World Views

Please try to avoid religious or political subjects in this forum.
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

:scratch: aka "The Collatz Conjecture Conjecture"

Re: https://www.youtube.com/watch?v=094y1Z2wpJg
"The Simplest Math Problem No One Can Solve - Collatz Conjecture"
... but Pattern 616 suggests otherwise! ;)

Re: https://en.wikipedia.org/wiki/Collatz_conjecture
"Jeffrey Lagarias stated in 2010 that the Collatz conjecture 'is an extraordinarily difficult problem,
completely out of reach of present day mathematics' " :duh

Re: https://www.quora.com/Why-is-the-Collat ... not-proved
"The problem with the Collatz conjecture that makes it so intimately difficult
is the unpredictable nature of the cycles." :roll:


:idea: Now consider Pattern 616 resulting from 3X+1 or /2
applied to these descending numbers:

Code: Select all

16  =  8    
15  =  46  
14  =  7   1    
13  =  40  6
12  =  6   1    
11  =  34  6 
10  =  5   1
 9  =  28  6
 8  =  4   1
 7  =  22  6
 6  =  3   1
 5  =  16  6
 4  =  2   1
 3  =  10  6
 2  =  1   1
 1  =  4   6
:hithere This pattern hints that all numbers from infinity -1 funnel to the 8,4,2,1 loop.
Also note that the first mate to a number (to the right of '=') identifies a string ...
suggesting that every number begins a string and that strings contain strings :!:

:farao: And Pattern 616 hints that, for many problems,
we should first come out of the rabbit hole. ;)

Q: How does UB's 606 relate to 616?
A: 606 is one of the decimal planets: 8)
"The number ten — the decimal system — is inherent
in the physical universe but not in the spiritual." (36:2.11)

:o Analysis: "3X+1" defines both infinity
and inevitable finality via linked "/2",
like the "Pi Corral" in another topic ...
making a solution a "God Equation"?

:scratch: Pop Quiz:
If infinity -1 is odd, what is 3X+1 :?:


:idea: Collatz Conjecture Numbers As Strings
(3X+1 or /2 applied to beginning number)

Lower strings incorporate into higher strings;
higher strings incorporate into lower strings.
Every number in a string is the beginning
of a string that terminates with 4,2,1.

:scratch: Evidence of a "God Equation" (infinity+finality)
lurking in the wild 'n crazy CC numbas :?: :!:

Code: Select all

308  >  154  =  77  232  116  58  29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
306  >  153  =  460  230  115  346  173  520  260  130  65  196  98  49  148  74  37  112  56  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1

296  >  148  =  74  37  112  56  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
294  >  147  =  442  221  664  332  166  83  250  125  376  188  94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1

284  >  142  =  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1
282  >  141  =  424  212  106  53  160  80  40  20  10  5  16  8  4  2  1  

272  >  136  =  68  34  17  52  26  13  40  20  10  5  16  8  4  2  1
270  >  135  =  406  203  610  305  916  458  229  688  344  172  86  43  130  65  196  98  49  148  74  37  112  56  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1

248  >  124  =  62  31  94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1
246  >  123  =  370  185  556  278  139  418  209  628  314  157  472  236  118  59  178  89  268  134  67  202  101  304  152  76  38  19  58  29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1

244  >  122  =  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1
242  >  121  =  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1

236  >  118  =  59  178  89  268  134  67  202  101  304  152  76  38  19  58  29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
234  >  117  =  352  176  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1

224  >  112  =  56  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
222  >  111  =  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1

220  >  110  =  55  166  83  250  125  376  188  94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1
218  >  109  =  328  164  82  41  124  62  31  94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1

216  >  108  =  54  27  82  41  124  62  31  94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1
214  >  107  =  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1

212  >  106  =  53  160  80  40  20  10  5  16  8  4  2  1
210  >  105  =  316  158  79  238  119  358  179  538  269  808  404  202  101  304  152  76  38  19  58  29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1

208  >  104  =  52  26  13  40  20  10  5  16  8  4  2  1
206  >  103  =  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1  

204  >  102  =  51  154  77  232  116  58  29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1  
202  >  101  =  304  152  76  38  19  58  29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1

200  >  100  =  50  25  76  38  19  58  29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
198  >   99  =  298  149  448  224  112  56  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1

196  >  98  =  49  148  74  37  112  56  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
194  >  97  =  292  146  73  220  110  55  166  83  250  125  376  188  94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1

192  >  96  =  48  24  12  6  3  10  5  16  8  4  2  1
190  >  95  =  286  143  430  215  646  323  970  485  1456  728  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1    

188  >  94  =  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1
186  >  93  =  280  140  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1

158  >  74  =  37  112  56  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
156  >  73  =  220  110  55  166  83  250  125  376  188  94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1    

144  >  72  =  36  18  9  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
142  >  71  =  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238   1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1

