> > > > > What sort of things are they if they are things? >
Space and time are indeed things. They are not abstractions or merely instruments neccessitated by physical laws, they are the substance of which everything consists.
Space and time are indeed tangible substance, no different than any other substance. They are the most fundamental substance, everything is composed of space and time and all of chemistry and physics should be constructible based on the bending of these things.
The strange thing about space and time is that it is very much like fundamental particles in the sense that a particle, say an electron may be regarded as being particle or wave. Space has some of these same properties and that is why it is poorly understood IMO. Some people argue it is continuous. Other argue it is discrete. It has properties of both, and yet continuous and discrete seem incompatible kind of like wave/particle aspects.
The truth is that you can correctly model particles as being waves or particles. And you can correctly model space as being continuous or discrete. Both views are correct. The difficulty lies in resolving that and making it rigorous with the tools that you have been given, and unfortunately those tools are insufficient to model such a thing.
If space is discretized - I ask - discretized BY WHAT ??? The only way to chop or demark a chunk of space which exists, is to place cuts into it which are nonexistent. That is the only way to chop up the existent. You chop it up into segments by inserting segments which are nonexistent - that is the only way.
To do that you must be able to grasp triviality, order, disorder, and conservation......all in a very new way. No scientist today has been trained to think like that and most wold reject the approach. But it does not matter whether someone likes it or not. If you can produce accurate models which are consistent with observations in the lab then you have a useful model.
It is very straightforward to model this way, yes you have tools which are not math, but are consistent with math, and equally as valid as mathematics though they be not math.