The verb ({) can be considered shorthand for ([:{.}.)
4 { i.7
4
4 ([:{.}.) i.7
4
showing that the argument (4) is actually a cardinal number rather than an
ordinal number. The element (4 { i.7) is not the fourth but rather the first
after having dropped 4 elements. The element (0 { i.7) is not the "zeroth" but
rather the first after having dropped 0 elements. There are no ordinal numbers
in J.
Den 1:54 torsdag den 31. maj 2018 skrev Jose Mario Quintana
<[email protected]>:
Raul Miller:
> This dating system dates back to the romans, and pre-dates the invention
of
> the zero.
Right, it preceded the invention of the zero in both, the New World, and
the Old World.
Bo Jacoby:
> Are you missing the point? The ordinal numbers used for counting centuries
> and years are 1. 2. 3. and so on. No such thing as a zeroth century.
I do not think so. I am aware that there are different perspectives.
There is no "zeroth century" in between the 1st century BC and the 1st
century AD (also written just as the 1st century). However, zeroth is
currently regarded as a word in English and, in that sense of the word, the
zeroth century AD is the 1st century BC and the zeroth century BC is the
1st century AD. (It is a mess precisely because there is no "zeroth
century" in between!)
One of the dates I mentioned, 13.0.0.0.0, is written in the modern notation
of the Long Count Calendar. This date, which coincided with a winter
solstice, refers to the day 0 (i.e., the first day in the context of the
common English language) of a new cycle.
Likewise, the finite mathematical ordinals are 0, 1, 2, ... and J seems to
follow this scheme; see, for example,
A. Nouns
http://www.jsoftware.com/help/dictionary/dicta.htm
In particular, as I showed it before in a previous message (see below), the
verb { selects the items of its right argument in this natural way.
Although, if one is prepared to go backward, one can also do the following,
_2 _1{ '3rd' ; '2nd' ; '1st'
┌───┬───┐
│2nd│1st│
└───┴───┘
_3 { '3rd' ; '2nd' ; '1st'
┌───┐
│3rd│
└───┘
PS. From my vantage point, a series of messages preceding this one
illustrates beautifully what happens when you do not start from zero ;)
On Wed, May 30, 2018 at 9:10 AM, Raul Miller <[email protected]> wrote:
> Right: the year 1941 was in the twentieth century.
>
> This dating system dates back to the romans, and pre-dates the invention of
> the zero.
>
> Thanks,
>
> —
> Raul
>
> On Wednesday, May 30, 2018, 'Bo Jacoby' via Chat <[email protected]>
> wrote:
>
> > Are you missing the point? The ordinal numbers used for counting
> centuries
> > and years are 1. 2. 3. and so on. No such thing as a zeroth century.
> > 0-origin indexing is useful, but the numbers are not ordinal. The degree
> of
> > a polynomial is the maximum exponent, and the exponents are cardinal
> > numbers. So "second degree" is bad language for degree 2.
> >
> > Den 0:59 onsdag den 30. maj 2018 skrev Jose Mario Quintana <
> > [email protected]>:
> >
> >
> > This nice day, May 29, 2018, according to some Day Keepers, is
> 13.0.5.9.5.
> > That is right, they have been counting days avoiding inevitable
> complicated
> > correction rules when trying to synchronize years and days (KISS). (Yet,
> > the date 13.0.0.0.0 corresponded to December 21, 2012.)
> >
> >
> > On Tue, May 29, 2018 at 9:16 AM, Raul Miller <[email protected]>
> > wrote:
> >
> > > Clearly, this year is 10 Prairial CCXXVI
> > >
> > > Well, unless you are using the Hebrew calendar - then it’s the year
> 5778.
> > >
> > > Etc...
> > >
> > > (Translation: the answer here depends on your religious beliefs)
> > >
> > > I hope this helps.
> > >
> > > Have a nice day.
> > >
> > > Thanks,
> > >
> > > —
> > > Raul
> > >
> > > On Tuesday, May 29, 2018, 'Bo Jacoby' via Chat <[email protected]>
> > wrote:
> > >
> > > > Do we agree that this year, AD 2018, is the eighth year of the of the
> > > > second decade of the first century of the third millenium? Or do you
> > > > consider it to be the seventh year of the first decade of the zeroth
> > > > century of the second millenium? The time passed until year 2018 are
> 2
> > > > millenia, 0 centuries, 1 decade and 7 years, but those are not
> ordinal
> > > > numbers.
> > > >
> > > > Den 3:41 tirsdag den 29. maj 2018 skrev Jose Mario Quintana <
> > > > [email protected]>:
> > > >
> > > >
> > > > Personally, I feel more comfortable with the usual mathematical
> > > > perspective: 0 is the first ordinal, 1 is the second, etc. Moreover,
> > > from
> > > > this perspective (as far as I remember), there is no difference
> between
> > > > finite cardinal and ordinal numbers.