100  >  50  =  25  76  38  19  58  29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
 98  >  49  =  148  74  37  112  56  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
 
 96  >  48  =  24  12  6  3  10  5  16  8  4  2  1  
 94  >  47  =  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1

 92  >  46  =  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1
 90  >  45  =  136  68  34  17  52  26  13  40  20  10  5  16  8  4  2  1

 88  >  44  =  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
 86  >  43  =  130  65  196  98  49  148  74  37  112  56  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1           

 84  >  42  =  21  64  32  16  8  4  2  1  
 82  >  41  =  124  62  31  94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1

 80  >  40  =   20  10  5  16  8  4  2  1  
 78  >  39  =  118  59  178  89  268  134  67  202  101  304  152  76  38  19  58  29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1

 76  >  38  =   19  58  29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
 74  >  37  =  112  56  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1  

 72  >  36  =   18  9  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1  
 70  >  35  =  106  53  160  80  40  20  10  5  16  8  4  2  1  

 68  >  34  =   17  52  26  13  40  20  10  5  16  8  4  2  1
 66  >  33  =  100  50  25  76  38  19  58  29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1  

 64  >  32  =   16  8  4  2  1  
 62  >  31  =   94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1

 60  >  30  =   15  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1
 58  >  29  =   88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1

 56  >  28  =   14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
 54  >  27  =   82  41  124  62  31  94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1

 52  >  26  =  13    40  20  10  5  16  8  4  2  1  
 50  >  25  =  76    38  19  58  29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1

 48  >  24  =  12     6  3  10  5  16  8  4  2  1
 46  >  23  =  70    35  106  53  160  80  40  20  10  5  16  8  4  2  1

 44  >  22  =  11    34  17  52  26  13  40  20  10  5  16  8  4  2  1
 42  >  21  =  64    32  16  8  4  2  1  

 40  >  20  =  10     5  16  8  4  2  1  
 38  >  19  =  58    29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1

 36  >  18  =   9    28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1  
 34  >  17  =  52    26  13  40  20  10  5  16  8  4  2  1

 32  >  16  =   8     4  2  1  
 30  >  15  =  46    23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1

 28  >  14  =   7    22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
 26  >  13  =  40    20  10  5  16  8  4  2  1  

 24  >  12  =   6     3  10  5  16  8  4  2  1
 22  >  11  =  34    17  52  26  13  40  20  10  5  16  8  4  2  1

 20  >  10  =   5    16  8  4  2  1  
 18  >   9  =  28    14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1

 16   >  8  =   4     2  1
 14   >  7  =  22    11  34  17  52  26  13  40  20  10  5  16  8  4  2  1  

 12   >  6  =   3    10  5  16  8  4  2  1  
 10   >  5  =  16     8  4  2  1  

  8   >  4  =   2     1  
  6   >  3  =  10     5  16  8  4  2  1  

  4   >  2  =   1     4  2  1  
  2   >  1  =   4     2  1

:scratch: A curious pattern ...
Add 1 to every odd number; divide every even by 2.
(hints that all Collatz calculations resolve to 4,2,1 ;)

194 97 98 49 50 25 26 13 14 7 8 4 2 1
323 324 162 81 82 41 42 21 22 11 12 6 3 4 2 1

Collatz sequence for numbers 194, 323 ...

194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1

323
970 485 1456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1


:hithere Note the tight linkage of even and odd (194 + 98 = 292),
shouting every number in Collatz stairway resolves to 4,2,1: ;)

200 > 100 = 50
198 > 99 = 298

196 > 98 = 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
194 > 97 = 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1

192 > 96 = 48
190 > 95 = 286


Apparently, the seducing influence of Morbus Collatzmetricus: ;)

:hithere More Pattern 616 linkage ('>' points to string's primary number;
note that every number in every string is in the stairway: 20, 22) 8)

(46 x 2 = 22 + 70), (42 + 22 = 64), (70 - 64 = 6), (12 - 11 = 1)

48 > 24 = 12 6 3 10 5 16 8 4 2 1
46 > 23 = 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1
44 > 22 = 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
42 > 21 = 64 32 16 8 4 2 1
40 > 20 = 10 5 16 8 4 2 1
38 > 19 = 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

(6 x 2 = 2 + 10), (2 x 2 = 4), (10 - 4 = 6), (2 - 1 = 1)

8 > 4 = 2 1
6 > 3 = 10 5 16 8 4 2 1
4 > 2 = 1 4 2 1
2 > 1 = 4 2 1

:idea: About this Collatzable Linkage ...

