In the corridors of academia, there are rare brilliant individuals who can smoothly bridge many scientific disciplines. Professor Leon Cooper is one such person. A man instantly recognizable by his no-nonsense New York accent, perfectly coiffed hair and fine Italian clothes, Cooper is a Nobel Laureate in physics and a master of interdisciplinary exploration.
In my early days of 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, ask the most fearless probing questions to the young researchers. “Do you really believe in what you are working for?” he asks, steering conversations beyond the technical and the philosophical.
Bonded by our shared love for music, our elevator ride became a canvas for lively discussions. It was during these exchanges that I discovered Cooper’s profound contribution to an electrical phenomenon called superconductivity.
What is this? Well, essentially, at room temperature, electric current meets resistance, but a surprising change occurs near absolute zero (-273.15C). At this temperature, the current that flows through superconductors with zero resistance is an ability that allows it, for example, to levitate magnets. This superconductivity effect could play a key role in our future clean energy, and medical and technological innovations.
But what CAUSE superconductivity? Cooper showed that a concept now called ‘Cooper Pairs’ was behind this. These are pairs of electrons that effectively bond, changing their properties so that they can cross a wire without hindrance. This insight earned Cooper the 1972 Nobel Prize in Physics, along with John Bardeen and John Robert Schrieffer.
However, it is not only Cooper’s mastery of quantum physics that sets him apart, but his ability to transcend disciplines.
A year after receiving the Nobel Prize, he headed the Institute of Brain and Neural Systems at Brown University, which applied theoretical approaches from particle physics to the enigmatic realm of the brain. At the time, it was the mid-90s and the machine learning landscape was developing rapidly.
Although computers at the time were not as powerful as they are today, the basic theory behind machine learning existed. And Cooper, with his passion 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 is the Ising Model, a theory that emerged from the physics of atomic spins.
To understand this, try to imagine the atoms in a slab of metal arranged at points on a grid. Then visualize each of these atoms as small magnets pointed up (representing positive spin) or down (negative spin). It is the collective behavior of how all the atomic magnets interact that determines whether a metal becomes a magnet or not.
Machine learning and neurons in the brain have many parallels between this Ising model of the atomic spin of the small magnetic field endowed by the atoms. The intricate dance of atomic spins finds a counterpart in how neurons communicate and form networks.
Extending this analogy, a wide variety of machine learning architectures draw parallels between the atoms of the Ising model and the neurons of the brain. The intricate dance of atomic spins finds a counterpart in how neurons communicate and form networks.
Why? In the Ising model, neighboring atoms communicate with each other through the mutual energy between their spins. And this atomic energy is lowered when neighboring spins align with each other. This is similar to how the brain works: neurons can send a signal to each other or not based on the signals of their neighbors.
New field of science
Inspired by Cooper’s spirit of mixing disciplines, I encouraged a bold new scientific endeavor 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 the Coopers’ thinking can be applied to overcoming the evolving challenges of music. Or, to be more specific, compose music using machine learning. While artificial intelligence has excelled at dissecting recorded tracks into their key components, actually creating original music has proven to be a formidable frontier.
Behind all music hides certain rules that govern how chord progressions are formed. And currently, AI models struggle to understand these rules.
In collaboration with Robert Rowe, a music machine learning composer at NYU, we embarked on a new journey to overcome a particular challenge in music composition. Our solution, the Pentahelix, is a geometric and physical model inspired by jazz improvisation, and it provides a glimmer of hope in solving this issue.
Think of the Pentahelix as a lattice, similar to the Ising model but with a honeycomb-like structure. Instead of representing spins, lattice points correspond to potential musical tones. Within this geometric structure, many tones can encode musical chords and melodic patterns. In fact, it provides a structured way of organizing 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 use in their creative process. This not only improves our understanding of musical improvisation but also opens up new possibilities for musical composition and performance.
Jazz, with its nuanced interplay of instruments and hierarchical chord changes that occur over time, could offer a training source for this new approach to music composition in the field of AI.
While we await the outcome, there is a deep sense that Cooper, with his ability to smoothly navigate different fields of knowledge, is proud of the continuous pursuit of innovative ideas and perspectives. .
This journey from superconductivity to jazz improvisation demonstrates the enduring power of interdisciplinary exploration. It shows what can be imagined in the field of science and technology and where the next frontiers can be broken.
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