Retorts

Counting Down to the Millennium

Some thoughts and queries on cardinality vs. ordinality following Bill Keir's column (Viewpoint, May).

Why, when we are counting things in an upward direction do we start at one ("one...two... three... four... five"), but when we are counting in a downward direction do we continue to zero ("five... four... three... two... one... zero")?

How long have we been doing this? That we have not always done so can be seen in those films that have a leader that consists of the numerals counting down: the last numeral you ever see is the "2" because the film itself starts at "1".

At Cape Canaveral, why do they never have lift-off at zero? The countdown always seems to put it about a second later ("three... two... one... zero... lift-off").

When dealing with ages, why in New Zealand do we not regard a person as being "over 9" (say) until the 10th birthday rolls around? A typical set of age limits for a colouring competition would read something like "under 5, 5-8, over 9" in England, but "under 5, 5-8, over 8" here.

Do people really "grasp that they are not eight years old until eight full years have elapsed since they were born"? Why then does the biography of Frank Sinatra report him as "about to enter his eightieth year" when it was published when he was already 79?

Incidentally, the Julian Day definition is incomplete unless you also specify that dates are to be evaluated using a proleptic Gregorian calendar, using the astronomical numbering of years, which does include a year zero. And what did happen at 1pm on 1st January 1994?

Does anyone know why the numbering starts in 4713BC? Admittedly, it is the start of Joseph Scaliger's Julian Period (of 7,980 years), but knowing that merely transfers the question.

Giving the first century only 99 years will not explain why the 20th century started on 1st January 1901 (try the Golden Edition of the Daily Mirror, or the choice of that date for the start of the Commonwealth of Australia for confirmation) or why the last year of the 18th century was 1800 (Les Misérables, Part 2, Book 5, Chapter 4).

In Russell Dear's 5th question, if you have drawn a ball once originally, and repeated that process four times, you have drawn a total of five balls, so the next one is the sixth, not the fifth.

Does all this have any real relevance to New Zealand? Yes: tourism is a significant industry. We should be aiming for two bites of the cherry by pulling the visitors in for the 1st January 2000 as "see the first sunrise of the year 2000", followed by a second set of tourists the next year as "see the first sunrise of the new millennium". For once, accurate and honest equals higher profits.

M. Strawson, Haywards

To answer just one question: Scaliger devised his Julian Period of 7,980 years by multiplying three chronological cycles in use in the late 16th century (an 18-year solar cycle, a 19-year lunar cycle and a 15-year Roman tax cycle). This would allow a Julian date within a single period to be established for any event dated by these cycles, or by correlated Christian, Hebrew, Greek, Roman or Arabic chronologies.

The Julian Period started with the cycles synchronized. Scaliger calculated Christ had been born in the period's 4,713th year. As a piece of mathematical convenience it was very handy, but never really caught on (it predated the calculated start of Creation!). See Alfred Crosby's The Measure of Reality (Cambridge 1997) for further interesting historical material.