A fortuitous random selection of groups to contrast (24 - 21 vs 4 -1)
which highlights the +20 influence on '3X+1' and 'X/2' calculations
(further proving that all numbers resolve to 4,2,1). ;)


:bana: Collatz Conjecture with application to X/Y axis:
These charts suggest "3X+1 or /2" of the Collatz Conjecture
effectively programs the consistent 4,2,1 ending loop :!:

Code: Select all

144   72   36   18    9   28   14    7   22   11   34   17   52   26   13   40   20   10    5  16   8   4   2   1
 72   36   18    9   28   14    7   22   11   34   17   52   26   13   40   20   10    5   16   8   4   2   1
 36   18    9   28   14    7   22   11   34   17   52   26   13   40   20   10    5   16    8   4   2   1  
 18    9   28   14    7   22   11   34   17   52   26   13   40   20   10    5   16    8    4   2   1    
  9   28   14    7   22   11   34   17   52   26   13   40   20   10    5   16    8    4    2   1  
 28   14    7   22   11   34   17   52   26   13   40   20   10    5   16    8    4    2    1
 14    7   22   11   34   17   52   26   13   40   20   10    5   16    8    4    2    1  
  7   22   11   34   17   52   26   13   40   20   10    5   16    8    4    2    1
 22   11   34   17   52   26   13   40   20   10    5   16    8    4    2    1
 11   34   17   52   26   13   40   20   10    5   16    8    4    2    1
 34   17   52   26   13   40   20   10    5   16    8    4    2    1
 17   52   26   13   40   20   10    5   16    8    4    2    1
 52   26   13   40   20   10    5   16    8    4    2    1
 26   13   40   20   10    5   16    8    4    2    1
 13   40   20   10    5   16    8    4    2    1
 40   20   10    5   16    8    4    2    1
 20   10    5   16    8    4    2    1
 10    5   16    8    4    2    1
  5   16    8    4    2    1
 16    8    4    2    1
  8    4    2    1
  4    2    1
  2    1
  1

:bana: 4,2,1 consistency by powers of 2

Code: Select all

164  =  82  41  124  62  31  94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1
82  =  41  124  62  31  94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1
41  =  124  62  31  94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1

44  =  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
22  =  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
11  =  34  17  52  26  13  40  20  10  5  16  8  4  2  1

40  =  20  10  5  16  8  4  2  1
20  =  10  5  16  8  4  2  1
10  =  5  16  8  4  2  1

36  =  18  9  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1  
18  =  9  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1  
 9  =  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1  

32  =  16  8  4  2  1  
16  =  8  4  2  1  
 8  =  4  2  1

28  =  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
14  =  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1
 7  =  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1  

30  =  15  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1
15  =  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1
10  =  5  16  8  4  2  1  
 5  =  16  8  4  2  1 

32  =  16  8  4  2  1  
16  =  8  4  2  1  
 8  =  4  2  1
 4  =  2  1

48  =  24  12  6  3  10  5  16  8  4  2  1
24  =  12  6  3  10  5  16  8  4  2  1
12  =  6  3  10  5  16  8  4  2  1
 6  =  3  10  5  16  8  4  2  1  
 3  =  10  5  16  8  4  2  1  

32  =  16  8  4  2  1  
16  =  8  4  2  1  
 8  =  4  2  1
 4  =  2  1  
 2  =  1  4  2  1 

32  =  16  8  4  2  1  
16  =  8  4  2  1  
 8  =  4  2  1
 4  =  2  1  
 2  =  1  4  2  1
 1  =  4  2  1

:roll Apparently, the Collatz Matrix, a triangle! 8)

Re: https://dictionary.cambridge.org/us/dic ... ish/matrix
"group of numbers or other symbols arranged in a rectangle used together
as a single unit to solve particular mathematical problems"

Code: Select all

 12    6    3   10    5   16    8    4    2    1
  6    3   10    5   16    8    4    2    1    1     
  3   10    5   16    8    4    2    1    3
 10    5   16    8    4    2    1    7
  5   16    8    4    2    1   15
 16    8    4    2    1   31
  8    4    2    1   36
  4    2    1   46
  2    1   49
  1   55
 67

:hithere This pattern suggests ALL numbers resolve with 4,2,1
regardless of the number of calculations required! ;)

30 days hath September, April, June, and November; All the rest hath 31,
'cepting February alone (hath 28 or 29), thence all quiesce with 4,2,1.

