[ExI] paradox perhaps

[spike at rainier66.com]

While climbing in the Sierras this week a fun thought experiment occurred to
me.  My companions and I were hiking from sunrise until almost sunset,
covered about 15 miles, but never saw another human the whole time.  We went
to the top of Deadwood Peak, where we signed the log book.  I noticed the
date on the previous page was from ten days previous.  OK, here's the
thought experiment, or possible paradox.

 

Suppose you sign the mountaintop log book and note the previous visitor was
10 days previous.  With only that information, one might estimate that
visitors come to the peak about every 10 days or so.  But what if. you
rigged a switch on the box which contains the log book which did nothing
more than set an LCD display to that day's date any time anyone opened the
box?  Then suppose you walk up, notice the display read 10 days ago.  But
you didn't open the box.  Rather you left without signing the book.  Then
what would you estimate the frequency of visit?  Every 20 days?

 

If you started to leave, but then reconsidered, turned back, signed the
book, would your estimate of frequency of visit revert to 10 days?

 

Do explain please.

 

spike

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