As an example_ suppose you have a big bag of coins

Document Sample
As an example_ suppose you have a big bag of coins Powered By Docstoc
					               Suppose you have a big
                    bag of coins



 37 pennies
 25 nickels
 59 dimes              You will make a series
 84 quarters
Value=$65.15
                       of transactions using the
Number = 205           coins in your bag. Then
                       you will value the final
                       contents of your bag.
                Exchange coins
               according to value



 37 pennies
                               ??? pennies
 25 nickles    There are a     ??? nickles
 59 dimes      large number    ??? dimes
 84 quarters   of possible     ??? quarters
Value=$65.15
               transactions:   Value=$65.15
Number = 205                   Number = ???
               Suppose you make this
                series of transactions

1.   Replace 1 nickel by 5 pennies
2.   Replace 1 quarter by 3 nickels and 1 dime
3.   Replace 1 dime by 1 nickel and 5 pennies
4.   Replace 1 quarter by 25 pennies
5.   Replace 1 quarter by 5 nickels
6.   Replace 1 dime and 15 pennies by 1
     quarter
 Knowing these ‘value rules,’ can
we predict the final contents of the
               bag?


 37 pennies    As long as       ??? pennies
 25 nickels    everyone         ??? nickels
 59 dimes      played fairly,   ??? dimes
 84 quarters   the value of     ??? quarters
Value=$65.15   the bag          Value=$65.15
Number = 205                    Number = ???
               should not
               change.
 Knowing these ‘value rules,’ can
we predict the final contents of the
               bag?


 37 pennies    As long as       57 pennies
 25 nickels    everyone         33 nickels
 59 dimes      played fairly,   58 dimes
 84 quarters   the value of     82 quarters
Value=$65.15   the bag          Value=$65.15
Number = 205                    Number = ???
               should not
               change.
               Suppose we exchange
                 coins one-for-one,
                regardless of value


 37 pennies                   ??? pennies
 25 nickels    Exchange       ??? nickles
 59 dimes      one coin for   ??? dimes
 84 quarters   one coin,      ??? quarters
Value=$65.15   regardless     Value = ???
Number = 205                  Number = 205
               of value
        Make this series of
          transactions
1.   Replace 1 nickel by 1 penny
2.   Replace 1 quarter by 1 nickel
3.   Replace 1 dime by 1 penny
4.   Replace 1 quarter by 1 penny
5.   Replace 1 quarter by 1 nickel
6.   Replace 1 quarter by 1 dime
  Knowing the count of coins, can
   we predict the contents of the
                bag?


 37 pennies                   ??? pennies
 25 nickels    Now it is      ??? nickels
 59 dimes      the number     ??? dimes
 84 quarters   of coins in    ??? quarters
Value=$65.15   the bag that   Value = ???
Number= 205                   Number= 205
               has not
               changed.
   Knowing the count of coins, can
    we predict the contents of the
                 bag?


 37 pennies                   40 pennies
 25 nickels    Now it is      26 nickels
 59 dimes      the number     59 dimes
 84 quarters   of coins in    80 quarters
Value=$65.15   the bag that   Value = ???
Number= 205                   Number= 205
               has not
               changed.
Suppose we do our coin transactions in
           different places
(but we always follow the same rules).
 Do we expect the same results each
                 time?

                  In other words: Are the
              transaction rules invariant with
               respect to position in space?
               Our coin experiment is self-
               contained, so it should not
                    vary with position.
If we do our coin transactions at
different times, do we expect the
           same results?



           Are the transaction rules
           invariant with respect to
                     time?
 If we do our coin transactions in
different orders, do we expect the
           same results?



           Do the transactions rules
           produce constant results
             with respect to order
               (who goes first)?
                                       Back

				
DOCUMENT INFO
Shared By:
Categories:
Stats:
views:3
posted:7/3/2011
language:English
pages:12