Sunday, February 17, 2008

Entropy

Entropy is a measure of how free a system of movement is. If there is a dance in which the dancer may occupy only one state then said dance has zero entropy, there are no surprises. As the number of possible states increases so does the entropy, the number of options increases. The mathematical definition is given below.
H is the entropy
i is the index of states
n is the number of states
p is the probability of inhabiting each state

max v2;
#N vpatcher 468 84 675 539;
#P origin -29 -43;
#P window setfont "Sans Serif" 9.;
#P message 80 51 23 196617 1 1;
#P message 41 99 31 196617 10 1;
#P message 47 76 23 196617 3 1;
#P message 46 52 23 196617 2 1;
#P flonum 68 400 96 9 0 0 0 3 0 0 0 221 221 221 222 222 222 0 0 0;
#P message 83 121 52 196617 1 1 1 1 1;
#P message 82 99 43 196617 1 1 1 1;
#P message 79 30 17 196617 1;
#P message 38 121 34 196617 1 2 7;
#P message 81 76 34 196617 1 1 1;
#P newex 68 368 27 196617 f;
#P newex 68 345 27 196617 + 0.;
#P newex 68 291 47 196617 zl iter 1;
#P newex 68 312 94 196617 expr -$f1*ln($f1);
#P hidden newex 0 206 48 196617 loadbang;
#P hidden message 0 226 70 196617 scalarmode 1;
#P newex 68 271 84 196617 vexpr $f1 / $f2;
#P newex 111 229 27 196617 f;
#P newex 111 206 27 196617 + 0.;
#P newex 68 151 70 196617 t l l 0.;
#P newex 77 179 47 196617 zl iter 1;
#P hidden connect 6 0 5 0;
#P fasten 12 0 1 0 43 140 73 140;
#P fasten 19 0 1 0 46 118 73 118;
#P fasten 18 0 1 0 52 95 73 95;
#P fasten 17 0 1 0 51 73 73 73;
#P fasten 15 0 1 0 88 140 73 140;
#P fasten 14 0 1 0 87 118 73 118;
#P fasten 11 0 1 0 86 95 73 95;
#P fasten 20 0 1 0 85 73 73 73;
#P fasten 13 0 1 0 84 49 73 49;
#P connect 1 0 4 0;
#P hidden fasten 5 0 4 0 5 261 73 261;
#P connect 4 0 8 0;
#P connect 8 0 7 0;
#P connect 7 0 9 0;
#P connect 9 0 10 0;
#P connect 10 0 16 0;
#P fasten 1 1 0 0 103 174 82 174;
#P fasten 10 0 9 1 73 393 101 393 101 337 90 337;
#P fasten 1 2 9 1 133 176 167 176 167 337 90 337;
#P fasten 0 0 2 0 82 201 116 201;
#P connect 2 0 3 0;
#P fasten 3 0 2 1 116 254 144 254 144 198 133 198;
#P fasten 1 2 2 1 133 202 133 202;
#P fasten 3 0 4 1 116 266 147 266;
#P pop;

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