In the corridors of academia, there are those rare brilliant individuals who can seamlessly bridge several scientific disciplines. Professor Leon Cooper was one such person. A man instantly recognisable by his no-nonsense New York accent, perfectly groomed hair and fine Italian suits, Cooper was a Nobel Laureate in physics – and a maestro of interdisciplinary exploration.
During my early days in graduate school in 1993, I witnessed his brilliance in the lecture halls and beyond. In the elevators of the physics department, he would, with an air of curiosity, pose questions the most fearlessly probing questions to young researchers. "Do you really believe in what you're working on?" he'd ask, steering conversations beyond the technical and into the philosophical.
Bonding over our shared love for music, our elevator rides became a canvas for passionate discussions. It was during these exchanges that I discovered Cooper's profound contributions to an electrical phenomenon called superconductivity.
What is this? Well, essentially, at room temperatures, electric current encounters resistance, but a mesmerising transformation occurs near absolute zero (-273.15°C). At this temperature, current flows through superconductors with zero resistance – an ability that allows it to, for instance, levitate magnets. This superconductivity effect could play a pivotal role in our future clean energy, and medical and technological innovations.
But what causes superconductivity? Cooper posed that a concept now called 'Cooper Pairs' was behind it. These are pairs of electrons that can effectively bind together, changing their properties so they can traverse a wire unimpeded. It was this insight that earned Cooper the 1972 Nobel Prize in Physics, along with John Bardeen and John Robert Schrieffer.
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However, it's not just Cooper's mastery of quantum physics that sets him apart, but his ability to transcend disciplines.
A year after receiving the Nobel Prize, he took the helm of the Institute of Brain and Neural Systems at Brown University, applying theoretical approaches from particle physics to the enigmatic realm of the brain. By then, this was the mid-90s and the landscape of machine learning was fast developing.
Although computers of that era were not as powerful as today's, the basic theory underpinning machine learning existed. And Cooper, with his penchant for integrating physics into neuroscience, made significant contributions to the creation of neural networks – algorithms inspired by the structure and function of the human brain.
One of his key tools for developing such networks was the Ising Model, a theory that emerged from the physics of atomic spins.
To understand this, try imagining atoms in a slab of metal arranged onto the points of a grid. Then envision each of these atoms as tiny magnets that are either pointed up (representing a positive ‘spin’) or down (a negative ‘spin’). It’s the collective behaviour of how all these atomic magnets interact that determines whether the metal becomes a magnet or not.
Machine learning and neurons in the brain hold many parallels between this Ising model of atomic spin – that tiny magnetic field that atoms are endowed with. The intricate dance of atomic spins finds a counterpart in how neurons communicate and form networks.
Extending this analogy, a broad class of machine learning architectures draws parallels between the Ising model's atoms and the neurons in the brain. The intricate dance of atomic spins finds a counterpart in how neurons communicate and form networks.
Why? In the Ising model, neighbouring atoms communicate with each other through mutual energy between their spins. And this atomic energy is lowered if the neighbouring spins ‘agree’ with each other. It's similar to how the brain works: neurons can send a signal to each other or not based on the signals of their neighbours.
New fields of science
Inspired by Cooper’s spirit of mixing disciplines, I spurred a bold new scientific endeavour with cosmologist Robert Brandenberger. Since 1997, we have sought to use neural networks (and thus the Ising model) to understand the very structure of our Universe.
Fast forward three decades and Cooper’s thinking could be used to overcome emerging challenges in music. Or, to be more specific, composing music with machine learning. While artificial intelligence has excelled in dissecting recorded tracks into its key components, actually creating original music has proven a formidable frontier.
Behind all music hides certain rules – laws that govern how chord progressions are formed. And at the current time, AI models struggle to grasp these rules.
In partnership with Robert Rowe, a music machine learning composer at NYU, we've embarked on an innovative journey to overcome a particular challenge in music composition. Our solution, the Pentahelix, is both a geometric and physical model inspired by jazz improvisation, and it offers a ray of hope in addressing this issue.
Imagine the Pentahelix as a lattice, similar to the Ising model but with a honeycomb-like structure. Instead of representing spins, the lattice points correspond to potential musical tones. Within this geometric framework, numerous tones can encode musical chords and melodic patterns. Essentially, it provides a structured way to organise musical elements.
This geometric model serves as a tool to understand how jazz improvisers navigate the vast space of musical tones and chords. By using the Pentahelix, we can gain insights into the strategies and patterns they employ in their creative process. This not only enhances our understanding of musical improvisation but also opens up new possibilities for music composition and performance.
Jazz, with its nuanced interplay of instruments and hierarchical chord changes that occur over time, could offer a source of training for this innovative approach to music composition in the realm of AI.
As we await the outcome, there's a profound sense that Cooper, with his ability to seamlessly navigate diverse realms of knowledge, would take pride in the continued pursuit of transformative ideas and perspectives.
This journey from superconductivity to jazz improvisation exemplifies the enduring power of interdisciplinary exploration. It shows what is conceivable in the realms of science and technology – and where the next boundaries could be broken.
Read more:
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- Clingy atoms and catastrophic iron: The strange science underpinning nuclear fusion
- Evil doppelgängers, alternate timelines and infinite possibilities: the physics of the multiverse explained