Code: Select all

 31  94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1  -  31

                   30  15  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1   -  30
                     29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1   -  29
                      28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1   -  28

 27  82  41  124  62  31  94  47  142  71  214  107  322  161  484  242  121  364  182  91  274  137  412  206  103  310  155  466  233  700  350  175  526  263  790  395  1186  593  1780  890  445  1336  668  334  167  502  251  754  377  1132  566  283  850  425  1276  638  319  958  479  1438  719  2158  1079  3238  1619  4858  2429  7288  3644  1822  911  2734  1367  4102  2051  6154  3077  9232  4616  2308  1154  577  1732  866  433  1300  650  325  976  488  244  122  61  184  92  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1  -  27

                                                     26  13  40  20  10  5  16  8  4  2  1   -  26  
 25  76  38  19  58  29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1   -  25
                                                     24  12   6   3  10  5  16  8  4  2  1   -  24 
                               23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1   -  23
                                 22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1   -  22
                                                                 21  64 32  16  8  4  2  1   -  21
                                                                 20  10  5  16  8  4  2  1   -  20
             19  58  29  88  44  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1   -  19
               18  9  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1   -  18
                                             17  52  26  13  40  20  10  5  16  8  4  2  1   -  17
                                                                            16  8  4  2  1   -  16
                       15  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1   -  15
                          14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1   -  14
                                                         13  40  20  10  5  16  8  4  2  1   -  13
                                                           12  6  3  10  5  16  8  4  2  1   -  12
                                     11  34  17  52  26  13  40  20  10  5  16  8  4  2  1   -  11
                                                                     10  5  16  8  4  2  1   -  10
                   9  28  14  7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1   -   9
                                                                                8  4  2  1   -   8
                              7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1   -   7
                                                               6  3  10  5  16  8  4  2  1   -   6
                                                                         5  16  8  4  2  1   -   5
                                                                                   4  2  1   -   4
                                                                  3  10  5  16  8  4  2  1   -   3
                                                                                      2  1   -   2
                                                                                         1   -   1                                                                                                                                                                                                                        

:hithere These patterns suggest 4,2,1 proof of any odd number
is proof for all odd numbers; 4,2,1 proof of any even number
is proof for all even numbers. HCIT :!:

26 13 40 20 10 5 16 8 4 2 1
24 12 6 3 10 5 16 8 4 2 1
22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
20 10 5 16 8 4 2 1
18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
16 8 4 2 1
14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
12 6 3 10 5 16 8 4 2 1
10 5 16 8 4 2 1
8 4 2 1
6 3 10 5 16 8 4 2 1
4 2 1
2 1 4 2 1

25 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1
21 64 32 16 8 4 2 1
19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
17 52 26 13 40 20 10 5 16 8 4 2 1
15 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1
13 40 20 10 5 16 8 4 2 1
11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
5 16 8 4 2 1
3 10 5 16 8 4 2 1
1 4 2 1


48 8 12 6 3 10 5 16 8 4 2 1
24 12 6 3 10 5 16 8 4 2 1
12 6 3 10 5 16 8 4 2 1
6 3 10 5 16 8 4 2 1


88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

72 36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
36 18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
18 9 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
9 28 14 7 22 11 34 17 6 3 10 5 16 8 4 2 1

56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

40 20 10 5 16 8 4 2 1
20 10 5 16 8 4 2 1
10 5 16 8 4 2 1
5 16 8 4 2 1

24 12 6 3 10 5 16 8 4 2 1
12 6 3 10 5 16 8 4 2 1
6 3 10 5 16 8 4 2 1
3 10 5 16 8 4 2 1

8 4 2 1 4 2 1
4 2 1 4 2 1
2 1 4 2 1
1 4 2 1


:idea: Every whole number is in Pattern 616
and always descends to 4,2,1 ... apparently. ;)
Every number in every string is in Pattern 616
and every number in the Pattern 616 stairway
always descends to 4,2,1 ... apparently. 8)

(2992 - 2986 = 6, 498 - 497 = 1, 2986 - 2980 = 6)
(1498 -1492 = 6, 249 - 248 = 1, 1492 - 1486 = 6)
(16 - 10 = 6, 2 - 1 = 1, 10 - 4 = 6)

997 2992 1496 .. 4 2 1
996 498 249 .. 4 2 1
995 2986 1493 .. 4 2 1
994 497 1492 .. 4 2 1
993 2980 1490 .. 4 2 1

499 1498 749 .. 4 2 1
498 249 748 .. 4 2 1
497 1492 746 .. 4 2 1
496 248 124 .. 4 2 1
495 1486 743 .. 4 2 1

5 16 8 4 2 1
4 2 1
3 10 5 16 8 4 2 1
2 1 4 2 1
1 4 2 1


:bike: The light at the end of the funnel :?:

Re: https://www.quantamagazine.org/why-math ... -20200922/

"The Simple Math Problem We Still Can’t Solve: Collatz Conjecture"
"if you start with any positive integer, you’ll always end up in this 4,2,1 loop."

