The role of dissonance in art, not to mention science and mathematics

 I was given a book for a birthday present just after the turn of the century, titled A Terrible Beauty; The People and Ideas that Shaped the Modern Mind, by Peter Watson. A couple of things worth noting: it covers the history of the 20th Century, but not geo-politically as you might expect. Instead, he writes about the scientific discoveries alongside the arts and cultural innovations, and he talks about both with equal erudition, which is unusual.
 
The reason I mention this, is because I remember Watson talking about the human tendency to push something to its limits and then beyond. He gave examples in science, mathematics, art and music. A good example in mathematics is the adoption of √-1 (giving us ‘imaginary numbers’), which we are taught is impossible, then suddenly it isn’t. The thing is that it allows us to solve problems that were previously impossible in the same way that negative numbers give solutions to arithmetical subtractions that were previously unanswerable. There were no negative numbers in ancient Greece because their mathematics was driven by geometry, and the idea of a negative volume or area made no sense.
 
But in both cases: negative numbers and imaginary numbers; there is a cognitive dissonance that we have to overcome before we can gain familiarity and confidence in using them, or even understanding what they mean in the ‘real world’, which is the problem the ancient Greeks had. Most people reading this have no problem, conceptually, dealing with negative numbers, because, for a start, they’re an integral aspect of financial transactions – I suspect everyone reading this above a certain age has had experience with debt and loans.
 
On the other hand, I suspect a number of readers struggle with a conceptual appreciation of imaginary numbers. Some mathematicians will tell you that the term is a misnomer, and its origin would tend to back that up. Apparently, Rene Descartes coined the term, disparagingly, because, like the ancient Greek’s problem with negative numbers, he believed they had no relevance to the ‘real world’. And Descartes would have appreciated their usefulness in solving problems previously unsolvable, so I expect it would have been a real cognitive dissonance for him.
 
I’ve written an entire post on imaginary numbers, so I don’t want to go too far down that rabbit hole, but I think it’s a good example of what I’m trying to explicate. Imaginary numbers gave us something called complex algebra and opened up an entire new world of mathematics that is particularly useful in electrical engineering. But anyone who has studied physics in the last century is aware that, without imaginary numbers, an entire field of physics, quantum mechanics, would remain indescribable, let alone be comprehensible. The thing is that, even though most people have little or no understanding of QM, every electronic device you use depends on it. So, in their own way, imaginary numbers are just as important and essential to our lives as negative numbers are.
 
You might wonder how I deal with the cognitive dissonance that imaginary numbers induce. In QM, we have, at its most rudimentary level, something called Schrodinger’s equation, which he proposed in 1926 (“It’s not derived from anything we know,” to quote Richard Feynman) and Schrodinger quickly realised it relied on imaginary numbers – he couldn’t formulate it without them. But here’s the thing: Max Born, a contemporary of Schrodinger, formulated something we now call the Born rule that mathematically gets rid of the imaginary numbers (for the sake of brevity and clarity, I’ll omit the details) and this gives the probability of finding the object (usually an electron) in the real world. In fact, without the Born rule, Schrodinger’s equation is next-to-useless, and would have been consigned to the dustbin of history.
 
And that’s relevant, because prior to observing the particle, it’s in a superposition of states, described by Schrodinger’s equation as a wave function (Ψ), which some claim is a mathematical fiction. In other words, you need to get rid (clumsy phrasing, but accurate) of the imaginary component to make it relevant to the reality we actually see and detect. And the other thing is that once we have done that, the Schrodinger equation no longer applies – there is effectively a dichotomy between QM and classical physics (reality), which is called the 'measurement problem’. Roger Penrose gives a good account in this video interview. So, even in QM, imaginary numbers are associated with what we cannot observe.
 
That was a much longer detour than I intended, but I think it demonstrates the dissonance that seems necessary in science and mathematics, and arguably necessary for its progress; plus it’s a good example of the synergy between them that has been apparent since Newton.
 
My original intention was to talk about dissonance in music, and the trigger for this post was a YouTube video by musicologist, Rick Beato (pronounced be-arto), dissecting the Beatles song, Ticket to Ride, which he called, ‘A strange but perfect song’. In fact, he says, “It’s very strange in many ways: it’s rhythmically strange; it’s melodically strange too”. I’ll return to those specific points later. To call Beato a music nerd is an understatement, and he gives a technical breakdown that quite frankly, I can’t follow. I should point out that I’ve always had a good ‘ear’ that I inherited, and I used to sing, even though I can’t read music (neither could the Beatles). I realised quite young that I can hear things in music that others miss. Not totally relevant, but it might explain some things that I will expound upon later.
 
It's a lengthy, in-depth analysis, but if you go to 4.20-5.20, Beato actually introduces the term ‘dissonance’ after he describes how it applies. In effect, there is a dissonance between the notes that John Lennon sings and the chords he plays (on a 12-string guitar). And the thing is that we, the listener, don’t notice – someone (like Beato) has to point it out. Another quote from 15.00: “One of the reasons the Beatles songs are so memorable, is that they use really unusual dissonant notes at key points in the melody.”
 
The one thing that strikes you when you first hear Ticket to Ride is the unusual drum part. Ringo was very inventive and innovative, and became more adventurous, along with his bandmates, on later recordings. The Ticket to Ride drum part has become iconic: everyone knows it and recognises it. There is a good video where Ringo talks about it, along with another equally famous drum part he created. Beato barely mentions it, though right at the beginning, he specifically refers to the song as being ‘rhythmically strange’.
 
A couple of decades ago, can’t remember exactly when, I went and saw an entire Beatles concert put on by a rock band, augmented by orchestral strings and horn parts. It was in 2 parts with an intermission, and basically the 1st half was pre-Sergeant Pepper and the 2nd half, post. I can still remember that they opened the concert with Magical Mystery Tour and it blew me away. The thing is that they went to a lot of trouble to be faithful to the original recordings, and I realised that it was the first time I’d heard their music live, albeit with a cover band. And what immediately struck me was the unusual harmonics and rhythms they employed. Watching Beato’s detailed technical analysis puts this into context for me.
 
Going from imaginary numbers and quantum mechanics to one of The Beatles most popular songs may seem like a giant leap, but it highlights how dissonance is a universal principle for humans, and intrinsic to progression in both art and science.
 
Going back to Watson’s book that I reference in the introduction, another obvious example that he specifically talks about is Picasso’s cubism.
 
In storytelling, it may not be so obvious, and I think modern fiction has been influenced more by cinema than anything else, where the story needs to be more immediate and it needs to flow with minimal description. There is now an expectation that it puts you in the story – what we call immersion.
 
On another level, I’ve noticed a tendency on my part to create cognitive dissonance in my characters and therefore the reader. More than once, I have combined sexual desire with fear, which some may call perverse. I didn’t do this deliberately – a lot of my fiction contains elements I didn’t foresee. Maybe it says something about my own psyche, but I honestly don’t know.