Very good points systematically presented. Here's some thought related to some areas of discussion.
--- Fraser Jackson <[EMAIL PROTECTED]> wrote: > When every data object is an array the number of axes or the conventional > concept of dimension of the array specifies an important attribute of the > data. Oleg suggested we should give more emphasis to both the terms, axes > and dimension. I agree. I did not mean that "dimension" need to replace the word rank, if only in phrasal expressions like 3-dimensional array. Otherwise "rank" of array is very clear and unambiguous. Cf. "surface has two dimensions", i.e. rank is 2, not "surface has dimension two". http://www.m-w.com/dictionary/dimension I was pointing out that _in the Dictionary_, "dimension" is synonymous with shape but applied as measure in index space rather to arrays, thus uncountable. However, _I am_ now more inclined to refer to shape or such measure as "dimentions" (plural), as in dimensions of a k-cell are k trailing axes of the shape. ... > Its shape is a single element vector, which is simply the number of items > (tally) in the list. I.e. is a vector whose single element is the tally... (rank usage) > A dimension n noun is simply a list of dimension n-1 nouns of the same I'd say, a rank-3 noun, or 3-dimensional noun, ... (otherwise, I think, it's neologism, whereas it good to stay in familiar paradigm) > shape. Each time we form a list, we add to the set of axes over which the > array is defined. Each atom in the array becomes a value at some point in a > discrete n dimensional space. Very well put. Even, ... we prepend a dimension to axes ... (if you like dimensions :) ) > I think Oleg suggests referring to the location in the shape vector as the > axis. For most high dimensional nouns it is essential to be able to refer > to specific axes. Using axis for that is consistent with common usage in > many contexts. How about: - rank (of noun) is length of shape or index vector - shape is vector of dimensions - dimention is extent of indices at axis - index is value (0..dimention-1 in index vector) at axis - axis is location (0..rank-1) in shape or index vector, Three-dimensional does not mean that its dimension is three, but that it has three dimensions. E.g. noun of shape 4 5 6 has dimentions 4 5 6 (or 4x5x6): dimension at axis 0 is 4 , dimension at axis 1 is 5, etc. ... > Using dimension, axis and shape in this way enables a clear specification of > different attributes of an array. It is different from the DoJ which uses > the term rank for what I have called dimension. That causes some confusion > for reasons outlined below. Note definition in Wikipedia: the dimensions of a space are the total number of different parameters If dimention were synonymous with rank, it should have been used in singular "the dimention of space is the total number of parameters". ... > In the DoJ rank is used three ways. It is used for the conjunction, it is > used to specify the dimension in the sense above (II.A) and it is used to > specify the dimension of a function argument or arguments(II.B). I have the > greatest respect for the years of careful work which Ken and Roger have put > into the DoJ but I think the word rank is used for too many related but > distinct ideas. I think on the contrary: the consistent reference to "rank" creates possitive association. > In general, the result shape is shape (shape of frame), (shape of result > applied to the cell shape). Good observation. ____________________________________________________________________________________ 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
