Hayflick Limit and Societies

Hayflick Limit and Societies .
Andre Willers
23 Feb 2011

Synopsis :
We calculate the Hayflick Limits of societies with elective systems , whether faux or not .

Discussion :
See http://andreswhy.blogspot.com "Hayflick Limit Calculation" Feb 2011

The underlying relationship holds :
1/3 = p*n*(n+1)/2 …(1)
This means that the rulers of a society are granted a leeway of 1/3 for mistakes , but anything over that means a loss of mandate (The Chinese concept of Mandate of Heaven)

The n means the number of turnover in decision makers , where errors creep in .
The p means the chance of an error in appointment of a decision maker at a turnover point .

Faux elections :
Popular with authoritarian regimes . Sadly for them , the system sees a faux election as a real election , and errors made during this counts as real errors .

The executive :
Let the executive ie people whose mistakes count , Cabinet ministers , deputies , etc number m . Then the probability of error can be approximated by p= 1/m at each appointment (ie n)
Let elections happen every R years (typically 5-7)
Then over time T , n can be approximated by n=T/R

Putting this in eq (1) above gives
1/3 = 1/m*T/R*(T/R+1)/2 …(2)
this gives a quadratic equation
T^2 + T*R – 2/3*m*R^2 =0

Which solves as
T = ½ +- (R^2 + 4*2/3*m*R^2)^(1/2) =0
T= ½+- R*(1+8/3*m)^(1/2) … (2)
This expresses the duration of a regime (dynasty , whatever) in terms of the number m of important officials (ministers) appointed every R years .

The table in Appendix A below shows this
Endless fun can be had with this .
Eg Stalin : m=1 and R= 1953-1917 = 36 . This gives an expected regime life of 69 years . Which brings us to 1917+69 = 1986 , fairly close to the collapse of the USSR .Remember , the various effects have to be summed .
Much easier with an AI .
Chinese Dynasties can likewise be estimated . (Easier actually)
I have not tried it on Ancient Egyptian Dynasties . Do it yourself .

Present North-African and Middle-Eastern Civilizations :
Faux elections : set R=5
Inner circle : These goes in sets of three from basic principles .
An inner cabinet of 15 with 5 year elections , gives an expected lifetime of 33 years .
This brings these regimes to the present .
It also means that they cannot maintain any pretence of legitimacy . In Chinese terms , they have lost the Mandate of Heaven.
They have exhausted the reserves any new system is granted by a long-suffering populace . Only genocide can stop this . And that is not so very certain . Mercenaries might be willing , but they know they will have to face the International Court in the Hague some time or other (especially their commanders .)

South Africa .
Zuma has a predeliction of an inner cabinet of three . Himself and two lieutenants .
Cf Shaik's . The present ones are the Gupta brothers .
This gives an m=3 and R= 2 The next election is due in two years . This gives an expected life of 7 years from 2010 from the table . This means he will lose or win the next election with a very slender margin . Unless he does the old invasion of Africa routine , as described previously .
Emperor Zuma !

And so it goes .

Andre

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Appendix A
Table of life-expectancies of Civilizations .

