My maternal grandfather’s family fled Poland in 1934 on the last boat to Canada before the war. He, his brother, and his parents spent a week on the ship, and then another two weeks quarantined for chicken pox, before they headed off to Montreal with ten dollars in their pockets. Around this time, according to family legend, my paternal grandmother’s brothers were spending their weekends playing hockey with frozen cakes of horse manure.
My great uncle, who told this story, has been known to tell tales, but this one rings true, because I can’t think of a more Canadian way to get through the Great Depression: We might not be have been able to afford rubber, but we had horse shit and damned if we were going to give up hockey.
My parents had it better, but apparently life in the fifties still sucked. For instance, my father and his siblings, for reasons I’m still not sure I understand, had to brush their teeth with salt. (Correction: Mom tells me it’s my grandmother who did that.) And the six members of my mother’s immediate family lived in a small house with one bathroom and when your grandfather went in, God bless him…
Not me. I grew up in an era of fluoridated water, small families, and multiple household bathrooms. For a time I resented my parents somewhat for depriving me of stories to tell my own children and grandchildren when they started bitching about how tough their lives were. I mean, what was I going to say? That our surround sound system had only six speakers? That we had to watch movies on lower-quality videotapes, without extras?
I needn’t have worried.
“I can’t believe you guys had to do all this stuff without graphing calculators,” said an incredulous high schooler this morning. “What did you do in your math classes?”
“Math,” replied Grandma Moebius Stripper, Luddite.
“No, seriously” (”seriously!”) “how did you guys do questions like this one?” – pointing to the Solve for x: tan x sin x – tan x = 0 example, which our tech-savvy student, following the instructions given by MATHPOWER 12, had just solved by first plotting the functions y = tan x sin x – tan x and y=0 on his TI-83+ and then invoking the INTERSECT command.
[I’d originally accidentally written tan x sin x – tan x = 1. Sorry! Thanks to Dog of Justice and Ronald for pointing that out.]
And from there, a five-minute digression into how when I was his age we knew the trigonometric ratios of the special angles by heart, and if we didn’t, at least we knew how to derive them from the triangles. (”You mean the ones you showed me yesterday?” “Yeah, those.” “Oh, so like you had to learn those?”) We had to actually factor expressions such as the one he was working on. Sometimes, we would sketch the graphs by hand, which we got to be very fast at, and then we’d apply our knowledge of periods and phase shifts and suchlike in order to find general solutions.
Replied the student, clearly a product of west coast ethos, “That musta taken lot of paper.”
Damned straight, it did. And this was before pulp and paper mills. And we had to cut down the trees by ourselves. With our teeth.