Well put. It’s imposing a sequence onto a process that is not entirely described by the sequence. 

I think I’ll try to write up my thoughts about the paradox at some point because I do think it contains some profound stuff.

Undisciplined

pdmonearth

I often feel that most of statistics is just the data range you choose. in this footrace paradox, you are choosing the data range that ends before the faster runner catches up. If you graphed it showing time elapsed by distance traveled, time would be a log scale or something (I think -- not a math person) and if you changed the time scale to linear it would be obvious that the faster runner 

 going to catch up. So, really the problem here is that the question chooses a range which is defined by being before the faster runner catches up.

math

AskSN

the_stacker_muse

What is your favorite paradox?

SimpleStacker

I often feel that most of statistics is just the data range you choose. in this footrace paradox, you are choosing the data range that ends before the faster runner catches up. If you graphed it showing time elapsed by distance traveled, time would be a log scale or something (I think -- not a math person) and if you changed the time scale to linear it would be obvious that the faster runner *is* going to catch up. So, really the problem here is that the question chooses a range which is defined by being before the faster runner catches up.