Today I started reading Chapter 3 of Practical Approach to Electroencephalography. And while reading about the essential terminology and concepts underlying EEG (frequency, amplitude, location, electrodes...) I was surprised to see the 10-20 system's proponent was introduced as "Jasper".

Jasper? Who is Jasper?

So I grabbed another book I have, Brainwaves by Cornelius Borck.

I found Jasper.

Jasper, as in Herbert Henry Jasper. He helped conceive the 10-20 System, which is a standard way of measuring and communicating brain activity.

Jasper was a psychologist and electrophysiologist and had good relations and communication with the best doctors in America and Europe. He had the connections, reputation, and expertise to help develop the EEG technology.

The one quote that stood out the most was this one:

"The closer the micro structures of those curves were analyzed, the more the link shifted from neurophysiological knowledge spaces." (Brainwaves, 174)

The quote was describing the sentiment in the medical field in the 1930s about complexity of brain wave signals and reliance on more advanced math and physics knowledge to uncover a deeper understand of brain activity.

Interestingly I can smell that same sentiment in Mark's Practical Approach to Electroencephalography. Which was published in 2025.

Why? Why are doctors cautious of jumping outside their domain so easily?

I think that sentiment is a mix of respect and fear. Respect of other fields and their complexities (for example, the respect of the math behind brain waves and Fourier Transforms) and simultaneously, the fear of delving too far away from their area of expertise.

Why is that?

The more I read about brain waves, the more curious I am about it's mathematical and computational roots. And since brainwaves are signal-like events, signal-like events can be analyzed using Fourier Transforms.

A Fourier Transform (mostly referred to as "FFT") is an algorithm used to take the graph of a signal in the time domain and graph it in the frequency domain.

This transformation is beautiful. Because when you graph a signal in the frequency domain the frequencies that compose the signal are revealed.

Signals can be composed of many sub-signals. Signals can add up and subtract down on each other. And the resulting shape of the signal can be decomposed into sub-signals with very specific frequencies.

That is beautiful. And at the same time, it's also quite confusing. How is that possible? And why is that possible?

The best video I've seen that shows how signals combine is Grant Sanderson's What is a Discrete Fourier Transform? posted in The Julia Programming Language channel.

For a math-heavy explanation, I found Reducible's Discrete Fourier Transforms video helpful (but hard to follow since I don't have a strong grasp on fundamental math concepts like trigonometry and linear algebra).

And for a historic explanation of Fourier Transforms, Veritasium's The Most Important Algorithm of All Time is a great video. Which I'd call a mini documentary. Want to guess how FFTs were used? To detect which countries were conducting nuclear tests.

These 3 videos have helped me get a better feel for the math of FFT. But it's still not enough for me to deeply understand it. Which is why, as I continue to read about EEGs and the history of the technology, I'm re-immersing myself into trigonometry, complex numbers, and then eventually, into the discrete fourier transform and the fast fourier transform.

Working through Khan Academy's Precalculus course. And learning about composite functions. I'm very familiar with composite functions because building user interfaces with React is all about composing functions.

In React, it's functions all the way down.

And the one thing I appreciate from this very basic unit I'm working through about composing functions is how sometimes, it's more efficient to skip nested functions if you have all the inputs needed to compute the last output in the chain of functions.

For example: f(a) → b, g(b) → c, h(c) → d.

If the end goal is to compute c, it might be worth thinking about how to create a new function, f'(a) → d.