Ian, The link http://www.nationmaster.com/encyclopedia/Ordinal-fraction contains my deleted wikipedia article. I wonder how it ended there!
I am not familiar with Frege's Begriffschrift. On this link http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Archives/Mathematics/2010_July_17#Algorithm_to_combine_trees.3F you will find another detailed example. I don't know how to use the J wiki. I don't think you can make the artificial catholic without using ordinal fractions. Not by an SQL database, nor by a J array. Those who hate it are not interested in artificial catholicism, and they don't understand that it is a general method for modelling data. - Bo >________________________________ > Fra: Ian Clark <earthspo...@gmail.com> >Til: programm...@jsoftware.com >Sendt: 19:34 torsdag den 29. november 2012 >Emne: Re: [Jprogramming] Translating BASIC into J > >Bo, > >Is this a numerical encoding of (say) Frege's Begriffschrift? That's >what it looks like to me, from your all-too-brief description. You'll >need to write it up somewhere, because nobody can experiment with it >for themselves otherwise. Should I be looking at your Göteborg paper? > >How about airing it in the J wiki? If this is capable of encoding & >deriving wff's in 1st order predicate calculus, then I can think of >practical uses for that. A J database of theorem dependencies in >Matrix Algebra, for example. It need only be at the level of a K-12 >teaching tool. Can you provide a link in my "credo" paper to a note on >the numbering scheme it uses? > >And as for people hating the idea: if it can solve practical problems >better than other known methods, animosity is misplaced. There are >metro systems running on Zadeh's Fuzzy Logic. To the numerous people >who hate it, one just has to ask: do the trains get to their >destinations or don't they? > >Ian > >On Thu, Nov 29, 2012 at 5:28 PM, Bo Jacoby <bojac...@yahoo.dk> wrote: >> Ian, >> >> Note that pray '0' and pray '00' is not the same thing. >> >> 0: CREDO CONFITEOR ET EXPECTO AMEN >> 00: CREDO IN DEUM ET IN JESUM ET IN SPIRITUM ET ECCLESIAM CONFITEOR BAPTISMA >> ET EXPECTO RESURRECTIONEM ET VITAM AMEN >> >> The linenumbers in the database may be padded to the right with zeroes, but >> not the question number. >> >> >> (Some authors spell EXSPECTO rather than EXPECTO, because it means 'look >> out' and has nothing to do with the heart). >> >> I invented Ordinal Fraction, the word, the concept, and the arithmetic, and >> everybody hates it but myself. It is far too simple. My article was deleted >> from wikipedia where original research is prohibited. >> >> Consider the digits (d=.i.>:9) and the proper digits (p=.>:i.9) . The >> ordinal fraction 0 is the infinite cartesian power of the proper digits. It >> is the total set of infinite sequences of proper digits. The subsets of 0 >> where a finite number of prescribed digit positions have prescribed values >> are the ordinal fractions. The prescribed digit positions are noted with the >> prescribed proper digit, and the other digit positions are marked with digit >> 0. So an ordinal fraction looks like a decimal number except that it is >> padded with zeroes to the right rather than to the left. >> 1=10=1000 &c. >> >> A concept is modelled by an ordinal fraction in such a way that the logical >> relations between concepts are modelled by arithmetical relations between >> ordinal fractions. >> >> 'Every man is mortal, Alexander is a man, so Alexander is mortal' is >> modelled like this >> 1 mortal >> 11 man >> 111 Alexander >> >> That's all for today. >> - Bo >> >> >> >> >>>________________________________ >>> Fra: Ian Clark <earthspo...@gmail.com> >>>Til: programm...@jsoftware.com >>>Sendt: 16:29 torsdag den 29. november 2012 >>>Emne: Re: [Jprogramming] Translating BASIC into J >>> >>>Bo, >>> >>>I am so sorry for slagging off your program! >>> >>>Had I known it was yours, I wouldn't have written what I did. I >>>assumed this was an educational curio you came across (as I often used >>>to do in hobby magazines) and hadn't quite known how it worked -- >>>because you had claimed you didn't know how to turn it into J. >>> >>>I don't either. But I cheated, and sidestepped the >> problem. >>> >>>I doubt if I'd have been able to write it better, for its purpose. >>>Which I'd say is to exhibit in lectures and not to support some >>>commercial (or religious :-) enterprise. I've written reams of BASIC >>>in my time, on all sorts of now-defunct machines, especially for IT >>>courseware. I've taught Software Engineering at postgrad level -- so I >>>think I'd be permitted to say that classic BASIC is not a language for >>>dogmatically sound programming! >>> >>>Nevertheless my little "slur" served to make the point that to re-cast >>>the algorithm to lend itself to J better, you actually find yourself >>>untangling the PRINTs from the string-processing, i.e. separating >>>processing from I/O (and preparation for I/O). I've migrated a lot of >>>heritage code too, from mainframe to MSDOS to Windows to web -- and >>>the more