Interaction between Language and Mathematics

I’ve noticed that quite often, just before, or in the middle of learning something new, I feel really stupid. Is that normal?

Today I tackled part 2 of the 2-part honey-do list. Remember – she very rarely asks me to do something for her, so when she does, I want to make sure to get right down to it. Don’t let any grass grow, so to speak. Part 2 of the list was to hang some pictures that have been sitting around. I can do that! Right? The first thing I found out is that I don’t have any picture-hanging hooks. So, part 2 starts with a trip to the hardware store. (I learned a long time ago never to begin any sort of home project if the hardware stores are not open.)

The next part of the task was to decide where to put the pictures. I was hanging a pair of prints that we brought back from our trip to Nova Scotia in 2011. Margie and Dawn Beaton are sisters who are both fiddlers that play traditional Gaelic music. We saw them in a couple of performances and loved their personalities and their music. As a souvenir of that trip, we brought home prints of the two sisters and never got them hung up.

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After holding the prints up in various locations around the house, E settled on a location that already had a picture hanging on it. No problem. Take that picture down, hang these two, and I’m still one picture ahead of the game. A quick measurement and calculation revealed that the wall was 74” and the nail hole for the picture being removed was at the 37” mark. Splitting that 37” space in half put me at the center of the half-wall space, and all I had to do was to get E to tell me how high she wanted it.

Now, you need to understand that E and I are both below-average height. I’m 5’6” in thick-soled shoes, and she’s shorter. So, if we’re not careful, things hung up around our house look … unusually low … to people of average height. As I held the picture up for her to tell me the right height, I thought the height she chose was too low. So – the next several minutes were spent in negotiation about the proper height of a picture on a wall. Enough said about that.

With the measurement for the horizontal dimension done and the eye-balling for the vertical dimension done, I was almost home. Picture #1 (Dawn) was hung. Now I just needed to repeat the process using the same horizontal and vertical on the other half-wall space. E needed to reassure herself that she wanted them both at the same height, so she asked me to hold Margie in place so she could see how they looked together. I centered her at the center mark I had made earlier and moved her to the same height as her sister.

“No, you have to move her several inches to the left.”

“No way. She’s at the center mark I made earlier!”

“There is way too much space between them!”

“Impossible! Look, here’s the center mark. It’s the same as Dawn’s.”

“I don’t care if it’s the same as Dawn’s, there is too much space between them and not enough on the sides.”

“If I move Margie to the left, there will be too much space on the right! Look!”

“You have to think of the pictures as a ‘group.’ You have to have the right amount of space around the ‘group,’ and between the pictures in the ‘group.’”

“Look. I started with the center of the wall, and I cut the two wall-halves in half, and that’s the location of the centers of the two pictures. It’s math. Don’t tell me about ‘groups.’ It’s just math.”

“OK. I see what you did. But it isn’t right.”

Well, at that point I saw what she was after, but it was really hard to admit that I was wrong in my math. I had split the wall into four parts by bisecting the half-wall spaces. Each of the two pictures had a half-wall space to itself. There was an equal margin of space on each picture’s right and left. When the margins of the two pictures joined together in the middle of the wall, they created a margin that was double-width. What I should have done was to split it into three spaces.  I suggested that to E.

“Well, that would be one way to do it, but I think there would still be too much space between them. I want them to be a “group,” and I don’t want them to have that much space between them.”

(Why does she keep saying that about a ‘group?’)

“How much space, exactly, do you want between them?” I finally asked.

“Oh, about 4 or 5 inches.”

“How much, exactly,” I repeated.

She got my measuring tape out and opened it up several inches and examined it. “I want 4 ½ inches between them,” she announced.

So I realized that what she wanted me to do was to think of the picture-space-picture as a unit, and that that unit (group in her language) needed to be centered on the wall.

After that it was easy.

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