Sorry for the many posts from my side, but:

After reading, and re-reading, though, I don’t quite understand.
How could hyperedges touch at most one element of each base set?
I obviously have a wrong picture of what is being referred to
by the term “base sets”.
I thought they correspond to sequences of digits without any 0s.
And the way I understand the system, as soon as those numbers
are given, the set of possible hyperedges is fixed.
So what is meant by “new hyperedges” then?

I feel I am the one being obtuse.
Could you elaborate on how this translates to sets of lines in
the CREDO example?


Am 10.01.21 um 07:46 schrieb Justin Paston-Cooper:
> 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 <[email protected]>
> 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 <
>> [email protected]> 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
>>> <[email protected]>:
>>>
>>>  On Sat, 9 Jan 2021 at 15:59, Hauke Rehr <[email protected]> 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 <
>>>>> [email protected]> 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 <
>>>>>> [email protected]>:
>>>>>>
>>>>>>  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
>>>>>> <[email protected]> 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 <[email protected]>:
>>>>>>>
>>>>>>>  Thanks. I have been meaning to look at that.
>>>>>>>
>>>>>>> On Thu, 7 Jan 2021 at 23:33, Joe Bogner <[email protected]>
>>> 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 <
>>>>>> [email protected]>
>>>>>>>> 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 <[email protected]>
>>>>>> 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.
>>>>>>>>>>
>>>>>>
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