• 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"?
I think this was a pretty neat explanation:
https://sites.google.com/site/butwhymath/m/convolution
The problem with convolutions, like many things in science, is that how you learn it, depends on what you're studying. Same theory, but with N different explanations, which can cause confusion if some of them are very different and tough to connect (i.e learning convolutions in a physics class vs leaning one in a statistics class)
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 can't say this will necessarily assuage your curiosity about consciousness, but I mostly stopped being overly curious about this once I realized that, it's likely only a manifestation of the aggregation of all of the individual sensory experiences our bodies have.
In other words, when you think about planet-scale phenomena such as how humans more or less all feel "connected" and non-hostile because civilization (in the most advanced countries) has reached a point where hostility is no longer essential for survival. That "experience", for each of us, is ours alone but it seems to be so ubiquitous that we can't take credit for that experience or insight as individuals. It leads me to believe a large part of our conscious experience of the world is shared and independent of the brain's capacity. More precisely, humans are (universally) experiencing phenomena that are independent of our brain's capacity to process and understand them.
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.
The idea is that it is in this waveform until you do something to observe it. Observation requires an exchange of energy, i.e., an interaction. This is why there is always uncertainty, because in order to observe something, that which observes has now intimately interacted with the waveform in order to cause its "collapse" into what we consider to be a particle. A particle very well may just be a highly localized energy that we perceive to be "solid"
You can't, for example, try to get a measurement of the location of a photon without putting a measuring device which absorbs the energy of the photon, modifying its wave function and thus the probability of where it will decide to reveal itself at that point in spacetime.
note: I consider energy, fundamentally, to simply be the consequence of fluctuating. The fluctuation of one thing can interact with the fluctuation of another and, minding conservation, transfer "fluctuation". The direction of that transfer of energy relying may be due to the fact that entropy always increases along the arrow of time, i.e., energy likes to spread itself out just as heat goes from high concentration to low concentration.