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Shortest Long Number (Posted on 2004-04-15) Difficulty: 3 of 5
What is the smallest positive integer that cannot be defined in less than twenty-five syllables?

See The Solution Submitted by Sam    
Rating: 3.0833 (12 votes)

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Solution Waiting For Godel | Comment 36 of 49 |

(With apologies to Samuel Becket, author of "Waiting For Godot").

Sorry I was being egotistical, Sam. Let me summarize my problem with this paradox.

It seems to be based on the following idea: "Since there are a finite number of syllables, there are a finite number of sentences of less than twenty-five syllables. But the number of positive integers is infinite...."

So far, so good.

"...Therefore, there is an infinite number of positive integers that cannot be defined in less than twenty-five syllables...."

Agreed.

"...Let us consider 'the smallest positive integer that cannot be defined in less than twenty-five syllables'...."

Yes ?

"Wait a second !! By defining it as 'the smallest positive integer that cannot be defined in less than twenty-five syllables', I have just defined it with a 24 syllable sentence." 

STOP !! STOP RIGHT THERE !!!!! THAT is where you are going wrong !!!! That is no more an acceptable definition of the integer in question, than "the shortest player in the NBA" is an acceptable definition of Muggsy Bogues. (He is 5'3", by the way). These statements are merely giving the integer (and Muggsy Bogues) an interesting attribute. The opponents of Socrates were always making this mistake. Once, during a philosophical debate, Socrates asked his opponent to define "rhetoric". The guy replied (quoting from memory) "Rhetoric, my dear Socrates, is the noblest and best and most beautiful art known to the Greeks." A bemused Socrates replied "I did not ask you to praise rhetoric, my good man. I asked you to define it."

So unless you explain how "the noblest and best and most beautiful art known to the Greeks" is an acceptable definition of rhetoric, or "the smallest positive integer that cannot be defined in less than twenty-five syllables" is an acceptable definition of any positive integer, I can only assume that your paradox has been vanquished.

P.S. The Electronic Frontier Foundation really is offering $100,000 to the first person or group to discover a ten million digit prime number. If you disagree with me, I invite you to claim that prize by "defining" the sought after prime as "the smallest ten million digit prime number."

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Edited on April 16, 2004, 7:09 am
  Posted by Penny on 2004-04-16 06:09:08

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