Let me tell you how calendars are treated with ordinal fractions. Consider the
years from 1 to 5000. Any year is a year in a decennium in a century in a
millenium, The year 2010 is the tenth year in the first decennium in the first
century in the third millenium.
(4$10)&#:&.<:2010
3 1 1 10
As 0 is not an ordinal number, ten objects should not be numbered neither
(i.10) nor (>:i.10) , but (10#.>:2 5#:i.10)
The year 2010 is the fifth year of the second half of the first decennium of
the first half of the first century of the first half of the third millenium.
10#.(7$5 2)&#:&.<:2010
3111125
This ordinal fraction corresponds to a condition like this:
(M=3)*.(D=1)*.(C=1)*.(L=1)*.(X=1)*.(V=2)*.(I=5)
Digit zero is position-filler, so 3110000 is "the 21st century", corresponding
to the condition (M=3)*.(D=1)*.(C=1).
There are
5000 = */7$5 2
individual years from 1 to 5000, and
34992 = */>:7$5 2
subsets are adressable as ordinal fractions. The total number of subsets of a
5000-set is 2^5000, so being an ordinal fraction is an exclusive property of a
subset.
This offers a simplification of data structures. The J concepts of arrays,
sparse arrays, and boxed arrays, are unified as ordinal fractions. Also
relational databases are simplified, because there is only one method of
adressing, rather than at least three.
Den 9:47 lørdag den 2. juni 2018 skrev PR PackRat <[email protected]>:
On 6/1/18, R.E. Boss <[email protected]> wrote:
> IMO there is definitely a year 0, ...
With all due respect, ask any historian (or others who deal with dates
in the various divisions of knowledge). I'm sure they will indicate
that the years at the switch between BC and AD are as follows (I can't
do nonproportional spacing in Gmail, so please excuse the possible
appearance):
BC AD
3 2 1 1 2 3
Or, using a numerical approach (negative dates for BC):
-3 -2 -1 1 2 3
Dec. 31, 1 BC was followed by Jan. 1, 1 AD (in our terminology). It's
a world standard. It's just the way it is.
Of course, nobody back then used those dates. The dates would would
have been in terms of A.U.C. (ab urbe condita = "from the founding of
the ciry [of Rome]"), which occurred in our 753 BC. So 753 AUC (1 BC)
would have been followed by 754 AUC (1 AD). The current year
numbering system (BC, AD) was developed by a monk named Dionysius
Exiguus in 525. So blame *him*. ;-)
> and whether Christ was born in that year, or not, I don't care?
The exact year of the birth of Jesus Christ is unknown, so it really
doesn't matter. But it certainly was not in a year 0 or even the year
1. He had to have been born before Herod the Great died, which is
usually dated as 2 BC or 1 BC. Some astronomers favor Christ's birth
as early as around 6 BC or 5 BC for astronomical/astrological reasons
(but the wise men = astrologers may have started 2 years earlier than
the birth). This leaves 4 BC to 2 BC as the most commonly stated
possibilities. Why the discrepancy? Dionysius (above) made an error
based on which Roman records he used for the dating.
Harvey
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