practical tips on Frans Absil’s YouTube channel – he also produced the Pitch-Class Set Graphical Toolkit you can see on my iPad in the photograph above.
Musical set theory starts from a few basic observations:
- The notes of the chromatic scale can be represented by integer “pitch-classes”: C = 0, C# = 1, D = 2 etc. After B = 11 you get back to C = 0, so additions and subtractions have to be done with mod-12 arithmetic.
- Intervals between pitch-classes are much more important than absolute pitches. So C major [0, 4, 7] and E flat major [3, 7, 10] are just different transpositions of the same set (it’s called 3-11).
- Inverting an interval (i.e. subtracting it from 12) doesn’t change its basic nature. So interval 7 (perfect fifth) can be grouped with 5 (perfect fourth), interval 8 (minor sixth) with 4 (major third) etc. This leaves us with just six “interval classes”: 1, 2, 3, 4, 5, 6.
- The characteristic sound of a set is mainly determined by its interval vector. For example, the major chord 3-11 = [0, 4, 7] has an interval vector 001110 (one minor third, one major third, one perfect fifth and nothing else).
Traditional Western music depends heavily on set 7-35 [0, 2, 4, 5, 7, 9, 11] – the white notes on a piano, aka the major or minor scale (remember you can transpose these notes up by any integer between 1 and 11 to get all the other major and minor scales). Within that 7-element set, there are a number of strongly favoured subsets – most notably the aforementioned 3-11 (the major triad and its inversion, the minor triad).
The purpose of set theory should be obvious now. It gives you access to dozens of other sets, all with their own unique sound. You might think “but they’re going to sound terrible”, and in some cases they do. Set theory helps you to avoid the terrible-sounding ones! But there are some great-sounding sets that simply don’t exist in traditional music theory, such as 4z-29 = [0, 1, 3, 7], with an eyecatching interval vector of 111111.
To teach myself how the system works, I wrote a short “symphony” using the above ideas. It’s my first ever musical composition, and the result sounds a lot more interesting than if I’d struggled with all that traditional stuff about sharps and flats, majors and minors, dominants and subdominants etc. That wouldn’t have told me how to get close to the kind of spooky, spacey, quirky music I wanted to write.
Here is a link to the YouTube video:
These days I always seem to be working on a lot of things at once, so “next book” has multiple meanings. There’s the next one to be published, which I finished writing several months ago and is now making its way through the publisher’s production process. There’s the one I’ve been asked to write and given a title for, but I’ve barely started to think about it yet. And then there’s the one I’m actually writing at the moment. That’s the one I’m talking about here. There’s a clue to its subject matter in the research material pictured above!
I recently came across the idea of applying set theory to musical analysis (which apparently has been around for some time, although I’d never heard of it before). For most people, who have a stronger intuitive grasp of music than mathematics, this must seem a pointless exercise, but for anyone like me who’s the other way around it’s really very illuminating.
Take symmetry, for example. In most areas of the arts and sciences, symmetry is seen as a good thing – but in music, that’s not the case. All the most popular chords are asymmetric in terms of interval content. You can see that in the left-hand image above, which shows the three notes of the C major chord on the chromatic circle. They’re separated by intervals of 3, 4, and 5 semitones.
In contrast, an augmented C chord, shown on the right, is perfectly symmetric, with all three intervals equal to 4 semitones. The problem (as far as musicians are concerned) is that it’s not very firmly tied to C major. It could equally well be A flat or E major. In the same way, the four-note symmetric chord C – E♭ – F♯ – A can be interpreted in four different ways: as Cdim7, E♭dim7, F♯dim7 or Adim7.
There’s even a completely symmetric two-note interval, in the form of the tritone, consisting of two notes 6 semitones apart (or 3 whole tones, which is how it gets its name). That’s exactly half an octave, for example from C to F sharp. But it’s also the distance from F sharp to C, so you really don’t know which key you’re in. That’s why composers spent centuries trying to avoid it. They called it diabolus in musica, or “the devil in music”.
Being a symmetry-loving scientist rather than a musician, I decided to try writing something that consisted only of symmetric chords. It’s a sort of canon, in the key of everything.
Here’s a link to a YouTube video, with added graphics depicting the various chords on the chromatic circle. Hopefully you’ll enjoy the graphics even if you don’t like the music!
I’ve just belatedly produced a promotional video for my book The Telescopic Tourist’s Guide to the Moon, which came out last summer. Here it is:
The background “music” (actually just a sequence of spacey sounding chords) is my own composition!
When I wrote The Telescopic Tourist’s Guide to the Moon last year, I wanted to refer, amongst other things, to descriptions of real lunar features in works of science fiction. Surprisingly, I found that many of the most famous Moon stories don’t actually refer to specific locations. Even more surprisingly, one of the few novels that does contain realistic descriptions of lunar geography is one of the earliest – Jules Verne’s Around the Moon, dating from 1870.
The surprise comes because Around the Moon – and its predecessor, From the Earth to the Moon (1865) – are probably best known for the completely unrealistic mode of travel, i.e. by means of a projectile launched from a giant cannon. But when I reread the novels, I was struck by just how scientifically knowledgeable they were – by the standards of their time, at any rate. As well as the physical descriptions of the Moon, Verne gets other subtleties right, too – such as the way things move once they get outside the Earth’s atmosphere (something Hollywood barely understands to this day).
So I thought I’d write another little book describing all the science Verne got right – and of course the science he got wrong, too. Here’s the blurb:
The idea of using a large gun to send humans into space is as impossible today as it was a century and a half ago, when Jules Verne wrote From the Earth to the Moon and Around the Moon. Yet he went to great lengths to persuade readers it wasn’t impossible – not through arm-waving and made-up technobabble, but using real physics and astronomy. No one had done anything like that in fiction before – and even today it’s unusual to see so much “real science” discussed in a work of science fiction. But just how much did Verne get right, and what did he get wrong? This book takes a closer look at the science content of his two great Moon novels – from Newton’s laws of motion and the conservation of energy to CO2 scrubbing, retro-rockets and the lifeless grey landscape of the Moon.
I was going through some old audio cassettes I recorded from the radio when I was a student, and came across a really interesting little snippet. It’s the physicist Paul Dirac reminiscing about Einstein on a BBC programme, though I’m afraid I’ve no idea which one. The note I made at the time says “recorded in March 1979″ – when Dirac would have been 76 (he lived to 82).
Although the quote is very short, it’s really fascinating – and a Google search didn’t turn up any other references to it. So I made a little YouTube video of it, which hopefully the following link will take you to:
Here is my transcript of what Dirac has to say about Einstein:
He wasn’t merely trying to construct theories to agree with observation. So many people do that; Einstein worked quite differently. He tried to imagine “If I were God, would I have made the world like this?” – and according to the answer to that question, he would decide on whether he liked a particular theory or not.
And I can’t resist adding a couple of Amazon links for my own book about Einstein:
- The British version – Albert Einstein: Pocket Giants
- The US version – Albert Einstein: Scientist (History Makers)