On Sun, 16 May 2021 11:26:06 +0000, Bo Jacoby wrote (to [email protected] <mailto:[email protected]>): ... ordinal fractions are more general than arrays. ----- Comments on "ORDINAL FRACTIONS / the algebra of data" by Bo Jacoby at: https://www.academia.edu/10031088/ORDINAL_FRACTIONS_the_algebra_of_data
Constricting the symbol set to ten characters requires the introduction of extraneous structure in the representation of data having some aspect with a greater than ninefold variation. The same principles could be applied to 16 hexadecimal digits, or any larger system. In J, a list of digits, lowercase letters, and uppercase letters could readily provide 62 symbols. Even more generally, arbitrary bitstrings of length n provide 2^n distinct values, which may be stored individually in arrays, or concatenated for storage and split apart for use. It is not immediately clear how to deal with data which receive two different representations in the hierarchy, as when "grandfather" of primary object A is also "grandfather" of object B. It would seem to require acceptance of an equation "A01 = B01", which would normally be erroneous. (This occurs when their relationships do not form a tree, but a lattice--or even loops!) --Art Anger ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
