It must be confessed, this is my first post to any blog, ever. I know, I'm a cave man. So for my 'test post', I thought I'd try a little mathematical riddle that may or may not be familiar...
Fast Fred and Slow Susan propose to have a race; a marathon of 100km. Given their (literal) track records, the outcome seems utterly predictable – Fred will easily outpace the slower Susan. As a result, he gives her a head start. Since she is 32 years old, he will allow her a 32 km head start before he even begins to run. Fred knows he runs at twice Susan’s pace, so that any head start of less than 50km should pose no problem for him. So that he may know when to begin, they will both carry phones with GPS devices, and be in constant contact.
The race begins, and Fred faithfully waits until Susan’s little blip shows her 32km along the route. Then he begins. After very little time (since Fred is so fast), he notices that he himself has come to the 32km mark. “Susan”, he says into his phone “I’ve reached your 32km already”.
“One point for you,” she replies “but I am still ahead; I have reached the 48km mark… I’m nearly half done!” Fred fixes the 48km mark in his mind's eye and presses on.
Before long, he reaches the 48km marker. “Susan”, he says “I’m at 48km now, and I’ll pass you before long”.
“two points for you, but I’m still ahead,” she replies “56km and counting… do you suppose you’ll have passed me by the time you reach 56 km?” Something bothers Fred about her comment, but he puts it our of his head and runs, the destination of 56km firm in his mind.
He soon reaches the 56km mark, and again calls his opponent “Susan, I’ve reached 56km”
“Very quick, three points” she says “and have you passed me yet?” Fred snorts in response. “I’m at 60km now. Do you suppose you’ll have passed me by the time you reach 60?”
“Surely, you’ll have gained some ground by then” Fred replies.
“Of course. In the time it takes you to reach my current spot, I’ll have moved on ahead. In fact, EVERY time you reach a spot where I’ve already been, I’ll have moved on further! Even when I'm saying 'a million points for you', I'll still be in the lead! We can keep this up forever, and I guess you can never catch me. It looks as though the race is mine Fred, you may as well give up!”
The easy question is, who will win the race? The harder question is: Why do we have a never-ending sequence of events in which Susan is winning, when it seems that Fred should win? The original version of this little riddle is called Zeno’s paradox, but I challenge you to use your head before your web browser to find the answer. So much more satisfying!