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49. Bring Something Beautiful

+/(1+⍳∞)*-s ←→ ×/÷1-(⍭⍳∞)*-s

The following e-mail exchange took place on 2010-06-24 during a discussion on numeric representation.

Morten Kromberg: And… I shall fight against adding any form of NaN/Infinity — to the death! They will horribly complicate our implementation and don’t help users do anything useful.

Roger Hui: In the year 2033 Earth was discovered by Survey Fleet MCXII of the Galactic Empire. The Emperor ordered Earth to send a representative to the court, with strict instructions to “bring something beautiful”.

Emperor
  What beautiful things does Earth have?
 
Earth Representative
  Your excellency, our mathematician Euler proved in our year 1737 that +/(1+⍳∞)*-s ←→ ×/÷1-(⍭⍳∞)*-s
 
Emperor
  What is the ⍭ symbol?
 
Earth Rep.
  ⍭i is the i-th prime.
 
Emperor
  And what is ∞? Does it do anything useful?
 
Earth Rep.
  It denotes infinity, your excellency.
 
Emperor
  (ponders equation for a minute or two) Respect!
 
Emperor
  Neat notation you have there. Tell me more.
 
Earth Rep.
  Your excellency, it’s called APL. It was invented by the Canadian Kenneth E. Iverson …
 

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