this is a mathematical convention, not simply an epidemiological term. the 0th term of any function, like R0, is generally understood as the initial condition constant (at time t=0). R(t) is a function of time and R0 is the value of R at time 0, the initial condition. R0 tells you exactly nothing about the future, it only pins down the starting point (which is important information, but not the be-all-and-end-all of it).

i’ve been mildly amused/dismayed by the constant misplaced focus on R0 over the past 2 years by the media/laypeople, given this essential context.