On the nature of reality, one sometimes wonders. . . what exactly is this?
If you'd been born twelve thousand years ago at the dawn of agriculture, your world would have been a small group of people, a forest, a lake, a vague notion of something beyond the mountain range where you'd never been. Forget questions like "what's beyond the sky?" as a matter of sophisticated linguistics, you're lucky to wonder about the lands beyond.
Four hundred generations pass and poles are placed around the world, the shadows measured, and now the world is round and finite. An estimate of its size is given. The lands beyond. . . up there, now in the gods' domain. What a transgression it would be to breach that ultimate barrier, to grasp at that brilliance, blazing sun-god on the throne.
Modern times, the world is now a whole universe — an ever-expanding differentiable manifold, and the skin on your hand the result of fluctuating probability fields forming the base layer of material reality. An attempt is made for a full description of "this," but any measurement of even the curvature of reality itself is just approximation under light-speed constraints. Any model reduces further and further into pure mathematics and distinctions blur away. One wonders: where exactly are the rules that govern this thing? What guarantees that things also fall down, far from here?
So our world is not all there is, this solar system is not all there is, the basic question seems to be: is there even any reasonable expectation that it ever ends? If this universe is "somewhere," then where? Not that say, a topological space needs to be embedded in any larger space, but an impossible inductive nightmare of a question. No, it's not even that. Why is there anything here in the first place? The usual answer is "because you wouldn't be asking this question if there weren't." Anthropic principle and all.
You know what? Forget reality. Let's think about mathematics. Given first-order logic, if we construct a set of axioms, then any consequence of those axioms is by definition true. You don't need a physical reality to say that given an axiomatic system that satisfies the Peano axioms, 1 + 1 in fact equals 2. This is always true, perhaps even if "nothing" exists. You wouldn't expect the consequences of any arbitrary set of (self-consistent) axioms to suddenly become false, regardless of what (non)physical reality prevailed. The anthropic principle is irrelevant. Whether our axioms of Zermelo-Fraenkel set theory are self-consistent is completely irrelevant.
Let's then posit that all physically consistent realities have an equally consistent mathematical description. You throw a ball, the ball begins to fall down. Down is some function of the surrounding spacetime. Tick forward. The primitive notion of a single-tape Turing machine with a countably infinite tape can simulate essentially any program. As far as we can tell, reality is at least somewhat granular, as time and space lose meaning in small enough increments, and our program can have as small an epsilon for a step as we'd like. Tick forward, the ball touches the ground. A complex system of chemistry and electromagnetism — a function with a million inputs produces an output of comparable magnitude; a thought is formed and a short text on the nature of reality begins to be written.
Do you know the general argument for the uncountability of the real numbers? You claim that we have a full list of all decimal sequences and then form a new number that differs from the first in its first digit, the second in its second, and so forth, forever. This number cannot be on the list, and so the list is incomplete. This set is much, much larger than the natural numbers, but at the same time, vanishingly small. From self-consistent axioms, we gain such unfathomable infinities of logically sound descriptions of any and all programs of reality, that in a very real way, almost all forms of reality must be purely mathematical.
From this point of view, the answer to "why is there anything at all?" is. . . there isn't.