• Qualia. What is this subjective experience that I know as consciousness? I've gone through Wiki, SEP and a fair number of books on philosophy and a few on neuroscience but I still don't understand what it is that I experience as the color "red" when in reality it's just a bunch of electric fields (photons). Why can't I get the same experience — i.e., color — when I look at UV or IR photons? These too are the very same electric fields as the red, blue, green I see all the time.
• Photographic composition. I'm a designer. I know them. I use them. But only empirically. I just do not understand them at a neuroscientific level. Why does rule-of-thirds feel pleasing? Is the golden ration bullshit? My gut says yes but I'm unable to come up with a watertight rebuttal. Why do anamorphic ultra-widescreen shoots feel so dramatic/cinematic? Yet to see an online exposition on the fundamental reasons underlying the experience. Any questions to artists are deflected with the standard "It's art, not science" reply.
• Wave-Particle duality. "It's a probability wave that determines when a particle will pop into existence out of nothingness." okay, where exactly does this particle come from? If enough energy accumulates in a region of empty space, a particle pops into existence? What is this "energy"? What is it made of? What even is an electron, really? I've followed quite a few rabbit holes and come out none the wiser for it.
• Convolution. It's disappointing how little I understand it given how wide its applications are. Convolution of two gaussians is a gaussian? Convolution in time domain is multiplication in frequency domain and vice-versa? How do these come out of the definition which is "convolution is sliding a flipped kernel over a signal"?
The universe is actually made of quantized fields. Both particles and waves are imprecise models/approximations. There's no such thing as a particle, instead there are just excitations of this field which we cannot measure with complete accuracy.
I very much dislike this phrasing, because it suggests that it is just us that are not capable of building an apparatus to enable us to do so.
Imagine a gear transmission or a lever: You can transform distance into force and vice versa. It is up to your choosing if you want to go with more speed or more force by changing the point along the lever, where your transmission happens. It is not possible to build a transmission, which gives you the most distance and the most force simultaneously. In this system of transmission, one is the other, just a different perspective.
And it is the same with the location and impulse of a quantum. You can choose to have more information in the shape of location or more in the shape of impulse by changing your measurement (like the point along the lever). But you can't have both, because there is only a constant amount of information which is represented in a combination of location and impulse.
Actually, the uncertainty part of heisenberg uncertainty principle is a purely mathematical limitation (called Gabor limit) and only the Planck constant makes it physical.
Gabor limit: a • b >= 1/(4•PI)
Heisenberg's uncertainty principle: a • b >= h/(4•PI)
So the Planck constant is kind of the maximal sampling resolution of the fields / signals in our universe.