Hi Devon Thank you for your interest!
Ordinal Fractions are easier to understand than to explain. You know that some book editors number the chapters like this: 1 chapter one 1.1 chapter one, section one 1.2 chapter one, section two 1.2.1 chapter one, section two, subsection one and so on. What mathematically is this beast: 1.2.1 ? It is not an integer, because it contains dots. It is not a decimal fraction because it contains more than one dot. It is not a complex number. It seems to be some new kind of number. It is highly intuitive and requires no explaination. It identifies a part of the totality. It is a actually an ordinal fraction. The dots seem to be superfluous. What happens if they are omitted ? 1 chapter one 11 chapter one, section one 12 chapter one, section two 121 chapter one, section two, subsection one Here the digit zero is not used, so it may be used for padding, like this 100 chapter one 110 chapter one, section one 120 chapter one, section two 121 chapter one, section two, subsection one Obviously the digit zero is a wildcard character, meaning 'everything'. Chapter one (100) contains the two subsections 110 and 120. So 100>110 and 100>120 are valid ordinal fraction inequalities. The expression 010 means the first subsection of every chapter. We have increased our power of expression! The inequality 0>1 says with Euclid that 'The whole is greater than the part'. Now you can number the Nicean Creed word by word and a very short program can extract the comprehensible subsets. You may object that we cannot delete the dots without trouble. The first subsection of chapter ten was numbered 10.1. Digit zero in the integer '10' means 'nothing'. To overcome this problem we must renumber the first 9 chapters (11+i.9) and then chapter ten gets number 21. Digit zero cannot simultaneously mean 'everything' and 'nothing'. Your questions below. How do you know the denominator in "10"? In the explanation I restricted myself to binary ordinal fractions, which is theoretically sufficient. Then the denominators are 2^>:i.4 . 'both eights' means 'both eights of each fourth'. 210 means (read from right to left) both eights of the first quarter of the second half. I hope this helps. - Bo >________________________________ > Fra: Devon McCormick <devon...@gmail.com> >Til: J-programming forum <programm...@jsoftware.com> >Sendt: 20:10 fredag den 30. november 2012 >Emne: Re: [Jprogramming] Translating BASIC into J > >Hi Bo - > >I looked at the page explaining ordinal fractions but still can't fathom >them. The second paragraph reads: > >10 means 'the first half, both quarters'. 100 means 'the first half, both >quarters, both eighths'. Obviously 1=10=100. You may pad with zeroes to the >right. This is like decimal<http://www.nationmaster.com/encyclopedia/Decimal> >fractions <http://www.nationmaster.com/encyclopedia/Fraction> where >1=1.0=1.00. > >Firstly, how do you know the denominator in "10"? Also, you must mean >"four eighths" rather than "both eighths", but how does this proceed: does >the last zero in "1000" correspond to sixteenths (and why)? Are the >trailing zeros conditioned by the leading digits? > >Thanks, > >Devon > > >On Fri, Nov 30, 2012 at 12:31 PM, Aai <agroeneveld...@gmail.com> wrote: > >> I use this for the database conversion: >> >> DB=: ({.,<@}:@(;: inv@}.))"1 ;:;. _2 (0 :0) >> >> 1 CREDO >> 11 IN >> 111 UNUM >> 11 DEUM >> >> ... >> >> 32 VITAM >> 3211 VENTURI >> 0 AMEN >> ) >> >> Following June Kim's suggestion about AMEN. >> >> _4 {. v >> ┌──┬─────┬───────┬────┐ >> │ET│VITAM│VENTURI│AMEN│ >> └──┴─────┴───────┴────┘ >> _4 {. k >> ┌──┬──┬────┬─┐ >> │39│32│3211│0│ >> └──┴──┴────┴─┘ >> >> Using June Kim's search: >> >> >> search=:*./@(+./)@( [ (= , '0'&=@,: )({.