As a young man, Benjamin Franklin drew up a “plan for attaining moral perfection” based on a list of 13 virtues. Half a century later he credited the plan for much of his success in life. In this episode of the Futility Closet podcast we’ll explore Franklin’s self-improvement plan and find out which vices gave him the most trouble.
We’ll also learn how activist Natan Sharansky used chess to stay sane in Soviet prisons and puzzle over why the Pentagon has so many bathrooms.
Three children return home after playing outside, and their father tells them that at least one of them has a muddy face. He repeats the phrase “Step forward if you have a muddy face” until all and only the children with muddy faces have stepped forward.
If there’s only one child with a muddy face, then she’ll step forward immediately — she can see that no other children have muddy faces, so her father must be talking about her. Each of the other children will see her muddy face and stand fast, since they have no way of knowing whether their own faces are muddy.
If there are two children with muddy faces, then no one will step forward after the first request, since each might think the father is addressing the other one. But when no one steps forward after the first request, each will realize that there must be two children with muddy faces, and that she herself must be one of them. So both will step forward after the second request, and the rest will stand fast.
A pattern emerges: If there are n children with muddy faces, then n will step forward after the nth request.
But now imagine a scenario in which more than one of the children has a muddy face, but the father does not tell them that at least one of them has a muddy face. Now no one steps forward after the first request, for the same reason as before. But no one steps forward at the second request either, because the fact that no one stepped forward after the first request no longer means that there is more than one child with a muddy face.
This is perplexing. In the second scenario all the children can see that at least one of them has a muddy face, so it seems needless for the father to tell them so. But without his statement the argument never gets going; despite his repeated requests, no child will ever step forward. What’s missing?
(From Michael Clark, Paradoxes From A to Z, 2007.)
Rotating the figure 60° counterclockwise around B carries A to R and P to C. And rotating it 60° clockwise around A carries B to R and Q to C. So AP = BQ = CR.
From Edward Barbeau, Murray Klamkin, and William Moser, Five Hundred Mathematical Challenges, 1995.
ArnoldC, a language devised by Finnish computer programmer Lauri Hartikka, assigns programming functions to catch phrases from Arnold Schwarzenegger movies. Some keywords:
False: I LIED
True: NO PROBLEMO
If: BECAUSE I’M GOING TO SAY PLEASE
Else: BULLSHIT
EndIf: YOU HAVE NO RESPECT FOR LOGIC
While: STICK AROUND
EndWhile: CHILL
MultiplicationOperator: YOU’RE FIRED
DivisionOperator: HE HAD TO SPLIT
EqualTo: YOU ARE NOT YOU YOU ARE ME
GreaterThan: LET OFF SOME STEAM BENNET
Or: CONSIDER THAT A DIVORCE
And: KNOCK KNOCK
DeclareMethod: LISTEN TO ME VERY CAREFULLY
MethodArguments: I NEED YOUR CLOTHES YOUR BOOTS AND YOUR MOTORCYCLE
Return: I’LL BE BACK
EndMethodDeclaration: HASTA LA VISTA, BABY
AssignVariableFromMethodCall: GET YOUR ASS TO MARS
ReadInteger: I WANT TO ASK YOU A BUNCH OF QUESTIONS AND I WANT TO HAVE THEM ANSWERED IMMEDIATELY
AssignVariable: GET TO THE CHOPPER
SetValue: HERE IS MY INVITATION
EndAssignVariable: ENOUGH TALK
ParseError: WHAT THE FUCK DID I DO WRONG
This program prints the string “hello world”:
IT'S SHOWTIME
TALK TO THE HAND "hello world"
YOU HAVE BEEN TERMINATED
It was well remarked by an intelligent old farmer, ‘I would rather be taxed for the education of the boy, than the ignorance of the man. For one or the other I am compelled to pay.’