> but definitely a brain (excluding plantlife to keep this short)

"brains" are quite diverse and come in many variations. Squids have donuts. Sea Squirts devour their own brains. Leeches have multiple brains, Octopi (cephalopod) don't have a centralized brain and it's distributed, mostly in their tentacles. They also don't show cognitive decline when losing limbs. Maybe Wittgenstein can't understand a lion, but certainly a cephalopod is completely alien.

  > I think neurons do 4 distinct types of things. 

I'm a bit curious, how much have you read about brains? What about signal theory?

I ask because I suspect you're trying to solve the problem yourself and not building on the wide breadth of literature and research we have.

Brains do not operate in waves the same way a wave of water or electromagnetic wave does. Though anything can be approximated by a wave too, but signals need not be waves. Yes neurons conduct electric signals, but neuron to neuron communication (synaptic transmission) is chemical. These are discrete particles. But as I mentioned before, if we're talking about the electrical transmission inside the neuron, these are spikey[0,1]. When you look at neurons firing, there is a digital like signal. If anything, these look like Gaussian mixtures.

  > There's no "woo woo" there.

I agree that there's no magic, and so I ask that you don't introduce it. You're imbuing waves with magic while not recognizing what waves actually are. Analogue and digital are both waves. They both can integrate, resonate, interfere, and all that jazz. The same wave mechanics work. Your call to Maxwell is meaningless because ALL OF ELECTROMAGNETISM (minus quantum) is explained through those 4 equations (and have been extended to incorporate the latter). And just think about what you are suggesting. That digital signals are not described by physics? That software can't be described by physics? It's all physics. Sure, the abstract representations of these things are not physics, but that's true for any abstract representation.

So don't try to dispel people who are calling to magic by making a call to a different kind of magic. I don't think you're dumb, but rather it is easy to oversimplify and end up with something that requires magic. It's FAR easier to do this than to get the right answers. There's a reason people study very narrow topics for decades. Because it is all that complicated and trying to reinvent their work (while a good exercise) is just more likely to end up making many of the same mistakes that were then later resolved. We have the power of literature and the internet makes it highly available (though can be hard to differentiate from hogwash and it can be hard to find truth). Use the tools to your advantage instead of trying to do everything from scratch. Do the exercise, but also check and find the mistakes, improve, and do this until you catch up. Hell, you may even find mistakes the experts made along the way! The good news is that its SO much easier to catch up than it is to extend knowledge. You can learn what took thousands of years to get to in a week! It's hard, but in comparison catching up is trivial. So don't squander humanity's greatest innovation just because you worked hard at building your model. But refine it and make sure it doesn't invoke magic.

[0] https://en.wikipedia.org/wiki/Biological_neuron_model

[1] https://en.wikipedia.org/wiki/Soliton_model_in_neuroscience