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There is a spot behind the 30 story apartment towers just outside my window where the acoustics are incredible. Someone is singing gospel on this cold early morning causing the pigeons to take flight wheel as one above the NYC skyline.
They fly over the pale yellow and pink clouds intermittently visible through the windows (which have been frosted over with condensation from the heater) And that fiery beast in the basement is also singing and banging.
It's going to be a beautiful day.
The cat is sleeping, purring in time with the hissing of the radiator.
My 9th grade students have at last begun to understand what it means to write a proof.
"Do you mean I could just write it out in words? Just explain why it's true?"
Yes! That is exactly what I mean. Or you could draw a diagram. Or you could sing.
"Oh, Lord, Oh Lord, It's a Beautiful Day..."
A very old nonverbal proof you undoubtedly know.
Every year I have a little crisis mentally thinking they will never understand the point of writing proofs, or what they really are. Somehow I forget that the dawn still comes.
@futurebird Interesting to me. I don't recall ever trying to teach this, despite teaching logic and philosophy. Maybe I just assumed they knew.
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@futurebird Evidently it's not diesel run.