A gazillion dollars have been spent, over the past decades, on cochlear research. How can you really believe that something as simple as EarSpring could explain the way we hear music?
Fair enough… An old graduate professor of mine used to say:
“If you can’t describe a problem and state a rough solution on the back of an envelope, then you don’t understand the problem well enough to spend more time and money on it.”
He had us learn a 1-place log table so that we could do our astrophysics calculations in our heads. No need for calculators or computers. I took Bob’s message to heart over the years in my career, and it has always served me well.
Bob eschewed ostentatious displays of math prowess, and often bragged that not a single integral sign would be found in his PhD Thesis. I’m not quite that extreme. I think math has its place. But I do agree with him about excessive displays for pretentious purposes. (…and because I’m a bit slow, I had to learn to write small…)
First of all, our hearing is not just the cochlea. Musical hearing involves the cochlea to be sure, but it also involves the entire system of cochlea, afferent 8th nerve, brain processing, and the feedback efferent 8th nerve. In detail, it is an enormously complex system, one that likely defies precise description today.
The EarSpring and Conductor equations are the simplest possible solutions to the problem of musical hearing that satisfy known boundary conditions – the degree of tone flattening as they grow louder, the ratio between the magic 40 dB level and the threshold of hearing. These equations are the simplest that could describe the whole system of musical hearing.
They also make verifiable predictions of linear behavior at threshold sound levels, and near cube-root compression at loud levels, the growth of odd harmonics at loud levels, the existence of elevated thresholds, the general agreement on the shape and asymptotic behavior of recruitment curves with patient surveys, and several others that aren’t on the top of my head at the moment.
But the real point of these equations, and this is especially true for the Conductor equations, is that it was a change in perspective away from the orthodox viewpoint that made them possible. There are several conceptual leaps contained in that Conductor Paper, and at least one in the EarSpring Paper.
The fact is, they work. And they work marvelously well. Whatever problems remain are really to be found in the temporal dynamics of the corrective system, not the applied hearing corrections themselves.
And to the best of my knowledge, we are the only ones offering any solutions for conditions of hyper-recruitment and decruitment. And we are certainly the only ones offering a single-knob tuning procedure for end users. Those are byproducts of our equations too, from the operator algebra developed in the Conductor paper. As a physicist, I certainly do believe in the power of equations to express how the world works.
Now, I don’t want to come across as defensive. Rather, I’m as puzzled as anyone, why such a simple system of equations should describe such a complex physical system. The best analogy I can imagine at the moment was the transition from the Newtonian worldview to Statistical Mechanics in the 19th and 20th centuries.
Newton would have us track every particle in a huge ensemble – completely impossible in scale. Whereas the methods of Statistical Mechanics were able to produce simplified equations that described gross behavior of the ensemble, e.g., the Boltzmann equation, and the Ising model, and the Navier-Stokes equation. The analogy here is toward describing ensembles of neurons and their interactions with each other and with the mechanical interface to sound.
In plain language, my approach describes ensemble behavior, while those investigating cochlear details are seeing the “particles”. It is like they are trying to read a newspaper through a microscope.
Finally, I wasn’t making my living off of research grants, drilling ever deeper into the minutiae of cochlear actions. I was motivated to find a practical solution to allow me to hear my music once again. That’s all that mattered to me.
After the passage of all these decades, and all the truckloads of money spent on cochlear research, can you find any other solutions for high quality musical hearing out there?
I rest my case.
- DM
[ PS: A rather famous physicist once wrote an equation even simpler than mine, which had enormous implications:
“Everything should be as simple as possible, but no simpler.” , A.Einstein ]
