Wednesday, March 23, 2022

Proposal: Hull-Dobell Theorem

Timed out and enacted, 7-1. Josh

Adminned at 25 Mar 2022 13:29:08 UTC

If “Simplification for the early days of a new dynasty” was not enacted, this proposal does nothing.
Then, if “More Digits” was enacted, revert all changes made to the Ruleset due to “More Digits”.

Add a new Probulator Function with the following properties:

Name: Wavefunction Observation
Output range: An integer between 0 and 999, inclusive.
Forecast output: 19
Method: Return forecast output and then change the forecast output to 1821 times the current forecast output plus 763 modulo 1000.

Add a material to the list of Materials with the name of Electron Microscope and a Function of Wavefunction Observation.

When c ≠ 0, correctly chosen parameters allow a period equal to m, for all seed values. This will occur if and only if:

  1) m and c are relatively prime,
  2) a − 1 is divisible by all prime factors (2,5)of m ,
  3) a − 1 is divisible by 4 if m is divisible by 4.


iter(n+1) = (a * iter + c) mod m


m = 1000
c = 763 satisfies 1
a = 1821 (1820 satisfies 2 & 3)

posted by Chiiika at 23 Mar 2022 13:29:00 UTC Comments (17)

Comments

Chiiika: she/her

23-03-2022 13:50:21 UTC

Chiiika’s observation on this Algorithm
Seed = 19
19 > 362 > 965 > 28 > 751 > 334 > 977 > 880 > 243 > 266
> 149 > 92 > 295 > 958 > 281 > 464 > 707 > 210 > 173 > 796
> 279 > 822 > 625 > 888 > 811 > 594 > 437 > 540 > 103 > 326
> 409 > 552 > 955 > 818 > 341 > 724 > 167 > 870 > 33 > 856
> 539 > 282 > 285 > 748 > 871 > 854 > 897 > 200 > 963 > 386
> 669 > 12 > 615 > 678 > 401 > 984 > 627 > 530 > 893 > 916
> 799 > 742 > 945 > 608 > 931 > 114 > 357 > 860 > 823 > 446
> 929 > 472 > 275 > 538 > 461 > 244 > 87 > 190 > 753 > 976
> 59 > 202 > 605 > 468 > 991 > 374 > 817 > 520 > 683 > 506
> 189 > 932 > 935 > 398 > 521 > 504 > 547 > 850 > 613 > 36
> 319 > 662 > 265 > 328 > 51 > 634 > 277 > 180 > 543 > 566
> 449 > 392 > 595 > 258 > 581 > 764 > 7 > 510 > 473 > 96
> 579 > 122 > 925 > 188 > 111 > 894 > 737 > 840 > 403 > 626
> 709 > 852 > 255 > 118 > 641 > 24 > 467 > 170 > 333 > 156
> 839 > 582 > 585 > 48 > 171 > 154 > 197 > 500 > 263 > 686
> 969 > 312 > 915 > 978 > 701 > 284 > 927 > 830 > 193 > 216
> 99 > 42 > 245 > 908 > 231 > 414 > 657 > 160 > 123 > 746
> 229 > 772 > 575 > 838 > 761 > 544 > 387 > 490 > 53 > 276
> 359 > 502 > 905 > 768 > 291 > 674 > 117 > 820 > 983 > 806
> 489 > 232 > 235 > 698 > 821 > 804 > 847 > 150 > 913 > 336
> 619 > 962 > 565 > 628 > 351 > 934 > 577 > 480 > 843 > 866
> 749 > 692 > 895 > 558 > 881 > 64 > 307 > 810 > 773 > 396
> 879 > 422 > 225 > 488 > 411 > 194 > 37 > 140 > 703 > 926
> 9 > 152 > 555 > 418 > 941 > 324 > 767 > 470 > 633 > 456
> 139 > 882 > 885 > 348 > 471 > 454 > 497 > 800 > 563 > 986
> 269 > 612 > 215 > 278 > 1 > 584 > 227 > 130 > 493 > 516
> 399 > 342 > 545 > 208 > 531 > 714 > 957 > 460 > 423 > 46
> 529 > 72 > 875 > 138 > 61 > 844 > 687 > 790 > 353 > 576
> 659 > 802 > 205 > 68 > 591 > 974 > 417 > 120 > 283 > 106
> 789 > 532 > 535 > 998 > 121 > 104 > 147 > 450 > 213 > 636
> 919 > 262 > 865 > 928 > 651 > 234 > 877 > 780 > 143 > 166
> 49 > 992 > 195 > 858 > 181 > 364 > 607 > 110 > 73 > 696
> 179 > 722 > 525 > 788 > 711 > 494 > 337 > 440 > 3 > 226
> 309 > 452 > 855 > 718 > 241 > 624 > 67 > 770 > 933 > 756
> 439 > 182 > 185 > 648 > 771 > 754 > 797 > 100 > 863 > 286
> 569 > 912 > 515 > 578 > 301 > 884 > 527 > 430 > 793 > 816
> 699 > 642 > 845 > 508 > 831 > 14 > 257 > 760 > 723 > 346
> 829 > 372 > 175 > 438 > 361 > 144 > 987 > 90 > 653 > 876
> 959 > 102 > 505 > 368 > 891 > 274 > 717 > 420 > 583 > 406
> 89 > 832 > 835 > 298 > 421 > 404 > 447 > 750 > 513 > 936
