I think you can still get an intuition. 10000 people standing next to each other so that each person has half a meter to themselves will give you a line of 5 ki

I think you can still get an intuition. 10000 people standing next to each other so that each person has half a meter to themselves will give you a line of 5 kilometers (just over 3 miles). That's a relatable distance - for example, the length of Central Park is 2.5 miles, apparently. It's not perfect, but gets you somewhere. Squaring and cubing makes it less relatable, but it's still a lot better than a completely abstract number IMO. Thinking about this just now made me realize both how long a line of 10000 people can be and how densely you can pack them in a square - or how many people (theoretically) fit into 5x5 kilometer area.