Music, Perception, AI and Mathematics

I gave this presentation on Wednesday (the day Trump won the election) to Liverpool University's Music Theory group (see http://www.chromatic-harmony.com/theoryclub/). 

Present were some of the key intellectual figures who have been important in my journey, not just my thinking about music, but about perception, AI and physics: Peter Rowlands, whose physics has fundamentally changed my outlook on perception, alongside John Torday, whose biology informs a much deeper integration between physics and physiology, which explains what curiosity is, and Bill Miller who has worked with John on cellular consciousness. Also there was Michael Spitzer, whose book "The Musical Human" treads a path into music and evolution to which I am very sympathetic, although perhaps now I would say, "we need to think about the physics!"  

This integrates with the AI work that I did, and particularly perception in AI, where I learnt a huge amount from my Liverpool colleague David Wong (who couldn't make the presentation). With David, we are further developing these ideas, and this has led to a medical diagnostic company, but also to a slew of new thinking about the role of AI in society. 

There are so many avenues to explore from this, but one of the most fascinating came from Peter Rowlands, who said that "music and mathematics are fundamentally 'abstract patternings'", and I had a conversation with Peter after about whether this was the deep connection between maths and music: it's not that music is mathematical (which is often how we think, particularly with composers like Bach), but that mathematics is musical: a mathematical proof is like a perceptual journey in a similar way to the way to how I describe music. 

Seymour Papert was on to this I think when he pointed out the root of the word "mathematics" is the Greek "mathmatikos" which literally means "to be disposed to learn". I don't think that's a million miles away from "disposed to going on a journey of perception". 

The really fascinating thing here is the primacy of statistics in the study of perception - the essence of Gustav Fechner's work. Statistics is an outlier in mathematics, because it is rarely presented as logic, but fact, from which calculations are made. Where this "fact" comes from is quite mysterious - how and why does the probability density function arise, with its Pi and e and square roots? The "central limit theorem" will be the typical answer - but that only goes so far, because among the limits of the central limit theorem is "finite variance": well, what makes it finite? That may be a question for biology.

But then, machine learning is statistical. It is all about statistics and recursion. And when we say "we don't know why it works", what we're really saying is "we don't really understand the ontology of the statistics". What I am suggesting in my presentation, is that the ontology of the statistics may be even more profound than the ontology of mathematics as we conventionally understand it, or even the ontology of logic. I think this thought has been with me for most of my life.