:idea: Consider strings created by '6' and '1' in Pattern 616:
(first mates of the sequential odd numbers differ by 6,
first mates of the sequential even numbers differ by 1)

Code: Select all

6  =  3  10  5  16  8  4  2  1
1  =  4  2  1
Both '6' and '1' funnel into the 4,2,1 loop, suggesting all sequential numbers
maintain the 616 pattern (differences) and are vulnerable to the 6,1 funnel
leading into the 4,2,1 trap. 8)


:bana: How to know if number > 1 is Pattern 616
If number odd: ((3X+1)-4)/6 = no remainder
If number even: add 1, then ((3X+1)-4)/6 = no remainder

Example:
157 = 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
156 = 78 39 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
155 = 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1
154 = 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

(((157 x 3) + 1) - 4) / 6 = 78
78 x 2 = 156 - 1 = 155
(((155 x 3) + 1) - 4) / 6 = 77
77 x 2 = 154 - 1 = 153

:idea: Apparently, every number in every string belongs to Pattern 616,
the defining pattern of the "unpredictable" Collatz Conjecture. :roll:
First number of every string downsteps predictably to next string
with strings 4,2,1 always the final strings. 8)

:bana: How to verify that string is Pattern 616

Proceed backward from ending number 1.
If previous number even, multiply current number by 2.
If previous number odd, subtract 1 from current number, divide by 3.

Examples: (Go figure!) ;)
6 = 3 10 5 16 8 4 2 1

:bana: How to prove these cycles are "unpredictable"?
"Completely out of reach of present day mathematics." :roll:

Collatz Conjecture, by definition (3X+1 or /2, depending on odd/even)
is "programmed predictability", confirmed by reverse calculations
(string cannot be confirmed if calculations were "unpredictable"). ;)

:idea: When this "programmed predictability" causes the ending loop
is unknown (unpredictable) without this program execution,
but hints all Collatz calculations create a string that funnels
into the ending loop (as suggested by Pattern 616). 8)

:shock: Since the downstep string (from infinity -1 to 1) proves(?)
that every number ends in the 4,2,1 loop (does not escape),
then every numbered string must also end in a 4,2,1 loop
... because "3X+1 or /2" logic applies to all strings. ;)


:duh Actually, the Collatz Conjecture presents two independent problems:

1) Proving that all numbers from infinity -1 do not escape the 4,2,1 loop.

2) Predicting how many calculations are necessary for each number to reach its 4,2,1 loop
(precisely predictable for the downstep string, but like tossing a coin for other strings):

:idea: The complexity might be illustrated by starting with a bitcoin of fixed value
where one side = '3X+1' and the other side 'X/2'. The odd/even of starting value
determines both next value and then the next calculation.

:lol: These calculations seem to parallel bitcoin "investing" with a calculation
relative to time investing and ending value of 4,2,1 the possible final profit
... at the end of time. :roll:


:hithere Columnar Collatz (CC Stairway)

The two rightmost columns are the only ones needed to construct
this stairway to infinity (God?), with addition the only calculation.
Once constructed, the path of any number to its 4,2,1 resolution
becomes "child's play" to even the simplest of computers :!:

:idea: This describes a computer pattern generator - not solution!
(refers to a 'linked list' with any number an index to the list;
the number's /2 or 3X+1 value becomes the next link.) 8)

Leftmost columns define possible Collatz path of primary number
(all columns should be generated for this linked list).
How many entries to generate in the list?
Why not start with a googol (10^100) :shock:

;) Example: Just follow '7' in the two columns:
7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

Code: Select all

                     3X+1    
/2   3X+1    --->     /2
200   33   = 100  =   50 
198        =  99  =  298
196        =  98  =   49
194        =  97  =  292
192        =  96  =   48
190        =  95  =  286
188   31   =  94  =   47
186        =  93  =  280
184        =  92  =   46
182        =  91  =  274
180        =  90  =   45
178        =  89  =  268
176   29   =  88  =   44
174        =  87  =  262

104   17   =  52  =   26
102        =  51  =  154
100        =  50  =   25
 98        =  49  =  148
 96        =  48  =   24
 94        =  47  =  142
 92   15   =  46  =   23
 90        =  45  =  136
 88        =  44  =   22
 86        =  43  =  130
 84        =  42  =   21
 82        =  41  =  124
 80   13   =  40  =   20
 78        =  39  =  118
 76        =  38  =   19
 74        =  37  =  112
 72        =  36  =   18
 70        =  35  =  106
 68   11   =  34  =   17
 66        =  33  =  100
 64        =  32  =   16
 62        =  31  =   94
 60        =  30  =   15
 58        =  29  =   88
 56    9   =  28  =   14
 54        =  27  =   82
 52        =  26  =   13
 50        =  25  =   76
 48        =  24  =   12
 46        =  23  =   70
 44    7   =  22  =   11
 42        =  21  =   64
 40        =  20  =   10
 38        =  19  =   58
 36        =  18  =    9
 34        =  17  =   52
 32    5   =  16  =    8
 30        =  15  =   46
 28        =  14  =    7
 26        =  13  =   40
 24        =  12  =    6
 22        =  11  =   34
 20    3   =  10  =    5
 18        =   9  =   28
 16        =   8  =    4
 14        =   7  =   22
 12        =   6  =    3
 10        =   5  =   16
  8    1   =   4  =    2
  6        =   3  =   10
  4        =   2  =    1
  2        =   1  =    4
 

