There's an obvious connection between how far away I am from something and the degree to which that thing can physically affect me. A rhinoceros, or an explosion, or a tornado, or what have you, is more dangerous to me the closer it is to me, and less dangerous to me the farther away it is from me. And we usually explain this to ourselves by saying that a distant explosion is less dangerous to me than a near one because the effects of a distant explosion have more space to cross, before they get to me, than the effects of a near one do.
New idea: With increasing excitement and intensity over the past 20 years or so, the following thought has occurred to scientists and philosophers: Maybe there is a way of eliminating the middleman here. We're used to thinking of the 'distances' between things as something that helps explain why some things affect one another a lot and others affect one another less – but maybe that's all backwards: maybe there's a way of thinking about the distances between things as nothing more than a measure of how much they affect one another!
Bottom line: Maybe the world, at its most fundamental level, is just this formless void in which things float, and affect one another – a void in which there is no distance, and no geometry, and no space – and that all the talk about distance and geometry and space is really just a way of keeping track of how those things affect one another.
Other voices in the conversation:
Sean Carroll, theoretical physicist, California Institute of Technology: Space is overrated
Izabella Laba, mathematician, University of British Columbia: We can work with space without understanding its essence
Bridget Falck, astrophysicist, University of Oslo: Space is a relation between things, not a thing itself