closely the programmer has stuck to the principle of >>>separating processing from I/O the easier it is to migrate. >> It can't >>>just be an accident. So I was grinding an axe there. >>> >>>I was doubtful about permitting (pray) to accept its y-arg as an >>>integer as well as a string of digits. I only permitted it for the >>>convenience of experimenters. Thus (pray '010') is decidedly not the >>>same as (pray '10') but (pray 010) confounds the two. >>> >>>Thanks for explaining where the record numbering system came from. >>>Since it didn't matter for the purpose of translating the code, I >>>didn't make the effort to understand how it worked. But it's really a >>>topic of investigation in its own right. It reminds me of >>>Wittgenstein's paragraph-numbering system in Tractatus. I'd be >>>grateful for a reference to "ordinal fractions" -- Wikipedia doesn't >>>seem to recognise the term in an arithmetical rather than a linguistic >>>sense. I guessed that it was a way of representing a tree as a single >>>integer. Such a domain would have interesting mathematical >> properties, >>>and a J library to handle it would have its uses, given the lack of an >>>agreed "natural" way of handling trees in J, as opposed to Python say. >>>(I'm forgetting of course the nested box structure delivered by 5!:1). >>> >>>IanClark >>> >>>On Thu, Nov 29, 2012 at 10:52 AM, Bo Jacoby <bojac...@yahoo.dk> wrote: >>>> Ian, you did an amazing job! Thank you very much! >>>> >>>> You write about my BASIC program: "Like many amateur programs, it >>>> thoroughly mixes up input, processing and output. Even in the 1960s when >>>> BASIC was invented (Kemeny & Kurtz, >>>> 1964) this was recognised to be a bad thing". Yes, everybody knew how to >>>> criticize, but few BASIC programs were actually easy to read and >>>> understand. My excuse, apart from being such an amateur, is that I kept it >>>> down to 8 lines. It could have been worse. The input statements were >>>> INPUT;C$ >> which reads a textstring from the terminal, and LINE INPUT#1,A$ which >>reads a line from the file into a textstring. The output statements were >>PRINT":"; which outputs a colon without carriage return, and PRINT >>which outputs the carriage return - in those days the typewriter terminal >>had a physical carriage to return - and PRINT" ";A$; which outputs >>first a blank sign, then the word, and no carriage return. The statements >>A%=ASC(A$)-48: A$=MID$(A$,2) translates the first digit in the line number >>into an integer, and chops if off the string. >>>> >>>> The database structure is flexible in that it fuses the array structure >>>> and the tree structure together into a single structure. Compare pray 0 >>>> with pray 00 and pray 000 to see the tree structure, while pray 13500 >>>> shows a 2*2 array. >>>> >>>> >>>> In extended versions of the program >> in FORTRAN and in Pascal I included an editor to insert, modify and delete >>records. (If a record was there already it was modified, otherwise it was >>inserted. Empty records were deleted.) Modifying a line number restructured >>the database. For example changing 0 to 2 ment that all line numbers in the >>database were prefixed by digit 2. >>>> >>>> >>>> The line numbers are ordinal fractions: "1" is the first half and "2" is >>>> the second half, "first" and "second" are ordinals and "half" is a >>>> fraction. That's why! "0" means both halfs. >>>> >>>> >>>> Ordinal fractions are like arrays except: >>>> >>>> * an array has only a finite number of dimension, while an >>>>ordinalfraction has an infinite number of dimensions. >>>> * arrays have different shapes, while all ordinalfractions have >>>>the same shape. >>>> * an array may have subarrays and >> elements, while an ordinalfraction has sub - ordinalfractions, but no >>elements. >>>> * arrayelements have values and subarrays do not have values, >>>>while ordinalfractions have values. >>>> I am fascinated by the power of ordinal fraction arithmetic, but it is far >>>> more heretical than artificial catholicism. Beware of the inquisition! >>>> >>>> - Bo >>>> >>>> >>>> >>>>>________________________________ >>>>> Fra: Ian Clark <earthspo...@gmail.com> >>>>>Til: programm...@jsoftware.com >>>>>Sendt: 3:58 torsdag den 29. november 2012 >>>>>Emne: Re: [Jprogramming] Translating BASIC into J >>>>> >>>>>Here's my take on the topic: http://www.jsoftware.com/jwiki/IanClark/credo >>>>> >>>>>There's a script at the bottom of the wiki page you can download. >>>>> >>>>>I haven't attempted to replicate BASIC's itty-bitty I/O, all mixed-up >>>>>in the processing. As well write a mini interpreter in J and get it to >>>>>run the BASIC code! >>>>> >>>>>Instead I've intuited the algorithm and done it as a J-er would. >>>>>Might. >>>>>Would. >>>>>(At least, as this J-er would). >>>>> >>>>>IanClark >>>>> >>>>>On Tue, Nov 27, 2012 at 6:31 AM, 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. >>>>>> ...snipped... >>>>>---------------------------------------------------------------------- >>>>>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
