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class16-Informatio - Information and Randomness Bits How...

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Information and Randomness
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Bits How many bits do I need to store one boolean value? How many bits do I need to store the outcome of one home pregnancy test? A home pregnancy test reveals 1 bit of information. It may be the most important life-changing bit of information, but it's still just 1 bit.
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Which has more information? 023514 795 084664452746 (A) (B) (C)
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Information More Digits = More Information Right?
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Memorizing Volunteer to memorize 10 digits 2737761413 Volunteer to memorize 100 digits 4444444444444444444444444444444444444 4444444444444444444444444444444444444 44444444444444444444444444
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Memorizing 10-digit volunteer: What was the 8th digit? 100-digit volunteer: What was the 78th digit? Which is easier to memorize? Which contains more information?
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Memorizing Another volunteer to memorize 100 digits 4859937766824805299839179081504751450913 5243678006736228445539731692238204213061 74607612086978543115 Is that harder to memorize than: 4444444444444444444444444444444444444444 4444444444444444444444444444444444444444 44444444444444444444 Why? Which contains more information?
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Information: a definition The amount of information in a sequence of digits is equal to the length of the shortest program that prints those digits.
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Write a program to print 44444444444444444444444444444444 44444444444444444444444444444444 44444444444444444444444444444444 4444 repeat 100: print "4"
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Write a program to print 4859937766824805299839179081504751 4509135243678006736228445539731692 23820421306174607612086978543115 print "4859937766824805299839179081504 75145091352436780067362284455397 31692238204213061746076120869785 43115"
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Memorizing Programs print "4859937766824805299839179081504 75145091352436780067362284455397 31692238204213061746076120869785 43115" is harder to memorize than repeat 100: print "4"
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Therefore 4859937766824805299839179081504751 4509135243678006736228445539731692 23820421306174607612086978543115 contains more information than 4444444444444444444444444444444444 4444444444444444444444444444444444 44444444444444444444444444444444
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Information More Random = More Information
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Pi and Information 3.14159265358979323846264338327... How much information is stored in the digits of pi?
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Calculating Pi pi = 4/1 - 4/3 + 4/5 - 4/7 + ...
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a program that prints pi sign 1 n 1 pi 0 repeat: pi pi + sign × 4 / n print pi sign 0 - sign n n + 2
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Information in Pi The digits of pi are output by a short program.
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