Error: Base sets of nodes, and not base hyperedges. Each hyperedge touches at most one element of each base set.
On Sun, 10 Jan 2021 at 09:35, Justin Paston-Cooper <paston.coo...@gmail.com> wrote: > Can we summarise all of this as: > > A representation of hypergraphs ordered in a certain way, with nodes > represented by numbers, and tuples of numbers for representing the > hyperedges. Node values are ordered sets of strings. > > There is a number of base hyperedges (columns), whose disjoint union gives > the set of starting nodes. Over the nodes in each base hyperedge is defined > an ordering. There is an ordering defined between the base hyperedges also. > This gives an ordering over all base nodes. > > Define new values for possibly new hyperedges at will by taking unions of > subsets from each base hyperedge, and adding a node to the ordered set > corresponding to this hyperedge if it exists, or creating a new one if it > doesn’t. > > The orders of these hyperedges and the nodes within are defined using the > orders of the constituent base hyperedges, and the orders of the ordered > sets of the new added nodes. > > Queries are hypergraph traversals. > > Sorry if I’m being obtuse again. > > On Sat, 9 Jan 2021 at 23:11, 'Bo Jacoby' via Programming < > programm...@jsoftware.com> wrote: > >> Justin wrote: "Quite an interesting paper. What were the reasons for its >> rejection?" >> Thank you! The referee wrote that he did not consider me serious. He >> thought I was joking. >> I wrote an article to en.wikipedia.org, but as original research is not >> allowed on wikipedia the article was deleted. However in the >> meantime someone copied it to StateMaster.com Encyclopedia, but by now it >> is not to be found. Most of my research turns out not to be original >> research, but the theory of ordinal fractions seems to be original >> research. >> The CREDO example was published in Danish in the NordDATA 89 conference >> procedings, volume 3, page 779-785. About one out of thousand read Danish. >> The example is in Latin. About one out of thousand read Latin. The program >> is in BASIC. About one out of thousand read BASIC. So about one out of a >> billion can read the paper. I think I do know the other 6. The title is >> 'ULTRA-FLEKSIBEL DATABASESTRUKTUR OG KUNSTIG KATOLICISME' meaning: ultra >> flexible data base structure and artificial catholicism. >> Hauke is suggesting improvements. I have worked with ordinal fractions >> for forty years. Understand before improving. >> The ordinal fraction data base may be a tree, or a wood, or an array, or >> a relational data base, or any combination of these. Knowing ordinal >> fractions you do no longer need trees, woods, arrays, or relational data >> bases. The CREDO example is neither a tree, a wood, an array, nor a >> relational data base. >> The CREDO file is not sorted. ' AMEN' is the last word, even if it has >> line number 0 because is is included in every prayer. In a sorted file AMEN >> would come first. >> J programs are compact. I love it! So I expect that 8 lines of BASIC can >> be converted into an even shorter J program. >> Thank you all ! >> Bo >> >> >> Den lørdag den 9. januar 2021 18.49.14 CET skrev Justin Paston-Cooper >> <paston.coo...@gmail.com>: >> >> On Sat, 9 Jan 2021 at 15:59, Hauke Rehr <hauke.r...@uni-jena.de> wrote: >> > >> > My two comments (or, my 2¢): >> > >> > >> > concerning the aleph numbers >> > >> > is this related to my concern about dependence on order? >> > I understand the fractional digits to be meant to encode >> > both (semantic) structure and order >> > (or else the prayer wouldn’t be the best kind of example). >> >> Yes I think so. >> >> > >> > After all, that’s why they’re doing ‘more’ than their >> > relational counterparts where all columns are considered >> > independent of each other and applicable to all of the data. >> > >> > >> > concerning people’s workflows >> > >> > now that’s why I had been talking about the LEO editor >> > because the discussion had been originated by a question >> > about structuring one’s research; and I wanted to offer >> > concrete suggestions as to how to actually get to using >> > a system like this without the need of setting up a kind >> > of database first. >> >> I didn't have time to look into it the first time, but Leo looks >> really interesting for the document management part. It got me >> thinking about Xanadu: https://xanadu.com/xUniverse-D6. Thank