Latkes vs. Hamantaschen by VU7Tgo

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									Latkes vs. Hamantaschen

      Prof. Jason Eisner
Department of Computer Science

  JHU Debate – Dec. 4, 2007
                            Jewish
Simplicity vs. Complexity
                            Jewish
Simplicity vs. Complexity
                                    Jewish
Simplicity vs. Complexity




  Establishing hamantaschic superiority:
    1. Informational complexity
    2. Linguistic complexity
    3. Computational complexity
Informational Complexity


• What is the information content
  of each food?
                    (measured in bytes)
Informational Complexity
• Asymmetries


            heads                   tails




• Alas, orientation is not reliably transmitted
Fine-grained Informational Complexity



                                      (x1,y1)


                                        (x2,y2)


 Strands are unordered:         •   n strands of potato
                                •   * 4 real #s per strand
       24 k 1 
log 2                         •
       n   4kn  n log 2 n
                                    * k bits recovered per real
                              •   = 4kn bits?
Fine-grained Informational Complexity
               (0,0,1,0)


                                                  (0,1,0,0)



                                           (each point’s
                                           coords sum to 1)
                           (1,0,0,0)


                      • n poppy seeds
                      • * 3 real #s per seed
                      • * k bits recovered per real
                                      23 k 
                               log 2    3kn  n log 2 n
                                      n 
                                      
 Fine-grained Informational Complexity
                            (0,0,1,0)


                                                               (0,1,0,0)

    (x1,y1)
                                                        (each point’s
      (x2,y2)                                           coords sum to 1)
                                        (1,0,0,0)


• n potato strands                 • n poppy seeds
• * 4 real #s per strand           • * 3 real #s per seed


                                  
• * k bits recovered per real      • * k bits recovered per real
         24 k 1                                 23 k 
  log 2          
         n   4kn  n log 2 n             log 2    3kn  n log 2 n
                                                   n 
                                                 
 Fine-grained Informational Complexity
                            (0,0,1,0)


                                                               (0,1,0,0)

    (x1,y1)
                                                        (each point’s
      (x2,y2)                                           coords sum to 1)
                                        (1,0,0,0)


• n potato strands                 • n poppy seeds
• * 4 real #s per strand           • * 3 real #s per seed


                                  
• * k bits recovered per real      • * k bits recovered per real
         24 k 1                                 23 k 
  log 2          
         n   4kn  n log 2 n             log 2    3kn  n log 2 n
                                                   n 
                                                 
Linguistic Complexity
• Gemetria
• The Bible Code


                                      = 10

                                      = 22

                   + 50-point length bonus!
Point of Order …
             Chanukah      This debate
2007-2008




                   Purim
Purim, a.k.a. the Feast of Lots
Purim, a.k.a. the Feast of Lots
Computational Complexity


                               
     NC                        NP
 (“Nosh Chanukah”)          (“Nosh Purim”)

 decidable in               decidable in
 polylogarithmic time       polynomial time with a
 with a polynomial          nondeterministic processor
 number of processors
Computational Complexity


                            
      NC                    NP
  (“Nosh Chanukah”)       (“Nosh Purim”)

• NP is more computationally complex!
• But don’t want to prove that   is NP-hard
Computational Complexity
• So let’s do a direct reduction:




• This is a poppynomial reduction
• Implies existence of a gastric reduction
• Therefore, if you can digest a hamantasch,
  you can digest a latke
• Therefore, the hamantasch is the more complex
  carbohydrate
Conclusions
•   Judaism loves complexity
•   Hamantaschen are more complex
    1. Informational complexity
    2. Linguistic complexity
    3. Computational complexity
•   And they’ll enhance your math!

								
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