Would it be possible to run a 3 minute mile?
Well, I am philosopher (and a lapsed scientist ; ) so,
- It is metaphysically possible (the speed required is less than C)
- It is logically possible (you can't both run and not run a 3 minute mile, so it does not lead to a contradiction)
- Is it physically possible (OK now we leave more deductive thinking and go modally inductive)...
- How likely is it?
As things stand it seems unobtainable. Over the last 100 years records of human achievement have tended towards stable minimums (when population and participation numbers are factored in).
Now we are not a stable species (none are) so who knows what the future holds.
The average speed required is 20 mph, that is insanely fast for the distance as it is effectively impossible not to go anaerobic very quickly at such speeds.
Running 12 mph at mid distance gives you a 5 minute mile (try and run one, it's pretty damn hard unless you're sporty, fit, and youngish).
It seems unlikely as things stand, but there is no certainty in this, just probability (so it can't be proven possible or impossible, it is like an unobserved quantum mechanical system; all the possibilities are in play, but we can't say until we "see").
If anyone is interested in something very challenging, in considering the philosophical issues involved much further, I was set on a day long expansion to this answer which turned into a Monster!
So, think of the above as the short version. Here is the long one:
Caveat Emptor: this is not for the faint of heart, it is for spiritual revolutionaries only.