Wikipedia:Reference desk/Archives/Mathematics/2015 October 27

= October 27 =

Counting starting with 0
Twenty years ago, John Conway wrote a story about a man named Sierpinski, showing that the natural way to count is to start with 0, not 1. Conway looks forward so hard to the day children learn to start counting with 0. Is Conway really expecting such a day?? (See the following URL for the story):

http://mathforum.org/kb/thread.jspa?forumID=13&threadID=31703&messageID=129435

Georgia guy (talk) 15:43, 27 October 2015 (UTC)


 * Related biographical links: John Horton Conway (who invented Life) and Wacław Sierpiński (who invented the triangle and carpteing). -- ToE 23:08, 27 October 2015 (UTC)
 * Subject link: Zero-based numbering. And relate to the thread you linked: Empty set. -- ToE 23:34, 27 October 2015 (UTC)


 * From the thread you linked, Conway wrote:
 * The old Roman mile ("mille", meaning "one thousand"), really consisted only of 999 paces, since it was counted in this way, from "1" at the start of the first pace to "1000" at the end of the 999th.
 * This is not supported by Mile. -- ToE 02:44, 28 October 2015 (UTC)


 * As for the Sierpinski anecdote Conway quotes:
 * Waclaw Sierpinski, the great Polish mathematician, was very interested in infinite numbers. The story, presumably apocryphal, is that once when he was travelling, he was worried that he'd lost one piece of his luggage. "No, dear!" said his wife, "All six pieces are here." "That can't be true," said Sierpinski, "I've counted them several times; zero, one, two, three, four, five."
 * See Off-by-one error, Fencepost problem, and (presumably) the transfinite sequence of Cardinal numbers. -- ToE 09:10, 28 October 2015 (UTC)


 * It's never easy to tell whether or not a mathematician is joking, but the fact that he describes consistency as being more important than ease of use, and that he takes into consideration how his counting method deals with counting infinity (which is impossible for any step-by-step counting method), suggests that his tongue is at least some way into his cheek. If you read on, it seems like a sarcastic interjection into a more serious discussion about how zero relates to the empty set. Smurrayinchester 11:05, 28 October 2015 (UTC)
 * (His description of musical intervals is also rather confused. A third contains three notes (eg. "C,D,E") and the number of semitones is irrelevant (that one contains five semitones, since C♯ and E♭ are also included, see major third). If you're talking about "how many notes do I have to go up by to play this as an arpeggio?" then starting your counting at zero makes sense, but if you're talking about "how wide is this chord", then you want to start counting at one.) Smurrayinchester 11:11, 28 October 2015 (UTC)
 * He does confuse semitones with scale steps, but aside from that what he says makes sense. His point is that a kth followed by an ℓth in the same direction ought to be a (k+ℓ)th but instead it's a (k+ℓ−1)th. It's more sensible to represent intervals by (scale steps, semitones) ordered pairs with a perfect unison being (0, 0) and a perfect octave being (7, 12). There's no advantage to making them (1, 1) and (8, 13) and subtracting 1 every time you add if the intervals are both upward, or adding 1 if the intervals are both downward, or inspecting the result and either adding or subtracting one if one is upward and the other downward. Perfect unison is the additive identity for intervals. -- BenRG (talk) 19:31, 28 October 2015 (UTC)
 * John Conway was advocating counting from zero in the 1960s. I can't claim to know him, because I only met him once, but I recall that some lecturers at Liverpool University counted from zero as a result of his suggestion.   D b f i r s   00:05, 29 October 2015 (UTC)

The ordinal numbers: first, second, third and so on, are not subject to calculations in the same way as the cardinal numbers: zero, one, two, three and so on. That is why programmers name the (cardinal) number of items to be skipped before reaching the interesting item, rather than naming the (ordinal) number of the interesting item. If you skip three items you reach the fourth item. Bo Jacoby (talk) 07:42, 1 November 2015 (UTC).