Observation: '/2' downsteps more than '3X+1' upsteps,
suggesting that Conjecture is biased in 4,2,1 direction. ;)
Also, '3X+1' immediately changes odd to even,
whereas '/2' eventually changes even to odd. 8)

00. 155 466 233
01. 700 350 175
02. 526 263
03. 790 395
04. 1186 593
05. 1780 890 445
06. 1336 668 334 167
07. 502 251
08. 754 377
09. 1132 566 283
10. 850 425
11. 1276 638 319
12. 958 479
13. 1438 719
14. 2158 1079
15. 3238 1619
16. 4858 2429
17. 7288 3644 1822 911
18. 2734 1367
19. 4102 2051
20. 6154 3077
21. 9232 4616 2308 1154 577
22. 1732 866 433
23. 1300 650 325
24. 976 488 244 122 61
25. 184 92 46 23
26. 70 35
27. 106 53
28. 160 80 40 20 10 5
29. 16 8 4 2 1

Also explains Pattern 616, since '+1' changes odd to even,
but is otherwise insignificant (especially for larger numbers);
which leaves '3X' vs '/2' for math relationship: 30 / 5 = 6

Number = 3X+1 = /2
10000 = 30001 = 5000
1000 = 3001 = 500
100 = 301 = 50
10 = 31 = 5

:farao: While quantum string theory fades into the background,
this number string theory seems to be leading us to infinity
and suggesting a "God Equation" (we go to Number 1). :roll

That 3X+1 cannot be known when X = infinity -1
suggests Collatz Conjecture can never be "proven". :shock:

:idea: Pattern 616 seems a necessary reference
since every number from 1 to infinity -1 exists
as a discrete step in the Pattern 616 stairway
and every number in the stairway downsteps
(calculates) to its 4,2,1 beginning. 8)

:cheers: If Pattern 616 is consistent and controlling,
'powers of 2' numbers predict 4,2,1 resolution
of all numbers in the Pattern 616 stairway:
512 = 256 128 64 32 16 8 4 2 1

Restated: '3X' is somewhat balanced by '/2', however
'+1' converts odd to even, giving /2 more influence. :roll:

Observation: Collatz Conjecture ('3X+1' or '/2')
defines constant math pressure to downstep
all calculations to their 4,2,1 resolution. ;)

:cheers: Every number in a string is the primary number of a string, therefore
4,2,1 proof of any number in the string extends proof to the primary number :!:

All numbers in this '27' string are a primary number
... and every string ends with 4,2,1:

27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1


:farao: There's no string with primary number in Pattern 616 stairway,
a linked computer list, that goes all the way Uptown (all numbers
from infinity -1 to 1 are sequential in the linked list). 8)

:idea: Descending the stairway from infinity is pre-ordained
(decisions based on odd or even), but ascending stairway
is traveler's choice (like ascension to Paradise). ;)

Downtown path: 3X+1 if number odd, X/2 if even.
Uptown path: if (X-1) odd, choose (X-1)/3 or 2X; else choose 2X.

:hithere Interestingly, this Downtown with Uptown verification
hints that Collatz Conjecture is indeed a Downtown path!

https://www.youtube.com/watch?v=Zx06XNfDvk0
"Things will be great when you're downtown!" 8)


:bana: Collatzable Linkage

These many patterns shout that no formula can define how every number resolves (or not) to 4,2,1,
but there's mathematical opportunity for development of rules associated with such "Collatzable Linkage"
(the infinity -1 to 1 "stairway"). That the pattern of a primary number's association with its neighbors
is similar to the stairway's 4,3,2,1 foundation supports the concept of Collatzable Linkage:

(6 x 2 = 2 + 10), (2 x 2 = 4), (10 - 4 = 6), (2 - 1 = 1)

8 > 4 = 2 1
6 > 3 = 10 5 16 8 4 2 1
4 > 2 = 1 4 2 1
2 > 1 = 4 2 1

:lol: Considering this Collatz Stairway (all numbers from infinity -1 to 1), proof of 4,2,1 resolution
may simply be proof that all numbers can be calculated as 3X+1 or X/2 (since these guarantee
that a number will eventually tag the primary number of a string which leads to the 4,2,1). 8)

:duh And consider the math ...
3X+1 converts odd to even, then X/2 divides by 2,
effectively contrasting (3X+1)/2 and X/2. :o

Since odd converts to even more than even to odd,
X/2 is the greater pressure to 4,2,1 resolution
and prevents 3X+1 domination (IMO). ;)

Hollandaze Conjecture In Totality (HCIT) :lol:

