On Sun, 10 Jan 2021 at 19:09, 'Bo Jacoby' via Programming < programm...@jsoftware.com> wrote:
> Dear friends. > I sincerely apologize to Hauke for wrongly accusing him for improving > before understanding. Talking about Aleph triggered me. > The ordinal fraction file is not merely a tree. To the branch 13500 is > attached a two times two matrix with rows 13510 ADORATUR and 13520 > GLORIFICATUR and columns 13501 PATRE and 13502 FILIO. > 13500: CREDO IN SPIRITUM QUI CUM PATRE ET FILIO SIMUL ADORATUR ET > GLORIFICATUR AMEN. > The two records > 135 QUI > 135 CUM > have the same line number so that no query can separate them. It means the > same thing as > 135 QUI CUM > The conjunctions > 13509 ET > 13509 SIMUL > 1359 ET > are marked with digit nine. They are omitted from the answer unless the > query has a zero (or nine) in the corresponding digit position. (The query > is not supposed to contain digit nine). > Ordinal fractions look a little like arrays, but: > > - the dimension of any ordinal fraction is infinite. > - an ordinal fraction does not have indivisible elements. > - an ordinal fraction may contain data. > - an ordinal fraction has sub-ordinal fractions. > Note that: > FACTOREM is incompatible to UNUM. 113><111. > FACTOREM is subordinate to DEUM. 113<110=11. > FACTOREM is superordinate to CÆLI. 1130>1131. > 1131: CREDO IN DEUM FACTOREM CÆLI AMEN > > To Raul: We are not limited to 9 labels at any level. Ten possibilities > are labeled 11 12 13 14 15 21 22 23 24 25. We do not need to label the > rows, 10 20, or the columns, 01 02 03 04 05, if it does not make sense. > To Justin: > "The base sets should also be hyperedges. For the values corresponding to > an edge, take the cartesian product over the corresponding subsets of base > edges usingthe order defined." I don't understand what you are saying. To > me ordinal fractions is about arithmetic rather than about geometry. Look up hypergraphs. Pictures help. > "I'm not quite sure what is implied by 11 DEUM coming after 111 UNUM, > and not next to 11 IN. I don't know enough latin to comment." > The text CREDO IN UNUM DEUM means: I believe in one god. They say that god takes many forms. Why create such a distinction between arithmetic and geometry? Algebraic geometry doesn’t. There is a proof of Fermat’s last theorem (arithmetic) in algebraic geometry. For another example, Euclidean and projective share some axioms but not all. However, certain statements, when mapped from Euclidean to projective, are more elegantly proved. > > Thank you very much, everyone! > Bo. > Den søndag den 10. januar 2021 12.54.03 CET skrev Hauke Rehr < > hauke.r...@uni-jena.de>: > > • 9 labels > > Yes, the “digit” restriction should be abstracted away when > reasoning about the concept; > When I read the paper, I tended to agree that in practice, > though, digits are easy to deal with, and it doesn’t hurt > introducing another fractional digit without semantics > only in order to have enough places to fit things into. > > But it doesn’t work well with the concept of having only > an existential (1–9) and universal (0) qualifier. > So sadly, we have to get around that limitation some way > or th’other, I think. > > • edges > I totally forgot about this when dealing with lines of the > example which never contained 0s (other than implicitely > trailing ones) because I think data should always look like > that (regex): [1-9]+ with implicit trailing 0* > > So that’s another question @Bo: > do we need to have things like 32051 in any place other than > in a query? it used to describe a concept, but I think that > was merely an aid for people thinking in terms of variables > and relational db > otoh, the example explicitely praised the benefits of being > able to see which concepts are met by a query so maybe we > have to deal with this > > I just had some ideas and they all don’t get it done correctly. > I need to take some rest first, but the representations we have > been constructing are obviously insufficient. > > Am 10.01.21 um 12:29 schrieb Raul Miller: > > This system supports different kinds of transitive or "edge" concepts. > > > > There's strict sequence (no zeros). > > > > There's also allowance for alternatives (with zeros). > > > > It's also a bit awkward that you're limited to 9 labels at any level, > > which implies some shenanigans with large and/or growing data sets. > > > > FYI, > > > > -- > ---------------------- > 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
