Tracy Harms wrote (fredag 2. april 2010 21.16) I love it, Bo. Just as I was thinking I was hitting the end-game on this topic, you showed me a whole new way to think about expression. The entirety of the cube as 0 0 0 is so striking! ----------------------------------------------------------------------
Thank you Tracy! I 'invented' the concept of Ordinal Fraction back in 1980, using it for administrative software. An ordinal fraction look like a decimal integer except that it is right-justified and can be padded with zeroes to the right (rather than to the left). 1=10=100 etc. An ordinal fraction is like an array except for this: - arrays have finite dimensionality while ordinal fractions have infinite dimensionality. (The 'shape' of every ordinal fraction is _ # 9). - arrays have both subarrays and elements while ordinal fractions have sub-arrays, but no elements. - the array elements contain data, while the ordinal fraction subarrays contain data. The example below (from my NordData89 conference contribution on ultraflexible database structure and artificial catholicism) is a database coded by ordinal fractions 1 CREDO 11 IN 111 UNUM 11 DEUM 112 PATREM 1121 OMNIPOTENTEM 113 FACTOREM 1131 CÆLI 1139 ET 1132 TERRÆ 11331 VISIBILIUM 1133 OMNIUM 11339 ET 11332 INVISIBILIUM 19 ET 12 IN 1211 UNUM 1211 DOMINUM 12 JESUM 1211 CHRISTUM 1212 FILIUM 1212 DEI 12121 UNIGENITUM 1219 ET 1213 EX 1213 PATRE 1213 NATUM 12131 ANTE 121311 OMNIA 12131 SÆCULA 1221 DEUM 12211 DE 12211 DEO 1222 LUMEN 12221 DE 12221 LUMINE 1223 DEUM 12231 VERUM 12232 DE 12232 DEO 122321 VERO 1231 GENITUM 12311 NON 12311 FACTUM 1232 CONSUBSTANTIALEM 1232 PATRI 12321 PER 12321 QUEM 12321 OMNIA 12321 FACTA 12321 SUNT 124 QUI 124101 PROPTER 124101 NOS 12410101 HOMINES 124109 ET 124102 PROPTER 12410201 NOSTRAM 124102 SALUTEM 12411 DESCENDIT 1241101 DE 1241101 CÆLIS 12419 ET 12412 INCARNATUS EST 1241201 DE 1241201 SPIRITU 124120101 SANCTO 1241202 EX 1241202 MARIA 124120201 VIRGINE 12419 ET 1241301 HOMO 12413 FACTUS EST 124211 CRUCIFIXUS 1242101 ETIAM 1242101 PRO 1242101 NOBIS 1242102 SUB 1242102 PONTIO 1242102 PILATO 124212 PASSUS 124219 ET 124213 SEPULTUS 12421 EST 12429 ET 12422 RESURREXIT 124221 TERTIA 124221 DIE 124222 SECUMDUM 124222 SCRIPTURAS 12429 ET 12423 ASCENDIT 124231 IN 124231 CÆLUM 12424 SEDET 124241 AD 124241 DEXTERAM 124241 PATRIS 12429 ET 124251 ITERUM 12425 VENTURUS EST 124252 CUM 124252 GLORIA 124253 JUDICARE 1242531 VIVOS 1242539 ET 1242532 MORTUOS 125 CUJUS 125 REGNI 125 NON ERIT 125 FINIS 19 ET 13 IN 13 SPIRITUM 131 SANCTUM 132 DOMINUM 139 ET 133 VIVIFICANTEM 134 QUI 134 EX 1341 PATRE 1342 FILIO 1349 QUE 134 PROCEDIT 135 QUI 135 CUM 13501 PATRE 13509 ET 13502 FILIO 13509 SIMUL 1351 ADORATUR 1359 ET 1352 GLORIFICATUR 136 QUI 136 LOCUTUS EST 1361 PER 1361 PROPHETAS 19 ET 141 UNAM 142 SANCTAM 143 CATHOLICAM 149 ET 144 APOSTOLICAM 14 ECCLESIAM 2 CONFITEOR 211 UNUM 21 BAPTISMA 212 IN 212 REMISSIONEM 2121 PECCATORUM 9 ET 3 EXPECTO 31 RESURRECTIONEM 311 MORTUORUM 39 ET 32 VITAM 3211 VENTURI 321 SÆCULI AMEN This browser for ordinal fraction databases was written in BASIC: 1 INPUT;C$: IF C$="" THEN END 2 OPEN"CREDO" FOR INPUT AS 1: PRINT":"; 3 IF EOF(1) THEN CLOSE:PRINT:GOTO 1 4 LINE INPUT#1,A$: B$=C$ 5 IF A$=""THEN A%=-1 ELSE A%=ASC(A$)-48:A$=MID$(A$,2) 6 IF B$=""THEN B%=-1 ELSE B%=ASC(B$)-48:B$=MID$(B$,2) 7 IF A%<0 THEN PRINT" ";A$;:GOTO 3 8 IF A%=0 OR B%=0 OR A%=B% THEN 5 ELSE 3 I have not yet converted it to J! - Bo __________________________________________________ Bruger du Yahoo!? Er du træt af spam? Yahoo!Mail har den bedste spambeskyttelse, der findes http://dk.mail.yahoo.com ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
