Re: Cactus Rules
Jon Awbrey <[email protected]> Sun, 04 Apr 2004 16:26:33 -0400
| Newsgroups | gmane.comp.inquiry,gmane.comp.misc.ontology.general |
|---|---|
| Message-ID | <[email protected]> |
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o CR. Note 21 o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o Table 17 gives another way of writing the "paisley propositions" that makes their symmetry class more manifest. The venn diagram that follows the Table may provide an idea of why I chose to dub them that, at least, until I can think up a Greek or Latin label. Table 17. Paisley Propositions o---------o------------o-----------------o------------------------------o | L_1 | L_2 | L_3 | L_4 | | | | | | | Decimal | Binary | Vector | Cactus | o---------o------------o-----------------o------------------------------o | | p : 1 1 1 1 0 0 0 0 | | | | q : 1 1 0 0 1 1 0 0 | | | | r : 1 0 1 0 1 0 1 0 | | o---------o------------o-----------------o------------------------------o | | | | | | q_216 | q_11011000 | 1 1 0 1 1 0 0 0 | p + pq + pqr + (p, q, r) | | | | | | | q_184 | q_10111000 | 1 0 1 1 1 0 0 0 | p + pr + pqr + (p, q, r) | | | | | | | q_228 | q_11100100 | 1 1 1 0 0 1 0 0 | q + pq + pqr + (p, q, r) | | | | | | | q_172 | q_10101100 | 1 0 1 0 1 1 0 0 | q + qr + pqr + (p, q, r) | | | | | | | q_226 | q_11100010 | 1 1 1 0 0 0 1 0 | r + pr + pqr + (p, q, r) | | | | | | | q_202 | q_11001010 | 1 1 0 0 1 0 1 0 | r + qr + pqr + (p, q, r) | | | | | | o---------o------------o-----------------o------------------------------o | | | | | | q_39 | q_00100111 | 0 0 1 0 0 1 1 1 | 1 + p + pq + pqr + (p, q, r) | | | | | | | q_71 | q_01000111 | 0 1 0 0 0 1 1 1 | 1 + p + pr + pqr + (p, q, r) | | | | | | | q_27 | q_00011011 | 0 0 0 1 1 0 1 1 | 1 + q + pq + pqr + (p, q, r) | | | | | | | q_83 | q_01010011 | 0 1 0 1 0 0 1 1 | 1 + q + qr + pqr + (p, q, r) | | | | | | | q_29 | q_00011101 | 0 0 0 1 1 1 0 1 | 1 + r + pr + pqr + (p, q, r) | | | | | | | q_53 | q_00110101 | 0 0 1 1 0 1 0 1 | 1 + r + qr + pqr + (p, q, r) | | | | | | o---------o------------o-----------------o------------------------------o o-------------------------------------------------o | | | | | o-------------o | | /%%%%%%%%%%%%%%%\ | | /%%%%%%%%%%%%%%%%%\ | | /%%%%%%%%%%%%%%%%%%%\ | | /%%%%%%%%%%%%%%%%%%%%%\ | | o%%%%%%%%%%%%%%%%%%%%%%%o | | |%%%%%%%%%% P %%%%%%%%%%| | | |%%%%%%%%%%%%%%%%%%%%%%%| | | |%%%%%%%%%%%%%%%%%%%%%%%| | | o---o---------o%%%o---------o---o | | / \%%%%%%%%%\%/ / \ | | / \%%%%%%%%%o / \ | | / \%%%%%%%/%\ / \ | | / \%%%%%/%%%\ / \ | | o o---o-----o---o o | | | |%%%%%| | | | | |%%%%%| | | | | Q |%%%%%| R | | | o o%%%%%o o | | \ \%%%/ / | | \ \%/ / | | \ o / | | \ / \ / | | o-------------o o-------------o | | | | | o-------------------------------------------------o q_216. p + p q + p q r + (p, q, r) Jon Awbrey o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o inquiry e-lab: http://stderr.org/pipermail/inquiry/ o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o