"Since every whole number identified by the most super of computers
exists in the Pattern 616 stairway (and every number in the stairway
is the primary number of a Collatz string that resolves to 4,2,1),
the 3X+1 vs X/2 mathematical tension must be the Collatz Key
with X/2 dominating the true direction of resolution no matter
how many calculations are required because of 3X+1 drift." 8)

:farao: Collatzable Linkage ...
might now become a legal term referring to a pattern of activity
so convincing that 'a,b,c' proves 'd,e,f' (beyond the shadow of doubt). :lol:


Rod :stars: :stars:
User avatar
Sandy
Staff
Posts: 23824
Joined: Sun Jan 30, 2005 8:51 pm
Please type in these numbers: 46373: 1111
Location: Illawarra District, New South Wales, Australia
Contact:

Re: World Views

Post by Sandy »

WOW! Totally lost but amazed all the same. :shock:
:stars:
:sunny:
Sandy
“We measure and evaluate your Spiritual Progress on the Wall of Eternity." – Guardian of Destiny, Alverana.
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.dailymail.co.uk/news/articl ... rater.html
"Turkmenistan president orders ministers to find experts who can seal off
the 230ft-wide methane-belching crater that has been burning since 1971" :o

:duh Challenging problem since what's burning inside the crater is methane gas
seeping through the walls of the crater ... and just stopping the fire causes
lotsa methane to escape into the air. :roll:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.breitbart.com/politics/2022 ... d-robbers/

"If you find yourself in a suspicious situation or witness a crime, blow your whistle. If you hear a whistle,
call the police, then move toward the source while blowing your own whistle."

:scratch: Might work if the robber doesn't have a gun
... with which to stop your whistle blowing. :roll:

:hithere "Whistle A Happy Tune" (from "The King and I" musical)
might actually defuse the crime (or at least confuse robber). :finger:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.reuters.com/business/financ ... 022-01-05/
"Goldman Sachs says bitcoin will compete with gold as 'store of value' "

:shock: A "new world order", financially speaking, when an intangible (unique computer number)
is believed to be just as secure as a centuries-proven tangible (precious metal) :!:

:idea: Whereas the computer number is unique, proof of ownership can be vulnerable
... and it's this proof of ownership that needs protection (like "money in the bank"
... or used to be like "money in the bank"). :roll:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.dailymail.co.uk/news/articl ... kdown.html

"Chinese woman has been stuck in blind date's house for A WEEK after city was thrown into lockdown
(but love has NOT blossomed because he's 'as mute as a mannequin' and his food is 'mediocre')" :o

:scratch: How many blind dates blossom into love even in the best of circumstances :?:
Is not "blind date" a clue that a cupid(s) is attempting matchmaking ...
and should have looked at the menu first? :roll:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.dailymail.co.uk/news/articl ... -herd.html
"lioness 'shows love' for wildebeest calf and leads it back to its herd"

:? ... where it can put more meat on its bones? since ...
"Wildebeest are among the prey animals most frequently targeted by lions"

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.dailymail.co.uk/news/articl ... -tidy.html
"Judge BERATES 72-year-old man with lymph node cancer for not keeping his lawn tidy
because his treatment left him too weak"

:? Apparently, the neighbors were not so neighborly ...
else some would have offered to help tidy the property. :roll:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

:bana: Subtle humor in the doo doo ...

Re: https://www.youtube.com/watch?v=XqZsoesa55w "Baby Shark Dance"

8) Notice how Grandma and Grandpa shark have no teeth :!:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.seattletimes.com/entertainm ... d-lawsuit/
"Nude baby on Nirvana’s ‘Nevermind’ refiles dismissed lawsuit"

:scratch: Apparently, he enjoyed celebrity status for several decades,
but now protests that use of his baby picture. :roll:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.brighteon.com/
(search for "The Fed's Doomsday Prophet Has A Dire Warning")

:idea: In this discussion about Thomas Hoenig (former U.S. Federal Reserve president),
Mark Moss seems to be promoting bitcoin (BTC) because it has limited quantity
but now there are thousands of cryptocurrencies (each with fixed quantity). :roll:

See also: https://en.wikipedia.org/wiki/Cryptocurrency

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.theepochtimes.com/china-rev ... 07963.html
"China Unveils AI News Anchor That’s Almost Indistinguishable From a Real Human"

"artificial intelligence has far surpassed humans in terms of calculation methods, performance, and learning ability.
But the biggest problem is that it has no ethics, morals, or personal values." :roll:

:idea: This article hints that "like father like son" is a potential pattern for this type of AI. ;)

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

:idea: Mensa level "See God Conjecture" (wry humor) ...