> 219 > 562 > 165 > 228 > 951 > 534 > 177 > 80 > 443 > 466
> 349 > 292 > 495 > 158 > 481 > 664 > 907 > 410 > 373 > 996
> 479 > 22 > 825 > 88 > 11 > 794 > 637 > 740 > 303 > 526
> 609 > 752 > 155 > 18 > 541 > 924 > 367 > 70 > 233 > 56
> 739 > 482 > 485 > 948 > 71 > 54 > 97 > 400 > 163 > 586
> 869 > 212 > 815 > 878 > 601 > 184 > 827 > 730 > 93 > 116
> 999 > 942 > 145 > 808 > 131 > 314 > 557 > 60 > 23 > 646
> 129 > 672 > 475 > 738 > 661 > 444 > 287 > 390 > 953 > 176
> 259 > 402 > 805 > 668 > 191 > 574 > 17 > 720 > 883 > 706
> 389 > 132 > 135 > 598 > 721 > 704 > 747 > 50 > 813 > 236
> 519 > 862 > 465 > 528 > 251 > 834 > 477 > 380 > 743 > 766
> 649 > 592 > 795 > 458 > 781 > 964 > 207 > 710 > 673 > 296
> 779 > 322 > 125 > 388 > 311 > 94 > 937 > 40 > 603 > 826
> 909 > 52 > 455 > 318 > 841 > 224 > 667 > 370 > 533 > 356
> 39 > 782 > 785 > 248 > 371 > 354 > 397 > 700 > 463 > 886
> 169 > 512 > 115 > 178 > 901 > 484 > 127 > 30 > 393 > 416
> 299 > 242 > 445 > 108 > 431 > 614 > 857 > 360 > 323 > 946
> 429 > 972 > 775 > 38 > 961 > 744 > 587 > 690 > 253 > 476
> 559 > 702 > 105 > 968 > 491 > 874 > 317 > 20 > 183 > 6
> 689 > 432 > 435 > 898 > 21 > 4 > 47 > 350 > 113 > 536
> 819 > 162 > 765 > 828 > 551 > 134 > 777 > 680 > 43 > 66
> 949 > 892 > 95 > 758 > 81 > 264 > 507 > 10 > 973 > 596
> 79 > 622 > 425 > 688 > 611 > 394 > 237 > 340 > 903 > 126
> 209 > 352 > 755 > 618 > 141 > 524 > 967 > 670 > 833 > 656
> 339 > 82 > 85 > 548 > 671 > 654 > 697 > 0 > 763 > 186
> 469 > 812 > 415 > 478 > 201 > 784 > 427 > 330 > 693 > 716
> 599 > 542 > 745 > 408 > 731 > 914 > 157 > 660 > 623 > 246
> 729 > 272 > 75 > 338 > 261 > 44 > 887 > 990 > 553 > 776
> 859 > 2 > 405 > 268 > 791 > 174 > 617 > 320 > 483 > 306
> 989 > 732 > 735 > 198 > 321 > 304 > 347 > 650 > 413 > 836
> 119 > 462 > 65 > 128 > 851 > 434 > 77 > 980 > 343 > 366
> 249 > 192 > 395 > 58 > 381 > 564 > 807 > 310 > 273 > 896
> 379 > 922 > 725 > 988 > 911 > 694 > 537 > 640 > 203 > 426
> 509 > 652 > 55 > 918 > 441 > 824 > 267 > 970 > 133 > 956
> 639 > 382 > 385 > 848 > 971 > 954 > 997 > 300 > 63 > 486
> 769 > 112 > 715 > 778 > 501 > 84 > 727 > 630 > 993 > 16
> 899 > 842 > 45 > 708 > 31 > 214 > 457 > 960 > 923 > 546
> 29 > 572 > 375 > 638 > 561 > 344 > 187 > 290 > 853 > 76
> 159 > 302 > 705 > 568 > 91 > 474 > 917 > 620 > 783 > 606
> 289 > 32 > 35 > 498 > 621 > 604 > 647 > 950 > 713 > 136
> 419 > 762 > 365 > 428 > 151 > 734 > 377 > 280 > 643 > 666
> 549 > 492 > 695 > 358 > 681 > 864 > 107 > 610 > 573 > 196
> 679 > 222 > 25 > 288 > 211 > 994 > 837 > 940 > 503 > 726
> 809 > 952 > 355 > 218 > 741 > 124 > 567 > 270 > 433 > 256
> 939 > 682 > 685 > 148 > 271 > 254 > 297 > 600 > 363 > 786
> 69 > 412 > 15 > 78 > 801 > 384 > 27 > 930 > 293 > 316
> 199 > 142 > 345 > 8 > 331 > 514 > 757 > 260 > 223 > 846
> 329 > 872 > 675 > 938 > 861 > 644 > 487 > 590 > 153 > 376
> 459 > 602 > 5 > 868 > 391 > 774 > 217 > 920 > 83 > 906
> 589 > 332 > 335 > 798 > 921 > 904 > 947 > 250 > 13 > 436
> 719 > 62 > 665 > 728 > 451 > 34 > 677 > 580 > 943 > 966
> 849 > 792 > 995 > 658 > 981 > 164 > 407 > 910 > 873 > 496
> 979 > 522 > 325 > 588 > 511 > 294 > 137 > 240 > 803 > 26
> 109 > 252 > 655 > 518 > 41 > 424 > 867 > 570 > 733 > 556
> 239 > 982 > 985 > 448 > 571 > 554 > 597 > 900 > 663 > 86
> 369 > 712 > 315 > 378 > 101 > 684 > 327 > 230 > 593 > 616
> 499 > 442 > 645 > 308 > 631 > 814 > 57 > 560 > 523 > 146
> 629 > 172 > 975 > 238 > 161 > 944 > 787 > 890 > 453 > 676
> 759 > 902 > 305 > 168 > 691 > 74 > 517 > 220 > 383 > 206
> 889 > 632 > 635 > 98 > 221 > 204 > 247 > 550 > 313 > 736
> 19
Check for duplicates, or you reached your goal.
...
=====
Printed 1000 numbers.

