Thursday, November 6, 2008

George Boole Would Freak


I had to take a picture of this sign at a rest area I stopped at along the way during my recent drive to North Carolina.  (Sorry, I can't remember what the offending state was--I passed through Indiana, Ohio, West Virginia, Virginia, Kentucky, and North Carolina, so take your best guess...)

Since I'm careful to obey all traffic laws, I spent the next few miles thinking through the nuances of this sign and why it might have been worded the way it was.  Good thing I'm a digital logic designer...

I reduced the sign to some variables...
P -- overnight parking
C -- camping
...and recalled a few boolean operators...
v -- AND
|  -- 'inclusive' OR
^ -- 'exclusive' OR
~ -- NOT 
So, we can re-write the sign as:
          P | ~C
assuming the OR in the sign is an inclusive OR, meaning that either or both could be true.  So in English, this sign is admonishing us to:
          Park overnight, or
          Don't camp, or
          Park overnight as long as you don't camp.

If it was referring to the exclusive or, it would be
          P ^ ~C                            --  which we can rewrite by definition as
          P v ~(~C) | ~(P) v (~C)    -- and reducing...
          P v C | ~P v ~C               -- and factoring out the negation...
          P v C | ~(P v C)
which in English would be "Either park overnight and camp or don't park overnight if you're not camping."

I guess I should have studied something else in school; I have two engineering degrees and I can't even read a simple traffic sign...

1 comment:

Unknown said...

Hilarious. This kind of reminds me of the time you rode with me to Urbana and constantly calculated the milage and mph to determine our arrival time.