• TheMadFool
    13.8k
    Cardinal numbers are numbers when used to count as exemplified by the statement "3 things" when given the set {y, &, *} or the set {u, @, £}

    Ordinal numbers are numbers used when we wish to order/rank objects; for instance they're commonly used in games to rank players with 1st, 2nd, and so on assigned to the champion, runners-up, and so on respectively.

    The 1st cardinal number is 1, the 2nd is 2, and so on with the nth cardinal number being n.

    Consider now the game of javelin throw which I use here to stand for, not all, but most games. Points are awarded based on the distance the javelin travels. Imagine 4 players A, B, C and D with throw distances, 10 feet, 20 feet, 30 feet and 40 feet respectively. D's distance earns him 1st place, C's distance earns him 2nd place, B's distance gets B to 3rd place and A is in 4th place. This describes the normal point scoring system and ranking system in most competitions.

    Notice here that the largest cardinal number, 40 feet, is assigned to the lowest ordinal number, 1st place, and the smallest cardinal number, 10 feet, goes to the largest ordinal number, 4th place.

    I'm not saying there's no logic to this, since the maximum points does belong to the highest ranking competitor. However, this kind of point scoring and ranking system violates the ordering 1 is 1st, 2 is 2nd, and so on, where the smallest ordinal number is matched with the smallest cardinal number.

    In addition there's a loss of information in terms of how tough the competition was. This can be illustrated by many jokes in which a person is ridiculed for having come 2nd in a game of only two competitors, exposing, as it were, the flaw with such systems.

    If, on the other hand, the system had stayed true to that of 1 being 1st, 2 being 2nd, and so on, a very valuable piece of information can be retained viz. an idea of how many competitors took part in the game. For instance in the javelin game above, had the champion been awarded 4th position, we would know from the champion's position, the ordinal number assigned to him, that there were a total of 4 players. Then if n players were taking part and the champion was awarded, like I'm suggesting here, the nth rank, we would immediately know there were n players and would come to know how tough the competition and so how great the win was.

    Why is it this way? Should we change the system like I'm suggesting? Why and why not?

    If I may offer a theory for why the ranking system in sports is inverted with respect to the points scored then we must travel back in time to the first Olympics

    At the first recorded ancient Olympic Games in 760 BC, there was only one event, a footrace — History of Sports

    In a footrace, the objective is to run faster than your opponent i.e. to try and attain a speed greater than the competition; this inevitably results in the player ranking being based on how much time it took the players to complete the footrace. Imagine 3 players in the footrace: A, B and C. A is the fastest and so completes the race in 15 seconds, B is next fast and completes the race in 20 seconds and B is the slowest and completes the race in 25 seconds. Now, calling A 1st, B 2nd and C 3rd doesn't violate the actual mathematical ordering of the cardinals in which 1 is 1st, 2 is 2nd and so on.

    If the first sports competition was a footrace and since in races it makes sense to call the winner 1st (he completes the race first), this practice spilled over into other sports as well.
  • ssu
    8k
    Did I get you right or are you proposing that instead of us now saying that the javelins went 10 feet, 20 ft, 30ft and 40 ft we would say the contestants threw -10ft, -20ft, -30ft and -40ft with the last one being the winner?
  • TheMadFool
    13.8k
    Did I get you right or are you proposing that instead of us now saying that the javelins went 10 feet, 20 ft, 30ft and 40 ft we would say the contestants threw -10ft, -20ft, -30ft and -40ft with the last one being the winner?ssu

    Well, I would prefer it stay natural and also using negative numbers complicates the matter because the signed value of the score tends to be confused with the absolute value and |-x| > -x. So, if I say "the winner scored -40", there's a chance that some might think the winner did extremely well (40) or extremely badly (-40).

    Also using negative numbers in this way prevents another well-known point scoring system where the winner is someone who's made the least number of mistakes. Imagine a game that's about making the least number of mistakes. If a player A makes 2 mistakes and another player B makes 5 mistakes and a third C makes 7 mistakes then A is the winner and in this case a point scoring system would look like A: -2, B: -5 and C: -7 and the ranking of the scores would be A(-2) > B(-5) > C(-7) and utilizing the schema suggested A, the winner, would be 3rd, B would be 2nd and C would be 1st. If done this way then from the winner's (A's) position, 3rd, we get to know that there were 3 players.
  • Hanover
    12k
    In golf the lowest ordinal score is ranked the lowest cardinal number, so I guess we keep golf the same.
  • TheMadFool
    13.8k
    In golf the lowest ordinal score is ranked the lowest cardinal number, so I guess we keep golf the same.Hanover

    Really? The winner isn't awarded first prize?

    A player scores one point for a bogey, two for par, three for a birdie, four for an eagle and five for an albatross. You win a competition by scoring the most points overall. — BBC Sports
bold
italic
underline
strike
code
quote
ulist
image
url
mention
reveal
youtube
tweet
Add a Comment

Welcome to The Philosophy Forum!

Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.