Josh: Observer he/they

23-03-2022 14:28:51 UTC

I’m very worried that this dynasty is going to heavily favour maths students.

pokes:

23-03-2022 14:30:39 UTC

But why is it important to have a period of 1000 and not 500?

pokes:

23-03-2022 14:31:00 UTC

I am very excited that this dynasty is going to heavily favor math students.

Roujo: he/him

23-03-2022 15:38:52 UTC

> But why is it important to have a period of 1000 and not 500?

Not that it’s important per se, but I think the point is more along the lines of “you don’t get every possible number as an output”. ^^

> I’m very worried that this dynasty is going to heavily favour maths students.

So far the Algorithms that have been proposed are either:
- Math-based like this one, but with predictable output so while _someone_ needs to do the math to figure out what the next numbers will be, others that are less math-enclined can look at the published sequence. This assumes that you trust the publish sequence is correct, mind you, but at least you don’t need to do the math yourself.
- Oracle-based, like the S&P 500 opening price one.

Things don’t have to be super math-heavy if we don’t want them to, we can propose algorithms that are fun for everyone. =)

Chiiika: she/her

23-03-2022 15:49:26 UTC

Having a period of 1k solves the problem of “More Digits”, in which that might be unable to generate a particular number from 0-999 if any other Dynastic Rules wants it

Josh: Observer he/they

23-03-2022 16:07:58 UTC

I think I feel like having weird lacunae in the output dispersal creates game mechanic opportunities rather than closing them?

@Roujo the comment box on this proposal makes me want to cry

Thunder: he/him

23-03-2022 16:59:32 UTC

Thanks for fixing my math.

Roujo: he/him

23-03-2022 17:30:19 UTC

@Josh soooo I should propose an algorithm based on elliptic curve crypto before poking the Emotion Engine? gotcha :D

Josh: Observer he/they

23-03-2022 22:02:03 UTC

against

Raven1207: he/they

24-03-2022 02:32:47 UTC

for

SingularByte: he/him

24-03-2022 05:58:10 UTC

imperial

GloopyGhost:

24-03-2022 15:28:01 UTC

imperial

Roujo: he/him

24-03-2022 17:48:26 UTC

imperial

Thunder: he/him

24-03-2022 18:50:43 UTC

for

MadisonSilver:

24-03-2022 21:06:37 UTC

for

Josh: Observer he/they

25-03-2022 13:30:39 UTC

Why would you make me repeal the effects of the old proposal when this one literally retains everything it does except the method 🤮