~ #)~ ) >> >> >> examples (not thoroughly tested): >> >> ;: inv v#~k search every < '13521' >> >> CREDO IN SPIRITUM QUI CUM PATRE GLORIFICATUR AMEN >> ;: inv v#~k search every < '11' >> CREDO IN DEUM AMEN >> ;: inv v#~k search every < '33' >> EXPECTO AMEN >> ;: inv v#~k search every < '13500' >> >> CREDO IN SPIRITUM QUI CUM PATRE ET FILIO SIMUL ADORATUR ET GLORIFICATUR >> AMEN >> ;: inv v#~k search every < '01' >> >> CREDO IN DEUM CONFITEOR BAPTISMA ET EXPECTO RESURRECTIONEM AMEN >> >> >> >> On 30-11-12 17:32, Bo Jacoby wrote: >> >>> Hi Aai. Thanks. I did, but still: >>> >>> 22{. DB >>> 1 CREDO >>> 11 IN >>> 111 UNUM >>> _18{.DB NB. it is necessary to put a blank character before AMEN. >>> 321 SÆCULI >>> AMEN >>> >>> $ DB >>> 1926 >>> >>> >>> 'key val'=: <"1 |: >({. , ([,' ',])&.>/@:}.)@:(' '&cut) each LF cut DB >>> |domain error >>> | 'key val'=:<"1|:> ({.,([,' ',])&.>/@:}.)@:(' '&cut)each LF cut DB >>> >>> >>> 3 {. cut DB >>> ┌─┬────────┬──────┐ >>> │1│CREDO 11│IN 111│ >>> └─┴────────┴──────┘ >>> >>> >>> The line number should be before the word. >>> >>> >>> - Bo >>> >>> >>> ______________________________**__ >>>> Fra: Aai <agroeneveld...@gmail.com> >>>> Til: programm...@jsoftware.com >>>> Sendt: 15:21 fredag den 30. november 2012 >>>> Emne: Re: [Jprogramming] Translating BASIC into J >>>> >>>> Hi Bo, you need to feed the animal, e.g. >>>> >>>> DB=: 0 :0 >>>> 1 CREDO >>>> 11 IN >>>> 111 UNUM >>>> ... >>>> ) >>>> >>>> and then: >>>> >>>> 'key val'=: <"1 |: >({. , ([,' ',])&.>/@:}.)@:(' '&cut) each LF cut DB >>>> >>>> >>>> >>>> On 30-11-12 15:03, Bo Jacoby wrote: >>>> >>>>> Hi June. I can't make it work. >>>>> require 'strings' >>>>> cut >>>>> ' '&$: :([: -.&a: <;._2@,~) >>>>> 'key val'=: <"1 |: >({. , ([,' ',])&.>/@:}.)@:(' '&cut) each LF >>>>> cut >>>>> |domain error >>>>> | 'key val'=:<"1|:> ({.,([,' ',])&.>/@:}.)@:(' '&cut)each LF cut >>>>> - Bo >>>>> >>>>> >>>>> >>>>> >>>>> ______________________________**__ >>>>>> Fra: June Kim (김창준) <junea...@gmail.com> >>>>>> Til: programm...@jsoftware.com >>>>>> Sendt: 9:30 fredag den 30. november 2012 >>>>>> Emne: Re: [Jprogramming] Translating BASIC into J >>>>>> >>>>>> I forgot to mention that cut is from strings. >>>>>> >>>>>> Hence, you should >>>>>> >>>>>> require 'strings' >>>>>> >>>>>> first, before running my other lines. >>>>>> >>>>>> On Wed, Nov 28, 2012 at 2:43 PM, June Kim (김창준) <junea...@gmail.com> >>>>>> wrote: >>>>>> >>>>>> Hi Bo, >>>>>>> >>>>>>> Firstly on the database file: >>>>>>> >>>>>>> I suppose there is no blank line in between the lines of the file. >>>>>>> I suppose AMEN at the end was actually, 0 AMEN, instead. >>>>>>> >>>>>>> Now a quick and dirty version -- notice that this doesn't fully >>>>>>> implement >>>>>>> the basic code exactly, but you'll get the key idea. >>>>>>> >>>>>>> 'key val'=: <"1 |: >({. , ([,' ',])&.>/@:}.)@:(' '&cut) each >>>>>>> LF cut >>>>>>> 1!:1<jpath'~user/temp/CREDO' NB. I put the CREDO file here >>>>>>> search=:*./@(+./)@( [ (= , '0'&=@,: ) ({.~ #)~ ) >>>>>>> val#~key search every < '13522' NB. query for 13522 >>>>>>> >>>>>>> >>>>>>> June >>>>>>> >>>>>>> >>>>>>> On Tue, Nov 27, 2012 at 3:31 PM, Bo Jacoby <bojac...@yahoo.dk> wrote: >>>>>>> >>>>>>> Dear J'ers. >>>>>>>> >>>>>>>> At the Norddata conference in Göteborg in the summer 1989 I gave a >>>>>>>> lecture (in Danish) on Ultraflexible Database Structure and >>>>>>>> Artificial >>>>>>>> Catholicism. >>>>>>>> >>>>>>>> >>>>>>>> It contained this 8-liner in BASIC. >>>>>>>> >>>>>>>> 1 INPUT;C$: 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 been able to translate this program into J, mainly (I >>>>>>>> think) because I have no experience in reading textfiles from J. I >>>>>>>> request >>>>>>>> your assistance! The line numbers in the file must be separated from >>>>>>>> the >>>>>>>> rest of the lines. The line numbers may be padded to the right with >>>>>>>> zeroes. >>>>>>>> >>>>>>>> >>>>>>>> The program is a database browser. The question put to the program >>>>>>>> is a >>>>>>>> number, and the answer from the program consists of the lines in the >>>>>>>> database having numbers compatible to that of the question. Like >>>>>>>> this: >>>>>>>> >>>>>>>> 