Raul Miller replied to my comment on order pairs: On 4/6/07, Tracy Harms <t_b_harms at yahoo.com> wrote: >> I consider the basic data structure to be the >> ordered pair. With less than ordered pairs, I >> don't see what would count as structuring. With >> ordered pairs, it seems to me that any data >> structure can be created. > > I used to think that way, but I've since decided > that ordered pairs are a special case of sequences.
I pointed to ordered pairs because Terrence seemed to be thinking about the basic underpinnings of data structuring, so it seemed to me worth pointing to the minimal case. The minimal case, with regard to sequencing, seemed to be two. You're getting me to reconsider that. It may be more minimal to put this in terms of concepts that are independent of magnitude. This approach fits with my thoughts on the recent topic of rank, which are: Arrays are defined by two qualities, substance and position. (Different terms may be used, such as presence and orientation.) The two edge cases are atoms, which instantiate substance without position, and null, which instantiates position without substance. Sequence is a plain term for the linear (minimal) positioning of items. The austerity of alignment (i.e. being-in-a-line) seems much more fundamental than the way two is the minimum count of items for a line (list, or vector) to "exist." What is important is not the tally of items listed, it is that the axis of measurement is a result of directional assessment. The discovery of zero involved extending the concept of magnitude to the absence of whatever thing might be counted. Sequence can be similarly extended, so that we need not think only of sequences that involve item counts of two and beyond. We can also think of rank-one nouns with one atom, and rank-one nouns that are entirely empty. #$,0 1 #$'' 1 An axis, then, is an abstract distinct direction in which things are counted. Having identified an axis, it is incidental how many items fall along it. From this it is right to say, as you indeed did say, that "ordered pairs are a special case of sequences." Tracy Harms ____________________________________________________________________________________ The fish are biting. Get more visitors on your site using Yahoo! Search Marketing. http://searchmarketing.yahoo.com/arp/sponsoredsearch_v2.php ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
