What is this thing called “Kurtosis?”

One of my guiding principles in communicating science and technology to the public is that I avoid using numbers. Scientific numbers seem to creep people out who are not using them all the time. Heck, they even creep out folks who do use them all the time, depending on which set of numbers you use – or more precisely, how you arrive at them.

Bioacoustics can straddle two disparate branches of science; physics and biology. Physics is all about properties and their measure, referenced back to absolute physical constants. Using calculus or algebraic geometry, they express relationships between time, space, and matter. So when a physicist says “6,” you better believe it.

Biology, on the other hand, is all about behavior – an adventure in shades of gray, which they express using “statistics.” Trends are assessed by bracketing data sets and predicting probabilities. So unless a biologist is expressing how many bears are in your backyard, when they say “6,” they mean “6ish.” And even the bears might be up for debate if you haven’t come to an agreement about what “in” means.

When biologists and physicists get together and have conversations about numbers, it can make their respective fingernails itch.

This preamble serves as a framing for the word “kurtosis,” which is a statistical term often found in descriptive sentences with the word “roughness.” But functionally it is an expression of “set variability.” So, for example, if you count the shoes in your closet and find you have eight black loafers, three brown boots, two white feather mules, and one sequined slipper, the variability of the set relative to shoe color and type would be a “high kurtosis” set. But relative to apparel, it would be “zero,” because they’re all footwear. It’s this sort of numeric legerdemain that physicists find annoying (at best).

But when you evaluate the variability of sound in terms of the physical measure of frequency and amplitude, we find a direct correlation between high kurtosis and nasty sound quality. High-kurtosis signals are also directly correlated to how physically damaging a sound is, so it would stand to reason that this expression of sound quality should be woven into the fabric of sound exposure regulations. Which is what I have been proposing for some time now.

Our first cuts were missing some pieces, but I think we’re getting close, which is what I advanced at the recent Aquatic Noise conference. Without digging down to deeply, my first cut used a signal analysis called “Fast Fourier Transform,” which would yield consistent numbers, but distorted the signal under scrutiny.

This most recent cut we use “wavelets analysis,” to assess set variability in sound frequencies and amplitudes. Wavelets analysis is a mathematical function that was originally derived to highlight aberrations in big data sets. So as a concise mathematical function used to evaluate specific (albeit dynamic) data to express noise impacts with a simple number, this approach may be the closest we can get to numeric rapprochement between physicists and biologists.

If this is the case, and we can persuade the regulators to climb on board, we may finally be arriving at a useful, and non-controversial tool to express noise exposure impacts on living critters.