You asked about "hermeneutical horizon" so I did decide on the religious aspect of the question.
2011/10/20 Viktor Cerovski <[email protected]> > > It's a bit longer post, but it demonstrates that numbers are > not arrays in J. > > > Björn Helgason wrote: > > > > It depends on what it is > > 123 can be a number > > 123 can be text > > You can change it from text to number and other way around. > > > > So 123 can be or become what you want it to be. > > > I was talking about 123 as defined in J, where > 123-as-text would be written '123'. > > Henry points out that any number can be interpreted as an > array with an empty shape. Then, there is also an interpretation > that an array with an empty shape can be considered a scalar. > So, in this above case this scalar is 123, so why not call, interpret, > think of it as of a number? > > > > What you believe it to be may not be what it really is. > > You have to test it and make sure it is the shape and character you > > believe > > in or not. > > After you find out what 123 is you can decide on what you want to do. > > To take 123 on in blind faith can prove to be a mistake and can cause > > problems and failures. > > > If by this you mean whether I believe that the printed representation > 123 of some noun tells us what the rank of the noun is, then of course > I don't believe this. For instance, if J session looks like: > > f x > 123 > > then I don't know whether the resulting 123 has rank 0 or 1, > but that's just how J prints nouns, and we can test the result > further to sort this out, as you also suggest. > > So I did some testing on whether it can be distinguished in J between > 123-as-number or 123-as-an-array. Basically, the issue cannot > be resolved simply by a single test: imagine that we call > all rank zero nouns that are numbers just, well, numbers. > > Let's instead look how the two concepts of 123 fit into the language. > > It indeed looks like 123 is an array: it has (empty) shape, rank 0, > and it has one element: > > e=:0$0 NB. empty array > > e -: $123 > 1 > #123 > 1 > 0{123 > 123 > 1{123 > |index error > | 1 {123 > > We get the index error because there is no second element of > 123-as-array. So far so good. But how do we then explain > the following: > > }.123 > > e -: }.123 > 1 > > 123 -: 123,e > 0 > > The problem with this can be stated in English as: > In J, when we drop the leading element of 123 we get > empty array, but when we append empty array to 123 we > don't get 123. > > Let us just say: that is how things are defined, a bit strange > as they might be. But then again, when 123 is a one > element array, I get the desired property *of arrays*: > > (1$123) -: 123,e > 1 > (1$123) -: 123,e,e > 1 > (1$123) -: 123,e,e,e,e,e,e,e > 1 > (1$123) -: e,e,e,123,e,e,e,e > 1 > > (In English: appending/prepending an empty array to > an array does not change it.) > > So from this follows the conclusion that 123 is not an array, > while 1$123 is. > > It is not anymore the matter of interpretation of 123, > but the structural/language issue with J, namely > that numbers are not arrays, unless, that is, we drop the > requirement that appending empty array doesn't do > anything to an array. > > > 2011/10/20 Viktor Cerovski <[email protected]> > > > > > > > Raul Miller-4 wrote: > > > > > > On Thu, Oct 20, 2011 at 9:43 AM, Viktor Cerovski > > > <[email protected]> wrote: > > >> Henry Rich wrote: > > >>> > > >>> Point of nomenclature: every noun has a shape. All shapes are lists. > > >>> The shape of an atom is an empty list. > > >>> > > >>> (also, all nouns are arrays, ecch) > > >>> > > >> Statements like "all nouns are arrays" is hard to make precise > > >> due to the dynamic typing of J. > > > > > > An array is a region of computer memory whose interpretation (and, if > > > we exclude things like sparse arrays, its size) is determined by its > > > shape and its type. > > > > > > A shape is a list of non-negative integers whose product is the number > > > of elements in an array. > > > > > > To make this precise you have to enumerate those types... > > > > > Given all these conditions and definitions (a big given!), > > what is then hermeneutical horizon of 123 in J: > > > > Should I interpret it as a number, or an array, or both, > > or neither? > > -- > > View this message in context: > > > http://old.nabble.com/%7B.-y-produces-an-array.-tp32687373s24193p32690306.html > > Sent from the J Programming mailing list archive at Nabble.com. > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > > > -- > Björn Helgason, Verkfræðingur > Fornustekkum II > 781 Hornafirði, > t-póst: [email protected] > gsm: +3546985532 > twitter: @flugfiskur > http://groups.google.com/group/J-Programming > > > Tæknikunnátta höndlar hið flókna, sköpunargáfa er meistari einfaldleikans > > góður kennari getur stigið á tær án þess að glansinn fari af skónum > /|_ .-----------------------------------. > ,' .\ / | Með léttri lund verður | > ,--' _,' | Dagurinn í dag | > / / | Enn betri en gærdagurinn | > ( -. | `-----------------------------------' > | ) | (\_ _/) > (`-. '--.) (='.'=) ♖♘♗♕♔♙ > `. )----' (")_(") ☃☠ > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > > -- > View this message in context: > http://old.nabble.com/%7B.-y-produces-an-array.-tp32687373s24193p32691792.html > Sent from the J Programming mailing list archive at Nabble.com. > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > -- Björn Helgason, Verkfræðingur Fornustekkum II 781 Hornafirði, t-póst: [email protected] gsm: +3546985532 twitter: @flugfiskur http://groups.google.com/group/J-Programming Tæknikunnátta höndlar hið flókna, sköpunargáfa er meistari einfaldleikans góður kennari getur stigið á tær án þess að glansinn fari af skónum /|_ .-----------------------------------. ,' .\ / | Með léttri lund verður | ,--' _,' | Dagurinn í dag | / / | Enn betri en gærdagurinn | ( -. | `-----------------------------------' | ) | (\_ _/) (`-. '--.) (='.'=) ♖♘♗♕♔♙ `. )----' (")_(") ☃☠ ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
