--- Fraser Jackson <[EMAIL PROTECTED]> wrote: > I have wondered if your spelling 'dimentions' and 'dimensions' are meant to
No, it's just spelling error. I and agree with Roger that if not used carefully, it can cause confusion, especially in normative definitions, such as ;. Cut. http://www.jsoftware.com/help/dictionary/d331.htm I just think if it is used it should be in accordance with everyday and scientific meanings which agree. One dimension refers to one axis. The whole shape or multiple axes is "dimensions" plural. > > How about: > > - rank (of noun) is length of shape or index vector > > - shape is vector of dimensions > > - dimension is extent of indices at axis > > - index is value (0..dimension-1 in index vector) at axis > > - axis is location (0..rank-1) in shape or index vector > > This terminology is a better reflection of the DoJ than the use of dimension > in my note. It still does not address the difference of usage of rank with > repect to verbs. I don't see this difference (that was also pointed out by Raul) It is clearly defined in B. Verbs. And I cannot say it better: The notion of verb rank is closely related to that of noun rank: a verb of rank k applies to each of the k-cells of its argument Informally, if noun rank qualifies matter, verb rank qualifies capacity of the opening through which the matter is passed. Rank is the same attribute of these complementary entities. > > Note definition in Wikipedia: > > the dimensions of a space are the total > > number of different parameters > > If dimension were synonymous with rank, it should > > have been used in singular "the dimension of space is > > the total number of parameters". > > I do not understand this. If I have a 3-dimensional array with shape 4 5 6 > I merely need three values to specify a point within that array. However if > I have a function defined over the array it may need 120 values or > parameters to specify it. The tasks of identifying a point in a three > dimensional space, and of defining a function over that space are quite > different. In Wikipedia definition, there was no additional function, just the space. I think there could a whole list of what these terms don't mean: - rank of matrix is always 2 and does not mean number of linearly independent vectors - rank of vector is always 1 and does not mean number of dimensions in a space whose coordinates it may represent - rank of verb is throughput capacity and not number of parameters it is defined with > It is a part of the genius of J that all interaction between verbs and the > data is controlled by the rank of the nouns on which the verbs operate, and > the rank of the nouns for which the verbs are defined. In every case if the > rank conjunction is not used with the verb there is an implicit conjunction > defined by the defaults. Calling these rules about the application of verbs > the 'rank' conjunction recognizes that they are all about the number of axes > of the arguments, but does associate a very different set of additional > concepts with the word 'rank'. As you noted unmodified execution Using conjunctions, including the rank conjunction, does not modify the capacity of verbs, it adds adapters with different openings, but the affected verbs continue to "see" the arguments with its original rank. atomicVerb=: <@+ atomicVerb i.3 4 +-+-+--+--+ |0|1|2 |3 | +-+-+--+--+ |4|5|6 |7 | +-+-+--+--+ |8|9|10|11| +-+-+--+--+ atomicVerb"1 i.3 4 NB. see? nothing happens +-+-+--+--+ |0|1|2 |3 | +-+-+--+--+ |4|5|6 |7 | +-+-+--+--+ |8|9|10|11| +-+-+--+--+ For this reason rank conjunction cannot "increase" the rank of affected verbs and only makes sense to decrease it, because application to higher rank nouns happens automatically. arrayVerb=: <@:+ arrayVerb i.3 4 +---------+ |0 1 2 3| |4 5 6 7| |8 9 10 11| +---------+ arrayVerb"1 i.3 4 +-------+-------+---------+ |0 1 2 3|4 5 6 7|8 9 10 11| +-------+-------+---------+ arrayVerb b. 0 _ _ _ atomicVerb b. 0 0 0 0 However, rank (and some other) conjunctions may change how the rest of the pipeline percieves the results <@+"1 i.3 4 NB. nothing happens +-+-+--+--+ |0|1|2 |3 | +-+-+--+--+ |4|5|6 |7 | +-+-+--+--+ |8|9|10|11| +-+-+--+--+ <@(+"1) i.3 4 NB. now <@ sees + differently +-------+-------+---------+ |0 1 2 3|4 5 6 7|8 9 10 11| +-------+-------+---------+ And so on. But all these mechanincs perfectly concord with and depend on the notion of array rank. > constrains the arrays which may be used to cells. Accessing subarrays > which are not a cell will require additional code. ____________________________________________________________________________________ Need Mail bonding? Go to the Yahoo! Mail Q&A for great tips from Yahoo! Answers users. http://answers.yahoo.com/dir/?link=list&sid=396546091 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