you. >> >> > >> > The ordinal fractions could then be implicit in the tree >> > structure of the nodes (you only have to have a convention >> > for which node will be considered the 0 (aka ANY) node; >> > and maybe another one on if/how an empty node is to be >> > represented). >> > >> > The query script could then ask for digits and after each >> > one give the list of subordinate valid digits and their >> > meanings (semantics will be documented at each level); >> > this will get a bit more complicated with queries with >> > early 0s but then again, they should make sense mostly >> > when the semantic structure at subordinate levels agrees >> > which could result in a merge of the respective display >> > of subordinate digits’ meanings. >> > >> > but this would require the fractions to be used >> > the way I first understood it: the data is to be stored >> > in “leaf” nodes only. I guess this would be the easiest >> > and most easily manageable – also in terms of maintenance – >> > approach. >> > >> > >> > Hauke >> > >> > >> > >> > Am 09.01.21 um 07:50 schrieb Justin Paston-Cooper: >> > > On Sat, 9 Jan 2021 at 00:13, 'Bo Jacoby' via Programming < >> > > programm...@jsoftware.com> wrote: >> > > >> > >> Answering Justin's questions. >> > >> 01 question >> > >> 02 answer >> > >> 11. The data in your solution seems to be similar to the data in >> > >> relational databases, but the query space seems to be the same. >> > >> Cyclic relations seem to be ruled out, but this maybe isn't a >> problem. Am >> > >> I wrong, and is either stronger than the other? >> > >> >> > >> 12. The relations between two ordinal fractions are: equality (a=b), >> > >> subordination (a<b), superordination (a>b), compatibility (a<>b) and >> > >> incompatility (a><b). You are right, no cyclic relation. The browser >> omits >> > >> the records incompatible with the query ordinal fraction from the >> answer. >> > >> (in another browser I painted an answer (a) to a query (b) white if >> a=b, >> > >> green if a<b, red if a>b, yellow if a<>b, and invisible if a><b.) >> > >> 21. Is it possible to provide a well-performing ordinal fraction >> > >> interface to multiple separate files (hopefully memory mapped) in >> > >> an intuitive way in J? For instance, if we are looking at a subset of >> > >> columns which does not intersect with the set of columns of a given >> table, >> > >> then we would like to skip reading the rows in that table seamlessly. >> > > >> > > >> > >> >> > >> 22. Two files are merged into one by prefixing the line numbers of >> the >> > >> first file by "1" and the line numbers of the second file by "2". The >> > >> resulting merged file is then another ordinal fraction file to >> replace the >> > >> original two files. Well-performing means fast. If the data base is >> big it >> > >> is conveniently stored as an indexed sorted file and the browser is >> made to >> > >> skip lines before a possible match. >> > > >> > > >> > > See aleph numbers comment below. >> > > >> > > >> > >> 31. I am not fully convinced that this is easier to manage than a >> > >> relational database. >> > >> >> > >> 32. How to fit the credo text into a relational data base? I don't >> think >> > >> it is at all feasible. >> > > >> > > >> > > You are right. I spoke too early. >> > > >> > > >> > >> 41. If we did need to define explicit tables (sets of columns), then >> > >> this could happen in a separate schema table. What are your thoughts? >> > >> >> > >> 42. No, there is no need for a separate schema table. A table (like >> this >> > >> one) with rows 10 20 30 40 50 60 and columns 01 02 has elements 11 >> 12 13 14 >> > >> 15 16 21 22 23 24 25 26. There is but one file containing everything. >> > > >> > > >> > > Yes this makes sense. I was worrying more about associating tables >> names >> > > and column names to digits, but this doesn’t seem to be such an issue. >> > > >> > > >> > >> 51. This doesn't fully solve the issue of coordinating the updating >> of all >> > >> resources and the dependencies between them for updating. I guess >> Make >> > >> would help. >> > > >> > > >> > >> 52. What is the problem? >> > > >> > > >> > > I am trying to figure out what people’s workflows are. Anyway, maybe >> not >> > > the best topic for the programming forum. >> > > >> > > >> > >> >> > >> 61. I wonder how Jd could contribute. >> > >> 62. So do I! >> > >> Thank you very much! >> > >> I will comment on Hauke's contribution tomorrow. Now