However, dark matter is measurable physics. I'm sure if technology and knowledge keep getting better we'll be able to solve this one, but it won't help with the aforementioned fundamental philosophical questions.
As a programmer, another interesting question involves dimensionless physical constants, such as the fine structure constant. Are these numbers rational? Irrational? Uncomputable? In computing theory, an uncomputable number is one that no finite algorithm given infinite time and storage can produce. Things like Pi and e are computable. Any randomly chosen real number is almost certain to be uncomputable. We may never know if the physical constants of the universe are computable, but I think it would tell us something very fundamental about our universe.
Well, there's a very well known (pun intended) pair of properties that are XOR unknowable (you can only know one or the other with any precision).
At some point we should be able to reach a set of fundamental laws that may be themselves be a manifestation of an unmeasurable set of fundamental laws. The takeaway I had from quantum mechanics was that, given infinite time and resources, we will reach a point where the answer is: "we can't know" or "that's the most basic truth we can ever show"
Why time is unidirectional may be answered, but questions about why there is time in the first place or what came "before" it will forever be fundamentally beyond the grasp of our science.
Who is to say that there will not be another revolutionary change in our understanding of the universe just like relativity and quantum mechanics? Or two or five. In ten years or a hundred years or a million years?
Maybe it comes from a totally unexpected direction. Maybe we next learn how minds work and this makes us discover that something build deep into it obstructs or view of reality. It wouldn't be the first time that our natural intuition about the world lead us astray for millennia.
Even in this universe, it's possible to be entirely cut off from regions. What does a black hole look like inside its event horizon? We have models, but it's impossible to measure. On a larger scale, assuming the continue expansion of the universe, the furthest galaxies will eventually be receding from us faster than the speed of light, making them un-observable.
The fundamental question is: what's the most basic truths that we can ever know?
If there are hyperdimensional branes the likelihood is that we wont be able to learn much about their origins because of their relationship to our universe. An acceptable answer then becomes "We can't know how they exist..."
Brane theory was what came to mind immediately for me.