Bob and the Septagon
In his seldom-used blog, Brian Lauber does some musing over mathematics and philosophy. First, he admits that there are certain things one cannot do in Euclidean geometry using a straight edge and a compass. For example, you cannot construct a seven-sided polygon and you cannot trisect angles.
Then Lauber poses an interesting twist: "Suppose there is an omnipotent being named Bob with the ability to do anything. You tell this being to construct a 7-sided figure using only the rules of Euclidean construction. After a cloud of magic, Bob hands you the figure and poofs off into a wisp of smoke."
Wait a sec? Did Bob, being omnipotent, overcome the impossible? Did Bob resort to cheating? Or, did Bob use an infinite number of steps (another no-no)? This last case bothered Lauber...
He posed a new "proven-impossible" problem to omnipotent Bob: You have a rod with 5 flexible hinges:
Now bend it at the hinges to form a tetrahedron.
Again, Bob accomplishes the task and vanishes. But, since this task has a finite number of moves, you have eliminated Bob's use of an infinite number of moves. So....
No conlcusion here...just food for Euclidean thinkers who believe in omnipotent Bobs!