1: CREDO AMEN >>>>>>>> 2: CONFITEOR AMEN >>>>>>>> 3: EXPECTO AMEN >>>>>>>> 0: CREDO CONFITEOR ET EXPECTO AMEN >>>>>>>> >>>>>>>> The digit zero is wild card character. A zero in the question >>>>>>>> indicate >>>>>>>> that the answer has many words, and zero in a word in the database >>>>>>>> indicate >>>>>>>> that this word answers many questions. So "AMEN" is included in all >>>>>>>> answers. Like this: >>>>>>>> >>>>>>>> 11: CREDO IN DEUM AMEN >>>>>>>> 12: CREDO IN JESUM AMEN >>>>>>>> 13: CREDO IN SPIRITUM AMEN >>>>>>>> 14: CREDO ECCLESIAM AMEN >>>>>>>> 15: CREDO AMEN >>>>>>>> 10: CREDO IN DEUM ET IN JESUM ET IN SPIRITUM ET ECCLESIAM AMEN >>>>>>>> 21: CONFITEOR BAPTISMA AMEN >>>>>>>> 22: CONFITEOR AMEN >>>>>>>> 31: EXPECTO RESURRECTIONEM AMEN >>>>>>>> 32: EXPECTO VITAM AMEN >>>>>>>> 33: EXPECTO AMEN >>>>>>>> 30: EXPECTO RESURRECTIONEM ET VITAM AMEN >>>>>>>> 01: CREDO IN DEUM CONFITEOR BAPTISMA ET EXPECTO RESURRECTIONEM AMEN >>>>>>>> 13500: CREDO IN SPIRITUM QUI CUM PATRE ET FILIO SIMUL ADORATUR ET >>>>>>>> GLORIFICATUR AMEN >>>>>>>> >>>>>>>> 13510: CREDO IN SPIRITUM QUI CUM PATRE ET FILIO SIMUL ADORATUR AMEN >>>>>>>> 13520: CREDO IN SPIRITUM QUI CUM PATRE ET FILIO SIMUL GLORIFICATUR >>>>>>>> AMEN >>>>>>>> 13501: CREDO IN SPIRITUM QUI CUM PATRE ADORATUR ET GLORIFICATUR AMEN >>>>>>>> 13502: CREDO IN SPIRITUM QUI CUM FILIO ADORATUR ET GLORIFICATUR AMEN >>>>>>>> 13511: CREDO IN SPIRITUM QUI CUM PATRE ADORATUR AMEN >>>>>>>> 13512: CREDO IN SPIRITUM QUI CUM FILIO ADORATUR AMEN >>>>>>>> 13521: CREDO IN SPIRITUM QUI CUM PATRE GLORIFICATUR AMEN >>>>>>>> 13522: CREDO IN SPIRITUM QUI CUM FILIO GLORIFICATUR AMEN >>>>>>>> >>>>>>>> The database is this. >>>>>>>> 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 >>>>>>>> 12412 EST >>>>>>>> 1241201 DE >>>>>>>> 1241201 SPIRITU >>>>>>>> 124120101 SANCTO >>>>>>>> 1241202 EX >>>>>>>> 1241202 MARIA >>>>>>>> 124120201 VIRGINE >>>>>>>> 12419 ET >>>>>>>> 1241301 HOMO >>>>>>>> 12413 FACTUS >>>>>>>> >>>>>>>> 12413 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 >>>>>>>> >>>>>>>> 12425 EST >>>>>>>> 124252 CUM >>>>>>>> 124252 GLORIA >>>>>>>> 124253 JUDICARE >>>>>>>> 1242531 VIVOS >>>>>>>> 1242539 ET >>>>>>>> 1242532 MORTUOS >>>>>>>> 125 CUJUS >>>>>>>> 125 REGNI >>>>>>>> 125 NON >>>>>>>> 125 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 >>>>>>>> ------------------------------**------------------------------** >>>>>>>> ---------- >>>>>>>> For information about J forums see http://www.jsoftware.com/** >>>>>>>> forums.htm <http://www.jsoftware.com/forums.htm> >>>>>>>> >>>>>>>> ------------------------------**------------------------------** >>>>>> ---------- >>>>>> For information about J forums see http://www.jsoftware.com/** >>>>>> forums.htm <http://www.jsoftware.com/forums.htm> >>>>>> >>>>>> >>>>>> ------------------------------**------------------------------** >>>>> ---------- >>>>> For information about J forums see http://www.jsoftware.com/** >>>>> forums.htm <http://www.jsoftware.com/forums.htm> >>>>> >>>> -- >>>> Met vriendelijke groet, >>>> @@i = Arie Groeneveld >>>> >>>> ------------------------------**------------------------------** >>>> ---------- >>>> For information about J forums see >>>> http://www.jsoftware.com/**forums.htm<http://www.jsoftware.com/forums.htm> >>>> >>>> >>>> ------------------------------**------------------------------** >>> ---------- >>> For information about J forums see >>> http://www.jsoftware.com/**forums.htm<http://www.jsoftware.com/forums.htm> >>> >> >> -- >> Met vriendelijke groet, >> @@i = Arie Groeneveld >> >> ------------------------------**------------------------------**---------- >> For information about J forums see >> http://www.jsoftware.com/**forums.htm<http://www.jsoftware.com/forums.htm> >> > > > >-- >Devon McCormick, CFA >^me^ at acm. >org is my >preferred e-mail >---------------------------------------------------------------------- >For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
