Language is a funny thing. I have talked about it before but the use of language and our ability to reason numerically is so interesting. I had a conversation with a student today where he told me about his dogs. It was one of those off topic conversations. He was describing the size of his dogs and he said "I have two hundred ten pound dogs." Now I have intentionally left out any dashes, because I want to let you in on what I understood. When he said that I thought of this massive group of hundreds of these ten-pound puppies. He meant he had two dogs that were 110 pounds.
Which brings me to my thought. In one sentence we can have three different meanings, the likes of which are such.
I have:
What does this tell us about the nature of quantity? They all sound the same but all produce different quantities. In scenario 1 we have 210x pounds of dogs. We do not know how many dogs I have, but they are all around the same size. In scenario 2 I have 2000 pounds of dogginess, and in scenario 3 I have 220 pounds of dogs. In some weird linguistic sense, these seem like they should all be similar in some sense, but they all produce different images, and different quantities entirely.
I do not know why this particular quantity pun amuses me so much, but I feel there is something here.
* Ya, I realise that mathematically we should say two one-hundred-ten pound dogs, but conversationally we rarely say that.
**Another fun quantity pun to ask kids especially is would rather have one and a half million dollars or one million and a half dollars? Something seems eerily the same about those, but they are screamingly different.
Which brings me to my thought. In one sentence we can have three different meanings, the likes of which are such.
I have:
- I have 210 pound dogs
- I have 200 10 pound dogs
- I have 2 110 pound dogs*
What does this tell us about the nature of quantity? They all sound the same but all produce different quantities. In scenario 1 we have 210x pounds of dogs. We do not know how many dogs I have, but they are all around the same size. In scenario 2 I have 2000 pounds of dogginess, and in scenario 3 I have 220 pounds of dogs. In some weird linguistic sense, these seem like they should all be similar in some sense, but they all produce different images, and different quantities entirely.
I do not know why this particular quantity pun amuses me so much, but I feel there is something here.
* Ya, I realise that mathematically we should say two one-hundred-ten pound dogs, but conversationally we rarely say that.
**Another fun quantity pun to ask kids especially is would rather have one and a half million dollars or one million and a half dollars? Something seems eerily the same about those, but they are screamingly different.
