Two dreams

The first dream was unusual for me in that it involved a public figure, in this case one of the few footballers of whom I have heard. It seems that I was doing something banal & innocent with his wife, perhaps going shopping, and towards the end of the expedition he joined in. He turned out to be a rather rough sort of chap, but underneath that decent enough. For some reason, I thought it polite to talk to him about something other than football - and that is about all that I can remember.

The second dream was something completely different and involved an unspecified mathematical object, but perhaps a group or a field, which evolved over time. The group was a function of time. As I woke, I started to ponder about what such a thing might mean.

Starting with, if time t1 was near time t2, then group(t1) should be near group(t2) in some sense. Which suggested that the group would need to be infinite for this to be interesting and that there would need to be some kind of a measure on the set underlying the group, a measure which could be used to define nearness.

Maybe we would say something about the sets over which the groups were defined. Maybe the set for time t2, later than time t1, would need to be a superset of that for time t1.

Then time would need to preserve group structure. If a and b were in both group(t1) and group(t2), then the product of a and b would need to be the same in both groups.

Now I have woken up, I have no idea if people work with such groups. But I was moved to remind myself of the definition of a group in my trusty Rotnam: associative & closed binary operation, identity and inverse. Maybe something more will come as the sun rises.