Saturday, June 30, 2007

"Obvious to Try" is Oxymoronic and Fatally Flawed

Three hikers are heading back to town along an unfamiliar back country trail when one of them is bit by a snake. The other two fashion a tourniquet and makeshift a stretcher for transporting their mate quickly to town, to a doctor's office about 5 miles away.

Alas they come upon an unmarked fork in the trail. No sign arises from its dirt to explicitly point the way to the correct choice. Just a mail box stands there, in the middle of nowhere.

Amazingly, they hear singing coming up from behind them. An old man is moseying his way towards the lone mailbox, letter in hand and entertaining himself with an old folksong.

"Quickly old man, please tell us which path is the quickest way back to town. Time is of the essence."

"Wish I could help you," sighs the elderly gent, "but it's been a long time since I traveled beyond this mailbox. If I recall correctly --and I'm not sure-- one of these paths leads to nowhere, a dead end if you please. With the other it's about a half hour to town. You know what? The McGuiver sisters know the answer. They are identical twins and one of them is sure to be along any minute now to drop her letters off. Problem is, one of them always lies and the other always tells the truth. And neither is willing but to answer one question a day."

At this juncture the injured hiker raises himself from the stretcher and says, "Let me ask the one question, after all it is my life on the line."

What one question does he ask?

A hat tip to the Fired-Up Genius for resurrecting the issue of "obvious to try".

Why not try just any old path? Flip a coin. There is after all, a 50-50 chance of being right.

But then again, in our example, what is the "cost" of being wrong? It could mean one's life.

Before you poo pooh the issue as being a mere fantasy, consider the real life story of Silicon Valley entrepreneur, James Kim who tragically lost his life in December 2006 because his family had driven up the wrong "via". (Via means "path" in Latin. Ob-Via means to come upon the one path. In that case your next step forward is "Ob-Via-ous".

As for the answer to the twin-sisters riddle, it's obvious. (Obvious in hindsight if someone told you the answer).
One sister is an Inverter of the truth. The other is a double inverter. Hook up the three (3) inverters in series and you get a deterministic logical outcome. Familiar objects operating in predictable ways. In fact, we gave away part of the answer "three" as the very first word in the story. A person of ordinary intelligence would have seen that and would have combined it with the well known logical operative of "NOT".

The injured hiker asks: If I had asked your sister which road is the quickest way back to town, which way would she point, left or right? The lying sister would point to the wrong road because her sister would point to the right choice. The truth telling sister would point to the wrong road because her sister would lie and point to the wrong road. Simple logic ... in hindsight.


Step Back said...

A recent example of a post-KSR obvious to try case:


"Given the small number of common, practical mid-line fold options, it does not take much reason to try one or the other. The never-ending search for aesthetic variation could be reason enough."

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