Yesterday's post sparked an interesting discussion with a friend of mine.
As is to be expected from a pool of curious people, this, itself, spawned a question:
Good question, JN, and one which I am happy to consider! Let's begin with an abstract definition of up, and see how it applies in different settings:
"Up" is defined relative to a two-dimensional surface embedded in three-dimensional space. It is one of the two directions that are perpendicular to said surface, with the opposite direction then being defined as "down."
On worlds such as Earth, down is typically considered to be the direction of the body's gravitational acceleration. Therefore, down points towards the planet's center (of mass) and up points the other way. This convention works well when the direction of gravity is readily determined, or when the planet's horizon is in view, but it quickly breaks down in the absence of these conditions. That is why, for example, airplane pilots can become disoriented in clouds, and "mystery spots" are a thing. It is also why defining up and down in space, where there might not be a perceptible gravitational acceleration or horizon, can be a challenge.
Nevertheless, it is possible to create new conventions to suit these environments. For example, our solar system describes a plane, and up and down are the two directions perpendicular to it. Determining which-is-which is done via the "right-hand rule:"
Hold out your right hand with your four fingers together, straight, and in line with your palm. Keep your thumb also in line with your palm but making a right angle with your fingers. Curl your fingers into your palm, but keep your thumb sticking out. Now, imagine the planets orbiting the Sun in the direction you just curled your fingertips. Congratulations, your thumb is now up!
When applied to our solar system, this convention means that "up and above" is the direction from which the planets appear to orbit the Sun counterclockwise. The rule also applies quite naturally to the Milky Way and other spiral galaxies—just use the galactic plane and the galaxy's direction of rotation. (Imagine yourself hitching a ride.) In fact, in our universe, any rotating system fits, even if it is not "flat," for they all describe planes of rotation. With this in mind, the right-hand rule tells you which way is up.
Of course, one could then ask about systems that do not rotate or those for which rotation is not easily discernable. In such cases, one must determine a new reference plane and preferred direction. Fortunately for cosmic adventurers, these already exist.
Finally, it should now be possible to say "what's up."