That is clever! However, if I am interpreting it correctly, the verb - - ~:&* in the context of the hybrid numbering below does not seem to be as general as - is in the context of the astronomical numbering:
Historical ... 4 BC 3 BC 2 BC 1 BC AD 1 AD 2 AD 3 ... Hybrid ... _4 _3 _2 _1 1 2 3 ... Astronomical ... _3 _2 _1 0 1 2 3 ... The offsets of some years (left argument) relative to a given year, for instance, 4 BC match: _3 _2 _1 0 1 2 3 - _3 0 1 2 3 4 5 6 _4 _3 _2 _1 1 2 3 (- - ~:&*) _4 0 1 2 3 4 5 6 Yet, for AD 3 do not: _3 _2 _1 0 1 2 3 - 3 _6 _5 _4 _3 _2 _1 0 _4 _3 _2 _1 1 2 3 (- - ~:&*) 3 _8 _7 _6 _5 _2 _1 0 I am afraid another complication is required. On Sun, May 20, 2018 at 8:36 PM, Raul Miller <[email protected]> wrote: > Of course, you could use an expression such as (- - ~:&*) if you like... > > But, yeah, that convention does seem to be slightly... different from > straight - > > Thanks, > > -- > Raul > > > On Sun, May 20, 2018 at 5:54 PM, Jose Mario Quintana > <[email protected]> wrote: > > Historians refer to specific years, using a well-known event as an > anchor, > > naturally as AD 1, AD 2, AD 3, ... and, going backward, as 1 BC, 2 BC, 3 > > BC, ... > > > > Dropping the AD and inserting a - (_ in J) instead of BC allows for a > > simple general consistent rule for calculating the years elapsed between > > two dates by subtracting the lower date from the higher date; for > example, > > the years elapsed between (say, the beginning of) the year _4 and (the > > beginning of) the year 30 can be calculated by 30 - _4 ... > > > > Nevermind, who cares if you are sometimes off by one year because the > year > > 0 is missing? Presumably, some people who like to date celestial events > > precisely : > > > > Astronomical year numbering > > https://en.wikipedia.org/wiki/Astronomical_year_numbering > > > > PS. There has been some debate about the exact year when the actual > > aforementioned event happened: 4 BC, 1 BC, AD 1, ... > > > > > > On Sat, May 19, 2018 at 9:38 AM, 'Bo Jacoby' via Chat < > [email protected]> > > wrote: > > > >> The terms "ordinal number" and "cardinal number" has advanced > mathematical > >> meanings in the theory of infinite sets and transfinite numbers, but the > >> words also have ancient meanings in grammar. The semantics of a cardinal > >> number is to count the elements of a finite set, and the semantics of an > >> ordinal number is to identify a single element. This century is the > >> twentyfirst century. That is a 1-origin ordinal number. The number of > whole > >> centuries that have passed so far is 20. That is a 0-origin cardinal > >> number. /Bo. > >> > >> Den 12:49 lørdag den 19. maj 2018 skrev R.E. Boss < > >> [email protected]>: > >> > >> > >> > A solution to the problem is to distinguish between the ordinal > numbers > >> (first, > >> > second, and so on) and cardinal numbers (zero, one, and so on). The > first > >> > ordinal number is "first", and the first cardinal number is "zero". > >> Cardinal > >> > number are for indexing, not for counting. Thanks. Bo. > >> > >> > >> I like that very much, although I read different things in > >> https://www.wikiwand.com/en/Ordinal_number > >> "A natural number (which, in this context, includes the number 0) can be > >> used for two purposes: to describe the size of a set, or to describe the > >> position of an element in a sequence." > >> (...) > >> " Whereas the notion of cardinal number is associated with a set with no > >> particular structure on it, the ordinals are intimately linked with the > >> special kind of sets that are called well-ordered (...) " > >> (...) > >> " Ordinals may be used to label the elements of any given well-ordered > set > >> (the smallest element being labelled 0, the one after that 1, the next > one > >> 2, "and so on") and to measure the "length" of the whole set by the > least > >> ordinal that is not a label for an element of the set." > >> See also https://www.wikiwand.com/en/Cardinal_number . > >> > >> > >> R.E. Boss > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> > >> > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > >> > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