> > > >
> > > > ] A=. 'First' ; 'Second' ; 'Third' ; 'Fourth' ; 'Fifth'
> > > > ┌─────┬──────┬─────┬──────┬─────┐
> > > > │First│Second│Third│Fourth│Fifth│
> > > > └─────┴──────┴─────┴──────┴─────┘
> > > > 0 { A
> > > > ┌─────┐
> > > > │First│
> > > > └─────┘
> > > > 1 2 3 4 { A
> > > > ┌──────┬─────┬──────┬─────┐
> > > > │Second│Third│Fourth│Fifth│
> > > > └──────┴─────┴──────┴─────┘
> > > >
> > > >
> > > > On Sat, May 26, 2018 at 12:38 AM, 'Bo Jacoby' via Chat <
> > > [email protected]
> > > > >
> > > > wrote:
> > > >
> > > > > Ordinal numbers are not considered in J. The expression 2{y should
> > not
> > > be
> > > > > read as "take the second element of y" but as "skip 2 elements and
> > take
> > > > the
> > > > > left element of y".
> > > > > Ordinal Fractions use one-digit ordinal numbers for indexing. There
> > are
> > > > > but nine one-digit ordinal numbers: 1 2 3 4 5 6 7 8 9, because 0 is
> > not
> > > > an
> > > > > ordinal number, and 10 is not a one-digit number. Digit 0 - not
> being
> > > an
> > > > > ordinal number - is available to indicate empty digit positions.
> > > > >
> > > > > Example: The roman numeral MMLIII means (M*2)+(L*1)+(I*3) . It can
> be
> > > > > encoded (arabic style) without delimiting spaces: 2001003 . The
> > zeroes
> > > > > in 2001003 mean that terms involving D C X and V are omitted.
> > Likewise,
> > > > the
> > > > > ordinal fraction 2001003 means (M=2)*.(L=1)*.(I=3). The zeroes
> > > > > in 2001003 mean that conditions involving D C X and V are omitted.
> > > > > Thanks.
> > > > > Bo.
> > > > > Den 0:06 lørdag den 26. maj 2018 skrev Jose Mario Quintana <
> > > > > [email protected]>:
> > > > >
> > > > >
> > > > > Stopwatches and odometers can also be used to label time intervals
> > to
> > > > > associate them to events occurring in those intervals and keep
> track
> > of
> > > > the
> > > > > order in which they take place. In fact, conceptual odometers
> > counting
> > > > > days have been used at least for two millennia and detecting a day
> > > when a
> > > > > big cycle ends and the day when the next begins is extremely hard
> to
> > > > miss.
> > > > >
> > > > > In addition, by starting at 0 when labelling sequential objects the
> > > > offset
> > > > > from the anchor is immediately evident; for instance, if the
> buttons
> > in
> > > > an
> > > > > elevator for the floors of the building are labelled: *G (0), 1 ,2,
> > ...
> > > > and
> > > > > I pressed 6, to get to the floor where I am then I know that if a
> > fire
> > > > > alarm goes off I will go down the stairs 6 floors and I will be on
> > the
> > > > > ground floor. However, if the fire alarm would go off right now in
> > my
> > > > > building, ... I would do nothing because there are too many damn
> > false
> > > > > alarms!
> > > > >
> > > > > In the context of the common English language, there is little
> doubt
> > > that
> > > > > the ordinal numbers are 1st, 2nd, 3rd, 4th, ... However, in
> another
> > > > > context (see, https://en.wikipedia.org/wiki/Ordinal_number ) they
> > are
> > > 0,
> > > > > 1,
> > > > > 2, ... (, ω, and so on).
> > > > >
> > > > > Personally, I have no problem relating both by saying 0 is the 1st
> > > > ordinal
> > > > > number, 1 is the 2nd ordinal, 2 is the 3rd ordinal, 3 is the 4th
> > > ordinal,
> > > > > etc.
> > > > >
> > > > > I understand that there could be instances where starting from 1
> > might
> > > be
> > > > > more desirable; apparently, that is the case for your Ordinal
> > Fractions
> > > > > where the digit 0 is used for a special purpose (although I cannot
> > see
> > > > the
> > > > > difficulty in starting from 0 and using, say, _ for the special
> > > purpose).
> > > > >
> > > > >
> > > > > On Fri, May 25, 2018 at 5:52 PM, Jose Mario Quintana <
> > > > > [email protected]> wrote:
> > > > >
> > > > > > :D
> > > > > >
> > > > > > It seems that these people like complications. They are not very
> > > smart
> > > > > or
> > > > > > maybe they are... Job security!
> > > > > >
> > > > > >
> > > > > > On Wed, May 23, 2018 at 7:14 PM, David Lambert <
> > [email protected]
> > > >
> > > > > > wrote:
> > > > > >
> > > > > >> Our credit union had used employee numbers for account numbers.
> > But
> > > > ran
> > > > > >> out of 5 digit numbers. Did they change our accounts to 0abcde?
> > > No!
> > > > > >> They
> > > > > >> multiplied 10 leaving us as abcde0.
> > > > > >> ------------------------------------------------------------
> > > > ----------
>
> > ----------------------------------------------------------------------
> > For information about J forums see http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
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