Remember , set R=40 for expected life of Ruler-for-life (Like a Pharaoh ) .At death there is an elective process . They usually start about 20 till 80 . Expand the table where necessary .
Dynasty table
The number of years a regime or dynasty is expected to last with an election every R years and with M important decision makers .
T= ½+- R*(1+8/3*m)^(1/2)
m
R 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 2 3 4 4 4 5 5 5 6 6 6 6 6 7 7 7 7 8 8 8 8 8 8 9 9 9 9 9 9 10
2 4 6 7 7 8 9 9 10 11 11 12 12 12 13 13 14 14 15 15 15 16 16 16 17 17 17 18 18 18 19
3 6 8 10 11 12 13 14 15 16 16 17 18 18 19 20 20 21 22 22 23 23 24 24 25 25 26 26 27 27 28
4 8 11 13 14 16 17 18 19 21 22 23 23 24 25 26 27 28 29 29 30 31 31 32 33 33 34 35 35 36 37
5 10 13 16 18 19 21 23 24 26 27 28 29 30 31 33 34 35 36 36 37 38 39 40 41 42 42 43 44 45 46
6 12 16 19 21 23 25 27 29 31 32 34 35 36 38 39 40 41 43 44 45 46 47 48 49 50 51 52 53 54 55
7 14 18 22 24 27 29 32 34 36 37 39 41 42 44 45 47 48 50 51 52 53 55 56 57 58 59 60 61 62 64
8 16 21 25 28 31 33 36 38 41 43 45 46 48 50 52 53 55 57 58 59 61 62 64 65 66 68 69 70 71 73
9 18 23 28 31 35 38 40 43 46 48 50 52 54 56 58 60 62 64 65 67 68 70 72 73 75 76 77 79 80 82
10 20 26 31 35 38 42 45 48 51 53 56 58 60 62 65 67 69 71 72 74 76 78 79 81 83 84 86 87 89 91
11 22 28 34 38 42 46 49 52 56 58 61 64 66 69 71 73 75 78 80 82 84 85 87 89 91 93 94 96 98 100
12 23 31 37 41 46 50 54 57 61 64 67 69 72 75 77 80 82 85 87 89 91 93 95 97 99 101 103 105 107 109
13 25 33 40 45 50 54 58 62 66 69 72 75 78 81 84 86 89 92 94 96 99 101 103 105 107 110 112 114 116 118
14 27 36 43 48 54 58 63 67 71 74 78 81 84 87 90 93 96 99 101 104 106 109 111 113 116 118 120 122 124 127
15 29 38 46 52 57 62 67 71 76 79 83 87 90 93 97 100 103 106 108 111 114 116 119 121 124 126 129 131 133 136
16 31 41 49 55 61 66 71 76 81 85 89 92 96 100 103 106 109 113 116 118 121 124 127 129 132 135 137 140 142 145
17 33 43 52 59 65 71 76 81 86 90 94 98 102 106 109 113 116 120 123 126 129 132 135 138 140 143 146 148 151 154
18 35 46 55 62 69 75 80 86 91 95 100 104 108 112 116 119 123 127 130 133 136 140 143 146 149 151 154 157 160 163
19 37 48 58 65 72 79 85 90 96 100 105 110 114 118 122 126 130 134 137 141 144 147 151 154 157 160 163 166 169 172
20 39 51 61 69 76 83 89 95 101 106 111 115 120 124 129 133 137 141 144 148 151 155 158 162 165 168 171 174 178 181
21 41 53 64 72 80 87 94 100 106 111 116 121 126 131 135 139 143 148 151 155 159 163 166 170 173 177 180 183 186 190
22 43 56 67 76 84 91 98 104 111 116 122 127 132 137 141 146 150 155 159 163 167 170 174 178 181 185 188 192 195 199
23 45 58 70 79 88 95 102 109 116 121 127 133 138 143 148 152 157 162 166 170 174 178 182 186 190 193 197 201 204 208
24 46 61 73 82 91 99 107 114 121 127 133 138 144 149 154 159 164 169 173 177 182 186 190 194 198 202 206 209 213 217
25 48 63 76 86 95 104 111 119 126 132 138 144 150 155 161 166 171 176 180 185 189 194 198 202 206 210 214 218 222 226
26 50 66 79 89 99 108 116 123 131 137 144 150 156 161 167 172 177 183 187 192 197 201 206 210 214 219 223 227 231 235
27 52 68 82 93 103 112 120 128 136 143 149 156 162 168 173 179 184 190 195 200 204 209 214 218 223 227 231 235 239 244
28 54 71 85 96 107 116 125 133 141 148 155 161 168 174 180 186 191 197 202 207 212 217 222 226 231 235 240 244 248 253
29 56 73 88 100 110 120 129 138 146 153 160 167 174 180 186 192 198 204 209 214 219 225 229 234 239 244 248 253 257 262
30 58 76 91 103 114 124 134 142 151 158 166 173 180 186 193 199 205 211 216 222 227 232 237 242 247 252 257 261 266 271
31 60 79 94 106 118 128 138 147 156 164 171 179 186 192 199 205 212 218 223 229 235 240 245 250 256 260 265 270 275 280
32 62 81 97 110 122 132 142 152 161 169 177 184 192 199 205 212 218 225 231 236 242 248 253 258 264 269 274 279 284 289
33 64 84 100 113 125 137 147 156 166 174 182 190 198 205 212 219 225 232 238 244 250 255 261 267 272 277 282 288 293 298
34 66 86 103 117 129 141 151 161 171 179 188 196 204 211 218 225 232 239 245 251 257 263 269 275 280 286 291 296 301 307
35 68 89 106 120 133 145 156 166 176 185 193 202 210 217 225 232 239 246 252 258 265 271 277 283 288 294 300 305 310 316
36 69 91 109 123 137 149 160 171 181 190 199 207 215 223 231 238 246 253 259 266 272 279 285 291 297 302 308 314 319 325
37 71 94 112 127 141 153 165 175 186 195 204 213 221 230 237 245 252 260 266 273 280 286 293 299 305 311 317 322 328 334
38 73 96 115 130 144 157 169 180 191 200 210 219 227 236 244 252 259 267 274 281 287 294 301 307 313 319 325 331 337 343
39 75 99 118 134 148 161 173 185 196 206 215 225 233 242 250 258 266 274 281 288 295 302 308 315 321 328 334 340 346 352
40 77 101 121 137 152 165 178 190 201 211 221 230 239 248 257 265 273 281 288 295 302 309 316 323 330 336 342 348 355 361