only this: I am >> very >> > >> impressed. Hauke's is the most qualified response I have ever >> received. >> > >> Note that a line number in the data base may be extended by zeroes. >> " AMEN" >> > >> = "0000000 AMEN". So "AMEN" is unavoidable in the answer to any >> query. >> > >> Thank you everyone! >> > >> Bo. >> > > >> > > >> > > I think AMEN and ET should be assigned to Aleph 1 the appropriate >> > > positions. BASIC should also incorporate this. This allows seamless >> updates >> > > of sub-tables. If one aleph bigger than next after update of >> sub-table, >> > > simply increment next. >> > > >> > > >> > >> Den fredag den 8. januar 2021 10.36.26 CET skrev Justin >> Paston-Cooper < >> > >> paston.coo...@gmail.com>: >> > >> >> > >> Quite an interesting paper. What were the reasons for its rejection? >> > >> >> > >> The mathematics is quite simple and well defined, however it doesn't >> > >> go too much into the application aspect. >> > >> >> > >> I don't have the time to actually explore this in depth right now, >> but: >> > >> >> > >> 1. The data in your solution seems to be similar to the data in >> > >> relational databases, but the query space seems to be the same. >> Cyclic >> > >> relations seem to be ruled out, but this maybe isn't a problem. Am I >> > >> wrong, and is either stronger than the other? >> > >> >> > >> 2. Is it possible to provide a well-performing ordinal fraction >> > >> interface to multiple separate files (hopefully memory mapped) in an >> > >> intuitive way in J? For instance, if we are looking at a subset of >> > >> columns which does not intersect with the set of columns of a given >> > >> table, then we would like to skip reading the rows in that table >> > >> seamlessly. >> > >> >> > >> 3. I am not fully convinced that this is easier to manage than a >> > >> relational database. >> > >> >> > >> 4. If we did need to define explicit tables (sets of columns), then >> > >> this could happen in a separate schema table. What are your thoughts? >> > >> >> > >> 5. This doesn't fully solve the issue of coordinating the updating of >> > >> all resources and the dependencies between them for updating. I guess >> > >> Make would help. >> > >> >> > >> 6. I wonder how Jd could contribute. >> > >> >> > >> On Fri, 8 Jan 2021 at 00:08, 'Bo Jacoby' via Programming >> > >> <programm...@jsoftware.com> wrote: >> > >>> >> > >>> "I am looking for a way to better organise my research. If not >> > >>> spreadsheets, do you have some advice on how to coordinate all this >> > >>> separate data in one place?" >> > >>> I have used ordinal fractions for structuring data since 1980. >> ORDINAL >> > >> FRACTIONS - the algebra of data >> > >>> >> > >>> | >> > >>> | >> > >>> | >> > >>> | | | >> > >>> >> > >>> | >> > >>> >> > >>> | >> > >>> | >> > >>> | | >> > >>> ORDINAL FRACTIONS - the algebra of data >> > >>> >> > >>> This paper was submitted to the 10th World Computer Congress, IFIP >> 1986 >> > >> conference, but rejected by the referee.... >> > >>> | >> > >>> >> > >>> | >> > >>> >> > >>> | >> > >>> >> > >>> >> > >>> >> > >>> I wrote software for processing this kind of data in fortran, >> BASIC, and >> > >> pascal, but not (yet) in J. >> > >>> A BASIC program for browsing the data base is this. >> > >>> 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 >> > >>> >> > >>> The test data base for illustrating the possibilities 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 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 >> > >>> >> > >>> Some test runs of the program look like this. >> > >>> 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 >> > >>> >> > >>> I realize that this is not easy to understand, but I know that it is >> > >> worth while. >> > >>> Good luck! >> > >>> Bo. Den torsdag den 7. januar 2021 21.35.12 CET skrev Justin >> > >> Paston-Cooper <paston.coo...@gmail.com>: >> > >>> >> > >>> Thanks. I have been meaning to look at that. >> > >>> >> > >>> On Thu, 7 Jan 2021 at 23:33, Joe Bogner <joebog...@gmail.com> >> wrote: >> > >>>> >> > >>>> Jupyter notebooks may help you with organizing your research - >> > >>>> https://code.jsoftware.com/wiki/Guides/Jupyter >> > >>>> >> > >>>> This has been my preferred tool - far above Excel. >> > >>>> >> > >>>> On Thu, Jan 7, 2021 at 2:39 PM Justin Paston-Cooper < >> > >> paston.coo...