3J + 1 = (see God sooner)
/2 = (see God later)

Rod :scratch:
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.dailymail.co.uk/news/articl ... orthy.html
"Sister of man who was stabbed by the first person to get a pig's heart in groundbreaking transplant says he is 'not a worthy recipient' "

:idea: Considering the huge risk (and cost) of this "groundbreaking transplant",
he should at least be considered a brave unworthy recipient. Then again,
how does anyone qualify as "worthy recipient" of a pig's heart? :roll:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://dnyuz.com/2022/01/14/can-a-gay- ... mid-covid/
"Can a Gay Cruise Keep 5,500 People Safe Amid Covid?"

(passenger comment) "This is going to be the wildest party for our community in two years.
I’m talking dirty dancing, sex, drugs, raves, orgies and sweet, sweet freedom." :o

:idea: Good potential to be a modern Darwinian test ("survival of the fittest'). :roll:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.yahoo.com/entertainment/gin ... 47218.html
"Ginnifer Goodwin Offered Husband Josh Dallas' Sperm to Friend Who Wanted to Be a Mom"

"While they were touched by the offer,
Ginnifer said it was the logistics of her plan that caused the others some concern." :roll:

:scratch: Probably related to package shipping and timely delivery.

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://sustainabilitymag.com/top10/top ... al-warming
"Top 10 Causes Of Global Warming"

:idea: "Global warming", often synonymous with "climate change", is complex with no easy solutions:
Can man stop volcanoes and earth crust movement? Can we live with less mass transportation (ships,
planes, trucks, trains, etc.) and less electricity for all of our modern devices and appliances?
What about all of the military hardware and tests/wars? But I digress. ;)

At least, less waste of food (like overeating requiring greater food production/transportation) and less pollution
of the environment with our personal discards are reasonable goals. There must be hundreds of "minor" solutions
that become significant en masse! As for volcanoes, skip the historical "toss in a virgin" and consider these
no-fossil-fuel methods of cremation. Even human composting is gaining acceptance. But I digress. :roll:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.the-sun.com/tech/4482978/as ... struction/

"A new study published in Nature Medicine found that space causes the human body
to destroy red blood cells at a faster rate than on Earth." :o

:scratch: Does this suggest that "aliens" might be humanoid (more robotic than human) :?: :!:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.investmentwatchblog.com/kyi ... se-of-war/

"residents of the 'square' were advised to equip their homes in advance and find out the location of the nearest shelter, stock up on water and medicines, collect things, documents, prepare private vehicles for evacuation, and also consider possible alternative sources of light and heat in case of a power outage and central heating. In addition, the document details how to assemble the 'alarm suitcase', as well as instructions in case hostilities begin in the country ... the brochure provides advice in case of shelling from small arms, artillery and multiple launch rocket systems"

:idea: Probably not "fear mongering" when a government instructs its citizens how to prepare for war. :roll:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

:study: Re: https://dailyexpose.uk/wp-content/uploa ... y_2022.pdf
"Criminal Complaint, January 17, 2022, Harris County, Texas" (Houston)

:idea: A Texas lawsuit about the continuing controversy,
with good potential for truth to be revealed! 8)

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.dailymail.co.uk/news/articl ... cream.html
"Russian lawyer plunged into a frozen river to mark Orthodox Epiphany before being swept away"

:idea: Another sad lesson about the forces of nature
(plunging into any hole in ice over water is risky). :roll:

Rod :(
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

:shock: Poignant grammar lesson in the news ...

Re: https://www.foxnews.com/
"State Dept orders diplomatic families to leave Ukraine as US lethal aid arrives in the country"

:idea: This "lethal aid" is a real world example of an oxymoron! :roll:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.usatoday.com/story/news/nat ... 606064001/
"During welfare check, police find dead man and 124 snakes inside Maryland home"

"some venomous and illegal, were 'meticulously cared for' in cages stacked throughout the home"

"A neighborly 49-year-old." :hithere

:idea: I once thought a snake would make a good pet, but saw the cost of snake chow rising
... and then the new leash law required a daily slow slither around the neighborhood
(my neighbors tolerate an aging shuffle but not a slow slither). :roll:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.dailymail.co.uk/femail/arti ... nters.html

"Woman who filmed man behind her while she was working out at the gym
divides opinion after revealing she was pleased her 'booty wasn't his focus' "

:scratch: Comparison of the attire worn by this man and woman
suggests that one of them was probably "camera shy"
but the other preferred maximum exposure. :roll:

Rod :)
Amigoo
Family
Posts: 12607
Joined: Fri Mar 17, 2006 8:32 pm
Please type in these numbers: 46373: 0
Please type in these numbers:91294: 0
Location: Dallas, TX

Re: World Views

Post by Amigoo »

Re: https://www.rt.com/business/546846-bitc ... mber-peak/
"Bitcoin drops 50% from its peak value" :o

:idea: Proof of a gambling-style "store of value"
... where "the house always wins" ...
and "my house is your house"
is just change of ownership. :roll:

Rod :)
Post Reply