Re:Why numbering should start at zero (1982)
by derefr on Thursday December 15, 2016 @04:37PM
(#13188679)
You're getting confused between cardinal and ordinal numbers.
Ordinal numbers (0, 1, 2) map to the world as amounts, and certainly it seems 'real' that there can be "one of something" in a way that it isn't that there is "zero of something" (though it isn't, really.)
Cardinal numbers (first, second, third) map to the world as rankings or positions. Positions, further, often almost always map to distances from an origin. "First" really almost always means "the item that is +0 positions away from the origin." The person who wins a competition ("first place") is zero positions down the leaderboard. The "first" book on your book shelf can be found +0cm away from the left edge of your bookshelf. Etc.
With your cars, you're talking about a third thing, though: serial numbers. "Car 1" is what you might call the first car you bought (if you were planning on buying several), because we conventionally assign serial numbers to things starting with 1. But that has nothing to do with counting or ranking; it's just a convention (as can be seen when we choose to use an alternate scheme, like UUIDs, for labelling items in a database.)
What we're talking about here is the relationship between counting and ranking: between cardinal and ordinal numbers. Since they're both abstract, and not structurally connected in any important way, there's actually no "essential, required" way to relate them to one-another, and we have to just make one up. Some people relate "first" to the natural number 0; some people relate "first" to the natural number 1.
Ordinal numbers (0, 1, 2) map to the world as amounts, and certainly it seems 'real' that there can be "one of something" in a way that it isn't that there is "zero of something" (though it isn't, really.)
Cardinal numbers (first, second, third) map to the world as rankings or positions. Positions, further, often almost always map to distances from an origin. "First" really almost always means "the item that is +0 positions away from the origin." The person who wins a competition ("first place") is zero positions down the leaderboard. The "first" book on your book shelf can be found +0cm away from the left edge of your bookshelf. Etc.
With your cars, you're talking about a third thing, though: serial numbers. "Car 1" is what you might call the first car you bought (if you were planning on buying several), because we conventionally assign serial numbers to things starting with 1. But that has nothing to do with counting or ranking; it's just a convention (as can be seen when we choose to use an alternate scheme, like UUIDs, for labelling items in a database.)
What we're talking about here is the relationship between counting and ranking: between cardinal and ordinal numbers. Since they're both abstract, and not structurally connected in any important way, there's actually no "essential, required" way to relate them to one-another, and we have to just make one up. Some people relate "first" to the natural number 0; some people relate "first" to the natural number 1.