@gmail.com> >> > >>>> wrote: >> > >>>> >> > >>>>> I am open to suggestions. Right now I'm researching a lot of >> related >> > >>>>> things concurrently. I'm storing some of the results in TSV files. >> > >>>>> Some of the scripts are Python, some are curl | jq | awk. Some of >> the >> > >>>>> results I am storing as variables in J scripts. I am constantly >> going >> > >>>>> back and forth between differing representations, differing >> > >>>>> environments, recalculating things needlessly, and so on. >> > >>>>> >> > >>>>> I am looking for a way to better organise my research. If not >> > >>>>> spreadsheets, do you have some advice on how to coordinate all >> this >> > >>>>> separate data in one place? A Make file could be a start, but this >> > >>>>> doesn't satisfy the requirement of having a nice editable GUI to >> > >>>>> arrange and display all the separate sources of data. Maybe wd >> would >> > >>>>> be a start in that direction. I haven't researched the >> alternatives. >> > >>>>> >> > >>>>> How do you organise your research? >> > >>>>> >> > >>>>> Application: Researching interactions between prices of a set of >> > >>>>> things in each of a set of places. There are many different >> analyses >> > >>>>> that can be made. I am finding it hard to keep track of all the >> > >> angles >> > >>>>> I have looked at. These angles all reside in separate directories, >> > >>>>> which is not ideal. I have hand-written notes, but those need to >> be >> > >>>>> updated by hand. >> > >>>>> >> > >>>>> By the way, I wasn't envisioning doing any calculation in the >> > >>>>> spreadsheet. The idea of the spreadsheet was simply to coordinate >> > >>>>> communication and (re)calculation between various calculation >> > >>>>> processes, display the results, and allow the display of the >> results >> > >>>>> to be edited. >> > >>>>> >> > >>>>> Imagine an actor system with the spreadsheet being the >> coordinator. >> > >>>>> >> > >>>>> On Thu, 7 Jan 2021 at 20:23, Devon McCormick <devon...@gmail.com> >> > >> wrote: >> > >>>>>> >> > >>>>>> It would be remiss of me not to mention that you really ought to >> > >>>>>> re-consider making a spreadsheet an integral part of your design, >> > >> not the >> > >>>>>> least due to the historically high rates of error that have been >> > >> measured >> > >>>>>> in spreadsheets - 1 to 5%: >> > >>>>>> https://arxiv.org/ftp/arxiv/papers/1602/1602.02601.pdf . It >> seems >> > >>>>>> incongruous to worry about the sixth decimal place in numbers >> with >> > >> many >> > >>>>>> digits before the decimal point but ignoring error rates that >> > >> dwarf this >> > >>>>>> imprecision. >> > >>>>>> >> > >>>>>> By way of comparison, in most code-bases where people measure >> > >> errors, an >> > >>>>>> error rate of 10 bad lines per 1000 lines of code would be >> > >> considered >> > >>>>>> unacceptably high. >> > >>>>>> >> > >> >> ---------------------------------------------------------------------- >> > >>>>>> For information about J forums see >> > >> http://www.jsoftware.com/forums.htm >> > >>>>> >> > >> >> ---------------------------------------------------------------------- >> > >>>>> For information about J forums see >> > >> http://www.jsoftware.com/forums.htm >> > >>>>> >> > >>>> >> ---------------------------------------------------------------------- >> > >>>> For information about J forums see >> http://www.jsoftware.com/forums.htm >> > >>> >> ---------------------------------------------------------------------- >> > >>> For information about J forums see >> http://www.jsoftware.com/forums.htm >> > >>> >> > >>> >> ---------------------------------------------------------------------- >> > >>> For information about J forums see >> http://www.jsoftware.com/forums.htm >> > >> >> ---------------------------------------------------------------------- >> > >> For information about J forums see >> http://www.jsoftware.com/forums.htm >> > >> >> > >> >> ---------------------------------------------------------------------- >> > >> For information about J forums see >> http://www.jsoftware.com/forums.htm >> > >> >> > > ---------------------------------------------------------------------- >> > > For information about J forums see >> http://www.jsoftware.com/forums.htm >> > > >> > >> > -- >> > ---------------------- >> > mail written using NEO >> > neo-layout.org >> > >> > ---------------------------------------------------------------------- >> > For information about J forums see http://www.jsoftware.com/forums.htm >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
